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IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Max. Marks : 237 Duration : 3 Hrs
1. This paper consists of 57 questions with 3 parts of Chemistry, Mathematics and Physics
Each Part consist of 4 Sections
Section – I : 6 Multiple Choice Questions with one correct answer (with negative marks). A
correct answer carries 5 Marks. A wrong answer carries a penalty of 2 mark
Section – II : 5 Integer type questions. A correct answer carries 3 Marks. No negative marks.
Section – III : 6 Comprehension Type questions. A correct answer carries 3 Marks. A wrong
answer carries a penalty of 1 mark
Section – IV : 2 Matrix Match type questions. A correct answer carries 8 Marks. No
negative mark.
2. Darken the appropriate bubble using a pen in the OMR sheet provided to you. Once
entered, the answer cannot be changed. Any corrections or modifications will
automatically draw a penalty of 1 mark.
3. Use of calculators and log tables is prohibited.
4. No clarification will be entertained during the examination. Doubts in the paper can be
reported to the coordinator after the exam.
5. All the best !!
Useful Data
At. Wt.:
N = 14; O = 16; H = 1; S = 32; Cl = 35.5; Mn = 55; Na = 23; C = 12; Ag = 108; K = 39; Fe = 56; Pb = 207
Physical constants:
346.626 10 J.sech , 23 -1
aN 6.022 10 mol , 8 -1C 2.998 10 ms , 31
em 9.1 10 kg
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 2
Chemistry
Section I
Multiple Choice Questions with one correct answer. A correct answer carries 5 marks. A wrong
answer carries a penalty of 2 marks 6 x 5 = 30
1. The shape and hybridisation of some xenon oxyfluorides are given choose the wrong set
(a) 32 ShapeXeOF T sp d (b) 3 2
4 Square pyramidalXeOF sp d
(c) 32 2 Distorted trigonalbipyramidalXeO F sp d (d) 3
3 2 OctahedralXeO F sp d
2. The standard half-cell reduction potential for |Ag Ag is 0.7991V at 25 c . Given the
experimental value spK = 101.56 10 for AgCl , calculate the standard half-cell reduction
potential for the |Ag AgCl electrode
(a) 0.2192V (b) 0.2192V (c) 1.2192V (d) 1.2192V
3. Give the structure of the compound X formed in the following reaction.
(a )
O
O
(b )
OCH3
OH
O
(c ) O O CH3
H5C2
(d)
O O
OCH3
O
O
X
2 5(i) C H MgI
3(ii) H OÅ
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 3
4. Which is optically inactive?
5. Which of the following acids will not evolve 2H gas on reaction with alkali metals?
(a) hydrazoic acid only (b) perxenic acid only
(c) boric acid only (d) all of these
6. Stomach acids, a dilute solution of HCl in water, can be neturalized by reaction with sodium
hydrogen carbonate. 3( ) ( ) ( ) 2 2( )aq aq aq glNaHCO HCl NaCl H O CO . How many millilitres
of 0.125 M 3NaHCO solution are needed to neutralize 18.0mL of 0.100M HCl ?
(a) 14.4 mL (b) 12.0 mL (c) 14.0 mL (d) 13.2mL
Section II
Integer answers type questions. Each carries 3 marks. No negative marks. 5 x 3 = 15
7. In a certain polluted atmosphere containing 3O at steady state concentration of 82.0 10 ,M
the hourly production of 3O by all sources was estimated as 157.2 10 .M if the only mechanism
for destruction of 3O is the second order reaction, 3 22 3 .O O The rate constant for the
destruction reaction defined by the rate law for 3 3 1 110
d Ois x Lmol s
dt
. Value of x is
C CC C
a
b
C
a
b
(a) (b)
(c) (d) CC C
a
b
a
b
CC C
a
b
C
a
b
a
N
d
e
b
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 4
8. The density of phosphorous vapour at 310 C and 775 torr is 32.64 /g dm . Number of
phosphorous atoms in a molecule is
9. When a compound, on reaction with 2 3Na CO gives compound B with which sulphur gives
compound C . The compound C is used in photography. The number of bonds in a
molecule of C is
10. 3
6Fe CN has
1.41BM and 3
2 6Fe H O
has 5.92 .BM The sum of unpaired
3d electrons in Fe in both the compounds is
11. An organic compound A fumes in moist air and reacts with cold water to give an acid B .
Acid B reacts with 3NH to give amide C . C on heating with 2 5P O gives propane nitrile.
The number of functional isomers of A is
Section III
Comprehension type questions. A correct answer carries 3 marks. A wrong answer carries a
penalty of 1 mark 6 x 3 = 18
Comprehension – I
In presence of metal catalyst , ,Ni Pt Pd hydrogen adds to
When nickel is used as a catalyst, the reaction is carried out at 200 300 C and in presence of Pt or
Pd , the hydrogenation can occur even at room temperature. Hydrogenation reactions are
exothermic in nature. Hydrogenation follows free radical mechanism. The metal catalysts are used
in finely divided state in solvent like ethanol. These are classified as heterogenous catalysts. Both
C C
C C and bonds
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 5
2H and alkene get adsorbed at the surface of metal. The less crowded alkene adsorbs with faster
rate. Both breaking of bond of alkene and bond of 2H take place at metal surface. If palladium
is precipitate at the surface of calcium carbonate and is treated with quinolone it becomes deactivated
for adsorption of alkenes. But it can effectively catalyse hydrogenation of C C . The alkene can
adsorb at the surface of poisoned metal catalyst and syn addition of hydrogen atoms take place.
If sodium or lithium metals dissolved in liquid ammonia are used with alkynes then the metal
transfers its electrons to framework of C C bond and an anion radical is formed. Liquid
ammonia provides H atom and a vinylic radical is formed
12. Which of the following involves homogeneous reduction?
(a) 2 /2 2 3 3
H NiCH CH CH CH
(b) 3( )/3 3 3 3 2
lNa NHCH C C CH CH CH CH CH NaNH
(c) 2 3/ / /3 3
H Pd CaCO QuinolineCH COCl CH CHO
(d) 2 4/ / /3 3 2
H Pd BaSO quinolineCH C CH CH CH CH
13. The relative rate of catalytic hydrogenation of following alkenes is
(a) I>IV>III>II (b) II>III>IV>I (c) III>IV>I>II (d) II>IV>I>III
(I) (II) (III) (IV)
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 6
14. In which case the reaction is most exothermic with 2 / ?H Ni
Comprehension – II
On adding copper sulphate to an aqueous solution of a compound A a brown precipitate is
obtained which turns white on addition of excess of sodium thiosulphate solution. When Ag ion
solution is added to the aqueous solution of A . A yellow curdy precipitate is obtained which is
insoluble in ammonium hydroxide
15. The yellow curdy ppt. which is insoluble in 4NH OH is of
(a) AgBr (b) AgCl (c) AgI (d) none of these
16. The compound (A) is
(a) KI (b) KCl (c) NaCl (d) NaBr
17. The brown ppt. which turns white on addition of excess of 2 2 3Na S O solution is of
(a) 2CuI (b) 2 2Cu I (c) 2CuCl (d) 2 2Cu Cl
(a) (b)
(c) (d)
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 7
Section IV
Matrix Match type questions (4 rows per matrix type, 2 marks per row) 2 x 8 = 16
18. Matrix Match –I
Column I (Complex)
Column II (Magnetic Moment in B. M)
(A)
4
6Fe CN
(p)
1.73
(B) 3
2 6Ti H O
(q) 5.91
(C) 2
2 6Ni H O
(r) 0.00
(D) 3
6FeF
(s) 2.83
19. Matrix Match –II
Column I
Column II
(A)
zero
(p)
1 1mol lit s
(B) first
(q) 1 1mol lit s
(C) second
(r) 1s
(D) third
(s) 2 2 1mol lit s
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 8
Mathematics
Section I
Multiple Choice Questions with one correct answer. A correct answer carries 5 marks. A wrong
answer carries a penalty of 2 marks 6 x 5 = 30
20. Two cards are selected randomly from a pack of 52 cards. The probability that the first is a club
and the second is not a queen is
(a) 82
221 (b)
51
221 (c)
1
221 (d)
4
17
21. Let 0x . If the angle between the vectors 2ˆˆ ˆlog 6 3a c x i j k and
2 2ˆˆ ˆlog 2 2 logb x i j c x k is obtuse, then c belongs to
(a) 0, (b) , 0 (c) 4
, 03
(d) 2
1, 0 0,3
22. If 2 2 2 2 0a b c ab , then the point of concurrency of the family of straight lines
0ax by c lies on the line
(a) y x (b) 1y x (c) y x (d) 1x y
23. Let , , ,x y z n be positive integers and let 6n . If 2 3x y z n , then the number of ordered
triplets , ,x y z satisfying the above equation is
(a) 6n
nC (b) 3n
nC (c) 23
n C (d) none of these
24. The quadratic equation
1
x b x c x c x a x a x b
b a c a c b a b a c b c
has
(a) two real and distinct roots (b) two equal roots
(c) complex roots (d) infinite roots
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 9
25. Let ,z w be complex numbers such that 0z iw and arg zw . Then arg z equals
(a) 4
(b)
2
(c)
3
4
(d)
5
4
Section II
Integer answers type questions. Each carries 3 marks. No negative marks. 5 x 3 = 15
26. Suppose a matrix A satisfies the equation 2 5 7 0A A I . If 5 ,A aA bI then the value of
2 3 1450a b is
27. Let [ ]x denote the greatest integer x . If the period of the function
sin cos tan
12 4 3
x xx
is , then the value of 201 4820 is
28. If
2 3 97
1
97lim
1x
x x x xl
x
, then 4760 l is equal to
29. A balloon is in the form of a right circular cylinder of radius 1.5 m and length 4 m and is
surmounted by hemispherical ends. If the radius is increased by 0.01 m and the length by
0.055 m, the percentage change in the volume of the balloon is %abcd . If abcd is equal to
2380 k , then k
30. A special dice is so constructed that the probabilities of throwing 1, 2, 3, 4, 5 and 6 are
1 1 2 1 1 1 2, , , ,
6 6 6 6 6
k k k k k
and
1
6
k respectively. If two such dice are thrown and the
probability of getting a sum equal to 9 lies between 1
9and
2
9, then the number of integral
solutions of k is
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 10
Section III
Comprehension type questions. A correct answer carries 3 marks. A wrong answer carries a
penalty of 1 mark 6 x 3 = 18
Comprehension – I
Euler’s substitution
Integrals of the form 2( , )R x ax bx c dx are calculated with the aid of one of three Euler
substitutions
1. 2ax bx c t x a if 0a
2. 2ax bx c tx c if 0c
3. 2ax bx c x t if 2ax bx c a x x , , if is a real root of
2 0ax bx c
31. Which of the following functions does not appear in the primitive of 2
1
1 2 2x x
if t is a function of x ?
(a) log 1e t (b) log 2e t (c) 1
2t (d) none of these
32. Which of the following functions does not appear in the primitive of 2 1
dx
x x x
if t is a
function of ?x
(a) loge t (b) log 2e t (c) log 1e t (d) log 1t
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 11
33. Which of the following substitutions can be used for evaluating 27 10
xdx
x x ?
(a) 2
2
5 2
1
tx
t
(b)
2
2
5
2
tx
t
(c)
2
2
2 5
3 1
tx
t
(d) none of these
Comprehension – II
Consider the relation 2 24 5 6 1 0,l m l where ,l mR and let the line 1 0lx my touch a
fixed circle C
34. The centre and radius of C are
(a) 2, 0 , 3 (b) 3, 0 , 3 (c) 3, 0 , 5 (d) none of these
35. Tangents PA and PB are drawn to C from the points P on the line 1 0x y . Then the
chord of contact AB passes though the fixed point
(a) 1 5
,2 2
(b)
1 4,
3 3
(c) 1 3
, 2 2
(d) none of these
36. The number of tangents which can be drawn from the point 2, 3 to the circle C is
(a) 0 (b) 1 (c) 2 (d) 1 or 2
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 12
Section IV
Matrix Match type questions (4 rows per matrix type, 2 marks per row) 2 x 8 = 16
37. Matrix Match –I
Column I Column II
(A) Let 2 7 .z i z i k The values of k for which the
locus of z is an ellipse are
(p) 7
(B) For any complex number ,z the minimum value of
2z z i is
(q) 8
(C) Let 3 4z z i k . The values of k for which the
locus of z is a hyperbola, are
(r) 2
(D) Let 3 4 ,
50
kz i az az b where 3 4 .a i Then
the locus of z is a hyperbola if k
(s) 4
(t) 5
38. Matrix Match –II
Let A and B are two independent events such that 1 1
, .3 4
P A P B
Column I
Column II
(A)
P A B
(p)
1
12
(B) P A A B
(q) 1
2
(C) P B A B
(r) 2
3
(D) P A B
(s) 0
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 13
Physics
Section I
Multiple Choice Questions with one correct answer. A correct answer carries 5 marks. A wrong
answer carries a penalty of 2 marks 6 x 5 = 30
39. A projectile of mass 3 m explodes at highest point of its path. It breaks into three equal parts.
One part retraces its path; the second one comes to rest. The range of the projectile was 100 m. If
no explosion would have taken place, the distance of the third part from the point of projection
when it finally lands on the ground is
(a) 100 m (b) 150 m (c) 250 m (d) 300 m
40. Three capillary tubes of same radius 1 cm but of lengths 1m, 2m and 3m are fitted horizontally to
the bottom of a long cylinder containing a liquid at constant pressure flowing through these
tubes. What is the length of a single tube which can replace the three capillaries
(a) 6
11m (b) 6m (c) 5 m (d)
13
4m
41. 5.6 litre of helium gas at STP is adiabatically compressed to 0.7 litres. Taking the initial
temperature to be 1T the work done in this process is
(a) 19
8RT (b) 1
3
2RT (c) 1
15
8RT (d) 1
9
2RT
42. The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 oA . The
wave length of second spectral line in the Balmer series of singly-ionized helium atom is
(a) 1215 oA (b) 1640 oA (c) 2430 oA (d) 4687 oA
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 14
43. A 2 F capacitor is charged as shown in figure. The
percentage of it’s stored energy dissipated after the switch S
is turned to position 2 is
(a) 6%
(b) 20%
(c) 75%
(d) 80%
44. A particle of charge q and mass m moves in a circular orbit of radius r with angular speed .
The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on
(a) and q (b) , q and m (c) q and m (d) and m
Section II
Integer answers type questions. Each carries 3 marks. No negative marks. 5 x 3 = 15
45. A car leaves station X for station Y every 10 min. The distance between X and Y is 60 km. The
car travels at speed 60 km/h. A man drives a car from Y towards X at speed 60 km/h. If he
starts the moment when first car leaves station X , how many cars would he meet on route?
46. Power supplied to a particle of mass 2 kg varies with time as 23
2
tP W . Here t is in second. If
velocity of particle at 0t is 0v . The velocity of particle at time 2t s in m/s will be
47. In Young’s double slit experiment 410d
D
( d = distance between slits, D = distance of screen
from the slits). At a point P on the screen resulting intensity is equal to the intensity due to
individual slit oI . Then the distance of point P from the central maximum in mm is (Wave
length of source is 6000Ao
)
2
s
1
2 F
8 F
V
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 15
48. Mean free path ( ) in a fission reaction is the average distance covered by a neutron between two
fissions. Generation of nearly 200 neutrons are needed to fission all the nuclei in 10kg of U 23592 .
If cm 4 and the fastest moving neutrons generated in a fission reaction have an energy of
2MeV, then the time for 200 neutron generation is found to be p 710 seconds. Find ' 'p .
49. Some magnetic flux is changed from a coil of resistance 10 . As a
result an induced current is developed in it, which varies with time
as shown in figure. the magnitude of change in flux through the coil
in webers is
Section III
Comprehension type questions. A correct answer carries 3 marks. A wrong answer carries a
penalty of 1 mark 6 x 3 = 18
Comprehension – I
Two rods 1 and 2 are released from rest as shown in figure. Given :
1 4l l , 1 2m m , 2 2l l and 2m m . There is no friction between the
two rods. If be the angular acceleration of rod 1 just after the rods
are released. Then
50. What is the normal reaction between the two rods at this instant?
(a) 16 3ml (b) 4
3
ml (c)
32
3 3
ml (d)12 3ml
( )t s
4
0.1
( )i amp
B
l
A
2
1
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 16
51. What is the horizontal force on rod 1 by hinge A at this instant?
(a) 32 12 3
3 3ml
(b) 16 2 3
3ml
(c) (14 2 3)ml (d) 3ml
52. What is initial angular acceleration of rod 2 in terms of the given parameters in the question?
(a) 2 3
2 32
g
l
(b)
3 33
g
l
(c)
6 35 3
8
g
l
(d)
3 3 8
8 3
g
l
Comprehension – II
(i) When a conducting rod of length l is moved in a magnetic field B , a potential difference V Bvl
is developed across its two ends. Here v is the velocity of the rod. Condition is that, the three vectors
,B v and I should be mutually perpendicular to each other.
(ii) ,R Cq
V iR VC
and Ldi
V Ldt
(iii) Magnetic force on a current carrying conductor in a magnetic field is given by ( )mF i l B .
In the figure shown a conducting wire PQ of length 1 ,l m is moved
in a uniform magnetic field 4B T with constant velocity 2 /v m s
towards right. Given : 2 , 1R C F and 4L H .
Current through resistance, capacitor and inductor at any time t are
1 2,I I and 3I respectively. Current through wire PQ is I .
53. At 2t s , the value of 3I is
(a) 0 (b) 2A (c) 4 A (d) 6 A
54. Find the force required to move the wire with the given constant velocity of 2m/s at 2t s
(a) 8 N (b) 16 N (c) 24 N (d) 32 N
R C L V
B
P
Q
IIT Section
Subject Topic Grand Test – Paper II Date
C + M + P Grand Test – 07 IIT – GT – 07
10th May 2014 I20140510
Ace Insignia Rough Work Page 17
55. At 2t s , suppose P is the total power generated by the applied force, 1P the power stored in
magnetic field of inductor and 2P the power dissipated in resistance, Then
(a) 72 /P J s (b) 1 40 /P J s (c) 2 32 /P J s (d) 2 80 /P J s
Section IV
Matrix Match type questions (4 rows per matrix type, 2 marks per row) 2 x 8 = 16
56. Matrix Match –I
A charged particle with some initial velocity is projected in a region, where non-zero electric
and / or magnetic fields are present. In column I, information about the existence of electric
and / or magnetic field and direction of initial velocity of charged particle are given, while in
column II the probable path of the charged particle is mentioned. Match the entries of Column I
with the entries of Column II.
Column I Column II
(A) 0, 0,E B and initial velocity of the
particle is at any angle with B
(p) Straight line
(B) 0, 0,E B and initial velocity of the
particle is at any angle with E
(q) Parabola
(C) 0, 0,E B E B and initial
velocity of the particle is perpendicular
to both
(r) Circular
(D) 0, 0,E B E perpendicular to B and
initial velocity of the particle is
perpendicular to both E and B
(s) Helical path with non-uniform pitch
IIT Section
Subject Topic Grand Test – Paper II Date
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10th May 2014 I20140510
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F
Ring
F
Disc
F
Solid Cylinder
R/2
57. Matrix Match –II
Assume sufficient friction to prevent slipping.
Column I Column II
(A)
(p) Body accelerates forward
(B)
(q) Rotation about the centre of mass is
clockwise
(C)
(r) Friction force acts backward
(D)
(s) No friction acts
F
Solid Cylinder
R/2
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