3 2 4 4 & m a r g o r P l o o h c S d e t a r g e t n I / m o o r s s a l C m r e T g n o L 6 1 m o 0 2 r f , s d t e n c e n d a u v t d S A 1 4 E 5 E 3 J . n i R I A d e i 0 f 0 i l 5 a p u o q T e n v a i 3 h 8 s 1 m , a R r I g A o 0 r 0 P 2 l l p A o T m n o r i f 5 s t 7 , n e R I d A t u 0 S 0 1 p o T n i 6 3 g a b s t n e d u t S E E J T I I F , 6 1 0 2 d e c n a v d A E E J n I
FIITJEE
JEE (Advanced), 2017 FULL TE TEST ST – IV Paper 1
Time Allotted: 3 Hours
Maximum Marks: 180 180
Please rea read d the instructions in structions caref carefully. ully. You are allotted 5 minutes specifica lly for t his purpose. You are not allowed allowed to leave the Examination Hall Ha ll before the e end nd of the test.
S E I INSTRUCTIONS R In st ru ct ion io n s E A. Gener al Inst S T S EB. Fill Sheet T Fill ing o f OMR Sheet A I DC. Marking Scheme For All Three Parts. N I L L A
1. 2. 3. 4. 5.
Attempt ALL the questions. Answers have to be marked on the OMR sheets. This question paper contains Three Parts. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. Each part is further divided into two sections: Section-A & Sectio n-C Rough spaces are provided for rough work work inside the question paper. No additional additional sheets will be provided for rough work. 6. Blank Papers, clip clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.
1. Ensure matching of OMR sheet with the Question Question paper before you start marking your answers on OMR sheet. 2. On the OMR sheet, darken the appropriate bubble with black pen for for each character of your Enrolment No. and write your Name, Test Centre and other details at the designated places. 3. OMR sheet contains contains alphabets, numerals & special special characters for marking marking answers.
(i)
Section-A (01 to 10) contains 10 multiple choice questions which have only one correct answer. Each question carries +2 marks for correct answer. There is no negative marking.
Section-A (11 to 15) contains 5 multiple choice questions which have one or more than one correct answer. Each question carries +4 marks for correct answer and – 1 mar k for wrong
answer.
(ii) Section-C (01 to 05) contains 5 Numerical based questions with answers as numerical value and each question carries +4 marks for correct answer and – 1 mar k for wrong answer.
Name of the Candidate Enrolment No.
I T J E E H o u se s e , 2 9 -A -A , K a l u FIITJEE L t d . , F I IT
S a r a i , S a r v a p r i y a V i h a r , Ne Ne w D e l h i -1 -1 1 0 0 1 6 , Ph Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. e. c o m
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Useful Data
PHYSICS Acceleration due to gravity
g = 10 m/s2
Planck constant
h = 6.6 1034 J-s
Charge of electron
e = 1.6 1019 C
Mass of electron
me = 9.1 1031 kg
Permittivity of free space
0 = 8.85 1012 C2/N-m2
Density of water
water = 103 kg/m3
Atmospheric pressure
Pa = 105 N/m2
Gas constant
R = 8.314 J K1 mol1
CHEMISTRY Gas Constant
R
Avogadro's Number N a Planck’s constant h 1 Faraday 1 calorie 1 amu 1 eV
= = = = = = = = = =
8.314 J K1 mol1 0.0821 Lit atm K1 mol1 1.987 2 Cal K1 mol1 6.023 1023 6.625 1034 Js 6.625 10 –27 ergs 96500 coulomb 4.2 joule 1.66 10 –27 kg 1.6 10 –19 J
Atomic No:
H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8, N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16, Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25, Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33, Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56, Pb=82, U=92. Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16, F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32, Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
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P h y s i i c s
PART – I SECTION – A Straight Objectiv e Type
This section contains 10 multiple choice questions numbered 1 to 10. Each question has 4 choices (A), (B), (C) and (D), out of which only ONE is correct. 1.
A cylindrical block of radius R, height h and density is floating in liquid of density 2 contained in a cylindrical container of radius 2R. Time period of small vertical oscillations of the block is 5h 3h (A) 2 (B) 6g 2g (C) 2
2.
h 2g
(D)
h 2g
A charge particle of mass m and charge q is suspended with the help of a string having breaking strength of 2mg and mass having
co-ordinates 1,
3 while the space carries a uniform magnetic
field in cylindrical region with centre at origin and radius R = 2 m. Maximum charge q if string does not break at the instant magnetic field start increasing with rate 0.5 Tesla per second is (A) 4mg (B) 8mg (C) 2mg (D) None
3.
R
m, q
1, 3
K . Taking potential at r = r 0 to r
In a certain region of space gravitational field is given by g
be V0 the potential at any general point is given by r r (A) V K ln V0 (B) V K ln V0 r 0 r 0
r 0 V0 r
(C) V K ln
r 0 V0 r
(D) V K ln Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
4 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
4.
A solid sphere of uniform density and radius R exerts a gravitational force F1 on a particle at P. A spherical cavity of R radius is now removed from the sphere. Now the same 2 sphere (with cavity) exerts a gravitational force F2 on the same F particle at P. Then, 1 is F2 9 7 1 (C) 2
2
2R
(B)
A cylinder of height h and radius R is made to move with constant velocity v at small angle with its flat bottom or flat top. In a polluted atmosphere having uniform and stagnant dust density . If dust particles stick to cylinder on striking them neglecting any change in size of cylinder, power to be delivered to cylinder to maintain its velocity is (A) 2v 2Rh (B) 2v 3Rh (C) 2v 3 Rhcos v 3 R2 sin
6.
P
R
7 9 4 (D) 3
(A)
5.
R
(D) None
Each of the pictures shows four objects tied together with rubber bands being pulled to right across a horizontal smooth surface by a horizontal force F. All the objects have same mass, all rubber bands are identical naturally and obey Hook’s law. Then which of the following possibility of the arrangement is most correct? x
x (A)
1
2
3
(B)
3
1
2
(C)
z
z
z
(D) Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
5 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
7.
A, B, C, D, E and F are conducting plates each of area A and any two consecutive plates with separation d. The net energy stored in system after the switch S i s closed is 30 AV 2 50 AV 2 (A) (B) 2d 12d AV 2 AV 2 (C) 0 (D) 0 2d d
8.
When the string of a sonometer wire of length L between the bridges vibrate in the first overtone, the amplitude of vibration is maximum at L L 3L (A) (B) and 2 4 4 L 3L 5L L 3L 5L 7L (C) , and (D) , , , 6 6 6 8 8 8 8
9.
A cubical container is filled with a liquid whose refractive index increases linearly from top to bottom. Which of the following represents the path of a ray of light inside the liquid? (A) (B)
(C)
10.
A
B
D
C
E
(D)
A convex lens of focal length 20 cm and another plano convex lens of focal length 40 cm are placed coaxially as shown in the diagram. The plano convex lens is silvered at plane surface. If final image of object O is formed on itself, then find the value of d. (A) 10 cm (B) 40 cm (C) 20 cm (D) 80 cm
10 cm
d
Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
6 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
Multiple Correct Choi ce Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE OR MORE THAN ONE is/are correct. 11.
A uniformly charged non-conducting ring is rotating with angular velocity 1 about its axis in gravity free space and a nearly horizontal but uniform magnetic field B is switched on, then after some time (A) Angular momentum of the ring must be parallel to its angular velocity (B) Magnitude of angular momentum may be more than mR 21 (C) Magnitude of angular momentum must be equal to mR 2 1 (D) Angular momentum must be coplanar with angular velocity
12.
A steel ball of mass 2m suffers one dimensional elastic collision with a row of three steel balls each of mass m. If ball of mass 2m has velocity v initially and the three balls with small separation were at rest. Then, after all possible collisions 2m v
m
m
1
2
m 3
(A) Ball 1 and ball of mass 2m would remain at rest 4v 0 (B) Ball 2 moves with velocity towards right 9 4v 0 (C) Ball 3 moves towards right with velocity 3 (D) Ball of mass 2m moves towards right with velocity one fourth that of ball 1 13.
A man is standing over a plank which is placed over a smooth horizontal surface. There is sufficient friction between feet of man and plank. Now, man starts running over the plank. Then, work done by friction (A) On man w.r.t. ground is negative (B) On man w.r.t. ground is positive (C) On plank w.r.t. ground is positive (D) On man w.r.t. plank is zero Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
7 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
14.
A liquid is filled upto height h in a rectangular vessel as shown in figure. Then, find correct option(s):
h
(A) Only if horizontal component of forces on left and right side of inclined faces will be equal and opposite (B) If horizontal component of forces on left and right side of i nclined faces are not equal (C) If still horizontal component of forces on the left and right inclined faces are equal and opposite (D) If base area is A, then force on bottom by liquid is more than ghA 15.
For an ideal gas at very high temperature, 3R (A) C V for a monoatomic gas 2 3R (B) C V for a monoatomic gas 2 5R (C) C V for a diatomic or linear poly atomic gas 2 5R (D) C V for a diatomic gas 2 Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
8 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
SECTION – C (One Integer Value Correct Type)
This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1.
2.
A non-conducting block of mass 1 kg and charge 1 C is connected to a nonconducting spring of force constant K 2 N/m and released. After one second from release a vertical uniform electric field 10 N/C is switched on. If time after switching on the electric field spring returns back to its natural length is T, then 1 find . T
K
A particle of charge q and mass m is projected with velocity 200 m/s at an angle of 60o with xaxis. At the instant speed of projectile becomes minimum a uniform magnetic field B0 kˆ is switched on. If time of flight of particle is T, then find
2 . (Given: m = 1 kg, q = 0.1 C, B = 1 T) T
3.
Figure shows two conducting thin concentric shells of radii r and 3r. The outer shell carries a charge q and the inner shell is neutral. The amount of charge that flows from inner shell to the earth after key K is closed is equal to nth part of charge of outer shell. Then the value of n is ………
4.
A vessel contains helium, which expands at constant pressure when 15 KJ of heat is supplied to it. What will be the variation in internal energy of gas in KJ?
5.
Two identical sinusoidal waves travel in opposite direction in a 15 m long wire and produce a standing wave in the wire with nodes at ends. If speed of wave is 12 m/s and there are 6 nodes in standing wave, find the frequency (in Hz) of wave.
Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
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C h e m m i s t t r y
PART – II SECTION – A Straight Objectiv e Type
This section contains 10 multiple choice questions numbered 1 to 10. Each question has 4 choices (A), (B), (C) and (D), out of which only ONE is correct. 1.
Which of the following process is used to remove temporary as well as permanent hardness of water? (A) only boiling (B) adding lime & boiling (C) adding Ca(OH)2 (D) adding Na2CO3
2.
When 10 gm mixture of KI and Fe2(SO4)3 is treated with 200 cc HCl, gives a solution which consumes 40 ml
N
10
Na2S2O3 solution. Then the correct statement is/are
(A) Equivalent weight of iodine in the reaction is
M
2
(B) Percentage of KI in the mixture is 66.4% (C) Sodium thiosulphate is converted to Na4S4O6 (D) Percentage of Fe2(SO4)3 is 66.4% 3.
Both AgCNS and AgBr are simultaneously dissolved in water. Ksp(AgBr) 5 × 10-13; Ksp(AgCNS) = 8.5 x 10-12. The concentration of Ag+ in final solution will be (A) 4 × 10 –7 M (B) 2 × 10 –7 M (C) 3 × 10 –6 M (D) 6.2 × 10 –7 M
4.
Compare basic strength of following compounds Aniline o-toluidine m-toluidine p-toluidine o-anisidine 1 2 3 4 5 (A) 1 > 2 > 3 > 4 > 5 (B) 2 > 5 > 3 > 4 > 1 (C) 4 > 3 > 1 > 5 > 2 (D) None of these Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
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5.
6.
7.
Na S O
H2 O 2 2 3 AgNO3 A B White
Black
PPt
PPt
Black PPt is (A) Na3 Ag(S2O3 )2
(B) Ag2S4 O6
(C) Ag2O
(D) Ag2 S
When glucose is heated with conc. H2SO4, charring occurs, it is due to (A) Reduction of glucose (B) Oxidation of glucose (C) Dehydration of glucose (D) Mutarotation of glucose 4 IUPAC name of Fe O2 CN4 Cl is
(A) chloridortetracyanodioxoferrate (II) ion (B) chloridortetracyanoperoxoferrate (II) ion (C) chloridortetracyanosuperoxoferrate (II) ion (D) tetracyanochloridosuperoxoferrate (II) ion 8.
The acid ligand which uses its d-orbital during synergic bonding in its complex compound is (A) CN (B) PR3 (C) NO (D) N2
9.
Efficiency of a cell with cell reaction under standard condition is 85%. 2 2 A (s) B(aq) A (aq) B(s) ; 285kJ The E0cell is: (A) 1.26 V (C) 2.96 V
(B) 1.34 V (D) 2.07 V Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
11 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
10. DMSO C2 H5 CH2 Cl A Py,
_
B (has two C atoms per molecule)
Cl N+ H
Which is true? (A) A gives Lucas test (B) A does not give Schiff’s test (C) B can be used in reductive ozonolysis of alkenes (D) A gives smell of burning S on combustion Multiple Correct Choi ce Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE OR MORE THAN ONE is/are correct. 11.
Me C
Me
C
Product H2O2
H
Me
N2H4
What is/are not the product of above reaction? NH2 OH (A)
(B)
NH2 NH2
H (C)
H
H
C
C
H (D)
H 12.
OH
OH
H
Which of the following crystal system does/do not have more than one Bravais lattice? (A) Triclinic (B) Monoclinic (C) Rhombohedral (D) hexagonal Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
12 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
13.
Which is/are white or not coloured? (A) Co(SCN)4
2
(B) Fe(H2 O)5 SCN
(C) CuSO4 .5H2O 14.
2
(D) anhyd CuSO4
Which is/are true for the following reaction? H 5 C2
O
C 2H 5
O2 hv
A + B Fe2+ KCNS red color
(A) Compounds A & B are explosives (B) If compounds A & B are present in ether, then prior to its use, A & B must be removed from ether (C) Compounds A & B can not be removed by adding Fe 3+ (D) When compounds A & B are treated with Fe 2+ followed by KCNS, no redox reaction is involved 15.
NaNO2 HCl converts an amino acid into hydroxyl acid with retention of configuration. Estimation of N2 gas evolved in the reaction is the basis of van slyke estimation of amino acids, which of the following can be analysed by this method? (A) Cysteine (B) Proline (C) Histidine (D) Valine Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
13 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
SECTION – C (One Integer Value Correct Type)
This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1.
How many moles I 2 is consumed per mole of isopropanol? H3C
CH
CH3 + I 2 + OH CHI3 CH3 COO I H2 O
OH 2.
How many octahedral voids per unit cell of BCC are present?
3.
The coagulation of 20 ml standard gold sol is completely prevented by addition of 0.04 gm starch solution to it. The gold number of starch solution is 2 x 10x. Find x.
4.
1 O2 (g) H2O ( l) (Let Cp = 32 J/K and H at 27oC = –28.58 KJ/mol) reaction 2 is carried out at 87oC in a fuel cell with 90% efficiency. The electrical energy produced is 3 x a KJ/mol. Find a (to nearest integer). (Let Cp remains same in this temperature range) If H2 (g) +
Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
14 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
5.
In how many of the following reactions end product is meso? H (a)
D
Br
D
Br
i) NaI, acetone ii) Baeyer's reagent
H H3C
H m-CPBA
(b) H
CH3
C 2H 5
C2 H 5
H /HO
(c)
2
H O
H
C 2 H5 (d)
H
Cl
H
Cl
C 2 H5 H3C
i) NaI, acetone ii) Baeyer's reagent
H i) MeCO H ii) H / H O 3
(e)
2
H
C2 H5
i) OsO ii) NaHSO
(f)
4
3
H (g)
H3C Me
H C
C
i) H2 / Ni2B CH3 ii) cold dil. alk. KMnO 4
Et Br in CCl
(h)
2
4
D
Et Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
15 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
M a t h e m m a t i c s
PART – III SECTION – A Straight Objectiv e Type
This section contains 10 multiple choice qu estions numbered 1 to 10. Each question has 4 choices (A), (B), (C) and (D), out of which only ONE is correct. 4
1.
If I f tan2x cos x dx and J 0
(A)
I
f cot 2x sin x dx , where f x f x , then J is equal to 0
2
(C) 2 2
2.
If A aij
1
(B) (D)
2 2
, B bij
2 2
such that aij
f x
2 1 2 2
2i j 2
and b
ij
f x
2 i j 1
and
2 1 1 f 1 1 x f x f x 4 x 2 1 x T , then f t dt is always equal to A B 1 1 1 1 f 1 x f 1 2 2 f x x x x (A) f 1 (B) f 1 1 (C) f 1 1 (D) None of these 3.
ˆ , g x tan x iˆ sin 3x ˆj cos 4 x kˆ and If f x cos x iˆ sin x ˆj cos 2 x k h x cos 3 x iˆ sin 5 x ˆj cos 6 x kˆ are three variable vectors given, then
f x , g x , h x dx , where [.] denotes scalar triple product, is belonging to 0
(A) (C)
1, 0 , 1 1,
(B)
0, 1
(D) (–1, 1) Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
16 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
4.
If a1
a1 2iˆ 5 ˆj and
aiˆ bjˆ ,
a2
1 a1.a1
1 a1.a2
a3
a1 2iˆ 5 ˆj , then
1 a1.a3
1 a2 .a2 1 a2 .a2 1 a2.a3 is equal to
1 a3 .a1
1 a3 .a2 1 a3.a3
(A) 0 (C) 40
5.
2
0
(A)
(B) 20 (D) 80
sin 3 x dx 1 tan x 1 2 1
1
ln
2 2 1 ln (C) 2 2 6.
2 1
(B)
2 1
2
1 2 2
ln
2 1
(D) None of these
If f x sin x and g x f ' x , then maximum value of g n for n I is (A) 0 (C)
7.
1
(B) 1 (D) 2
If f x tan x tan x tan 2x and g n 2
(A) 0 (C) tan1
n n
f 2 , then g 2013 tan 2 is equal to n
2014
n0
(B) tan1 (D) None of these Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
17 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
8.
The value of product sin tan
2
2
2
tan tan
(A) 1 for (C)
9.
sin
2
tan
2
23
tan
3
2
22
tan
23
sin
.......... tan
2
2n
tan
(B) 1 for
2
1 for 2 4
(D)
2
2n
2n 1
tan
......... upto is
2n
4
for
4
x 1 x R & 1 & 1 is a self – inverse function such that x f(4) f(12) 1 f , then “” is equal to 4 12 1
If f(x)
(A) 2 (C) 8 10.
(B) 4 (D) 16
If f(x) x 1
&
h1(x) h1(1) x 1 x 1
g1(x) x3 x 1, let gof(x) = h(x), then It
(A) 2 (C) 1
(B) 4 (D) 8 Multiple Correct Choi ce Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE OR MORE THAN ONE is/are correct. 2
11.
If
2 x 2 x 1 x
1 x 3
1
(A) p m (C)
p 2 1 1 cos , p, q I , HCF (p, q) = 1, then m 6 q 3 2 (B) p m 2 (D) pq 4m
dx ln
1 q m 1 2
Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
18 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
12.
13.
If a singular matrix A aij
a22 a21 2a12
(B) a11
(C)
(D)
If logk a a and logk b b for exactly two distinct positive real numbers a and b, then k can’t be equal to 1 2e
(C) e
(B) e
1 2
(D) e
2 e 1 3
cos x 1 cos 2 x 1 sin2 x sin2x sin2x , then If x sin x 2 sin x 2 sin2x 22 cos 2x 2
(A)
2
x dx 4
(B)
0
(C)
x dx 4 0
x dx 4
(D)
2
15.
2a12 a11 2 a21
(A) a11
(A) e
14.
22
1 1 , then 2 1
always commute with B
x dx 4
2
If curve A z :| z 3 | | z 3 | 8 & B z :| z 3 | K , K R touches the curve ‘A’ internally, and given another curve C z | z 3 | | z 3 | 4, then; (A) A & C intersect orthogonally & k = 1 (B) K = 1 (C) K = 3/2 (D) B touches also C internally Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m
19 AITS-FT-IV-(Paper-1)-PCM-JEE(Adv anced)/17
SECTION – C (One Integer Value Correct Type)
This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 2
1.
If I
1
2.
x 3 3 x 2
ln x 1
3 x 5 dx , then ln 2 x 2 3
dx and J
aiˆ bjˆ ckˆ and
Position vector of a point A is
e I J equals ………..
ˆ and p another point B is piˆ qjˆ rk
2
a2 b2 c 2
q 2 r 2 9 .
origin. If AQ is perpendicular to angle bisector of
Given
4;
and position vector of
AOB 2cos 1
1 5
, where O is
AOB i.e. line OQD where D lies on AB, then
value of 25 QD = ?
3.
If
3 x 2 1
f x , where
x 2 3 x 2 1 dx x
0
4
x
2
4
x
2
f x is a constant function in 0 x
2 , then minimum value of
is ………
adj A
4
4.
If adj adj adj A
5.
If AB BA I such that A aij
, then number of entries in diagonal of A is ……..
2 2
, B bij
are co prime natural numbers, then a21 a12
2 2
, aii
bii ,
a12
b12 ,
a21
b21 and
aij
……….
Space for rough w ork
FIITJEE L t d . , F I IT J E E H o u se, 2 9 -A , K a l u
S a r a i , S a r v a p r i y a V i h a r , New D e l h i -1 1 0 0 1 6 , Ph 4 6 1 0 6 0 0 0 , 2 6 5 6 9 4 9 3 , F a x 2 6 5 1 3 9 4 2 w e b s i t e : w w w . f i i t j e e. c o m