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2 0 1 9 _ Jee-Main Question Paper_ Key & Solutions


Sri Chaitanya IIT Academy # 304, Kasetty Hegihts, Ayappa Society, Madhapur, Hyderabad – 500081

www. srichaitanya.net, iconcohyd@ srichaitanyacollege.net

MATHEMATICS

1. For 1x , if 2 2 22 4y x y

x e , then 2

1 log 2e

dyx

dx is equal to

1) log 2e x

2) log 2 log 2

e ex x

x

3) log 2ex x

4) log 2 log 2

e ex x

x

Key: 4

Sol: 2 2 22 4y x y

x e 2 2 4 2 2y n x n x y

2

1 2

x ny

n x

1

2

11 2 2

1 2

n x x nxy

n x

21 2 2

1 2x n x n

y n xx

2. The sum of the distinct real values of , of rwhich the vectors,

ˆ, ,i j k i j k i j k are co-planer, is:

1) 2

2) 0

3) -1

4) 1

Key: 3

Sol:

1 1

1 1 0

1 1

2 1 1 1 1 1 0

3 1 1 0

3 3 2 0

3 1 3 1 0

21, 2 0

1 , 2 Sum of distinct solutions =-1




3. Let S be the set of all points in ( , at which the function, f ( x ) = m i n

sin ,cosf x x x is not differentiable. Then S is a subsest of which of the following?

1) 3 3

, , ,4 4 4 4

2) 3 3

, , ,4 2 2 4

3) , , ,2 4 4 4

4) ,0,4 4

Key: 1

Sol:

4. The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first

and the second of these terms, the three terms now from an A.P. Then the sum of the

original three terms of the given G.P. is

1) 36

2) 24

3) 32

4) 28

Key: 4

Sol: Let terms are a

r, a, .ar G P

3 512 8a a

8

4.12,8 . .r A Pr

824 4 8r

r

1

2,2

r r

r=2 (4, 8, 16)

116,8,4

2r

Sum=28




5. The integral cos loge x dx is equal to :

(where C is a constant of integration)

1) sin log cos log2 e e

xx x C

2) cos log sin log2 e e

xx x C

3) cos log sin loge ex x x C

4) cos log sin loge ex x x C

Key:2

Sol: cosI nx dx

cos sinI nx x nx dx

cos sin cosnx x nx x nx dx

sin cos2

xI nx nx C

6. Let 1 2 3 ...

k

kS

k

. If 2 2 2

1 2 10

5...

12S S S A , then A is equal to

1) 303

2) 283

3) 156

4) 301

Key:1

Sol: 1

2K

KS

2 1

2k

KS

2 5

12kS A

10 5

12Ki

A

2 2 2 210 1 2 3 .......... 11 5

2 4 12Ki

KA

11 12 23 5

16 3

A

5

5053

A , A=303




7. Let S={1,2,3,….100}. The number of non-empty subsets A of S such that the product of

elements in A is even is

1) 50 5020 2 1

2) 1002 1

3) 502 1

4) 502 1

Key: 1

Sol: 1,2,3......100S

=Total non empty subjects-subsets with product of element is odd

100 502 1 2 1

100 502 2 50 502 2 1

8. If the sum of the deviations of 50 observations from 30 is 50, then the mean of

these observation is :

1) 50

2) 51

3) 30

4) 31

Key:4

Sol: 50

1

30 50i

i

x

50 30 50ix 50 50 30ix

Mean 1 50 30 5030 1 31

50

xx

n

9. If a variable line, 3x+4y–=0 is such that the two circles x2+y2–2x–2y+1= 0 and

x2+y2–18x–2y+78 = 0 are on its opposite sides, then the set of all values of is the

interval :-

1) [12, 21]

2) (2, 17)

3) (23, 31)

4) [13, 23]




Key:1

Sol: Centre of circles are opposite side of line 3 4 27 4 0

7 31 0

7,31

Distance from 1S

3 41 ,2 12,

5

Distance from 2S

27 4,21 41,

5

So 12,21

10. A ratio of the 5th term from the beginning to the 5th term from the end in the

binomial expansion of

1/31/3

12

2 3

is:

1) 1

31:4 16

2) 1

31: 2 6

3) 1

32 36 :1

4) 1

34 36 :1

Key: 4

Sol:

410 4110 3

4 13

1/3510 41

5

410 1/34 1

3

12

2 34. 36

12

2 3

C

T

T

C

11. let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–

6y+4= 0 respectively. If P and Q are the points of in tersection of these circles,

then the area (in sq. units) of the quadrilateral PC1 C2 is :




1) 8

2) 6

3) 9

4) 4

Key:4

Sol:

Area = 1

2 .4 22

12. In a random experiment, a fair die is rolled until two fours are obtained in succession.

The probability that the experiment will end in the fifth throw of the die is equal to :

1) 5

150

6

2) 5

175

6

3) 5

200

6

4) 5

225

6

Key: 2

Sol:

3 2

12 3 3 5

1 5 2 5 175

6 6 6 6

C

13. If the straight line, 2x–3y+17 = 0 is perpendicular to the line passing

through the points (7, 17) and (15, b), then b equals

1) -5

2) 35

3

3) 35

3

4) 5




Key: 4

Sol: 17 2

18 3

5

14. Let f and g be continuous functions on [0, a] such that f(x) = f(a– x) and

g(x)+g(a–x)=4,then 0

a

f x g x dx is equal to

1) 0

4a

f x dx

2) 0

2a

f x dx

3) 0

3a

f x dx

4) 0

a

f x dx

Key:2

Sol: 0

a

I f x g x dx

0

a

I f a x g a x dx

0

4a

I f x g g x dx

0

4 1a

I f x dx

0

2a

I f x dx

15. The maximum area (in sq. units) of a rectangle having its base on the x-axis and its

other two vertices on the parabola, y = 12–x2 such that the rectangle lies inside the

parabola, is :

1) 20 2

2) 18 3

3) 32

4) 36

Key:3




Sol: 22 12f a a a

2' 2 12 3f a a

Maximum at a=2 Maximum area a=f(2)=32

16. The Booleean expression p q p q p q is equivalent to :

1) p q

2) p q

3) p q

4) p q

Key:3

Sol:

17.

3

4

cot tanlim

cos4

x

x x

x

is

1) 4

2) 8 2

3) 8

4) 4 2

Key: 3

Sol: 3

4

cot tanlim

cos4

x

x x

x

2

4

1 tanlim

cos 4x

x

x

2

4

1 tan2 lim

cos 4x

x

x

2 2

24

cos sin 12 lim

cos sin cos2

x

x x

x x x

4

4 2 lim cos sin 8x

x x




18. Considering only the principal values of inverse functions, the set

1 10 : tan 2 tan 34

A x x x

1) is an empty set

2) contains more than two elements

3) contains two elements

4) is a singleton

Key:4

Sol: 1 1tan 2 tan 3 4x x

2

51

1 6

x

x

26 5 1 0x x

1x or 1

6x

1

6x 0x

19. An ordered pair(a,b) for which the system of linear equations 1 2x x z

1 3x y z 2 2x y z has a unique solution is

1) (1,-3)

2) (-3,1)

3) (2,4)

4) (-4,2)

Key:3

Sol: For unique solution

1 1

0 1 1 0

2

1 1 0

0 1 1 0 2

2

20. The area (in sq. units) of the region bounded by the parabola, 2 2y x and the lines,

y=x+1, x=0 and x=3, is




1) 15

4

2) 15

2

3) 21

2

4) 17

4

Key:2

Sol:

Req. area = 3

2

0

1 15 152 .5.3 9 6

2 2 2x dx

21. If be the ratio of the roots of the quadratic equation in x, 2 23 4 2 0m x m m x ,

then the least value of m for which 1

1

is

1) 2 3

2) 4 3 2

3) 2 2

4) 4 2 3

Key:2

Sol: 2 23 4 2 0m x m m x

1 1

, 1

, 2 2

23

2 2

2 2 2

4 3 2 4 6,

3 3 9 3

m m m

m m m m

24 18m , 4 18m , 4 3 2




22. If the vertices of a hyperbola be at (-2,0) and (2,0)and one of its foci be at (-3,0), then

which one of the following points does not lie on this hyperbola?

1) 4, 15

2) 6,2 10

3) 6,5 2

4) 2 6,5

Key:3

Sol:

Ae=3, 3

2e , 2 9

4 14

b

, 2 5b

2 2

14 5

x y

23. If zR

z

is a purely imaginary number and 2z , then a value of is:

1) 1

2) 2

3) 2

4) 1

2

Key:2

Sol: 0

z z

z z

2 2 0zz z z zz z z a

2 2

z , 2a

24. Let 4, 4P and 9,6Q be tow points on the parabola, 2 4y x and let X be any point on

the are POQ of this parabola, where O is the vertex of this parabola, such that the area of

PXQ is maximum. Then this maximum area (in sq. units) is :




1) 125

4

2) 125

2

3) 625

4

4) 75

2

Key:1

Sol: 2 4y x 2 ' 4yy

1

' 2yt

, 1

2t

Area=

11 1

41 125

9 6 12 4

4 4 1

25. The perpendicular distance from the origin to the plane containing the two lines

2 2 5

3 5 7

x y z and

1 4 4

1 4 7

x y z , is

1) 11

6

2) 6 11

3)11

4) 11 6

Key:1

Sol:

3 5 7

1 4 7

i j k




ˆˆ ˆ35 28 21.7 12 5i j k

ˆˆ ˆ7 14i j k

ˆˆ ˆ2i j k

1 2 2 2 1 15 0x y z

25 11 0x z

11 11

4 1 1 6

26. The maximum value of 3cos 5sin6

for any real value of is

1) 19

2) 79

2

3) 31

4) 34

Key:1

Sol: 3 1

3cos 5 sin cos2 2

y

5 3 1sin cos

2 2

max

75 119

4 4y

27. A tetrahedron has vertices 1,2,1 , 2,1,3 , 1,1,2 0,0,0P Q R and O . The angle between

the faces OPQ and PQR is

1) 1 9cos

35

2) 1 19cos

35

3) 1 17cos

31

4) 1 7cos

31

Key:1




Sol: ˆ ˆˆ ˆ ˆ ˆ2 2 3OP OQ i j k i j k

ˆˆ ˆ5 3i j k

ˆ ˆˆ ˆ ˆ ˆ2 2PQ PR i j k i j k

ˆˆ ˆ5 3i j k

28. Let y y x bet he solution of the differential equation, log , 1e

dyx y x x x

dx . If

2 2 log 4 1ey , then y(e) is equal to

1) 2

4

e

2) 4

e

3) 2

e

4) 2

2

e

Key:2

Sol: dy y

nxdx x

1

dxxe x

xy x nx C 2 21

.2 2 2

x xnx

2

2 4

x xxy nx C , for 2 2 2 2 1y n

0C 2 4

x xy nx

4

ey e

29. Let

1 0 0

3 1 0

9 3 1

P

and ijQ q be two 3 3 matrices such that 5

3Q P I . Then 21 31

32

q q

q

is

equal to




1) 15

2) 9

3) 135

4) 10

Key:4

Sol:

1 0 0

3 1 0

9 3 1

P

2

1 0 0

3 3 1 0

9 9 9 3 3 1

P

3

1 0 0

3 3 3 1 0

6.9 3 3 3 1

P

2

1 0 0

3 1 0

13 3 1

2

nP n

n nn

5

1 0 0

5.3 1 0

15.9 5.3 1

P

53Q P I

2 0 0

15 2 0

135 15 2

Q

21 31

32

15 13510

15

q q

q

30. Consider three boxes, each containing 10 balls labelled 1,2, .. .. ,10. Suppose one

ball is randomly drawn from each of the boxes. Denote by ni, the label of the

ball drawn from the ith box, (i = 1, 2, 3). Then, the number of ways in which the balls

can be chosen such that n1 < n2 < n3 is

1) 82

2) 240

3) 164

4) 120

Key:4

Sol: Number of ways = 310 120C




PHYSICS

31. Two light identical springs of spring constant k are attached horizontally at the two ends

of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre

'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed

to rigid supports as shown in figure. The rod is gently pushed through a small angle and

released. The frequency of resulting oscillation is:

1) 2 6

2

k

m

2) 1 2

2

k

m

3) 1

2

k

m

4) 1 3

2

k

m

Key:1

Sol:

2 cos2

lK

2

2

KlC




2

2

1 1 22 2

12

KlC

fMlI

1 6

2

Kf

M

32. A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer

radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and that of

the outer cylinder is K2. Assuming no loss of heat, the effective thermal conductivity of

the system for heat flowing along the length of the cylinder is:

1) 1 2K K

2) 1 2

2

K K

3) 1 22 3

5

K K

4) 1 23

4

K K

Key:4

Sol:

1 1 2 2

1 2

eq

K A K AK

A A

2 2

1 2

2

3

4

K R K R

R

1 23

4

K K

33. A travelling harmonic wave is represented by the equation y (x, t) = 10–3 sin (50 t + 2x),

where x and y are in meter and t is in seconds. Which of the following is a correct

statement about the wave?

The wave is propagating along the

1) negative x-axis with speed 25ms–1




2) The wave is propagating along the positive x-axis with speed 25 ms–1

3) The wave is propagating along the positive x-axis with speed 100 ms–1

4) The wave is propagating along the negative x-axis with speed 100 ms–1

Key:1

Sol: siny a t kx

wave is moving along –ve x-axis with speed

50

25 / sec2

v v mK

34. A straight rod of length L extends from x = a to x=L + a. The gravitational force is exerts

on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx2, is given by:

1) 1 1

Gm A BLa L a

2) 1 1

Gm A BLa a L

3) 1 1

Gm A BLa L a

4) 1 1

Gm A BLa a L

Key:2

Sol: dm= (A + Bx2)dx

2

GMdmdF

x

2

2

a L

a

GMF A Bx dx

x

a L

a

AGM Bx

x

1 1

GM A BLa a L




35. A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light

gets reflected and the amplitude of the electric field of the incident light is 30V/m, then

the amplitude of the electric field for the wave propogating in the glass medium will be:

1) 10 V/m

2) 24 V/m

3) 30 V/m

4) 6 V/m

Key:2

Sol: 1

96

100refractedP P 2 22 1

96

100t iK A K A 2 22 1

96

100t ir A r A

22 96 130

100 3tA 26430 24

100tA

36. The output of the given logic circuit is :

1) AB

2) AB

3) AB AB

4) AB AB

Key:2

Sol:

Y A B A

A AB A AB

A A B

A AB AB




37. In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the

energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is:

1) 23

8

Q

C

2) 23

4

Q

C

3) 21

8

Q

C

4) 25

8

Q

C

Key:1

Sol: 21

2iV CE

2 21

2 4 2 4f

CE CEV

c

2 21 3 3

2 4 8E CE CE

38. A particle of mass m moves in a circular orbit in a central potential field 21

2U r kr .

If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels

vary with quantum number n as:

1) 2

2

1,n nr n E

n

2) 1

,n nr n En

3) ,n nr n E n

4) ,n nr n E n

Key:4




Sol: 2

dV mvF kr

dr r

2

nhmvr

2r n 2r n

2 2 21 1

2 2E kr mv r

n

39. Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series

across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P1 and P2

respectively, then:

1) P1 = 9 W, P2 = 16 W

2) P1 = 4 W, P2 = 16W

3) P1 = 16 W, P2 = 4W

4) P1 16 W, P2 = 9W

Key:3

Sol: 2

1

220

25R

2

2

220

100R

1 2

220L

R R

21 1P i R

22 2 4P i R W

2 2

2 2

220 220

25220 220

25 100

400

1625

W

40. A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A

meteorite of the same mass, falling towards the earth, collides with the satellite

completely inelastically. The speeds of the satellite and the meteorite are the same, just

before the collision. The subsequent motion of the combined body will be :




1) in a circular orbit of a different radius

2) in the same circular orbit of radius R

3) in an elliptical orbit

4) such that it escapes to infinity

Key:3

Sol: ˆ ˆmvi mvj 12mv 1

2

GMy

R

41. Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and

outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass

such that its moment of inertia about its axis is also I, is:

1) 12 cm

2) 18 cm

3) 16 cm

4) 14 cm

Key:3

Sol: Conceptual

42. A passenger train of length 60m travels at a speed of 80 km/hr. Another freight train of

length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger

train to completely cross the freight train when : (i) they are moving in the same

direction, and (ii) in the opposite directions is

1) 5

2

2) 25

11

3) 3

2

4) 11

5

Key:4

Sol: Conceptual




43. An ideal gas occupies a volume of 2m3 at a pressure of 3×106 Pa. The energy of the gas

is:

1) 3× 102

2) 108 J

3) 6×104 J

4) 9×106 J

Key:4

Sol: 1

2 2

fEnergy nRT PV

63 10 22

f

Considering gas is monoatomic i.e. f = 3 E. = 9 × 106 J

Option-(4)

44. A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal.

What is the modulation index?

1) 0.6

2) 0.5

3) 0.3

4) 0.4

Key:1

Sol: 160m cE E

100 160mE

60mE

60

100m

C

E

E

0.6

45. The galvanometer deflection, when key K1 is closed but K2 is open, equals q0 (see

figure).On closing K2 also and adjusting R2 to 5 , the deflection in galvanometer

becomes 0

5

. The resistance of the galvanometer is, then, given by [Neglect the internal

resistance of battery]:




1) 12

2) 25

3) 5

4) 22

Key:4

Sol: Case – I

0220g

g

Ei C

R

_________ (i)

Case – II

055 55

2205

gg g

g

CEi

R R

R

_________ (ii)

05

225 1100 5g

CE

R

_____________ (ii)

0220 g

EC

R

______________ (i)

225 1100

51100 5

g

g

R

R

5500 25 225 1100g gR R

200 4400gR 22gR Ans : - 4

46. A person standing on an open ground hears the sound of a jet aeroplane, coming from

north at an angle 60° with ground level. But he finds the aeroplane right vertically above

his position. If is the speed of sound, speed of the plane is :

1) 2

3

2)

3) 2

4) 3

2




Key:3

Sol: AB = Vp × t

BC = Vt

cos60AB

BC

1

2p

V t

Vt

2p

VV

47. A proton and an -particle (with their masses in the ratio of 1:4 and charges in the ratio

of (1:2) are accelerated from rest through a potential difference V. If a uniform magnetic

field (B) is set up perpendicular to their velocities, the ratio of the radii rp : r of the

circular paths described by them will be :

1) 1: 2

2) 1: 2

3) 1:3

4) 1: 3

Key:1

Sol: KE q V

2mq V

rqB

m

rq

1

2

pr

r

48. A point source of light, S is placed at a distance L in front of the centre of plane mirror

of width d which is hanging vertically on a wall. A man walks in front of the mirror along

a line parallel to the mirror, at a distance 2L as shown below. The distance over which the

man can see the image of the light source in the mirror is :




1) 3d

2) 2

d

3) d

4) 2d

Key:1

Sol:

3d

49. The least count of the main scale of a screw gauge is 1 mm. The minimum number of

divisions on its circular scale required to measure 5 m diameter of wire is :

1) 50

2) 100

3) 200

4) 500

Key:3

Sol: Pitch

Least count=Number of division on circular scale

3

6 105 10

N

N = 200




50. A simple pendulum, made of a string of length l and a bob of mass m, is released from a

small angle 0 . It strikes a block of mass M, kept on a horizontal surface at its lowest

point of oscillations, elastically. It bounces back and goes up to an angle 1 . Then M is

given by :

1) 0 1

0 12

m

2) 0 1

0 12

m

3) 0 1

0 1

m

4) 0 1

0 1

m

Key:3

Sol: Before colision After collision

0 1 12 1 2 1v gl cos v gl cos

By momentum conservation

0 12 1 2 1mm gl cos MV m gl cos

0 12 1 1 mm gl cos cos MV

And

1

0

2 11

2 1

mV gl cose

gl cos

0 12 1 1 mgl cos cos V ____________ (i)

0 12 1 1 mm gl cos cos MV _________ (ii)

Dividing

0 1

0 1

1 1

1 1

cos cos M

mcos cos

By componendo divided




1

1

00

sin1 2

1 sin2

cosm M

m M cos

0 1 0 1

0 1 0 1

MM

m

51. What is the position and nature of image formed by lens combination shown in figure?

(f1, f2 are focal lengths)

1) 70 cm from point B at left; virtual

2) 40 cm from point B at right; real

3) 20

3cm from point B at right , real

4) 70 cm from point B at right, real

Key:4

Sol: For first lens

1 1 1

20 5V

20

3V

For second lens

20 14

23 3

V

1 1 1

14 53

V

V = 70 cm 52. In the figure shown, a circuit contains two identical resistors with resistance R = 5 and

an inductance with L = 2mH. An ideal battery of 15 V is connected in the circuit. What

will be the current through the battery long after the switch is closed?




1) 6A

2) 7.5A

3) 5.5A

4) 3A

Key:1

Sol: Ideal inductor will behave like zero resistance long time after switch is closed

2 2 15

65

I AR

53. Determine the electric dipole moment of the system of three charges, placed on the

vertices of an equilateral triangle, as shown in the figure:

1) 2

i jql

2) 32

j iql

3) 3ql j

4) 2ql j

Key:3




Sol:

1P q d 2P qd Resultnat 2 cos30P 3

2 32

pd pd

54. The position vector of the centre of mass r

cm of an symmetric uniform bar of negligible

area of cross-section as shown in figure is :

1) 13 5

8 8rcm Lx Ly

2) 11 3

8 8rcm Lx L y

3) 3 11

8 8rcm Lx L y

4) 5 13

8 8rcm Lx Ly

Key:1

Sol:

52 2 132

4 8cm

mLmL mL

X Lm

2 052

4 8cm

Lm L m m

LY

m

55. As shown in the figure, two infinitely long, identical wires are bent by 90° and placed in

such a way that the segments LP and QM are along the x-axis, while segments PS and

QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude of the magnetic field

at O is 10–4 T, and the two wires carry equal currents (see figure), the magnitude of the

current in each wire and the direction of the magnetic field at O will be ( 0 = 4×10–7

NA– 2) :




1) 40 A, perpendicular into the page

2) 40 A, perpendicular out of the page

3) 20 A, perpendicular out of the page

4) 20 A, perpendicular into the page

Key:4

Sol: Magnetic field at ‘O’ will be done to ‘PS’ and ‘QN’ only i.e. B0 = BPS + BQN Both inwards Let current in each wire = i

0 00 4 4

i iB

d d

or 7

4 02

2 1010

2 4 10

i i

d

i = 20A

56. In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the

variation dR

dl of its resistance R with length l is

1dR

dl l . Two equal resistances are

connected as shown in the figure. The galvanometer has zero deflection when the jockey

is at point P. What is the length AP?

1) 0.25 m

2) 0.3m

3) 0.35 m

4) 0.2 m

Key:1

Sol: For the given wire : ,dl

dR Cl

where C = constant.

Let resistance of part AP is R1 and PB is R2

1

2

'

'

RR

R R or R1 = R2 By balanced WSB concept.




Now dl

dR cl

1

1/21

0

.2.R C l dl C l

1

1/22

0

2 2R C l dl C l Putting R1 = R2

2 2 2C l C l 2 1l 1

2l

i.e., 1

0.254

l m m

57. For the given cyclic process CAB as shown for a gas, the work done is :

1) 1 J

2) 5 J

3) 10 J

4) 30 J

Key: 3

Sol: Since P–V indicator diagram is given, so work done by gas is area under the cyclic diagram.

W Work done by gas = 1

2 × 2 × 4 × 5 J

= 10 J

58. An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a

potentiometer of length 1 m and resistance 5 . The value of R, to give a potential

difference of 5 mV across 10 cm of potentiometer wire, is :

1) 490

2) 480

3) 395

4) 495

Key:3




Sol: Let current flowing in the wire is i.

4

5i A

R

If resistance of 10 m length of wire is x

then 0.1

0.5 51

x

Dv = P. d. on wire = i. x

3 45 10 0.5

5R

2410 or 5 400

5R

R

395R

59. A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V.

Another particle B of mass '4 m' and charge 'q' is accelerated by a potential difference of

2500 V. The ratio of de-Broglie wavelengths A

B

is close to :

1) 10.00

2) 14.14

3) 4.47

4) 0.07

Key:2

Sol: K.E. acquired by charge = K = qV

2 2

h h h

p mK mqV

2 4 . .2500

2 50. .502

B B BA

B A A A

m q V m q

m qm q V

= 2 × 7.07 = 14.14

60. There is a uniform spherically symmetric surface charge density at a distance R0 from the

origin. The charge distribution is initially at rest and starts expanding because of mutual

repulsion. The figure that represents best the speed V(R(t)) of the distribution as a

function of its instantaneous radius R (t) is :




1)

2)

3)

4)

Key:1

Sol: At any instant 't' Total energy of charge distribution is constant

i.e. 2 2

2

0

10

2 2 2

KQ KQmV

R R

2 22

0

1

2 2 2

KQ KQmV

R R

2

0 0

2 1 1.

2

KQV

m R R R

2

0 0

1 1 1 1KQV C

m R R R R

Also the slope of v-s curve will go on decreasing Graph is correctly shown by option(1)




CHEMISTRY

61. Iodine reacts with concentrated HNO3 to yield Y along with other products. The

oxidation state of iodine in Y, is :-

1) 5

2) 3

3) 1

4) 7

Key: 1

Sol: 2 3 3 2 210 2 10 4I HNO HIO NO H O

In 3HIO oxidation state of iodine is +5

62. The major product of the following reaction is:

1)

2)

3)

4)

Key: 3

Sol:

DIBAL-H will reduce cyanides & esters to aldehydes.




63. In a chemical reaction, 2 2K

A B C D , the initial concentration of B was 1.5 times

of the concentration of A, but the equilibrium concentrations of A and B were found to be

equal. The equilibrium constant(K) for the aforesaid chemical reaction is :

1) 16

2) 4

3) 1

4) 1

4

Key: 2

Sol: 2 2A B C D 0 00 1.5 0 0t a a 0 01.5 2 2eqt t a x a x x x

At equilibrium [A] = [B]

0 0 0

0 0 0 0

1.5 2 0.5

0.5 0.5 0.5eq

a x a x x a

t t a a a a

22

0 02 2

0 0

0.54

0.5 0.5C

a aC DK

A B a a

64. Two solids dissociate as follows

1

2; PA s B g C g K x atm

2

2; PD s C g E g K y atm

The total pressure when both the solids dissociate simultaneously is :-

1) 2 2x y atm

2) x y atm

3) 2 x y atm

4) x yatm

Key: 3

Sol:

1

1 2 1 1 2

.

..... 1

P B CA s B g C g K x P P

P P x P P P




2

2 2 1 2 2

.

..... 2

P C ED s C g E g K y P P

P P y P P P

Adding 1 and 2 X+y = (P1 + P2)

2 Now total pressure T C B EP P P P

1 2 1 2 1 22P P P P P P

2TP x y

65. Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous

solution of Y. If molecular weight of X is A, then molecular weight of Y is :-

1) A

2) 3A

3) 4A

4) 2A

Key: 2

Sol: For same freezing point, molality of both solution should be same. x ym m

4 1000 12 1000

96 88x yM M

96 12

, 3.274 88yM M A

Closest option is 3A

66. Poly-b-hydroxybutyrate-co-bhydroxyvalerate( PHBV) is a copolymer of___.

1) 3-hydroxybutanoic acid and 4-hydroxypentanoic acid




Key: 4

Sol: PHBV is a polymer of 3-hydroxybutanoic acid and 3-Hydroxy pentanoic acid.

67. Among the following four aromatic compounds, which one will have the lowest melting

point ?




1)

2)

3)

4)

Key: 1

Sol: M.P. of Napthalene 80°C

68. cannot be prepared by

1) 3 2HCHO PhCH CH CH MgX

2) 2 3 3PhCOCH CH CH MgX

3) 3 3 2PhCOCH CH CH MgX

4) 3 2 3CH CH COCH PhMgX

Key: 1

Sol:

69. The volume of gas A is twice than that of gas B. The compressibility factor of gas A is

thrice than that of gas B at same temperature. The pressures of the gases for equal

number of moles are :




1) 2 3A BP P

2) 3A BP P

3) 2A BP P

4) 3 2A BP P

Key: 1

Sol: 2A BV V

3A BZ Z

3. .

.A A B B

A A B B

P V P V

n RT n RT

2 3A BP P

70. The element with Z = 120 (not yet discovered) will be an/a :

1) transition metal

2) inner-transition metal

3) alkaline earth metal

4) alkali metal

Key: 3

Sol: Z = 120 Its general electronic configuration may be represented as [Nobal gas] ns2 , like other

alkaline earth metals.

71. Decomposition of X exhibits a rate constant of 0.05 mg/year. How many years are

required for the decomposition of 5 mg of X into 2.5 mg ?

1) 50

2) 25

3) 20

4) 40

Key: 1

Sol: Rate constant (K) = 0.05 g/year means zero order reaction

21/2

550

2 2 0.05 /

a gt year

K g year




72. The major product of the following reaction is :

1)

2)

3)

4)

Key: 4

Sol:

73. Given

Gas H2 CH3 CO2 SO2

Critical 33 190 304 630

Temperature/K On the basis of data given above, predict which of the following gases

shows least adsorption on a definite amount of charcoal ?

1) H2

2) CH4

3) SO2

4) CO2

Key: 1




Sol: Smaller the value of critical temperature of gas, lesser is the extent of adsorption. so least adsorbed gas is H2

74. For diatomic ideal gas in a closed system, which of the following plots does not correctly

describe the relation between various thermodynamic quantities ?

1)

2)

3)

4)

Key: 2

Sol: At higher temperature, rotational degree of freedom becomes active.

7

2PC R (Independent of P)

5

2VC R (Independent of V)

Variation of U vs T is similar as CV vs T.

75. The standard electrode potential E and its temperature coefficient dE

dT

for a cell are

2V and –5×10–4 VK–1 at 300 K respectively. The cell reaction is

2 2Zn s Cu aq Zn aq Cu s

The standard reaction enthalpy , H at 300 K in kJ mol–1 is, [Use R = 8jK–1 mol–1 and

F = 96,000 Cmol–1]

1) –412.8




2) –384.0

3) 206.4

4) 192.0

Key: 1

Sol: Chiefly NO2 , O3 and hydrocarbon are responsible for build up smog.

76. The molecule that has minimum / no role in the formation of photochemical smog, is:

1) CH2=O

2) N2

3) O3

4) NO

Key: 2

Sol: Conceptual

77. In the Hall-Heroult process, aluminium is formed at the cathode. The cathode is made out

of :

1) Platinum

2) Carbon

3) Pure aluminium

4) Copper

Key: 2

Sol: In the Hall-Heroult process the cathode is made of carbon.

78. Water samples with BOD values of 4 ppm and 18 ppm, respectively, are :

1) Highly polluted and Clean

2) Highly polluted and Highly polluted

3) Clean and Highly polluted

4) Clean and Clean

Key: 3

Sol: Clean water would have BOD value of less than 5 ppm whereas highly polluted water

could have a BOD value of 17 ppm or more.

79. In the following reactions, products A and B are :




1)

2)

3)

4)

Key: 4

Sol:

80. What is the work function of the metal if the light of wavelength 4000 Å generates

photoelectrons of velocity 6×105 ms–1 form it ?

(Mass of electron = 9×10–31 kg Velocity of light = 3×108 ms–1 Planck's constant = 6.626

× 10–34 Js Charge of electron = 1.6 × 10–19 JeV–1)

1) 0.9 eV




2) 4.0 eV

3) 2.1 eV

4) 3.1 Ev

Key: 3

Sol: ºhv hv 2

0

1 1 1

2mv he

21

2hv mv

34 8

231 5

10

6.626 10 3 10 19 10 6 10

4000 10 2

193.35 10 2.1J eV

81. Among the following compounds most basic amino acid is :

1) Lysine

2) Asparagine

3) Serine

4) Histidine

Key: 4

Sol: Histidine

82. The metal d-orbitals that are directly facing the ligands in K3[Co(CN)6] are :

1) 2,xz yz zd d and d

2) ,xy xz yzd d and d

3) 2 2xy x yd and d

4) 2 2 2x y zd and d

Key: 4

Sol: 3 6K Co CN 3 6

183Co Ar d

83. The hardness of a water sample (in terms of equivalents of CaCO3) containing




10–3MCaSO4 is:

(molar mass of CaSO4 = 136 g mol–1)

1) 100 ppm

2) 50 ppm

3) 10 ppm

4) 90 ppm

Key: 1

Sol: 3ppmof CaCO

3 310 10 100 100 ppm

84. The correct order for acid strength of compounds

3 2 2,CH CH CH C CH and CH CH

1) 2 2 3CH CH CH CH CH C CH

2) 3 2 2HC CH CH C CH CH CH

3) 3 2 2CH C CH CH CH HC CH

4) 2 22CH C CH CH CH CH CH

Key: 2

Sol: 3 2 2CH CH CH C CH CH CH (Acidic strength order)

85. Mn2(CO)10 is an organometallic compound due to the presence of :

1) Mn – Mn bond

2) Mn – C bond

3) Mn – O bond

4) C – O bond

Key:2

Sol: Compounds having at least one bond between carbon and metal are known as organometallic compounds.




86. The increasing order of reactivity of the following compounds towards reaction with

alkyl halides directly is :

1) (B) < (A) < (D) < (C)

2) (B) < (A) < (C) < (D)

3) (A) < (C) < (D) < (B)

4) (A) < (B) < (C) < (D)

Key: 2

Sol: Nucleophilicity order

87. The pair of metal ions that can give a spinonly magnetic moment of 3.9 BM for the

complex [M(H2O)6]Cl2, is :

1) Cr2+ and Mn2+

2) V2+ and Co2+

3) V2+ and Fe2+

4) Co2+ and Fe2+

Key:2

Sol:




88. In the following reaction Aldehyde + Alcohol HCl Acetal

Aldehyde Alcohol

HCHO tBuOH

CH3CHO MeOH

The best combinations is:

1) HCHO and MeOH

2) HCHO and tBuOH

3) CH3CHO and MeOH

4) CH3CHO and tBuOH

Key: 1

Sol:

1

rate steric crowding of aldehyde

t-butanol can show formation of carbocation in acidic medium

89. 50 mL of 0.5 M oxalic acid is needed to neutralize 25 mL of sodium hydroxide solution.

The amount of NaOH in 50 mL of the given sodium hydroxide solution is :

1) 40 g

2) 20 g

3) 80 g

4) 10 g

Key: 0 (add)

Sol: 2 2 4 2 2 4 22 2H C O NaOH Na C O H O

eqm of 2 2 4 eqH C O m NaOH

50 0.5 2 25 1NaOHM

2NaOHM M

Now 1000ml solution 2 10 gram NaOH




50 ml solution = 4 gram NaOH

90. A metal on combustion in excess air forms X, X upon hydrolysis with water yields H2O2

and O2 along with another product. The metal is :

1) Rb

2) Na

3) Mg

4) Li

Key:1

Sol: 22 excessRb O RbO

2 2 2 2 22 2 2RbO H O RbOH H O O

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