LEADER TEST SERIES / JOINT PACKAGE COURSE€¦ · 0000CT103115004 1/35 SPACE FOR ROUGH WORK / ALL...

Paper Code : 0000CT103115004

TARGET : JEE (MAIN) 2016

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LEADER TEST SERIES / JOINT PACKAGE COURSE

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DISTANCE LEARNING PROGRAMME(Academic Session : 2015 - 2016)

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3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks

are 360.

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

Physics, Chemistry and Mathematics having 30 questions in

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

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6. One Fourth mark will be deducted for indicated incorrect response

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

TEST # 06 TEST DATE : 20 - 03 - 2016

1/350000CT103115004

SPACE FOR ROUGH WORK /

ALL INDIA OPEN TEST/JEE (Main)/20-03-2016

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

PART A - PHYSICS

1. An ideal gas heat engine operates in a Carnot's

cycle between 227°C and 127°C. It absorbs

6 × 104 J at high temperature. The amount of

heat converted into work is :

(1) 4.8 × 104 J (2) 3.5 × 104 J

(3) 1.6 × 104 J (4) 1.2 × 104 J

2. Which one of the following graphs represents the

behaviour of an ideal gas for isothermel process.

(1)

PV

V

(2)

PV

V

(3)

PV

V

(4)

PV

V

1. 227°C

127°C

6 × 104 J

(1) 4.8 × 104 J (2) 3.5 × 104 J

(3) 1.6 × 104 J (4) 1.2 × 104 J

2.

(1)

PV

V

(2)

PV

V

(3)

PV

V

(4)

PV

V

0000CT1031150042/35



3. A parallel plate air capacitor has a capacitance

C (figure-1). When it is half filled with a

dielectric of dielectric constant 5 (figure-2),

the percentage increase in the capacitance will

be:-

Cfigure-1 figure-2

(1) 400% (2) 33.3%

(3) 66.6% (4) 200%

4. Identify the logic operation performed by the

circuit given below.

A

B

A

B

y

(1) NOT (2) AND

(3) OR (4) NAND

5. A thin prism P1 with angle 4° and made from

a glass of refractive index 1.54 is combinedwith another thin prism P2 made from glass

o f refract ive index 1.72 to producedispersion without deviation. The angle of

the prism P2 is :-

(1) 5.33° (2) 4° (3) 3° (4) 2.6°

3. C

-1 -2 5

Cfigure-1 figure-2

(1) 400% (2) 33.3%

(3) 66.6% (4) 200%

4.

A

B

A

B

y

(1) NOT (2) AND

(3) OR (4) NAND

5. P1 4° 1.54

1.72

P2

P2 (1) 5.33° (2) 4° (3) 3° (4) 2.6°

3/350000CT103115004



6. The following four wires of length L and radius

r are made of the same material. Which of these

will have the largest extension, when the same

tension is applied?

(1) L = 100 cm, r = 0.2 mm

(2) L = 200 cm, r = 0.4 mm

(3) L = 300 cm, r = 0.6 mm

(4) L = 400 cm, r = 0.8 mm

7. Eight equal drops of water are falling through

air with a steady velocity of 10 cm s–1. If the

drops combine to form a single drop big in size,

then the terminal velocity of this big drop is :-

(1) 40 cms–1 (2) 10 cms–1

(3) 30 cms–1 (4) 80 cm s–1

8. Three identical rods A, B and C are placed end

to end. A temperature difference is maintained

between the free ends of A and C. The thermal

conductivity of B is THRICE that of C and

HALF of that of A. The effective thermal

conductivity of the system will be :- (KA is the

thermal conductivity of rod A).

(1) 1/3 KA (2) 3 KA

(3) 2 KA (4) 2/3 KA

6. L r

(1) L = 100 cm, r = 0.2 mm

(2) L = 200 cm, r = 0.4 mm

(3) L = 300 cm, r = 0.6 mm

(4) L = 400 cm, r = 0.8 mm

7. 10 cm s–1

(1) 40 cms–1 (2) 10 cms–1

(3) 30 cms–1 (4) 80 cm s–1

8. A, B C

A C

B C

A

(KA, A

)

(1) 1/3 KA (2) 3 KA

(3) 2 KA (4) 2/3 KA

0000CT1031150044/35



9. Which one of the following is m – T graph for

perfectly black body? m is the frequency of

radiation with maximum intensity. T is the

absolute temperature.

A B

CD

T(K)

v(H

z)m

(1) A (2) B

(3) C (4) D

10. Two tuning forks, A and B, produce notes of

frequencies 258 Hz and 262 Hz. An unknown

note sounded with A produces certain beats.

When the same note is sounded with B, the

beat frequency gets doubled. The unknown

frequency is :-

(1) 250 Hz (2) 252 Hz

(3) 254 Hz (4) 256 Hz

9. m – T

m T

A B

CD

T(K)

v(H

z)m

(1) A (2) B

(3) C (4) D

10. A B, 258 Hz 262 Hz

A

B

(1) 250 Hz (2) 252 Hz

(3) 254 Hz (4) 256 Hz

5/350000CT103115004



11. A wire under tension vibrates with a

fundamental frequency of 600 Hz. If the

length of the wire is doubled, the radius is

halved and the wire is made to vibrate under

one-ninth the tension. Then the fundamental

frequency will become :-

(1) 200 Hz (2) 300 Hz

(3) 600 Hz (4) 400 Hz

12. The critical angle of a certain medium is

1 3sin

5

. The polarizing angle of the medium

is :-

(1) 1 4

sin5

(2) 1 5

tan3

(3)1 3

tan4

(4) 1 4

tan3

13. A conductor wire having 1029 free electrons/m3

carries a current of 20A. If the cross-section

of the wire is 1mm2, then the drift velocity of

electrons will be :- (e = 1.6 × 10–19C).

(1) 1.25 × 10–4ms–1 (2) 1.25 × 10–3 ms–1

(3) 1.25 × 10–5 ms–1 (4) 6.25 × 10–3 ms–1

11. 600 Hz

1

9

(1) 200 Hz (2) 300 Hz

(3) 600 Hz (4) 400 Hz

12. 1 3sin

5

(1) 1 4

sin5

(2) 1 5

tan3

(3)1 3

tan4

(4) 1 4

tan3

13. 1029 m3

20A

1mm2

(e = 1.6 × 10–19C).

(1) 1.25 × 10–4ms–1 (2) 1.25 × 10–3 ms–1

(3) 1.25 × 10–5 ms–1 (4) 6.25 × 10–3 ms–1

0000CT1031150046/35



14. If n-p-n transistor is to be considered to be

equivalent to two diodes connected (according

to biasing only). Which of the following figures

is the correct one:-

(1) B

E C

(2) B

E C

(3) B

E C

(4) B

E C

15. The viscosity of a fluid µ, can be determinedby measuring the terminal velocity VT of asphere when it descends in the fluid. The fluidhas a density f while the sphere has a densitys and a diameter of d. The viscosity can thenbe calculated by the formula

2s f

T

5( )d

9V

The values measured areVT = (1.60 ± 0.04) ms–1

s = (2700 ± 20) kg m–3

f =(900 ± 10) kg m–3

d = (20.0 ± 0.4) mmWhat is the percentage uncertainty in the valueof µ?

(1) 6.2% (2) 7.1% (3) 8.2% (4) 8.4%

14. n-p-n

(1) B

E C

(2) B

E C

(3) B

E C

(4) B

E C

15. µ, VT f s d

2s f

T

5( )d

9V

VT = (1.60 ± 0.04) ms–1

s = (2700 ± 20) kg m–3

f =(900 ± 10) kg m–3

d = (20.0 ± 0.4) mm

µ (1) 6.2% (2) 7.1% (3) 8.2% (4) 8.4%

7/350000CT103115004



16. A person of weight 500 N does a bungee jump

using an elastic rope of unstretched length

40 m and having a spring constant k equal to

50 N/m. During the initial fall there is a

transfer of energy from gravitational potential

energy to kinetic energy and elastic potential

energy. The person falls through a distance of

80 m before beginning to move upwards.

Which set of graphs correctly represent the

variation of the three energies?

GravitationalPotential Energy

ElasticPotential Energy

Kinetic Energy

(1)

0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

(2)

0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

(3)

0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

(4)

0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

16. 500 N

40 m 50 N/m

80m

GravitationalPotential Energy

ElasticPotential Energy

Kinetic Energy

(1)

0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

(2)

0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

(3)

0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

(4)

0 10 20 30 40 50 60 70 80 90 10005

101520253035404550

0000CT1031150048/35



17. The graphs in figure show how the

displacement x, velocity v and the accelerationa of a body vary with time t when it is oscillating

with simple harmonic motion. What is the valueof T?

x/m

t/s20

–2 T

v/m s–1

t/s

6

0

–6T

a/m s–2

t/s

18

0

–18T

(1) s9

(2)

2s

9

(3) s

3

(4)

2s

3

18. A current balance is used to measure themagnetic flux density B of a electromagnet. Theside PQ of a current balance is inserted insidea large electromagnet. The direction ofmagnetic field is as shown in figure. Length ofPQ is L. Perpendicular distances of PQ and RSare d1 and d2 respectively from the pivot. A loadof mass m is placed along side RS. Takeacceleration due to gravity to be g. The directionand magnitude of the current along PQ are

P

Q R

SB

17. x, v a t T

x/m

t/s20

–2 T

v/m s–1

t/s

6

0

–6T

a/m s–2

t/s

18

0

–18T

(1) s9

(2)

2s

9

(3) s

3

(4)

2s

3

18. B PQ PQ L PQ RS d1 d2 m RS g PQ

P

Q R

SB

9/350000CT103115004



Direction Magnitude

(1) from P to Q2

1

md

BLd

(2) from P to Q2

1

mgd

BLd

(3) from Q to P2

1

md

BLd

(4) from Q to P2

1

mgd

BLd

19. The graph represents the decay of a newly

prepared sample of radioactive nuclide X to a

stable nuclide Y. The half-life of X is . The

growth curve for Y intersects the decay curve

for X after time T. What is the time T?

number ofatoms

x Y

0 T time

(1) 2

(2) In

2

(3) (4) 2

(1) P Q 2

1

md

BLd

(2) P Q 2

1

mgd

BLd

(3) Q P 2

1

md

BLd

(4) Q P 2

1

mgd

BLd

19. X

Y X

Y T X

T

number ofatoms

x Y

0 T time

(1) 2

(2) In

2

(3) (4) 2

0000CT10311500410/35



20. Ball 1 is launched up an inclined plane from

point A with an initial speed that is the minimum

speed for it to just reach point B at the top of

the plane. At the same moment that ball 1 is

launched up the plane, ball 2 is released from

rest from point B. The two balls make their first

contact at a point C somewhere on the inclined

plane between A and B. What is the ratio of the

distance AC to the distance BC?

Ball 1

Ball 2

A

B

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

21. A block and a sphere of equal mass m are placed

on an inclined plane. If the maximum frictional

force that can exist between the block and the

plane is equal to the weight of the block, and

there is no frictional force between the sphere

and the plane, what is the maximum angle at

which the plane can be inclined before the block

starts to slip?

(1) 30° (2) 45° (3) 60° (4) 90°

20. 1 A B 1 2B C A B AC BC

Ball 1

Ball 2

A

B

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

21. m

(1) 30° (2) 45° (3) 60° (4) 90°

11/350000CT103115004



22. A hollow metal cylinder floats upright in a bodyof water with the bottom of the cylinder at adepth of D below the water surface as shownin the figure below. The cylinder is pressedfurther down into the water and upon release,performs simple harmonic motion. Which ofthe following graphs (all drawn to scale) showshow the upthrust U and net force F acting onthe cylinder vary with d, the depth the bottomof the cylinder below the water surface?

D

(1)

U,F

0d

F

U

D

(2)

U,F

0d

F

UD

(3)

U,F

0d

F

U

D

(4)

U,F

0d

F

U

D

22. D U F d

D

(1)

U,F

0d

F

U

D

(2)

U,F

0d

FU

D

(3)U,F

0d

F

U

D

(4)

U,F

0d

F

U

D

0000CT10311500412/35



23. A progressive wave travelling to the right hits

a hard surface and gets reflected after suffering

a phase change of 180°. The diagram below

shows the incident wave at a particular instant

of time. Which of the following shows the

corresponding reflected wave?

(1)

(2)

(3)

(4)

23.

180°

(1)

(2)

(3)

(4)

13/350000CT103115004



24. A guitar string of length L is stretched between

two fixed points P and Q and made to vibrate

transversely as shown in the figure. Two

particles A and B on the string are separated by

a distance s. The maximum kinetic energies of

A and B are KA and KB respectively. Which of

the following gives the correct phase difference

and maximum kinetic energies of the particles?

A

Bs

P Q

L

Phase difference Maximum kinetic

energy

(1)3s

3602L

KA < KB

(2)3s

3602L

same

(3) 180° KA < KB

(4) 180° same

24. L P

Q

A B

s A B

KA KB

A

Bs

P Q

L

(1)3s

3602L

KA < KB

(2)3s

3602L

(3) 180° KA < KB

(4) 180°

0000CT10311500414/35



25. An atom X is excited to an energy level E2 from its

ground state E0 by collision with another atom Y.

Atom X is initially at rest. Which of the following

gives possible energy values of X and Y?

Kinetic energy of atom Kinetic energy of atom

Y before collision X after the collision

(1) less than (E2– E0) zero

(2) (E2 – E0) non-zero

(3) (E2 – E0) zero

(4) greater than (E2–E0) non-zero

26. In the figure shown, pan C is massless.

All strings and pulleys are ideal. Block B is

dropped from a height on pan C. Collision

between block B and pan C is perfectly

inelastic. Just after collision tension in string A

differ from tension in string A before collision

by a magnitude of :-

M

ABM

C

(1) Mg (2) Mg

2(3)

Mg

4(4) 2Mg

25. X Y E0 E2 X X Y

Y X (1) (E2– E0) (2) (E2 – E0) (3) (E2 – E0) (4) (E2–E0)

26. C B CB C A A

M

ABM

C

(1) Mg (2) Mg

2(3)

Mg

4(4) 2Mg

15/350000CT103115004



27. In a screw gauge, there are 100 divisions oncircular scale and each main scale division isof 1 mm. When there is no gap between thejaws, 97th divisions coincides with the mainscale zero and zero of main scale is not visible.While measuring the diameter of a ball, thecircular scale is between 3 mm mark and 4 mmmark such that the 76th division of circular scalecoincides with the reference line. Select thecorrect alternative :-(1) the least count of the micrometer is 0.01 cm

(2) the zero error is – 0.04 mm

(3) the diameter of the ball is 3.79 cm

(4) the main scale reading is 4 mm

28. A uniform solid square plate ABCD of mass m

and side a is moving in x – y horizontal smooth

plane. The velocity of centre of mass is

0ˆ ˆv 2i 4 j m / s . The end A of square plate

is suddenly fixed by a pin, find the new velocity

of centre of mass of square :-

(1) 0ˆ ˆv 2i 4 j

(2) 0 03v 3vˆ î j4 4

x

y

B C

A D

v = v i jcm 0(2 + 4 )^ ^

(3) 0 03v 3vˆ î j

2 2

(4) 0 0ˆ ˆ3v i 3v j

27. 100 1 mm 97 3 mm 4 mm 76 (1) 0.01 cm (2) – 0.04 mm (3) 3.79 cm (4) 4 mm

28. m a

ABCD x – y

0ˆ ˆv 2i 4 j m / s

A

(1) 0ˆ ˆv 2i 4 j

(2) 0 03v 3vˆ î j4 4

x

y

B C

A D

v = v i jcm 0(2 + 4 )^ ^

(3) 0 03v 3vˆ î j

2 2

(4) 0 0ˆ ˆ3v i 3v j

0000CT10311500416/35



29. In Young's double slit experiment with light of

wavelength = 600 nm, intensity of central

fringe is I0. Now one of the slit is covered by

glass plate of refraction index 1.4 and thickness

t = 5 µ m, the new intensity at the same point

on screen will be :-

(1) 0I

4(2)

03I

4

(3) I0

(4) 0I

2

30. Heat is supplied to a diatomic gas at constant

pressure, with the usual notation the ratio

Q : U : W is

(1) 5:2:2

(2) 5:2:3

(3) 7:5:2

(4) 7:2:5

29. = 600 nm

I0

1.4 t = 5 µm

(1) 0I

4(2)

03I

4

(3) I0

(4) 0I

2

30.

Q : U : W

(1) 5:2:2

(2) 5:2:3

(3) 7:5:2

(4) 7:2:5

17/350000CT103115004



PART B - CHEMISTRY

31. In a constant pressure calorimeter, 224 ml of

0.1M KOH (aq.) solution at TK is mixed with

50 ml of 0.1M H2SO

4 (aq.) solution at TK then

increase in temperature of solution will be

(assume heat capacity of calorimeter is

negligible) -

Given : neut

H for strong acid base

is = 13.7 kcal / eq.

Specific heat of solution = 1 cal/gm–K

Density of solution = 1 gm/ml

(1) 0.5 K (2) 1K

(3) 2K (4) 0.25

32. Small amount of HCl(aq) is added in freshly

precipitated Al(OH)3 to form a colloidal sol.

The only correct statement regarding the

characteristic of this sol is

(1) Coagulation will occur near anode in

electrophoresis.

(2) The level of water will increase in cathode

compartment during electro- osmosis.

(3) The coagulation power of electrolytes for

this sol is in the order :

3 4 3 4A C MgSO K PO

(4) Basic dye like methylene blue will result

mutual coagulation.

31. TK 224 ml 0.1M KOH

(aq.) 50 ml 0.1M H2SO

4 (aq.)

neut

H = 13.7 kcal / eq.

= 1 cal/gm–K

= 1 gm/ml

(1) 0.5 K (2) 1K

(3) 2K (4) 0.25

32. Al(OH)3 HCl(aq)

(1)

(2)

(3)

3 4 3 4A C MgSO K PO

(4)

0000CT10311500418/35



33. Calculate the mass of anhydrous oxalic

acid, which can be oxidised to CO2 (g) by

100 ml of a MnO-4 solution, 10 ml of which

is capable of oxidising 50 ml of 1N I– to I2.

(Consider acidic medium for both reaciton)

(1) 45 gm (2) 22.5 gm

(3) 30 gm (4) 12.25 gm

34. Sulphuric acid leaching is involved in

hydrometallurgy of

(1) low grade gold ore

(2) high grade copper ore

(3) low grade copper ore

(4) low grade aluminum ore

35. Which oxy acid/salt can convert AgNO3 aq.

to Ag.

(1) H3PO

4(2) H

3PO

2

(3) CuSO4 solution (4) conc. HNO

3

36. When finely powdered iron react with HCl

solution it produce

(1) ferric chloride + H2

(2) ferrous chloride + H2

(3) ferrous chloride + ferric chloride + H2

(4) Fe does not react with HCl solution

33.

100 ml MnO-4 CO2 (g)

MnO-4

10 ml, 50 ml 1N I– I2

(1) 45 gm (2) 22.5 gm

(3) 30 gm (4) 12.25 gm

34.

(1)

(2)

(3)

(4)

35. AgNO3 aq.

Ag

(1) H

3PO

4(2) H

3PO

2

(3) CuSO4 (4) HNO

3

36. HCl

(1) + H2

(2) + H2

(3) + + H2

(4) Fe, HCl

19/350000CT103115004



37. CH3 CH CH2

CH3

CH2 CH3

Number of monochlorinated product when

following compound undergo reaction with

Cl2/hv is -

(1) 10 (2) 15

(3) 8 (4) 20

38. Which of the following is a pair of Enantiomer

(1)HCH3

Me

CH3H

Me

HCH3

Me

Me

CH3 H

(2) OHH

Me

COOH

HHO

COOH

Me

(3)OH

HO H

COOH

COOH

H

OH

HO H

COOH

COOH

H

(4) OHH

COOH

COOH

H

HO

H

COOH

COOH

H

OHOH

37. CH3 CH CH2

CH3

CH2 CH3

Cl2/hv

(1) 10 (2) 15

(3) 8 (4) 20

38.

(1)HCH3

Me

CH3H

Me

HCH3

Me

Me

CH3 H

(2) OHH

Me

COOH

HHO

COOH

Me

(3)OH

HO H

COOH

COOH

H

OH

HO H

COOH

COOH

H

(4) OHH

COOH

COOH

H

HO

H

COOH

COOH

H

OHOH

0000CT10311500420/35



39. The compound which is least stable among

following -

(1) (2)

(3)

O

(4)

40. Which of the following is more soluble in water

(1) MnS (Ksp = 8 × 10-37 M2)

(2) ZnS (Ksp = 7 × 10–16 M2)

(3) Bi2S3 (Ksp = 1×10-72 M5)

(4) Ag3 (PO4) (Ksp = 1.8 × 10-18 M4)

41. At 273 K temp and 9 atm pressure, the

compressibility for a gas is 0.9. The volume of

1 millimoles of gas at this temperature &

pressure is

(1) 2.24 litre (2) 0.020 ml

(3) 2.24 ml (4) 2.48 ml

42. An atomic orbital having equal number of radial

and angular nodes is

(1) 2s (2) 2p

(3) 3p (4) 3d

39. -

(1) (2)

(3)

O

(4)

40.

(1) MnS (Ksp = 8 × 10-37 M2)

(2) ZnS (Ksp = 7 × 10–16 M2)

(3) Bi2S3 (Ksp = 1×10-72 M5)

(4) Ag3 (PO4) (Ksp = 1.8 × 10-18 M4)

41. 273 K 9 atm

0.9 1

(1) 2.24 litre (2) 0.020 ml

(3) 2.24 ml (4) 2.48 ml

42.

(1) 2s (2) 2p

(3) 3p (4) 3d

21/350000CT103115004



43. X (Halogen atom)

[other then F]

= ns np nd

Above excited state electronic configuration

(before hybridisation) is NOT responsible for

(1) +3 oxidation state of X in interhalogen

compound of X

(2) bent 'T' shape geometery in interhalogen

compound to X

(3) bent shape geometry of XO2– anion of X

(4) lowest possible oxidiation number of X in

their compounds

44. Which of the following specie does NOT haved10 or d0 configuration of metal ion

(1) [Cu(NCCH3)

4]BF

4

(2) (NH4)

2[TiCl

6]

(3) MnO42–

(4) CrO42–

45. Which acid of boron is monobasic proton donoracid

(1) Ortho-boric acid (2)Tetrafluroboric acid

(3) Boron trifluoride (4) All of the above46. Compound which can consume more than one

mole of Ph–NHNH2 per mol is-

(1) O

(2) HO O

(3)

OH

O

(4)

OH

O

43. X (F )

[ ]

= ns np nd

(1) X X +3

(2) X (bent)'T'

(3) X XO2

–

(4) X

44.

d10 dº

(1) [Cu(NCCH3)

4]BF

4(2) (NH

4)

2[TiCl

6]

(3) MnO42– (4) CrO

42–

45.

(1) - (2)

(3) (4)

46. Ph–NHNH2

(1) O

(2) HO O

(3)

OH

O

(4)

OH

O

0000CT10311500422/35



47. Which of the following are incorrect statement

(1) Benzil benzylic acid rearrangement is not

an oxidation reduction reaction

(2) Michael addition follows 1,4-addition an

unsaturated carbonyl compound

(3) Zn is used as a reactant in Reformtasky

reaction

(4) Attacking nucleophile is generated from

aliphatic acid anhydride in perkin's reaction

48. Which one of the following represent correct

major product for the given reaction.

CH –CH –CH=CH3 2 2

CH3

HBrPeroxide

(1) Br

(2)

Br

(3) Br

(4) Br

49. In the parallel radioactive decay,1A B

2A C

the time when number of radioactive nuclei of

A, B & C becomes equal is

[Given 1 = n3 hr–1,

2 = n3 hr–1]

(1) 0.5 min (2) 30 min

(3) 60 min (4) 90 min

47. -(1)

(2) (Michael) 1,4-

(3) Zn,

(4)

48.

CH –CH –CH=CH3 2 2

CH3

HBrPeroxide

(1) Br

(2)

Br

(3) Br

(4) Br

49. 1A B

2A C

A, B C

[ 1 = n3 hr–1,

2 = n3 hr–1]

(1) 0.5 min (2) 30 min

(3) 60 min (4) 90 min

23/350000CT103115004



50. In between A and B layers in ABABAB.....

type packing of a metal, there is

(1) Only tetrahedral voids

(2) cubic void, tetrahedral void & octahedral

voids

(3) Only cubic voids

(4) Tetrahedral & octahedral voids.

51. The freezing point of a 0.1M formic acidaqueous solution is –0.2046ºC. Find

equilibrium constant of the reaction -

HCOO–(aq.)+H2O (l)

HCOOH(aq.)+OH–(aq.)

Given : Kf(H

2O) = 1.86 K-kg mole–1

Assume solution to be very dilute

(1) 1.1 × 10–3 M (2) 9 × 10–12 M

(3) 9 × 10–13 M (4) 1.1 × 10–11 M

52. If some (CH3)

3 SiCl is mixed with (CH

3)

2 SiCl

2

and hydrolysed followed by condensationpolymerisation then(1) It will increase the length of straight chain

polymer

(2) It will increase the branches of straight chainpolymer

(3) It does not affect the formation of chainpolymer

(4) It will block the end of straight chainpolymer

50. ABABAB..... A B

.................................

(1)

(2)

(3)

(4)

51. 0.1M –0.2046ºC

HCOO–(aq.)+H2O (l) HCOOH(aq.)+OH–(aq.)

Kf(H

2O) = 1.86 K-kg mole–1

(1) 1.1 × 10–3 M (2) 9 × 10–12 M

(3) 9 × 10–13 M (4) 1.1 × 10–11 M

52. (CH3)

3 SiCl (CH

3)

2 SiCl

2

(1)

(2)

(3)

(4)

(block)

0000CT10311500424/35



53. Which of the following have same bond order

& magnetic nature like dioxygen

(1) S2

(2) C2

(3) B2

(4) O3

54. Which ions of lanthanides have completelyfilled 'N' shell

(1) La3+, Ce+4 (2) Lu3+, Yb2+

(3) Gd3+, Tb3+ (4) La3+, Lu3+

55. Product P3

in following reaction sequence :

NBS P1Mg

P2D.E.

CH –CH3 P3

O

H /+

(Majorproduct)

(1)

(2)

(3)

OH

(4)

56. Major product in following reaction sequence :

1. O3

2. H O2

Product

(1) HO OH

O O

(2) H OH

O O

(3) H H

O O

(4) HO OH

O O

53. (1) S

2(2) C

2(3) B

2(4) O

3

54. 'N'

(1) La3+, Ce+4 (2) Lu3+, Yb2+

(3) Gd3+, Tb3+ (4) La3+, Lu3+

55. P3

NBS P1Mg

P2D.E.

CH –CH3 P3

O

H /+

(Majorproduct)

(1) (2)

(3)

OH

(4)

56.

1. O3

2. H O2

(1) HO OH

O O

(2) H OH

O O

(3) H H

O O

(4) HO OH

O O

25/350000CT103115004



57. Which of the following is the correct oxidation

product of CH3–CH=CH–CH

3 by H/KMnO

4

(1) CH3–CH

3(2) CH

3–CH

2–OH

(3) CH3–CHO (4) CH

3–COOH

58. 0.1M HNO3(aq) solution is being titrated with

0.05M NH4OH(aq.) The correct plot for the

titration is

(1)

Vol of NH OH(ml)4

cond

ucta

nce

ofso

luti

on

(2)

Vol of NH OH(ml)4

cond

ucta

nce

ofso

luti

on

(3)

Vol of NH OH(ml)4

cond

ucta

nce

ofso

luti

on

(4)

Vol of NH OH(ml)4

cond

ucta

nce

ofso

luti

on

57. CH3–CH=CH–CH

3 H/KMnO

4

(1) CH3–CH

3(2) CH

3–CH

2–OH

(3) CH3–CHO (4) CH

3–COOH

58. 0.1M HNO3(aq) 0.05M NH

4OH(aq.)

(1)

Vol of NH OH(ml)4

cond

ucta

nce

ofso

luti

on

(2)

Vol of NH OH(ml)4

cond

ucta

nce

ofso

luti

on

(3)

Vol of NH OH(ml)4

cond

ucta

nce

ofso

luti

on

(4)

Vol of NH OH(ml)4

cond

ucta

nce

ofso

luti

on

0000CT10311500426/35



59. Copper is in metallic form in

(1) Schweizer's salt

(2) Bordeaux mixture

(3) German silver

(4) Chalcopyrites

60.

OH

+ CHCl3 + NaOH

O Na+–

CHO

The electrophile involved in the above reaction is

(1) Dichlorocarbene ( :CCl2)

(2) Trichloromethyl anion 3(C Cl )

(3) Formyl cation (CHO)

(4) Dichloromethyl cation 2(CHCl )

59.

(1) (Schweizer's)

(2)

(3)

(4)

60.

OH

+ CHCl3 + NaOH

O Na+–

CHO

(1) (:CCl2)

(2) 3(C Cl )

(3) (CHO)

(4) 2(CHCl )

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PART C - MATHEMATICS

61. The image of line x 2 y 1 z

1 2 3

in the plane

2x + y + z = 5 is the line-

(1) x 2 y 1 z

11 1 2

(2) x 2 1 y z

11 1 2

(3) x 2 y 1 z

11 1 2

(4) x 2 1 y z

11 1 2

62. If a b 2c b c a 2c a b c

, then

is equal to-

(1) –1 (2) 1 (3) 2 (4) 3

63. The integral 2 1

x2 x

11 2x e dx

x

is equal

to-

(1) 2 1

xx2x 1 e C

(2) 2 1

xx2x 1 e C

(3) 2 1

xxxe C

(4) 2 1

xxx e C

(where C is integeration constant)

61. 2x + y + z = 5 x 2 y 1 z

1 2 3

-

(1) x 2 y 1 z

11 1 2

(2) x 2 1 y z

11 1 2

(3) x 2 y 1 z

11 1 2

(4) x 2 1 y z

11 1 2

62. a b 2c b c a 2c a b c

,

-

(1) –1 (2) 1 (3) 2 (4) 3

63. 2 1

x2 x

11 2x e dx

x

-

(1) 2 1

xx2x 1 e C

(2) 2 1

xx2x 1 e C

(3) 2 1

xxxe C

(4) 2 1

xxx e C

(C )

0000CT10311500428/35



64. The common tangent of Parabola y2 = 4x and

Hyperbola 2 2x y

14 3 touches them at P and

Q respectively, then Q can be-

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

(3) (–4,–3) (4) (4,–3)

65. Three positive numbers form an increasing GP.

If the first term is doubled and second term is

trebled, the new numbers are in AP. Then the

common ratio of the G.P. is-

(1) 3 7 (2) 3 7

(3) 2 (4) 7

66. A line L passing through (1, 1) intersect lines

L1 : 12x + 5y = 13 and L

2 : 12x + 5y = 65 at A

and B respectively. If AB = 5, then line L can

be -

(1) 16x – 33y + 17 = 0

(2) 8x + 9y – 17 = 0

(3) 16x + 63y – 79 = 0

(4) 56x – 33y – 33 = 0

64. y2 = 4x 2 2x y

14 3

P Q

Q -

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

(3) (–4,–3) (4) (4,–3)

65.

-

(1) 3 7 (2) 3 7

(3) 2 (4) 7

66. (1, 1) L,

L1 : 12x + 5y = 13 L

2 : 12x + 5y = 65

A B AB = 5

L -

(1) 16x – 33y + 17 = 0

(2) 8x + 9y – 17 = 0

(3) 16x + 63y – 79 = 0

(4) 56x – 33y – 33 = 0

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67. Let

3 0 5 6 2

2 5 0 1 y

A 5 2 x 8 0

0 3 2 3 5

4 7 2 1 9

is a 5 × 5

square matrix.

Each row and column of matrix A has a value

assigned to it. Every element is the sum of its

row and column values. For example –9 is the

sum of the value assigned to 5th

row and 5th

column. Then the value of x + y is-

(1) –7 (2) 0 (3) 7 (4) 14

68. Let matrix 4 1

B9 2

, then which of the

following will not be an element of matrix B100 -

(1) 300 (2) 301 (3) –299 (4) 100

69. 20 soldiers are standing in a row and theircaptain want to send 7 out of them for a mission.In how many ways can captain select them suchthat at least one soldier find the soldier next tohim is also selected.

(1) 20C7

(2) 14C7

(3) 20C7 – 13C

7(4) 20C

7 – 14C

7

67.

3 0 5 6 2

2 5 0 1 y

A 5 2 x 8 0

0 3 2 3 5

4 7 2 1 9

, 5 × 5

A

–9, 5

5x + y

-

(1) –7 (2) 0 (3) 7 (4) 14

68. 4 1

B9 2

B100-

(1) 300 (2) 301 (3) –299 (4) 100

69. 20 7 (1) 20C

7(2) 14C

7

(3) 20C7

– 13C7

(4) 20C7

– 14C7

0000CT10311500430/35



70.3 2

x 2

60 x 4lim

sin(x 2)

(1) 1

4(2) 0

(3) 1

12(4) Does not exist

71./ 2

0

sin 4x cot xdx

is equal to-

(1) 2

(2) 0 (3)

2

(4)

72. If ƒ(x) = –x3 – 3x

2 – 2x + a, a R, then the real

values of x satisfying ƒ(x2 + 1) > ƒ(2x2 + 2x + 3)

will be-

(1) (–) (2) (0,)

(3) (–,0) (4)

73. If is a solution of [cot–1x] < [tan–1x], then

[cot–1] + [tan–1] is (where [.] greatest integer

function)

(1) 0 (2) 1

(3) 2 (4) greater than 2

74. The value of

2x4

2x 00

n 1 4tlim cosec x dt

t 1

is

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

70.3 2

x 2

60 x 4lim

sin(x 2)

-

(1) 1

4(2) 0

(3) 1

12(4)

71./ 2

0

sin 4x cot xdx

-

(1) 2

(2) 0 (3)

2

(4)

72. ƒ(x) = –x3 – 3x2 – 2x + a, a R

ƒ(x2 + 1) > ƒ(2x2 + 2x + 3) x

-(1) (–) (2) (0,)

(3) (–,0) (4)

73. [cot–1x] < [tan–1x] [cot–1] + [tan–1]

([.] )

(1) 0 (2) 1

(3) 2 (4) 2

74.

2x4

2x 00

n 1 4tlim cosec x dt

t 1

-

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

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75. A box contains 20 identical balls of which 5

are white and 15 black. The balls are drawn at

random from the box one at a time with

replacement. The probability that a white ball

is drawn for the 3rd time on the 6th draw is-

(1) 1

2(2)

135

2048

(3) 135

1024(4)

27

4096

76. Let a = 8 and b = 39 and we define a sequence

{un} as follows

u1 = b,

n nn 1

n

1u ; if u ismultiple of 3

u 3

u a ; otherwise

then u500 – u300 – u400 is equal to

(1) 1 (2) 3 (3) 5 (4) 7

77. Let a,b,c R0 and each of the quadratic

equations in x, x2 + 2(a2 + b2)x + (b2 + c2)2 = 0

and x2 + 2(b

2 +c

2)x + (c

2 + a

2)2 = 0 has two

distinct real roots. Then equation

x2 + 2(c2 + a2)x + (a2 + b2)2 = 0 has-

(1) Two distinct positive real roots

(2) Two equal real roots

(3) Two distinct negative real roots

(4) No real roots

75. 20 5

15

-

(1) 1

2(2)

135

2048

(3) 135

1024(4)

27

4096

76. a = 8 b = 39 {un} :

u1 = b,

n nn 1

n

1u ; u ,3

u 3

u a ;

u500 – u300 – u400

(1) 1 (2) 3 (3) 5 (4) 7

77. a,b,c R0 x

x2 + 2(a2 + b2)x + (b2 + c2)2 = 0

x2 + 2(b2 + c2)x + (c2 + a2)2 = 0

x2+ 2(c2+ a2)x + (a2 + b2)2 = 0

-

(1)

(2)

(3)

(4)

0000CT10311500432/35



78. The ellipse with equation 2 2x y

19 4

is rotated

couterclockwise about origin by 45°.

Then resulting equation can be written as

ax2 + bxy + cy

2 = 72, then (a + b + c) is

(1) 6 (2) 16 (3) 26 (4) 36

79. Consider a set 'A' of vectors ˆ ˆ ˆxi yj zk where

x,y,z {1,2,3}. Three vectors are selected atrandom from set A. If the probability that theyare mutually perpendicular is p, then-

(1) 1

p27

(2) 1 1

p ,27 9

(3) 1 1

p ,9 3

(4) 1

p ,13

80. The statement ~p (r p) is -

(1) equivalent to negation of p r

(2) equivalent to ~ p r

(3) a tautology

(4) a fallacy

81. Let S = {(x, y)|siny = sinx, x, y R}, then S is

(1) not transitive

(2) equivalence

(3) transitive but not reflexive

(4) partial order relation

78. 2 2x y

19 4

,

45°

ax2 + bxy + cy2 = 72 (a + b + c)

(1) 6 (2) 16 (3) 26 (4) 36

79. ˆ ˆ ˆxi yj zk 'A',

x,y,z {1,2,3} A

p -

(1) 1

p27

(2) 1 1

p ,27 9

(3) 1 1

p ,9 3

(4) 1

p ,13

80. ~p (r p) -

(1) p r

(2) ~ p r

(3)

(4)

81. S = {(x,y)|siny = sinx, x,y R} S

(1)

(2)

(3)

(4)

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82. Let 2 is variance of following frequency

distribution

i

i

x 1 2 3 4 5 6 7 8 9

ƒ 1 0 1 7 9 4 1 1 1

then 2 is equal to-

(1) 2.4 (2) 2.5 (3) 2.6 (4) 2.7

83. Let 1 be a complex cube root of unity.

If 2 22 n 2 2 n 2(4 5 6 ) (6 5 4 )

22 n 2(5 6 4 ) 0 , then n can be -

(1) 133 (2) 113 (3) 111 (4) 331

84. The coefficient of x3 in the expansion of

(1 + 2x – 3x2)10 is -

(1) less than 200

(2) less than 400 but greater than 200

(3) 400

(4) 420

85. A curve y = ƒ(x) which passes through (4,0)

sat isfy the differential equation

xdy + 2ydx = x(x – 3)dx.

The area bounded by y = ƒ(x)

and line y = x (in square unit) is-

(1) 32 (2) 64

3(3)

128

3(4) 64

82.

i

i

x 1 2 3 4 5 6 7 8 9

ƒ 1 0 1 7 9 4 1 1 1

2 2 -

(1) 2.4 (2) 2.5 (3) 2.6 (4) 2.7

83. 1

2 22 n 2 2 n 2(4 5 6 ) (6 5 4 )

22 n 2(5 6 4 ) 0 n -

(1) 133 (2) 113 (3) 111 (4) 331

84. (1 + 2x – 3x2)10 x3-

(1) 200

(2) 400 200

(3) 400

(4) 420

85. (4,0) y = ƒ(x),

xdy + 2ydx = x(x – 3)dx

y = ƒ(x) y = x

() -

(1) 32 (2) 64

3(3)

128

3(4) 64

0000CT10311500434/35



86. Let x x 1 2

2 3

sin x(2 2 ) tan (x x 1)ƒ(x)

(7x 3x 1)

,

then ƒ'(0) is equal to -

(1) 0 (2)

(3) (4) does not exist

87. If ƒ(x) is a different iable function and

ƒ(1) = sin1, ƒ(2) = sin4, ƒ(3) = sin9, then the

minimum number of distinct solutions of

equation ƒ'(x) = 2xcosx2 in (1, 3) is -

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

88. Let z1, z

2, z

3 are three complex number

satisfying |z| = 1 and 4z3 = 3(z

1 + z

2),

then |z1 – z

2| is equal to -

(1) 2

3(2)

5

3

(3) 3

2(4)

2 5

3

89. Radius of largest circle with center (0, 1) which

can be inscribed in the ellipse 4x2 + y2 = 4 is -

(1) 2

3(2)

2

3(3)

2

3(4)

1

3

90. Let ƒ(x) is a cubic polynomial with real

coefficients, x R such that ƒ"(3) = 0, ƒ'(5) = 0.

If ƒ(3) = 1 and ƒ(5) = –3, then ƒ(1) is equal to-

(1) 2 (2) 3 (3) 5 (4) 6

86. x x 1 2

2 3

sin x(2 2 ) tan (x x 1)ƒ(x)

(7x 3x 1)

ƒ'(0) -

(1) 0 (2)

(3) (4)

87. ƒ(x) ƒ(1) = sin1,

ƒ(2) = sin4, ƒ(3) = sin9 (1, 3)

ƒ'(x) = 2xcosx2

-

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

88. z1, z

2, z

3 |z| = 1

4z3 = 3(z

1 + z

2) |z

1 – z

2|

-

(1) 2

3(2)

5

3

(3) 3

2(4)

2 5

3

89. 4x2 + y2 = 4 (0, 1)

-

(1) 2

3(2)

2

3(3)

2

3(4)

1

3

90. ƒ(x) x R ƒ"(3) = 0, ƒ'(5) = 0 ƒ(3) = 1 ƒ(5) = –3 ƒ(1) -(1) 2 (2) 3 (3) 5 (4) 6

35/350000CT103115004




LEADER TEST SERIES / JOINT PACKAGE COURSE€¦ · 0000CT103115004 1/35 SPACE FOR ROUGH WORK / ALL...

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