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PRE FOUNDATION DIVISON IMO Stage-II Exam.-2016
CLASS-8 MATHEMATICS Q.1
Q.2
Three different containers contain different quantities of mixtures of milk and water, whose measurements are 403 kg, 434 kg and 465 kg. What biggest measure must be there to measure all the different quantities exactly ? (A) 1 kg (B) 7 kg (C) 31 kg (D) 41 kg Three rational numbers lying between and
1 3 , 0, 2 4 1 1 , 0, (C) 4 4
(A) –
Q.3
Q.4
The total number of girls in colleges D and E together are approximately what per cent of the total number of girls in colleges A, B and C together ? (A) 87 % (B) 75 % (C) 70 % (D) 88 %
Q.5
What is the respective ratio of the number of boys in college D to the number of boys in college B ? (A) 5 : 4 (B) 8 : 9 (C) 4 : 5 (D) 9 : 8
Q.6
In the given figure (not drawn to scale), AFGB, CFE and CGD are straight lines. Find y.
3 4
1 are 2
Date : 14-02-2016
1 1 3 , , 4 4 4 5 1 , 0, (D) 4 4
(B)
x6 2x 1 x4 – + =0 x5 x4 x2 (B) –2 (C) 2 (D) 1
Solve for x : (A) 3
Direction (4 and 5) : Study the following graph carefully and answer the questions given below : Total number of Boys and Girls In Various Colleges
(A) 90º (C) 94º Q.7
Select the correct statement. (A) A cuboid has 4 faces. (B) A cylinder has 2 flat faces. (C) A sphere has 1 vertex. (D) A cone has no vertex.
Q.8
Which of the following figures do not satisfy any of the following properties ? – All sides are equal. – All angles are right angles. – Opposite sides are parallel.
(A) P CAREER POINT : 128, Shakti Nagar, Kota - 324009 (Raj.), Ph: 0744-2503892
(B) 86º (D) 92º
(B) Q
(C) R
(D) S 1
Q.9
Three unbiased coins are tossed. What is the probability of getting at least two tails ? (A)
Q.10
1 4
(B)
1 2
(C)
3 8
(D)
7 8
x remains constant y
(B) x – y remains constant. (C) x + y remains constant. (D) x × y remains constant.
If x =
1 3 2
2
2 3
4
(A) 62º
2 (C) 3
Q.13
6
3 (B) 2
The greatest among ( 7 –
12
3 (D) 2
5 ), ( 5 – 3 ),
7 ) and ( 11 – 9 ) is ………….. .
(A) ( 7 – 5 )
(B) ( 5 – 3 )
(C) ( 9 – 7 )
(D) ( 11 – 9 )
8
The perimeters of a square and a rectangle are equal. If their areas are respectively A m2 and B m2, then which of the following is a true statement ? (A) A < B
(B) A B
(C) A < B/2
(D) None of these
–
(D) 38º
Q.16
, then find the value of
( 9 – 10
(C) 52º
By what least number 25920 be divided to obtain a number which is a perfect cube ? (A) 35 (B) 25 (C) 15 (D) 5
x . 2 (A) 3
(B) 28º
Q.15
–3
Q.12
In the given figure (not drawn to scale), ABC and CDE are straight lines, ACE is a right angle, DF || CG}||BH. Find y.
If two quantities x and y vary directly with each other, then (A)
Q.11
Q.14
3 1 1 3 + = + is an example to show 8 7 7 8
that (A) Addition of rational numbers is commutative (B) Rational numbers are closed under addition. (C) Addition of rational numbers is associative. (D) Rational numbers are distributive under addition. CAREER POINT : 128, Shakti Nagar, Kota - 324009 (Raj.), Ph: 0744-2503892
Q.17
The value of
(856 167) 2 (856 167 ) 2 is 856 856 167 167
equal to (A) 1 (B) 2
(C) 689
(D) 1023
Q.18
If x + 0 = 0 + x = x, which is rational number, then 0 is called (A) Identity for addition of rational numbers (B) Additive inverse of x (C) Multiplicative inverse of x (D) Reciprocal of x
Q.19
Solve for x : (A) 10
Q.20
3 2 5 – = 2 x 1 x 1 x 1 (B) 12 (C) 8 (D) 9
If two quantities p and q vary inversely with each other, then p (A) remains constant q (B) p + q remains constant (C) p × q remains constant (D) p – q remains constant 2
Q.21
Which of these is equal to (3)–3 –
( 81)
Q.27
A machine was sold at a gain of 10 %. Had it been sold at ` 80 less, the seller would have lost 10 %. What was the cost price of the machine ? (A) ` 350 (B) ` 400 (C) ` 450 (D) ` 520
Q.28
The areas of three adjacent faces of a cuboid are in the ratio 2 : 3 : 4 and its volume is 9000 cm3. The smallest side has a length …….. . (A) 10 cm (B) 15 cm (C) 20 cm (D) 30 cm
Q.29
Which of the following is NOT the net of a solid ?
25
2 / 3
( 64 ) (16) 1 / 4 1 (A) 54
Q.22
? (B) –
The value of
1 54
(C)
341 341 (D) – 270 270
x 2 ( y z) 2 y 2 ( x z) 2 + + ( x z) 2 y 2 ( x y) 2 z 2
z 2 ( x y) 2 is equal to ( y z) 2 x 2 (A) –1 Q.23
Q.24
(B) 0
(C) 1
(D) 1/2
The length of a rectangular field is 11 m more than its width. If the length is decreased by 12 m and the width is increased by 10 m, the area decrease by 24 m2. Find the original length and width of the field respectively. (A) 18 m, 7m (B) 9m, 5m (C) 7m, 5m (D) 12m , 5m In the given figure (not drawn to scale), ABCD is a trapezium with AB parallel to DC, ADE is an isosceles triangle with AD = AE. Find AEB and EAB respectively –
(A) 105º; 34º (C) 41º; 105º
(B) 105º; 41º (D) 105º; 54º
Q.25
Two dice are thrown simultaneously. Find the probability of getting a multiple of 4 as the product of numbers 1 7 1 5 (A) (B) (C) (D) 2 12 12 12
Q.26
The compound interest on a sum at 12 % p.a. for 2 years is ` 1590. What will be the simple interest on this sum ? (A) ` 1500 (B) ` 1540 (C) ` 1470 (D) ` 1530
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(A)
(B)
(C)
(D)
Q.30
Which of the following statements is true ? (i) Points (3, 4) and (4, 3) represent the same point on the graph. (ii) The y coordinate of any point laying on the x axis will be 0. (A) Only (i) (B) Only (ii) (C) both (i) and (ii) (D) Neither (i) nor (ii)
Q.31
Arrange the given steps in CORRECT order while constructing a rhombus ABCD in which diagonal AC = 6.6 cm and AB = 5 cm. (1) Join AB, BC, CD and DA. (2) Again with C as centre and radius equal to 5 cm draw two arcs one above the line segment AC a another below the line segment AC cutting first two arcs at point D and B respectively. (3) With A as centre and radius equal to 5 cm, draw an arc above the line segment AC and another below AC. (4) Draw AC = 6.6 cm (5) Then, ABCD is the required rhombus. (A) 1 2 3 4 5 (B) 2 3 4 1 5 (C) 3 2 1 4 5 (D) 4 3 2 1 5 3
Steps of construction (1) Draw AB = 4.3 cm (2) At B, draw XBA = 60º (3) With B as centre and radius equal to 5 cm, draw an arc cutting BX at C. (4) AT C draw YCB = 120º (5) With C as centre and diameter equal to 4.5 cm, draw an arc cutting CY at D (6) Join AD. ABCD is the required quadrilateral. (A) Step 3 (B) Step 4 (C) Step 5 (D) Both A and C
Direction (31 and 33) : The given pie chart shows the break-up of the cost of construction of a house. Assuming that the total cost of construction is ` 600000, answer the questions given below :
Q.32
Q.33
Q.34
The amount spent on cement is ………. . (A) ` 200000 (B) ` 160000 (C) ` 120000 (D) ` 100000 The amount spent on cement, steel and supervision is what percent of the total cost of construction ? (A) 40 % (B) 45 % (C) 50 % (D) 55 %
Q.37
A grocer buys 80 kg of rice at ` 13.50 per kg and mixes it with 120 kg of rice available at ` 16 per kg. At what rate per kg should he sell the mixture to gain 20 % on the whole ? (A) ` 12 (B) ` 18 (C) ` 15 (D) ` 16
Q.38
A cylinder has a diameter of 14 cm and the area of its curved surface is 220 sq. cm. The volume of the cylinder is ………… . (A) 770 cm3 (B) 1000 cm3 3 (C) 1540 cm (D) 6622 cm3
Q.39
The point (3, 4) is at a distance of ………… . (A) 3 units from both the axis (B) 4 units from both the axis (C) 4 units from the x axis and 3 units from y axis (D) 3 units from x axis and 4 units from y axis
Q.40
A rectangular block 6 cm × 12 cm × 15 cm is cut into exact number of equal cubes. The least possible number of cubes will be …………. . (A) 6 (B) 11 (C) 33 (D) 40
Q.41
In the given figure (not drawn to scale), ABCD is a parallelogram and GBEF is rectangle. Find x and y respectively. F E
The figure shows a solid.
Which of the following is a net of the given solid ? (A)
(C)
(B)
(D) None of these
y
Q.35
Q.36
Simplify 3xy (9xy + 14x) – 27x2y2 – 42x2y (A) 0 (B) 84x2y 2 2 (C) 54x y (D) 1 Identify the INCORRECT step while constructing a quadrilateral ABCD, given that AB = 4.3 cm, BC = 5 cm, CD = 4.5 cm, B = 60º and C = 120º.
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D 30º 90º 60º A G (A) 30º, 27º (C) 23º, 30º
90º 67º
C
x B (B) 30º, 23º (D) 30º, 21º 4
Q.42
Factorise : 4x2 + 12xy + 9y2 – 8x – 12y (A) (2x – 3y) (2x – 3y – 4) (B) (2x + 3y) (2x + 3y – 4) (C) (2x – 3y) (2x + 3y – 2) (D) (2x + 3y) (3x + 2y – 4)
Q.43
Megha plants 15376 mango trees in her garden and arranges them so that there are as many rows as there are mango trees in each row. The number of rows is (A) 124 (B) 126 (C) 134 (D) 144
Q.44
Q.45
Q.47
Quotient and remainder when x4 – 3x3y – 8xy3 + 8x2y2 + 8y4 is divided by x2 + 2y2 – xy is (A) x2 – 2xy + 4y2 and 0 (B) x2 – 4xy + 5y2 and 2 (C) x2 – 6xy + 4y2 and –2 (D) x2 + 2xy – 4y2 and 0
Q.48
The given question is followed by two statements. You have to study the question and the two statements given to decide which of the statement (s) is/are required to answer the questions. What is the are of the right-angled triangle ?
The perimeters of a circular field and a square field are equal. If the area of the square field is 12100 m2, the area of the circular field will be (A) 15500 m2 (B) 15400 m2 (C) 15200 m2 (D) 15300 m2
(I) Length of the hypotenuse is 10 cm. (II) Perimeter of triangle is four times its base. (A) Only I (B) Only II (C) Both I and II (D) Data inadequate
In the given graph, the coordinates of point x are Q.49
(A) (0, 2) (C) (3, 2)
(B) (2, 3) (D) (3, 0)
The measure of each angle is evenly divisible by 12.
ACHIEVERS SECTION Q.46
The following statements are true about triangle XYZ.
Find the area of the following polygon, if AL = 10 cm, AM = 20, AN = 50 cm, AO = 60 cm, AD = 90 cm, FM = 20 cm, EO = 60 cm, CN = 40 cm and BL = 30 cm.
The measure of angle Z is greater than the measure of angle Y.
The measure of angle Y s greater than te measure of angle X.
The measure of angle X is greater than
40º. Which of the following is true for all four statements for angles X, Y and Z ? (A) mX = 72º, mY = 60º, mZ = 84º (B) mX = 48º, mY = 60º, mZ = 84º (A) 337.5 cm2 (C) 5500 cm2
(B) 384 cm2 (D) 5050 cm2
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(C) mX = 50º, mY = 60º, mZ = 70º (D) mX = 48º, mY = 60º, mZ = 72º 5
Q.50
Match the columns : Column-I (i) A shopkeeper gives two successive discounts on an article marked ` 450. The first discount given is 10 %. If the customer pays ` 344.25 for the article, the second discount given is (ii) A fan is listed at ` 1500 and a discount of 20 % is offered on the list price. What additional discount must be offered to the customer to bring the net price to ` 1104 ? (iii) A retailer buys a sewing machines at a discount of 15 % and sells it for ` 1955. Thus, he makes a profit of 15 %. The discount he get is
Column-II (ii) ` 300
(b) 15 %
(c)
8%
(A) (i) – (a), (ii) – (b), (iii) – (c) (B) (i) – (b), (ii) – (c), (iii) – (a) (C) (i) – (c), (ii) – (a), (iii) – (b) (D) (i) – (b), (ii) – (a), (iii) – (c)
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