qp. code : xxxx.x physics, chemistry & mathematics - fiitjee … paper class 12.pdf · 2017. 9....
TRANSCRIPT
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 1
_______________________________________________________________________________________________________________________________________________
FIITJEE Limited, DURGAPUR CENTRE: A-3, Nandalal Bithi, City Centre, Durgapur, West Bengal - 713216. Ph : 03432542642, 03436450238, 9679997745 National Admissions Office : FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph-46106000, 26569493, Fax 26513942
FIITJEE - JEE (Mains)
QP. Code : xxxx.x
PHYSICS, CHEMISTRY & MATHEMATICS
Time Allotted: 3 Hours
Maximum Marks: 360
Do not open this Test Booklet until you are asked to do so. Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
Important Instructions:
1. Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is
strictly prohibited.
2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer
Sheet and fill in the particulars carefully.
3. The test is of 3 hours duration.
4. The Test Booklet consists of 90 questions. The maximum marks are 360.
5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30
questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.
6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. ¼ (one
fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will
be made if no response is indicated for an item in the answer sheet.
7. There is only one correct response for each question. Filling up more than one response in any question will be treated
as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above.
8. Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side-1 and Side-2 of the Answer
Sheet. Use of pencil is strictly prohibited.
9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any
electronic device, etc. except the Admit Card inside the examination hall / room.
10. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room / Hall.
However, the candidates are allowed to take away this Test Booklet with them.
11. Do not fold or make any stray marks on the Answer Sheet.
Name of the Candidate (in Capital Letters) :_____________________________________
Enrolment Number :_________________________________________________________
Batch :________________________ Date of Examination : ________________________
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 2
_______________________________________________________________________________________________________________________________________________
FIITJEE Limited, DURGAPUR CENTRE: A-3, Nandalal Bithi, City Centre, Durgapur, West Bengal - 713216. Ph : 03432542642, 03436450238, 9679997745 National Admissions Office : FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph-46106000, 26569493, Fax 26513942
Section 1 (Part A) PHYSICS
1. Two cells of emf’s approximately 5V and 10V are to be accurately compared using a potentiometer of length 400cm. (a) The battery that runs the potentiometer should have voltage of 8V (b) The battery of potentiometer can have a voltage of 15V and R adjusted so that the potential drop across the wire slightly exceeds 10V. (c) The first portion of 50 cm of wire itself should have a potential drop of 10V (d) Potentiometer is usually used for comparing resistances and not voltages.
2. A metal rod of Length 10 cm and a rectangular cross-section of 1 cm × 1
2cm is connected to
a battery across opposite faces. The resistance will be
(a) maximum when the battery is connected across 1 cm × 1
2 cm faces.
(b) maximum when the battery is connected across 10 cm × 1 cm faces.
(c) maximum when the battery is connected across 10 cm × 1
2 cm faces.
(d) same irrespective of the three faces.
3. Which of the following characteristics of electrons determines the current in a conductor? (a) Drift velocity alone (b) Thermal velocity alone (c) Both drift velocity and thermal velocity (d) Neither drift nor thermal velocity.
4. A capacitor of 4F is connected as shown in the circuit.
The internal resistance of the battery is 0.5. The amount of charge on the capacitor plates will be
(a) 0 (b) 4C (c) 16C (d) 8C
5. The electrostatic potential on the surface of a charged conducting sphere is 100V. Two
statements are made in this regards S1: At any point inside the sphere, electric intensity is zero. S2: At any point inside the sphere, the electrostatic potential is 100V. Which of the following is a correct statement? (a) S1 is true but S2 is false (b) Both S1 & S2 are false (c) S1 is true, S2 is also true and S1 is the cause of S2 (d) S1 is true, S2 is also true but the statements are independent.
6. Equipotentials at a great distance from a collection of charges whose total sum is not zero
are approximately (a) spheres (b) planes (c) paraboloids (d) ellipsoids.
7. A parallel plate capacitor is made of two dielectric blocks
in series One of the blocks has thickness d1 and dielectric constant k1 and the other has thickness d2 and dielectric constant k2 as shown in figure. This arrangement can be thought as a dielectric slab of thickness d(=d1+d2) and effective dielectric constant k. The k is
(a) 1 1 2 2
1 2
k d k d
d d
(b) 1 1 2 2
1 2
k d k d
k k
(c)
1 2 1 2
1 1 2 2
k k d d
k d k d
(d) 1 2
1 2
2k k
k k
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 3
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8.
Five charges q1, q2, q3, q4 and q5 are fixed at their positions as shown in the figure. S is a Gaussian
surface. The Gauss’s law is given by 0s
qE.ds
. Which
of the following statements is correct? (a) E on the LHS of the above equation will have a contribution from q1, q5 and q3 while q on the RHS will have a contribution from q2 and q4 only. (b) E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q2 and q4 only. (c) E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q1, q3 and q5 only. (d) Both E on the LHS and q on the RHS will have contributions from q2 and q4 only.
9. A point charge +q, is placed at a distance d from an isolated conducting plane. The field at a
point P on the plane is (a) directed perpendicular to the plane and away from the plane (b)directed perpendicular to the plane but towards the plane. (c) directed radially away from the point charge. (d) directed radially towards the point charge.
10. Figure shows electric field lines in which an electric dipole
moment p is placed as shown. Which of the following statement is correct? (a) The dipole will not experience any force. (b) The dipole will experience a force towards right. (c) The dipole will experience a force towards left. (d) The dipole will experience a force upwards.
11. A particle of mass m and charge q enters a region of
magnetic field (as shown) with speed v. There is a region in which the magnetic field is absent, as shown. The particle after entering the region collides elastically with a rigid wall. Time after which the velocity of particle becomes anti parallel to its initial velocity is
(a) m
42qB
(b) m
2qB
(c) m
24qB
(d) m
2 34qB
12. A current carrying circular loop of radius R is placed in the x-y plane with centre at the
origin. Half of the loop with x>0 is now bent so that it now lies in the y-z plane. (a) The magnitude of magnetic moment now diminishes. (b) The magnetic moment does not charge. (c) The magnitude of B at (0.0.z),x>>R increases. (d) The magnitude of B at (0.0.z),x>>R unchanged.
13. A circular current loop of magnetic moment M is in an arbitrary orientation in an
external magnetic field B. The work done to rotate the loop by 30° about an axis perpendicular to its plane is
(a) MB (b) MB
32
(c) MB
2 (d) zero.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 4
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14. A toroid of ‘n’ turns, mean radius R and cross-sectional radius ‘a’ carries current I. It is
placed on a horizontal table taken as x-y plane. Its magnetic moment M (a) is non-zero and points in the z-direction by symmetry.
(b) points along the axis of the tortoid m M
(c) is zero, otherwise there would be a field falling as 3
1
r at large distances outside the
toroid. (d) is pointing radially outwards.
15. A block of mass m and charge q is connected to a point O with help of an inextensible
string. The system is on a horizontal table. An electric field is switched on in direction perpendicular to string. What will be tension in string when it becomes parallel to electric field?
(a)qE
2 (b)3qE (c)
qE
(d).
3qE
5
16. A loop carrying current I lies in the x-y plane as shown in
the figure. The unit vector k is coming out of the plane of the paper. The magnetic moment of the current loop is
(A) 2 ˆa I k (B) 2 ˆ1 a I k2
(C) 2 ˆ1 a I k2
(D) 2 ˆ(2 1)a I k
y
x
a
a
I
17.
The figure shows two infinite semi-cylindrical shells: shell-1 and shell-2. Shell-1 carries current i1 in inward direction normal to the plane of paper, while shell-2 carries same current i1, in opposite direction. A long straight conductor lying along the common axis of the shells is carrying current i2 in direction same as that of current in shell-1.
force per unit length on the wire is
(a) zero (b) 0 1 2i i
2 r
(c) 0 1 22 i i
r
(d) 0 1 2
2
2 i i
r
18. A meter bridge is set up as shown, to determine an
unknown resistance ‘X’ using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of ‘X’ is (a)10.2 ohm (b) 10.6 ohm (c) 10.8 ohm (d) 11.1 ohm
B
10
A
X
19. A parallel plate capacitor C with plates of unit area and
separation d is filled with a liquid of dielectric constant K =
2. The level of liquid is d
3 initially. Suppose the liquid level
decreases at a constant speed V, the time constant as a
C
d R d
3
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 5
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function of time t is
(a) 06 R
5d 3Vt
(b) 0
2 2 2
(15d 9Vt) R
2d 3dVt 9V t
(c) 06 R
5d 3Vt
(d) 0
2 2 2
(15d 9Vt) R
2d 3dVt 9V t
20. A wire of length L and 3 identical cells of negligible internal resistance are connected in
series. Due to the current, the temperature of the wire is raised by T in a time t. A number N of similar cells is now connected in series with a wire of the same material and cross
section but of length 2L. The temperature of the wire is raised by the same amount T in the same time t. The value of N is
(A) 4 (B) 6 (C) 8 (D) 9
21.
The resultant capacitance of given circuit is
(a) 3C (b) 2C (c) C (d) 3
C
22. A and B two concentric spheres. If A is given a charge Q
while B is earthed as shown in figure: (a) the charge density of A and B are same (b) the field inside and outside A is zero (c) the field between A and B is not zero (d) the field inside and outside B is zero.
23. n small drops of the same size are charged to V volt each. If they coalesce to form a single large drop, then its potential will be (a) (V/n) (b) Vn (c) Vn1/3 (d) Vn2/3
24. An electric field is given by NE yi x jC
. The work done by the E in moving 1 C charge
from Ar 2i 2j m
to Br 4i j m
is
(a) +4 J (b) –4 J (c) +8 J (d) zero 25. In a certain region of space, the potential field depends on x and y coordinates as V=(x2–y2) .
The corresponding electric field lines in x–y plane are correctly represented by:
26. In a permanent magnet at room temperature (a) magnetic moment of each molecule is zero. (b) the individual molecules have non-zero magnetic moments which are all perfectly
aligned. (c) domains are partially aligned.
(d) domains are all perfectly aligned. 27. A paramagnetic sample shows a net magnetization of 8 Am–1 when placed in an external
magnetic field of 0.6T at a temperature of 4K. When the same sample is placed in an external magnetic field of 0.2T at a temperature of 16K, the magnetization will be
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 6
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(a) 32
3Am–1 (b)
2
3Am–1 (c) 6Am–1 (d) 2.4Am–1.
28. Find charge on capacitor in steady state in given circuit
(a) 9.6 C (b) 7.2C (c) 4.8C (d) 2.4C.
29. Plates of a parallel plate capacitor C have charges CV
and 3 CV on its plates. If switch is closed at t=0. Then initial rate at which heat energy is produced in resistance R is
(a) 2V
R (b)
24V
R
(c)29V
R (d)
216V
R
30. Two wires are of same length and same area of cross-section. If first wire has resistivity
1 and temperature coefficient of resistance 1 but second wire has resistivity 2 and
temperature coefficient of resistance 2. Their series equivalent resistance is independent of small temperature changes. Then
(a) 1+2=0 (b) 11=22 (c) 11+22=0 (d) 12+21=0
Section 2 (Part A) CHEMISTRY 1. Propanone and propanal are:
(a) geometrical isomers (b) chain isomers
(c) functional isomers (d) position isomers
2. Which type of isomerism is shown by diethyl ether and methyl propyl ether?
(a) chain (b) functional (c) metamerism (d) position
3. Which of the following is chiral carbon ?
(a) CH4 (b) CH3I (c) CH2Cl2 (d) CHIBrCl
4. Which of the following is optically active ?
(a) Butane (b) 4-methyl heptanes
(c) 3-methyl heptane (d) 2-methyl heptane
5. The correct statement about the compounds (A), (B) and (C) is
H C OH
COOCH3
H C OH
COOH
(A)
H C OH
COOH
H C OH
COOCH 3
(B)
H C OH
COOH
OH C H
COOCH 3
(C) (a) A and B are identical (b) A and B are diastereomers
(c) A and C are enantiomers (d) A and B are enantiomers.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 7
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6. Which of the following pairs of structures represent enantiomers ?
(a) OH C H
COOH
CH3
and H C OH
CH3
COOH
(b) CH3 C OH
H
COOH
and HO C CH3
COOH
H
(c) H C CH3
COOH
OH
and CH3 C H
OH
COOH
(d) HOOC C OH
CH3
H
and HOOC C H
OH
CH3
7. The most stable conformer of 2, 3-dimethylbutane is
(a)
CH3
CH3H
CH3
CH3H
(b)
CH3
HCH3CH3
CH3H
(c)
H
CH3CH3
CH3
CH3H
(d)
CH3 CH3
HCH3
CH3
H
8. Which of the following carbocation is most stable?
CH2+
(a)
CH2
+
NO2
(b)
CH2
+
OH
(c)
CH2
+
OH
(d)
9. Which of the following shows maximum enol content
O(a)
(b) O
(c) O
(d) O
10. The compound, whose stereochemical formula is written below, exhibits x-geometrical
isomers and y-optical isomers.
CH3
Br
H
OH
H
CH3
(a) 4 and 4 (b) 2 and 2 (c) 2 and 4 (d) 4 and 2
11. An organic compound, C3H6O does not give a precipitate with 2, 4-dinitrophenylhydrazine
reagent and does not react with metallic sodium. It could be
(a) CH3 – CH2 – CHO (b) CH2 = CH – CH2OH
(c) CH3 – CO – CH3 (d) CH2 = CH – O – CH3
22. CH3 CH2 Cl
CH3
OH Ag+ (aq.)
?
The major product formed is
CH3 C CH2 CH3
O
(a)
CH3 C CH2 OH
OH
CH3
(b)
CH3 C
CH3
H O
(c)
CH3 C CH2
CH3
HO
CH3(d)
12.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 8
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13. Which products of the following reactions give iodoform test ?
(a) Ph – C CH 2
2
/?
H O H
Hg
(b) 4
||/
3 2
OPd BaSOCH C Cl H
(i) CH3MgBr(c)
CN
(ii) H3O+ ?
(d) All of them
14. In the given reaction:
C CH2CH3 CH2 CH2 CH2 Cl
OCH3MgBr
(P)
(P) will be :
(a)O
CH3
CH3
(b)
O
CH3
CH3
(c) CH3 C
MgBr
CH3
CH2 CH2 CH2 CH2Cl
(d) CH3 C
OH
CH3
CH2 CH2 CH2 CH2 Cl
15. Which of the following is not a resonating form of benzaldehyde ?
C OH
(a)
C O+
H
(b)
C OH
(c)+
C OH
(d)
+
16. How will you convert butan-2-one to propanoic acid ? (a) Tollen’s reagent (b) Fehling solution (c) NaOH/I2/H+ (d) NaOH/NaI/H+
27.CH3
OC2H5
O
O
(A)
(B)
NaBH4
LiAlH4
A & B are respectively
(a)
CH3
OC2H5
O
OH
and CH3
OH
OH
+ C2H5OH
(b)
CH3
OH
OH
CH3
OC2H5
O
OH
and
(c)
CH3
OC2H5
OH
OH
andCH3
OC2H5
O
OH
(d) None
17.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 9
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18. Ph – C C – CH3 2+ +Hg /HA, A is:
(a) Ph
CH3
O
(b)
Ph
CH3
O
(c)Ph
CH3
OH
(d)Ph
CH3
OH
19. When m-chloro benzaldehyde is treated with 50% KOH solution; the product(s) obtained is
(are)
(a)
OH
COO
+
OH
CH2OH
(b)
Cl
COO
+
Cl
CH2OH
(c)
Cl
CH CH
OH OH
OH
(d)
OH
CH CH
OH OH
OH
30.
MgBr
(i) CO2
(ii) H3+O
P
In the above reaction, product P is CHO
(a)
COOH
(b)
(c)
OH
(d) C6H5CC6H5
O
21. Which of the following does not give canizarro reaction :
CHO(a)
CH2CHO(b)
CHOCH3(c)
CHOO2N(d)
22. The product(s) obtained via oxymercuration (HgSO4 + H2SO4) of 1-butyne would be
(a) CH3CH2COCH3 (b) CH3CH2CH2CHO
(c) CH3CH2CHO + HCHO (d) CH3CH2COOH + HCOOH
23. In the Cannizaro’s reacting given below:
2Ph – CHO OH Ph - CH2OH + PhCO2
The slowest step is:
(a) the attack of OH at the carbonyl group
(b) the transfer of hydride to the carbonyl group
(c) the abstraction of proton from the carboxylic acid
(d) the deprotonation of Ph-CH2OH
24. Which of the following will react with water to form stable hydrate
(a) HCOOH (b) Cl3C.CHO (c) CCl4 (d) CH3CHO
20.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 10
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25. Compound A (molecular formula C3H8O) is treated with acidified potassium dichromate to form a product B (molecular formula C3H6O). B forms a shining silver mirror on warming with ammonical silver nitrate. B when treated with an aqueous solution of H2NCONHNH2 and sodium acetate gives a product C. Identify the structure of C:
(a) CH3CH2CH = N.NHCONH2 (b)
3
3 2|
CH
CH C N.NHCONH
(c)
3
3 2|
CH
CH C N.CONHNH (d) CH3CH2CH = N.CONHNH2
26. Which of the following is inert towards SN-1 reaction ? (a) Ethyl chloride (b) Isopropyl chloride
(c)
Cl (d)
Cl
BCOO
N2
+30.
The product (B) is
(a)
(b)
(c)
(d)
C N
+Ether
AH3O
+
B.
MgBr
31.
C
O
(a)
C
N- MgBr
(b)
C
N - H
(c)
C
N- OH
(d)
29. At isoelectric point pH of the compound below is
(a) 3.22 (b) 6.96 (c) 8.05 (d) 5.93
27.
28.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 11
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NH2
CH3OH
NaNO2 + HCl
?33.
The product formed is
(a)
O
CH3OH
(b)
OCH3
(c)
COOH
CH2NH2
(d)
CH3 OH
O
Section 3 (Part A) MATHEMATICS
1. Which of the following have same graph.
. 1 a b
Ix y
II. bx+ ay = xy .
bxIII y
x a
&a I II only &b II III only
&c I III only d nonehavethesame graph
2. The function : 1,1 0,f R , defined as 2 3 2 1
cos1 1
x x x x xf x
x x
, is
a even function b onto function c periodic function d invertible
3. The range of cos
;11
xf x where Fractional part function, is
[0,1 11] [10 11,1)a [0,1 11) [10 11,1)b [0,1 11] (10 11,1)c [0,1 11) (10 11,1)d
4. Which of the following is an identical function
2
2; a f x x g x x 2
sin sin 2; g
21 tan
x xb f x x
x
1 1 ;c f x sin x cos x 1 1g x tan x cot x 2 4 ;d f x cos x sin x 4 2g x cos x sin x
5. If 0; 0, ;g x f x x then which of the following is true
0
x
a g t f t dt is decreasing 0
1 1
x
b g t f t dt is decreasing
1
0
x
c g t f t dt is decreasing 1
0
1 1
x
d g t f t dt is increasing
30.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 12
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6. tanx , ,
tan 2 tan, ,
1 tanx tan 2 x
when xis rational
f x x xwhen xis irrational
Then in , , the number of points where f x is discontinuous is
0a 2b 4c 6d
7. If 2d
f ax xdx
, then ' f bx
2x
ab
2 2
3
b xb
a
2 2
2
b xc
a
2 2b xd
a
8.
2
3
0
sin3 ln . 1 1 2
lim. sin . 1 cos
x
xx x x x
x
x x x x
0a 2b 4c 6d
9. Let 2
sin sinlim sinxt x
x tf
x t
. Then the range of f x is
( ,1]a 1,0b 0,1c [ 1, ) d
10. The value of
2 29 11 1 4 13 3limx
x x x x
x
5a 3b 3c 5d
11. Let R be a relation on the set A = {1,2,3,4,…..,2013}. If { (1,2), (2,3), (4,5), (6,6) } R and n be
the number of ordered pairs in R, then the least possible value of n, for R to be symmetric
and transitive but not reflexive is
(a) 16 (b) 14 (c) 12 (d) 10
12. Let 1
0
xe dx a – ln a, where [.] → Greatest Integer Function then ' 'a equal to a N
1a 2b 3c 4d
13. Let 5 4 3 2
15 4 3 2 1
x x x x xf x then value of 1 1
df x at x is
dx
1a 2b 3c d not exist
14. Let 1
1 11 & 1
x x
f x g xx x
; 0,x . Then which of the following is increasing
function for positive x
a g x f x b g f x c g f g x d f f g x
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 13
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15. Let y =f(x) be a continuous function with f(0)=0, say. Given below is the graph of its derivative
function y= 'f x . Let , , &a b c d denotes the number of points of maximum, minimum,
inflexion & critical points of y=f(x) respectively in (0,11). Then
3a a 4b b 5c c 7d d
16. Let f : [1,5] →[2,4] be a bijective function such that 1df (x) 0 x [1,5]
dx
, then
5 4
1
1 2
f(x)dx f (x)dx
(a) 12 (b) 16 (c) 18 (d) 24
17. Let 2
, 0& 0 0; ,x
f x x f a b Rx
such that a b then the value of b
a
f x dx is
(a) a–b (b) a b (c) b a (d) b–a
18. If
441 1 6
2 2
1 0
1
1 1
x x x
dx A and dx Bx x
then value of 3 12A B , where Greatest Integer
function.
0a 1b 1c d noneof these
19. Let f x be a quadratic polynomial where 1 0f . Then
1
0
16 0 4
2
1
f x dx f f
f
1a 2b 3c 4d
20. Consider the function 2 27 12 . 4 3 . 2 . 5 f x x x x x x x . Then Rolle’s Theorem for
f(x) is NOT applicable in the interval
(a) [1,3] (b) [2,4] (c) [3,5] d noneof these
21. The range of the interval f: 1,3 →R under the mapping 34 12f x x x is
(a) [–72,8] (b) [–8,72] (c) [–8,8] (d) [8,72]
22. Let f(x+T)=f(x), where T>0, The minimum possible value of T for
f(x) = sin2x – cot2x + sec2x.cosec2x – tan2x + cos2x.
(a)1 (b) /2 (c) (d) None of these.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 14
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23. If 2
7 8 71 2
a
x xx x x dx c
a
then value of ' 'a is
2a 4b 6c 8d
24. The value of
11
210
tan1
1 2 2tan
2
xdx
x
x x =
(a) 0 (b) 1/2 (c) 1 2d
25. If 2
3
1
2 4
x
x
f x t t dt
then ' 1f has the value
4a 8b 12c 16d
26. Let f be the function such that 216
1; 0.1
f x x xx
Then 8f equals
(a) 1 (b) 7 (c) 73 (d) 91
27. A continuous real function ( )f x satisfiy 4 2f x f x x R . If 1
0
2 f x dx , then 4
1
f x dx
a 10 b 12 c 14 d 16
28. The function :f R R defined as 12 tan2
xf x e
is
a odd b even c onto &d manyone into
29. The integral values of n, the value of 2 2lim 1 1
n
n n n n , where [.] → Greatest
Integer Function
1
2a 1b 2c 3d
30. Let 3100 99f x x x then set of values of x satisfying the inequality
3
100 99 100 1f x f x f x is
99,0 99, a , 1 0,1b 1,0 1,c 100,0 100,d
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 15
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FIITJEE - JEE (Mains)
ANSWER KEY Physics:
1. b 2. a 3. a 4. d 5. c
6. a 7. c 8. b 9. b 10. c
11. a 12. a 13. d 14. c 15. b
16. b 17. d 18. b 19. c 20. c
21. a 22. c 23. d 24. d 25. d
26. c 27. b 28. a 29. c 30. c
Chemistry:
1 2 3 4 5 6 7 8 9 10
C C D C D B B D B C
11 12 13 14 15 16 17 18 19 20
D A D B B C C A B B
21 22 23 24 25 26 27 28 29 30
B A B B A C A A A B
MATHEMATICS
1 2 3 4 5 6 7 8 9 10
D A A D C D B A C D
11 12 13 14 15 16 17 18 19 20
B B A D D C C C A C
21 22 23 24 25 26 27 28 29 30
B B D B C D C A A C
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 16
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PHYSICS, CHEMISTRY & MATHEMATICS
Time Allotted: 3 Hours
Maximum Marks: 210
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. You are not allowed to leave the Examination Hall before the end of the test.
BA
TC
HE
S –
12
14
FIITJEE
CPT1 - 1
CODE: Set- A
PAPER - 1
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 17
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INSTRUCTIONS
Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet
before attempting the paper. Wrong CODE or no CODE will give wrong results.
A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Parts.
3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
4. Each part is further divided into two sections: Section-A & Section-C
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.
B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.
2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and
write in ink your Name, Test Centre and other details at the designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.
C. Marking Scheme For All Three Parts.
(i) Section-A (01 – 10) contains 10 multiple choice questions which have only one correct answer. Each question
carries +3 marks for correct answer and – 1 mark for wrong answer.
Section-A (11 – 15) contains 5 multiple choice questions which have one or more than one correct
answer. Each question carries +4 marks for correct answer. There is no negative marking.
(ii) Section-C (01 – 05) contains 5 Numerical based questions with single digit integer as answer, ranging from 0 to
9 and each question carries +4 marks for correct answer. There is no negative marking..
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 18
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FIITJEE Limited, DURGAPUR CENTRE: A-3, Nandalal Bithi, City Centre, Durgapur, West Bengal - 713216. Ph : 03432542642, 03436450238, 9679997745 National Admissions Office : FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph-46106000, 26569493, Fax 26513942
Name of the Candidate :____________________________________________
Batch :____________________ Date of Examination :___________________
Enrolment Number :_______________________________________________
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 19
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Useful Data Chemistry:
Gas Constant R = 8.314 J K1 mol1
= 0.0821 Lit atm K1 mol1
= 1.987 2 Cal K1 mol1
Avogadro's Number Na = 6.023 1023
Planck’s Constant h = 6.626 10–34 Js
= 6.25 x 10-27 erg.s
1 Faraday = 96500 Coulomb
1 calorie = 4.2 Joule
1 amu = 1.66 x 10-27 kg
1 eV = 1.6 x 10-19 J
Atomic No : H=1, D=1, Li=3, Na=11, K=19, Rb=37, Cs=55, F=9, Ca=20, He=2, O=8,
Au=79.
Atomic Masses: He=4, Mg=24, C=12, O=16, N=14, P=31, Br=80, Cu=63.5, Fe=56, Mn=55,
Pb=207, Au=197, Ag=108, F=19, H=2, Cl=35.5, Sn=118.6
Useful Data Physics:
Acceleration due to gravity g = 10 2m/ s
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 20
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PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS
SSEECCTTIIOONNAA
Single Correct Choice Type
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE is correct.
1. An ideal ammeter and an ideal voltmeter are connected as
shown. The ammeter and voltmeter reading for
R1 = 5, R2 = 15, R3 = 1.25 and E = 20V are given as
(a) 6.25 A, 3.75 V (b) 3.00 A, 5 V
(c) 3.75 A, 3.75 V (d) 3.75 A; 6.25 V
E
A V R1
R2 R3
2. Two spheres of radii r and R carry charges q and Q respectively. When they are connected by a wire, there will
be no loss of energy of the system if
(a) qr = QR (b) qR = Qr (c) qr2 = QR
2 (d) qR
2 = Qr
2
3. An electric field given by 2ˆ ˆE 4i 3(y 2)j
pierces Gaussian cube of side 1m placed at origin such that its three
sides represents x, y and z axes. The net charge enclosed within the cube is
(a) 04 (b)
03 (c) 05 (d) zero
4. A dipole of dipole moment p is kept at the centre of a ring of radius R and charge q. The dipole moment has direction along the axis of the ring. The resultant force on the ring due to the dipole is
(a) zero (b) 3
0
pq
4 R
(c) 3
0
pq
2 R (d)
3
0
pq
4 R only if the charge is uniformly distributed on the ring.
5. A conductor in the form of a right angle ABC with AB = 3 cm and BC = 4 cm carries a current of 10 A. There is a
uniform magnetic field of 5 T perpendicular to the plane of the conductor. The force on the conductor will be
(a) 1.5 N (b) 2.0 N (c) 2.5 N (d) 3.5 N
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 21
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6. A parallel plate capacitor of capacitance C = 2 F (without dielectrics) is filled by dielectric slabs as shown in
figure. Then the new capacitance of the capacitor is :
(a) 7.8 F (b) 3.9 F
(c) 2.4 F (d) 8 F
7. A long straight wire, carrying current I, is bent at its midpoint to form an angle of 45°. Magnetic field at point P,
distance R from point of bending is equal to :
(a) 0( 2 1) I
4 R
(b) 0( 2 1) I
4 R
(c) 0( 2 1) I
4 2 R
(d) 0( 2 1) I
2 2 R
8. Figure shows an amperian path ABCDA. Part ABC is in vertical
plane PSTU while part CDA is in horizontal plane PQRS.
Direction of circulation along the path is shown by an arrow near
point B and at D. B.d for this path according to Ampere’s law
will be :
(a) 1 2 3 0(i i i ) (b)
1 2 0( i i )
(c) 3 0i (d)
1 2 0(i i )
9. Five conducting plates are placed parallel to each other, Separation between them is d and area of each plate
is A. Plate number 1, 2 and 3 are connected with each other and at the same time through a cell of emf E. The
charge on plate number 1 is :
(a) 0E A
d
(b) 0E A
2d
(c) 02E A
d
(d) zero
T
U
1i
3i
Q
R 1i
S
D C
P 3i
2i
2i
A B
45° R
P
I
I
E
1 2 3
4
5
3K 6
1K 2
w w
d
d
2K 4
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 22
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10. Half part of ring is uniformly positively charged and other half is
uniformly negatively charged. Ring is in equilibrium in uniform
electric field as shown and free to rotate about an axis passing
through its centre and perpendicular to plane. The equilibrium is
(a) stable (b) unstable
(c) neutral (d) can be stable or unstable
E0
+ +
+
+ +
+ + + – –
– – – – – – –
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 23
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SSEECCTTIIOONN -- BB
(Multi Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONE OR MORE may be correct.
11. In the circuit shown in figure:
(a) i =2.5 A when S1is closed and S2 is open
(b) 20
i A3
when S1 is open and S2 is closed
(c) 5
i3
A when S1 and S2 both are open
(d) i =20A when both S1 and S2 are closed
S2 S1
1 2 3 10V
20V i
12. An observer A and a charge Q are fixed in a stationary
frame 1F . An observer B is fixed in a frame
2F , which is
moving with respect to 1F :
(a) both A and B will observe electric field
(b) both A and B will observe magnetic field
(c) neither A nor B will observe magnetic field
(d) B will observe magnetic field but A will not
•Q A B
F1 F2
13. Two plates of a parallel plate capacitors carry charges q and –q and
are separated by a distance x from each other. The capacitor is
connected to a constant voltage source0V . The distance between the
plates is changed to x dx. Then in steady state.
(a) change in electrostatic energy stored in the capacitor is Udx
x
,
where U is initial potential energy.
(b) change in electrostatic energy stored in the capacitor is Ux
dx
V0
x
–q +q
(c) attraction force between the plates is 1
qE2
(d) attraction force between the plates is qE. (where E is electric field between the plates)
14. When some potential difference is maintained between A
and B, current I enters the network at A and leaves at B.
(a) The equivalent resistance between A and B is 8 .
(b) C and D are at the same potential.
(c) no current flows between C and D.
(d) current 3I
5 flows from D to C.
20 5 C
20 5 D
A B
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 24
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15. A charged particle moves in a gravity-free space without change in velocity. Which of the following is/are
possible?
(a) E = 0, B = 0 (b) E = 0, B 0 (c) E 0, B = 0 (d) E 0, B 0
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 25
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SSEECCTTIIOONNCC
Integer Answer Type
1 The following curve represents the variation of
potential of points along x-axis due to two-point
charges q1 and q2 separated by a distance 2a. Find
the ratio of magnitude of two charges (point O is
origin and coordinates of point P is a
, 03
(-a,0) O
2q
V
1q
(a,0) P
x
y
2. The region between X = 0 and X = Lm is filled with uniform steady magnetic field ˆ2Tk . A particle of mass 2
kg, positive charge 1C and velocity 2(m/s) i travels along x-axis and enters the region of the magnetic field
(neglect gravity). Find the value of L if the particle emerges from the region of magnetic field with its final
velocity at an angle 300 to its initial velocity.
3. In the diagram there are four conducting plates A, B, C and D placed parallel to each other at equal separation
L. If plate C starts moving towards plate B with velocity v. Find the current (in mA) flowing in the wire connecting
A and D. (assume all other plates to be fixed)
(Given: q2 = 2C, q3 = 3C, v = 30 m/s, L = 0.05 m )
+q1
–q1
+q2
–q2
–q3 +q3
v A B C D
4. The figure shows a RC circuit with a parallel plate capacitor.
Before switching on the circuit, plate A of the capacitor has a
charge –Q0 while plate B has no net charge. Now, at
t = 0, the circuit is switched on. How much time (in second) will
elapse before the net charge on plate A becomes zero. (Given C =
1F, Q0 = 1mC, = 1000 V and 62 10
Rln3
)
R
A B
–Q0
S
5. A thin insulated wire forms a plane spiral of N = 100 tight turns
carrying a current I = 8 mA. The radii of inside and outside turns
as shown in figure are equal to a = 50 mm and b = 100 mm.
Find the magnetic induction (in micro tesla) upto the nearest
integer at the centre of the spiral;
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 26
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PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY
SSEECCTTIIOONNAA
Single Correct Choice Type
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE is correct.
1. The correct IUPAC NAME of the following compound is
(a) 4-Methyl-5-chloronitrobenzene (b) 2-chloro-1-methyl-4-Nitrobenzene
(c) 3-chloro-4-methyl-1-nitrobenzene (d) 1-chloro-2-methyl-5-nitrobenzene
2. Allyl isocyanide has
(a) 9 & 4 bonds (b) 8 and 5 bonds
(c) 9 ,3 bonds & 2-nonbonded electrons (d) 8 ,3 , bonds and 4 non bonded electrons.
3. In the following groups
OAC,
(I)
OMe
(II)
2OSO Me
III
2 3OSO CF
IV
The order of leaving groups ability is
(a) I > II > III > IV (b) IV > III > I > II
(c) III > II > I > IV (d) II > III > IV > I
4.
Column-I (Comp.) Column – II (Ka)
(a) Benzoic acid (p) 53.3 10
(b) p-nitrobenzoic acid (q) 510.2 10
(c) p-chlorobenzoic acid (r) 530.6 10
(d) p-methoxy benzoic acid (s) 56.4 10
(e) p-methyl benzoic acid (t) 54.2 10
Space for Rough Work
NO2
Cl
CH3
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 27
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Which is correct match for acids in column I with their ka’s in column II
a b c d e
A T P Q R S
B S R P Q T
C R S P T Q
D S R Q P T
5. Among the following compounds I, II & III
Which of the following statement is incorrect
(a) I & III are enantiomers
(b) I & II are diastereomers
(c) II & III are diastereomers
(d) All are incorrect
6. In the given reaction
2
KCN/EtOH
H O Product
(a) & (b)
(c) (d)
Space for Rough Work
CH3
CH3
OH H
OHH
III
CH3
CH3
OH H
HOH
II
CH3
CH3
H OH
HOH
I
OCHO2
OC
O
OK+
OCH2OH
OC
OH
CN
H2
OC
O
CO
O
OC
O
CHO
OH
OH
O
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 28
_______________________________________________________________________________________________________________________________________________
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7. OH
Product (major)
Product in the above reaction
(a) (b) (c) (d) None
8. When phenol is reacted with 3CHCl and NaOH followed by acidification, salicylaldehyde is obtained, which of
the following species are involved in the above mentioned reaction as intermediate.
(a) (b) (c) (d)
9. The reaction of with HBr gives
(a) (b)
(c) (d)
10. When benzene sulphonic acid and p-nitrophenol is treated with 3NaHCO , the gases released respectively are
(a) 2 2SO ,NO (b) 2SO ,NO (c) 2 2SO ,CO (d) 2 2CO ,CO
Space for Rough Work
O
CH3
O
O-
O
CHCl2
O-
O
H
CHCl
OH
CHCl2
OHO
H
OH
CH3 CH CH OH
CH3 CH2 CH
Br
OH CH3 CHBrCH2 OH
CH3 CH2 CH
Br
Br CH3 CHBrCH2 Br
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 29
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SSEECCTTIIOONN -- BB
(Multi Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONE OR MORE may be correct.
11.
Identify the reagents that can perform this conversion successfully
(a) 2H ,Raney Ni (b)
2Mg,THF,H O
(c) 4 2NaBH ,H O (d)
||
O
H C H , OH
12. The correct statement(s) about solvent effect is/are
(a) Decreasing solvent polarity causes a large increase in the rate of the 2NS attack by ammonia on an alkyl
halide 3 3R X NH RNH X
(b) Increasing solvent polarity causes a large decrease in the rate of the 2NS attack by hydroxide ion on
trimethyl sulphonium ion.
3 3 3 3 2Trimethyl sulphoniumion DMS
HO (CH ) S CH OH (CH ) S
(c) Increasing solvent polarity causes a small decrease in the rate of the 2NS attack by trimethyl amine on
trimethyl sulphonium ion
3 3 3 3 3 3 3 3 2(CH ) N (CH ) S CH N(CH ) (CH ) S
(d) All are incorrect.
Space for Rough Work
OCH2OH
OC
O
H
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 30
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13. KOH
3CHCl X Y
X & Y are
(a) X = (b) X =
(c) Y = (d) Y =
14. In the given reaction
2 6 2 2B H ,THF H O ,NaOH TsCl t BuO K (Y)
The product ‘Y’ is
(a) Position isomer of X (b) Identical to X
(c) Chain isomer of X (d) An oxidation product of (X)
15. Which of the following reactions give alkylation product.
N
H
N
H
CHO N
H
CHCl2
N
Cl
N
Cl
(X)
CH3
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 31
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(a) + H
(b) + H
(c) 3AlCl
3CH COCl (d) 3AlCl
3Me CCOCl
Space for Rough Work
OH
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 32
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SSEECCTTIIOONNCC
Integer Answer Type
1. The sum of total stereoisomers and fractions on the fractional distillation of 2,3-Dichloropentane is
2. OH
3CH CHO nHCHO
in the preparation of final product if aldol formed is (x) then what is (x + n)?
3. Total no. of chiral centres present in the following compounds is
OH
OHOH
OH
OH
O
H
OH
OH
H
H
OH
CH2OH
H
O
H
OH
OH
H
CH2OH
H CH2OH
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 33
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4. Observe the following reaction and find out that how many number of reactant stereoisomers can be reduced to
optically inactive meso products
4NaBH
5. How many 3CHI will be released from the given compound.
2I /NaOH
Space for Rough Work
CHO
CHOH
CHOH
CHOH
CHOH
CH2OH
CH2OH
(CHOH)4
CH2OH
O O
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 34
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PPPAAARRRTTT ––– IIIIIIIII ::: MMMAAATTTHHHEEEMMMAAATTTIIICCCSSS
SSEECCTTIIOONNAA
Single Correct Choice Type
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE is correct.
1. Let |x|{e sgnx}f(x) e and
|x|[e sgnx]g(x) e ,x R where { x } and [ ] denotes the fractional part and integral part
functions respectively. Also h(x) ln(f(x)) ln(g(x)) then for all real x, h (x) is
(A) an odd function (B) an even function
(C) neither an odd nor an even function (D) both odd as well as even function
2. Which of the following function is surjective but not injective
(A) f : R R 4 3 2f(x) x 2x x 1 (B) f : R R 3f(x) x x 1
(C) f : R R 2f(x) 1 x (D) f : R R 3 2f(x) x 2x x 1
3. If 3f(x) 2x 7x 5 then 1f (4) is
(A) equal to 1 (B) equal to 2 (C) equal to 1/3 (D) non existent
4. The function x b,x 0
g(x)cosx,x 0
can be made differentiable at x = 0.
(A) if b is equal to zero (B) if b is not equal to zero
(C) if b takes any real value (D) for no value of b
5. If y is a function of x then 2
2
d y dyy 0
dxdx . If x is a function of y then the equation becomes
(A) 2
2
d x dxx 0
dydy (B)
32
2
d x dxy 0
dydy
(C)
22
2
d x dxy 0
dydy
(D)
22
2
d x dxx 0
dydy
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 35
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6. Which one of the following statement is true?
(A) If x cLimf(x) g(x)
and x cLimf(x)
exist, then x cLimg(x)
exists.
(B) If x cLimf(x) g(x)
exists, then x cLimf(x)
and x cLimg(x)
exist.
(C) If x cLim(f(x) g(x))
and x cLimf(x)
exist, then x cLimg(x)
exist.
(D) If x cLim(f(x) g(x))
exists, then x cLimf(x)
and x cLimg(x)
exist.
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 36
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7. 2 2 2 2
3 3 3 3n
1 n 2 (n 1) 3 (n 2) ..... n .1Lim
1 2 3 ..... n
is equal to :
(A) 1
3 (B)
2
3 (C)
1
2 (D)
1
6
8. If 2
2
x bx 25f(x)
x 7x 10
for x 5 and f is continuous at x = 5, then f (5) has the value equal to
(A) 0 (B) 5 (C) 10 (D) 25
x 3 x
x 1 x
2 2 6
2 2
if x 2
9. Let f(x) then
2x 4
x 3x 2
if x 2
(A) f(2) 8 f is continuous at x = 2 (B) f(2) 16 f is continuous at x = 2
(C) f(2 ) f(2 ) f is discontinuous (D) f has a removable discontinuity at x = 2
10. If x
2
x e cos2xf(x) ,x 0
x
is continuous at x = 0, then
(A) 5
f(0)2
(B) [f(0)] = – 2 (C) {f(0)} = –0.5 (D) [f(0)] . {f(0)} = –1.5
where [x] and {x} denotes greatest integer and fractional part function
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 37
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SSEECCTTIIOONN -- BB
(Multi Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONE OR MORE may be correct.
11. The function 1
lnxf(x) x
(A) is a constant function (B) has a domain (0,1) (e, )
(C) is such that x 1
Limf(x)
exist (D) is aperiodic
12. The function f(x) = (sgn x) (sin x) is
(A) discontinuous no where. (B) an even function
(C) aperiodic (D) differentiable for all x
13. Which of the following function(s) has/have the same range?
(A) 1
f(x)1 x
(B) 2
1f(x)
1 x
(C)
1f(x)
1 x
(D)
1f(x)
3 x
14. Let 2
x 1f(x)
2x 7x 5
. Then:
(A) x 1
1Limit f(x)
3 (B)
x 0
1Limit f(x)
5 (C)
xLimit f(x) 0
(D)
x 5/2Limit
does not exist
15. The function 2
| x 3 | ,x 1
f(x) x 3x 13,x 1
4 2 4
is :
(A) continuous at x = 1 (B) diff. at x = 1
(C) continuous at x = 3 (D) differentiable at x = 3
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 38
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SSEECCTTIIOONNCC
Integer Answer Type
1. Let f be the function defined by (x y z)(xy xz yz)
f(x,y,z)xyz
for all positive real numbers x, y and z. The
smallest possible value of f, is
2. The value of n
n
2nn 0
1lim 1
2
is
3. f(x) | x 2 | 3 is not differentiable at number of points = ?
4. Evaluate : 2 x
2
0
xe sin
2 4
dx
5. Let 1 2 3 4 5 6
1 1 x x 1f (x) x,f (x) 1 x;f (x) ,f (x) ;f (x) ;f (x)
x 1 x x 1 x
Suppose that 6 m 4f (f (x)) f (x) and
n 4 3f (f (x)) f (x) then n is ________
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 39
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FIITJEE COMMON TEST
PHASE TESTI (PAPER1)
ANSWER KEY WITH Concept Code
PART – I (PHYSICS) PART – II (CHEMISTRY) PART –III (MATHS)
SECTIONA SECTIONA SECTIONA
Q.N. Ans. Con. Code Q.N. Ans. Con. Code Q.N. Ans. Con. Code
1. B P120212,213 1. B C121201 1. A M120321
2. B P120103 2. C C121207 2. D M120308
3. B P120108 3. B C121202 3. A M120311
4. B P120113 4. D C121207 4. D M120311
5. C P120306 5. D C121203 5. C M120516
6. A P120114 6. D C121206 6. C M110602
7. A P120302 7. A C121206 7. A M110611
8. D P120303 8. D C121205 8. A M120404
9. D P120115 9. B C121202 9. C M120401
10. A P120113 10. D C121205 10. D M120404
SECTION-B SECTION-B SECTION-B
11. ABCD P120205,206 11. CD C121206 11. ABC M120319
12. AD P120305 12. BC C121202 12. ABC M120322
13. AC P120114 13. AC C121206 13. BC M120317
14. ABD P120207 14. A C121202 14. ABCD M110602
15. ABD P120305 15. ABD C121206 15. ABC M120408
Paper Code
XXXX.X
CODE: Set- A
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 40
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SECTION –C SECTION -C SECTION -C
1. 2 P120105 1. 6 C121202 1. 9 M120323
2. 1 P120305 2. 7 C121206 2. 2 M110606
3. 1 P120114 3. 9 C121209 3. 3 M120410
4. 2 P120216 4. 4 C121209 4. 0 M120701
5. 7 P120302 5. 0 C121206 5. 5 M120323
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 41
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HINT & SOLUTIONS-PHYSICS
SECTION – A CPT1-1 SET-A
(Single Correct Choice Type)
1. eqR of the circuit = 1 2
3
1 2
R RR
R R
= 5 15 125 75 5
5 15 100 20 4
5
eq
E 20I
R 5 = 4 A
20V
15
5 A V
1.25
R1 R2 R3
Current in 21
1 2
IRR 3A
R R
P.D. across 3 3R IR 5V
(b)
2. There will be no loss of energy if the potential of the spheres is the same i.e. if
0 0
q QV
4 r 4 R
or
q Q
r R
(b)
3. Net flux in x-direction = 0
Net flux in y-direction 2A[3(1) 2] A[3(0) 2]
0
q3A
0 0q 3 A 3 , (as 2A 1m )
(b)
x
y
z
4. The electric field due to the dipole on the circumference of the ring 3
0
pE
4 R
and it is directed normal to the
plane of charged ring.
Hence force on the charged ring 3
0
pqF qE
4 R
(b) 5. Force on the conductor ABC
= Force on the conductor AC
= 5 × 10 × (5 × 10–2
) = 2.5 N
(c)
3cm
10A
A
B C 4cm
× B
3cm
10A A
B C 4cm
× B
F
6. (A)
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 42
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as the potential difference across dielectric of dielectric constant 2 & 4 is not same.
7. (A)
8. (D)
0 1 3 2 3 0 1 2B.d (i i i i ) (i i )
Since for the given direction of circulation 3i entering at PSTU is positive while
3i at PQRS is negative]
9. (D)
10. Assuming ring as dipole, then dipole moment P
and E
are in same direction, so potential energy U = –PE
(A)
(Multi Correct Choice Type)
11. S1 closed , S2 opened , 20 10
i4
= 2.5 A
S1 opened, S2 closed , 20
i3
A
S1 and S2 both open , 20 10 5
i6 3
A
S1 and S2 both closed, i = 20 A
(a) (b) (c) (d)
12. For frame F1, the charge Q is at rest and for frame F2, the charge Q is in motion. Charge at rest or in motion
produces electric field. So both A and B will observe electric field.
Hence, choice (a) is correct.
Only moving charges produces magnetic field. So B will observe magnetic field but A will not observe any
magnetic field.
3K 6
1K 2
w w
d
d
2K 4
3K 6
1K 2 2K 4
3K 6
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 43
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Hence, choice (d) is correct and choices (b) and (c) are wrong.
(a) and (d)
13. Initial stored energy 2
0 0i
AV1U
2 x
Final stored energy 2
0 0f
AV1U
2 (x dx)
so 2
f i 0 0
1 1 1U U U AV
2 x dx x
2
0 0
1 x x dxAV
2 x(x dx)
2 2
0 0 0 0
2
AV AV1 1 dx Udxdx .
2 2 x x xx
So, choice (a) is correct and choice (b) is wrong. dU U
Fdx x
2
0 0 0 00
A V A V1 1 1F . .V . qE
2 x x 2 x x 2
So magnitude of attractive force is 1
qE.2
So, choice (c) is correct and choice (d) is wrong.
(a) and (c)
14. A D A CV V V V or 20i 5 I i or i = I/5
2I I
I 2i I5 5
Current flowing from D to C.
(a) (b) (d)
20
A
5
5 20
C
D B
20 5 C
20 5 D
A B 1-2i
i 1-i
15. (a) (b) (d)
SECTION–C (Integer Type)
1. Since potential is decreasing, so q 1 is +ve and q 2 is –ve
1 2Kq Kq
a aa a
3 3
, 1
2
q 2
q 1 , 1 2q : q 2 : 1
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 44
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2. 0 Lsin30
r
0
1 L
2 mv
qB
0mv 2 2L
2qB 2 1 2
1m L = 1
r
300
300
2m/s
2m/s
r
X = 0 X = L
3. 31 2
0 0 0
2q (2L x)2q L 2q x0
2A 2A 2A
… (i)
31 2dqdq dq
Idt dt dt
… (ii)
From (i), 1 2 3 3q L q x 2q L q x 0
L x 2L–x
+q1
–q1
+q2
–q2
–q3 +q3
v
I
3 31 22 3
dq dqdq dq dx dxL x q 2 L x q 0
dt dt dt dt dt dt
2 3
vI (q q )
3L = 1 mA
4. Let at any time t charge flown through the plate B to plate A is q and instantaneous current is I.
I
A B
–Q0+q
– q
R
From loop theorem 02q QIR 0
2C
02q 2 C QdqR
dt 2C
0
dq dt
2 C Q 2q 2RC
Now for charge on plate A to be zero q = Q0.
Integrating 0Q t
00 0
dq dt
2 C Q 2q 2RC
= 0
0
2 C Qt RCln
2 C Q
Putting the value of C, Q0, and R
We get t = 2 seconds.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 45
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5. B = 0INln (b / a)7 T
2(b a)
;
CChheemmiissttrryy HHiinntt aanndd ssoolluuttiioonnss
SECTION – A
(Single Correct Choice Type)
1. (B)
2. (C) 2 2CH CH CH N C
3. (B)
4. (D) Acid character
> > > >
5. (D)
6. (D) This is abnormal benzoin.
CN
H Exchange
+
OCH3
COOH
CH3
COOHCOOH
Cl
COOH
NO2
COOH
OC
O
HO
C
O-
H
CN
OC
O-
H+ O
C-
OH
CNO
C
O-
C
H
CNOH
O
H Exchange
OC
-
OH
CN
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 46
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CN
7. (A)
Sol. This is retro aldol
OH
Intramolecular
aldol
2H O
8. (D)
3 3 2CHCl OH HOH : CCl Cl : CCl
OH
2:CCl
2
2NaOH
H O2NaCl
H
9. (B) H
Stable Carbocation
10. (D)
(Multi Correct Choice Type)
11. (C,D)
OC
O
CH
OHO
OH
O
O-
O
CH3 C
O
CH-
CH2
CH2
C O
CH3
OH
O
O
OH
CHO
O-
CHO
O-
CHCl2
O-
OH
CH3 CH CH OH CH3 CH2 CH+
OH
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 47
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12. (B,C) Polar forms are more stable in polar solvents.
13. (A, C)
Sol. 3 2CHCl OH CCl
OH
2CCl
& H
KOH
14. (A)
2 6
2 2
(i)B H ,THF
(ii)H O ,NaOH
Tscl t BuO
15. (A,B,D)
Sol. (a) + (b) +
N
H
NN
Cl
Cl
Cl
(Y)
N
Cl
Cl
N
H
CCl2 N
H
CHCl2N
CHO
H
(X)
CH3CH3
HH
OH
syn addition
CH3
HH
OTs
TsOh+t BuOH+
CH3
H
Anti el imination
OH
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 48
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(c) + MeCoCl
(d) 3AlCl CO
3 3 3Me C COCl Me C CO Me C
SECTION–C (Integer Type)
1. (6) + + +
I II III IV
Fraction 1st + Fraction II
nd
2. (7) 2
3 2H OCH CHO OH CH CHO
+ → repeat infor 2moretimer
COCH3
CMe3
Fractional Distillation
(I+II) III & II
CH
H
O
C CH2
O
H
OH
OH
OH
OH
CH
OH
CH2
H
C
O
H
Aldol
C
OH
OH
OH
CHO
Aldol
CH3
CH2CH3
Cl H
H Cl
CH3
CH2CH3
H Cl
Cl H
CH3
CH2CH3
Cl H
Cl H
CH3
CH2CH3
H Cl
H Cl
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 49
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HCO HCHO
Cannizaro reaction
So, 3-Aldol & 4 HCHO
3+ 4 =7
3. (9)
OH
O
H
OH
OH
H
H
OH
CH2OH
H
O
H
OH
OH
H
CH2OH
H CH2OH
*
**
*
*
**
*
*
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 50
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4. (4)
4NaBH
CHO
CH2OH
H OH
H OH
H OH
H OH
(I)
CH2OH
CH2OH
H OH
H OH
H OH
H OH
Meso
CHO
CH2OH
H OH
OH H
OH H
H OH
(II)
CH2OH
CH2OH
H OH
OH H
OH H
H OH
Meso
( )
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 51
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So, in total 4 stereoisomers are reduced to meso products.
5. (0)
MMAATTHHSS HHiinntt aanndd ssoolluuttiioonnss
SECTION – A PAPER - 1
(Single Correct Choice Type)
1. {y} {y} |x|h(x) ln(f(x) g(x)) lne {y} [y] y e sgnx
x
|x|
x
e if x 0
h(x) e sgnx 0 if x 0
e if x 0
x
x
e if x 0
h( x) 0 if x 0
e if x 0
h(x) h( x) 0 for all x
2. (A) 4 3 2f(x) x 2x x 1 → A polynomial of degree even will always be into say
2n 2n 1 2n 2
0 1 2 2nf(x) a x a x a x ..... a
x x
Limit f(x) Limit
02n 1 2 2n
0 2 2n0
if a 0a a a[x a .....
if a 0x x x
Hence it will never approach /
(B) 3f(x) x x 1 2f '(x) 3x 1 - injective as well as surjective
( )
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 52
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(C) 2f(x) 1 x neither injective nor surjective (minimum value =1)
3 2f(x) x 2x x 1 2f '(x) 3x 4x 1 D > 0
Hence f(x) is surjective but not injective.
3. Note that f is bijective hence 1f exist
When y 4
32x 7x 9 0
22x (x 1) 2x(x 1) 9(x 1) 0
2(x 1)(2x 2x 9) 0
x 1 only A ; as 22x 2x 9 0 has not other roots.
4. h 0
cosh 1g'(0 ) lim 0
h
h 0
h b 1g'(0 ) lim
h
for existence of line b 1 thus g'(0 ) 1
Hence g can not be made differentiable for any value of b.
5. Given 2
2
d y dyy 0
dxdx
now dy 1
dxdx
dy
2 2
2 2 2
d y d 1 d 1 dy 1 d x 1. . .
dx dx dxdx dy dxdx dydxdy dy dydy
2
2 2
2 3
d x
d y dy
dx dx
dy
(putting in (1))
2
2
3
d x
dyd yy 0
dxdx
dy
2 2
2
dx d xy 0
dy dy
C
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 53
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6. (A) This is false . f(x) x;g(x) cosecx
now x 0limf(x) g(x)
exists =1 also x 0Limf(x) 0
exist but x cLimg(x)
does not exist.
(B) This is false. Let f be defined as 1 if x 0
f(x)2 if x 0
. Let g(x) 0 . Then, f(x)g(x) 0 , and so
x 0Limf(x) g(x)
exits, while x 0Limf(x)
does not.
(C) This is true. Notice that g (f g) f. Therefore, by the limit theorem,
x c x c x cLim g(x) Lim(f(x) g(x)) Limf(x)
(D) This is false.
7. 2 2 2 2
3n
1 n 2 (n 1) 3 (n 2) ............. n (n (n 1))lim
n
r 2 2 2 2 2 2 2N n(1 2 ....n ) (1.2 2.3 3.4 ...... (n 1)n )
n
2 2
r 2
n n (r 1).r
n
2 3 2 2 3 2
r 1
n n (r r ) n n n n
2 3(n 1) n n
2 3
3n
(n 1) n nLim
n
n
(n 1)n(n 1)(2n 1)lim 1
6n(n 1)n(n 1)
4
4 1
13 3 A
Alternatively 2 2 2 2 2 2
3 3 2 3 3
1 n 2 (n 1) ..... n .1 1 (n 1) 2 (n 1) ..... n (n 1)1 1 1
1 2 3 ..... n n
2
3
(n 1) nl 1
n
8. 2x bx 25
f(x) .(x 2)(x 5)
for existence of limit 25 5b 25 0 b 10
now (x 5)(x 5)
f(x)(x 2)(x 5)
and
x 5Limf(x) 0
(A) s
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 54
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9. f(2 ) 8; f(2 ) 16
10. x
2x 0
x e 1 (1 cos2x) 1 5Lim 2 ;
2 2x
hence for continuity
5f(0)
2
[f(0)] 3; 5 1
{f(0)}2 2
hence 3
[f(0)]{f(0)} 1.52
SECTION-B
(Multi Correct Choice Type)
11. xlog ey x e (constant) A and C
as x 1
Limf(x) e
12. sinx x 0
f(x)sinx x 0
13. Domain is R { 1}; Range = R {0}
Domain is x R; Range (0,1]
Domain is [0, ); Range (0,1]
Domain is ( ,3); Range (0, )]
14. (A,C,D)
15. 2
x 3 if x 3
f(x) 3 x if 1 x 3
x 3x 13if x 1
4 2 4
h 0 h 0
f(1 h) f(1) 3 (1 h) 2f '(1 ) Limit Limit 1
h h
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 55
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2
2
h 0 h 0
(1 h) 3 13(1 h) 2
(1 h) 6(1 h) 54 2 4f '(1 ) Limit Limith 4h
2
h 0
h 2h 6hLimit 1
4h
f is continuous at x=1
SECTION–C (Integer Type)
1. (x y z)(xy xz yz) 1 1 1 x y y z z x
f(x,y,z) (x y z) 3xyz x y z y x z y x z
minf(x,y,z) 9 ]
2.
2 n n 12 2 2 n
n n
1 1 1 1 1 11 1 1 1 ..... 1 1
2 2 2 2 2 2lim lim 211
1122
Ans. ]
3.
4. 2x x
2
0
xI e sin dx
2 4
put
xt
2
t t t
0 0 0
I 2 e sin t dt 2 e sintcos costsin dx 2 e (sint cost)dt4 4 4
t
02 e sint 0
Ans.]
5. Given 6
x 1f (x)
x
……….(1)
6 m 4
1f (f (x)) f (x)
1 x
(given)
m6 m
m
f (x) 1 1f (f 9x))
f (x) 1 x
(using given relation 6
x 1f (x) )
x
-1 2 5
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 56
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Put mf (x) k
k 1 1
k 1 x
k kx 1 x k x 1
kx
m 6
x 1f (x) f (x)
x
m = 6
again m 4 3
1f (f (x)) f (x)
x
m
1 1f ;
1 x x
let
1t
1 x
t tx 1
t 1x
t
m
tf (t)
t 1
n 5
xf (x) f (x)
x 1
Hence n 5 Ans.]
PHYSICS, CHEMISTRY & MATHEMATICS
Time Allotted: 3 Hours
Maximum Marks: 198
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
You are not allowed to leave the Examination Hall before the end of the test.
BA
TC
HE
S –
12
14
FIITJEE
CPT1 - 2
CODE: Set - A
PAPER - 2
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 57
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INSTRUCTIONS
Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet
before attempting the paper. Wrong CODE or no CODE will give wrong results.
C. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Parts.
3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
4. Each part is further divided into one section: Section-A
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.
D. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.
2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and
write in ink your Name, Test Centre and other details at the designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.
C. Marking Scheme For All Three Parts.
(i) Section-A (01 – 08) contains 8 multiple choice questions which have only one correct answer. Each question
carries +3 marks for correct answer and – 1 marks for wrong answer.
Section-A (09 – 14) contains 3 paragraphs. Based upon paragraph, 2 multiple choice
questions have to be answered. Each question has only one correct answer and carries +3 marks for correct
answer and – 1 mark for wrong answer.
Section-A (15 – 20) contains 6 multiple choice questions which have one or more than one correct
answer. Each question carries +4 marks for correct answer. There is no negative marking.
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 58
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Name of the Candidate :____________________________________________
Batch :____________________ Date of Examination :___________________
Enrolment Number :_______________________________________________
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 59
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Useful Data Chemistry:
Gas Constant R = 8.314 J K1 mol1
= 0.0821 Lit atm K1 mol1
= 1.987 2 Cal K1 mol1
Avogadro's Number Na = 6.023 1023
Planck’s Constant h = 6.626 10–34 Js
= 6.25 x 10-27 erg.s
1 Faraday = 96500 Coulomb
1 calorie = 4.2 Joule
1 amu = 1.66 x 10-27 kg
1 eV = 1.6 x 10-19 J
Atomic No : H=1, D=1, Li=3, Na=11, K=19, Rb=37, Cs=55, F=9, Ca=20, He=2, O=8,
Au=79.
Atomic Masses: He=4, Mg=24, C=12, O=16, N=14, P=31, Br=80, Cu=63.5, Fe=56, Mn=55,
Pb=207, Au=197, Ag=108, F=19, H=2, Cl=35.5, Sn=118.6
Useful Data Physics:
Acceleration due to gravity g = 10 2m/ s
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 60
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PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS
SSEECCTTIIOONNAA
Single Correct Choice Type
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.
1. A point charge + q is fixed at point B. Another point charge + q at A of
mass m vertically above B at height h is dropped from rest. Choose the
correct statement
(a) It will collide with B
(b) It will execute S.H.M
(c) It will go down only if 2
0
q
4 < mgh
2
h
A
B
+q
+q
(d) go down up to a point and then come up.
2. In the given diagram, the potential difference between A and
B is V1, when switch is open. The potential difference
between A and B when switch is closed is V2. Then
S
Q0
A
C
+ + + +
– – – –
(a) 01
QV
2C , 0
2
QV
C (b)
1V zero , 2V zero
(c) 01
QV
2C ,
2V zero (d) 01
QV
2C , 0
2
QV
2C
3. There is a uniform magnetic field perpendicular to the
plane of paper. A positive charged particle enters in the
region, perpendicularly and collides inelastically at point Q
to the rigid wall MN. If Co-efficient of restitution e = ½ then
particle
(a) Retraces its path (b) Strikes at point O
(c) Strikes at point M (d) strikes at point N
a
N M O
a/2
Q
a/2
Space for Rough Work
B
Q0
2C
– – – –
+ + + +
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 61
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4. The potentiometer wire AB is 600 cm long. At what distance
from A should the jockey J touch the wire to get zero deflection
in the galvanometer?
(a) 320 cm (b) 120 cm
(c) 20 cm (d) 450 cm
E r
A B J
r
R=15r
E/2 G
5. A miliammeter of range 10mA and resistance 9 is joined in a
circuit as shown. The meter gives full scale deflection for current I
when A and B are used as its terminals, i.e. current enters at A and
leaves at B (C is left isolated). The value of I is
(a) 100 mA (b) 900 mA
(c) 1 A (d) 1.1 A
9 ,10mA
0.1 0.9
A B C
6. A capacitor of capacitance ‘C’ is connected with a battery of emf ε as shown. After full charging a dielectric of
same size of capacitor and dielectric constant k is inserted then choose correct statements. (capacitor is always
connected to battery)
(a) electric field between plates of capacitor remain same
(b) charge on capacitor is Cε
(c) energy on capacitor decreased
(d) electric field between plates of capacitor increased.
7. The electric field in a region is given by ˆ ˆE 4i j
N/C. Work done by this field is zero when a particle is
moved along the line
(a) y + 4x = 2 (b) 4y + x = 6 (c) x + y = 5 (d) x – y = 5
8. The time constant of an RC circuit shown in the figure is
(a) 0 (b) 2/3 RC
(c) 6RC/5 (d) 2 RC
R
R
C
E
Space for Rough Work
C
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 62
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SSEECCTTIIOONNBB
Comprehension Type
This section contains 3 paragraphs. Based upon each paragraph 2 multiple choice questions have to be
answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Paragraph for Question 9 to 10
Read the paragraph carefully and answer the following questions:
A hollow cube of side L has two parallel sides conducting and remaining four sides are non-conducting. It is filled with a liquid of dielectric constant k. A small hole of area A at the bottom of the cube is opened at t = 0 and liquid starts leaking through it. The two
conducting sides are connected by a battery of emf .
(Take: L = 9 m, 218A m
20 , k = 10, = 81 V, g = 10 m/s
2 )
L
9. The capacitance of the capacitor as a function of time is
(a) 20 (t 54t 64)9
(b) 20 (t 54t 810)
9
(c) 20 (t 54t 810)9
(d) 20 (t 54t 64)
9
10. The current through the connecting wire as a function of time is
(a) 0 (54 2t) (b)
09 (54 2t) (c) 09 (54 2t) (d) 0 (54 2t)
9
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 63
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Paragraph for Question 11 to 12
A charge particle of charge 1C and mass 10gm is moving with
velocity 10 i m/s in horizontal plane consisting of magnetic field –
0.1 k T of width 2
3m and electric field –0.1 j N/C of width d.
Particle enters the magnetic field at t = 0 perpendicularly and
follows the path as shown in the figure and strikes the wall AB
perpendicularly at A (neglect gravity)
d B
A
A
m2
3
O
E
B
y
x
11. The time t after which it strikes the wall
(a) 1.2 s (b) 0.97 s (c) 1.07 s (d) 1.98 s
12. Taking O as origin y-coordinate of A will be
(a) 3.75 m (b) 0.50 m (c) 4.25 m (d) 3.25 m
Paragraph for Question 13 to 14
A capacitor of capacitance C 0.1F is charged by a battery of
e.m.f. E1 = 100 V and internal resistance r1 = 1 by putting switch
S in position 1 as shown in figure.
100V
0.1F
50V
r2
1
r1
1
99 1
2
E1
R
E2
13. Find out heat generated in R = 99 till steady state
(a) 500 J (b) 495 J (c) 1000 J (d) 485 J
14. Now switch is thrown to position 2. Find the work done on the battery till steady state
(a) 250 J (b) 300 J (c) 275 J (d) 325 J
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 64
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SSEECCTTIIOONNCC
Multiple Correct Answers Type
This section contains 6 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and
(D),
15. A charged particle enters a region which offers some resistance against its
motion and a uniform magnetic field exists in the region. The particle traces
a spiral path as shown. Then:
(a) angular velocity of particle remains constant
(b) speed of particle decreases continuously
(c) total mechanical energy of the particle remains conserved
(d) net force on the particle is always perpendicular to its direction of motion
16. Four charges, all of the same magnitude, are placed at the four corners of a square. At the centre of the square,
the potential is V and the field is E. By suitable choices of the signs of the four charges, which of the following
can be obtained?
(a) V = 0, E = 0 (b) V = 0, E 0
(c) V 0, E = 0 (d) V 0, E 0
17. In the network shown, points A, B and C are at potentials of 70 V, zero and 10 V respectively.
(a) Point D is at a potential of 40 V.
(b) The currents in the sections AD, DB, DC are in the ratio 3 : 2 : 1
(c) The currents in the sections AD, DB, DC are in the ratio 1 : 2 : 3
(d) The network draws a total power of 200 W
Space for Rough Work
A
B(0 V)
20
30 30
C (10 V)
D
(70 V) 10
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 65
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18. In the circuit shown in figure 1 2C C 2μF . Then charge stored in
(a) capacitor C1 is zero
(b) capacitor C2 is zero
(c) both capacitors is zero
(d) capacitor C1 is 40 C
1 2 3
3 1 2
C1 C2
120V
19. Figures shows the lines of force of the electric field of a positive charge (+q) and a negative charge (-q) respectively.
Which of the following statements are correct?
Q
P
+q
O
(a)
B
A
–q
O
(b)
(a) potential at P is greater than that at Q.
(b) potential at A is greater than that at B.
(c) potential energy at P is less than that at Q
(d) potential energy at A is greater than that at B.
20. H+, He
+ and O
++ ions having same kinetic energy pass through a region of space filled with uniform magnetic
field B directed perpendicular to the velocity of ions. The masses of the ions H+, He
+ and O
++ are respectively in
the ratio 1 : 4 : 16. As a result
(a) H+ ions will be deflected most
(b) only O++
ions will be deflected least
(c) He+ and O
++ ions will suffer same deflection
(d) All ions will suffer the same deflection
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 66
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PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY
SSEECCTTIIOONNAA
Single Correct Choice Type
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.
1. Compound A (molecular Formula 3 8C H O) is treated with acidified
2 2 7K Cr O to form a product B3 6(MF C H O) . B
forms a shining silver mirror on warning with ammonical 3AgNO . B when treated with an aqueous solution of
2 2H NCONHNH . HCl and sodium acetate gives a product C. Identify the structure of C.
(a) 3 2 2CH CH CH NNHCONH (b)
(c) (d) 3 2 2CH CH CH NCONHNH
2. 3 2 3CH NH CHCl KOH Nitrogen containing compound is
(a) 3CH C N (b)
3 3CH NH CH (c) 3CH N C
(d) 3CH N C
3. Among cellulose, poly (vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of
attraction is weakest is
(a) Nylon (b) Poly (vinyl chloride) (c) Cellulose (d) Natural rubber.
4. The two forms of D-glucopyranose obtained from the solution of D-glucose are called.
(a) Isomers (b) Anomers (c) epimers (d) enantiomers
5. The product of acid hydrolysis of P and Q can be distinguished by
P → Q →
(a) LUCAS Reagent (b) 2, 4 –DNP
(c) Fehling’s solution (d) 3NaHSO
Space for Rough Work
CH3 C NNHCONH2
CH3
CH3 C NCONHNH2
CH3
CH2
OCOCH3
CH3
CH3
OCOCH3
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 67
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6. Which of the following is true for SN1 when solvent is 50% water & 50 % acetone.
(a) > > >
(b) > > >
(c) > > >
(c) > > >
7. + (X) 3
3
CH COONa
H O
The compound (X) is
(a) 3CH COOH (b)
2BrCH COOH (c) 3 2(CH CO) O (d) HC C COOH
8. When propionic acid is treated with aq 3 2NaHCO ,CO is liberated. The carbon of 2CO comes from
(a) Methyl group (b) Carboxylic group (c) Methylene group (d) bicarbonate
Space for Rough Work
Cl
Cl Cl
Ph Cl
Cl
Ph Cl
Cl Cl
Cl
Ph Cl
Cl Cl
Cl
Ph ClCl
Cl
Me CHO Me CH CHCOOH
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 68
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SSEECCTTIIOONNBB
Comprehension Type
This section contains 3 paragraphs. Based upon each paragraph 2 multiple choice questions have to be
answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Paragraph for Question 9 to 10
A water insoluble organic mixture contained following compounds.
1. Benzoic acid 2. Salicylaldehyde 3. p-hydroxybenzaldehyde 4. Naphthylanine
5. Naphthalene
The following sequence of reagents are used to separate this mixture
1+2+3+4+5
aq HCl (step X)
[Insoluble] [soluble]*
aq 3NaHCO (step-Y)
[ Insoluble] [soluble]*
aq NaOH
(step-Z)
[Insoluble]*
[soluble]
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 69
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Fill up the serial No. of starred comp. obtained in steps X, Y, Z, W respectively and answer the following
questions
X Y Z W
Space for Rough Work
Steam distillation (step-W)
[distilled]* [left behind]
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 70
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9. Soluble compound at step – Y is
(a) Benzoic acid (b) p-hydroxybenzaldehyde
(c) naphthylamine (d) Naphthalene
10. Insoluble compound at step-Z is
(a) p-hydroxybenzaldehyde (b) Salicylaldehyde
(c) Naphthylamine (d) Naphthalene
Paragraph for Question 11 to 12
Observe the esterificaiton mechanisms for primary and tertiary alcohols.
Type- 1 2 4
||conc.H SO
3 3 2 2 3 2 2 3
O
CH COOH CH CH CH OH CH C OCH CH CH
Mechanism : H
step I
pr O H
step 2
2
Step 3
HH O
Type – 2
+ 2 4conc. H SO
Mechanism
H
Step 1
+
2H O
Space for Rough Work
CH3 C OH
O
CH3 COH
OH+
CH3 COH
OH+
CH3 C
OH
OH
O+
Pr H
CH3 C
O
OCH2CH2CH3
CH3 COH
O
CH3 C
CH3
OH
CH3
CH3 C
CH3
O
CH3
C
O
CH3
CH3 C
CH3
OH
CH3
CH3 C
CH3
CH3
+
CH3 C
CH3
O
CH3
C
O
CH3
CH3 C
O
O H
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 71
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11. 2 4
18conc. H SO
3 2 5CH COOH C H OH (P)
2 4
18conc.H SO
3 3 3CH COOH (CH ) C OH (P)
In the above reactions (P) & (Q) are respectively
(a) ,
(b) ,
(c) ,
(d) ,
12. 3CH COOH 2 4conc.H SO
(X)
3CH COOH 2 4conc.H SO(Y)
(a) (X) solution is optically active while (Y) solution is optically inactive
(b) Both (X) & (Y) solutions are optically active
(c) Both (X) & (Y) solutions are optically inactive
(d) (X) solution is optically inactive while (Y) solution is optically active
Space for Rough Work
CH3 C
O
O C CH3
CH3
CH3
18 CH3 C
O
OC2H5
CH3 C
O
O C CH3
CH3
CH3
CH3 C
O
OC2H5
18
C2H5 C
O
O CH3
18
CH3 C
O
O C CH3
CH3
CH3
CH3 C
O
O C2H5
18
CH3 C
O
O C CH3
CH3
CH3
18
H
CH3
D OH
CH3
C
C2H5
Ph OH
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 72
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Paragraph for Question 13 to 14
Read the following reaction sequence
2ClH NaOEt/ NBS NaOH
hvP Q R S T
Then answer the following question.
13. Compounds ‘T’ is
(a) (b) (c) (d)
14. When ‘S’ is treating with strong base, product obtained is
(a) (b) (c) (d)
Space for Rough Work
O
OH
OH
OH
OH
OH
OH
OH
OH
OH
Br
OHOHOH
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 73
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SSEECCTTIIOONNCC
Multiple Correct Answers Type
This section contains 6 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and
(D),
15. The correct statement(s) about the following reaction sequence is/are
2 3 3 2 4 3 2 4 2 2Cl /FeCl Conc.HNO /Conc.H SO conc.HNO conc.H SO , NH NH , (R)
1 2 3 4 5(P) (Q)
(a) ‘R’ gives an aldol condensation reaction on heating with NaOH solution
(b) The compounds ‘Q’ gives a yellow p.pt in acetone
(c) step (4) is an aromatic nucleophillic substitution reaction
(d) the end product is a mixture of three compounds.
16. Which of the following products is/are correctly mentioned in the following reactions
(a) NaOD
3HCHO HCOONa CH OD
(b) NaOH
2HCDO DCOONa CH DOH
(c) NaOEt
2HCDO DCOOEt DCH ONa
(d) NaOD
2 3D CO DCOONa CD OD
17. trans-2-methyl cyclohexanol + acetyl chloride X
X NaOH(aq) Y sodium acetate
(a) X is (b) X is
(c) Y is (d) Y is
Space for Rough Work
CH N NH NO2
O2N
CH3
H
H
OCOCH3
H
CH3
H
OCOCH3
H
CH3
H
OH
CH3
H
H
OH
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 74
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18. The correct statements about peptides are
(a) A dipeptide has one peptide linkage between two amino acids.
(b) By convension N-Terminus is kept at left and C-terminus at right in the structure of a peptide.
(c) If only one amino acid is available for reaction, than only one dipeptide can be formed.
(d) A polypeptide with more than hundred amino acid (mol. Mass > 10,000) is called a protein
19. Salicin (structure given below) is a glycoside, found in the bark of willow tree, used in relieving pain.
Observe the following reaction of salicin.
dil HCl
CarbohydrageP Q
The correct statement(s) is (are) :
(a) P is D-Glucose
(b) Q is 2-hydroxybenzyl alcohol
(c) Q can be converted to a modern analgesic (pain-killer), aspirin
(d) The above reaction occurs through a carbocation
20. Lysine a amino acid has 1 2 3pKa 2.18, pKa 8.95, pKa 10.53
The isoelectric point of Lysine will be
(a) 6.35 (b) 9.74 (c) 2.77 (d) 10.76
Space for Rough Work
O
H
OH
CH2OH
H
OH
H
H
OH
OCH2OH
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 75
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PPPAAARRRTTT ––– IIIIIIIII ::: MMMAAATTTHHHEEEMMMAAATTTIIICCCSSS
SSEECCTTIIOONNAA
Single Correct Choice Type
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.
1. 1 1
0
tan xdx
x
(A) /4
0
sinxdx
x
(B) /2
0
xdx
sinx
(C) /2
0
1 xdx
2 sinx
(D) /4
0
1 xdx
2 sinx
2. The set of values of 'a' which satisfy the equation 2
2 2 2
0
4(t log a)dt log
a
is
(A) a R (B) a R (C) a 2 (D) a 2
3. The value of the function x
2
1
f(x) 1 x (ln t 2lnt)dt where f’ (x) vanishes is :
(A) 1e (B) 0 (C) 12e (D) 1 + 2 1e
4. 2 3/2
(2x 1)dx
(x 4x 1)
(A) 3
2 1/2
xC
(x 4x 1)
(B)
2 1/2
xC
(x 4x 1)
(C) 2
2 1/2
xC
(x 4x 1)
(D)
2 1/2
1C
(x 4x 1)
5. If 4 2
2
x x 1y
x 3x 1
and
dyax b
dx then the value of a + b is equal to
(A) cot 5
8
(B) cot
5
12
(C) tan
5
12
(D) tan
5
8
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 76
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6. If 2 2 2x y R (R 0) then
3
2
y"k
1 y '
where k in terms of R alone is equal to
(A) 2
1
R (B)
1
R (C)
2
R (D)
2
2
R
7. If the function 2t 3x x
f(x) ,x 4
where 't' is a parameter has a minimum and a maximum then the range of
values of 't' is
(A) (0, 4) (B) (0, ) (C) (– , 4) (D) (4, )
8. A particle moves along the curve 3/2y x in the first quadrant in such a way that its distance from the origin
increases at the rate of 11 units per second. The value of dx/dt when x = 3 is
(A) 4 (B) 9
2 (C)
3 3
2 (D) none
SSEECCTTIIOONNBB
Comprehension Type
This section contains 3 paragraphs. Based upon each paragraph 2 multiple choice questions have to be
answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Paragraph for Question 9 to 10
Read the paragraph carefully and answer the following questions:
If , (where ) are the points of discontinuity of the function g(x) f(f(f(x))), where 1
f(x)1 x
, and
2P(a,a ) is any point on xy-plane.
9. The points of discontinuity of g(x) is
(a) x 0, 1 (b) x 1 only (c) x 0 only (d) x 0,1
10. The domain of f(g(x)) is
(a) x R (b) x R {1} (c) x R {0,1} (d) x R {0,1, 1}
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 77
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Paragraph for Question 11 to 12
If nf(x) (x ) g(x), then n 1f '( ) f "( ) .... f ( ) 0 where f(x) and g(x) are polynomials.
For a polynomial f(x) with rational coefficients, answer the following questions.
11. If f(x) touches x-axis at only one point, then the point of touching is
(a) always a rational number (b) may or may not be a rational number
(c) never a rational number (d) none of these
12. If f(x) is of degree 3 and touches x-axis, then
(a) all the roots of f(x) are rational (b) only one roots is rational
(c) both (a) and (b) may be possible (d) none of these
Paragraph for Question 13 to 14
Let us consider the integrals of the following forms 1/2
2f x, mx nx p
Case 1 : If m 0 , then put 2mx nx p u x m
Case 2 : If p 0 , then put 2mx nx p ux p
Case 3 : If quadratic equation 2mx nx p 0 has real roots and there put 2mx nx p (x )u or
(x )u
13. If 2
dxI
x 9x 4x 6
to evaluate I, one of the most proper substitution could be
(a) 29x 4x 6 u 3x (b) 29x 4x 6 3u x
(c) 1
xt
(d) 2 19x 4x 6
t
14.
152
2
x 1 xdx
1 x
is equal to
(a)
162x 1 x
c10
(b)
2
1c
15 1 x x
(c)
2
15c
1 x x
(d)
15
2x 1 xc
15
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 78
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SSEECCTTIIOONNCC
Multiple Correct Answers Type
This section contains 6 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and
(D),
15. 1 cosec x dx equals
(A) 12sin sinx c (B) 12cos cosx c
(C) 1c 2sin (1 2sinx) (D) 1cos (1 2sinx) c
16. A continuous and differentiable function ' f ' satisfies the condition ,
x
2
0
f(t)dt f (x) 1 for all real ‘x’. Then :
(A) ' f ' is monotonic increasing x R
(B) ' f ' is monotonic decreasing x R
(C) ' f ' is non monotonic
(D) the graph of y = f (x) is a straight line.
17. Let x
0
sintf(x) dt(x 0)
t then f (x) has :
(A) Maxima if x n where n = 1, 3, 5,.....
(B) Minima if x n where n = 2, 4, 6,......
(C) Maxima if x n where n = 2, 4, 6,......
(D) The function is monotonic
18. The value of
1 2
20
2x 3x 3dx
(x 1) x 2x 2
is :
(A) 12ln2 tan 24
(B) 1 1
2ln2 tan4 3
(C) 12ln2 cot 3 (D) 1ln4 cot 24
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 79
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19. The value of the definite integral, /2
0
sin5xdx
sinx
is
(A) 0 (B) 2
(C) (D) 2
20. The extremum values of the function 1 1
f(x) ,sinx 4 cosx 4
where x R is :
(A) 4
8 2 (B)
2 2
8 2 (C)
2 2
4 2 1 (D)
4 2
8 2
Space for Rough Work
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 80
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FIITJEE COMMON TEST
PHASE TESTI (PAPER2)
ANSWER KEY WITH Concept Code
PART – I (PHYSICS) PART – II (CHEMISTRY) PART –III (MATHS)
SECTIONA SECTIONA SECTIONA
Q.N. Ans. Con. Code Q.N. Ans. Con. Code Q.N. Ans. Con.
Code
1. C P120101 1. A C121206 1. C M120702
2. D P120105 2. D C121208 2. B M120704
3. D P120305 3. D C121211 3. D M120606
4. A P120208 4. B C121209 4. B M120702
5. C P120212 5. C C121206 5. B M120307
6. A P120214 6. B C121202 6. B M120516
7. A P120104 7. C C121207 7. C M120608
8. A P120216 8. D C121207 8. A M120508
SECTION B SECTION B SECTION B
9. B P120115 9. A C121212 9. D M120405
10. C P120115 10. D C121212 10. C M120316
11. B P120313 11. B C121207 11. A M120307
12. C P120313 12. A C121207 12. A M120318
13. B P120216 13. B C121203,204 13. A M120701
14. A P120216 14. B C121203,204 14. D M120705
Paper Code
XXXX.X
CODE: Set - A
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 81
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SECTION –C SECTION –C SECTION –C
15. AB P120305 15. BC C121202,206 15. AD M120705
16. ABCD P120104,P120105 16. ABCD C121206 16. AD M120604
17. ABD P120207 17. AD C121203 17. AB M120607
18. BD P120205,P120215 18. ABCD C121210,211 18. ACD M120704
19. A P120105 19. ABCD C121209,205 19. B M120702
20. AC P120305 20. B C121210 20. AC M120612
HINT & SOLUTIONS-PHYSICS
SECTION – A
(Single Correct Choice Type)
1. For charge + q at A to come down, Fe < mg
2
2
0
qmg
4 h
(c)
2. Charge flow is zero after closing the switch, so, 01 2
QV V
2C
(d)
3. After collision velocity becomes v/2 so radius becomes a/2 and hence diameter is a and O will be the centre. So
particle strikes at point N.
D
4. In case of zero deflection in galvanometer
AJ
EV
2 , AJ
EiR
2 ,
E 15r EAJ
15r r 600 2
AJ = 320 cm
(a)
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 82
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5. 3 310 10 9.9 0.1 i 10 10
or I = 1A
(c)
9 10mA
0.1 0.9
A B C
6. P.D. same and electric field same
(a)
7. Work done will be zero when displacement is perpendicular to the field. The field makes an angle
1
1
1tan
4
with positive x-axis
while the line y + 4x = 2 makes an angle
1
2 tan 4 with positive x-axis
0
1 2 90
i.e. the line y + 4x = 2 is perpendicular to E
.
(a)
8. (a)
Comprehension #1
9. 2 dyL A 2gy
dt
(y is height of liquid)
y t1
22
L 0
Ay dy 2g dt
L
22
2
A 2g t ty L 3
92L
0 0(L y)L k yLC
L L
= 0 (L y ky) = 20 (t 54t 810)
9
(b)
10. q C , dq
idt
, 0i 9 (54 2t)
(c)
Comprehension #2
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 83
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SOLUTION
In magnetic field
mv
R 1qB
m
2 m
TqB
0.2
In electric field
Acceleration a qE
m =10 m/s
2
P
A
O
600
R/2
R/2
R
300
R/2 R
2
3
Now, PA' maximum height 2 2v sin
2a
3.75m
y-co-ordinate of A ' is 4.25 m
T' time elapsed in E
is half the time of flight v sin 3
a 2
time t = T
T'6 0.97 sec
11. (b)
12. (c)
Comprehension #3
13. When switch in position 1 and steady state is reached q0 = CE1 = 10 C W1 = Energy supplied by battery = q0E1 = 1000 J
Energy stored on the capacitor 2
01
qU
2C = 500 J
H1 = W1 – U1 = 500 J
99
99H 500
100 = 495 J
(b) 14. Position (2), in steady state q =5C
2 2 0W E (q q) = 250 J
(a)
Multiple Choice Questions
15. Time period of revolution of particle in magnetic field is given by 2 m
TqB
Since for a given particle, m and q are constant. So, in constant magnetic field T is constant
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 84
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Angular velocity 2
T
Hence, angular velocity of particle is constant.
Hence, choice (a) is correct.
Due to resistive force, particle experiences a retardation and an energy is lost during motion against it. Hence
speed and total mechanical energy, both decrease continuously.
Hence, choice (b) is correct and (c) is wrong.
Since, speed of electron is decreasing continuously, therefore it is experiencing a tangential retardation. It is
possible only when the component of resultant force opposite to the direction of motion has non-zero values.
This implies, net force on electron cannot be perpendicular to its direction of motion.
Hence, choice (d) is wrong.
(a) and (b)
16. (a) (b) (c) (d)
17. Let VD be the potential of D, then
C DA D B DV VV V V V
010 20 30
VD = 40 V
Also, ratio of current in AD, DB and DC are 70 40 40 40 10
: :10 20 30
i.e. 3 : 2 : 1
Also total power network draws, 2P I R 200 W
(a) (b) (d)
18. Now, potential difference across C1 is 20 V and across C2 is zero.
charge stored in C1 is 40 C and in C2 is zero.
(b) and (d)
3 1 2
C1 C2
120V
20V 40V 60V
1 2 3
40V 20V 60V
19. (a)
20. m
rq
H He 0r : r : r 1 4 16
: : 1: 2 : 21 1 2
Radius is smallest for H+, so it is deflected most
(a)(c)
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 85
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HINT & SOLUTIONS-CHEMISTRY
SECTION – A CPT1-2 SET-A
(Single Correct Choice Type)
1. (A)
2. (D)
3. (D)
4. (B)
5. (C)
6. (B) The stability of carbocation
3° > benzylic > 2° > 1°
7. (C) Perkin reaction
8. (D)
Comprehension #1
9. (A)
10. (D)
Comprehension #2
11. (B) P is by type 1, Q is type – 2
12. (A) X→ Type 1 , Y=Type-2
↓ ↓
Hence configuration racemic product
is retained is obtained.
Comprehension #3
13. (B)
14. (B)
OH+
OH
+
OH
H+
OH
(P)
OH
Cl
(Q)
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 86
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Sol. Ring
Expansion
2Cl
hv
NaOH NBS
Multiple Choice Questions
15. (B,C)
16. (A,B,C,D) See mechanism of cannizaro reaction
17. (A,C)
18. (A,B,C,D)
Dipeptide is formed by iamide linkage b/w 2-amino acid moleculus.
OH
(R)
OH
Br
(S)
OH
OH
(T)
EtO-
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 87
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19. (A,B,C,D)
H Cl
2H O +
20. (B)
Pl 2 3pKa pKa 8.95 10.539.74
2 2
O
H
OH
CH2OH
H
OH
H
H
OH
OCH2OH O
H
OH
CH2OH
H
OH
H
H
OH
O+
CH2OH
H
CH2OH
OH
Q
O
H
OH
CH2OH
H
OH
H
H
OH
+
Carbocation
O
H
OH
CH2OH
H
OH
H
H
OH
H
OH
D Glucose
D Glucose
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 88
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FIITJEE Limited, DURGAPUR CENTRE: A-3, Nandalal Bithi, City Centre, Durgapur, West Bengal - 713216. Ph : 03432542642, 03436450238, 9679997745 National Admissions Office : FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph-46106000, 26569493, Fax 26513942
HINT & SOLUTIONS-MATHEMATICS
Single Correct Choice Type
1. 1 1
0
tan xI dx
x
2x tan ;dx sec d
/4 /4 /42
0 0 0
.sec 2I d d d ; 2 y
tan sin cos sin2
/2 /2
0 0
1 y 1 xdy dx
2 siny 2 sinx
(C)
2.
22
2
2 2
0
tlog a t 2 log (a )
2
2 2(2 2log a) 2 2log a
2 22log a 2log a a R
3. 2f '(x) 1 ln x 2lnx 0 2(1 lnx) 0 1
e
Hence
11 ee
2 2 1
1
1
1 1 1 1 1f 1 (ln t 2lnt)dt 1 t ln t 1 1 2e
e e e e e
(D)
4. 2 3
2 3/2 3/2 3/2
3
2 2
2x 1 2x 1 2x xdx dx dx
(x 4x 1) 4 1 4 1x 1 1
x xx x
Now put 2
2
1 41 t
xx
5. 2 2 2 2 2
2 2
(x 1) 3x (x 1 3x)(x 1 3x)y
x 3x 1 x 1 3x
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 89
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dy
2x 3dx
a 2 & b 3
a b 2 3 5
tan cot12 12
6. 2x 2yy' 0
x yy' 0 x
y 'y
…...(1)
21 yy'' (y ') 0
21 (y ')
y ''y
now 2
2 3/2 3 2 2 2 22
2
y '' 1 (y ') 1 1 1 1k
R(1 (y ') ) y 1 (y ') x y xy 1 (y ') y 1y
7. 2t 3x x
f(x) ;x 4
2
2
(x 4)(3 2x) (t 3x x )f '(x)
(x 4)
for maximum or minimum, f '(x) 0
2 22x 11x 12 t 3x x 0
2x 8x (12 t) 0
For one M and m,
D 0
64 4(12 t) 0
16 12 t 0 4 t or t 4
8. 2 2 2r x y ; dr dx dy
r x ydt dy dt
where x 3;y 3 3 and r 6 ; hence dx dy
6 11 3 3 3dt dt
but dy 3 dx 3 3 dx
xdt 2 dt 2 dt
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 90
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Comprehension #1
9. (d)
Sol 1 x 1
f(x) x 1 f(f(x)) x 0,1.1 x x
Hence points of discontinuity are x 0,1 .
10. (c)
Sol g(X) f(f(f(x))) x,x R {0,1}
1
f(g(x)) x 0,1.1 x
Comprehension #2
11. (a)
Sol If f(x) touches x-axis at only one irrational point, then 2f(x) (x ) g(x), where is irrational.
coefficients of f(x) can’t be rational
for f(x) with rational coefficients, then point of touching is rational.
12. (a)
Sol. The point of touching has to be rational
the two roots of f(x) 0 are rational third root is also rational.
Comprehension #3
13. (a)
Sol. As m 9 0 , hence we can substitute 29x 4x 6 u 3x .
14. (d)
Sol. Here as per notations given, we can substitute 21 x (u x) as m 1 0 and p 1 0 .
15 15
14 15 2u 1 1I du u du u c x 1 x c.
u 15 15
Multiple Correct Type
15. 2 2
2
(1 sinx)(1 sinx) cosx cosx dtI
sinx(1 sinx) sinx(1 sinx) 1 1 1sinx t
4 2 2
16. Differentiating f(x) 2f(x).f '(x) 1
f '(x) ; f(x) 02
Hence x
f(x) c.2
Put x 0 ; f(0) c; but 2f (0) 1
Two Year CRP – 1214, Phase IV – Mains – Set A Page Number 91
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f(0) 1
Hence x
f(x) 12
17. sinx
f '(x) ;x
2
xcosx sinxf ''(x)
x
Now f ''(2m ) we have f ''(x) 0 & f ''((2m 1) ) we have f ''(x) 0
18. Numerator 22(x 2x 2) (x 1)
19. sinnx sin(n 2)x 2cos(n 1)xsinx
sinnx sin(n 2)x
dx 2cos(n 1)dx dxsinx sinx
/2 /2 /2 /2 /2
0 0 0 0 0
sin5x sin3x sin3xdx 2cos4xdx dx 0 dx dx
sinx sinx sinx 2
20. f '(x) 0 (sinx cosx)(non zeroquantity) 0
tanx 1 x 3 / 4 or 7 / 4 .
Global Min = x 2n (3 / 4); global max x 2n (7 / 4)
4 4
M ; m8 2 8 2
*****