JEE (Main + Advanced) : ENTHUSIAST COURSE · 2016-02-08 · E-4/18 1001CT102115077 Target : JEE...

Test Type : FULL SYLLABUS Test Pattern : JEE-Main

TEST DATE : 07 - 02 - 2016

SCORE-I

JEE (Main + Advanced) : ENTHUSIAST COURSE

Paper Code : 1001CT102115077Form Number :

CLASSROOM CONTACT PROGRAMME(Academic Session : 2015 - 2016)E

NG

LIS

H

PAPER – 2

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E-1/181001CT102115077

SPACE FOR ROUGH WORK

PART A - PHYSICS

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

1. A particle is thrown with velocity v0 at an angle

0 with the horizontal. For which of the

following combinations of v0 and

0, the radius

of curvature at the highest point of motion will

be maximum?

(1) v0 = 10 m/s,

0 = 30o

(2) v0 = 10 m/s,

0 = 45o

(3) v0 = 20 m/s,

0 = 45o

(4) v0 = 20 m/s,

0 = 60o

2. A carbon resistor is marked with the rings

coloured brown, black, green and gold. The

resistance (in ohm) is :-

(1) 1 × 105 ± 5 % (2) 1 × 106 ± 10%

(3) 1 × 107 ± 5 % (4) 1 × 106 ± 5 %

3. A man watches a steamboat starting from a

point directly in front of him on the opposite

bank of river flowing at a speed of 5 km/hr.

The boat has a velocity v0 with respect to river

flow at an angle 0 with the bank. If the

steamboat blows a whistle of frequency f0, then

for which of the following combinations of v0

and 0 the frequency registered by the man will

be highest?

(1) v0 = 10 m/s,

0 = 30o

(2) v0 = 10 m/s,

0 = 45o

(3) v0 = 10 m/s,

0 = 60o

(4) same for all the above

4. The equivalent resistance between the points

A and B is (R is the resistance of each side of

smaller square)

A

B

R

R

(1) R (2) 2

3R

(3) R2 (4) 2

R

1001CT102115077E-2/18

Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2


5. N particles of masses of m, 2m, 4m, 8m, ………

2N-1m respectively are kept along a frictionless

horizontal surface at non-uniform distances

between them, but in increasing order of masses

as shown. The plane is curved on its right end

as shown upto a height H. A particle of mass m

is released from the top of the plane and collides

perfectly inelastically with the mass m on the

horizontal surface. All the subsequent collisions

are inelastic. The value of H so that the velocity

of the system after last collision becomes 1 m/s

is:-

H

m

m 2m 4m 2N-1m

(1) g

N 12

(2) g

N2

(3) g

N 122

(4)

g

N 122

6. A radioactive nuclei is being produced in a

reactor at constant rate Q = 2No (where is

the decay constant and initial number of

radioactive nuclei is No). Which of the

following curves represents the number of

nuclei as a function of time t ?

(1)

No

t

N

(2)

2No

t

N

No

(3)

2No

t

N

No

(4)

2No

t

N

No


E-3/181001CT102115077


7. If the frequency of the incident radiation is

doubled in a photoelectric effect experiment,

the kinetic energy of the fastest photoelectron

becomes

(1) double (2) more than double

(3) less than double (4) none of these

8. In YDSE distance between slits S1 and S

2 is d.

P1 and P

2 are two points equidistant from O at

an angular position as shown. A parallel beam

of monochromatic light is incident at an angle

on the slits. Then the ratio of path difference

at P1 and P

2 is :-

D (>>d) O

P1

P2

d

S1

S2

(1) 2

cot2

tan

(2) 2

cot2

tan

(3) 2

cos2

sin

(4) 2

sin2

cos

9. The primary winding of the transformer to

power the radio receiver has 1200 turns with

input voltage of 120 V. What should be the

number of turns of the transformer in secondary

winding to power the lamp filament, if it

requires 3.6 V voltage and current of 1A?

Secondary has a resistance of 0.4 ohms. The

loss in the primary winding may be neglected :

(1) 40 (2) 36

(3) 4800 (4) 4320

10. A thin plano-convex glass lens ( = 1.5) has

its plane surface silvered and R is the radius of

curvature of curved part, then which of the following

ray diagram is true for an object placed at O?

(1)

2R

R

O

(2)

2R

R

O

(3)

3R

R

O

(4)

2R

R

O

1001CT102115077E-4/18



11. A conducting rod is moving with a constant

velocity v over the parallel conducting rails

which are connected at the ends through a

resistor R and capacitor C as shown in the

figure. Magnetic field B is into the plane.

Consider the following statements.

A

L

B

C R

E H

G

v

F

(i) Current in loop AEFBA is anticlockwise

(ii) Current in loop AEFBA is clockwise

(iii) Current through the capacitor branch is zero

(iv) Energy stored in the capacitor is 222

2

1vLCB

Which of the following options is correct?

(1) statements (i) and (iii) only are correct.

(2) statements (ii) and (iv) only are correct.

(3) statements (i), (iii) and (iv) only are correct.

(4) all the above

12. An electromagnetic wave travels in vacuum

along z direction : 0ˆE E i

cos(kz – t). AA

rectangular area is to be kept such that at t = 0

displacement current may flow through the

area. Which of the following is correct

orientation :-

(1)

y

x

z

(2)

y

x

z

(3)

y

x

z

(4) None of these

13. In the given figure, block executes SHM with

total energy of oscillation E. The ratio of

K1 and K

2 is 2 : 1. The energy associated with

spring of spring constant K1 when block is at

A/2 distance away from mean position

(A is amplitude) is :-

K1 K2

(1) E/4 (2) E/3 (3) E/12 (4) E/6


E-5/181001CT102115077


14. A sphere of radius 0.625 m is rotating about a

horizontal axis with angular velocity 2 rad/s

and is released from rest in vertical plane under

gravity as shown in the figure. The ratio of

displacement of point P to that of point C after

0.5 s from the start will be (g = 10 m/s2) :-

P

C

(1) 1 : 1 (2) 2 : 1

(3) 3 : 1 (4) 4 : 1

15. A tunnel is dug inside the earth across one of

its diameters. A particle is projected inside the

tunnel with velocity R

GM from one of its

ends. Then maximum velocity attained by the

particle in the subsequent motion is (assuming

tunnel to be frictionless)

(1) R

GM(2)

R

GM2

(3)R

GM

2

3(4)

R

GM2

16. Consider an open-circuited p-n junction in

thermal equilibrium. Let Jp, drift

and Jp, diff

be the

hole drift and diffusion current densities,

respectively, and let Jn, drift

and Jn, diff

be the

corresponding electron current densities. Of the

following equalities, mark true, at all points in

the p-n junction structure :

(1) Jp, drift

+ Jn, drift

= Jp, diff

+ Jn, diff

= 0

(2) Jn, drift

+ Jn, diff

= 0

(3) Jp, drift

+ Jp, diff

= 0

(4) Jp, drift

+ Jn, drift

+ Jp, diff

+ Jn, diff

= 0

17. An experiment is performed to obtain the value

of acceleration due to gravity g by using a

simple pendulum of length L. In this

experiment time for 100 oscillations is

measured by using a watch of 1 second least

count and the value is 90.0 seconds. The length

L is measured by using a meter scale of least

count 1 mm and the value of 20.0 cm. The

error in the determination of g would be :-

(1) 2.7 % (2) 2.27 %

(3) 1.7 % (4) 4.4 %

1001CT102115077E-6/18



18. A body at rest breaks into two fragments ofmasses m

1 and m

2 respectively. The ratio of

their de-Broglie wavelengths is :-

(1) 2

1

m

m(2)

1

2

m

m(3) 1 : 1 (4)

2

1

m

m

19. Statement-1 : When a P-N Junction is heavilydoped, width of depletion region becomes verysmall.

Statement-2 : When a semiconductor is doped,the molarity of charge carrier increases.

(1) Statement-1 is true, statement-2 is true andstatement-2 is correct explanation forstatement-1

(2) Statement-1 is true, statement-2 is true andstatement-2 is NOT the correct explanationfor statement-1.

(3) Statement-1 is true, statement-2 is false.

(4) Statement-1 is false, statement-2 is true.20. A bar magnet is suspended from the ceiling by

a string as shown. If a uniform magnetic fielddirected parallel to the ceiling and to the left isthen established, the resulting orientation of themagnet and the string in equilibrium will becorrectly shown by :-

S

N

(1)

S

N

(2)

S

N

(3)

S

N

(4)

S

N

21. A water barrel stands on a table of height h. If

a small hole is punched in the side of the barrel

at its base, it is found that the resultant stream

of water strikes the ground at a horizonatl

distance R from the barrel. The depth of water

in the barrel is :-

(1) 2

R(2)

h4

R2

(3) h

R 2

(4) 2

h


E-7/181001CT102115077


22. Consider the following statements about aconducting rod of length l hung from fixedpoints at a distance a from a infinitely longcurrent carrying wire by means of two flexibleconducting wires connected with an emf sourceas shown in the figure. All are in the same plane.

l a

I

A. Body will gain rotational tendency.B. Body will not gain any rotational tendencyC. Centre of magnetic force will be shifted

towards left of the centre of mass of therod.

D. Centre of magnetic force will be shiftedtowards right of the center of mass of therod.

E. Centre of magnetic force will coincide withthe center of mass of the rod.

Choose the correct option(1) A and C are correct (2) B and C are correct(3) A and D are correct (4) A and E are correct

23. In a common-base configuration of transistor, = 0.98, I

B = 0.02 mA, R

L = 5 k. Output

voltage across load is :

(1) 3.2 V

(2) 4.9 VIB

RL

VBCVBE

(3) 5.2 V

(4) 6.2 V

24. The energy band diagrams for threesemiconductor samples of silicon are as shown.We can then assert that :-

X Y Z

(1) Sample X is undoped while samples Y andZ have been doped with a trivalent and apentavalent impurity respectively

(2) Sample X is undoped while both samples Yand Z have been doped with a pentavalentimpurity

(3) Sample X has been doped with equalamounts of trivalent and pentavalentimpurities while samples Y and Z areundoped

(4) Sample X is undoped while samples Y andZ have been doped with a pentavalent anda trivalent impurity respectively

25. Which one of the following is INCORRECTstatement in the t ransmission ofelectromagnetic waves?(1) Ground wave propagation is for high

frequency transmission(2) Sky wave propagation is facilitated by

ionospheric layers(3) Space wave is used for satellite

communication(4) Very high frequency waves cannot be

reflected by the ionospheric layers

1001CT102115077E-8/18



26. A solid sphere of mass M and radius R is givenvelocity as shown. Then the value of angularmomentum of the sphere with respect to originis given by :-

(1) kRMvoˆ

5

3

(2) kRMvoˆ

5

3

x

y

vo

vo/R

R

z

O

(3) kRMvoˆ

5

7

(4) 5

7 kRMvoˆ

27. A sound wave propagates through nitrogenunder NTP. At what frequency will thewavelength be equal to the mean free path ofthe gas molecules? Diameter of N

2 molecules is

0.4 nm.(1) 6.5 GHz (2) 2.9 MHz(3) 8.4 GHz (4) 7.3 MHz

28. One mole of an ideal monatomic gas is takenfrom temperature T

o to 2T

o by the process

CPT 4 . Considering the following

statements choose the correct alternative.

I. Molar heat capacity of the gas is 2

3R

II. Molar heat capacity of the gas is 2

3R

III. Work done by the gas is oRT3

IV. Work done by the gas is oRT3

(1) Statements I and IV are correct.

(2) Statements I and III are correct.

(3) Statements II and IV are correct

(4) Statements II and III are correct.

29. Consider a system of n particles of masses m1,

m2, …., m

n moving with velocities 1v

, 2v

, …..,

nv

. Assuming no external forces are acting on

the system, consider the following statements.

I. K. E. of system of particles is minimum in

the center of mass frame.

II. K. E. of system of particle is maximum in

the center of mass frame.

III. Centre of mass will either be at rest or

moving along straight line.

(1) Only statement I is correct.

(2) Only statement III is correct.

(3) Statements I and III are correct.

(4) Statements II and III are correct.

30. A longitudinal sound wave given by P = 2.5

sin 2

(x – 660t) (P is in N/m2 and x is in m

and t is in s) is sent down an closed organ

pipe. If the pipe vibrates in its second overtone,

the length of the pipe is :-

(1) 6 m (2) 8 m

(3) 5 m (4) 10 m


E-9/181001CT102115077


PART B - CHEMISTRY

31. [Co(H2N – CH

2 – CH

2 – NH

2)

3]

2S

3oxidation

Co+4 + CO3–2 + NO

3– + SO

4–2

What is the equivalent weight of the reactant

in the above reaction ?

(1) 3M

182(2)

M

182(3)

11M

182(4)

7M

182

32. Standard entropy of X2, Y

2 and X

2Y

3 are 60,

40 and 150 in J/K mol

X2 +

3

2Y

2 X

2Y

3H = +30 kJ

The temperature at which reaction will attain

equilibrium is :

(1) 250 K (2) 1000 K

(3) 750 K (4) 200 K

33.

r

4 r 2 r

This radial probability distribution graph can

represent the orbital.

(1) 5s (2) 5d

(3) 4p (4) 6d

34. A graph showing variation of osmotic pressure

() versus molar concentration 'C' of an

aqueous solution at temperature T is given

below :

C

The slope of the line is equal to :

(1) Solution constant R

(2) Absolute temperature T

(3) RT

(4) Degree of ionization of solute

35. We can represent the decomposition of N2O

5(g)

at a fixed temperature by the following two

chemical equations :

(a) 2N2O

5(g) 4NO

2(g) + O

2(g) ;

Activation energy Ea

(b) N2O

5(g) 2NO

2(g) +

1

2O

2(g) ;

Activation energy Ea' then

(1) Ea = Ea' (2) Ea > Ea'

(3) Ea < Ea' (4) Ea = 2Ea'

1001CT102115077E-10/18



36. Latimer diagram for Cu in an acidic solution is

Cu+2 +0.15 V Cu+

Cu+0.50 V

Find 2Cu / CuE

(1) +0.65 volt (2) +0.325 volt

(3) –0.0325 volt (4) –0.325 volt

37.

I-Cube II-Cylinder III-Sphere

5cm5cm

5cm 5cm

There are three closed containers in which

equal moles of gas is filled if the containers

are placed at the same temperature, then which

of the following is correct

(1) Pressure in I is the maximum.

(2) Pressure in II is the maximum.

(3) Pressure in III is the maximum.

(4) All the vessel have equal pressure.

38. A crystalline solid is made of X, Y and Z

elements. Atoms of X form f.c.c. packing Y

occupy octahedral voids, while atoms of Z

occupy tetrahedral voids. What will be the

simplest formula of the solid if atoms along

any one body diagonal are removed.

(1) X5Y

4Z

8(2) XYZ

(3) X8Y

4Z

5(4) X

2YZ

39. Relationship between volume strength of H2O

2

aqueous solution and molarity depends on

pressure and temperature of O2(g) collected

Example :

At 1 atm, 273K , volume strength = 11.2 × M

At STP , volume strength = 11.35 × M

[Note : By default STP is taken for volume

strength calculation].

Find the relationship between volume strength

& molarity at 300K & 1 atm

(1) 12.315 × M (2) 24.63 × M

(3) 11.35 × M (4) 22.7 × M

40. Hydrogen peroxide ionises as H2O

2H+

+ HO2– . If pH of H

2O

2 is 5.7 at 25°C, the ionic

product of H2O

2 is

(1) 2 × 10–12 (2) 4 × 10–12

(3) 1 × 10–14 (4) 1.4 × 10–12

41. Planar geometry around the central atom is

shown by :

(1) N(SiH3)

3(2) ICl

2–

(3) XeF2

(4) All of these


E-11/181001CT102115077


42. Match the following

(a) Smithsonite (p) Iron

(b) Carnallite (q) Copper

(c) Azurite (r) Magnesium

(d) Limonite (s) Zinc

(1) a - p, b - q, c - r, d - s

(2) a - s, b - r, c - p, d - q

(3) a - s, b - r, c - q, d - p

(4) a - q, b - p, c - s, d - r

43. When copper reacts with hot conc. H2SO

4 gives ?

(1) H2

(2) SO2

(3) O2

(4) None of these

44. Which of the following is not arranged in

correct sequence ?

(1) MO, M2O

3, MO

2, M

2O

5 - decreasing order

of basic nature (M = d block metal)

(2) Sc, Ti, V, Cr, Mn - increasing order of

highest possible oxidation state

(3) d5, d3, d1, d4 - increasing magnetic moment

(4) Mn+2, Fe+2, Cr+2, Co+2 - decreasing stability

45. NHCl + A4

Microcosmic salt

B Heat+DO

(C)

Violet colour

(oxide of D)

A, B, C & D are respectively

(1) Na3PO

4, NaPO

3, MnNaPO

4, MnO

(2) Na2HPO

4, NaPO

3, MnNaPO

4, MnO

(3) Na3PO

4, NaPO

3, CuNaPO

4, CuO

(4) Na2HPO

4, NaPO

3, CuNaPO

4, CuO

46. Match the following.

Column I Column II

(A) Borax (i) SiO2

(B) B2H

6 + H

2O (ii) H

2SiO

3

(C) B2H

6 + Excess of (iii) BN

NH3

(D) SiCl4

2(i) H O

(ii) 1000 C (iv) NaBO

2 + B

2O

3

(v) H3BO

3

A B C D

(1) i iii iv v

(2) ii iii iv v

(3) iv v iii ii

(4) iv v iii i

1001CT102115077E-12/18



47. Xenon hexafluoride reacts with silica to form

oxygen and xenon compound (X). The

hybridisation and oxidation state of xenon in the

compound

(1) sp3d2, +6 (2) d2sp3, +6

(3) sp3, +8 (4) sp3d, +6

48. In octahedral complex Ma2b

2cd, total number

of steroisomers is

(1) 2 (2) 4 (3) 5 (4) 8

49. The compound which is not associated with

Solvay ammonia process for the production

of Na2CO

3

(1) NH4HCO

3(2) NaHCO

3

(3) NaCl (4) Na2C

2O

4

50. Which of the following molecule or molecular

ion has highest number of total electrons in

antibonding molecular orbitals

(1) O2

(2) N2

(3) N2+ (4) O

22–

51. Acidic hydrolysis of an ester CH3CH

2COOCH

3

produces A & B, which can be distinguished

by :

(1) Na metal (2) NaHCO3

(3) Fehling solution (4) Tollen's Reagent

52. Which of the following is a biodegradable

polymer ?

(1) Cellulose (2) Polyethene

(3) Poly vinyl chloride (4) Dacron

53. Among following the most reactive towards

alcoholic KOH is :

(1) CH2 = CHBr

(2) Ph–CH2–CH

2–Br

(3) CH3CH

2Br

(4) CH3CH

2CH

2Br

54. Consider the following reaction :

3 4

3 2 4

CH Cl KMnOZn

dust Anhy. AlCl dil.H SOPhenol X Y Z

the product Z is -

(1) Benzaldehyde (2) Benzoic acid

(3) Benzene (4) Toluene


E-13/181001CT102115077


55. Which is the most basic among the following :

(1) C6H

5NH

2

(2) (C6H

5)

2NH

(3) C2H

5NH

2

(4) (C2H

5)

2NH

56. The final product of the reaction given below

is

3 2 2

O||

CH – CH C NH 2

2

HNONaOH

BrA B

(1) Ethanol (2) Methanol

(3) Methyl amine (4) Ethyl amine

57. Pyrimidine bases present in RNA are -

(1) cytosine + adanine

(2) thymine + cytosine

(3) cytosine + uracil

(4) thymine + uracil

58. Aromatic nitriles (ArCN) is not obtained as a

major product in reaction :

(1) ArCONH2 + P

2O

5

(2) ArN2

+ CuCN

(3) ArX + KCN

(4) ArCONH2 + SOCl

2

59. How many stereoisomers are possible for

a compound of the molecular formula

CH3 – CH = CH – CH

2 – CH(Br) – CH

3

(1) 2 (2) 4

(3) 6 (4) 8

60. Which of the following compound yields

acetone on ozonolysis ?

(1) 2-Methyl-1-butene



(4) 2,3-Dimethyl-1-butene

1001CT102115077E-14/18



PART C - MATHEMATIC

61. If k

1r

r 1

ksin (B )

2

and

k

rr 1

1A B

k

, then

the value of x A

xlim(1 x) tan

2

is

(1) 2

(2)

2

(3) 0 (4)

62. The distance of the point (–9, 0) from the

director circle of the parabola y2 = 16(x + 3) is

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

63. Let

1 x x 0

f(x) 1 [x] sin x 0 x2

x32

If f(x) is discontinuous at x = then is

(where [.] is greatest integer function)

(1) 0 (2) 1

(3) 2

(4) none of these

64. The tens digit of 1! + 2! + 3! + .... + 73! is :-

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

65. Let a differentiable function 'f' satisfying

f(x + y) = f(x) f(y) for all x, y R and

ƒ'(0) = 4. If f(x0) = 200 then f'(x

0) =

(1) 800 (2) 240

(3) 0 (4) none of these

66. For real valued functions fr(x) = cos2p

rx

r = 1, 2, 3; pr N such that period of

f1(x) + 2f

2(x) + 3f

3(x) is , period of

2f1(x) + 3f

2(x) is

2

and period of

3f1(x) + 2f

3(x) is ,

3

then minimum value of

(p1 + p

2 + p

3) is

(1) 6 (2) 10 (3) 11 (4) 17

67. If the function f(x) = x3 + x

5e and g(x) = f–1(x),

then the value of g'(1) + log5(g'(1)) is

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

268. The plane x + y + z = 5 is rotated by 90° along

the line of intersection with the plane x – y – z = 2.If the equation of plane in new position isax + by + cz + d = 0 where a, b, c, d I, then

least value of |a + b + c + d| is

(1) 10 (2) 9 (3) 4 (4) 11


E-15/181001CT102115077


69. If and are the roots of quadratic equation

12x2 – 5x – 1 = 0, then the value of r r

r 1

( )

is

(1) 3

8(2)

5

8

(3) 7

6(4) none of these

70. If u = f(tan x), v = g(sec x) and f'(x) = tan–1x;

g'(x) = cosec–1x then du

dv at x

4

is

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

2(4) 3 2

71. The position vector of point of intersection of

the planes 2 3ˆ ˆr (n n ) 1,

3 1ˆ ˆr (n n ) 2 and

1 2ˆ ˆr (n n ) 3,

1 2 3

ˆ ˆ ˆ([n n n ] 0) is

(1) 1 2 3

1 2 3

ˆ ˆ ˆn 2n 3n

ˆ ˆ ˆ[n n n ]

(2) 1 2 3

21 2 3

ˆ ˆ ˆn 2n 3n

ˆ ˆ ˆ[n n n ]

(3) 2 3 3 1 1 2

1 2 3

ˆ ˆ ˆ ˆ ˆ ˆn n 2n n 3n n

ˆ ˆ ˆ[n n n ]

(4) 2 3 3 1 1 2

21 2 3


ˆ ˆ ˆ[n n n ]

72. If x,y

R, satisfying equation

2 2(x 4) y1

4 9,

then the maximum value of 2 2x y

8 18 is

(1) 9 (2) 7

2(3)

9

2(4) 10

73. The general solution of the equation

sin106x – cos106x = 1 is

(1) 2n + 2

(2) n +

2

(3) 2n – 2

(4) n

(where n I)

74. The area of the region bounded by the curves

y = x2 + 7, y = x, x = 3 and x = 0 is

(1) 61

2(2)

51

2(3)

31

2(4)

21

2

75. xe 2

9e log (3x 2) dx

(3x 2)

is -

(1) xe

3e log (3x 2) C

3x 2

(2) xee log (3x 2) C

(3) xe

1e log (3x 2) C

3x 2

(4) none of these

(where 'C' is the constant of integration)

1001CT102115077E-16/18



76. The number of real roots of the equation

x5 + e8x = 0 is

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

77. If

2 5 7 9

0 1 9 7A

0 0 1 8

0 0 0 1

then the value of

|adj (adjA)| is

(1) 1024 (2) 512

(3) –512 (4) –1024

78. If roots of the equation

(m – 1)x2 + (1 + 3m)x – (8 – 3m) = 0 are

opposite in sign, then the number of integral

value(s) of m is

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

79.

4

18 11

0

sin x cos x dx is equal to -

(1) 11

32(2)

11

64(3) 0 (4)

3

8

80. The number of complex numbers which satisfy

both the equations |z – 3 – 4i| = 2 and |z| = 1 is

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

81. The coefficient of x7 in

1 + (1 + x) + (1 + x)2 + ..... + (1 + x)100 is

(1) 101C93

(2) 100C93

(3) 100C7

(4) 0

82. If the matrix A is given by 3 2

A4 3

then

determinant value of (A27 – 2A26) is

(1) –5 (2) –7 (3) –10 (4) 0

83. In a multiple choice examination with 7

possible answers (out of which only one is

correct) for each of the four questions, what is

the probability that a candidate would get three

or more correct answers just by guessing is

(1) 4

1

7(2) 4

24

7(3) 4

25

7(4) 4

16

7

84. Given p and q are respectively the maximum and

minimum value of f(x) = 5sinx + 12cosx + 1. If

(p, q) are the centre of the circle touching the

x-axis, then radius of the circle is

(1) 14 (2) 12 (3) 13 (4) 11

85. A tangent of slope 2 of the ellipse 2 2

2

x y1

a 1

is normal to the circle x2 + y2 + 4x + 1 = 0, then

the value of log4(4a2 + 1) is

(1) 1 (2) 2 (3) 0 (4) 16


E-17/181001CT102115077


86. If is the angle between the line

x 1 y 1 z 2

3 2 4

and the plane

2x + y – 3z + 4 = 0, then 64 cosec2 is equal to

(1) 1264 (2) 1624

(3) 1628 (4) 1648

87. All the 7 digit numbers containing each of the

digits 1, 2, 3, 4, 5, 6, 7 exactly once and not

divisible by 5 are arranged in increasing order.

Then 1201th number is

(1) 3124567 (2) 3765421

(3) 3124675 (4) 3124657

88. If a,b,c

are non-coplanar vectors,

[3a b c a b c 7a] is equal to [a b c] ,

then =

(1) 1 (2) 8

(3) 9 (4) 6

89. If the variance of 1, 2, 2, 3 is , then the value

of log2 is

(1) 8 (2) 1 (3) –1 (4) –2

90. If the length of subnormal at any point on the

parabola y2 = kx is 2 units, then |k| is equal to

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

1001CT102115077E-18/18




1.

2.

3. 3

4. 90360

5. A, B, C 30

4

6.

7.

8.

9.

10.

11.

Paper Code : 1001CT102115077Form Number :

CLASSROOM CONTACT PROGRAMME(Academic Session : 2015 - 2016)

HIN

DI

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

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

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

Test Type : FULL SYLLABUS Test Pattern : JEE-Main

TEST DATE : 07 - 02 - 2016

SCORE-I

JEE (Main + Advanced) : ENTHUSIAST COURSE

PAPER – 2

H-1/181001CT102115077


PART A - PHYSICS

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

1. v0

0

v0

0

(1) v0 = 10 m/s,

0 = 30o

(2) v0 = 10 m/s,

0 = 45o

(3) v0 = 20 m/s,

0 = 45o

(4) v0 = 20 m/s,

0 = 60o

2.

(1) 1 × 105 ± 5 % (2) 1 × 106 ± 10%

(3) 1 × 107 ± 5 % (4) 1 × 106 ± 5 %

3. 5 km/hr

v0

0 f

0

v0

0

(1) v0 = 10 m/s,

0 = 30o

(2) v0 = 10 m/s,

0 = 45o

(3) v0 = 10 m/s,

0 = 60o

(4)

4. A B

(R )

A

B

R

R

(1) R (2) 2

3R

(3) R2 (4) 2

R

1001CT102115077H-2/18


5. m, 2m, 4m, 8m, ……… 2N-1m N Hm m H 1 m/s

H

m

m 2m 4m 2N-1m

(1) g

N 12

(2) g

N2

(3) g

N 122

(4)

g

N 122

6. Q = 2N

o (

N0

) t ?

(1)

No

t

N

(2)

2No

t

N

No

(3)

2No

t

N

No

(4)

2No

t

N

No

H-3/181001CT102115077


7.

(1) (2)

(3) (4)

8. YDSE S1 S

2 d

P1 P

2, O

P1 P

2

D (>>d) O

P1

P2

d

S1

S2

(1) 2

cot2

tan

(2) 2

cot2

tan

(3) 2

cos2

sin

(4) 2

sin2

cos

9.

1200

120 V

3.6 V 1A

0.4 ohms

(1) 40 (2) 36 (3) 4800 (4) 4320

10. ( = 1.5)

R

O

?

(1)

2R

R

O

(2)

2R

R

O

(3)

3R

R

O

(4)

2R

R

O

1001CT102115077H-4/18


11. v

R C

B

A

L

B

C R

E H

G

v

F

(i) AEFBA

(ii) AEFBA

(iii)

(iv) 222

2

1vLCB

(1) (i) (iii)

(2) (ii) (iv)

(3) (i), (iii) (iv)

(4)

12. : 0ˆE E i

cos(kz – t)

z t = 0

(1)

y

x

z

(2)

y

x

z

(3)

y

x

z

(4)

13. E K

1 K

2 2 : 1

A A/2

K1

K1 K2

(1) E/4 (2) E/3

(3) E/12 (4) E/6

H-5/181001CT102115077


14. 0.625 m

2 rad/s

d s 0.5 s P C

(g = 10 m/s2)

P

C

(1) 1 : 1 (2) 2 : 1

(3) 3 : 1 (4) 4 : 1

15.

R

GM

(1) R

GM(2)

R

GM2

(3) R

GM

2

3(4)

R

GM2

16. p-n

Jp, drift

Jp, diff

Jn, drift

Jn, diff

p-n

(1) Jp, drift

+ Jn, drift

= Jp, diff

+ Jn, diff

= 0

(2) Jn, drift

+ Jn, diff

= 0

(3) Jp, drift

+ Jp, diff

= 0

(4) Jp, drift

+ Jn, drift

+ Jp, diff

+ Jn, diff

= 0

17. L

g

1

100

90.0 L 1 mm

20.0 cm g

(1) 2.7 % (2) 2.27 %

(3) 1.7 % (4) 4.4 %

1001CT102115077H-6/18


18. m1 m

2

(1) 2

1

m

m(2)

1

2

m

m(3) 1 : 1 (4)

2

1

m

m

19. -1 : P-N -2 : (1) -1 , -2 -2

-1 (2) -1 , -2 -2

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

20.

S

N

(1)

S

N

(2)

S

N

(3)

S

N

(4)

S

N

21. h

R

(1) 2

R(2)

h4

R2

(3) h

R2

(4) 2

h

H-7/181001CT102115077


22. l a

l a

I

A. B. C.

D.

E.

(1) A C (2) B C (3) A D (4) A E

23. = 0.98,

IB = 0.02 mA, R

L = 5 k

(1) 3.2 V

(2) 4.9 V IB

RL

VBCVBE

(3) 5.2 V

(4) 6.2 V

24.

:-

X Y Z

(1) X Y Z

(2) X Y Z

(3) X

Y Z

(4) X Y Z

25.

(1)

(2)

(3)

(4)

1001CT102115077H-8/18


26. M R

(1) kRMvoˆ

5

3

(2) kRMvoˆ

5

3

x

y

vo

vo/R

R

z

O

(3) kRMvoˆ

5

7

(4) 5

7 kRMvoˆ

27. N

2

0.4 nm (1) 6.5 GHz (2) 2.9 MHz

(3) 8.4 GHz (4) 7.3 MHz

28. T

o 2T

o PT–4 = C

I. 2

3R

II. 2

3R

III. –3RT0

IV. 3RT0

(1) I IV (2) I III (3) II IV (4) II III

29. m1, m

2, …., m

n n

1v

, 2v

, ….., nv

I.

II.

III.

(1) I

(2) III

(3) I III

(4) II III

30. P = 2.5 sin 2

(x – 660t)

(P, N/m2 x, m t, s )

(1) 6 m (2) 8 m

(3) 5 m (4) 10 m

H-9/181001CT102115077


PART B - CHEMISTRY

31. [Co(H2N – CH

2 – CH

2 – NH

2)

3]

2S

3oxidation

Co+4 + CO3–2 + NO

3– + SO

4–2

?

(1) 3M

182(2)

M

182

(3) 11M

182(4)

7M

182

32. X2, Y

2 X

2Y

3 J/K mol

60, 40 150

X2 +

3

2Y

2 X

2Y

3H = +30 kJ

(1) 250 K (2) 1000 K

(3) 750 K (4) 200 K

33.

r

4 r 2 r

(1) 5s (2) 5d

(3) 4p (4) 6d

34. T ()

'C'

C

:

(1) R

(2) T

(3) RT

(4)

35. N

2O

5(g) :

(a) 2N2O

5(g) 4NO

2(g) + O

2(g);

Ea

(b) N2O

5(g) 2NO

2(g) +

1

2O

2(g);

Ea'

(1) Ea = Ea' (2) Ea > Ea'

(3) Ea < Ea' (4) Ea = 2Ea'

1001CT102115077H-10/18


36. Cu

Cu+2 +0.15 V Cu+

Cu+0.50 V

2Cu / CuE

(1) +0.65 volt (2) +0.325 volt

(3) –0.0325 volt (4) –0.325 volt

37.

I-Cube II-Cylinder III-Sphere

5cm5cm

5cm 5cm

(1) I (2) II

(3) III

(4)

38. X, Y Z X fcc Y Z

(1) X5Y

4Z

8(2) XYZ

(3) X8Y

4Z

5(4) X

2YZ

39. H2O

2

O2(g)

:

1 atm, 273K , = 11.2 × M

STP , = 11.35 × M

[:

STP ]

300K 1 atm

(1) 12.315 × M (2) 24.63 × M

(3) 11.35 × M (4) 22.7 × M

40.

H2O

2H+ + HO

2– . 25°C H

2O

2

pH, 5.7 H2O

2

(1) 2 × 10–12 (2) 4 × 10–12

(3) 1 × 10–14 (4) 1.4 × 10–12

41.

(1) N(SiH3)

3 (2) ICl

2–

(3) XeF2 (4)

H-11/181001CT102115077


42. -

(a) (p)

(b) (q)

(c) (r)

(d) (s)

(1) a - p, b - q, c - r, d - s

(2) a - s, b - r, c - p, d - q

(3) a - s, b - r, c - q, d - p

(4) a - q, b - p, c - s, d - r

43. H2SO

4

(1) H2

(2) SO2

(3) O2

(4)

44.

(1) MO, M2O

3, MO

2, M

2O

5 -

(M = d )

(2) Sc, Ti, V, Cr, Mn -

(3) d5, d3, d1, d4 -

(4) Mn+2, Fe+2, Cr+2, Co+2 -

45. NHCl + A4

B +DO

(C)

(D )

A, B, C D

(1) Na3PO

4, NaPO

3, MnNaPO

4, MnO

(2) Na2HPO

4, NaPO

3, MnNaPO

4, MnO

(3) Na3PO

4, NaPO

3, CuNaPO

4, CuO

(4) Na2HPO

4, NaPO

3, CuNaPO

4, CuO

46.

I II

(A) (i) SiO2

(B) B2H

6 + H

2O (ii) H

2SiO

3

(C) B2H

6 + NH

3(iii) BN

(D) SiCl4

2(i) H O

(ii) 1000 C (iv) NaBO

2 + B

2O

3

(v) H3BO

3

A B C D

(1) i iii iv v

(2) ii iii iv v

(3) iv v iii ii

(4) iv v iii i

1001CT102115077H-12/18


47.

(X)

(1) sp3d2, +6 (2) d2sp3, +6

(3) sp3, +8 (4) sp3d, +6

48. Ma2b

2cd

(1) 2 (2) 4 (3) 5 (4) 8

49. Na2CO

3

(1) NH4HCO

3(2) NaHCO

3

(3) NaCl (4) Na2C

2O

4

50.

(1) O2

(2) N2

(3) N2+ (4) O

22–

51. CH3CH

2COOCH

3

A B

(1) Na (2) NaHCO3

(3) (4)

52.

(1) (2)

(3) (4)

53. KOH

(1) CH2 = CHBr

(2) Ph–CH2–CH

2–Br

(3) CH3CH

2Br

(4) CH3CH

2CH

2Br

54.

3 4

3 2 4

CH Cl KMnOZn

dust Anhy. AlCl dil.H SOX Y Z

Z

(1) (2)

(3) (4)

H-13/181001CT102115077


55.

(1) C6H

5NH

2(2) (C

6H

5)

2NH

(3) C2H

5NH

2(4) (C

2H

5)

2NH

56.

3 2 2

O||

CH – CH C NH 2

2

HNONaOH

BrA B

(1) (2)

(3) (4)

57. RNA

(1) +

(2) +

(3) +

(4) +

58.

(ArCN)

(1) ArCONH2 + P

2O

5

(2) ArN2

+ CuCN

(3) ArX + KCN

(4) ArCONH2 + SOCl

2

59. CH3–CH=CH–CH

2–CH(Br)–CH

3

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

60.

(1) 2--1-

(2) 2--2-

(3) 3--1-

(4) 2,3--1-

1001CT102115077H-14/18


PART C - MATHEMATICS

61. k

1r

r 1

ksin (B )

2

k

r

r 1

1A B

k

x A

xlim(1 x) tan

2

(1) 2

(2)

2

(3) 0 (4)

62. y2 = 16(x + 3) (–9, 0) -

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

63.

1 x x 0

f(x) 1 [x] sin x 0 x2

x32

f(x), x =

([.])

(1) 0 (2) 1

(3) 2

(4)

64. 1! + 2! + 3! + .... + 73! :-

(1) 1 (2) 2

(3) 3 (4) 4

65. 'f', x, y R f(x + y) = f(x)f(y) ƒ'(0) = 4 f(x

0) =

200 f'(x

0)

-

(1) 800 (2) 240

(3) 0 (4)

66. fr(x) = cos2p

rx

r = 1, 2, 3; pr N f

1(x) + 2f

2(x) + 3f

3(x)

2f1(x) + 3f

2(x)

2

3f1(x) + 2f

3(x)

3

(p1 + p

2 + p

3)

(1) 6 (2) 10 (3) 11 (4) 17

67. f(x) = x3 + x

5e g(x) = f–1(x)

g'(1) + log5(g'(1))

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

2

68. x + y + z = 5 x – y – z = 2 90° ax + by + cz + d

= 0, a, b, c, d I |a + b + c + d|

(1) 10 (2) 9 (3) 4 (4) 11

H-15/181001CT102115077


69. 12x2 – 5x – 1 = 0

r r

r 1

( )

(1) 3

8(2)

5

8

(3) 7

6(4)

70. u = f(tan x), v = g(sec x) f'(x) = tan–1x;

g'(x) = cosec–1x x4

du

dv

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

2(4) 3 2

71. 2 3ˆ ˆr (n n ) 1,

3 1ˆ ˆr (n n ) 2

1 2ˆ ˆr (n n ) 3,

1 2 3

ˆ ˆ ˆ([n n n ] 0)

(1) 1 2 3

1 2 3

ˆ ˆ ˆn 2n 3n

ˆ ˆ ˆ[n n n ]

(2) 1 2 32

1 2 3

ˆ ˆ ˆn 2n 3n

ˆ ˆ ˆ[n n n ]

(3) 2 3 3 1 1 2

1 2 3


ˆ ˆ ˆ[n n n ]

(4) 2 3 3 1 1 22

1 2 3


ˆ ˆ ˆ[n n n ]

72. x, y R,

2 2(x 4) y

14 9

2 2x y

8 18

(1) 9 (2) 7

2(3)

9

2(4) 10

73. sin106x – cos106x = 1 -

(1) 2n + 2

(2) n +

2

(3) 2n – 2

(4) n

( n I)

74. y = x2 + 7, y = x, x = 3 x = 0 -

(1) 61

2(2)

51

2(3)

31

2(4)

21

2

75.x

e 2

9e log (3x 2) dx

(3x 2)

-

(1) xe

3e log (3x 2) C

3x 2

(2) xee log (3x 2) C

(3) xe

1e log (3x 2) C

3x 2

(4) ( 'C' )

1001CT102115077H-16/18


76. x5 + e8x = 0 -(1) 0 (2) 1 (3) 2 (4) 3

77.

2 5 7 9

0 1 9 7A

0 0 1 8

0 0 0 1

|adj (adjA)|

-

(1) 1024 (2) 512

(3) –512 (4) –1024

78. (m – 1)x2 + (1 + 3m)x – (8 – 3m) = 0

m

-

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

79.

4

18 11

0

sin x cos x dx -

(1) 11

32(2)

11

64

(3) 0 (4) 3

8

80. |z – 3 – 4i| = 2 |z| = 1 -

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

81. 1 + (1 + x) + (1 + x)2 + ..... + (1 + x)100 x7 -

(1) 101C93

(2) 100C93

(3) 100C7

(4) 0

82. A, 3 2

A4 3

(A27 – 2A26) -

(1) –5 (2) –7 (3) –10 (4) 0

83. () 7 -

(1) 4

1

7(2) 4

24

7

(3) 4

25

7(4) 4

16

7

84. p q, f(x) = 5sinx + 12cosx + 1

(p, q)

x-

-(1) 14 (2) 12 (3) 13 (4) 11

85. 2 2

2

x y1

a 1 2

x2 + y2 + 4x + 1 = 0 log

4(4a2 + 1) -

(1) 1 (2) 2 (3) 0 (4) 16

H-17/181001CT102115077


86. x 1 y 1 z 2

3 2 4

2x+y–3z+4=0 64 cosec2

-(1) 1264 (2) 1624

(3) 1628 (4) 1648

87. 7 1, 2, 3, 4,

5, 6, 7 5 1201 -(1) 3124567 (2) 3765421

(3) 3124675 (4) 3124657

88. a,b,c

[3a b c a b c 7a] =

[a b c]

-

(1) 1 (2) 8 (3) 9 (4) 6

89. 1, 2, 2, 3 log2

-

(1) 8 (2) 1 (3) –1 (4) –2

90. y2 = kx

2 |k| -

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

1001CT102115077H-18/18


JEE (Main + Advanced) : ENTHUSIAST COURSE · 2016-02-08 · E-4/18 1001CT102115077 Target : JEE...

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Transcript of JEE (Main + Advanced) : ENTHUSIAST COURSE · 2016-02-08 · E-4/18 1001CT102115077 Target : JEE...