2703 AIOt Paper

7/26/2019 2703 AIOt Paper

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Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Main

TEST DATE : 27 - 03 - 2016

TARGET : JEE (MAIN) 2016LEADER & ENTHUSIAST COURSE

Paper Code : 0000CT103115005Form Number :

CLASSROOM CONTACT PROGRAMME(Academic Session : 2015 - 2016)

H I N D I

Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005

+91-744-5156100 [email protected] www.allen.ac.in

our Target is to secure Good Rank in JEE (Main) 2016

Important Instructions

Do not open this Test Booklet until you are asked to do so.

1. Immediately fill in the form number on this page of the Test Booklet

with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited .

2. The candidates should not write their Form Number anywhere else

(except in the specified space) on the Test Booklet/Answer Sheet.

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 ineach part of equal weightage. Each question is allotted 4 (four)

marks for correct response.

6. One Fourth mark will be deducted for indicated 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. Use Blue/Black Ball Point Pen only for writting particulars/

marking responses on Side–1 and Side–2 of the Answer Sheet.

Use of pencil is strictly prohibited.

8. No candidate is allowed to carry any textual material, printed or

written, bits of papers, mobile phone any electronic device etc,

except the Identity Card inside the examination hall/room.

9. Rough work is to be done on the space provided for this purpose

in the Test Booklet only.

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

candidate are allowed to take away this Test Booklet with them.

11. Do not fold or make any stray marks on the Answer Sheet.

eg oi . u n '

b l i i rd d rc rd u [ y tc rd dg u t ,A

1. i j h k k i q f L r d k d s b l i ` " B i j v k o ' ; d f o o j . kuh y s @ dk y s ck W y ik

i s u ls r R d k y H k j s a Ai s f U ly dk i z ;k s x f cY d q y oftZ r g S a A

2. i j h k k F k h Z v i u k Q k e Z u a - ( f u/ k k Z f j r tx g d s v f r f j ‰ ) i j h@ m Ÿ k j i = i j d g h a v k S j u f y [ k s a A

3. i j h k k d h v o f / k3 V

g S A

4. b l i j h k k i q f L r d k e s a90 i z ' u g a S A v f / k d r e v a d360 g S a A

5. b l i j h k k i q f L r d k e s a r h u H k k xA, B, C g S a ] f tld s i z R ; s d H k k x

rd oK u

]l ;u oK u

, o ax . r

d s 30 i 'u

g S a v k S j lH k h i z ' u d s v a d le k u g S a A i z R ; s d i z ' u d s

lg

m Ÿ k j d s f y ,4 ( p k j)v a d f uË k k Z f j r f d ; s x ; s g S a A

6. i z R ; s d x y r m Ÿ k j d s f y , m l i z ' u d s d q y v a d d k,d p b v d

d k V k tk ; s x k A m Ÿ k j i q f L r d k e s a d k s b Z H k h m Ÿ k j u g h a e s a ls

Ω. ed v du

u g h a g k s x k A

7. m Ÿ k j i = d si B & 1

, o ai B & 2

i j o k a f N r f o o j . k , o a m Ÿ k j v a f d r d j u s g s r q d s o y

u y d y c y i b V i u

d k g h i z ; k s x d j s a A i ly d i ; x lo o t r g A

8. i j h k k F k h Z k j k i j h k k d k @ g k W y e s a i f j p ; i = d s v

i z d k j d h i k B ~ ; lk e x z h e q f Ê r ; k g L r f y f [ k r d k x t d h i f pZ e k s c k b y Q k s u ; k f d lh H k h i z d k j d s b y s D V ™ k f u d m i d j . k k s a i z d k j d h lk e x z h d k s y s tk u s ; k m i ; k s x d j u s d h v u q e f r u

9. j Q d k ; Z i j h k k i q f L r d k e s a d s o y f u/ k k Z f j r tx g i j g h d h f

10. i j h k k le k I r g k s u s i j] i j h k k F k h Z d k @ g k W y N k s M + u s ls i wv o ' ; lk S a i n s a A

i viu l b li i rd d y

g A

11. m i= d u e M ,o u g m l i v ; u' u y

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SPACE FOR ROUGH WORK / dP p d ; d y, L u

ALL INDIA OPEN TEST/JEE (Main)/27-03-2016

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

PART A - PHYSICS

1. If the unmodulated level peak carrier amplitudeis double of modulating signal in an AM signal,

the amplitude modulation is ________ :-

(1) 20% (2) 50%

(3) 100% (4) 200%

2. The dc output polarity from a half-wave

rectifier can be reversed by reversing :-

(1) the diode

(2) transformer's primary coil(3) transformer's secondary coil

(4) both (2) and (3)

3. The acceleration time graph of a particle is

shown in the figure. What is the velocity of

particle at t = 8 s if its initial velocity is 3 m/s ?

O 4 8 t

–1

4

a

(1) 4 m/s (2) 5 m/s (3) 6 m/s (4) 7 m/s

1. ; f n AM la d s r e s a f ' k [ k j o k g d v k ; k e ( e k s M q f y r u g h e k s M q f y r la d s r d k n q x u k g k s r k s v k ; k e e k s M ________ :-

(1) 20% (2) 50%

(3) 100% (4) 200%

2. f d lh v ºZ r j a x f n " V d k j h ls i z k I rdc f u x Z r / k z q o r k f u E u

e s a ls f d l i z f ÿ ; k k j k O ; q R ÿ f e r d h tk ld r h g S %

(1) M k ; k s M d k s O ; q R ÿ f e r d j

(2) V ™ k a lQ k W e Z j d h i z k F k f e d d q . M y h d k s O(3) V ™ k a lQ k W e Z j d h f r h ; d d q . M y h d k s O ; q R

(4) i z f ÿ ; k (2) , o a (3) n k s u k s a d s k j k

3. f d lh d . k d k R o j . k & le ; v k j s [ k f p = e s a i z n f ' k Z r

d . k d k t = 8 s i j o s x D ; k g k s x k ; f n b ld k i z k j f E H k

o s x3 m/s g S ?

O 4 8 t

–1

4

a

(1) 4 m/s (2) 5 m/s (3) 6 m/s (4) 7 m/s

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4. Two concentric rings each of radius R and massM are joined together such that their planes are

perpendicular to each other as shown in figure.The moment of inertia of the system about theaxis AA' is :-

(1)2MR

5

(2)23

MR 2

A

M

R

A(3)25

MR 3

(4) MR 2

5. A hollow sphere of radius R moves with initial

linear and angular velocities as shown in thefigure on a rough horizontal surface. Theangular velocity of the sphere when its linear velocity becomes zero is :-

V3VR

(1)V

R anticlockwise

(2) VR

clockwise

(3)3V

2R clockwise

(4)3V

2R anticlockwise

4. f = T ; kR rF k k Ê O ; e k uM o k y h n k s la d s U Ê h ; o y ; k s av k i l e s a b l i z d k j tk s M + k tk r k g S f d b u d s r y f p = k

, d& n w lj s d s y E c o r ~ g S A v kAA' d s lk i s k f u d k ; d k tM + R o v k ? k w . k Z g k s x k % &

(1)2MR

5

(2)23

MR 2

A

M

R

A(3)25

MR 3

(4) MR 2

5. f = T ; kR o k y s , d x f r ' k h y [ k k s [ k y s x k s y s d k i z k j f E

j s [ k h ; , o a d k s . k h ; o s x f p = e s a n ' k k Z ; k x ; k g S A [ k q j n j h k S f r t lr g i j g S A x k s y s d k j s [ k h ; o s x ' k w i j b ld k d k s . k h ; o s x g k s x k % &

V3VR

(1)V

R o k e k o r Z

(2) VR

n f k . k k o r Z

(3)3V

2R n f k . k k o r Z

(4)3V

2R o k e k o r Z

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6. A simple pendulum consisting of a mass M

attached to a string of length L is released from

rest at an angle . A pin is located at a distance

below the pivot point. When the pendulum

swings down, the string hits the pin as shownin the figure. The maximum angle which

string makes with the vertical after hitting the

pin is :-

L

(1)1 Lcos

cosL

(2) 1 Lcos

cosL

(3) cos –1Lcos

L

(4)

1 Lcoscos

L

7. In the figure a conducting wire of length a is

moving in a uniform and constant magnetic

field B with a constant velocity v parallel to its

length. The potential difference between the

ends P and Q is equal to :-× × × × × ×× × × × × ×

× × × × × ×P QB

xv

a

(1) 0 (2)Bav (3)1

Bav2

(4)3

Bav2

6. , d lj y y k s y d e s a Ê O ; e k uM, y E c k b ZL o k y h j L lh ls

tq M + k g S rF k k b ls f o j k e k o L F k k ls d k s . k i j N k s M + k tk r k g S

d h y d f c U n q ls n w j h u h p s , d f i u y x h g q b Z g S A

y k s y d u h p s d h v k s j v k r k g S r k s j L lh f i u ls f p = k

V d j k r h g S A f i u ls V d j k u s d s i ' p k r ~ j L lh k j k ≈ Ë o

ls c u k ; k x ; k v f / k d r e d k s . k g k s x k % &

L

(1)1 Lcos

cosL

(2) 1 Lcos

cosL

(3) cos –1Lcos

L

(4)

1 Lcoscos

L

7. i z n f ' k Z r f p = e s aa y E c k b Z o k y k , d p k y d r k j le :i

rF k k f u ; r p q E c d h ; k s =B e s a b ld h y E c k b Z d s le k U r j

f u ; r o s xv ls x f r ' k h y g S A f lj k s aP rF k kQ d s e/ ;

f oH k o k U r j g k s x k:-

× × × × × ×× × × × × ×

× × × × × ×P QB

xv

a

(1) 0 (2)Bav (3)1

Bav2

(4)3

Bav2

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8. In a certain region of space there exists a

constant and uniform magnetic field of

induction B. The width of the magnetic field is

a. A charged particle having charge q, is

projected perpendicular to B

and along thewidth of the field. If deflection produced by

the field perpendicular to the width is d, then

the magnitude of the momentum of the particle

is :-

×××××××

×××××××

×××××××

a

d

q

(1)

2 2d aqB

2d

(2)2

2

aqB

2d

(3)

24dqB

a d (4) 2 2a d

qB2d

9. In a certain region of space electric field is given

by ˆ ˆ Ê 2i 3 j 4k

. The change in potential

observed by a man who moves from point (1 , 0, 5) to the po int (4, 2, 6) is.

(Electric field is in N/C and coordinates are in

meter) :-

(1) 4V (2) –4V (3)1

3 V (4)

53V

18

8. v a r f j k e s a f d lh L F k k u i j i z s j . kB o k y k , d f u ; r rF k k

le :i p q E c d h ; k s = f o |e k u g S A p q E c d h ; k s =

p k S M + k b Za g S A v k o s ' kq o k y s , d v k o s f ' k r d . k d k sB

d s

y E c o r ~ rF k k k s = d h p k S M + k b Z d s v u q f n ' k i z

tk r k g S A ; f n p k S M + k b Z d s y E c o r ~ k s = k j k m

d g k s r k s d . k d s la o s x d k i f j e k . k g k s x k % &

×××××××

×××××××

×××××××

a

d

q

(1)

2 2d aqB

2d

(2)2

2

aqB

2d

(3)

24dqB

a d (4) 2 2a d

qB2d

9. v a r f j k e s a f d lh L F k k u i j f o |q r k s =ˆ ˆ Ê 2i 3 j 4k

k j k f n ; k tk r k g S A f c U n q(1, 0, 5) ls (4, 2, 6) r d x f r

d j j g s O ; f ‰ k j k i z s f " k r f oH k o e s a i f j o r Z( f o |q r k s = N/C e s a rF k k f u n s Z ' k k a d e h V j e s a g S) :-

(1) 4V (2) –4V (3)1

3 V (4)

53V

18

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10. Every iron atom in a ferromagnetic domain in

iron has a magnetic dipole moment equal to

9.27 × 10 –24 A–m2. A ferromagnetic domain in

iron has the shape of a cube of side 1 µm. The

maximum dipole moment occurs when all thedipoles are aligned. The molar mass of iron is

56g, and its specific gravity is 8. The

approximate magnetization of the domain

is :-

(1) 8.0 × 105 A/m (2) 8.0 × 108 A/m

(3) 8.0 × 1011 A/m (4) 8.0 × 1014 A/m

11. A particle is placed at the lowest point of a

smooth wire frame in the shape of a parabola,

lying in the vertical xy-plane having equation

x2 = 5y (x, y are in meter). After slight

displacement, the particle is set free. Find

angular frequency of oscillation (in rad/sec)

(take g = 10 m/s2) :-

(1) 2 rad/s (2) 4 rad/s

(3) 6 rad/s (4) 8 rad/s

12. Two particles A and B have de-Broglie's

wavelengths 30Å and 20Å, combined to forma particle C. Momentum is conserved in this

process. The possible de-Broglie's wavelength

of C is :-

(1) 10Å (2) 20Å

(3) 65Å (4) 80Å

10. y k S g s e s a y k S g p q E c d h ; i z k a r e s a i z R ; s d y k S

p q E cd h ; f/k z q o vk ? k w .k Z9.27 × 10 –24 A–m2 g k s r k g S A

y k S g s e s a , d y k S g p q E c d h ; i z k a r1 µm H k q tk o k y s ? k u d h

v k d ` f r e s a g S A tc lH k h f / k z q o la j s f [ k r g k s r s g S a f / k z q o v k ? k w . k Z i z k I r g k s r k g S A y k S g s d k e k 56g

rF k k b ld k f o f ' k " V x q :R o8 g k s r k g S A i z k a r d k y xH k

p q E c d u g k s x k % &

(1) 8.0 × 105 A/m (2) 8.0 × 108 A/m

(3) 8.0 × 1011 A/m (4) 8.0 × 1014 A/m

11. , d d . k ≈/ o k Z / k j xy- r y e s a f L F k r i j o y ;

x2

= 5y (x, y e h V j e s a g S) d h v k d ` f r o k y s , d f p d u s r k j ›s e d s f u E u r e f c U n q i j f L F k r g S A d . k d k s

f o L F k k f i r d j N k s M + f n ; k tk r k g S A n k s y u d h d k s

(rad/sec e s a) K k r d h f t, (g = 10 m/s2) :-

(1) 2 rad/s (2) 4 rad/s

(3) 6 rad/s (4) 8 rad/s

12. n k s d . k k s aA rF k kB d h M h & c z k s X y h r j a x n S / ; Z ÿ

30Å rF k k20Å g S A ; s la ; q ‰ g k s d j , d d . kC c u k r s g S a A b l i z f ÿ ; k e s a la o s x la j f k r j g r k g S AC d h la H k k f o r

M h & c z k s X y h r j a x n S / ; Z g k s x h :-

(1) 10Å (2) 20Å

(3) 65Å (4) 80Å

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13. In an experiment of photoelectric effect, thevariation of photoelectric current is plottedagainst potential difference across emitter andcollector plates for different intensities. On the

basis of graph choose the incorrect option :-

I1

I2

V

Photoelectriccurrent

(1) All emitted photoelectrons do not have samekinetic energy

(2) If frequency of incident light is kept

constant, the maximum kinetic energy of emitted photoelectron is independent of intensity.

(3) Maximum value of photoelectric current isindependent of intensity of radiation if itsfrequency is constant.

(4) From the graph, we can conclude radiationintensity I

1 > I

2.

14. A passenger in an aeroplane shall :-

(1) Never see a rainbow.(2) May see a primary and a secondary rainbowas concentric circles.

(3) Will see a primary and a secondary rainbowas concentric arcs.

(4) Shall never see a secondary rainbow.

13. i z d k ' k f o |q r i z H k k o i z ; k s x e s a f o f H k U u r h o z r k m R ltZ d rF k k la x z k g d I y s V k s a i j f oH k o k U r j f o |q r / k k j k d s e/ ; i f j o r Z u v k j s [ k i j n ' k k Z ; k x ; k x y r f o d Y i p q f u , % &

I1

I2

V

Photoelectriccurrent

(1) lH k h m R lf tZ r Q k s V k s b y s D V ™ k W u k s a d h u g h a g S A

(2) ; f n v k i f r r i z d k ' k d h v k o ` f Ÿ k f u ; r j [ k h tk , r k s

m R lf tZ r Q k s V k s b y s D V ™ k W u d h v f / k d r e r h o z r k i j f uH k Z j u g h a d j r h A

(3) i z d k ' k f o |q r / k k j k d k v f / k d r e e k u f o f d j . k d h r h o z r k i j f uH k Z j u g h a d j r k ] ; f n b ld h v k o ` f Ÿ k g k s A

(4) v k j s [ k d s v k / k k j i j d g k tk ld r k g S f d f o f d j . k r h o z r kI

1 > I

2 g S A

14. o k ; q ; k u e s a c S B s ; k = h d k s % &(1) dH k h H k h b U Ê / k u q " k f n [ k k b Z u g h a n s x k A(2) i z k F k f e d rF k k f r h ; d b U Ê / k u q " k la d s U Ê h

:i e s a f n [ k k b Z n s ld r s g S a A(3) i z k F k f e d rF k k f r h ; d b U Ê / k u q " k la d s U Ê h ;

:i e s a f n [ k k b Z n s x s a A(4) dH k h H k h f r h ; d b U Ê / k u q " k f n [ k k b Z u g h a

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15. Two identical spherical stars each having a massequal to that of the sun move in a commoncircular orbit of radius equal to the earth'sorbital radius, under their mutual gravitationalinteraction. Their time period of rotation

equals:-

(1) 2yr (2)1

2 yr (3) 2 2 yr (4) 2 yr

16. An equimolar mixture of a monoatomic and adiatomic ideal gas is suddenly compressed to1

8th of its original volume. The ratio of final

temperature to the initial temperature :-

(1) 80.53 (2) 80.5 (3) 81.53 (4) 82/3

17.

In an experiment to determine the inertial massof an object using Newton's second law,following graph is obtained between net forceon the object and the acceleration produced init. The mass of the object within error limitsis :-

1 2 3

F(N)

1

2

3

a(m/s )2

(1) 1.0 kg (2) 1 kg(3) (1.0 ± 0.1) kg (4) (1.0 ± 0.15)kg

15. lw ; Z d s le k u Ê O ; e k u o k y s n k s , d tS ls x k s y k d k

v i u s v U ; k s U ; x q :R o k d " k Z . k d s i z H k k o e s a i ` F o

f = T ; k d s c j k c j f = T ; k o k y h m H k ; f u " B o ` Ÿ k k d k j

x f r d j r s g S a A b u d s ? k w . k Z u d k v k o r Z d k y g k s x

(1) 2yr (2)1

2 yr (3) 2 2 yr (4) 2 yr

16. , d i j e k f . o d rF k k f & i j e k f . o d v k n ' k Z x S l d s

le& e k s y j f eJ . k d k s v p k u d i z k j f E H k d v k ; r u d s1

8 x q u k r d la i h f M + r f d ; k tk r k g S A v f U r e rF k k i z k r k i e k u d k v u q i k r g k s x k % &(1) 80.53 (2) 80.5 (3) 81.53 (4) 82/3

17. U ; w V u d s f r h ; f u ; e d s m i ; k s x k j k f d lh f i . M tM + R o h ; Ê O ; e k u d k s K k r d j u s lE c U / k h i z ; k s x i j y x k ; s x ; s d q y c y rF k k b le s a m R i U u R o j . k d sv k j s [ k f p = e s a n ' k k Z ; k x ; k g S A = q f V lh e k d s

d k Ê O ; e k u g S % &

1 2 3

F(N)

1

2

3

a(m/s )2

(1) 1.0 kg (2) 1 kg

(3) (1.0 ± 0.1) kg (4) (1.0 ± 0.15)kg

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18. A point object O is placed at a distance of 20cm

in front of a equi-convex lens (a

g = 1.5) of

focal length 10 cm . The lens is placed on a

liquid of refractive index 2 as shown. Image

will be formed at a distance h from lens. Thevalue of h is :-

2 0 c m

O

=2

(1) 5 cm (2) 10 cm

(3) 20 cm (4) 40 cm

19. The frequency of first overtone of a closed

organ pipe of length L is f 1. A hole is made at a

distanceL

6 from the closed end so that it

becomes an open pipe. Now the frequency of

first overtone of open pipe is f 2. Then

1

2

f

f is :-

(1)4

5(2)

5

4(3)

8

5(4)

5

8

18. , d f c U n q f c E cO d k s10 cm Q k s d l n w j h o k y s le k s Ÿ k

y s a l (a

g = 1.5) d s lk e u s20 cm n w j h i j j [ k k x ; k g S A

y s a l d k s v i o r Z u k a d2 o k y s n z o i j f p = k u q lk j j [ k k x ; k

g S A i z f r f c E c y s a l l sh n w j h i j c u r k g S Ah d k e k u

g k s x k % &

2 0 c m

O

=2

(1) 5 cm (2) 10 cm

(3) 20 cm (4) 40 cm

19. y E c k b ZL o k y s c U n v k W x Z u i k b i d s i z F k e v f / k L o

v k o ` f Ÿ kf 1 g S A c U n f lj s ls

L

6 n w j h i j , d f N Ê b l i z d k j

c u k ; k tk r k g S f d ; g , d [ k q y k i k b i c u tk r k g S A

[ k q y s i k b i d s i z F k e v f / k L o j d d h v k o ` f Ÿ kf 2 g S A r c12

f

f

d k e k u g k s x k:-

(1)4

5(2)

5

4(3)

8

5(4)

5

8

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20. A transverse wave is passing through a stringshown in figure. Mass density of the string is1 kg/m3 and cross section area of string is0.01m2. Equation of wave in string is y = 2sin(20t – 10x). The hanging mass is (in kg)

['t' is in second and 'x' is in meter] :-

m

(1) 40 (2) 0.2 (3) 0.004 (4) 0.4

21. There is a set of 4 tuning forks, one with lowestfrequency vibrating at 552 Hz. By using anytwo forks at time, the beat frequencies heard

are 1, 2, 3, 5, 7, 8. The possible frequencies of other three forks are :-

(1) 553, 554 and 560 Hz

(2) 553, 555 and 560 Hz

(3) 553, 556 and 558 Hz

(4) 551, 554 and 560 Hz

22. In an experiment to determine the radius of achalk by screw gauge, the diameter is measuredand readings are d

1 = 1.002 cm, d

2 = 1.004 cm

and d3

= 1.006 cm. Select the correctalternatives:-

(1) Mean absolute error in radius is 0.0013 cm

(2) Mean absolute error in diameter is 0.0013cm

(3) Error is 0 cm(4) % age error in the measurement of diameter

is 1.3%

20. f p = e s a , d v u q i z L F k r j a x j L lh ls g k s d j x q tj j g h j L lh d k Ê O ; e k u ? k u R o1 kg/m3 rF k k j L lh d k v u q i z L F k d k V k s = Q y0.01m2 g S A j L lh e s a r j a x d h le h d j . k y = 2sin (20t – 10x) g S A y V d s g q , Ê O ; e k u d k e k(kg e s a) g S ['t' ls d . M e s a rF k k'x' e h V j e s a g S]:-

m

(1) 40 (2) 0.2 (3) 0.004 (4) 0.4

21. 4 L o f j = k s a d s le w g e s a ls U ; w u r e v k o ` f Ÿ k o k 552 Hz i j d E i U u d j j g k g S A f d U g h a H k h n k s L o

, d lk F k i z ; q ‰ d j u s i j lq u k b Z n s u s o k y h f o L i U n

1, 2, 3, 5, 7, 8 g S A ' k s " k r h u k s a L o f j = k s a d h a v k o ` f Ÿ k ; k ° g k s x h a % &(1) 553, 554 rF k k 560 Hz

(2) 553, 555 rF k k 560 Hz

(3) 553, 556 rF k k 558 Hz

(4) 551, 554 rF k k 560 Hz

22. L ÿ w x s t k j k f d lh p k s d d s V q d M + s d h f = T ; k lE c U / k h i z ; k s x e s a O ; k l d k e k i u f d ; k tk r k g S i k B ~ ; k a dd

1 = 1.002 cm, d

2 = 1.004 cm rF k k

d3 = 1.006 cm i z k I r g k s r s g S a A lg h f o d Y i p q f u , %(1) f = T ; k e s a e k / ; f u j i s k = q f V0.0013 cm g S A

(2) O ; k l e s a e k / ; f u j i s k = q f V0.0013 cm g S A

(3) = q f V0 cm g S A

(4) O ; k l d s e k i u e s a% = q f V1.3% g S A

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23. The ratio of average translational K.E. torotational K.E. of a linear polyatomic moleculeat temperature T is :-

(1) 3 (2) 5 (3)3

2(4)

7

524. Two spheres of emissive power 0.6 and 0.8 and

radii 2cm and 4 cm are heated to 27°C and

127°C and placed in room of temperature 0K.

The ratio of heat radiated per second is :-

(1) 0.059 (2) 0.044 (3) 0.079 (4) 0.831

25. Two short dipoles of dipole moment p are

placed at two corners of a square as shown in

the figure. What is the ratio of magnitudes of electric field at two points O & A :-

O

A p

p

(1) 2 (2) 2 2 (3) 1 (4) 2

26. Rate of dissipation of joule heat in resistance per unit volume is (E is elect ric field, resistivity):-

(1)E

(2)2E

(3) E2 (4) None of these

23. r k i e k uT i j , d j S f [ k d c g q i j e k f . o d v . k q d h v k S lr L F k k u k U r j . k x f r t ≈ tk Z , o a ? k w . k Z u x f r t ≈ tk Z d k v

g k s r k g S % &

(1) 3 (2) 5 (3)

3

2 (4)

7

524. n k s x k s y k s a d h m R ltZ u k e r k0.6 o 0.8 rF k k f = T ; k ÿ e ' k %

2cm o 4 cm g S A b U g s a0K r k i e k u o k y s d e j s e s a ÿ e ' k %

27°C o 127°C r d x e Z f d ; k tk r k g S A i z f r ls d . M

f o f d f j r ≈ " e k d k v u q i k r g k s x k % &(1) 0.059 (2) 0.044 (3) 0.079 (4) 0.831

25. f / k z q o v k ? k w . k Z p o k y s n k s y ? k q f / k z q o f p = k u q lk j , d

n k s d k s u k s a i j j [ k s g q , g S a A f c U n qO rF k kA i j f o |q r k s = d s

i f j e k . k k s a d k v u q i k r g k s x k :-

O

A p

p

(1) 2 (2) 2 2 (3) 1 (4) 2

26.

i z f r j k s / k i z f r b d k b Z v k ; r u e s a tw y ≈ " e k d s ‚ k l d h g k s r h g S(E f o |q r k s = , i z f r j k s / k d r k g S):-

(1)E

(2)2E

(3) E2 (4) m i j k s ‰ e a s ls d k s b Z u

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27. Three rings each having equal radius R, are

placed mutually perpendicular to each other and

each having its centre at the origin of coordinate

system. If current I is flowing through each ring

then the magnitude of the magnetic field at thecommon centre is :-

x

y

(1) 3 I2R (2) 03 I2R

(3) 0 (4) 0I3 1

2R

28. If the system is released from rest, then the

reading of spring balance is :-

1kg 2kg

(1)1

kg3

(2)2

kg3

(3) 1kg (4)4

kg3

27. i z R ; s dR f = T ; k o k y h r h u o y ; , d& n w l j s d s y E c o r ~

j [ k h g q b Z g S rF k k i z R ; s d d k d s U Ê f u n s Z ' k k a d

f c U n q i j g S A ; f n i z R ; s d o y ; l sI / k k j k i z o k f g r g k s r h g S

r k s m H k ; f u " B d s U Ê i j p q E c d h ; k s = d k i f j e k . k

x

y

(1)3 I

2R

(2) 0

3 I

2R

(3) 0 (4) 0I3 1

2R

28. i z n f ' k Z r f u d k ; d k s f o j k e k o L F k k ls N k s M + s tk

r q y k d k i k B ~ ; k a d g k s x k % &

1kg 2kg

(1)1

kg3

(2)2

kg3

(3) 1kg (4)4

kg3

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29. An open U tube contains two immiscible liquids

of densities 1 and

2 (

1 >

2) as shown in

figure. If PA, P

B, P

C and P

D refer to the pressure

at points A, B, C and D respectively then :-

A B

C D

1

2

C

(1) PA = P

B > P

C > P

D

(2) PA = P

B > P

D > P

C

(3) PA = PB > PC = PD

(4) It is not possible to predict the correct

relation between PA, P

B, P

C and P

D with

given information

30. An irregular shaped body of mass m, density is falling with a terminal speed v in a viscous

medium of density and viscosity . The

viscous drag force acting on the body has a

magnitude :-

(1) mg (2) mg 1

(3) 6v (4) mg 1

29. , d [ k q y hU u y h e s a ? k u R o1 o

2 (

1 >

2) o k y s n k s

v f eJ . k h ; Ê o H k j s g q , g S a A ; f nPA, P

B, P

C rF k kP

D

ÿ e ' k % f c U n qA, B, C o D i j n k c g k s a r k s % &

A B

C D

1

2

C

(1) PA = P

B > P

C > P

D

(2) PA = P

B > P

D > P

C

(3) PA = P

B > P

C = P

D

(4) n h x ; h tk u d k j h d s v k / k k j i jPA, P

B, P

C o P

D d s

e/ ; lg h lE c U / k K k r d j u k v la H k o g S A

30. Ê O ; e k um rF k k ? k u R o o k y h v f u ; f e r v k d ` f r d h

o L r q lh e k U r p k yv ls ? k u R o rF k k ' ; k u r k o k y s

' ; k u e k / ; e e s a f x j j g h g S A o L r q i j d k ; Z j r ' ; k u c

d k i f j e k . k g k s x k % &

(1) mg (2) mg 1

(3) 6v (4) mg 1

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H-13/310000CT103115005



PART B - CHEMISTRY

31. e k s y j p k y d R o( m ) d h b d k b Z g S-

(1) Scm3 mol –1 (2) Scm mol –1

(3) Sm mol –1 (4) Scm2 mol –1

32. H- i j e k . k q e s a tc , d b y S D V ™ k W u , d , s ls d k d

x k s y h ; u k s M d s lk F k n k s d k s . k h ; u k s M j [ k r k

, d u k s M j [ k u s o k y s d k d e s a d w n r k g S r k s m R lf

d h r j a x n S / ; Z D ; k g k s x h-

f n ; k g S %hc = 1240 eV.nm

(1) 1240 nm10.2

(2) 1240 nm1.89

(3)1240

2.55 nm (4)

1240nm

0.66

33. l g h dF k u g S-

(1) j k lk ; f u d v f / k ' k k s " k . k ] i z d ` f r e s a v u q R ÿ e . k h

(2) n z o d s ≈ i j x S l d s v f / k ' k k s " k . k d s f y ,G > 0

(3) o S |q r d . k l a p y u d s n k S j k u x k s Y M d s d k s

f o y ; u e s a i f j f k I r i z k o L F k k d S F k k s M d h v k s j x

(4) d k s y k s b M h d . k d k v k d k j1Å ls 1000Å d s c h p

i f j o f r Z r g k s r k g S

31. Units of molar conductivity ( m ) is -

(1) Scm3 mol –1 (2) Scm mol –1

(3) Sm mol –1 (4) Scm2 mol –1

32. Wavelength of photon emited when an electron in

H-atom jumps from an orbital having 2 angular

nodes with one spherical node to an orbital having

total 1 node is -

Given hc = 1240 eV.nm

(1) 1240 nm10.2

(2) 1240 nm1.89

(3)1240

2.55 nm (4)

1240nm

0.66

33. Correct statement is -

(1) Chemical adsorption is irreversible in nature

(2) G > 0 for adsorption of gas over liquid

(3) Dispersed phase in colloidal solution of gold

moves towards cathode during electrophoresis

(4) Size of colloidal particle varies between 1Å to

1000Å

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34. 1 e k s yv k n ' k Z x S l 10 bar d s f u ; r c k g ~ ; n k c d s f o :º

(5 y h V j , 300K) ls (10 y h V j , 200K) r d :ºk s " e h ;

i z l k j e s a y h x ; h g S r k s f d ; k x ; k d k ; Z c j k c j g S-

(1) – 50 J (2) –300 cal(3) – 5000 J (4) – 500 cal

35. n h x ; h v f H k f ÿ ; k d s f y ; s lk E ; o L F k k f u ; r k a d g

aA bB + cC

( u k s V : a , b rF k k c U ; w u r e v k a f d d j lle h d j . k f e r h ; x q . k k a d g S)

Time

conc. [C]

1

2

3

4

5

6

[B]

[A]

(1) 48 (2) 4 3

(3) 64 (4) 36

36. A2+(aq.)

+ 2e – A(s) ; E = 0.8 volt

B3+(aq.)

+ 3e – B(s) ; E = 0.6 volt

; f n A2+(aq.) rF k k B3+(aq.) ; q D r f o y ; u o S |q r v i ? k f V r g k s r k g S ] r k s m i j k s D r lw p u k d k m i ; k g q , o g v k ; u c r k b ; s tk s d S F k k s M i j i g y s f u k s f i r

(1) A2+(aq.)

(2) B3+(aq.)

(3) H+(aq.)

(4) OH(aq.)

34. 1 mol of an ideal gas undergoes adiabaticexpansion from (5 litre, 300K) to (10 litre, 200K)against constant external pressure of 10 bar. Work done equals to -

(1) – 50 J (2) –300 cal(3) – 5000 J (4) – 500 cal

35. Equilibrium constant for the given reactionwill be

aA bB + cC

(Note : a , b & c are minimum integralstoichiometric coefficients )

Time

conc. [C]

1

2

3

45

6

[B]

[A]

(1) 48 (2) 4 3 (3) 64 (4) 36

36. A2+(aq.)

+ 2e – A(s) ; E = 0.8 volt

B3+

(aq.) + 3e –

B(s) ; E = 0.6 voltUsing above information find the ion which will bedeposited first at cathode if solution containingA2+(aq.) & B3+(aq.) is electrolysed.

(1) A2+(aq.)

(2) B3+(aq.)

(3) H+(aq.)

(4) OH(aq.)

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37. , d v . k q d k l j y r e lw = c r k b ; s f tu e s a'A' i j e k . k q

:f U M r (truncated) v " V Q y d d s i z R ; s d d k s u s i j

m i f L F k r g S rF k k'B' i j e k . k q i z R ; s d f d u k j s d s d s U n z

m i f L F k r g S(1) AB (2) AB

2

(3) A2B

3(4) A

3B

2

38. l g h dF k u d k p ; u d h f t; s-

(1) ' k w U ; d k s f V v f H k f ÿ ; k d s f y ; s, t1/2

i z k j f E H k d lk U n z r k

i j f u H k Z j d j r k g S

(2) 1st d k s f V v f H k f ÿ ; k d s f y ; s n j] v f H k f ÿ ; k c < +

d s l k F k l k F k f u ; r j g r h g S

(3) 2nd d k s f V v f H k f ÿ ; k d s f y ; s, t1/2

i z k j f E H k d lk U n z r k

e s a o ` f º d s l k F k c < + r k g S

(4) , d 1st d k s f V v f H k f ÿ ; k ] i z k F k f e d g h g k s x h

39. f o y ; u -I (S-I) = 0.2 M HCl (aq.)

f o y ; u -II (S-II) = 0.2 M BOH (aq.) (K b= 10 –2M)

f o y ; u -III (S-III) = 1 y h V j f o y ; u - I + 1 y h V j

f o y ; u - II

f o y s ; d k s v o k " i ' k h y rF k k f o y ; u d k s v k n ' k Z e k

g q , l g h dF k u d k p ; u d h f t; s(1) i j k lj . k n k c d k ÿ e g S %S-II < S-I < S- III

(2) o k " i n k c d k ÿ e g S %S-I < S-III < S- II

(3) D oF k u k a d f c U n q d k ÿ e g SS-II < S-III < S- I

(4) f g e k a d f c U n q d k ÿ e g S S-I < S-II < S -III

37. Find the simplest formula of a molecule in which'A' atoms are present at each corner and 'B' atomsare present at each edge centre of a truncatedoctahedron

(1) AB (2) AB2

(3) A2B

3(4) A

3B

2

38. Select the correct statement -

(1) For zero order reaction, t1/2

depends on initial

conc.

(2) For 1st order reaction, rate remains constant

as reaction proceed

(3) For 2nd order reaction, t1/2

increases with

increase in initial conc.

(4) A 1st order reaction must be elementry

39. Solution-I (S-I) = 0.2 M HCl (aq.)

Solution-II (S-II) = 0.2 M BOH (aq.) (K b=10 –2M)

Solution-III (S-III) = 1 litre solution- I + 1 litre

solution- II

Considering solute to be non-volatile and solution

to be ideal, select the correct statement(1) Order of osmostic pressure is S-II < S-I<S-III

(2) Order of vapour pressure is S-I < S-III <S-II

(3) Order of boiling point is S-II < S-III <S-I

(4) Order of freezing point is S-I< S-II < S-III

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40. FeO rF k kFe0.8

O d s le k u e k s y o k y s1 y h V j f o y ; u

d k s v E y h ; e k / ; e e s a70 ml, 0.3M KMnO4 d s lk F k

m i p k f j r f d ; k x ; k g S m R i k f n rFe3+ d s f e y h e k s y g S-

(1) 126 (2) 75

(3) 30 (4) 135

41. f u E u e s a ls d k S u lk ; k S f x d , s D o k j s f t; k e s a f o g S :-(1) Hg (2) HgS

(3) (Hg + HgS) (4) m i j k s D r lH k h

42. f u E u e s a ls d k S u lk / k u k ; u] c k s j s D l e u d k i j h k . k

e u d k n s r k g S &(1) Ag+ (2) Cu+2

(3) Al+3 (4) Cd+2

43. f u E u e s a ls d k S u ls r R o NH3 f o y ; u e s a f o y s ; g k s tk r s

g S rF k k m u d s f o y ; u v i p k ; d d s :i e s a d k ; Z d j r s g S(1) Ca (2) Eu

(3) Yb (4) m i j k s D r lH k h

44. b u e s a ls d k S u ls ; k S f x d d k s g k b M ™ k s f yF k d s lk

l e k u g k b M ™ k b M d s :i e s a tk u k tk r k g S &(1) CaH

2(2) SrH

2

(3) NaH (4) KH45. 'X' x S l lM + h g q b Z e N y h tS lh x a / k j [ k r h g S A

CuSO4 f o y ; u d s lk F k f ÿ ; k d j k ; h tk r h g S r k s v o k s

d k j a x D ; k g k s r k g S &

(1) i h y k (2) H k w j k

(3) y k y (4) d k y k

40. A 1 litre solution containing equal moles of FeO

and Fe0.8

O was titrated with 70 ml 0.3M KMnO4

in acidic medium. Millimoles Fe3+ produced are

(1) 126 (2) 75

(3) 30 (4) 135

41. Which of the following compound is soluble in

aqua regia :-

(1) Hg (2) HgS

(3) (Hg + HgS) (4) All of these

42. Which of the following cation gives coloured bead

in borax bead test

(1) Ag+ (2) Cu+2

(3) Al+3 (4) Cd+2

43. Which of the following elements dissolved in NH3

solution and their solution act as reducing agent.

(1) Ca (2) Eu

(3) Yb (4) All of these

44. Which of the following compound is known ashydrolith as well as salt like hydride.

(1) CaH2

(2) SrH2

(3) NaH (4) KH

45. 'X' gas has rotten fish smell, when react with CuSO4

solution, then what is the colour of ppt.

(1) Yellow (2) Brown

(3) Red (4) Black

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46. l k s f M ; e u k b V ™ k s i z q l k b M d s d s U n z h ; i j e k . k q

D ; k g S:-

(1) sp3d2 (2) d2sp3

(3) sp3

d (4) sp3

47. f u E u e s a l s d k S u lh L i h ' k h t e s a3d –2p

i ' p c a / k u

m i f L F k r g S:-

(1) O(SiH3)

2(2) OCl

2

(3) N(SiH3)

3(4) m i j k s D r lH k h

48. f u E u e s a ls d k S u ls / k k r q v k W D lk b M d k s v k S

d k c Z u v i p ; u f o f / k k j k v i p f ; r u g h a f d ; k tk r k g S

(1) Cr 2O3 (2) Mn3O4

(3) ZnO (4) (1) o (2) n k s u k s a

49. f u E u e s a ls d k S u lh f o f / k d k i z ; k s x d s o y v L F k k ; h

d k s g V k u s d s f y , f d ; k tk r k g S:-

(1) m c k y d j (2) D y k d Z

(3) f tv k s y k b V (4) (1) o (2) n k s u k s a

50.

f u E u e s a ls d k S u lk v . k q @ L i h ' k h t le r y h ; d s lk F k / k q z o h ; g S &

(1) XeF2

(2) I3 –

(3) ICl4 – (4) ClF

3

46. What is the hybridisation of central atom of sodium

nitroprusside :-

(1) sp3d2 (2) d2sp3

(3) sp

3

d (4) sp

3

47. Which of the following specie has 3d –2p

back

bonding :-

(1) O(SiH3)

2(2) OCl

2

(3) N(SiH3)

3(4) All of these

48. Which of the following metal oxide are not reduced

commercially by carbon reduction method.

(1) Cr 2O3 (2) Mn3O4

(3) ZnO (4) Both (1) and (2)

49. Which of the following methods are used for

removal of temporary hardness only :-

(1) Boiling (2) Clark's

(3) Zeolite (4) Both (1) and (2)

50.

Which of the following molecule/specie is planar as well as polar :-

(1) XeF2

(2) I3 –

(3) ICl4 – (4) ClF

3

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51. f u E u e a s ls d k S u ls ; q X e e s a(I) d h r q y u k e s a(II) SN1

v f H k f ÿ ; k d s i z f r v f / k d f ÿ ; k ' k h y g S:

(1) ,Br

Br

(2) ,ClClO

(3) ,Br Br

(4) ,I Br

52. f u E u e s a l s d k S u l k ; k S f x d v k s t k s u h v i ? k"3- e s f F k y -6- v k W D lk s g s I V s u s y " m R i k f n r d j s x k?

(1) (2)

(3) (4)

53. f u E u ; k S f x d k s d s f y ; s ] x y r f o d Y i d k p ; u d h f t; s?

CH –NH3 2 (CH ) NH3 2 (CH ) N3 3

(a) (b) (c)

(1) x S l i z k o L F k k e s aa, b, c e s a ls(c) lo k Z f / k d k k j h ; g S(2) ty h ; i z k o L F k k e s aa, b, c e s a ls(b) lo k Z f / k d k k j h ; g S(3) lH k h ] l e k u l e tk r J s . k h d s l n L ; g S(4) d s o y(a) d k s x s f c z ; y F k s y h e k b M l a ' y s " k . k

i z k I r f d ; k tk l d r k g S

51. Among the following pairs, in which pair (II) ismore reactive than (I) for SN1 reaction :

(1) ,Br

Br

(2) ,ClClO

(3) ,Br Br

(4) ,I Br

52. Which of the following compound on ozonolysiswill produce "3-methyl-6-oxoheptanal" ?

(1) (2)

(3) (4)

53. For the following compounds, choose the incorrectoption ?

CH –NH3 2 (CH ) NH3 2 (CH ) N3 3

(a) (b) (c)

(1) (c) is most basic among a, b, c in gas phase(2) (b) is most basic among a, b, c in aq. phase(3) All are member of same homologous series(4) Only (a) can be obtained by gabriel

phthalimide synthesis

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54. v . k q lw =C9H

10O d k , d d k c Z f u d ; k S f x d2,4-DNP

O ; q R i U u c u k r k g S ] V k W y s U lv f H k d e Z d d k s v

g S rF k k d s f u tk j k s v f H k f ÿ ; k n s r k g S r h o z v k

i j ; s 1,3- M k b Z d k c k s Z f D lf y d v E y n s r k g S ] r k s ; k :

(1)

CHO

CH –CH2 3

(2)

CH3

CH –CHO2

(3)CH –CH2 3

CHO

(4)CH3

C–CH3

O

55. C H NO6 5 2

Fe/HCl (P) HNO2 (Q)

273 K H

O 2

(R)

b o

i l

m R i k n(R) g S :

(1) (2)

OH

(3)

NH2

(4)

N Cl2

+ –

54. An organic compound with molecular formula

C9H

10O forms 2,4-DNP derivative, reduces

tollen's reagent & undergo cannizzaro reaction. On

vigrous oxidation it gives 1,3-dicarboxylic acid,

then compound is :

(1)

CHO

CH –CH2 3

(2)

CH3

CH –CHO2

(3)

CH –CH2 3

CHO

(4)

CH3

C–CH3

O

55. C H NO6 5 2

Fe/HCl (P) HNO2 (Q)

273 K H

O 2

(R)

b o

i l

Product (R) is :

(1) (2)

OH

(3)

NH2

(4)

N Cl2

+ –

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56.OsO4 (P)

CrO3

Acetone (Q)

m R i k n(P) rF k k (Q) ÿ e ' k % g S:

(1)

OH

OH

CH3

O

OH

(2)

OH

OH

CH3

O

(3)

CH3

OH

OH

O

OH

(4) CH3

OH

OH

OH

O

56.OsO4 (P)

CrO3

Acetone (Q)

Product (P) & (Q) respectively is :

(1)

OH

OH

CH3

O

OH

(2)

OH

OH

CH3

O

(3)

CH3

OH

OH

O

OH

(4) CH3

OH

OH

OH

O

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57. f u E u e s a l s d k S u l h v f H k f ÿ ; k d s d k c Z f u d m R

u k b V ™ k s tu i j e k . k q m i f L F k r u g h a g S?

(1)

COOH

CH3

H CH3

N H , H3

+

(2)

COOH

NH3

(3)COOH

NH2

(4) NH2

O

Br 2KOH

58. x y r f o d Y i d k p ; u d h f t; s ?

NH2

NaNO2

HCl (P) Cu/HBr (Q)

(1) m R i k n (Q), c z k s e k s c s a th u g S(2) (Q) d k f u e k Z . k ] ls . M e s ; j v f H k f ÿ ; k d s u k e

tk u k tk r k g S

(3) m R i k n(P), c s a th u M k b Z , s tk s f u ; e D y k s j k b M

(4) b u e s a l s d k s b Z u g h a

57. Which of the following reaction organic productdoes not contain nitrogen atom ?

(1)

COOH

CH3

H CH3

N H , H3

+

(2)

COOH

NH3

(3)COOH

NH2

(4) NH2

OBr 2

KOH

58. Choose the incorrect option ?

NH2

NaNO2

HCl (P) Cu/HBr (Q)

(1) Product (Q) is bromobenzene

(2) Formation of (Q) is known as sandmayer

reaction

(3) Product (P) is benzene diazonium chloride

(4) None of these

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0000CT103115005H-22/31



59. f u E u e s a l s d k S u l k ; k S f x d T ; k f e r h ; d s l k F k

i z dk f ’k d lek o;ork i z nf ’k Z r dj s xk?

(1) 3- e s f F k y i s U V -1- b Z u

(2) 3- e s f F k y g s D l -3- b Z u

(3) 4- e s f F k y g s D l -2- b Z u

(4) 4- e s f F k y i s U V -2- b Z u

60. l g h f o d Y i d k p ; u d h f t; s ?

(1) i k W y h F k h u ] , d J ` a [ k y k o/ k Z d c g q y d g S

(2) lk c q u e s a , s U V h ls I V h d x q . k y k u s d s f y ; s c k

f e y k ; k tk r k g S

(3) f le s f V M h u d k i z ; k s x i z f rv E y(antacid) d s :i

e s a f d ; k tk r k g S

(4) m i j k s D r lH k h

59. Which of the following compound will show

geometrical as well as optical isomerism ?

(1) 3-methyl pent-1-ene

(2) 3-methyl hex-3-ene

(3) 4-methyl hex-2-ene

(4) 4-methyl pent-2-ene

60. Choose the correct option ?

(1) Polythene is a chain growth polymer

(2) Bithional is added to soaps to impart

antiseptic properties

(3) Cimetidine is used as antacid

(4) All of these

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PART C - MATHEMATICS

61. If ƒ(x) and g(x) are functions such that ƒ(x)

approaches to infinity as x and

xlim ƒ x 5g x 10 , then

x

ƒ x 5g x

lim 10g x 5ƒ x

is

equal to-

(1) 10 (2)1

10(3) –1 (4)

2

3

62. The dimensions of a rectangle are continuously

changing. The width increases at rate of

3 inch/sec. while the length decreases at rate of

2 inch/sec. At one instant if the each side of rectangle

is 20 inch, then the rate of change of area after 3

seconds is-

(1) 16 inch2/sec (2) –16 inch2/sec


63. Let 2 3x x x

x 1 ...2 4 8

(where x [–1,1]), then the value of

1

0

x dx

e

is

equal to-

(1) 1 (2) 2 (3) 3 (4) 4

64. Let ƒ(x) = min(4x + 1, x + 2, –2x + 4), x R,

then the maximum value of ƒ(x) is -

(1)1

3(2)

1

2(3)

2

3(4)

8

3

61. ; f n Q y u ƒ(x) rF k kg(x) b l i z d k j g S f dx i j ƒ(x), v u U r d h v k s j v x z l j g S rF k k

xlim ƒ x 5g x 10 g k s ] r k s x

ƒ x 5g x

lim 10g x 5ƒ x

c j k c j g k s x k &

(1) 10 (2)1

10(3) –1 (4)

2

3

62. , d v k ; r d h T ; k f e f r f u j a r j i f j o f r Z r g k s r h g S A b ld p k S M + k b Z e s a3 inch/sec d h n j ls o ` f º g k s r h g S tc f d b ld h y E c k b Z e s a2 inch/sec d h n j ls d e h g k s r h g S A ; f n f d l h , d k . k i j v k ; r d h i z R ; s d H k q tk d h y E c k b Z20 inch g S ] r k s3 ls d . M i ' p k r b ld s k s = Q y e s a i f j o r Z u d h n j g k s x h-



63. e k u k 2 3x x x

x 1 ...2 4 8

( tg k °x [–1,1]) g k s ] r k s

1

0

x dx

e

d k e k u g k s x k &

(1) 1 (2) 2 (3) 3 (4) 4

64. e k u kƒ(x) = U ; w u r e(4x + 1, x + 2, –2x + 4),

x R g k s ] r k sƒ(x) d k v f / k d r e e k u g k s x k &

(1)1

3(2)

1

2(3)

2

3(4)

8

3

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65. Let A = [aij] be a 3 × 3 invertible matrix. If

determinant value of matrix A is 3, then the value

of det((adjAT)T) + det.((adj A –1) –1) (where det(B)

denotes determinant value of matrix B)-

(1) 3 (2) 6 (3) 9 (4) 1866. Area of triangle whose vertices are (a,a2), (b,b2),

(c,c2) is1

2 and area of another triangle whose

vertices are (p,p2), (q,q2) and (r,r 2) is 4, then the

value of

2 2 2

2 2 2

2 2 2

1 ap 1 bp 1 cp

1 aq 1 bq 1 cq

1 ar 1 br 1 cr

is-

(1) 2 (2) 4 (3) 8 (4) 16

67. Let

2

2

4 sec 1 0

A 0 3tan 1

0 1 2

and

2

2

cot 2 0

B 1 3cosec 1

1 1 2

, then minimum

value of tr.(AB) is (where tr(A) denotes trace of

square matrix A)-

(1) 12 (2) 20

(3) 32 (4) 64

65. e k u kA = [aij], , d 3 × 3 d k O ; q R ÿ e . k h ; v k O ; w g g S

; f n v k O ; w gA d k lk j f . k d e k u3 g S ] r k sdet((adjAT)T) + det.((adj A –1) –1) d k e k u g k s x k ( tg k °det(B), v k O ; w gB d s lk j f . k d d k s n ' k k Z r k g S)-

(1) 3 (2) 6 (3) 9 (4) 18

66. ' k h " k Z(a,a2), (b,b2), (c,c2) o k y s f =H k q t d k k s = Q y1

2

rF k k ' k h " k Z(p,p2), (q,q2) rF k k(r,r 2) o k y s v U ; f =H k q t d k

k s = Q y4 g k s ] r k s

2 2 2

2 2 2

2 2 2

1 ap 1 bp 1 cp

1 aq 1 bq 1 cq

1 ar 1 br 1 cr

d k e k u g k s x k &(1) 2 (2) 4 (3) 8 (4) 16

67. e k u k

2

2

4sec 1 0

A 0 3tan 1

0 1 2

rF k k

2

2

cot 2 0

B 1 3cosec 1

1 1 2

g k s ] r k str.(AB) d k

U ; w u r e e k u g k s x k( tg k ° tr(A), o x Z v k O ; w gA d s v u q j s [ k d k s n ' k k Z r k g S)-

(1) 12 (2) 20

(3) 32 (4) 64

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68. Let a be a positive real number and

a a a

a a an

n 1 n 2 .... n nlim 15

1 2 ... n

,

then the value of a is-(1) 1 (2) 2 (3) 3 (4) 4

69. Let x > 0 and y > 0, then the maximum value of

2

2 2

5x 12y

x y

is-

(1) 25 (2) 144 (3) 169 (4) 256

70. Consider the polynomials

2P x x 2 x 2x 2

2Q x x 2 x 2x 2

2 8R x x 2 x 16 ,

then the coefficient of x4 in P(x). Q(x). R(x) is-

(1) 0 (2) 2 (3) 2 (4) 4

71. A biased coin has2

3 probability of landing heads.

If the coin is flipped 50 times, then the probability

that the number of heads is zero or even is-

(1)

50 50

50

3 2

2.3

(2)

50

50

3 1

2.3

(3)

50

50

3 1

2.3

(4)

50 50

50

3 2

2.3

68. e k u k a , d / k u k R e d o k L r f o d l a [ ; k rF k k

a a a

a a an

n 1 n 2 .... n nlim 15

1 2 ... n

g k s ]

r k sa d k e k u g k s x k &(1) 1 (2) 2 (3) 3 (4) 4

69. e k u kx > 0 rF k ky > 0 g k s ] r k s

2

2 2

5x 12y

x y

d k

v f / k d r e e k u g k s x k &

(1) 25 (2) 144 (3) 169 (4) 256

70. e k u k c g q i n

2P x x 2 x 2x 2

2Q x x 2 x 2x 2

2 8R x x 2 x 16

g k s ] r k sP(x). Q(x). R(x) d s i z lk j e s ax4 d k x q . k k a d g k s x k &

(1) 0 (2) 2 (3) 2 (4) 4

71. , d i k i k r h f lD d s d s f p Ÿ k o k j f x j u s d h i z k f ; d r k2

3

g S ; f n f lD d s d k s50 c k j m N k y k tk r k g S ] r k s i z k I r f d h d q y l[ a ; k ] ' k w U ; ; k le la [ ; k e s a i z k I r g k s u s i z k f ; d r k g k s x h &

(1)

50 50

50

3 2

2.3

(2)

50

50

3 1

2.3

(3)

50

50

3 1

2.3

(4)

50 50

50

3 2

2.3

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72. Consider the system of equations

2 3 4 5

1 2 3 4 5x x x x x 5 and

x1 + 2x

2 + 3x

3 + 4x

4 + 5x

5 = 15

where x1,x

2,x

3,x

4,x

5 are positive real numbers, then

the number of (x1,x

2,x

3,x

4,x

5) is-

(1) 0 (2) 1 (3) 2 (4) 3

73. The differential equation of family of lines which

passes through (1,2) is-

(1) dy

y x 1 2dx

(2) dyy x 1 2dx

(3) dy

y x 1 2dx

(4) dy

y x 1 2dx

74. Perimeter of the locus represented by

z iargz i 4

(where i 1 ) is equal to-

(1)3

2

(2)

3

2

(3)2

(4) None of these

72. e k u k le h d j . k f u d k ;

2 3 4 5

1 2 3 4 5x x x x x 5 rF k k

x1 + 2x

2 + 3x

3 + 4x

4 + 5x

5 = 15

tg k °x1,x

2,x

3,x

4,x

5 / k u k R e d o k L r f o d la [ ; k ; s a g k s ] r

(x1,x

2,x

3,x

4,x

5) d h d q y la [ ; k g k s x h &

(1) 0 (2) 1 (3) 2 (4) 3

73. f c U n q(1,2) ls x q tj u s o k y s j s [ k k f u d k ; k s a d k v o le h d j . k g k s x k -

(1) dy

y x 1 2dx

(2) dyy x 1 2dx

(3) dy

y x 1 2dx

(4) dy

y x 1 2dx

74.z i

argz i 4

k j k i z n f ' k Z r f c U n q iF k d k i f j e k i g

( tg k ° i 1 ) -

(1)3

2

(2)

3

2

(3)2

(4) b u e s a ls d k s b Z u g h a

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75. If 0 < < < <2

, then the equation

(x – sin) (x – sin) + (x – sin) (x – sin)

+ (x – sin) (x – sin) = 0, has-

(1) real and unequal roots

(2) non-real roots

(3) real and equal roots

(4) real and unequal roots greater than 2.

76. Let P1 and P

2 be two fixed points in xy-plane.

A line L1 = 0 passes through P

1 intersects y-axis

at B and the line L2 = 0 passes through P

2 and

intersects x-axis at A. If L1 = 0 and L

2 = 0 are

perpendicular then the locus of mid-point of

AB is-

(1) Straight line (2) Circle

(3) Ellipse (4) Parabola

77. If ˆˆ â, b,c are unit vectors, then the number of

integers in the range of the expression

2 2 2ˆ ˆˆ ˆ ˆ ˆ2a 3b 2b 3c 2c 3a is-

(1) 51 (2) 53 (3) 55 (4) 57

78. The complete set of real values of such that

point P(, sin) lies inside the triangle formed by

lines x – 2y + 2 = 0, x + y = 0 and x – y – = 0 is-

(1) ,3 2

(2) 0, ,6 3 2

(3)2

0, ,2 3

(4) (0,)

75. ; f n 0 < < < <2

g k s ] r k s le h d j . k

(x – sin) (x – sin) + (x – sin) (x – sin)

+ (x – sin) (x – sin) = 0 d s &

(1) o k L r f o d rF k k v le k u e w y g k s x s a A(2) v o k L r f o d e w y g k s x s a A(3) o k L r f o d rF k k le k u e w y g k s x s a A(4) 2 ls c M + s o k L r f o d rF k k v le k u e w y g k s x s a A

76. e k u kP1 rF k kP

2 , xy- le r y e s a n k s v p j f c U n q g S A f c U

P1 ls x q tj u s o k y h , d j s [ k kL

1 = 0, y- v k d k s f c U n qB

i j d k V r h g S rF k k f c U n qP2 ls x q tj u s o k y h j s [ k kL

2 = 0,

x- v k d k s f c U n qA i j d k V r h g S A ; f nL1 = 0 rF k k

L2 = 0 y E c o r ~ g k s ] r k sAB d s e/ ; f c U n q d k f c U n q iF k

g k s x k &(1) lj y j s [ k k (2) o ` Ÿ k (3) n h ? k Z o ` Ÿ k (4) i j o y ;

77. ; f n ˆˆ â,b,c b d k b Z l f n ' k g k s ] r k s O ; a t2 2 2ˆ ˆˆ ˆ ˆ ˆ2a 3b 2b 3c 2c 3a d s i f j l j e s a

i w . k k ± d k s a d h la [ ; k g k s x h -

(1) 51 (2) 53 (3) 55 (4) 57

78. d s o k L r f o d e k u k s a d k i w . k ± le q P p ; b l i z d k j f c U n qP(, sin), j s [ k k v k s ax – 2y + 2 = 0, x + y = 0

rF k kx – y – = 0 k j k f u f e Z r f =H k q t d s v U n j d h v k f L F k r g S &

(1) ,3 2

(2) 0, ,6 3 2

(3)2

0, ,2 3

(4) (0,)

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79. The variable plane (2 + 1)x + (3 – )y + z = 4,

( R) always contains the line :

(1)x y z 4

0 0 1

(2)

x y z

1 2 3

(3)x y z 4

1 2 7

(4) None of these

80. Let ˆ ˆ ˆ ˆˆ â ti 3j 2tk, b i 2 j 2k

and

ˆ ˆ ˆc 3i tj k

, then the value of the integral

2

1

a. b c dt

equals-

(1) 0 (2) 6 (3) –2 (4) 4

81. Let ƒ(x) be a continuous function such that

3

3

x dx 0

and 3

0

x dx 3 , then the area

bounded by y = ƒ(x), x-axis, x = –3 and x = 3 is

equal to -

(1) 1 (2) 3

(3) 6 (4) cannot be evaluated

82. In a set of 2n observations, half of them are equal

to '' and the remaining half are equal to '-'.

If the standard deviation of all the observations is

2, then || is equal to-

(1) 2 (2) 2

(3) 2 2 (4) 4

79. p j le r y (2 + 1)x + (3 – )y + z = 4, ( R)

ln S o f u E u j s [ k k d k s j [ k r k g S &

(1)x y z 4

0 0 1

(2)

x y z

1 2 3

(3)x y z 4

1 2 7

(4) b u e s a ls d k s b Z u g h a

80. e k u k ˆ ˆ ˆ ˆˆ â ti 3j 2tk, b i 2 j 2k

rF k k

ˆ ˆ ˆc 3i tj k

g k s ] r k s 2

1

a. b c dt

d k e k u

g k s x k -

(1) 0 (2) 6 (3) –2 (4) 4

81. e k u k ƒ(x) , d l a r r ~ Q y u b l i z d k j g S f d

3

3

x dx 0

rF k k 3

0

x dx 3 g k s ] r k sy = ƒ(x),

x- v k ]x = –3 rF k kx = 3 k j k i f j c º k s = Q y g k s x k -

(1) 1 (2) 3

(3) 6 (4) g y u g h a f d ; k tk ld r k A

82. 2n i z s k . k k s a d s le q P p ; e s a ] v k / k s i z s k . k'' d s c j k c j rF k k

' k s " k v k / k s i z s k . k'-' d s c j k c j g S A ; f n lH k h i z s k . k k s a

e k u d f o p y u2 g k s ] r k s|| c j k c j g k s x k &

(1) 2 (2) 2

(3) 2 2 (4) 4

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83. Let A(z1), B(z

2), C(z

3) are three points on Argand

plane such that |z1| = |z

2| = |z

3| = 4. The image of

2 3

1

z zP

z

about the line BC is-

(1) z1 + z

2 + z

3(2) z

1 – z

2 – z

3

(3) 2z1 + z

3(4) None of these

84. AB is a vertical pole resting at the end A on the

level ground. P is a point on the level ground such

that AP = 3AB. If C is the mid point of AB and

CB subtends an angle at P, then the value of

tan is-

(1)18

19(2)

3

19(3)

1

6(4)

1

3

85. Consider at three dimensional figure represented

by xyz2 = 2, then its minimum distance from origin

is-

(1) 2 (2) 4 (3) 6 (4) 8

86. x

2e sec2x 1 4 tan 2x dx is equals-

(1) 4ex/2 sec2x + C (2) 2ex/2 sec2x + C

(3) ex/2 sec 2x + C (4)x /21

e sec2x C2

(where C is constant of integration)

83. e k u kA(z1), B(z

2), C(z

3) v k x Z . M le r y i j r h u f c U n q

b l i z d k j g S f d|z1| = |z

2| = |z

3| = 4 g S A f c U n q

2 3

1

z zP

z

d k j s [ k kBC d s lk i s k i z f r f c E c g k s x k &

(1) z1 + z

2 + z

3(2) z

1 – z

2 – z

3

(3) 2z1 + z

3(4) b u e s a ls d k s b Z u g h a

84. AB , d m / o k Z / k j [ k E H k k g S ] tk s / k j k r y i j f c U n q A i j

f o j k e o L F k k e s a [ k M + k g q v k g S A / k j k r y i j , d fP b l

i z d k j g S f dAP = 3AB g S A ; f nC, AB d k e/ ; f c U n q

g S rF k k f c U n qP, CB i j d k s . k v U r f j r d j r k g S ] r k s

tan d k e k u g k s x k &

(1)18

19(2)

3

19(3)

1

6(4)

1

3

85. e k u k r h u T ; k f e r h ; v k j s [ kxyz2 = 2 k j k i z n f ' k Z r g S ] r k s

e w y f c U n q ls b ld h U ; w u r e n w j h g k s x h -

(1) 2 (2) 4 (3) 6 (4) 8

86.

x

2e sec 2x 1 4 tan 2x dx c j k c j g k s x k &

(1) 4ex/2 sec2x + C (2) 2ex/2 sec2x + C

(3) ex/2 sec 2x + C (4)x / 21

e sec2x C2

( tg k ° C le k d y u v p j g S )

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0000CT103115005H-30/31



87. A relation R 1 is defined on the set R of real numbers

as follows : (x,y) R 1 x3 = x2y , then relation

R 1is-

(1) only symmetric relation

(2) only transitive relation

(3) only reflexive relation

(4) reflexive and transitive relation

88.1 11 5 1 5

tan cos cot cos4 2 7 4 2 7

is equal to-

(1)5

7(2)

10

7(3)

14

5(4)

7

5

89. The sum of the solutions in x (0,4) of the

equationx x 2 x

7sin sin sin 13 3 3

is-

(1) 6 (2) 4

(3) 2 (4) None of these

90. The contrapositive of ' If Kapil is rich then he is

honest' is-

(1) If Kapil is not rich then he is dishonest

(2) If Kapil is dishonest then he is not rich

(3) Kapil is not rich or he is dishonest

(4) Kapil is dishonest and not rich

87. , d la c a / k R 1 o k L r f o d la [ ; k v k s a d s le q P p ;R e s a

(x,y) R 1 x3 = x2y k j k i f jH k k f " k r g S ] r k s la

R 1 ln S o g k s x k -

(1) d s o y le f e r la c a / k

(2) d s o y la ÿ k e d la c a / k (3) d s o y L o r q Y ; la c a / k

(4) L o r q Y ; la c a / k , o a la ÿ k e d la c a / k

88.1 11 5 1 5

tan cos cot cos4 2 7 4 2 7

c j k c j g k s x k &

(1)5

7

(2)10

7

(3)14

5

(4)7

5

89. v U r j k y x (0,4) e s a l e h d j . k

x x 2 x7sin sin sin 1

3 3 3

d s g y k s a d k

; k s x Q y g k s x k &

(1) 6 (2) 4

(3) 2 (4) b u e s a ls d k s b Z u g h a

90. ; f n d f i y / k u o k u g k s r k s o g b Z e k u n k j H k h g k s

i z f r i f j o r h Z(contrapositive) g k s x k -

(1) ; f n d f i y / k u o k u u g h a g k s r k s o g b Z e k u n k j u g h

(2) ; f n d f i y b Z e k u n k j u g h a g k s r k s o g / k u o k u u g h a

(3) d f i y / k u o k u u g h a g S ; k o g b Z e k u n k j u g h a g S

(4) d f i y b Z e k u n k j u g h a g S v k S j o g / k u o k u u g h a

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