Q.P.-2015
Paper Code: UN412(1 - 24)
(Code: 412) Q.P.-2016
Paper Code: UN415(1 - 24)
(Set A - Code: 415) Q.P.-2016
Paper Code: UN418(1 - 24)
(Set B - Code: 418) Q.P.-2016
Paper Code: UN421(1 - 24)
(Set C - Code: 421)
Key & Solutions
Class–II
CLASS : X
Class : X
Mathematics
If cot θ + cos θ = p and cot θ cos θ = q, find the value of (p2 q2)2 in terms of p and q. (A) 16 pq
(B) 8 pq
(C) 4 pq
(D) 12 pq
A bag contains 5 red balls and n green balls. If the probability of drawing a green ball is three times that of red ball, find the total number of balls. (A) 5
(B) 15
(C) 20
(D) 25
26. In the figure, AD = 4 cm, AB = 3 cm and CD = 9 cm What is the area of triangle AEC? A
B
E
D
C
(A) 9.5 cm
2
(B) 4.5 cm
2
(C) 3.5 cm2
(D) 13.5 cm2
A cuboid of size 8 cm × 4 cm × 2 cm is cut into cubes of equal size of 1 cm side. What is the ratio of the surface area of the original cuboid to the surface areas of all the unit cubes so formed? (A) 13 : 4
(B) 8 : 3
(C) 7 : 24
(D) 7 : 12
Space for rough work
Paper Code: UN412
1
CLASS : X
The numbers x, y, z are such that xy = 96050 and xz = 95625 and y is greater than z by one. Find value of the number z. (A) 425
(B) 220
(C) 525
(D) 225
If a, b, c are three natural numbers such that c is a factor of ab and c is co-prime to a, which of the following is true? (A) b is a factor of c
(B) c is a factor of b
(C) a is a factor of b
(D) b is a factor of a
Two vertical poles 20 m and 80 m high stand apart on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is a meters. What is the value of a? (A) 12 m
(B) 10 m
(C) 16 m
(D) 20 m
The given figure shows 4 identical circles enclosed in a square of sides 20 cm.
20 cm
Find the area of the unshaded region of the figure. (A) 320 cm2 (B) 200 cm2
(C) 280 cm2
(D) 350 cm2
Space for rough work
Paper Code: UN412
2
CLASS : X
In the xy-plane, points Q and S are the centers of the circles, which are tangent to the x-axis. What is the slope of line QS (not shown)? y
R(11, 10) P(3, 6) S
Q
x
O
(A)
1
(B)
8
1
(C)
4
1 2
(D)
7 8
If the 9th term of an A.P. is 99 and 99th term is 9, find 108th term. (A) 0
(B) 2
(C) 4
(D) 6
In the given xy-coordinate plane, line n is perpendicular to line l. What is the slope of line n? y
n 3 l
2 1 O
(A) 3
x 1
(B) −
2
1 3
3
(C)
1 3
(D) 2
Space for rough work
Paper Code: UN412
3
CLASS : X
The radius and height of a right solid circular cone (ABC) are respectively 6 cm and 2 7 cm. A coaxial cone (DEF) of radius 3 cm and height 7 cm is cut out of the cone as shown in the figure. What is the whole surface area of the remaining solid thus formed? B
E
F C
A D
(A) 96 π cm2 (B) 87 π cm2 (C) 60 π cm2
(D) 36 π cm2
The given figure shows a circle with centre O and a diameter of 20 cm. Find the area of the shaded part of the circle. (Take π = 3.14) 25o O 25o
(A) 270
7 cm2 18
(B) 290
7 cm2 18
(C) 250
11 cm2 18
(D) 220
1 cm2 18
Space for rough work
Paper Code: UN412
4
CLASS : X
In the given figure, what is the median of the slopes of OA, OB, OC, OD and OE ?
y 5 4 3
A
B
C
D
E
3
4
5
6
2 1 1
O 1
(A)
4 3
1
2
(B) 1
(C)
3 4
x
(D)
3 5
A ladder is inclined to a wall making an angle of 30o with it. A man is ascending the ladder at the rate of 2 m/s. How fast is he approaching the wall? (A) 2 m/s
(B) 1.5 m/s
(C) 1 m/s
(D) 0.5 m/s
What is the equation of the axis of symmetry of the graph y = 3x2 + 12x 2? (A) x = 2
(B) x = 2
(C) y = 2
(D) y = 2
Space for rough work
Paper Code: UN412
5
CLASS : X
There are 4 numbers. The H.C.F. of each pair is 3 and the L.C.M. of all the four numbers is 126. Find the product of 4 numbers. (A) 1512
(B) 6048
(C) 3402
(D) 378
The line AB is 6 metres in length and is tangent to the inner one of the two concentric circles at point C. It is known that the radii of the two circles are integers. Find the radius of the inner circle. A C B
(A) 8 m
(B) 4 m
(C) 6 m
(D) 3 m
If both a and b belong to the set {1, 2, 3, 4}, find the number of equations of the form ax2 + bx + 1 = 0 having real roots. (A) 10 If tan α = (A) π / 3
(B) 7
(C) 6
(D) 12
1 m and tan β = , find α + β . 2m + 1 m+1
(B) π / 2
(C) π / 4
(D) π / 6
Space for rough work
Paper Code: UN412
6
CLASS : X
Which of the following is the graph of a linear function with a negative slope and a positive y-intercept?
y (A)
y x
o
(B)
o
y
y
o
(C)
x
x
(D)
o
x
In the given figure, BD and CD are angle bisectors of ∠ ABC and ∠ ACE, respectively, find ∠ BDC. D A
B
(A) ∠ BAC
E
C
(B) 2 ∠ BAC
(C)
1 1 ∠ BAC (D) ∠ BAC 3 2
If a, b, c and d are four positive numbers such that a + b + c + d = 4, what is the maximum value of (a + 1)(b + 1)(c + 1)(d + 1)? (A) 32
(B) 8
(C) 16
Paper Code: UN412
(D) 81
7
CLASS : X
If AB is the chord at the circle with centre O, PAN and RBM are the tangent at A and B respectively, which of the following is correct? P
R
A
O x
y
N
M
B
(A) x ≠ y
(B) ∠ PAB = y
(C) ∠ PAB = y and ∠ RBA = x
(D) x = y
If x + a is a factor of the polynomial x4 a2x2 + 3x a, find the value of a. (A) 0 (B) 1 (C) 2 (D) 2 Space for rough work
Paper Code: UN412
8
CLASS : X
Class : X
Physics
A student has three resistors, 3 ohms, 4 ohms and 6 ohms respectively. He wants to make use of these three resistors to form a new value of resistance for his electrical circuit. Which value is he NOT able to get ? (A) 2 ohms (B) 2.4 ohms (C) 8 ohms (D) 9 ohms A painter leans his back against a painted wall while looking into a 1 m long mirror at the opposite end of a rectangular room. 1 m long mirror
Painted wall
12 m
Painter
How much of the painted wall can he see through the 1 m long mirror? (A) 1 m (B) 2 m (C) 6 m (D) 12 m What is the main reason for using a solenoid instead of a straight wire to produce magnetic field? (A) To concentrate the magnetic field produced throughout the wire to flow through the core of the solenoid. (B) To reduce the space taken up by the long wire. (C) To ensure that the magnetic field strength is constant. (D) To reduce the amount of wires used to produce the same magnetic field strength as a straight wire. Given below is the path taken by light as it enters the human eye. Light
X
Brain
Aqueous humour Op c nerve
Pupil
Z
Y
Vitreous humour
Which part of the human eye represents Z ? (A) Cornea (B) Lens (C) Retina (D) Ciliary muscles Paper Code: UN412
9
CLASS : X
Which is NOT the way to increase the efficient use of energy sources ? (A) Getting the least use of energy with maximum wastage. (B) Good planning and management is using the energy sources. (C) Developing and using highly efficient equipment. (D) Developing a wider use of alternative sources such as biomass and wind energy. Which of the given have a virtual image ? (i) The image formed by an image projector. (ii) The image formed by a plane mirror. (iii) The upright image formed by a magnifying glass.
(A) Only (ii) (C) Only (ii) and (iii)
(B) Only (i) and (ii) (D) (i), (ii) and (iii)
A charge of 200 C flows through an electric bulb of resistance 20 Ω for 25 s. Calculate the potential difference across the bulb. (A) 120 V (B) 140 V (C) 160 V (D) 180 V Which of the given statements are true ? (i)
There are three types of cone cells sensi ve to primary colours. (ii) Cone cells are sensi ve to high intensity of coloured light. (iii) An owl has large number of rod cells in its re na. (iv) Rod cells are sensi tive to low intensity of black and white light.
(A) Only (i), (ii) and (iv) (C) Only (i), (iii) and (iv)
(B) Only (ii), (iii) and (iv) (D) (i), (ii), (iii) and (iv)
What is the use of slip rings in a simple a.c. generator? (A) To increase the rotational speed of the coil. (B) To prevent the wires from entanglement. (C) To change the direction of current flowing to the load in every half a turn. (D) To ensure good contacts between the moving parts and the stationary parts. Paper Code: UN412
10
CLASS : X
Which pair of lenses can be used to construct a compound microscope? (A) Two convex lenses with focal lengths of 5 cm and 100 cm. (B) Two concave lenses with focal lengths of 5 cm and 100 cm. (C) Two convex lenses with focal lengths of 5 cm and 7 cm. (D) Two concave lenses with focal lengths of 5 cm and 7 cm. Identify the renewable sources of energy. (A) Coal, natural gas
(B) Sunlight, tidal waves
(C) Ethanol fuel, sunlight
(D) Wood, wind
Which part of the human eye is responsible for absorbing light and preventing reflection of light within the eyeball ? (A) Vitreous humour (B) Yellow spot (C) Retina (D) Choroid Which coil produces the strongest electromagnet for a given flow of current ? (A) A 10 cm coil with 100 turns (B) A 5 cm coil with 200 turns (C) A 10 cm coil with 200 turns (D) A 20 cm coil with 200 turns A photocopy machine uses a converging lens to focus images for printing on papers. If the focal length of the lens is 6 cm, what is the distance from the original copy to the lens during photocopying ? (A) 2 cm (B) 6 cm (C) 10 cm (D) 12 cm The most appropriate fuse rating for a 240 V, 1.2 kW heater is (A) 3 A. (B) 5 A. (C) 10 A. (D) 13 A. Space for rough work
Paper Code: UN412
11
CLASS : X
Carnivores such as tigers have their eyes in front of the head. This enables them (i) to estimate distance accurately. (ii) to see things in three dimensions. (iii) to have a large field of monocular vision.
(A) Only (i) and (ii) (C) Only (ii) and (iii)
(B) Only (i) and (iii) (D) (i), (ii) and (iii)
Identify the earthwire in the given circuit. II
I
IV M ains supply III
(A) II
(B) III
(C) I
(D) IV
Which option is not the effect of refraction ? (A) Chopsticks appear to bent in clear soup. (B) A fish appears to be larger than its actual size in water. (C) Light travelling through optical fibre. (D) A man appears to be smaller than his actual size from the point of view of a fish underwater. A 2 m long wire with a cross sectional area of 1 mm2 has a resistance of 16 Ω . What is the resistance of the same type of wire which is 4 m long and has a cross-sectional area of 2 mm2? (A) 4 Ω (B) 8 Ω (C) 16 Ω (D) 32 Ω The given figure shows an object placed at X and its image is formed at Z.
Identify the object distance, focal length and image distance respectively. (A) XY, OZ, YZ (B) XZ, OY, YZ (C) OX, OY, OZ (D) XY, OY, YZ Paper Code: UN412
12
CLASS : X
Choose the correct option. Materials
Property
Usage
(A)
Iron
Easily magnetised
Electromagnet
(B)
Iron
Easily demagnetised
Permanent magnet
(C)
Steel
Easily magnetised
Electromagnet
(D)
Steel
Easily demagnetised
Permanent magnet
Why is the filament in an electric bulb made from tungsten? (A) It has a melting point higher than 3000 oC. (B) It has high resistance to allow high current to pass through. (C) It has high mass so that more heat can be stored in the filament. (D) It has high specific heat capacity so that small amount of heat can increase the temperature to a large extent. A converging lens has a focal length of 15 cm. Given that an object is placed 31 cm from the optical centre of the lens, what are the characteristics of the image formed ? (A) Real, inverted and diminished (B) Real, inverted and same size as object (C) Real, inverted and enlarged (D) Virtual, upright and enlarged Which is the safest method to dispose off radioactive wastes? (A) (B) (C) (D)
To dispose into the sea. To keep it in a thick lead container and bury it under the sea. To bury it under the ground. To dispose in an uninhabited island.
An appliance marked 240 V, 2 A is being connected to a 120 V supply. What is the output power of the appliance ? (A) 60 W
(B) 120 W
(C) 240 W
Paper Code: UN412
(D) 480 W 13
CLASS : X
Chemistry
Class : X
Why do noble gases exist as monoatomic gases ? (A) (B) (C) (D)
They have low melting point. They have high boiling point. Their atoms have duplet or octet electron arrangement. The forces of attraction between their atoms are very weak.
Three different metals of the same size and thickness reacted with equal volumes of dilute hydrochloric acid in 3 different test tubes. The time taken to collect 5 cm3 of hydrogen gas is recorded in seconds. Which option gives the correct recording? Magnesium
Zinc
Sodium
(A)
20
30
10
(B)
20
10
30
(C)
30
20
10
(D)
10
20
30
Identify a balanced equation for the given reaction. Aluminium + Iron (III) oxide Aluminium oxide + Iron
(A) (B) (C) (D)
2Al(s) + Fe2O3(s) → Al2O3(s) + 2Fe(l) 2Al(s) + Fe2O3(s) → Al2O3(s) + 2Fe(g) Al(s) + Fe2O3(s) → Al2O3(g) + 2Fe(s) 2Al(s) + Fe2O3(s) → Al2O3(s) + Fe(s) Space for rough work
Paper Code: UN412
14
CLASS : X
The table given below shows the volume, concentration and pH value of two acids. Acids Hydrochloric acid
Volume and concentra on
pH
50 cm3 of 1 mol dm3
1
3
Ethanoic acid
50 cm of 1 mol dm
3
4
Why is there a difference in pH value between the two acids? (A) The number of moles of ethanoic acid is less than that of hydrochloric acid. (B) Ethanoic acid is more soluble in water than hydrochloric acid. (C) The degree of ionisation of ethanoic acid is less than that of hydrochloric acid. (D) The concentration of hydrogen ions is higher in ethanoic acid than in hydrochloric acid. One mole of a hydrocarbon X reacted completely with one mole of hydrogen gas in the presence of a heated catalyst. What could be the formula of X ? (A) C 2 H 6 (B) C 3 H 8 (C) C 5 H 10 (D) C 7 H 16 Which steps can be taken to prevent the oxidation of fried foods ? (i) (ii)
Addition of BHA and HBT to foods prior to frying. Storing fried foods in air-tight containers and also away from the light. (iii) Filling unreactive gas in bags/ containers in which fried foods are stored.
(A) Only (i) and (ii) (C) (i), (ii) and (iii)
(B) Only (ii) and (iii) (D) Only (i) and (iii)
From which ore is manganese extracted ? (A) Haematite (C) Pyrolusite
(B) Bauxite (D) Calamine Paper Code: UN412
15
CLASS : X
What is P in the given chemical reaction ? Vegetable oil + Alkali
(A) Fat
Boiling
(B) Ester
Soap + P
(C) Glycerol
(D) Ethanol
The formulae of some oxides are given below. Na2O , Al2O3 , CO2 , MgO , SO2
Which option gives the correct number of each type of oxide? (A) (B) (C)
Acidic 1 2 1
Amphoteric 2 0 1
Basic 2 3 3
(D)
2
1
2
Identify an equation that represents the complete combustion of CH3OH. (A) 2CH3OH + O2 → 2C + 4H2O (B) 2CH3OH + 2O2 → 2CO + 4H2O (C) 2CH3OH + O2 → 2CO2 + 4H2 (D) 2CH3OH + 3O2 → 2CO2 + 4H2O The given bar chart shows a period of elements from lithium to neon.
Property
Li Be B C N O F
Ne
Elements
Which property of these elements is shown on the chart ? (A) The number of electrons used in bonding (B) The number of orbits holding electrons (C) The (proton) atomic number (D) The relative atomic mass Paper Code: UN412
16
CLASS : X
Identify the numbers in places of (i), (ii), (iii) and (iv) respectively to balance the given equation. (i) PbS + (ii) H2O2
(iii) PbSO4 + (iv) H2O
(A) 1, 4, 1, 4 (B) 1, 3, 1, 2
(C) 2, 2, 2, 2
(D) 1, 4, 1, 3
The metals iron, lead and zinc can each be extracted by the reduction of the oxides with coke. What is the correct order of the ease of reduction of the metal oxides ? (A) Iron, lead, zinc
(B) Iron, zinc, lead
(C) Lead, iron, zinc
(D) Zinc, iron, lead
A white solid is often seen around the stoppers of bottles containing sodium hydroxide solution. Which substance has reacted with sodium hydroxide to form the solid? (A) Water in the solution (C) Oxygen in the air
(B) Glass (D) Carbon dioxide in the air
Few reactions are given below in which ethanol is either a reactant or a product. (i) (ii) (iii) (iv)
Combus on of ethanol Conversion of ethene to ethanol Fermenta on of glucose Oxida on of ethanol to ethanoic acid
In which reactions is water also either a reactant or a product? (A) Only (i), (iii) and (iv) (B) Only (ii), (iii) and (iv) (C) Only (i), (ii) and (iv)
(D) Only (iii)
Which option has electrovalent bonds between its particles? (A) Chlorine
(B) Hydrogen
(C) Carbon dioxide
(D) Magnesium oxide
Paper Code: UN412
17
CLASS : X
When two liquids are mixed, a solution with a pH value of 7 is formed. What are the pH values of the two liquids ? (A) 5, 2 (B) 5, 12 (C) 6, 1 (D) 14, 7 X, Y and Z are elements in the periodic table. X forms an acidic oxide, Y forms a basic oxide and Z forms an amphoteric oxide. If X, Y and Z are placed in order of increasing atomic number (lowest atomic number first), which order is correct? (A) X, Y, Z (B) X, Z, Y (C) Y, X, Z (D) Y, Z, X Given below is the structural formula of a substance. CH3 CH2 CH2 CH2 CH2 CH2
O
+
CH2 CH2 CH2 CH2 CH2 CH2 O S O Na O
What is the substance ? (A) Sulphonic acid (C) Soap
(B) Fatty acid (D) Detergent
Which reactions given below are oxidation reactions? Ethanol C2H5 OH X Ethyl ethanoate CH3CO 2C2H5
(A) Only X (C) Only Y
Z
Ethanoic acid CH3CO2H
Y
Sodium ethanoate CH3CO 2Na
(B) Only X and Y (D) Only Y and Z Space for rough work
Paper Code: UN412
18
CLASS : X
Class : X
Biology
Which of the following is NOT true concerning photosynthesis in green plants? (A) Absorb carbon dioxide (B) Releases oxygen (C) Occurs in the presence of sunlight (D) Absorbs carbohydrates Which of these statements about the given food chain is correct?
A
B
C
D
(A) Living thing A makes its own food so it does not need energy from any sources. (B) Living Thing D gets the most energy as it is at the end of the food chain. (C) Not all the energy from living thing B can be transferred to living thing C. (D) More energy is transferred from living thing C to D than from living thing B to C. Peripheral nervous system consists of (i) (iii)
cranial nerves spinal cord
(ii) spinal nerves (iv) brain
(A) (i) and (ii) (B) (i) and (iii) (C) (ii) and (iv) (D) (iii) and (iv) Which two arrows show the path of blood vessels carrying oxygen-rich blood? Lungs
P R
(A) P and Q only (C) Q and S only
Q Heart
Parts of the Body S
(B) P and R only (D) R and S only
In humans what is the probability for the baby to be a baby boy? (A) 25% (B) 50% (C) 75% (D) 100% Paper Code: UN412
19
CLASS : X
A ring of bark is removed by cutting round the stem of a plant. After three weeks, the part of the stem above the ring is observed to be swollen. The swollen part contains mainly (A) mineral salts. (B) sugar. (C) oxygen. (D) water. Arrange the living organisms below into a correct food chain. (i) Frog (iii) Rice plant
(ii) Eagle (iv) Grasshopper (v) Snake
(A) (i), (ii), (iii), (iv) and (v) (B) (iii), (iv), (i), (v) and (ii) (C) (iii), (i), (iv), (v) and (ii) (D) (iii), (iv), (i), (ii) and (v) Which of these is a hermaphrodite? (A) Yeast (C) Ascaris
(B) Paramecium (D) Earthworm
F in the diagram is an endocrine gland in human body.
What is the function of the hormone released by F? (A) Response to stress (B) Stimulates the ovaries to produce eggs. (C) Stimulates growth (D) Regulates the amount of oxygen in the blood Space for rough work
Paper Code: UN412
20
CLASS : X
What is represented by processes E and F in the given flowchart. Father
Mother
Sperm
Egg
E Zygote F
E
F
(A)
Mitosis
Meiosis
(B)
M eiosis
Mitosis
(C)
Fer lisa on
Mitosis
(D)
Cross over
Meiosis
Baby
What will be the genetic material found in a sperm? (i) 22 + X
(ii) 22 + Y
(iii) 24 + XY
(iv) 23 + XY
(A) (i) and (ii)
(B) (i) and (iv)
(C) (ii) and (iii)
(D) (iii) and (iv)
The diagram shows losses from a rat to the environment.
What will not be returned to the ecosystem and recycled? (A) Carbon dioxide
(B) Heat energy
(C) Salts
(D) Urea Paper Code: UN412
21
CLASS : X
Which part of the human brain controls breathing rate and regulates blood pressure? (A) Cerebrums (B) Medulla (C) Cerebellum (D) Spinalcord The diagram shows the female reproductive system. Where do fertilisation and implantation occur?
Y
Study the experimental set-up below.
Which of the following describes the appearance of the limewater after the set-up was placed in the sun for six hours? (A) The limewater turned cloudy. (B) The limewater turned brown. (C) The limewater turned dark blue. (D) The limewater remained colourless. What is the function of oxygen in our body? (A) (B) (C) (D)
To fill in the lung To keep the bodys temperature To burn the food in our body To maintain blood circulation Paper Code: UN412
22
CLASS : X
The diagram below shows the drawing of a human heart. The blood vessel that is labelled X carries blood from the heart to the lungs.
Which of the following is/are transported by the blood found in X? P. Oxygen
(A) P only
Q. Carbon dioxide
R. Water
(B) P and R only (C) Q only (D) P and Q only
What type of movement is shown by Mimosa pudica plant in response to external stimulus? (A) Nastic movement (B) Thigmotropism (C) Hydrotropism (D) Geotropism The potato plant produces daughter plants through (A) suckers. (B) corms. (C) bulbs. (D) tubers. Study the diagram below which shows two different samples of blood drawn out from Tom. red blood cells
Sample A was taken before Tom climbed a mountain
Sample B was taken a er Tom had been living on top of the mountain
Toms ability to produce more red blood cells at the top of the mountain shows an adaptation to (A) lower oxygen levels. (B) higher oxygen levels. (C) lower surrounding temperature. (D) higher surrounding temperature. Paper Code: UN412
23
CLASS : X
Class : X
General Awareness
On which river bank is Goa located? (A) Ganga
(B) Mandovi (C) Gomati
(D) Sabarmati
Who is called a numismatist? (A) Collector of stamps (B) Collector of coins (C) Collector of matchsticks (D) Collector of books B.B.C. is a (A) pharmaceutical concern (B) famous radio and television broadcasting corporation of U.K. (C) unit of united nations (D) company concerned with bank affairs Worlds tallest statue of Sardar Vallabhai Patel is laid in (A) Gujarat (B) Rajasthan (C) Uttarpradesh (D) Kolkata When is the National Youth Day in India celebrated? (A) August 20th (B) January 12th th (C) July 15 (D) April 20th Who won the Magsaysay Award 2014 for Emergent leadership? (A) T.N. Seshan (B) Randy Halasan (C) Arvind Kejriwal (D) Manmohan Singh In which game the expression Banana Kick is used? (A) Wrestling (B) Hockey (C) Football (D) Boxing Which is the only Asian country represented in the G-8 group? (A) China (B) Japan (C) India (D) Malaysia Who is the author of Half Girlfriend? (A) Narrottam Puri (B) R.K. Laxman (C) J.K. Rowling (D) Chetan Bhagat Government of India has decided to dedicate year 2015-16 to which of the following? (A) Water Conservation year (B) Nuclear Energy Year (C) Year of Clean India (D) Year of Digital India Paper Code: UN412
24
CLASS :X
Class : X
Mathematics
1.
A cineplex has 13 rows of seats with 10 seats in the first row, 12 in the second, 14 in the third and so on. What is the total number of seats in the cineplex ? (A) 252 (B) 256 (C) 258 (D) 286
2.
If cos (α + β) = 0 for all α , β being acute angles, what is the value of sin (α + β) ? (A) cos β
(B) cos 2 β
(C) sin α
(D) sin 2 α
3.
O is the centre of the circle. Find the diameter of the circle if PK = 1 cm is the perpendicular bisector of chord AB = 6 cm. (A) 10 cm (B) 1 cm (C) 19 cm (D) 5 cm
4.
The difference of the L.C.M. and H.C.F. of 210 and 55 is expressed as 210 × 6 + 55y. What is the value of y3 ? (A) 1331 (B) 3375 (C) 55 (D) 6859 Space fo r rou gh w ork
Paper Code: UN 415
1
CLASS :X
5.
Three chairs and two tables cost 1850. Five chairs and three tables cost 2850. Find the total cost of one chair and one table. (A) 800 (B) 850 (C) 900 (D) 950
6.
In trapezium ABCD, AB 2 CD and diagonals AC and BD intersect at point O. If OA = N 4, OB = 3N 19, OC = 4 and OD = N 3, find 'N'. (A) 10 units (B) 9 units (C) 12 units (D) 8 units
7.
Which triangle is formed by the points A (2a, 4a),
(
)
B (2a, 6a) and C 2a + 3a, 5a ? (A) (B) (C) (D)
A right-angled triangle An isosceles triangle An equilateral triangle An acute-angled triangle
Space for rough w ork
Paper Code: UN 415
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CLASS :X
8.
9.
10.
If P and Q are the zeros of the polynomial aN2 + bN + c, what is the value of P2 + Q2 ? (A)
b2 + 2ac a2
(B)
a2 + 2bc b2
(C)
a2 − 2bc b2
(D)
b2 − 2ac a2
If the roots of N2 + 4mN + 4m2 + m + 1 = 0 are real, which of the following is true ? (A) m = 1
(B) m ≤ − 1
(C) m ≥ − 1
(D) m ≥ 0
From a tower of 200 m, the angles of depression of two buildings in opposite sides of the tower are found to be 60° and 45°. What is the distance between the buildings ? 1 + 1) m 3
(A) 200( 3 + 1) m
(B) 200(
(C) 200 3 m
(D) 200( 3 1) m
Space fo r rou gh w ork
Paper Code: UN 415
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CLASS :X
11.
If OA and OB are radii and PA and PB are tangents to the circle, which of the following is quadrilateral OAPB ? (A) Rectangle (B) Square (C) Parallelogram (D) Kite
12.
∆ ABC is an isosceles triangle with the unequal side
measures 12 cm. If the attitude measures 6 cm, what is the measure of ∠ BAC ? (A) 36.8o (B) 45o (C) 90o (D) 38o 13.
What is the area of a triangle whose vertices are P(p, q + r), Q(q, r + p), and R(r, p + q) ? (A) 16 sq. units (B) 12 sq. units (C) 19 sq. units (D) 0 sq. units
14.
If ∆ ABC ~ ∆ DFE, ∠ A = 30o, ∠ C = 50o, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Which of the following is true ? (A) DE = 12 cm, ∠ F= 50o (B) DE = 12 cm, ∠ F= 100o (C) EF = 12 cm, ∠ D= 100o (D) EF = 12 cm, ∠ D= 30o Space fo r rou gh w ork
Paper Code: UN 415
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CLASS :X
15.
How many numbers between 100 and 1000 are divisible by 7 ? (A) 7 (B) 128 (C) 132 (D) 127
16.
If the sum of the zeros of the polynomial f( N) = (k 2 − 14 ) N 2 − 2 N − 12 is 1, which is one of the possible values of 'k' ?
(A)
14
(B) 14
(C) 2
(D) 4
17.
Three bulbs are connected in such a manner that they glow for every 24 sec, 36 sec and 54 sec respectively. All of them glow at once at 8 a.m. When will they again glow simultaneously ? (A) 8 : 30 : 36 a.m. (B) 8 : 03 : 36 a.m. (C) 8 : 36 : 03 a.m. (D) 8 : 36 : 30 a.m.
18.
A two digit number is 4 times the sum of its digits and also 16 more than the product of digits. Find the number. (A) 48 (B) 36 (C) 44 (D) 32 Space fo r rou gh w ork
Paper Code: UN 415
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CLASS :X
19.
In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ? A
B E
C
D
(A) 18 (C) 9 20.
(B) 13.5 (D) 4.5
1⎞ ⎛ 2⎞ ⎛ 3⎞ ⎛ Find the sum of ⎜ 1 − n ⎟ + ⎜ 1 − n ⎟ + ⎜ 1 − n ⎟ ...... upto n ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ terms. (A)
n 2
(B)
n−1 2
(C)
n+1 2
(D)
n (n + 1 ) n2
21.
In what ratio is the line segment joining the points (7, 3) and (4, 5) divided by the Y-axis ? (A) 2 : 3 (B) 4 : 7 (C) 3 : 5 (D) 7 : 4
22.
What is the angle between the hour and minute hands of a clock at 02 : 15 hours ? (A) 15o
(B) 7
1o 2
(C) 22
1o 2
(D) 30o
Space fo r rou gh w ork
Paper Code: UN 415
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CLASS :X
23.
In the given circle, O is the centre, QP is a diameter and PT is a tangent. Q O S P
T
If ∠ QOS = 120o, find ∠ PTS. (B) 40o (C) 60o (A) 30o
(D) 80o
24.
Given N > y and z ≠ 0 and N, y, z are any real numbers. The inequality which is not always true is : (A) N + z > y + z (B) Ny > yz 2 2 (D) (N z) > (y z) (C) Nz > yz
25.
The sum of first n terms of an AP, whose first term is π , is zero. What is the sum of next m terms ? (A)
πm (m +n) n −1
(B)
π (m +n)m 1 −n
(C)
πn (m + n) 1 −n
(D) None
Space fo r rou gh w ork
Paper Code: UN 415
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CLASS :X
Class : X
Physics
26.
Given three different resistors, which arrangement will cause it to have a maximum resistance ? (A) Arrange all resistors in parallel. (B) Arrange all resistors in series. (C) Arrange the largest resistor in series with the battery. (D) Arrange the smallest resistor in parallel with the battery.
27.
Five different solar panels, P, Q, R, S and T, were placed at different locations. The conditions for each set-up are given below. Which solar panel would likely provide the most power ?
28.
29.
(A)
10
30
25
60
(B)
10
50
50
60
(C)
12
40
75
20
(D)
12
25
20
If the angle of incidence of a ray of light hitting the surface of a liquid was 45 o, what would the angle of refraction be ? (B) 45o (C) 55o (D) 60o (A) 35o What is true about electrical current ? (A) To measure electrical current, ammeters are always connected to the circuit in series. (B) The unit for electrical current is ampere. (C) An electrical current consists of moving positive charges. (D) Both (A) and (B) Paper Code: UN 415
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CLASS :X
30.
Identify a statement that is not true. (A) The pattern of the magnetic field around a conductor due to an electric current flowing through it depends on the shape of the conductor. (B) The magnetic field of a solenoid carrying a current is similar to that of a bar magnet. (C) Magnitude of magnetic field is directly proportional to the quantity of current flowing through the current. (D) Magnetic field produced by the passage of current through a straight were is permanent.
31.
Which alternative source of energy at the same time helps us to get rid of organic waste ? (A) Solar energy (B) Wind (C) Biomass (D) Geothermal energy
32.
An object placed at F of a concave mirror will produce an image (A) at infinity. (B) highly enlarged. (C) real and inverted. (D) all of these
33.
Which material does NOT make the electromagnet stronger ? (A) Increasing the number of turns of wire in the coil. (B) Increasing the current in the coil. (C) Using a soft iron core. (D) Using a bigger resistor.
34.
Which appliance uses the most electricity ? (A) 60 W light bulb used for 1 hour. (B) 1 kW hair-dryer used for 5 minutes. (C) 40 W tablet computer used for 2 hours. (D) 600 W microwave used for 10 minutes. Paper Code: UN 415
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CLASS :X
35.
In a power station run by waterfall, which energy conversion occurs ? (A) Potential → kinetic → electrical (B) Heat → chemical → mechanical → electrical (C) Chemical → heat → electrical → mechanical (D) Light → mechanical → electrical
36.
Why is electricity such a popular form of energy ? (A) Electricity is the most harmless form of energy. (B) Electricity is very easy to produce. (C) Electricity can easily be converted into other forms of energy. (D) Electricity will never run out.
37.
What happens when light travels from air into water ? (A) It is absorbed by the water completely. (B) It bends towards the normal. (C) It travels with slower speed. (D) Both (B) and (C).
38.
A child is standing in front of a magic mirror. She finds the image of her head bigger, the middle portion of her body of the same size and that of the legs smaller. Identify the order of combination of mirrors in the magic mirror from the top. (A) Plane, convex and concave (B) Convex, concave and plane (C) Concave, plane and convex (D) Convex, plane and concave
39.
Which part of the eye converts light rays into electric signals to be sent by the optic nerves to the brain ? (A) Retina (B) Iris (C) Cornea (D) Pupil Paper Code: UN 415
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CLASS :X
40.
Light is deviated as it emerges from the prism. !
41.
"
Identify the angle of deviation. (A) 3 (B) 2 (C) 1 (D) 4 A magnet is inserted into the centre of a coil and an e.m.f. is induced across the coil. The magnitude of the induced current depends on (A) the diameter of the coil. (B) the strength of a magnet. (C) the thickness of the wire of coil. (D) all the three
42.
What is the function of a nuclear reactor ? (A) To change nuclear energy into kinetic energy. (B) To produce steam under high pressure. (C) To split radioactive atoms such as uranium atoms. (D) To drive the dynamo to produce electrical energy.
43.
The cone cells in human eyes help us to (A) identify different shapes of the object. (B) identify different colours of the object. (C) respond to different chemical substances. (D) respond to the intensity of the light.
44.
The resistance of a metal wire of length 2 m is 40 Ω at 20 °C. If the diameter of the wire is 1 mm, what will be the resistivity of the metal at that temperature ? (A) 1.28 × 108 Ω m
(B) 1.57 × 108 Ω m
(C) 1.75 × 109 Ω m
(D) 1.88 × 108 Ω m
Paper Code: UN 415
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CLASS :X
45.
An (A) (B) (C)
inverted image can be seen in a convex mirror, under no circumstances. when the object is very far from the mirror. when the object is at a distance equal to the radius of curvature of the mirror. (D) when the distance of the object from the mirror is equal to the focal length of the mirror.
46.
The diagram below shows the magnetic field of two current carrying wires perpendicular to the plane of the paper.
Which set of compasses shows the correct directions of the needles ? 1 2 3 (A) ↑ ↑ ↓
47.
(B)
↑
↓
↓
(C)
↑
↑
↑
(D) ↓
↑
↓
Light sensitive cells get activated on (A) illumination. (B) seeing the different colours. (C) facing opaque objects. (D) receiving message from the brain. Paper Code: UN 415
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CLASS :X
48.
The outside of a microwave oven has a label with the figures 230, 700 and 13 (units omitted). Choose the option which allocates all the three figures to their correct electrical unit.
) * + ,
Power (W) 230 13 13 700
Voltage (V) 700 230 700
Current (A) 13 700 230 13
49.
In torches, search lights and headlights of vehicles, the bulb is placed (A) between the pole and the focus of the reflector. (B) at the focus of the reflector. (C) between the focus and centre of curvature of the reflector. (D) at the centre of curvature of the reflector.
50.
A light steel bar and a light iron bar are attracted to a magnet as shown below. What will possibly happen when the magnet is removed ?
iron
steel
N
S
(A) The steel and iron bars repel each other. (B) Both steel and iron bars lose their magnetism. (C) Steel bar retains its magnetism and iron bar loses its magnetism. (D) Iron bar retains its magnetism and steel bar loses its magnetism.
Paper Code: UN 415
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CLASS :X
Chemistry
Class : X 51.
The bonding in sulphuric acid can be represented by the structure shown.
H H
O O
O S
O
What is the total number of electrons in the covalent bonds surrounding the sulphur atom ? (A) 4 (B) 6 (C) 8 (D) 12 52.
The reaction, H2 + Br2 → 2HBr is (A) a reduction reaction. (B) an oxidation reaction. (C) a displacement reaction. (D) a combination reaction.
53.
Which equation correctly shows the chemical reaction between ethanoic acid and sodium hydroxide ? (A) CH3COOH + NaOH → No reaction
(B) CH3COOH + NaOH → CH3CONa + H2O
(C) CH3COOH + NaOH → CH3COONa + H2O
(D) CH3COOH + NaOH → NaCH2COOH + H2O 54.
Chromium metal reacts with oxygen to form chromium trioxide, CrO3, which is soluble in water and forms a solution that turned universal Indicator orange. Chromium trioxide is a/an (A) basic oxide. (B) acidic oxide. (C) neutral oxide. (D) amphoteric oxide.
Paper Code: UN 415
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CLASS :X
55.
Identify a characteristic of semi-metals. (A) They have lower electrical conductivities than metals. (B) They are identical to semiconductors. (C) They combine with metals to form alloys. (D) All of the above.
56.
Which reaction is endothermic ? (A) C + O2 → CO2 (B) CaCO3 → CaO + CO2 (C) CH4 + 2O2 → CO2 + 2H2O (D) CaO + H2O → Ca(OH)2
57.
The substance that does not produce copper (II) sulphate when added to dilute sulphuric acid is (A) copper. (B) copper(II) carbonate. (C) copper(II) hydroxide. (D) copper(II) oxide.
58.
The element tin can be located in the periodic table in (A) group IIIB of 4th period. (B) group IVA of 4th period. (C) group IIIB of 5th period. (D) group IVA of 5th period.
59.
Heating sodium hydrogencarbonate to constant mass gives a residue and a gas that turns limewater cloudy. The addition of acid to the residue releases more of the same gas. What is the equation for heating sodium hydrogencarbonate ? (A) 2NaHCO3 → 2NaOH + 2CO2
(B) 2NaHCO3 → 2NaOH + 2CO + O2 (C) 2NaHCO3 → Na2CO3 + H2 + O2
(D) 2NaHCO3 → Na2CO3 + H2O + CO2 Paper Code: UN 415
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CLASS :X
60.
Which compound will burn with the sootiest flame ? (A) Butane (B) Methanol (C) Polyethene (D) Ethyl ethanoate
61.
Covalent bonding is least likely to be formed (A) between different elements in group VII. (B) in a substance with high melting and boiling points. (C) in a compound with low melting and boiling points. (D) between elements in group I and elements in group VII.
62.
Pentane has the molecular formula C5H12. It has (A) 5 covalent bonds. (B) 12 covalent bonds. (C) 16 covalent bonds. (D) 17 covalent bonds.
63.
Both zinc and zinc carbonate react with dilute hydrochloric acid. In what way are both these reactions the same ? (A) A gas is released. (B) Water is a product. (C) Neutralisation has occurred. (D) Both involve redox reactions.
64.
What remains unchanged on moving down a group ? (A) Density (B) Atomic radius (C) Valence electrons (D) Metallic character
65.
Pure gold is soft. Which metal is added to 22 carat gold to make ornaments ? (A) Platinum (B) Aluminium (C) Copper (D) Iron Paper Code: UN 415
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CLASS :X
66.
Which chemical equation best describes the formation of rust ? (A) 4Fe + 3O2 + xH2O → 2Fe2O3.xH2O (B) Fe + H2SO4 → FeSO4 + H2 (C) 2Fe3O4 + H2O → 3 Fe2O3 + H2 (D) 2FeSO4 → Fe2O3 + SO2 + SO3
67.
Match the entries of Column-I with those in Column-II.
a. b. c. d. e.
Column - I Hexane Ethane Pentene Hexene Butane
1. 2. 3. 4. 5.
(A) a-5, b-4, c-3, d-1, e-2 (C) a-5, b-4, c-3, d-2, e-1
Column - II C"H C$H C#H C H$ C$H " (B) a-3, b-4, c-2, d-5, e-1 (D) a-5, b-2, c-1, d-4, e-3
68.
Two drops of universal indicator are added to a solution in a test tube. The solution turns purple. This indicates that the solution in the test tube is (A) neutral. (B) alkaline. (C) slightly acidic. (D) very acidic.
69.
Thermite is a mixture of iron (III) oxide and (A) zinc powder. (B) sodium. (C) potassium. (D) aluminium powder.
70.
A student added dilute HCl to a test tube containing zinc granules and made following observations : (A) The zinc surface became dull and black. (B) A gas evolved which burnt with a pop sound. (C) The solution remained colourless. (D) All the three Paper Code: UN 415
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CLASS :X
Class : X 71.
Biology
Which of the following completes the given equation ?
Glucose + Oxygen (A) (B) (C) (D) 72.
Only Only Only Only
carbon dioxide + water + energy carbon dioxide + water carbon dioxide water + energy
Identify the gas that is evolved as gas bubbles in the test tube.
(A) Oxygen (C) Nitrogen 73.
?
(B) Carbon dioxide (D) Hydrogen
Which of the following parts make the peripheral nervous system ?
(i) Brain (ii) Spinal nerves (iii) Cranial nerves (A) (B) (C) (D)
Only (i) Only (i) and (ii) Only (ii) and (iii) All the three Paper Code: UN 415
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CLASS :X
74.
Which of these diagrams correctly shows the formation of the zygote of a male baby ? Egg
Sperm
Fertilised egg
(A)
X
+
(B)
X
+
Y
XY
(C)
Y
+
X
XY
(D)
YY
+
Y
YY
X
XX
75.
What is the connecting link between the birds and reptiles ? (A) Dinosaurs (B) Mammoths (C) Archaeopteryx (D) Pliohippus
76.
Which of the following sequences show how energy moves in a food chain ? (A) Grass → Frogs → Insects → Sun (B) Sun → Grass → Insects → Frogs (C) Frogs → Insects → Grass → Sun (D) Insects → Frogs → Sun → Grass
77.
With which tree is Amrita Devi Bishnoi associated ? (A) Khejri (B) Keekar (C) Khejrali (D) Khajoor Paper Code: UN 415
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CLASS :X
78.
The two organisms which breathe only through their moist skin are (A) fish and frog. (B) frog and earthworm. (C) Prawn and earthworm. (D) fish and earthworm.
79.
What cannot be added in a composting pit to prepare compost ? (A) Sunflower plants (B) Fruit and vegetable peels (C) Plastic flower (D) Red worms
80.
Which event does not occur in photosynthesis ? (A) Conversion of light energy into chemical energy (B) Reduction of carbon dioxide to carbohydrates (C) Oxidation of carbon to carbon dioxide (D) Absorption of light energy by chlorophyll
81.
Which statement is/are true about the given figure ?
(A) (B) (C) (D)
The food below the ring has been used up. Food cannot be transported to the part below the ring. Water and mineral salts cannot be transported Both (A) and (B) Paper Code: UN 415
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CLASS :X
82.
Which is used artifically to remove nitrogenous waste products from the blood ? (A) Ventilator (B) Transfusion (C) Hemodialysis (D) Angiogram
83.
Flowers like tulip, croccus open at high temperature, but close with fall of temperature. Which of the following movements does it involve ? (A) Photonasty (B) Nyctinasty (C) Seismonasty (D) Thermonasty
84.
Which of these is a mode of asexual reproduction ? (A) Budding (B) Binary fission (C) Spore formation (D) All of these
85.
Hargobind Khorana was awarded the Nobel prize for his work in the field of (A) hormones. (B) immunology. (C) genetic Engineering. (D) chromosomal abberation.
86.
Identify a herbivore in an ecosystem ? (A) Secondary consumers (B) Primary consumers (C) Producers (D) Decomposers
87.
Which of these reproduce by fragmentation ? (A) Rhizopus (B) Salmonella (C) Plasmodium (D) Spirogyra
88.
Ravi bought a device X, which could cook food items and can be used to produce electricity. It does not generate energy at night. What is the source of energy used in the device X ? (A) Air (B) Water (C) Sunlight (D) Coal Paper Code: UN 415
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CLASS :X
89.
When Anvesh's cerebellum is injured in an accident, Anvesh is unable to do which of the following actions ? (A) Hand movements (B) Balancing of body (C) Coordinate his body movements (D) All of these
90.
What happens to the air as it passes through the nasal cavity ? (A) Filtered in the nostrils (B) Moistened by mucus (C) Warmed to the body temperature (D) All of these Space fo r rou gh w ork
Paper Code: UN 415
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CLASS :X
Class : X
General Awareness
91.
Which cricketer has lent his voice to Swachh Bharat anthem which was released on 2nd October, 2015 ? (A) Sourav Ganguly (B) M.S. Dhoni (C) Sachin Tendulkar (D) Kapil Dev
92.
The famous tagline Think Different belongs to which company ? (A) Accenture (B) IBM (C) Blackberry (D) Apple
93.
Which political party Kiran Bedi joined to contest Delhi Assembly elections on 15th January, 2015 ? (A) Aam Aadmi Party (B) Bharatiya Janata Party (C) Indian National Congress (D) Communist Party
94.
Recently, government has decided to release a commemorative postal stamp and also a coin in honor of which Indian politician ? (A) Jyotirao Phule (B) Vallabhbhai Patel (C) BR Ambedkar (D) Lal Bahadur Shastri
95.
Which technology giant has agreed to provide Wi-Fi hotspots at 500 railway stations in India ? (A) Microsoft (B) Google (C) IBM (D) Facebook
96.
How many British Satellites did ISRO launched from Satish Dhawan Space Centre (SDSC) in Sriharikota in July, 2015 ? (A) 4 (B) 5 (C) 6 (D) 2 Paper Code: UN 415
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CLASS :X
97.
Who sworn-in as the Chief Minister of Delhi on 14th February, 2015 ? (A) Sheila Dikshit (B) Arvind Kejriwal (C) Kiran Bedi (D) Sushma Swaraj
98.
Which is the first state to ink mandatory voting rule within state government ? (A) Rajasthan (B) Gujarat (C) Punjab (D) Tamilnadu
99.
Who got appointed as chairman of Indias Oscar Jury ? (A) Amol Palekar (B) Amitabh Bachchan (C) Anupam Kher
100.
(D) Goutam Ghose
Pointing to a photograph of a boy Suresh said, "He is the son of the only son of my mother." How is Suresh related to that boy ? (A) Brother (B) Uncle (C) Cousin (D) Father Space fo r rou gh w ork
Paper Code: UN 415
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CLASS :X
Class : X
Mathematics
1.
∆ ABC is right-angled at C. If p is the length of perpendicular from C to AB and AB = c, BC = a and CA = b, which of the following is true ? (A) pc = ab (B) pb = ab (C) pc = bc (D) pb = ac
2.
An arithmetic progression has 10 terms. The sum of the odd terms is 245 whereas the sum of the even terms is 305. Find the common difference. (A) 2 (B) 7 (C) 3 (D) 1
3.
Find the area of the triangle whose vertices are (a, b + c), (a, b c) and ( a, c). (A) 2ac (B) 2bc (C) b(a + c) (D) c(a b) Space fo r rou gh w ork
Paper Code: UN 418
1
CLASS :X
4.
ABC is a right - angled triangle with ∠B = 90o , AB = 12 cm and AC = 13 cm. A circle with centre O is inscribed inside the triangle.
A
13 cm
12 c
m
C
O B
Find the radius of the circle. (A) 8 cm (B) 7 cm (C) 4 cm (D) 2 cm 5.
1 If sinθ = − , what are the respective possible values of 2 θ between 0 and 2π ? (B) 240o and 330o (A) 210o and 300o (C) 240o and 300o (D) 210o and 330o Space fo r rou gh w ork
Paper Code: UN 418
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CLASS :X
6.
In what ratio does the X-axis divide the line segment joining the points (3, 4) and (2, 6) ? (A) 2 : 3 (C) 1 : 2
7.
(B) 3 : 2 (D) 2 : 1
In the given figure, ∆ RSP : ∆ RPQ. Identify the true statement. P
Q
R
RS = RP2 RQ
(B) RP × RQ = RS2
(C) RS × RQ = RP2
(D) RQ × RS = RP
(A)
8.
S
The first two terms of an arithmetic progression are 27 and 24 respectively. How many terms of the progression are to be added to get 30 ? (A) 15 (B) 20 (C) 25 (D) 18 Space for rough w ork
Paper Code: UN 418
3
CLASS :X
9.
What number must be added to each of the numbers, 5, 9, 17, 27 to make them proportionate ? (A) 2 (B) 1 (C) 3 (D) 5
10.
The remainder when a number is divided by 143 is 31. What is the remainder when the same number is divided by 11 ? (A) 5 (B) 7 (C) 6 (D) 9
11.
Find the value of cos1°cos2°cos3°.....cos89°cos90° . 1 1 (C) (D) 0 (A) 1 (B) 2 2
12.
AP is a secant and PT is a tangent to a circle. If PT = 15 cm and AB = 8BP, find AP.
A
B P T
(A) 45 cm (C) 25 cm
(B) 36 cm (D) 62 cm Space fo r rou gh w ork
Paper Code: UN 418
4
CLASS :X
13.
Which of the following is not correct ? (A) The degree of a zero polynomial is zero. (B) The polynomial x4 + 1 has 4 zeros. (C) The degree of a cubic polynomial is 3. (D) A quadratic polynomial has two zeros.
14.
What is the angle of elevation of a light source when the length of the shadow of a flagpost is equal to its height ? (A) 45° (B) 30° (C) 60° (D) 90°
15.
The prime factorization of two numbers are 32 × 73 × 11 and 3 × 72 × 113 × 17. Which of the following is a common factor of the numbers ? (A) 1683 (B) 5831 (C) 1089 (D) 539
16.
What type of a system of equations is the pair of linear equations 2N 3y = 8 and 4N 6y = 9 ? (A) Consistent system (B) Inconsistent system (C) Dependent system (D) Independent system Space fo r rou gh w ork
Paper Code: UN 418
5
CLASS :X
17.
Given sinθ + cosθ = 3, what is the value of tanθ + cotθ ? (A)
1 2
(B)
2 3
(C)
3 2
(D) 1
18.
If two opposite vertices of a square are (1, 2) and (5, 6), what are the other two vertices ? (A) (2, 5), ( 6, 1) (B) (2, 5), (6, 1) (C) (2, 5), (6, 1) (D) (2, 6), (5, 1)
19.
If all the sides of a parallelogram touch a circle, what is the parallelogram ? (A) A rectangle (B) A rhombus (C) A square (D) A trapezium
20.
The zeros of a quadratic polynomial f( N) = N2 − 7 N + k are α and β such that α − β = 3 . Find the value of 'k'. (A) 10
21.
(B) 2
(C) 5
(D) 15
The perimeter and area of a rectangular park are 80 m and 400 m2. What is its length ? (A) 20 m (B) 15 m (C) 30 m (D) 40 m Space fo r rou gh w ork
Paper Code: UN 418
6
CLASS :X
22.
A paper is cut in the following shape.
E
D C
A B Which of the following is the correct statement ? (B) AC2 = AD2 + DE2 (A) AE2 = AD2 + ED2 (C) AC2 = AB2 + AD2 (D) AE2 = AB2 + BC2 23.
The sum of the first 10 terms of an arithmetic progression is four times the sum of its first five terms. Find the ratio of the first term to the common difference. (A) 1 : 4 (B) 4 : 1 (C) 2 : 1 (D) 1 : 2
24.
If the height of a cylinder is 4 times its circumference, what is the volume of the cylinder in terms of its circumference, C ? (A)
C3 π
(B)
2C3 π
(C)
C π
(D)
π+ "
Space fo r rou gh w ork
Paper Code: UN 418
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CLASS :X
25.
Find the value of 'p' so that N2 + 5pN + 16 = 0 has no real root. 8 (A) Greater than 5 −8 (B) Less than 5 & −& (C) Lies between and # # 15 (D) Less than 8 Space fo r rou gh w ork
Paper Code: UN 418
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CLASS :X
Class : X 26.
Physics
Observe the given circuit. 6Ω B
C
1.2 A F
E
D A 4Ω Find the current passing through 6 Ω resistor. (A) 0.72 A (B) 0.80 A
(C) 0.48 A
(D) 0.62 A
27.
The Sun obtains its energy from nuclear fusion. During this process, (A) helium atoms combine to form hydrogen atoms. (B) hydrogen atoms combine to form helium atoms. (C) helium atoms break up to form hydrogen atoms. (D) hydrogen atoms break up to form helium atoms.
28.
Magnification produced by a rear view mirror fitted in vehicles (A) is less than one. (B) is more than one. (C) is equal to one. (D) can be more than or less than one.
29.
Which factor does NOT increase the power of a D.C. motor ? (A) An increase in the number of turns in the coil (B) An increase in the area of cross-section of the coil (C) An increase in the size of the core (D) The winding of a large number of coils on the soft iron core Paper Code: UN 418
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CLASS :X
30.
The diagram shows the direction of the current in a wire and the circular magnetic field around it.
Identify the correct directions of the current and magnetic fields respectively.
Direction of current
Direction of magnetic field
(A)
Into the page
Clock wise
(B)
Into the page
Anti-clockwise
(C) Out of the page
Clock wise
(D) Out of the page
Anti-clockwise
31.
The refractive index of water is 1.33. What will be the speed of light in water ? (A) 3 × 108 m/s (B) 2.25 × 108 m/s (D) 1.33 × 108 m/s (C) 4 × 108 m/s
32.
Why is the neck of the glass bulb of an electric bulb sealed ? (A) To protect the filament from oxidation (B) To maintain the temperature inside (C) To prevent the effect of humidity (D) All of the above
33.
A tall man of height 6 feet, want to see his full image. Then required minimum length of the mirror will be (A) 12 feet. (B) 3 feet. (C) 16 feet. (D) 24 feet. Paper Code: UN 418
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CLASS :X
34.
Which of these are advantages of using biomass as a source of energy ?
(A) 2 only (C) 1 and 3 only 35.
(B) 1 and 2 only (D) 2 and 3 only
When a small magnetic needle is placed below a horizontal conductor carrying a strong current from west to east, its north pole will point in the direction of +
B
A
B S
(A) west - east. (C) north - south. 36.
N
(B) south - west. (D) east - west.
A photovoltaic cell (solar cell) is usually made of silicon. How does it produce electricity ? (A) Liquids contained inside the cells contain chemical energy that can be converted to electrical energy (B) Using solar energy (C) Using batteries (D) Using wind power
Paper Code: UN 418
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CLASS :X
37.
Three resistors of 2.5 Ω , 12 Ω and 3.5 Ω are connected in series. Which single resistor can replace all the three of them in a circuit ? (A) 16 Ω
(B) 4 Ω
(C) 18 Ω
(D) 8 Ω
38.
Negative value of focal length of a spherical mirror indicates that it is a (A) concave mirror. (B) convex mirror. (C) plane mirror. (D) none of these
39.
Which factor does NOT affect the focal length of a convex lens ? (A) Refractive index of the material for making the lens (B) Material of the lens (C) Object distance (D) Thickness of the lens
40.
An iron box has a resistance coil of 30 Ω and takes a current of 10 A. Calculate the heat developed by it in kJ in 1 minute. (A) 180 kJ (B) 90 kJ (C) 45 kJ (D) 135 kJ
41.
The colour of an object is determined by the colour of light (A) reflected by it. (B) absorbed by it. (C) incident on it. (D) none of the above
42.
The use of which source of energy pollutes the air ? (A) Hydro energy (B) Nuclear energy (C) Solar energy (D) Fossil fuels Paper Code: UN 418
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CLASS :X
43.
Which field pattern given below is valid for both electric and magnetic fields ? (A)
(B)
(C)
(D)
44.
The cameras diaphragm works like the humans eye pupil. What is the function of the pupil ? (A) Focus on a view (B) Control the amount of incoming light (C) To get proper reflection (D) To protect the eyes from dangerous object
45.
Resistance is the ratio of the X in volts across the component to the Y passing through, measured Z . in Which key has the three words that complete the sentence correctly ?
46.
What is the distance between a real object and its real image when the object is placed at the centre of curvature of a concave mirror ? (A) f (B) 2f (C) 4f (D) Zero Paper Code: UN 418
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CLASS :X
47.
Flemings left hand rule is used in finding the direction of the magnetic field around a (A) circular loop. (B) moving coil. (C) straight conductor. (D) magnetic loop.
48.
Match the entries in Column-I with those in Column- II correctly.
Column- I
Column - II
a. The blue colour of the sky
1.
Total internal reflection
b. The glittering of diamond
2.
Refraction of light
c. The formation of rainbow
3.
Scattering of light
d. The visibility of sun for something even after sunset
4.
Dispersion of light
(A) a-3, b-1, c-4, d-2 (C) a-2, b-3, c-4, d-1 49.
(B) a-1, b-3, c-2, d-4 (D) a-4, b-1, c-3, d-2
What is the potential difference across bulb X in the circuit shown below ? X Dry Cell
(A) 1.5 V 50.
(B) 3.0 V
(C) 4.5 V
(D) 6.0 V
A concave mirror has a focal length of 10 cm. Where should an object be placed to obtain a real, inverted and same size image as the object ? (A) 5 cm (B) 15 cm (C) 20 cm (D) 30 cm Paper Code: UN 418
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CLASS :X
Chemistry
Class : X 51.
A particular metal forms an invisible protective layer and prevents further oxidation. Identify the metal, its oxide and chemical formula. (A) Iron, iron oxide, Fe2O3 (B) Aluminium, aluminium oxide, Al2O3 (C) Zinc, zinc oxide, ZnO (D) Copper, copper oxide, CuO
52.
Which of the given chemical equations is balanced? (A) H2O2 → H2O + O2 (B) NaNO3 → NaNO2 + O2 (C) CaCO3 → CaO + CO2 (D) Al2CO3 → Al2O3 + CO2
53.
Identify the functional group of ketone. (A) OH (B) CO (C) COOH (D) CHO
54.
Free mobile hydroxide ions are found in (A) dry ammonia gas. (B) dilute sulphuric acid. (C) dry barium hydroxide. (D) sodium hydroxide solution.
55.
Which set of elements belong to the same period ? (A) Li, Na, K (B) Li, Mg, Ca (C) F, Cl, Br (D) Ga, Ge, As Space fo r rou gh w ork
Paper Code: UN 418
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CLASS :X
56.
Identify a decomposition reaction. (A) MgCO3 → MgO + CO2 (B) Fe2O3 + 2Al → 2Fe + Al2O3 (C) BaCl2 + H2SO4 → BaSO4 + 2HCl (D) Zn + H2SO4 → ZnSO4 + H2
57.
Sulphuric acid does not react with (A) iron (B) gold (C) zinc (D) magnesium
58.
Which structure represents the electron arrangement of Group 17 element in the periodic table ? (A)
(B)
(C)
(D)
59.
What changes occur due to water of crystallisation ? (A) Crystals of salts obtain their shape. (B) Crystals of salts obtain their colour. (C) Crystals of salts form a part of crystal structure. (D) All of the above
60.
Which hydrocarbon exhibits isomerism ? (A) Ethane (B) Propane (C) Butane (D) Methane
61.
Which pair of metals are extracted just by heating with their sulphide ores in air ? (A) Mercury, copper (B) Mercury, magnesium (C) Silver, mercury (D) Iron, mercury Paper Code: UN 418
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CLASS :X
62.
Which compounds form a part in the homologous series ? (A) Haloalkanes and alcohols (B) Aldehydes and ketones (C) Carboxylic acids (D) All of the above
63.
A strong acid (A) ionises completely in water. (B) has a small pH value. (C) has a high concentration of hydrogen ions. (D) all the three
64.
Which element is NOT a metalloid ? (A) Boron (B) Arsenic (C) Antimony (D) Strontium
65.
Why is aluminium a suitable material for building air crafts ? (A) It is a good conductor of heat. (B) It has a high melting point. (C) It is shiny. (D) It is light and does not rust easily.
66.
Identify X and Y in the given chemical reaction. X + YSO4 → Y + XSO4 (A) Na and Mg (B) Zn and Cu (C) Ag and K (D) H and Al Space fo r rou gh w ork
Paper Code: UN 418
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CLASS :X
67.
While cooking, if the bottom of the vessel is getting blackened on the outside. It means that (A) the food is not cooked completely. (B) the fuel is not burnt completely. (C) the fuel is wet. (D) the fuel is burning completely.
68.
Identify a weak mineral acid. (A) H2SO4 (B) H2CO3 (C) HCl (D) HNO3
69.
A metal that cannot be reduced by carbon is (A) magnesium. (B) iron. (C) zinc. (D) lead.
70.
Which of the given reactions is a compound compound combination reaction ? (A) Reaction of water with calcium oxide. (B) Reaction of iodine with white phosphorus. (C) Reaction of iron with sulphur. (D) Electrolysis of water. Space fo r rou gh w ork
Paper Code: UN 418
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CLASS :X
Class : X
Biology
71.
Which cell organelle traps solar energy and helps in synthesising food through photosynthesis ? (A) Chloroplast (B) Mitochondria (C) Cytoplasm (D) Nucleus
72.
Which process occurs in the part shown below ?
(A) Tubular secretion (C) Ultrafiltration 73.
(B) Tubular reabsorption (D) All of the above
In which part of the female reproductive system does the process shown below occur ?
(A) Ovary (C) Vagina
(B) Uterus (D) Fallopian tube
74.
What provide(s) evidence of organic evolution ? (A) Morphological evidence (B) Anatomical evidence (C) Embryological evidence (D) All of the above
75.
Conversion of glucose into glycogen in the liver is controlled by (A) thyroxine. (B) insulin. (C) adrenaline. (D) oestrogen. Paper Code: UN 418
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CLASS :X
76.
Identify the logical sequence of a food chain. (A) Producer → consumer → decomposer (B) Decomposer → consumer → producer (C) Producer → decomposer → consumer (D) Consumer → producer → decomposer
77.
Which instrument is used to measure the blood pressure ? (A) Manometer (B) Barometer (C) Sphygmomanometer (D) Photometer
78.
Which of the following is NOT a product of fossil fuel ? (A) LPG (B) Natural gas (C) Biogas (D) CNG
79.
The climbing organs of plants like tendrils grow towards any support which they happen to touch and wind around the support. This is an example of (A) chemotropism. (B) nastic movement. (C) thigmotropism. (D) geotropism.
80.
Which of these organisms exhibit regeneration ? (A) Paramecium and Hydra (B) Hydra and Amoeba (C) Planaria and Amoeba (D) Hydra and Planaria
81.
A zygote which develops into a baby girl will have (A) 44 + YY chromosomes. (B) 44 + XX chromosomes. (C) 44 + XY chromosomes. (D) 46 Y chromosomes.
Paper Code: UN 418
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CLASS :X
Which of these samples is most probably from a pulmonary artery ? Oxygen content
82.
P
Q R S Blood sample (B) Q (C) R
(A) P 83.
The equation given below represents photosynthesis. Identify P and Q.
P + water (A) (B) (C) (D) 84.
(D) S
P P P P
-
sunlight glucose + Q chlorophyll
Carbondioxide, Q - Oxygen Oxygen, Q - Oxygen Carbondioxide, Q - Carbondioxide Oxygen, Q - Carbondioxide
What is the immediate effect on a person if the gland shown below is removed ?
(A) (B) (C) (D)
Calcium and phosphorous levels are decreased. The blood sugar levels in blood are disturbed. Growth rate decreases. Growth rate increases. Paper Code: UN 418
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CLASS :X
85.
In the figure given below, where does the germination of pollen and fertilisation take place ?
(A) Only I and II (C) Only I and IV
(B) Only I and III (D) Only I, II and III
86.
Which blood group is known as the universal recipient ? (A) AB (B) O (C) A (D) B
87.
Which of these controls and coordinates body movements ? (A) Cerebrum (B) Medulla oblongata (C) Cerebellum (D) Pons varoli
88.
Which of the following is the correct sequence of events of sexual reproduction in a flower ? (A) Pollination, seed, fertilisation, embryo (B) Seed, embryo, fertilisation, pollination (C) Pollination, fertilisation, embryo, seed (D) Embryo, seed, pollination, fertilisation
89.
Which of these activities does not cause pollution ? (A) Cars for transportation (B) Polybags for shopping (C) Windmills for generating power (D) Dyes for colouring clothes
90.
Amoeba reproduces by which of the following methods ? (A) Binary fission (B) Budding (C) Germination (D) All of the above Paper Code: UN 418
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CLASS :X
Class : X
General Awareness
91.
Who is the author of 'War and Peace' ? (A) Leo Tolstoy (B) Mahatma Gandhi (C) Charles Dickens (D) Kipling
92.
The SI unit for which of these is named after James Watt, a Scottish inventor and engineer ? (A) Temperature (B) Power (C) Force (D) Electric Current
93.
In which state, a cricket stadium in the name of Sachin Tendulkar is going to start ? (A) Tamil Nadu (B) Kerala (C) Maharashtra (D) Gujarat
94.
The given logo belongs to which company ?
(A) Mazda (C) Toyota
(B) Maruti Suzuki (D) Mahindra
95.
Which state government has launched M-Shiksha-Mitra mobile app for teachers which is developed by National Informatics Centre ? (A) Chattisgarh (B) Madhya Pradesh (C) Himachal Pradesh (D) Haryana
96.
Where is the National Institute of Sports located ? (A) Ranchi (B) Delhi (C) Mohali (D) Patiala
97.
Who is the Indian industrialist honoured by UK City of Coventry as Honorary Freeman recently ? (A) Mukhesh Ambani (B) Laxmi Mittal (C) Ratan Tata (D) Kumara Manglam Birla Paper Code: UN 418
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CLASS :X
98.
Which of these markings is given by the Bureau of Indian Standards to identify the purity of precious metals ? (A) ISI Mark (B) Trademark (C) Hallmark (D) FPO Mark
99.
Which is the heaviest internal organ in the human body ? (A) Pancreas (B) Heart (C) Liver (D) Lungs
100.
What does the acronym ISD stand for ? (A) Internal Subscribers Department (B) International Subscriber Dialling (C) International Subscriber Details (D) Internet Subscriber Details Space fo r rou gh w ork
Paper Code: UN 418
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C L A S S : 10
Class : 10
Mathematics
1.
The smallest angle of a triangle is one-fifth the sum of the other two and the largest angle exceeds the sum of the other two by 20 o. Find the largest angle of the triangle. (B) 90o (C) 120o (D) 110o (A) 100o
2.
Find the number of points on X-axis which are at a distance 'c' units (c < 3) from (2, 3). (A) 1 (B) 2 (C) 0 (D) 3
3.
In terms of radians, what is the equivalent of 45o ? 45° 180°π (A) 25 π (B) 0.25 π (C) (D) π 45° PT is a tangent and PAB is a secant of the circle meeting the circle at A and B. If PA = 4 cm and AB = 5 cm. What is the length of PT ? (A) 8 cm (B) 6 cm (C) 3 cm (D) 1 cm
4.
Space fo r rou gh w ork
Paper Code: UN421
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C L A S S : 10
5.
The L.C.M. of 318 and 477 is expressed as 159 × p + 318. What is the value of p ? (A) 2 (B) 4 (C) 3 (D) 0
6.
The side of a square is 4 m more than the side of another square. The sum of their areas is 208 sq. m. What is the side of the larger square ? (A) 12 m (B) 8 m (C) 9 m (D) 5 m
7.
For what value of N are A(2, 3), B(N, y) and C(4, 3) the vertices of a right triangle with right angle at A ? (A) 2 (B) 4 (C) 5 (D) 3
8.
α, β and γ are the zeros of a cubic polynomial. If α + β + γ = 2 , αβ + βγ + γα = (−7) and αβγ = (−14) , find the polynomial. (B) m3 + 2m2 7m 14 (A) x3 2x2 7x + 14 (C) n3 2n2 + 7n 14 (D) y3 + 2y2 7y 14 Space fo r rou gh w ork
Paper Code: UN421
2
C L A S S : 10
9.
Three circles with centres A, B and C touch one another externally. The three centres are joined to one another to form a triangle. ) *
+
If AB = 7 cm, BC = 11 cm and AC = 6 cm, find the radii of the three circles. (A) 2 cm, 7 cm, 9 cm (B) 1 cm, 6 cm, 5 cm (C) 12 cm, 5 cm, 6 cm (D) 3 cm, 10 cm, 7 cm 10.
What is the sum of first n odd numbers starting from 11 ? (A) n2 + 10n (B) n2 10n (C) 10n n2 (D) n2
11.
The string of a kite is 200 m long. It makes an angle of 30° with the ground. What is the height of the kite above the ground ? (A) 120 m (B) 150 m (C) 100 m (D) 200 m Space fo r rou gh w ork
Paper Code: UN421
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C L A S S : 10
12.
∆ ABC is an isosceles triangle right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of ∆ ABE and ∆ ACD. (A) 1 : 2 (B) 3 : 1 (C) 1 : 3 (D) 4 : 1
13.
If the co-ordinates of points A, B, C and D are (6, 3), ( 3, 5), (4, 2) and (N, 3N) respectively and if
area of ∆DBC 1 = area of ∆ ABC 2 , find the value of 'N'. (A) 14.
8 11
&
(C)
% '
(D) 0
If ∆ ABC is right angled at C, find the value of cos (A + B).
1 2
3 2 If an equilateral triangle ABC is inscribed in a circle, which of the following is formed by the tangents at their vertices ? (A) A scalene triangle (B) An equilateral triangle (C) An isosceles triangle (D) A right triangle (A) 0
15.
(B)
(B) 1
(C)
(D)
Space fo r rou gh w ork
Paper Code: UN421
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C L A S S : 10
16.
Find a quadratic polynomial, whose sum and product of −10 and 7 respectively. zeros are 3 (A) x + (C)
10 7 x+ 3 3
3 x + 10 x + 7 3
3N2 − 10 N + 7 3
(B)
(D) x + 10 x + 7 3
17.
A quadratic equation αN 2 + 5 N + β = 0 has two roots 1 N = and N = 2. Find the respective values of α and β. 3 (A) 3, 2 (B) 2, 5 (C) 3, 5 (D) 3, 2
18.
For what value of 'N' does 6N end with 5 ? (A) 0 (B) 1 (C) 5 (D) Never ends with 5.
19.
What is the sum of n arithmetic means between 'a' and 'b' ? (A)
3 (a + 2b ) 2
(B)
n (a + b ) 2
(C)
n (a − b ) 2
(D)
n (a + b ) 4
Space for rough w ork
Paper Code: UN421
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C L A S S : 10
20.
Identify the incorrect statement. (A) A right angled triangle may have 1, 1 and 2 as its sides. (B) 1, 2, 3 are the sides of a right angled triangle. (C) The ratio of corresponding sides of two squares whose areas are in the ratio 4 : 1 is 2 : 1. (D) 17, 8 and 15 are the sides of a right angled triangle.
21.
Find the point of trisection of the line joining the points (2, 19) and (5, 4). (A) (2, 3) (B) (1, 2) !4 ⎞ ⎛ (C) ⎜ ! , − ! ⎟ ⎝ ⎠
22.
⎛ 8 ⎞ (D) ⎜ ! , ! ⎟ ⎝ ⎠
What is the numerical value of the expression sin9o cos81o − ? sin48o cos42o 1 (C) 0 (D) 1 (A) 1 (B) 2 Space fo r rou gh w ork
Paper Code: UN421
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C L A S S : 10
23.
In ∆ ABC , ∠ B > 90o and AD ⊥ CB (produced). Identify the correct statement. (A) AC = AB + BC + BC.BD (B) AC = AB + BC + BC.AB (C) AB = AC − BC + BC.BD (D) AB = AC + BC + BC.AC
24.
The numbers 28, 22, 'N', 'y', 4 are in arithmetic progression. What are the respective values of 'N' and 'y' ? (A) 10, 16 (B) 20, 18 (C) 18, 16 (D) 16, 10
25.
The sum of squares of two consecutive positive even numbers is 340. Find them. (A) 12, 14 (B) 12, 10 (C) 10, 8 (D) 14, 16 Space fo r rou gh w ork
Paper Code: UN421
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C L A S S : 10
Class : 10
Physics
26.
A bird stands on a current-flowing electrical wire, getting ready to fly. Why does it NOT get electrocuted ? (A) The bird does not have any resistance. (B) The bird is too small to get electrocuted. (C) The bird will get electrocuted once it flies. (D) The birds two feet have the same potential.
27.
The top of box-type solar cooker is covered with glass to (A) allow one to see the food being cooked. (B) allow more sunlight into the box. (C) prevent dust from entering the box. (D) reduce heat loss by radiation.
28.
At which of the following positions do the given mirrors form a virtual image ? (A) In convex mirror at infinity (B) In concave mirror between F and P (C) In plane mirror at all positions (D) All of the above
29.
Which core with same number of turns in all can be made a strongest electromagnet ? (A) Steel core, 2 cells (B) Iron core, 2 cells (C) Steel core, 1 cell (D) Iron core, 1 cell
30.
How does the eye change its focus to see near or distant objects ? (A) The lens moves diagonally. (B) The retina expands and contracts. (C) The lens becomes thicker and thinner. (D) The pupil becomes larger and smaller. Paper Code: UN421
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C L A S S : 10
31.
What is the effective resistance of the four resistors in the circuit shown below ? (A) 0.25 Ω (B) 4 Ω (C) 6 Ω (D) 18 Ω
32.
A typical solar cell develops a potential difference of (A) 0.5 1 V and 0.7 W of electricity (B) 0.7 V and 0.5 W of electricity (C) 0.7 V and 1.0 W of electricity (D) None of these
33.
Identify an incorrect statement. (A) A medium with larger refractive index is optically denser than a medium with smaller refractive index. (B) The speed of light is less in a rarer medium than a denser medium. (C) Refraction is due to the change in speed of light as it enters from one medium to another. (D) The absolute refractive index of a medium is simply called its refractive index.
34.
Three vertical conducting wires have the same amount of current flowing through them. Given that the distance between the wires are the same, what is the direction of the resultant electromagnetic force acting on the middle wire ? (A) To the left. (B) To the right. (C) Perpendicular to the plane of the paper. (D) Resultant electromagnetic force is zero. Paper Code: UN421
9
C L A S S : 10
35.
Identify the parameters of electricity supply in India.
36.
Which gas is derived from biomass in our effort to conserve our energy sources ? (A) Methane (B) Coal (C) Natural (D) Petroleum
37.
Three conductors are joined as shown below. 2 4
5
3 The current in conductor RS is 10 A. The current in conductor QR is 6 A. What will be the current in conductor PR ? (A) 4 A (B) 6 A (C) 10 A (D) 16 A
38.
A converging lens has a focal length of 10 cm. If an object is placed 18 cm from the optical centre of the lens, how far will the image be from the optical centre of the lens ? (A) 20.0 cm (B) 22.5 cm (C) 24.0 cm (D) 25.5 cm
39.
A soft iron bar is introduced inside a current carrying solenoid, its magnetic field will (A) become zero. (B) decrease. (C) increase. (D) remain the same. Paper Code: UN421
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C L A S S : 10
40.
A person is not able to see near objects clearly, because (A) image is formed behind the retina. (B) focal length of the eye lens is more. (C) use of convex lens has been ignored, though it was advised. (D) all of the above.
41.
Four magnetic materials used to pick up paper clips after they were taken out from a coil which is connected to a strong direct current is given below. Which is the best magnetic material to be used as an electromagnet ?
42.
Which element contained in a fuel contributes to its high calorific value ? (C) O2 (D) N2 (A) C (B) H2 Which source produces yellow light ? (A) Sodium lamp (B) Sunlight (C) LPG (D) Both (A) and (B)
43.
44.
A man wearing yellow coloured glass for left eye and red coloured glass for right eye stands in front of a plane mirror. Which statement about his image is correct ? (A) Both the eyes appear red. (B) Both the eyes appear yellow. (C) Left eye appears yellow and right eye red. (D) Left eye appears red and right eye yellow. Paper Code: UN421
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C L A S S : 10
45.
What is the current flowing through an appliance marked 240 V, 40 W ? (A) 0.17 A (B) 3.00 A (C) 6.67 A (D) 6.00 A
46.
The red sky during the sunset is due to (A) reflection of light. (B) refraction of light. (C) dispersion of light. (D) scattering of light.
47.
Identify the formula of ethyl mercaptan added to LPG cylinders to detect its leakage. (A) C2H4S (B) CH4S (C) C2H6S (D) C3H8S
48.
An image formed by a convex mirror is always (A) virtual, erect and diminished. (B) virtual, real and magnified. (C) real, inverted and diminished. (D) real, erect and magnified.
49.
Wire A and wire B have the following ratios.
length LA 2 diameter DA 2 resistivity ρA 4 = ; = ; = . length LB 1 diameter DB 3 resistivity ρB 3 Given that wire B is 2 Ω, What is the resistance of wire A ? (B) 4 Ω (A) 0.17 Ω (C) 6 Ω (D) 12 Ω 50.
If a real object is placed in front of a convex lens of focal length f at its principal focus, where is the image formed ? (A) At zero (B) At infinity (C) At a distance of 2f (D) At a distance f/2 Paper Code: UN421
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C L A S S : 10
Chemistry
Class : 10 51.
The metal with lowest density is (A) sodium. (B) potassium. (C) lithium. (D) caesium.
52.
Which statement is true ? (A) Ammonia and hydrogen chloride react to form ammonium hydroxide (B) Removal of hydrogen from a compound is an example of reduction (C) The reaction of copper sulphate with hydrogen sulphide is an example of a double displacement reaction (D) A matchstick gets ignited when inserted in the blue flame of a candle Identify the molecular formulae of the acid and the alcohol respectively from which an ester can be prepared. (A) CH3COOH + C2H5OH (B) HCOOH + C2H5OH (C) HCOOH + CH3OH (D) CH3CH2COOH + CH3OH
53.
54.
Equal moles of each of the following substances were dissolved in an equal volume of water. Which of them will form the solution with the highest pH ? (A) Ammonia (B) Sulphur dioxide (C) Potassium oxide (D) Hydrogen chloride
Paper Code: UN421
13
C L A S S : 10
55.
The atomic radius of elements in Group 1 of the Periodic Table increases down the group because (A) the number of valence electrons increase. (B) the number of valence electrons decrease. (C) the number of occupied shells increase. (D) the distance between the nucleus and the outermost electron shell decrease.
56.
Which condition is necessary for a chemical reaction ? (A) It must be accompanied with change in temperature and pressure. (B) At least one of the reactants must be in a fixed quantity. (C) It must follow the law of conservation of mass. (D) All of the above
57.
Which method is employed for obtaining a pure metal ? (A) Froth floatation (B) Electrolytic reduction (C) Magnetic separation (D) Gravity separation
58.
Three elements X, Y and Z form a Dobereiner triad. Their atomic weights are in the ratio 5:11:17. If the sum of the atomic weights of extreme elements is 176, then find their atomic weights.
Paper Code: UN421
14
C L A S S : 10
59.
Which gas is given off when dilute hydrochloric acid reacts with aluminium ? (A) Oxygen (B) Chlorine (C) Hydrogen (D) Carbon dioxide
60.
What is the difference in the formulae and molecular masses of CH3OH and C2H5OH ? (B) CH2 and 14 units (A) CH3 and 16 units (D) CH3 and 18 units (C) CH4 and 18 units
61.
Copper (II) oxide is reduced to copper as shown. The burner is then turned off but the hydrogen is kept flowing until the tube is cold.
What is the main reason why the hydrogen is kept flowing ? (A) to lessen the risk of explosion in the hot tube (B) to make certain that the reaction is complete (C) to prevent the copper from reacting with the air (D) to remove any traces of water left in the tube 62.
Identify an unsaturated hydrocarbon that has a cyclic structure. (A) Ethene (B) Butene (C) Benzene (D) Pentene
Paper Code: UN421
15
C L A S S : 10
63.
An excess of dilute sulphuric acid reacts with both aqueous barium hydroxide and aqueous barium chloride respectively. In what way are the two reactions the same ? (A) A gas is evolved. (B) An insoluble salt is formed. (C) Their final pH is 7. (D) A base is produced.
64.
The table given below shows some of the elements across Period 3 of the Periodic Table, starting from phosphorus.
What is y ? (A) Iodine
(B) Silicon
(C) Oxygen
(D) Chlorine
65.
Aluminium is extracted from purified bauxite by electrolysis but iron is extracted from haematite by reduction with coke. Why is iron not extracted by electrolysis ? (A) Haematite needs to be purified but bauxite does not. (B) Iron is less reactive than aluminium. (C) Reduction with coke is cheaper than electrolysis. (D) Reduction with coke gives a purer product than electrolysis.
66.
Identify a slow, combustion reaction in which glucose present in the body cells combines with oxygen to produce energy. (A) Digestion (B) Excretion (C) Respiration (D) Transpiration
Paper Code: UN421
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C L A S S : 10
67.
Soaps can remove dirt or grease from clothes by the formation of a/an (A) acid. (B) base. (C) micelle. (D) ethyl alcohol.
68.
A boy took four substances gastric juice, milk of magnesia, lemon juice and pure water respectively to identify their pH. What is the correct ascending order of pH of these substances ? (A) Gastric juice, lemon juice, pure water, milk of magnesia (B) Lemon juice, pure water, gastric juice, milk of magnesia (C) Pure water, gastric juice, lemon juice, milk of magnesia (D) Milk of magnesia, lemon juice, pure water, gastric juice
69.
Complete the reaction given below. ZnO + 2NaOH → ? (B) Na2ZnO2 + H2O (A) Zn(OH)2 + H2O (C) Zn(OH)2 + Na2O (D) Na2ZnO2 + Na2O
70.
X is an equation which contains equal number of atoms of each element on both the sides. What is X ? (A) A balanced equation (B) An unbalanced equation (C) A chemical equation (D) All of the above
Paper Code: UN421
17
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Class : 10 71.
Biology
Gas 'P' diffuses from a capillary into an alveolus in the lungs. When is gas 'P' expelled out from the alveolus ?
(A) During inhalation (C) During inspiration 72.
The aim of the given experiment is to prove that
(A) (B) (C) (D) 73.
(B) During exhalation (D) None of these
sunlight is essential for photosynthesis. carbon dioxide is essential for photosynthesis. water is essential for photosynthesis. chlorophyll is essential for photosynthesis.
What prevents the mixing of the blood of the foetus with that of the mother ? (A) Umbilical cord (B) Uterus wall (C) Placenta (D) Water sac
Paper Code: UN421
18
C L A S S : 10
74.
What will happen if part R is injured ?
(A) Breathing will be affected. (B) The person will not be able to think rationally. (C) Coordination and stability of the body will be adversely affected. (D) The person will not be able to see. 75.
Identify the characteristic(s) of vegetative reproduction.
X Involves two individuals Y Daughter cells are genetically identical to the parent. Z The cell division is only mitotic. (A) Only X (C) Only Y and Z
(B) Only X and Z (D) X, Y and Z
76.
Why is it important to boil the leaf in alcohol, while carrying out the starch test on a leaf ? (A) To dissolve the waxy cuticle (B) To make the cells more permeable to iodine solution (C) To remove the chlorophyll (D) To stop chemical reactions in the cells.
77.
What is the common phase between aerobic and anaerobic respiration ? (A) Glycolysis (B) Kreb's cycle (C) TCA cycle (D) EMP pathway Paper Code: UN421
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C L A S S : 10
78.
Which of these form a food chain ? (A) Grass, wheat and mango (B) Grass, goat and human (C) Goat, cow and elephant (D) Grass, fish and goat
79.
The procedure of cleaning the blood of a person by using a kidney machine is known as (A) ketolysis. (B) hydrolysis. (C) dialysis. (D) photolysis.
80.
Which of these is present in grey matter ? (A) Nerve cell bodies (B) Nerve axons (C) Pons (D) Myelin sheath
81.
Identify the type of nutrition exhibited by the given figure.
(A) (B) (C) (D) 82.
Autotrophic nutrition Saprophytic nutrition Parasitic nutrition Symbiotic nutrition
The sheath which covers the axon of a neuron is chiefly made up of (A) glucose. (B) protein. (C) minerals. (D) fat.
Paper Code: UN421
20
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83.
Why are egg cells larger than sperm cells ? (A) Because they have more cells in them. (B) Because they have thicker cell membranes. (C) Have larger nuclei. (D) Have food store to help growth after fertilisation.
84.
Identify 'X' and its function.
(A) (B) (C) (D)
X Ribosome Lysosome Vesicle Granule
Function Synthesises proteins Produces enzyme Release chemicals Stores starch
Palaeontologists deals with the evidences of (A) embryology (B) fossil (C) homologous and analogous organs. (D) all of these
Paper Code: UN421
21
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The term cardiac refers to which organ in the body ? (A) Heart (B) Kidney (C) Stomach (D) Brain 87.
Identify P, Q and R. Male Female
(A) (B) (C) (D)
P P P P
P
Sperm
Ovary
Ovum, Q Testes, Testes, Q Ovum, Ovum, Q Testes, Testes, Q Ovum,
Q
R
R Ovulation. R Implantation. R Implantation. R Fertilisation.
88.
Which of these represents the accumulation of harmful substances in organisms at successively higher trophic levels ? (A) Food web (B) Carbon cycle (C) Biomagnification (D) Population
89.
Which of these helps in the curdling of milk ? (A) Pepsin (B) Renin (C) HCl (D) Trypsin
90.
Which part of nervous system controls involuntary actions ? (A) Medulla oblongata (B) Cerebellum (C) Hypothalamus (D) Spinal cord
Paper Code: UN421
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Class : 10
General Awareness
91.
Where is the headquarters of Election Commission of India located ? (A) Chennai (B) New Delhi (C) Mumbai (D) Kolkata
92.
Which International Cricket Council President resigned after Cricket world cup 2015 ? (A) Mustafa Kamal (B) Alan Isaac (C) Sharad Pawar (D) N.Srinivasan
93.
The famous tagline The Ultimate Driving Machine belongs to automobile company ? (A) Ford (B) Chevrolet (C) BMW (D) Hundai
94.
Which of these awards is not named after a person? (A) Nobel Prize (B) Pulitzer Prize (C) Magsaysay Prize (D) Grammy Awards
95.
Which actor along with business tycoon Ratan Tata has joined hands for the Indian governments initiative Call to Action for a TB-free India ? (A) Amitabh Bachchan (B) Anupam Kher (C) Hritik Roshan (D) Shahrukh Khan
96.
Which company owns the Android operating system ? (A) Microsoft (B) Apple (C) Google (D) Ericsson
97.
Which Greek philosopher tutored Alexander the Great in the childhood ? (A) Pythagoras (B) Aristotle (C) Socrates (D) Plato Paper Code: UN421
23
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98.
The given logo belongs to which brand ? (A) Titan (B) Fastrack (C) Rolex (D) Omega
99.
How many scientists share the Nobel Prize in Medicine for the year 2015 ? (A) 2 (B) 3 (C) 5 (D) 4
100.
Prime Minister Narendra Modi visited which country in September,2015 on a five day visit ? (A) Russia (B) Singapore (C) London (D) USA Space fo r rou gh w ork
Paper Code: UN421
24
UNIFIED COUNCIL A n I S O 9 0 0 1 : 2008 C e r t i f i e d O r g a n i s a t i o n
NATIONAL LEVEL SCIENCE TALENT SEARCH EXAMINATION - 2015 (UPDATED) Solutions for Class : 10 Paper Code: UN412 Mathematics (A)
p2 q2 = 4 cos θ cot θ = 4 cos2 θ /sin θ
4.
(C)
The required ratio 2 (8 × 4 + 4 × 2 + 8 × 2 ) = (8 × 4 × 2 ).2 (1 × 1 + 1 × 1 + 1 × 1) = 7 : 24
5.
(D)
xy = 96050 xz = 95625
⇒ (p2 q2)2 = 16 cos4 θ /sin2 θ
pq = cot2 θ cos2 θ 1 − sin2 θ cos4 θ = cos θ sin2 θ = sin2 θ 2
2.
(C)
and y z = 1 ⇒ y=z+1
Probability of drawing green ball = 3 × probability of drawing red ball ⇒
n 3×5 = 5+n 5 + n
6.
(B)
7.
∆ CDE : BAE
CD ED = ∴ AB AE
⇒ 4= ⇒ 4=
∆ ABC ≅ ∆ DCB, AF AB 80 4 = = = CF CD 20 1
A D F
80
ED +1 AE
O
ED + A E AE
B
⇒
AD AE
⇒ AE =
(C)
∴
9 ED ⇒ = 3 AE ⇒ 3+1=
As c is factor of ab and a is factor of ab as c and a are coprime, so ca is factor of ab then, if ab = (ca) x for x ∈ N, then b = cx. ∴ c is a factor of b.
∴ Total no. of balls = 5 + 15 = 20
(B)
.... (iv)
from eq. (iii) and (iv), we get z = 225
⇒ n = 15
3.
y 3842 = [Dividing (i) by (ii)] .... (iii) z 3825
⇒
∴ (p2 q2)2 = 16 pq
.... (i) .... (ii)
a E
20
1.
C
AF 4 = CF 1
AF + FC 4 + 1 5 = = FC 1 1 ∆ ABC : ∆ FEC [Since AB and FE are parallel]
⇒
4 = 1 cm 4
1 ∴ Area of ∆ AEC = × AE × CD 2 =
1 ×1× 9 2
= 4.5 cm2
⇒ ⇒
AB AC = FE FC 80 5 = FE 1 FE = 16
Hence, the value of a = 16 m website : www.unifiedcouncil.com
8.
(D)
= 20 cm
14. (C)
310o 7 2 cm2 o × 314 cm = 270 360 18
Median of the slopes of
3 4 Let AB be the ladder inclined at an angle of 30o with the wall BC.
OA, OB, OC, OD, OE = slope of OC =
Area of square = 20 cm × 20 cm = 400 cm2
15. (C)
Out of 16 parts, 2 are shaded.
B
14 × 400cm2 ∴ Area of unshaded region = 16 = 350 cm2 y
O
10 11, 2
S
Q
(B)
A
x
6 3, 2
5− 3
2
1
∴ a + 8d = 99
∴ a + 98d = 9
..... (ii)
Thus after every second, the man is approaching the wall a distance equal to 1 m, i.e., at 1 m/ sec. 16. (A)
Given parabolic equation is y = 3x2 + 12x 2 −b −12 = −2 = 6 2a
Subtracting (ii) from (i) ⇒ 90 d = 90
y = f(2) = 12 24 2 = 14
∴ d = 1
∴ Vertex of the parabola = (2, 14)
Substituting this value of d in (i) a + 8(1) = 99
∴ The axis of symmetry is x = 2
17. (C)
⇒ a = 99 + 8 = 107 ∴ a108 = a + (108 1) d
Product of m numbers = (H.C.F. of pairs)m 1 × L.C.M. of m numbers. Hence, product of 4 numbers = (3)4 1 × 126 = 3402
= 107 + 107 (1) = 0 18. (B)
11. (Del) Correct answer is 3.
Given AB = 6 m ⇒ AC = CB = 3 m A
The whole surface area of the remaining solid = π RL + π rl + π [R2 r2]
o
= π[6 × 36 + 28 + 3 × 9 + 7 + (36 − 9 )] = π [6 × 8 + 3 × 4 + 27] = 87 π cm2 13. (A)
1 = 1m 2
∴ AG = 2 m
..... (i)
Also, a99 = 9
360 25 25 = 310 o
C
Similarly after 2 seconds, the man will be at F such that AF = 4 m.
Let a be the first term and d be the common difference of A.P.
o
E G
∴ AE = AD cos 60o = 2 ×
Since a9 = 99
12. (B)
60o
After one second the man will be at D such that AD = 2 m.
∴ Slope of QS = 11 − 3 = 8 = 4
10. (A)
130
R(11, 10) P(3, 6)
9.
D
30
F
o
Radius of circle = 20 cm ÷ 2 = 10 cm
Area of shaded part
B
Since, the radius of two circles are integers, then for OC = 4 m and OB = 5 m, the value of CB is 3 m
o
Area of circle = πr 2 = 3.14 × 10 cm × 10 cm = 314 cm2
C
∴ The radius of inner circle is 4 m.
19. (B)
ax2 + bx + 1 = 0 has real roots if b2 4a ≥ 0
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C Value of a
R
P A
2
3, 4
2
3
4
1
4
4
1
tan (α + β ) = =
m / m + 1 + 1 / 2m + 1 1 − (m / m + 1) )(1 / 2m + 1)
25. (A)
⇒ (a)4 a2 (a)2 + 3(a) a = 0
⇒ a4 a4 3a a = 0 ⇒ 4a = 0
In option (D), the slope is negative and y-interept is positive. In ∆ ABC, ∠ ACE = ∠ ABC + ∠ BAC Similarly in ∆ BCD, ∠ BDC = ∠ DCE ∠ DBC [Ext. angle prop. of a ∆ ]
∠DBC =
Now,
26. (C)
1 ∠ABC 2 ∠ BDC = ∠ DCE ∠ DBC
1 1 ∠ACE − ∠ABC 2 2
=
1 (∠ACE − ∠ABC) 2
=
1 (∠ACE + ∠BAC − ∠ACE) 2
∴∠BDC =
Physics If two resistors (a and b) are connected in series, the value of the total resistance will be a + b. If two resistors (a and b) are connected in parallel, the value of the total resistance a×b . will be a+b Using different combinations of 3, 4 and 6 ohm resistors, we can make new resistors with the following values: 9 ohms : 3 ohms and 6 ohms in series, 3+6=9 2.4 ohms : 4 ohms and 6 ohms in parallel, 4 × 6 24 = = 2.4 4 + 6 10 2 ohms : 3 ohms and 6 ohms in parallel,
1 ∠BAC 2
23. (C)
27. (B)
a
b
c
d
1
1
1
1
(2) (2) (2) (2) = 16
2
1
1
0
(3) (2) (2) (1) = 12
24. (D)
⇒ a=0
1 ∠ACE and 2
=
Let p(x) = x4 a2 x2 + 3x a. Since x + a, i.e. x (a) is a factor of p(x), we must have p(a) = 0
2m2 + m + m + 1 2m2 + 2m + m + 1 − m
But ∠DCE =
M
⇒ x=y
∴ á+â = π / 4
22. (C)
B
Now ∠ ACB = x (angle in alternate segment) ∠ ACB = y (angle is in alternate segment)
2m2 + 2m + 1 = =1 2m2 + 2m + 1 21. (D)
y
N
Total number of ways = 7 20. (C)
x
Hence, maximum value of (a + 1) (b + 1) (c + 1) (d + c) is 16. Take any point C on circle and join C to A and B.
3 × 6 18 = =2 3+6 9 There is no combination that can produce a total resistance of 8 ohms. Assume that the painter is facing the centre of the mirror. To see the maximum range, he has to look at the two extreme ends of the mirror. By applying the laws of reflection, angle of incidence = angle of reflection as per the figure given below, the maximum length of painted wall, the painter can see is 2 m.
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31. (C)
through the optic nerve in the form of electrical signals. Statements (B), (C) and (D) are the best ways to increase the efficient use of various sources of energy. Only image projector emits light rays on a screen and forms real images. The image formed in the plane mirror is virtual and erect. The image formed by a magnifying glass (convex lens) is also virtual and erect.
32. (C)
Using Ohms law,
1 m long mirror
30. (A) 12 m
0.5 m
28. (A)
29. (C)
1m
0.5 m
The solenoid is a long coil containing a large number of close turns of insulated copper wire. The magnetic field produced by a current carrying solenoid is similar to the magnetic field produced by a bar magnet. The lines of magnetic force pass through the solenoid and return to the other end. If a current carrying solenoid is suspended freely, it comes to rest pointing North and South like a suspended magnetic needle. One end of the solenoid acts like a N-pole and the other end a S-pole. Since, the current in each circular turn of the solenoid flows in the same direction, the magnetic field produced by each turn of the solenoid adds up, giving a strong resultant magnetic field inside the solenoid.
(i) The light coming from the objects enters the human eye through cornea (X). Just behind the cornea is the iris. There is a hole in the middle of the iris called pupil. (ii) The lens lies behind the pupil (Y). It is convex, transparent, soft and flexible. It is held in proper position with the help of suspensory ligaments at one end and ciliary muscles at the other end. (iii) The space between the cornea and the lens is filled with aqueous humour. (iv) The focal length of the convex lens present inside the eye can be changed (made thicker / thinner) by the action of ciliary muscles. (v) The space between the lens and the retina is filled with vitreous humour. (vi) Behind the lens is the natural screen called retina (Z) on which the image is formed. It is conveyed to the brain
∴ V=I ×R= ∴ V=
33. (D) 34. (B)
35. (C)
V =R I
Q ×R t
200 × 20 = 160 V 25
All the statements are true. The slip rings are used to prevent entanglement of the wires in the external circuit. If a coil of wire is placed in a magnetic field and rotated, an alternating (sinusoidal) current is induced. As it rotates, sometimes it is cutting through lots of flux, and so lots of current is induced. At other times, it is moving parallel to the flux, and so no flux is cut, and no current is induced. In between, some current is induced. This creates an alternating current. Either end of the coil can be connected to wires outside of the generator in order to use the current elsewhere. This would be fine for the first few rotations, but after this, the wires would get tangled up and the generator would be useless. In an AC generator, this is a pair of rotating conducting slip rings attached to either end of the coil. Carbon brushes bring these into contact with the outside world. Two convex lenses of focal lengths 5 cm and 7 cm respectively are used to construct a compound microscope. A compound microscope consists of two converging lenses, (i) the objective O ' , and (ii) the eyepiece E. The lens facing the object is called the objective and the lens close to the eye is called the eyepiece. The objective is of very short focal length and has a smaller aperture than the eyepiece. The eyepiece is also of short focal length but of large aperture. The objective is a combination of two lenses, which acts as a converging lens. The eyepiece is a combination of two lenses separated by a small distance. The focal length of the eyepiece is slightly greater than that of the objective. The two lenses are
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placed coaxially at the ends of an adjustable tube. The distance between the two lenses can be adjusted. B I1
E
O' Fo
O Fo
Fe
I
M
Fo β
Eye
M1
The object OB is placed just beyond the focus of the objective, which forms a real, inverted and magnified image. This image is formed within the focus of the eyepiece, which produces a virtual, erect and magnified image. The final image I1M1 is adjusted to be formed at the least distance of distinct vision. The eyepiece acts as a magnifier. 36. (B,C,D) Renewable sources of energy are sunlight, tidal waves, ethanol fuel, wood and wind while non-renewable sources of energy are coal, natural gas and petroleum. 37. (D) The human eye ball is almost spherical and has a thick, tough coating called sclerotic on the external side. About 5/6th of this portion is opaque and the remaining part is in front of the eye which is a transparent structure called the cornea. The coating within the sclerotic is called choroid which consists of black pigment cells. Choroid absorbs light and prevents the reflection of light within the eyeball. 38. (B) One of the factors that determines the strength of the electromagnet is the number of coils per unit length. The more concentrated the coils are being packed, the stronger will be the magnetic field strength. 39. (D) To reproduce a similar print, the real image must be the same size as the object. It can only be achieved when u = 2f. This implies that u = 12 cm. 40. (C) I = V ÷ R = 1200 ÷ 240 = 5 A The operating current of the heater is 5 A. The fuse should be slightly higher than the operating current. The function of the fuse is to allow operating current to flow through but melts when the current becomes too high so as to protect the equipment from being damaged by the undesirably high current. The next higher rate of fuse is the 10 A fuse. 41. (A) Statements (i) and (ii) are true for carnivores. (i) Human beings and all the predators like tiger, lion, cheetah etc. have their eyes in front of the head.
42. (D)
43. (C) 44. (C)
45. (C)
46. (A)
47. (A)
(ii) The two eyes are a few centimetres apart from each other. Due to this reason, the two eyes see the same object from two slightly different angles and send two slightly different images of the same object to the brain. (iii) The brain combines these two slightly different images to build a three dimensional picture of the object which enables us and animals to judge the distance of the object more accurately. (iv) Most of the animals have a large field of view to see around due to binocular vision but not monocular vision. Earth wire connects the conducting casing of the appliance to the ground. It is used to conduct any leaked charges from the conducting casing of the appliance to the ground. This prevents people from getting an electric shock should there be a leakage of charges. When light travels through optical fibre, total internal reflection takes place and not refraction. Doubling the length of the wire will double the resistance. (R ∝ L). Doubling the cross-sectional area of the 1 wire will have the resistance. R ∝ . A Resistance of the wire which is 4 m and has 2 mm2 cross-sectional area.
1 16 × 2 × = 16 Ω 2 (i) The distance between the optical centre (O) of the convex lens and object placed at X is the object distance OX. (ii) The distance between the optical centre (O) and principal focus Y of the convex lens is the focal length - OY. (iii) A ray of light parallel to the principal axis of a convex lens passes through its focus after refraction through the lens. The distance between the optical centre (O) of the convex lens to the point where the image Z is formed is the image distance - OZ. Iron is a soft magnetic material which can be easily magnetised and demagnetised. It is used as an electromagnet. Steel is a hard magnetic material which cannot be easily magnetised nor demagnetised. It is used as a permanent magnet. Tungsten has a melting point higher than 3000 oC. When the filament is so hot that it produces white light, its temperature must be
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48. (A)
49. (B)
50. (B)
greater than 2500 oC. The material of the filament must have a melting point higher than 2500 oC. Option (B): Tungsten has high resistance to allow high current to pass through. When a material has high resistance, the current flowing through it is low (with other factors held constant). Option (C): Tungsten has high mass so that more thermal energy can be stored in the filament. When a material has high mass, more thermal energy is required to increase its temperature. The filament would need more energy to produce the same brightness. Option (D): Tungsten has high specific heat capacity so that small amount of heat can increase the temperature to a large extent. When a material has high specific heat capacity, it requires more energy to increase its temperature. Focal length f is 15 cm. Object distance u is 31 cm. For u > 2f, the image formed will be real, inverted and diminished. The safest method to dispose radioactive wastes is given below. The radioactive wastes must be kept in a thick, lead containers with narrow mouth and plugged with thick lead corks. These containers can be buried under the sea. Resistance of the appliance
53. (A)
= V ÷ I = 240 V ÷ 2A = 120 Ω Current flowing through the appliance at 120 V supply = V ÷ R
51. (C)
= 120 V ÷ 120 Ω = 1 A Power of appliance = I2R = (1)2 × (120) = 120 W Chemistry Noble gases are elements of Group 18. They exist as monoatomic gases because their outermost shells are filled with two or eight electrons as shown below.
Element
Atomic Number
Helium Neon Argon Krypton Xenon Radon
2 10 18 36 54 86
52. (A)
Electron Arrangement 2 2, 2, 2, 2, 2,
8 8, 8, 8, 8,
8 18, 8 18, 18, 18, 18,
8 32, 8
Metals react with dilute hydrochloric acid to give metal chlorides and hydrogen gas is released. Based on the reactivity series of
54. (C)
metals, sodium is the most reactive metal followed by magnesium and zinc. (i) Sodium metal is very reactive. It reacts violently with dilute hydrochloric acid to form sodium chloride and hydrogen. (ii) Magnesium metal is less reactive than sodium. It reacts quite rapidly with dilute hydrochloric acid to form magnesium chloride and hydrogen. (iii) Zinc metal is less reactive than magnesium and aluminium. It reacts less rapidly with dilute hydrochloric acid to form zinc chloride and hydrogen. As the reactivity of metals decreases from sodium to zinc, sodium metal releases hydrogen gas faster followed by magnesium and zinc. Chemical reaction between aluminium and iron (III) oxide is balanced. Both being metals are solids as reactants. The reduction of a metal oxide to form metal by using aluminium powder as a reducing agent is called a thermite reaction. (A) A mixture of iron (III) oxide and aluminium powder is ignited with a burning magnesium ribbon. Aluminium reduces iron oxide to produce iron metal with the evolution of lot of heat. Due to this heat, iron metal is produced in the molten state. The molten iron is then poured between the broken pieces of heavy iron objects like girders, railway tracks or cracked machine parts to join them. (B) Chemical reaction is balanced but iron being a metal is shown as (g) gas, which is not correct. (C) Chemical reaction is not balanced on the reactants side (Aluminium) and aluminium oxide being a metallic oxide is represented as gas, which is not correct. (D) Chemical reaction is not balanced as less number of iron atoms are shown on products side. (i) Hydrochloric acid is a strong acid and the pH of this acid lies between 0 to 3 on the pH scale. Strong acids completely ionise in water to form a large number of H+ ions. (ii) Ethanoic acid is a weak acid and its pH is above 3 on the pH scale. Weak acids do not ionise completely in water and produce a small number of H+ ions (iii) HCl is a strong acid and it ionises completely to form H + and Cl ions respectively. CH 3COOH is a weak acid because it does not ionise completely.
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56. (B)
57. (C)
58. (C)
62. (A)
63. (D)
64. (D) 65. (C)
Yeast, absence of air C6H12O6 → 2CO2 + 2C2H5OH
66. (D)
Mg : O: + Oxygen atom Magnesium atom 2,6 2, 8, 2 Mg2+ Magnesium ion 2, 8
Soap + Glycerol (P) (Sodium salt of (An alcohol) fatty acid)
60. (D)
61. (A)
O Oxide ion 2,8
or MgO
Magnesium oxide
We find that the magnesium ion has 2 units of positive charge whereas the oxide ion has 2 units of negative charge. The oppositely charged magnesium ions, Mg2+, and oxide ions O2, are held together by a strong force of electrostatic attraction to form magnesium oxide compound Mg2+O2 or MgO. Thus, magnesium oxide contains ionic bonds.
So, P is glycerol. Acidic oxide : SO2, CO2 Amphoteric oxide : Al2O3 Basic oxide : Na2O , MgO Chemical equation for complete combustion of methanol is given in option (D). Chemical equations given in options (A), (B) and (C) show incomplete combustion of methanol. From Li to C, the elements use 1 to 4 electrons for bonding respectively. However, from C to F, the number of electrons used declines from 4 to 1. Ne does not form any compound readily since it is a noble gas.
Oxidation of ethanol: C2H5OH + 2[O] → CH3COOH + H2O The bond formed between two oppositely charged ions is ionic or electrovalent bond, Mg+2 and O2 . Two chlorine atoms and two hydrogen atoms separately form a single covalent bond as shown below. Cl Cl Cl + Cl → Cl2 HH H + H → H2 Carbon dioxide forms a double covalent bond O = C = O. Transfer of electrons
∆ Vegetable oil + Alkali → (Castor, cotton, (Sodium linseed or hydroxide) soyabean oil)
59. (D)
Option (A) gives the correct balanced equation as per the numbers given under (i), (ii), (iii) and (iv) respectively as shown below. (i) PbS + (ii) 4H2O2 → (iii) PbSO4 + (iv) 4H2O Reactive metal oxides form more stable oxides. Zinc is the most reactive metal and lead the least reactive of the three metals given. 2NaOH + CO2 → Na2CO3 + H2O The white solid is Na2CO3. Combustion of ethanol : C2H5OH + 3O2 → 2CO2 + 3H2O Manufacture of ethanol: C2H4(g) + H2O(g) → C2H5OH(l) Fermentation of glucose :
: :
55. (C)
It forms CH3COO (Acetate ion) and H+ (ion respectively. The difference in pH value between the two acids is ionisation. So, the degree of ionisation is less in ethanoic acid than that of hydrochloric acid. Hydrocarbon X must be an unsaturated hydrocarbon with a C=C bond i.e. an alkene C 5H 10 (pentene). C 2H6 , C3H 8 and C7H 16 are saturated hydrocarbons in the homologous series of alkanes. Due to typographical error (i) is not considered because BHT is printed as HBT. To prevent oxidation of fried foods, the following methods must be adopted. (i) Adding antioxidants like butylated hydroxy-anisole or butylated hydroxy toluene to food substances before frying them in oil. (ii) Storing fried foods in air-tight containers prevents the contact of food with oxygen. Absence of light slows down the oxidation of oil and fats in fried foods. (iii) Filling the huge bags / containers in which the fried foods would be stored with nitrogen gas. The ore from which manganese is extracted is pyrolusite. Haematite - Iron Bauxite - Aluminium Calamine - Zinc The given chemical reaction is used in the manufacture/preparation of soap.
67. (B)
First liquid pH
Second liquid pH
(A)
5
2
(B)
5
12
(C)
6
1
(D)
14
7
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68. (D)
69. (D)
70. (A)
71. (D)
72. (C)
73. (A) 74. (A) 75. (B)
In options (A) and (C), the solutions are acidic (pH < 7). When mixed, the pH of the resulting solution will also be acidic. In option (D), the first solution is alkaline while the second one is neutral. When they are mixed, the resulting solution will be alkaline. Metals tend to form basic oxides while nonmetals tend to form acidic oxides. Hence, Y is a metal and X is a non-metal. Z would be between the 2 elements since the oxide is amphoteric. The given structural formula is of a detergent. A detergent has a large non-ionic hydrocarbon group and an ionic group like sulphonate group SO 3 Na + , or sulphate group. SO4 Na+. The structure CH3 (CH2)10 CH2 SO4 Na+ is of sodium n-dodecyl sulphate. X : Oxidation reaction The conversion of C 2 H 5OH to CH 3CO 2 H involves the removal of H and addition of O. C2H5OH + 2[O] → CH3CO2H + H2O Y : Acid/base reaction CH3CO2H + NaOH → CH3CO2Na+ + H2O Z : Esterification CH3CO2H + C2H5OH → CH3CO2C2H5 + H2O Biology Photosynthesis takes place in green plants by the absorption of water and carbon dioxide in the presence of sunlight and chlorophyll pigment by the liberation of oxygen and produce carbohydrates. Some of the energy in each level of food chain is lost as heat. Hence, not all the energy from living things is transfered to living thing C. Peripheral nervous system consists of cranial and spinal nerves. The arrows (showing) labelled as P and Q blood vessels carries oxygen rich blood. The sex of a baby is determined by the X and Y chromosomes. Females have two X chromosomes. Males have one X and one Y chromosome. Each parent gives one copy of their chromosome to the baby.
Male
X
Y
X
XX
XY
X
XX
XY
Female
76. (B)
50% Male, 50% Female The swollen part above the girdle is due to the accumulation of food in phloem.
77. (B)
Rice plant → Grasshopper → Frog → Snake → Eagle
78. (D) 79. (A)
Earthworm is a hermaphrodite. F is the adrenal gland. It releases adrenline which responds to stress, for example , sugar is released studdenly to enable us to run fast and escape when there is danger. In the given flowchart E represents Fertilisation and F Mitosis The genetic material found in a sperm can be 22 + X or 22 + Y Heat energy that is lost from the body cannot be returned to the ecosystems and recycled. Medulla oblongata controls breathing rate and regulates blood pressure. In human beings fertilisation occurs in fallopian tubes and implantation in uterus. Under the sun plants perform photosynthesis and releases oxygen hence the limewater remains colourless. Oxygen is helpful to oxidised or burn the food in our body to release energy. The arrow labelled X is pulmonary artery. It carries deoxygentated blood from heart to lungs. Movement of the plant in response to external stimulus is called nastic movements. The potato plant reproduces by stem tubers. The air at the top of the mountains has less amount of oxygen hence people who live on mountain top produce more RBC to absorb more oxygen as compared to land level.
80. (C) 81. (A) 82. (B) 83. (B) 84. (A) 85. (D)
86. (C) 87. (C)
88. (A)
89. (D) 90. (A)
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UNIFIED COUNCIL A n I S O 9 0 0 1 : 2008 C e r t i f i e d O r g a n i s a t i o n
NATIONAL LEVEL SCIENCE TALENT SEARCH EXAMINATION Paper Code: UN415 Solutions for Class : 10 Mathematics 1.
(D)
Given arithmetic progression is 10, 12, 14, .....
Difference of L.C.M. and H.C.F.
⇒ a = 10, d = 2, n = 13
Given 2305 = 210 × 6 + 55y
⇒ Sn =
n ⎡2a + (n − 1) d⎤⎦ 2⎣
⇒ y=
5.
(B)
13 [20 + 24 ] 2
= 13 × 22 = 286
2.
(Del)
3.
(A)
N'.
Let the cost of a table be '
y'.
Given 3N + 2y = 1850
..... (1)
5N + 3y = 2850
..... (2)
9 N + 6y = 5550 10 N + 6y = 5700 − N = −150
C
3 cm
o P 3 cm
⇒ N = 150
B
Substituting the value of 'N' in eq. (1)
K
⇒ 450 + 2y = 1850
O is the centre of the circle.
⇒ 2y = 1400
CP × PK = AP × PB
⇒ y = 700
CP =
Hence, the cost of one chair and one table = N + y = 150 + 700 = 850.
AP × PB 3 × 3 = = 9 cm PK 1
∴ Diameter CK = CP + PK = (9 + 1)cm
= 10 cm (D)
Let the cost of a chair be '
Solving eq. (1) and (2), we get
A
4.
2305 − 210 × 6 = 19 55
∴ y 3 = 19 3 = 6859
13 S13 = ⎡⎣2 (10 ) + 12 (2 )⎤⎦ 2 =
= 2310 5 = 2305
(D)
Since the diagonals of a trapezium divide each other proportionally,
210 = 2 × 3 × 5 × 7 55 = 5 × 11 ∴ L.C.M. = 2 × 3 × 5 × 7 × 11
= 2310
6.
⇒
N − 4 3N − 19 = 4 N−3
⇒ ( N − 4) ( N − 3) = 4(3 N − 19)
H.C.F. = 5 website : www.unifiedcouncil.com
OA OB = OC OD
⇒ 4m + 4 ≤ 0
⇒ N2 − 7 N + 12 − 12 N + 76 = 0
⇒ m ≤ −1
⇒ N2 − 19 N + 88 = 0 ⇒ N2 − 11 N − 8 N + 88 = 0
10. (B)
45°
⇒ N( N − 11) − 8( N − 11) = 0 45°
∴ The required value of 'N' is 8 units.
(C)
ym
D
AB = (2a − 2a)2 + (6a − 4a)2
The distance between the height is (N + y) m.
BC = (2a + 3a − 2a)2 + (5a − 6a)2
∴ tan45° =
= ( 3a)2 + (−a)2 = 3a2 + a2 = 4a = 2a
)
2
2
3a − 2a + (5a − 4a)
⎛ 1
= 200 ⎜
Hence, ∆ ABC is an equilateral triangle. Given P and Q are the zeros of the polynomial aN2 + bN + c, 2
2
⎝ 3
11. (D)
⇒ P + Q = (P + Q) − 2PQ
O
2
⎛ −b ⎞ ⎛c⎞ ⎟ − 2⎜ ⎟ a ⎝ ⎠ ⎝a⎠
=
(B)
b2 2c b2 − 2ac − = a2 a a2
P
OA = OB, as radii of a circle are equal. PA = PB, as tangents to a circle from an external point are equal.
b2 − 2ac . a2
Given, N2 + 4mN + 4m2 + m + 1 = 0 have real roots.
∴
12. (C)
OAPB is a kite.
In ∆ABC, AB = AC = 19 cm and BD = DC = 6 cm . A
⇒ b2 − 4ac ≥ 0 ⇒
⎠
A
Hence, the value of P2 + Q2 = 9.
⎞
+ 1⎟ m
B
2
=⎜
200 + 200 3
= N+y =
= 4a2 = 2a (D)
(2)
∴ The required distance
= 3a2 + a2
8.
200 ⇒ y = 200 m y ..... (1)
200 200 ⇒ N= N 3 .....
tan60° =
2
(2a +
60° B xm C
According to the problem, from the figure, AB is the tower of height 200 m.
= (2a)2 = 2a
AC =
60°
200 m
⇒ N = 11 or 8
7.
A
2 (4m) − 4 (1) (4m2 + m + 1) ≥ 0
6
⇒ 16m2 − 16m2 − 4m − 4 ≥ 0
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D 12
C
In ∆ABD, AB2 = AD2 + BD2 = 72
⇒ k2 = 16
⇒ AB = 6 2
⇒ k = ±4
sinθ =
17. (B)
BD 6 1 = = AB 6 2 2
All the three bulbs glow at once at 8 a.m. The time when they glow simultaneously again
⇒ θ = 45o
= L.C.M. (24, 48, 54) seconds
⇒ ∠ BAC = 2 (∠ BAD) = 2 × 45o
= 90 13. (D)
= 216 seconds
o
= 3 minutes 36 seconds
Area of ∆PQR
∴ The time when the three bulbs glow
1 = [p(r + p − p − q) + q(p + q − q − r) 2
together again is at 8 : 03 : 36 a.m. 18. (A)
+ r(q + r r p)]
14. (B)
Then, according to the problem,
=
1 [p(r − q) + q(p − r) + r(q − p)] 2
=
1 [pr − pq + pq − qr + rq − pr ] 2
10N + y = 4(N + y) ⇒ y = 2N and 10N + y = Ny + 16 ⇒ 10N + 2N = N(2N) + 16
1 = × 0 = 0 sq. units. 2
⇒ 12N = 2N2 + 16
∆ABC ∼ ÄDEF
⇒ N2 6N + 8 = 0
AB AC ⇒ = DF DE
⇒ N2 4N 2N + 8 = 0
⇒
⇒ 2N2 12N + 16 = 0
⇒ N(N 4) 2(N 4) = 0
5 8 = 7.5 DE
⇒ DE =
⇒ (N 4) (N 2) = 0 ⇒ N = 4 or 2
8 × 7.5 5
If N = 2, then y = 2N = 4. ∴ The number is 24.
⇒ DE = 12
If N = 4 then y = 8.
and ∠F = 100o 15. (B)
∴ The number is 48.
The numbers divisible by seven are 105, 112, 119, ......, 994.
tn = a + (n − 1) d ⇒
994 = 105 + (n 1)7
889 = n−1 7 ⇒ 127 + 1 = n ⇒
⇒
16. (D)
Let the digits in the tens place and the ones place be N and y respectively.
128 = n
α +β =
2 k2 − 14
2 = −1 (Given) ⇒ 2 k − 14 2
⇒ 2 = k − 14
Hence, the required number is 48. 19. (D)
If we take AE as the base of triangle AEC, then the height is CD. The height of the triangle is therefore, 9 (given). To find the base we need to see that triangles AEB and CDE are similar. The ratio AB : CD, is therefore equal to the ratio AE : ED. The given information shows that the ratio is 3 : 9, or 1 : 3. Now dividing AD (4) in this ratio gives us AE as 1. The area of AEC = =
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1 × 9 = 4.5 2
1 base × height 2
20. (B)
(1 + 1 + ....... 'n' terms) ⎛1 2 ⎞ ⎜ n + n + ..........'n' terms ⎟ ⎝ ⎠
25. (B)
= 21. (D)
d] 0
n (n + 1 ) n+1 =n− 2 2n
n−1 2
= mπ + nπ +
(m2 + n2 + 2mn − m − n)d 2
(n2 − n)d (m2 + 2mn - m)d + mπ + 2 2
= nπ +
Since, the line segment is divided by Y-axis
n m(m + 2n − 1)d = [π + (n − 1)d] + mπ + 2 2
7 4 ⇒ The required ratio = 7 : 4
= 0 + mπ +
The minute hand moves 6o in one minute.
Also the hour hand moves 30 o in one hour. o
⎛ 30 × 15 ⎞ ∴ It will move ⎜ ⎟ in 15 minutes, ⎝ 60 ⎠ ⎛ 1⎞ i.e., ⎜ 7 ⎟ ⎝ 2⎠
o
So, the angle between the two hands is o
o
1 ⎛ 1⎞ = 30 − ⎜ 7 ⎟ = 22 . 2 ⎝ 2⎠ o
m(m + 2n − 1)d 2
Physics R
R
R!
26. (B)
2 to 3).
When resistors are connected in series, their values add up. This arrangement will always give the maximum resistance. 27. (D)
A solar panel is a packaged interconnected assembly of solar cells (photovoltaic cells). Solar cell converts light energy into electrical energy. The solar panel can be used as a component of a larger photovoltaic system to generate and supply electricity for commercial and residential use. The power generated by a solar panel would most likely be affected by the surface area of the solar panel itself and the cloud cover percentage.
∠QOS = 120° (Given ) ⇒ ∠OQS = ∠OSQ 180o − 120o = = 30 o 2
∠OPT = 90° [Since, QP ⊥ PT.] ⇒ ∠PTS = 180° − [90° + 30°]
⇒ ∠PTS = 60°
24. (B)
(m + n)(m + n − 1)d 2
7 − 4λ 7 − 4λ N= =0 or λ+1 λ +1
∴ It will move 30o in 5 minutes (from
23. (C)
(m + n) [2 π + (m + n 1) 2
= (m + n) π +
If the ratio is λ : 1 ,
∴λ =
22. (C)
n [2 π + (n 1) d] = 0 2
Sm = Sm + n Sn =
⎛ 1 + 2 + 3 + ...... + 'n' terms ⎞ =n−⎜ ⎟ n ⎝ ⎠
=n−
Sn =
Since the nature of z is not known. If z = + ive = + k then, N > y ⇒ Nk > yk If z = ive = k then, N > y ⇒ Nk < yk.
-
The greater the surface area, the greater the power generated.
-
The lesser the cloud cover percentage, the greater the power generated.
Wind and humidity do not affect the power generated by a solar panel. Solar panel (D) has the greatest surface area and it is put at a place with the least cloud cover percentage. Therefore, solar panel (D) would likely provide the most power.
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28. (A)
The refracted angle in a denser medium is less than the incident angle because the speed of light slows down in a denser medium. In slowing down, the light bends towards the normal and the refracted angle is therefore less than the angle of incidence. 35 o is less than 45o. The other options are incorrect.
29. (D)
Ammeter is used to measure the amount of current flowing in an electrical circuit, and it must be connected in series to the circuit. Electrical current (unit: Ampere) consists of moving negative charges (also known as electrons).
30. (D)
Electromagnetic effect is temporary.
31. (C)
Biomass is an alternative source of energy that contains organic wastes which includes continuous crop residues, wood, cow dung etc., These organic wastes are used immediately for the production of biogas.
32. (D)
An object placed at F of a concave mirror produces a highly enlarged, real and inverted image at infinity.
34. (D)
To calculate the number of units of electrical energy used by the appliance, multiply the power (in kW) of the appliance by the amount of time (in h) that the appliance was used. 600 W microwave for 10 minutes = 0.6 kW × 10/ 60 hour = 0.1 kWh.
35. (A)
In waterfalls, gravitational potential energy is first converted to kinetic energy of water which then will be converted into electric energy by a generator. This type of electricity production using kinetic energy of water is called hydroelectricity. It is a renewable source of energy.
36. (C)
Electricity can easily be converted into other useful forms of energy like heat, light and sound.
37. (D)
Water has higher refractive index than air. When light travels from air into water, it bends towards the normal line as it moves with lower speed inside the water. This phenomenon is called refraction.
38. (C)
A combination of mirrors arranged in a magic mirror can be easily identified without touching it based on the characteristics of the image formed in each mirror of an object/girl.
33. (D)
An electromagnet is a solenoid with an iron core inserted into it. If a current flows in the coil, a magnetic field is generated. The core greatly enhances the strength of the eiectromagnet. There are three ways to make the electromagnet stronger: - Increasing the number of turns of wire in the coil - Increasing the current in the coil - Using a soft iron core
(i)
The girls head appeared bigger as a concave mirror will produce a magnified image.
(ii)
The middle portion of the girls body appeared to be of same size indicates that it is a plane mirror as the object and image size are same for any position.
(iii)
As a convex mirror produces a diminished image, the girls legs appeared smaller.
39. (A)
Resistance will decrease the amount of current flowing in the coil, and hence it cannot improve the strength of the electromagnet. Retina which is located at the back part of the eye is the film of the eye. The retina has a large number of lightsensitive cells. When the image falls on website : www.unifiedcouncil.com
the retina of an object, then these lightsensitive cells get activated and generate electrical signals. The retina sends these electrical signals to the brain through the optic nerve and gives rise to the sensation of vision.
45. (A)
A convex mirror forms virtual, erect and diminished images of objects when placed at infinity and anywhere between the pole and infinity. A convex mirror does not form an inverted image of the object.
40. (C)
Deviation angle (or the angle of deviation) is the angle between the original incident ray and the emergent ray.
46. (A)
The correct field pattern and directions are shown below.
41. (D)
When the diameter of the coil increases, the magnetic field cutting the conducting coil will be weaker because the magnet is further away from the coil. The induced e.m.f. will be smaller and thus the induced current is also smaller. The induced e.m.f. depends on the rate of change of magnetic flux cutting the coil. Therefore the stronger the magnet, the higher will be the induced e.m.f and thus the higher will be the induced current. The thickness of the wire will affect the resistance of the wire. Although the induced e.m.f is not affected, the induced current will increase if the diameter of the wire is increased.
47. (A)
Light sensitive cells get activated on illumination enabling formation of image.
48. (D)
The power is 700 W, the voltage is 230 V and the current is 13 A.
49. (B)
A bulb is placed at the focus of a concave mirror that acts as reflector in torch, search and headlights respectively to produce a powerful beam of parallel light rays to see objects upto a considerable distance in the darkness of night.
50. (C)
Steel is a hard magnetic material. It retains some magnetism after the magnet is being removed. Steel will continue to attract the iron based on induced magnetism.
51. (D)
There are 2 double bonds (4 electrons each) and 2 single bonds (2 electrons each) surrounding the sulphur atom. Hence, the total number of electrons around S = 2(4) + 2(2) = 12.
52. (D)
H 2 and Br 2 are the two elements that combine chemically to form a compound 2HBr. It is an element-element combination reaction to form a single compound.
53. (C)
The acidic portion of ethanoic acid is the COOH portion, with the H from the OH being lost during reaction with the base.
54. (B)
Since the solution turns universal indicator orange, it is acidic in nature. Only an acidic oxide will produce an acidic solution in water.
42. (C)
Uranium atoms are split in a nuclear reactor to produce nuclear energy, which is used to boil water to obtain steam. Steam under high pressure is used to turn a turbine which then drives a dynamo to produce electrical energy. The steam which has been used for turning the turbine is later condensed to water in a condenser to be used in the boiler again.
43. (B)
44. (B)
The retina of our eye has two kinds of light sensitive cells called rods and cones. Cone cells are sensitive to bright light and also cause sensation of colour of objects in our eyes. Cone cells help us to see, identify and distinguish between various colours.
Chemistry
R = 40 Ω , d = 1mm, l = 2m ρ= =
RA Rπd2 40 ×22 ×1 880 , ρ= , = l 4l 4 × 7 ×2 ×108 56 ×108
880 × 10 −8 ∴ρ = 1.57 × 10−8 Ω m 560
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55. (D)
All the given characteristics belong to semi metals.
66. (A)
Iron reacts with moist air and forms Fe2O3 that is the formation of rust.
56. (B)
Heat is required to decompose calcium carbonate. Thus, this reaction proceeds with absorption of heat therefore, it is an endothermic reaction.
67. (C)
57. (A)
Copper is below hydrogen in the reactivity series and therefore does not react with H 2SO4.
The general formula of : alkanes is C nH 2n+2. The formula of Hexane- C 6 H 14 , Ethane-C2H6, Butane C4H10. Alkenes have general formula CnH 2n. The formula of Pentene is C 5H 10 and Hexene is C 6H 12 .
58. (D)
Tin is in group IV A of 5 th period.
59. (D)
The residue formed is Na2CO3 which can react with more dilute acid to form carbon dioxide gas. Na2CO3 + 2HCl → 2NaCl + H2O + CO2 ↑
60. (C)
61. (D)
Polyethene has a high C:H ratio of 1:2. It is also a long chain molecule and will require a large supply of oxygen to burn completely. Hence, in normal circumstances, polyethene will burn with the sootiest flame.
68. (B)
On adding a few drops of universal indicator to a solution in a test tube that turned purple indicates that it is alkaline and its pH is >11.
69. (D)
Thermite is a mixture of iron (III) oxide and aluminium powder.
70. (D)
Statements (A), (B) and (C) describe the given observations. Zn (s) + 2 HCl (aq) → ZnCl2 (aq) + H2
Biology 71. (A)
The given equation represents aerobic respiration. Glucose + oxygen → carbon dioxide + water + energy
72. (A)
During photosynthesis plants take in carbon dioxide and give out oxygen.
73. (C)
Spinal nerves and cranial nerves together constitute the peripheral nervous system.
74. (C)
The sex of a baby is determined by the fathers chromosomes. If a sperm carries and a egg Y chromosome X chromosome than the zygore formed as XY is a male baby.
75. (C)
Archaeopteryx is a connecting link between reptiles and birds.
76. (B)
Zinc will give hydrogen gas and zinc carbonate will give carbon dioxide with an acid.
The given sequence shows movement of energy sun → grass → insects → frog.
77. (A)
Zn + 2HCl → ZnCl2 + H2 ↑
Amrita Devi Bishnoi is associated with the conservation khejri tree.
78. (B)
Frog and earthworm have moist skins. Most skin helps in breathing in these organisms.
79. (C)
Plastic is a non-biodegradable substance. Hence it is not used in compost pit.
80. (C)
Reduction of carbon dioxide takes place during photosynthesis.
81. (D)
In the given experiment the part below the ring is shrivelled as the food has been used up and above is swollen due to the accumulation of food.
The atoms of Group I elements (being metals) have 1 outermost shell electron each which is easily given away. Atoms of Group VII elements (being non-metals) have 7 outermost shell electrons and easily accept 1 more electron to form a stable octet structure. Hence, these two types of elements are most likely to form ionic compounds with transfer of electrons.
62. (C)
H
63. (A)
a-5, b-4, c-3, d-2, e-1
H
H
H
H
H
C
C
C
C
C
H
H H H Pentane
H
H
ZnCO3 + 2HCl → ZnCl2 + H2O + CO2 ↑ 64. (C)
65. (C)
On moving down any group in a periodic table, the number of valence electrons in the outermost shell of respective elements remains the same. 24 carat gold is soft and not suitable for making ornaments as it is not malleable. 22 parts of pure gold is alloyed with 2 parts of copper or silver to make ornaments.
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the
82. (C)
Hemodialysis is used to remove nitrogenous waste products from the blood.
86. (B)
Primary consumers in an ecosystem are herbivores. They feed directly on producers.
83. (D)
Movements induced in plants due to temperature are called thermonastic movements.
87. (D)
Spirogyra reproduces by fragmentation method.
88. (C)
Sunlight is used to produce electricity in solar cells.
89. (D)
Cerebellum maintains posture, balancing of body and coordination of body movements.
90. (D)
Before air is breathed into the lungs, it is filtered in the nostrils, moistened by mucus and gets warmer equal to the body temperature.
84. (D)
85. (C)
Budding, binary fission and spore formation are types of asexual reproduction. Hargobind Khorana was an Indian born scientist who settled in the United States. He did a lot work in the field of molecular biology. He solved the genetic code for several amino acids along with other scientists. He was the first person to synthesize gene. He did extensive work in the discovery of genetic code and for this he was awarded the Nobel Prize.
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UNIFIED COUNCIL A n I S O 9 0 0 1 : 2008 C e r t i f i e d O r g a n i s a t i o n
NATIONAL LEVEL SCIENCE TALENT SEARCH EXAMINATION Paper Code: UN 418 Solutions for Class : 10 Mathematics 1.
(A)
Area of =
1 Base Altitude 2
= S5 =
B
5 a + d + a + 9d = 305 2
2a + 10d = 122
a + 5d = 61
..... (2)
(2) – (1) d = 12 c D
Note: Answer is not given in options so it is deleted.
a
3.
p
A
(A)
C
b
Taking AC as base,
area ABC = =
1 AC BC 2
1 ba 2
1 a(b c c) + a(c b c) a(b + c b + c) 2
=
1 a(b 2c) ab a(2c) 2
1 ab 2ac ab 2ac 2 = 2ac
Taking AB as base, area ABC
From (1) & (2),
=
= ...... (1)
1 1 = AB CD = c p 2 2
Area of triangle
4.
(D)
13 cm R r
A
...... (2) 12 c
1 1 pc = ab 2 2
m
r
P
O
(Del)
t1 + t3 + t5 + t7 + t9 = Sn =
Using Pythagoras’ theorem,
AC2 = AB2 + BC2
n a + l 2
S5 =
2
2a + 8d = 98
a + 4d = 49
2
BC2 = 13 12 = 25
5 a + a + 8d = 245 2
Q B
pc = ab
2.
C
BC = 5 cm
OP = OQ = OR = r (radius) POQB is a square
..... (1)
PO = BQ = r
t2 + t4 + t6 + t8 + t10
AP = 12 – r, QC = 5 – r, AR = AP = 12 – r, RC = QC = 5 – r
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Let 'x' be added to each of the given numbers to make the numbers proportionate.
AR + RC = AC
12 – r + 5 – r = 13
17 – 2r = 13
2r = 4
5.
(D)
Then, (5 + x) (27 + x) = (9 + x) (17 + x)
r = 2 cm
sin =
135 + 32 x + x2 = 153 + 26 x + x2
1 2
32 x 26 x = 153 135 6x = 18
sin is negative in 3rd and 4th quadrants. Hence the angles are 210o and 330o. 6.
(A)
x=3
Suppose X-axis divides the line joining (2, 6) and (3, –4) in : 1 ratio.
10. (D)
A (x, y)
Let the quotient when the given number is divided by 143 be 'q'. Given that the remainder is 31, the number = 143q + 31 = 11 × 13q + 11 × 2 + 9 = 11(13q + 2) + 9
B (4, –3)
C (–9, 7)
Hence the remainder when the same number is divided by 11 is 9.
6 1 + 1 Then y = 0 = +1
11. (D)
6 4 = 0
.. cos90° 2° cos 90° 1° cos90°
3 = 2
cos1°cos2°.....cos45°...
The required ratio is 1 : = 2 : 3 .
7.
(C)
...sin2°sin1°sin0° = 0
12. (A)
As RSP RPQ
(B)
AP = AB + BP = 8BP + BP = 9 BP. Let BP be x. Then AP = 9x
RS RP = RP RQ
8.
cos1°cos2°cos3°.....cos45°....
RS × RQ = RP2
Now, AP BP = PT2 , as the product of the segments of a secant is equal to the square of the tangent.
a = 27, d = – 3
2 2 9 x x = 15 cm
n Sn = 2a + n 1 d 2
x = 5 cm
AP = 9x = 45 cm
n 30 = 2 27 + n 1 3 2 =
13. (A)
n 54 3n + 3 2
– 60 = n(57 – 3n)
– 60 = 57n – 3n2
3n2 57n 60 = 0
n2 19n 20 = 0
n2 20n + n 20 = 0
The coefficients of the variable in a zero polynomial are zeros. Hence, the degree of a zero polynomial is zero is not correct.
(n – 20) (n + 1) = 0
n = 20 or –1
9.
(C)
Four numbers are in proportion if First Fourth = Second Third websit e : www.unif iedcouncil.com 2
19. (B)
A
14. (A)
We have,
AP = AS BP = BQ CR = CQ
hm
DR = DS
C
B
hm
D
According to the problem, AB is the flagpost and BC is its shadow, both equal to h m. tan =
15. (D)
Q A
Since tan45° = 1.
B
The required angle of elevation = 45°.
= AS + BQ + CQ + DS
539 = 7 2 × 11 is common in the given numbers.
= (AS + DS) + (BQ + CQ) = AD + BC Since, AB = CD and AD = BC. ( opp. sides of a parallelogram are equal.)
Given, system of equations 'is' 2x – 3y = 8 and 4x – 6y = 9
AB = AD
a1 2 1 b1 3 1 a = 4 = 2 ; b = 6 = 2 2 2
CD = AB = AD = BC
Hence ABCD is a rhombus.
c1 8 and c = 9 2
20. (A)
a1 b1 c1 = a2 b2 c2
If and are the zeros of the polynomial f(x) = x2 7 x + k ,
+ = 7 and = k . Given that = 3 ,
Thus, the given system of equations is inconsistent. 17. (D)
P
AB + CD = AP + BP + CR + DR
Hence 539 is the common factor of the given numbers. 16. (B)
C
S
h =1 h
= 45°
R
solving + = 7 and = 3 , we get
sin + cos = 3
= 5 and = 2 .
sin2 + cos2 + 2sin cos = 3
= 10 and k = 10.
2 sin cos = 2
= k
sin cos = 1 = sin2 + cos2
sin2 + cos2 =1 sin cos 2
21. (A)
Also area = xy = 400 m2
2
sin cos + =1 sin cos sin cos
= x(40 – x) = 400 x2 40 x + 400 = 0
sin cos + =1 cos sin
18. (A)
The perimeter of the rectangular park = 2(x + y) = 80 m, where x is the length and ‘y’ the breadth.
x2 20 x 20 x + 400 = 0
tan + cot = 1
x(x 20) 20(x 20) = 0
Mid point of (1, –2) and (–5, 6) = (–2, 2)
(x 20) (x 20) = 0
Mid-point of the points in option (A) is
x = 20 or 20
2 6 5 1 2 , 2 = 2, 2
The length of the rectangle is 20 m.
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22. (A)
In AED, hypotenuse is AE. According to Pythagoras' theorem,
27. (B)
The sun obtains its energy from nuclear fusion reactions that occur inside the sun all the time. During this process hydrogen atoms combine to form helium atoms to produce heat and light. Nuclear fusion reactions of hydrogen are the source of sun’s energy.
28. (A)
A convex or rear-view mirror used in vehicles forms images of objects that are always smaller than the object. The linear magnification produced by a convex mirror is always less than one.
29. (C)
The power of a D.C motor can be increased by laminating the soft core, and not by increasing the size of core.
30. (A)
The “X” symbol indicates that the current is flowing into the plane of the paper. Using right-hand screw rule, the magnetic field can be identified as turning in the clockwise direction.
31. (B)
Speed
AE2 = AD2 + DE2 .
23. (D)
24. (A)
S10 = 4S5
5 2a + 5 - 1 d 1 2 = 4 10 2a + 10 - 1 d 2
1 1 2a + 4d = 4 2 2a + 9d
1 1a + 2d = 4 2a + 9d
2a + 9d = 4a + 8d
d = 2a
1 a = 2 d
Since, V = r2h, you need to express r and h in terms of C. It is given that h = 4C. C = r r C 2
25. (C)
C 2
2
V
=
3×108 = 2.25×108 m / s 1.33
Min. length of mirror to see full image =
2
5p 4 1 16 < 0
64 25
p <
8 5
p lies between
8 8 and . 5 5
1 1 1 = + R R1 R2
=
4+6 24
=
10 24
(in parallel), , Total R =
24 10
1 R
=
1 6
+
2.88 6
6 2
= 3 feet
35. (C)
The magnetic needle will be perpendicular to the current carrying conductor, i.e., it points in north - south. direction.
1 4
= 2.4
= 0.48A
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2
=
Being renewable and not running out are the advantages of using biomass energy.
Total I = 1.2 A, V = IR = 1.2 2.4 = 2.88 V V = IR1 , I =
Height
34. (A)
Physics 26. (C)
water
33. (B)
b2 – 4ac < 0
2 p <
in
The sealed glass bulb in an electric bulb helps in maintaining high temperature, protects the filament from directly coming into contact with moisture (humidity) and oxygen.
C2 C3 4C 2 4
25p2 64 < 0
light
32. (D)
4C
Given x2 + 5px + 16 = 0 has no real root
of
36. (B)
A solar cell (photovoltaic cell) is a device that converts the energy of sunlight directly into electricity by the photovoltaic effect. Assemblies of cells are used to make solar modules (solar panels). The energy generated from these solar modules, referred to as solar power, is an example of solar energy.
46. (D)
When the object is placed at C of a concave mirror, the distance between a real object and its real image is zero.
47. (C)
Fleming's left hand rule is used to find the direction of magnetic field around a straight conductor.
48. (A)
The correct matching is a-3, b-1, c-4, d-2
37. (C)
The blue colour of the sky – Scattering of light.
(ii)
The glittering of diamond – Total internal reflection.
(iii)
The formation of rainbow – Dispersion of light.
(iv)
The visibility of sun for some time even after sunset – Refraction of light.
RE = R1 + R2 + R3 = 2.5 + 12 + 3.5 = 18 A single resistor of 18 can replace all the three resistors.
38. (A)
Focus of a concave mirror is towards the left, so focal length is negative.
39. (C)
The object distance does not affect the focal length which is a property of the lens.
40. (A)
H = I2 Rt = 102 30 60 = 180000 = 180 kJ
41. (A)
Colour of an object is determined by the colour of light reflected by it. The reflected light causes the sensation of the colour in the eye.
42. (D)
Fossil fuels are easy to burn and release a lot of energy except coal. Coal on burning produces acidic gases and soot that pollutes the environment. Incomplete burning of fossil fuels releases carbon monoxide into the atmosphere. It is a poisonous gas. When inhaled by humans reduces oxygen carrying capacity of the blood.
43. (C)
The field pattern in option (C) is valid for both electric and magnetic fields.
44. (B)
The human eye pupil’s function is to control the amount of light coming towards the eyes. The function to focus on the view is performed by the eye lens which will be reflected onto the retina. The eyelids function is to cover and protect the eyes from dust and other dangerous objects.
45. (B)
(i)
49. (A)
The potential difference of the bulb is 1.5 V (as the e.m.f. of a dry cell is 1.5 V) since a closed switch is a conductor and has zero voltage.
50. (C)
When the image formed by a concave mirror is real, inverted and of the same size as the object, then the object must be placed at its centre of curvature (C). Now, the centre of curvature of a concave mirror is at a distance of ‘twice the focal length’ or ‘2f’. Here, Focal length, f = 10 cm So, 2f = 2 10 cm = 20 cm Thus, the object should be placed at a distance of 20 cm in front of this concave mirror.
Chemistry 51. (B)
Aluminium is a metal which forms an invisible protective layer and prevents further oxidation. Aluminium oxide is the covering of film formed with its chemical formula, Al 2O3.
52. (C)
Decomposition of calcium carbonate is balanced.
53. (B)
The ketone group consists of one carbon atom and one oxygen atom. The oxygen atom of the ketone group is joined to the carbon atom by a double bond.
Resistance is the ratio of potential difference in volts across the component to the current passing through measured in amperes. websit e : www.unif iedcouncil.com 5
54. (D)
Sodium hydroxide is a base. When it dissolves in water, it forms sodium ions and hydroxide ions respectively. Water Na+ + OH– NaOH Sodium hydroxide is a strong base which completely ionises in water to produce a large number of free, mobile hydroxide ions.
55. (D)
Gallium, germanium and arsenic all belong to the same period (4 th).
56. (A)
Magnesium carbonate decomposes to form magnesium oxide and carbon dioxide gas is evolved.
57. (B)
Gold does not show any reaction with H2SO4 under any conditions.
58. (C)
The structure in option (C) represents an halogen fluorine of group 17 of the periodic table. It has seven valence electrons.
59. (D)
60. (C)
61. (A)
62. (D)
63. (D) 64. (D)
65. (D)
66. (B)
‘X’ is zinc and ‘Y’ is copper. Zinc is more reactive than copper. Z inc displaces copper from copper sulphate compound so that copper is set free. It is a displacement reaction.
67. (B)
When fuels burn in a very limited supply of air or oxygen, carbon is not oxidised completely to give carbon dioxide and water. The unburnt carbon forms a black soot and gets deposited on the bottom of the cooking vessels.
68. (B)
Carbonic acid (H 2CO3) is a weak mineral acid.
69. (A)
Magnesium is a highly reactive metal which is extracted by the electrolysis of molten magnesium chloride. Moderately reactive metals like zinc, iron, lead and copper are extracted by the reduction of their oxides with carbon.
70. (A)
Reaction of water with calcium oxide is a compound - compound combination reaction.
During water of crystallization, the crystals of salts form a part of their structure, obtain shape and colour.
H O + CaO Ca OH2
2 compound + compound
Isomerism is not possible in methane, ethane and propane. It is possible only in hydrocarbons having 4 or more carbon atoms. Butane has two isomers, n-butane and iso-butane respectively.
compound
Biology
Both mercury and copper can be extracted just by heating their sulphide ores in air. The oxides obtained are further heated to get pure metals. Compounds like haloalkanes, alcohols, aldehydes, ketones and carboxylic acids all form a part in the homologous series. All the given statements are true about a strong acid. Metalloids are elements with both the characteristics of metal and that of nonmetal. In the periodic table we can find the metalloids between the intersection where metals and non-metals meet. They are roughly positioned in a staircase manner in the periodic table. Strontium is an alkaline earth metal. A thin impervious layer of aluminium oxide is formed on the surface of aluminium when exposed to air and prevents further corrosion. Also, aluminium is light in weight. Due to this two reasons, aluminium is used for building air crafts.
71. (A)
Photosynthesis occurs in the chloroplast of a plant cell.
72. (C)
Ultra filtration of liquid take place in glomerulus.
73. (D)
The given figure represents fertilisation. It takes place in the fallopian tubes.
74. (D)
Morphological, anatomical and embryological evidences support evolution.
75. (B)
Glucose is converted into glycogen by insulin and stored in the liver.
76. (A)
The sequence of food chain is producer consumer decomposer..
77. (C)
Sphygmomanometer is used to measure the blood pressure.
78. (C)
Biogas is produced by the action of decomposers on organic wastes.
79. (C)
The winding of tendrils and climbing of the stem to the support is called thigmotropism.
80. (D)
Hydra and planaria exhibit regeneration type of reproduction.
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81. (B)
Female destined zygote cell contains 44+XX chromosomes.
82. (D) 83. (A)
85. (C)
Pulmonary arteries carry impure blood to the lungs.
Germination of pollen take place on stigma that is labelled as I and fertilisation in ovary tablelled as IV.
86. (A)
Photosynthesis can be represented in the following way
Blood group AB is called the universal recipient.
87. (C)
Cerebellum controls and coordinates body movements.
88. (C)
The correct sequence followed in event of sexual reproduction in a flower is as pollination, fertilisation, embryo and seed.
89. (C)
Windmills generate power by using wind energy without causing pollution.
90. (A)
Amoeba reproduces by binary fission.
CO2 + water
84. (B)
sunlight glucose + O2 chlorophyll
The given figure is that of pancreas. It controls blood sugar level.
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UNIFIED COUNCIL A n I S O 9 0 0 1 : 2008 C e r t i f i e d O r g a n i s a t i o n
NATIONAL LEVEL SCIENCE TALENT SEARCH EXAMINATION (UPDATED) Paper Code: UN 421 Solutions for Class : 10 2.
Mathematics 1.
(A)
(C)
Let the smallest angle be C and the largest angle be A.
Let the point on x-axis be (x, 0). 2
Then, c = 2 x + 3 0
Then according to the problem,
2
2 2 x + 9 3
=
1 (A + B) 5
.....(1)
(For x = 0, 1, .... etc)
and A = B + C + 20°
.....(2)
But as it is given that c < 3, no such point exists.
C =
Since A + B + C = 180° ,
c
.....(3)
C = 180° (A + B)
3.
(B)
45o o 180
45o =
From (1) and (3),
c
1 (A + B) = 180° (A + B) 5
= = 0.25 4
1 1 A + B + A + B = 180° 5 5
4.
(B)
Given PA = 4 cm and AB = 5 cm
6 (A + B) = 180° 5
A + B =
O
180° × 5 = 150° 6
A = 150° B and C =
A
1 × 150° = 30° 5
P
T
.....(4)
PT2 = AP PB
.....(5)
PT 2 = 4 9
PT = 6
From (2) and (4),
Hence, the length of PT is 6 cm.
150° B = B + C + 20° 130° = 2B + C
5.
.....(6)
(B)
318 = 2 × 3 × 53 477 = 3 × 3 × 53
= 2B + 30°
B =
B
L.C.M. (318, 477)
130° 30° = 50° 2
= 2 × 3 × 3 × 53 = 954 Given that
A = 150° 50° = 100°
954 = 159 × p + 318,
Hence the largest angle is 100o . p= websit e : www.unif iedcouncil.com 1
954 318 =4 159
6.
(A)
9.
Let the length of the side of the smaller square be 'x' m. Then its area is x2 sq. m.
(B)
Let x, y and z be the three radii.
square = (x + 4) m
x + y = 7 cm y + z = 11 cm and x + z = 6 cm
Its area = (x + 4)2 sq. m
Subtracting eq. (2) from eq. (1), we get
The length of the side of the larger
= x2 + 8x + 16 sq. m
x–z=–4
Given that the sum of their areas is 208 sq. m. 2 x2 + 8 x + 16 = 208 x2 + 4 x + 8 104 = 0
2x = 2
x = 1 cm
from eq. (1)
y = 6 cm
from eq. (3)
z = 6 – 1 = 5 cm
2
x + 4 x 96 = 0
10. (A)
2
x + 12 x 8 x 96 = 0
x = 1 cm, y = 6 cm, z = 5 cm
Odd numbers starting from 11 are 11, 13, 15, 17, 19, .... Sum to ‘n’ odd numbers, where a = 11, d = 2 is
x(x + 12) 8(x + 12) = 0 x = 12 or 8
Sn
Since the side of a square cannot be negative, the side of the smaller square is 8 m.
=
n [2a + (n 1)d] 2
=
n 2 11 + (n 1)2 2
The side of the larger square is 12 m.
(A)
..... (4)
Adding eq.(3) and eq.(4), we get
x2 + x2 + 8 x + 16 = 208
7.
..... (1) ..... (2) ..... (3)
n = [22 + 2n 2] 2
According the problem, BC2 = AB2 + AC 2
n = [20 + 2n] 2
C(4, 3)
= n(10 + n) = 10n + n2 A
11. (C) A(2, 3)
200
B(x, y)
(x 4)2 + (y 3)2 = [( x 2)2 + (y 3)2 ] C
x2 8 x + 16 + y 2 6y + 9
B
According to the problem, sin30° =
= (x2 – 4x + 4 + y2 – 6y + 9) + 4 + 0
1 = 200 = 100 m 2 The kite is 100 m above the ground.
8 x + 25 = 4 x + 17 4x = 8 x = 2 12. (A)
Given + + = 2, = (14) and
Let AB = BC = x
+ + = (7) , the required polynomial is x3 ( + + )x2 + ( + + )x
= x3 2 x2 + (7)x (14) 3
h 200
h = 200 sin30°
8 x 6y + 25 = 4 x 6y + 13 + 4
(A)
hm
o
30
+ (4 2)2 + (3 3)2
8.
m
2x
2
= x 2 x 7 x + 14 Hence, the polynomial is x3 – 2x2 – 7x + 14. websit e : www.unif iedcouncil.com 2
Given that ABC is right angled at B. 2
2
Therefore, AC = AB + BC
A
X
Y
2
AC2 = x2 + x2
C
B
AC = 2x Z
Also, ABE ACD
Area ABE = Area ACD
13. (B)
Since XY is a tangent to the circle at the point A,
Area ABE AB2 = Area ACD AC2
XAB = ACB = 60o
x2
2x
Similarly, ABX = 60o .
2
Area ABE 1 = =1:2 Area ACD 2
= 180o 60o + 60o = 60o
Similarly it can be shown that Y = 60o and Z = 60o .
The given points are A (6, 3), B (– 3, 5), C (4, –2) and D (x, 3x).
XYZ is an equilateral triangle.
Area of DBC = 1 x 5 + 2 3 x 3 4 + 1 6 20 2
=
16. (C)
1 7x + 21x 14 = 14 x 7 2
Let and be the zeros of the required polynomial f(x). Given, + =
Area of ( ABC)
10 x+7 3
= x2
1 49 42 + 21 14 = 2 2
f(x) = x2 +
Area DBC 14 x 7 1 = = (given) Area ABC 49 / 2 2
Hence, the quadratic polynomial is 3 x 2 + 10 x + 7 3 . 17. (D)
7 2x 1 = 4
x=
14. (A)
Product = (3x – 1)(x + 2)
= 3x2 + 6 x x 2 = 3 x2 + 5x 2
11 8
= 3 and = 2 18. (D)
A + B + C = 180°
Since C = 90°.
If 6x ends with 5, then 6x would contain the prime 5. But 6x = (2 × 3)x = 2x × 3x .
cos A + B = cos90° = 0 15. (B)
The factors are (3x – 1) and (x + 2).
11 4
A + B = 90°
10 x+7 3
= 3 x2 + 10 x + 7 3
2 2 x 1 1 = 7 2
2x =
10 , = 7 3
f(x) = x2 + x +
1 = 6 5 + 2 3 3 4 + 1 6 20 2 =
In AXB, AXB
The only prime numbers in the factorization of 6x are 2 and 3.
Let XY, YZ and ZX be the tangents to the circle at the vertices of an equilateral ABC .
By uniqueness of fundamental theorem, there are no primes other than 2 & 3 in 6x. So, 6x will never end with 5.
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19. (B)
1st term of 'n' A.M.s between 'a' & 'b'
= AB2 + BC2 + 2.BC.BD (Since AD2 + DB2 = AB2.)
ba = a+ n+1 =
24. (D)
Here, a = 28, a + d = 22, a + 4d = 4 d = (–6).
an + b n+1
Since 'x' is the 3rd term,
Last term of 'n' A.M.s between 'a' & 'b'
x = a + 2d = 28 + 2(–6)
b a =b n+1
= 28 – 12 = 16 and 'y' is the 4th term = a + 3d
bn + a = n+1
= 28 + 3 (–6) = 28 – 18 = 10
Sum of the terms
The required values are 16 and 10.
n na + b bn + a = + 2 n + 1 n + 1
25. (A)
n n + 1 a + b = 2 n+1 =
20. (A)
21. (C)
Then, according to the problem, n2 + (n + 2)2 = 340
n a + b 2
n2 + n2 + 4n + 4 = 340 2n2 + 4n + 4 = 340
In a right angled triangle, hypotenuse is the square root of sum of squares of other two sides. Hence, the sides cannot have values as 1, 1 and 2.
2n2 + 4n 336 = 0 n2 + 2n 168 = 0
The ratio in which a line is trisected is 1 : 2.
n2 + 14n 12n 168 = 0
1(5) + 2(2) (4) + 2(19) , 1+2 1+2
n(n + 14) 12(n + 14) = 0
=
(n + 14) (n 12) = 0
The point of trisection of the line
n = 14 or 12
1 34 joining the points = , 3 3
22. (C)
23. (A)
The required numbers are 12 and 14.
Physics
sin 90° 81° cos81° sin 90° 42 cos42° =
26. (D)
Yes, the body of the bird behaves like a resistor in an electrical circuit. But since the two feet of the bird have the same potential, the current will not flow through the body, i.e. the bird will not get electrocuted. Remember that current can only flow when there is a potential difference.
27. (D)
The top of box-type solar cooker is covered with glass so that the heat radiated from inside the box is reflected back into the box. Thus, radiation loss is reduced.
28. (D)
All the given mirrors form a virtual image of a real object according to the given positions.
cos81° cos81° =0 cos42° cos42°
A
D
B
C
AC2 = AD2 + DC2 2
Let the two consecutive even numbers be ‘n’ and (n + 2).
2
= AD + BC + BD
= AD2 + BC2 + BD2 + 2.BC.BD
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29. (B)
One of the factors that determines the strength of the electromagnet is the magnitude of the current flowing in the solenoid. Having more cells connected in series can increase the voltage across the solenoid and hence increase the current flowing through the solenoid.
The interaction between wire 2 and wire 3 is also similar as their current directions are the same as wire 1 and wire 2.
Another factor is the type of materials. Iron is a soft magnetic material. It will make a stronger electromagnet than steel which is a hard magnetic material. 30. (C)
31. (B)
This implies that wire 2 will be attracted to both wire 1 and wire 3. These two forces will have zero resultant force as the current flowing through the three wires is of the same magnitude.
When the ciliary muscles contract the lens becomes thick. The focal length decreases and enables us to see near objects. When the ciliary muscles relax, the lens becomes thin and the focal length increases which helps us to see distant objects clearly. The 3 resistor and the 9 resistor are connected in series. Their effective resistance is 12 .
35. (A)
Parameters of electricity supply is different in different countries. In India it has a potential difference of 220 V, frequency of 50 Hertz and current rating of 5A/15A.
36. (A)
Biogas is produced when wet organic matter is decomposed by bacteria in the absence of oxygen. A type of anaerobic bacteria break down biomass to sugars, organic acids and other compounds. These are further decomposed by other bacteria to form CO 2 and H 2 which combine to form methane and water as given below.
The 5 resistor and the 1 resistor are connected in series. Their effective resistance is 6 .
CO2 + 4H2 CH4 + 2H2O Biogas is a mixture of several gases like methane (75%), carbon dioxide (23%) and other gases including hydrogen and hydrogen sulphide is (2%). The above combustible gases form an excellent, renewable fuel and help to conserve our energy sources.
The 12 (combined) resistor and the 6 resistor (combined) are connected in parallel. 37. (A)
Current in PR is 4 A as PR (4 A) + QR (6 A) = RS (10 A). Based on the calculation, all other options are incorrect.
38. (B)
Use the lens equation
1 1 1 1 1 , , R = 4 R 12 6 R 4 32. (A)
A typical solar cell develops a potential difference of 0.5 – 1 V and 0.7 W of electricity.
33. (B)
The speed of light is higher in a rarer medium than in a denser medium.
34. (D)
By using the right-hand grip rule on wire 1 and wire 2, it can be seen that the interaction between the two fields create opposite signs. This implies that there is an attractive force caused by the interaction of the fields.
1 1 1 + = u v f
where u is the object distance, v is the image distance and f is the focal length. 1 1 1 + = 18 v 10 1 1 1 v = 10 18
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39. (C)
Internal magnetic field lines are developed in the bar which increases the magnetic field inside the bar.
40. (D)
The focal length of the eye lens is more or the eye ball has shrunk. The image is formed behind the retina and the person faces difficulty in seeing the near objects clearly. Use of convex lens is advised for correcting the defect.
41. (A)
An ideal electromagnet has very strong magnetic strength when in operation and zero magnetic strength when it is switched off. To achieve that, the core of the electromagnet must not retain any magnetism when it is taken out from the coil.
42. (B)
Hydrogen has a high calorific value of 1,50,000 kJ/kg.
43. (D)
If light from two different sources has the same colour, it also has the same wavelength even if the origins are different. Sodium lamp is an artificial source of light while sunlight is a natural source of light.
45. (A)
Light scattering occurs when light passes through air particles. The blue light is scattered the most while the red light is scattered the least. Natural phenomena such as the blue skies and the red skies during sunset are examples of light scattering.
47. (C)
A strong smelling substance called ethyl mercaptan (C 2 H 6 S) is added to LPG cylinders to help in the detection of gas leakage. Ethyl mercaptan has a foul smell resembling that of hydrogen sulphide gas which can be easily detected.
48. (A)
When an object is placed anywhere between the pole and infinity in front of a convex mirror, the image is formed between the pole and focus. It is virtual, erect and diminished (smaller than the object).
49. (D)
R=
L , R : RB A A
(2 4) (2)2 : (1 3) (3)2 2:
Our sun produces more yellow light than any other color because its surface temperature is 5,500 o C. If the sun’s surface is cooler i.e., 3000 o C it would look reddish and if the sun’s surface is hotter i.e., 12000o C, it would look blue. The earth’s atmosphere acts as a kind of light filter. Some colours are filtered more than others. The sun is a yellow star, but the earth’s atmosphere makes the sun look more yellow than it appears. If you observe it from space, it would appear more white than yellow. 44. (D)
46. (D)
1 ,6 : 1 3
When resistor B is 2 , resistance of resistance of resistor A = 2 6 = 12 50. (B)
When a real object is placed infront of a convex lens of focal length ‘f’ at its principal focus, then the image is formed at infinity.
–
1 1 1 1 = – , = 0 (or) v = f v f v
Chemistry
When a man wearing yellow coloured glass for left eye and red coloured glass for right eye and stands in front of a plane mirror, he observes his image in the mirror as left eye coloured red and right coloured yellow due to lateral inversion.
51. (C)
The metal with lowest density is lithium – 0.534 g cm–3
52. (C)
When hydrogen sulphide gas is passed through copper sulphate solution, then a black precipitate of copper sulphide is formed alongwith sulphuric acid. CuSO4 (aq.) H2 S(g) CuS(s) H2 SO4 (aq.)
When an appliance is marked “240 V, 40 W”, it means that a 240 V across the appliance will produce a power of 40 W.
Two compounds copper sulphate and hydrogen sulphide react by an exchange of ions to form two new compounds copper sulphide and sulphuric acid.
P = VI
Blue zone is at the base of the candle flame i.e., below the wick of the candle. So, a match stick does not get ignited when inserted in the blue flame of a candle.
40 = 240 I 40 I = 240 A = 0.17 A
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53. (A,B,C,D) 54. (C)
55. (C)
All the given carboxylic acids and alcohols respectively form esters.
The highest pH is the most alkaline solution. Potassium oxide dissolved in water to form potassium hydroxide, a strong alkali.
The reaction of aluminium with dilute hydrochloric acid is less rapid than that of magnesium, so aluminium is less reactive than magnesium.
Statements (A), (B) and (D) are not true. As the atomic radius of elements of group 1 increases down the group, the number of electrons occupied in various shells also increases from 1 to 7 as given below: Number of shells
Rubidium
5
Cesium
6
Francium
7
56. (C)
A chemical reaction must follow the law of conservation of mass.
57. (B)
The highly reactive metals such as potassium, sodium, calcium, magnesium and aluminium are extracted by the electrolytic reduction of their molten chlorides or oxides. The metals extracted by this process are very pure and do not contain any impurities.
58. (B)
in acid, then fresh aluminium metal is exposed which reacts rapidly with dilute hydrochloric acid.
60. (B)
CH 2 and 14 units is the difference in formula and molecular masses of CH3OH and C 2H5OH
61. (C)
CuO is reduced to copper metal by hydrogen. Dry hydrogen gas continues to flow through to prevent the hot copper metal from reacting with oxygen in air to form back CuO again.
62. (C)
Ethene, butene and pentene are unsaturated hydrocarbons. In addition to straight chain and branched chain there exists closed chain or ring type chain called cyclic hydrocarbons that are saturated and unsaturated. Benzene is an unsaturated, cyclic hydrocarbon.
63. (B)
In both the cases, precipitation occurs. A white precipitate of BaSO4 is formed as shown below.
Most of the acids react with metals to form salt and evolve hydrogen gas. This shows that hydrogen is common in all acids. 2Al 6HCl 2AlCl3 3H2
Aluminium metal at first reacts slowly with dilute hydrochloric acid due to the presence of a tough protective layer of aluminium oxide on its surface. But when the thin, outer oxide layer gets dissolved
BaCl 2 + H 2SO4 BaSO4 + 2HCl
65. (B)
Iron, being a less reactive metal than aluminium, forms a less stable oxide that can be reduced by heating with a reducing agent. Aluminium oxide (bauxite) is very stable to reduction by reducing agents; aluminium can only be extracted by electrolysis of molten bauxite.
66. (C)
During the process of respiration, the glucose present in the body cells combines with oxygen to produce energy.
67. (C)
When soap is dissolved in water, it forms a colloidal suspension in water and the soap molecules cluster together to form spherical micelles. When a cloth with dirt, oil or grease is soaked in soap solution, the micelles attach to the dirt, oil or grease particles. They entrap with their hydrocarbon ends and on agitation in soap solution get dispersed by removing the dirt, oil or grease and on rinsing several times, the dirty cloth becomes clean.
At wt. of X = 5 8 = 40, Y = 11 8 = 88, Z = 17 8 = 136.
59. (C)
(ii)
y is chlorine.
Sum of extreme elements (5x + 17x) = 176 (given).
176 =8 22
Ba(OH)2 + H 2SO4 BaSO4 + 2H 2O
64. (D)
Let the given ratio of atomic weights of X, Y, Z be 5x, 11x, 7x respectively.
22x = 176, x =
(i)
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68. (A)
69. (B)
70. (A)
The correct ascending order of pH of given substances is as given below :
77. (A)
Glycolysis is the common phase between aerobic and anaerobic respiration.
(i) Gastric juice - 1.5 to 3.5 (ii) Lemon juice - 2 to 2.4 (iii) Pure water - 7 (iv) Milk of magnesia - 10.5 When ZnO reacts with NaOH (a strong base), sodium zincate and water are formed.
78. (B)
Grass
79. (C)
The process of cleaning the blood in kidney failures using a kidney machine is called dialysis. Nerve cell bodies are present in the grey matter. The given figure is that of the bread mould. It exhibits saprophytic nutrition Myelin sheath covers the axon of a neuron. It is made up of schwann cells and chiefly consists of fatty material. Egg cells contain yolk which help growth after fertilisation. X represents a vesicle. It releases chemicals that act as neurotransmitters. Palaeontologists deals with the evidences of fossils. Cardiac refers to heart. In the given flow chart P is testes Q is ovum and R is Fertilisation The progressive increase in the accumulation of a harmful substance in organisms at successively higher trophic levels is called biomagnification. Renin helps in curdling of milk. Spinal cord and medulla oblongata controls involuntary actions.
80. (A) 81. (B)
A balanced equation is the one in which the atoms of every element will be the same on both the sides of the equation.
82. (D)
Biology 71. (B)
72. (B)
73. (C) 74. (A)
75. (C)
76. (C)
The gas that diffused out from a capillary into an alveolus is carbon dioxide. During exhalation carbon dioxide gas is expelled out. The experimental set up is used to prove that carbon dioxide is essential for photosynthisis. Placenta prevents the mixing of the blood of the foetus with that of the mother. ‘R’ represents Medulla oblongata. Medulla oblongata controls heart beating, respiration swallowing, coughing and sneezing. The characteristic features of vegetative reproduction are: cell division takes place only by mitosis and daughter cells formed are geneticaly identical to the parent. To remove chlorophyll, the leaf is boiled in alcohol.
83. (D) 84. (C) 85. (B) 86. (A) 87. (D) 88. (C)
89. (B) 90. (A,D)
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Goat
Human
