leader test series / joint package course · 2016. 3. 28. · paper code : 0000ct103115005 target :...

Paper Code : 0000CT103115005

TARGET : JEE (MAIN) 2016

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LEADER TEST SERIES / JOINT PACKAGE COURSE

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

Form Number :

DISTANCE LEARNING PROGRAMME(Academic Session : 2015 - 2016)

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3. The test is of 3 hours duration.

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are 360.

5. There are three parts in the question paper A,B,C consisting of

Physics, Chemistry and Mathematics having 30 questions in

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

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Test Type : ALL INDIA OPEN TEST (MAJOR) Test Pattern : JEE-Main

TEST # 07 TEST DATE : 27 - 03 - 2016

1/310000CT103115005

SPACE FOR ROUGH WORK /

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 amplitude

is 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. AM

________ :-

(1) 20% (2) 50%

(3) 100% (4) 200%

2. dc

(1)

(2)

(3)

(4) (2) (3)

3.

t = 8 s

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

0000CT1031150052/31



4. Two concentric rings each of radius R and massM are joined together such that their planes areperpendicular 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) MR2

5. A hollow sphere of radius R moves with initiallinear and angular velocities as shown in thefigure on a rough horizontal surface. Theangular velocity of the sphere when its linearvelocity becomes zero is :-

V3VR

(1) V

R anticlockwise

(2) V

R clockwise

(3) 3V

2Rclockwise

(4) 3V

2R anticlockwise

4. R M AA'

(1) 2MR

5

(2) 23 MR

2

A

M

R

A(3) 25 MR

3

(4) MR2

5. R

V3VR

(1) V

R

(2) V

R

(3) 3V

2R

(4) 3V

2R

3/310000CT103115005



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 shown

in the figure. The maximum angle which

string makes with the vertical after hitting the

pin is :-

L

(1) 1 L coscos

L

(2)

1 L coscosL

(3) cos–1L cos

L

(4)

1 L coscosL

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 QBxv

a

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

Bav2

(4) 3

Bav2

6. M, L

L

(1) 1 L coscos

L

(2)

1 L coscosL

(3) cos–1L cos

L

(4)

1 L coscosL

7. a

B

v P Q

:-

× × × × × ×× × × × × ×

× × × × × ×P QBxv

a

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

Bav2

(4) 3

Bav2

0000CT1031150054/31



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 the

width 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 ˆE 2i 3 j 4k

. The change in potential

observed by a man who moves from point (1,

0, 5) to the point (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. B

a q B

d

×××××××

×××××××

×××××××a

d

q

(1)

2 2d aqB

2d

(2) 2

2

aqB

2d

(3)

24dqB

a d (4) 2 2a d

qB2d

9. ˆ ˆ ˆE 2i 3 j 4k

(1, 0, 5) (4, 2, 6)

(

N/C ) :-

(1) 4V (2) –4V (3) 1

3 V (4)

53V

18

5/310000CT103115005



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 the

dipoles 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 form

a 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.

pqEcdh; f}/kzqo vk?kw.kZ 9.27 × 10–24 A–m2

1 µm

56g

8

(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. xy- x2 = 5y

(x, y )

(rad/sec ) (g = 10 m/s2) :-

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

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

12. A B

30Å 20Å C

C

:-

(1) 10Å (2) 20Å

(3) 65Å (4) 80Å

0000CT1031150056/31



13. In an experiment of photoelectric effect, the

variation of photoelectric current is plotted

against potential difference across emitter and

collector plates for different intensities. On the

basis of graph choose the incorrect option :-

I1I2

V

Photoelectriccurrent

(1) All emitted photoelectrons do not have same

kinetic 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 is

independent of intensity of radiation if its

frequency is constant.

(4) From the graph, we can conclude radiation

intensity I1 > I

2.

14. A passenger in an aeroplane shall :-

(1) Never see a rainbow.

(2) May see a primary and a secondary rainbow

as concentric circles.

(3) Will see a primary and a secondary rainbow

as concentric arcs.

(4) Shall never see a secondary rainbow.

13.

I1I2

V

Photoelectriccurrent

(1)

(2)

(3)

(4) I

1 > I

2

14. (1) (2)

(3)

(4)

7/310000CT103115005



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 rotationequals:-

(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 to

1

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 3F(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.

(1) 2yr (2) 1

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

16.

1

8(1) 80.53 (2) 80.5 (3) 81.53 (4) 82/3

17.

1 2 3F(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

0000CT1031150058/31



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. The

value of h is :-

20

cmO

=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 f1. A hole is made at a

distance L

6 from the closed end so that it

becomes an open pipe. Now the frequency of

first overtone of open pipe is f2. Then

1

2

f

f is :-

(1) 4

5(2)

5

4(3)

8

5(4)

5

8

18. O 10 cm

(a

g = 1.5) 20 cm

2

h h

20

cm

O

=2

(1) 5 cm (2) 10 cm

(3) 20 cm (4) 40 cm

19. L

f1

L

6

f2

1

2

f

f

:-

(1) 4

5(2)

5

4(3)

8

5(4)

5

8

9/310000CT103115005



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 lowest

frequency vibrating at 552 Hz. By using anytwo forks at time, the beat frequencies heard

are 1, 2, 3, 5, 7, 8. The possible frequencies ofother 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 measured

and readings are d1 = 1.002 cm, d

2 = 1.004 cm

and d3 = 1.006 cm. Select the correct

alternatives:-

(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 diameteris 1.3%

20. 1 kg/m3 0.01m2 y = 2sin (20t – 10x) (kg ) ['t' 'x' ]:-

m

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

21. 4 552 Hz 1, 2, 3, 5, 7, 8 (1) 553, 554 560 Hz(2) 553, 555 560 Hz(3) 553, 556 558 Hz(4) 551, 554 560 Hz

22. d

1 = 1.002 cm, d

2 = 1.004 cm

d3 = 1.006 cm

(1) 0.0013 cm

(2) 0.0013 cm

(3) 0 cm

(4) % 1.3%

0000CT10311500510/31



23. The ratio of average translational K.E. to

rotational K.E. of a linear polyatomic molecule

at temperature T is :-

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

2(4)

7

5

24. 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 electric field,

resistivity):-

(1) E

(2)

2E

(3) E2 (4) None of these

23. T

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

2(4)

7

5

24. 0.6 0.8

2cm 4 cm 0K

27°C 127°C

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

25. p O A

:-

O

A p

p

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

26. (E , ):-

(1) E

(2)

2E

(3) E2 (4)

11/310000CT103115005



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 the

common centre is :-

x

y

(1) 3 I

2R

(2) 0

3 I

2R

(3) 0 (4) 0I3 12R

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. R

I

x

y

(1) 3 I

2R

(2) 0

3 I

2R

(3) 0 (4) 0I3 12R

28.

1kg 2kg

(1) 1

kg3

(2) 2

kg3

(3) 1kg (4) 4

kg3

0000CT10311500512/31



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 D1

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) 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. U 1

2 (

1 >

2)

PA, P

B, P

C P

D

A, B, C D

A B

C D1

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) PA, P

B, P

C P

D

30. m

v

(1) mg (2) mg 1

(3) 6v (4) mg 1

13/310000CT103115005



PART B - CHEMISTRY

31. ( m ) -

(1) Scm3 mol–1 (2) Scm mol–1

(3) Sm mol–1 (4) Scm2 mol–1

32. H-

-

hc = 1240 eV.nm

(1) 1240

nm10.2

(2) 1240

nm1.89

(3) 1240

2.55 nm (4)

1240nm

0.66

33. -

(1)

(2) G > 0

(3)

(4) 1Å 1000Å

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

0000CT10311500514/31



34. 1 10 bar

(5 , 300K) (10 , 200K)

-(1) – 50 J (2) –300 cal

(3) – 5000 J (4) – 500 cal

35.

aA bB + cC

( : a , b c )

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

A2+(aq.) B3+(aq.) (1) A2+

(aq.)(2) B3+

(aq.)

(3) H+(aq.)

(4) OH(aq.)

34. 1 mol of an ideal gas undergoes adiabatic

expansion 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 reaction

will be

aA bB + cC

(Note : a , b & c are minimum integral

stoichiometric coefficients )

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

Using 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.)

15/310000CT103115005



37. 'A'

(truncated)

'B'

(1) AB (2) AB

2

(3) A2B

3(4) A

3B

2

38. -

(1) , t1/2

(2) 1st

(3) 2nd , t1/2

(4) 1st

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

-II (S-II) = 0.2 M BOH (aq.) (Kb= 10–2M)

-III (S-III) = 1 - I + 1

- II

(1) S-II < S-I < S- III

(2) S-I < S-III < S- II

(3) S-II < S-III < S- I

(4) 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' atoms

are present at each edge centre of a truncated

octahedron

(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.) (Kb=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

0000CT10311500516/31



40. FeO Fe0.8

O 1

70 ml, 0.3M KMnO4

Fe3+ -

(1) 126 (2) 75

(3) 30 (4) 135

41. :-(1) Hg (2) HgS

(3) (Hg + HgS) (4)

42. (1) Ag+ (2) Cu+2

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

43. NH3

(1) Ca (2) Eu

(3) Yb (4)

44. (1) CaH

2(2) SrH

2

(3) NaH (4) KH

45. 'X' CuSO

4

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

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

17/310000CT103115005



46.

:-

(1) sp3d2 (2) d2sp3

(3) sp3d (4) sp3

47. 3d–2p

:-

(1) O(SiH3)

2(2) OCl

2

(3) N(SiH3)

3(4)

48.

(1) Cr2O

3(2) Mn

3O

4

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

49.

:-

(1) (2)

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

50.

(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) sp3d (4) sp3

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) Cr2O

3(2) Mn

3O

4

(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

0000CT10311500518/31



51. (I) (II) SN1

:

(1) ,Br

Br

(2) , ClClO

(3) , BrBr

(4) ,I Br

52. "3--6-" ?

(1) (2)

(3) (4)

53. ?CH –NH3 2 (CH ) NH3 2 (CH ) N3 3

(a) (b) (c)

(1) a, b, c (c) (2) a, b, c (b) (3) (4) (a)

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

(1) ,Br

Br

(2) , ClClO

(3) , BrBr

(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 incorrect

option ?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

19/310000CT103115005



54. C9H

10O 2,4-DNP

1,3- :

(1)

CHO

CH –CH2 3

(2)

CH3

CH –CHO2

(3)CH –CH2 3

CHO

(4) CH3

C–CH3

O

55. C H NO6 5 2Fe/HCl (P)

HNO2 (Q)273 K

HO2

(R)

bo il

(R) :

(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 2Fe/HCl (P)

HNO2 (Q)273 K

HO2

(R)

boil

Product (R) is :

(1) (2)

OH

(3)

NH2

(4)

N Cl2+ –

0000CT10311500520/31



56.OsO4 (P)

CrO3Acetone

(Q)

(P) (Q) :

(1)

OH

OH

CH3O

OH

(2)

OH

OH

CH3

O

(3)

CH3

OH

OHO

OH

(4) CH3

OH

OH

OH

O

56.OsO4 (P)

CrO3Acetone

(Q)

Product (P) & (Q) respectively is :

(1)

OH

OH

CH3O

OH

(2)

OH

OH

CH3

O

(3)

CH3

OH

OHO

OH

(4) CH3

OH

OH

OH

O

21/310000CT103115005



57.

?

(1)

COOH

CH3

H CH3N H , H3

+

(2)

COOH

NH3

(3)COOH

NH2

(4) NH2

OBr2

KOH

58. ?

NH2

NaNO2HCl

(P) Cu/HBr (Q)

(1) (Q),

(2) (Q)

(3) (P),

(4)

57. Which of the following reaction organic product

does not contain nitrogen atom ?

(1)

COOH

CH3

H CH3N H , H3

+

(2)

COOH

NH3

(3)COOH

NH2

(4) NH2

OBr2

KOH

58. Choose the incorrect option ?

NH2

NaNO2HCl

(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

0000CT10311500522/31



59.

izdkf'kd leko;ork iznf'kZr djsxk ?

(1) 3- -1-

(2) 3- -3-

(3) 4- -2-

(4) 4- -2-

60. ?

(1)

(2)

(3) (antacid)

(4)

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

23/310000CT103115005



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 xlim

10g x 5ƒ x

is

equal to-

(1) 10 (2) 1

10(3) –1 (4)

2

3

62. The dimensions of a rectangle are continuouslychanging. The width increases at rate of3 inch/sec. while the length decreases at rate of2 inch/sec. At one instant if the each side of rectangleis 20 inch, then the rate of change of area after 3seconds is-

(1) 16 inch2/sec (2) –16 inch2/sec


63. Let 2 3x x x

ƒ x 1 ...2 4 8

(where x [–1,1]), then the value of

1

0

ƒ 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. ƒ(x) g(x) x ƒ(x),

xlim ƒ x 5g x 10

x

ƒ x 5g xlim

10g x 5ƒ x

(1) 10 (2) 1

10(3) –1 (4)

2

3

62. 3 inch/sec 2 inch/sec 20 inch 3 -(1) 16 inch2/sec (2) –16 inch2/sec


63. 2 3x x x

ƒ x 1 ...2 4 8

(x [–1,1])

1

0

ƒ x dx

e

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

64. ƒ(x) = (4x + 1, x + 2, –2x + 4),

x R ƒ(x)

(1) 1

3(2)

1

2(3)

2

3(4)

8

3

0000CT10311500524/31



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

determinant value of matrix A is 3, then the valueof det((adjAT)T) + det.((adj A–1)–1) (where det(B)denotes determinant value of matrix B)-

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

66. Area of triangle whose vertices are (a,a2), (b,b2),

(c,c2) is 1

2 and area of another triangle whose

vertices are (p,p2), (q,q2) and (r,r2) 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 ofsquare matrix A)-

(1) 12 (2) 20

(3) 32 (4) 64

65. A = [aij], 3 × 3

A 3 det((adjAT)T) + det.((adj A–1)–1) (det(B), B)-(1) 3 (2) 6 (3) 9 (4) 18

66. (a,a2), (b,b2), (c,c2) 1

2

(p,p2), (q,q2) (r,r2)

4

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

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

67.

2

2

4 sec 1 0

A 0 3tan 1

0 1 2

2

2

cot 2 0

B 1 3cosec 1

1 1 2

tr.(AB)

(tr(A),A )-(1) 12 (2) 20

(3) 32 (4) 64

25/310000CT103115005



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 has 2

3 probability of landing heads.

If the coin is flipped 50 times, then the probabilitythat 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. a

a a a

a a an

n 1 n 2 .... n nlim 15

1 2 ... n

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

69. x > 0 y > 0

2

2 2

5x 12y

x y

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

70.

2P x x 2 x 2x 2

2Q x x 2 x 2x 2

2 8R x x 2 x 16 P(x). Q(x). R(x) x4

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

71. 2

3

50

(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

0000CT10311500526/31



72. Consider the system of equations

2 3 4 51 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 whichpasses through (1,2) is-

(1) dy

y x 1 2dx

(2) dy

y x 1 2dx

(3) dy

y x 1 2dx

(4) dy

y x 1 2dx

74. Perimeter of the locus represented by

z iarg

z i 4

(where i 1 ) is equal to-

(1) 3

2

(2)

3

2

(3) 2

(4) None of these

72.

2 3 4 51 2 3 4 5x x x x x 5

x1 + 2x

2 + 3x

3 + 4x

4 + 5x

5 = 15

x1,x

2,x

3,x

4,x

5

(x1,x

2,x

3,x

4,x

5)

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

73. (1,2) -

(1) dy

y x 1 2dx

(2) dy

y x 1 2dx

(3) dy

y x 1 2dx

(4) dy

y x 1 2dx

74.z i

argz i 4

( i 1 ) -

(1) 3

2

(2)

3

2

(3) 2

(4)

27/310000CT103115005



75. If 0 < <

0000CT10311500528/31



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 ˆa ti 3 j 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

ƒ x dx 0

and 3

0

ƒ x dx 3 , then the area

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

(1) 1 (2) 3

(3) 6 (4) cannot be evaluated

82. In a set of 2n observations, half of them are equalto '' and the remaining half are equal to '-'.If the standard deviation of all the observations is2, then || is equal to-

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

79. (2 + 1)x + (3 – )y + z = 4, ( R)

(1) x y z 4

0 0 1

(2)

x y z

1 2 3

(3) x y z 4

1 2 7

(4)

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

ˆ ˆ ˆc 3i tj k

2

1

a. b c dt

-

(1) 0 (2) 6 (3) –2 (4) 4

81. ƒ(x)

3

3

ƒ x dx 0

3

0

ƒ x dx 3 y = ƒ(x),

x-x = –3 x = 3 -

(1) 1 (2) 3

(3) 6 (4)

82. 2n ''

'-'

2 ||

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

29/310000CT103115005



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 C

2

(where C is constant of integration)

83. A(z1), B(z

2), C(z

3)

|z1| = |z

2| = |z

3| = 4

2 3

1

z zP

z

BC

(1) z1 + z

2 + z

3(2) z

1 – z

2 – z

3

(3) 2z1 + z

3(4)

84. AB A

P

AP = 3AB C, AB

P, CB

tan

(1) 18

19(2)

3

19(3)

1

6(4)

1

3

85. xyz2 = 2

-

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

86. x

2e sec 2x 1 4 tan 2x dx

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

(3) ex/2 sec 2x + C (4) x / 21 e sec2x C

2

(C )

0000CT10311500530/31



87. A relation R1 is defined on the set R of real numbers

as follows : (x,y) R1 x3 = x2y , then relation

R1is-

(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

equation x 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 ishonest' 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. R1 R

(x,y) R1 x3 = x2y

R1 -

(1)

(2)

(3)

(4)

88. 1 11 5 1 5

tan cos cot cos4 2 7 4 2 7

(1) 5

7(2)

10

7(3)

14

5(4)

7

5

89. x (0,4)

x x 2 x7sin sin sin 1

3 3 3

(1) 6 (2) 4

(3) 2 (4)

90. (contrapositive) -

(1)

(2)

(3)

(4)

31/310000CT103115005




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