04-jee main full length test-04!28!03-2016

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JEE Main

Subject Topic Mock Test – 04 Date

C + M + P Full Length Mock Test – 04 JEE Main – 12 – MT

28th Mar 2016 JM1220150408

Max. Marks: 360 Duration: 3 Hours

1. This paper consists of 90 questions with 3 parts of Chemistry, Mathematics and Physics

Each Part consists of 2 Sections

Part – A : 27 Multiple Choice Questions with one correct answer. A correct answer carries 4

Marks. A wrong answer carries a penalty of 1 mark.

Part – B : 3 Assertion and Reason type questions. A correct answer carries 4 marks. A wrong

answer carries a penalty of 1 mark.

2. The OMR sheet for 200 questions is to be used

3. Use of calculators and log tables is prohibited

4. Darken the appropriate bubble using a pen in the OMR sheet provided to you. Once

entered, the answer cannot be changed. Any corrections or modifications will

automatically draw a penalty of 1 mark

5. No clarification will be entertained during the examination. Doubts in the paper can

be reported to the coordinator after the exam

6. If the details in the OMR Sheet are not filled, If the OMR sheet is mutilated, torn, white

Ink used, the circles filled and scratched, then the OMR sheet will not be graded

All the best!!

Useful Data

At. Wt.:

N = 14; O = 16; H = 1; S = 32; Cl = 35.5; Mn = 55; Na = 23; C = 12; Ag = 108; K = 39; Fe = 56; Pb = 207

Physical Constants:

346.626 10 Jsh , 23 -1a N 6.022 10 mol ,

8 -1c 2.998 10 ms , 31em 9.1 10 kg


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Ace Insignia Rough Work Page 2

Chemistry

Part –

A

Multiple Choice Questions with one correct answer. A correct answer carries 4 marks. A wrong

answer carries a penalty of 1 mark. 27 x 4 = 108

1. A Zwitter ion is

(a) negatively charged ion without metal atom

(b)

heavy ion with a small charge on it

(c) an ion with positive and negative charge at different points on it

(d)

a positively charged ion without a metal ion

2.

Which of the following hexoses will form the same osazone when treated with excess of phenyl

hydrazine?

(a) D-glucose, D-fructose and D-galactose (b) D-glucose, D-fructose and Mannose

(c) D – glucose, D-mannose and D-galactose (d) D-fructose, D-mannose and D-galactose

3. Which of the following is the strongest base?

(a) (b)

(c) (d)

4.

403 300

LiAlH Cu Dilute

NaOH C CH COOH X Y Z In the above reaction Z is

(a) butanol (b) aldol (c) ketol (d) acetol

NH2 NH CH3

NH2

CH3

CH2 NH2


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5.

32 2

H H O

RCOOH X RCH NH

Identify the X in the above sequence.(a) Alkane nitrile (b) Alkyl isonitrile (c) Aldoxime (d) Alkyl nitrile

6. Which of the following compounds would be the main product of an aldol condensation of

acetaldehyde and acetone?

(a) 3 .CH CH CH CHO (b) 3 3CH CH CHCOCH

(c) 3 2 .CH C CH CHO (d) 3 32CH C CHCOCH

7.

Both HCHO and 3CH CHO gives similar reactions with all the reagents except

(a) Schiff reagent (b) Fehling solution (c) Ammoniacal 3 AgNO (d) Ammonia

8.

Which of the following is expected to be aromatic?

(a) (b) (c) (d)

9. Which of the following complexes are diamagnetic ?

(A) 4 6 K Fe CN (B) 3 6 K Cr CN

(C) 3 6 K Co CN (D) 2 4 K Ni CN

(a) (A), (B) and (C) (b) (B), (C) and (D) (c) (A), (C) and (D) (d) (A), (B) and (D)

10. The hybridization of central metal ion and shape of wilkinson’s catalyst is

(a) 3 , sp d trigonal bipyramidal (b) 3, sp tetrahedral

(c) 2 ,dsp square planar (d) 2 2 ,d sp octahedral

11.

Most basic hydroxide among the following is

(a) 3 Lu OH (b) 3 Eu OH (c) 3Yb OH (d) 3Ce OH

H

H

+


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12.

Identify the incorrect statement among the following

(a) Ozone reacts with 2SO to gives 3SO

(b) Silicon reacts with NaOH(aq) in the presence of air to give 2 3 Na SiO and 2 H O

(c) 2Cl reacts with excess of 3 NH to give 2 N and HCl

(d) 2 Br reacts with cold and dilute NaOH solution to give NaBr, 3 NaBrO and 2 H O

13. In pyrophosphoric acid, 4 2 7 H P O , number of bonds and d p bonds are respectively

(a) 8 and 2 (b) 6 and 2 (c) 12 and zero (d) 12 and 2

14.

Which of the following can show oxidation state higher than +3?

(a) B (b) Al (c) Ce (d) Ga

15. Which pair of the following chlorides do not impart colour to the flame?

(a) 2 BeCl and 2SrCl (b) 2 BeCl and 2 MgCl

(c) 2CaCl and 2 BaCl (d) 2 BaCl and 2SrCl

16.

Extraction for zinc from zinc blende is achieved by

(a)

electrolytic reduction

(b)

roasting followed by reduction with carbon

(c) roasting followed by reduction with another metal

(d) roasting followed by self-reduction

17. Peptisation denotes

(a) digestion of food

(b) hydrolysis of proteins

(c) breaking and dispersion into colloidal state

(d) precipitation of solid from colloidal dispersion.


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18. The concentration of a reactant X decreases from 0.1 M to 0.005M in 40 min. If the reaction follows

first order kinetics, the rate of the reaction when the concentration of X is 0.01 M will be

(a) 4 11.73 10 min M (b) 4 13.47 10 min M (c)5 1

3.47 10 min M (d) 4 17.5 10 min M

19.

Electrolysis of dilute aqueous NaCl solution was carried out by passing 10mA current. The time

required to liberate 0.01 mole of 2 H gas at the cathode is (1F1

96500 )C mol

(a) 49.65 10 s (b) 419.3 10 s (c) 428.95 10 s (d) 438.6 10 s

20. Osmotic pressure of 0.4% urea solution is 1.64 atm and that of 3.42% cane sugar is 2.46 atm. When the

above two solutions are mixed, the osmotic pressure of the resulting solution is

(a) 0.82 atm (b) 2.46 atm (c) 1.64 atm (d) 4.10 atm

21. a K for HCN is10

5 10 at 025 .C For maintaining a constant pH = 9, the volume of 5 M KCN solution

required to be added to 10 mL of 2 M HCN solution is antilog 0.699 5of

(a) 2 mL (b) 4 mL (c) 8.2 mL (d) 6.4 mL

22. Two moles of 5 PCl is heated in a closed vessel of 2L capacity. When the equilibrium is attained 40%

of it has been found to be dissociated. What is the c K in mol/ 3

?dm

(a) 0.532 (b) 0.266 (c) 0.133 (d) 0.174

23.

Among the following, the pair in which the two species are not isostructural is

(a) 3 IO and 3 XeO (b) 6 PF

and 6SF (c) 4 BH and 4 NH

(d) 23CO and 2 NO

24.

In a compound, atoms of element Y form ccp lattice and those of element X occupy 2/3 rd of

tetrahedral voids. The formula of the compound will be

(a) 4 3 X Y (b) 2 3 X Y (c) 2 X Y (d) 3 4 X Y

25. If temperature of 1 mole of a gas is increased by 50 C , calculate the change in kinetic energy of the

system.

(a) 623.25 J (b) 6.235 J (c) 62.35 J (d) 6235.0 J


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26. Which of the following complexes is expected to be coloured ?

(a) 3 4Ti NO (b) 3 4Cu NCCH BF

(c) 4

6 Fe CN

(d) 3 6 K VF

27.

Which alcohol will be most reactive for dehydration?

Part – B

Assertion and Reason type questions. A correct answer carries 4 marks. A wrong answer carries

a penalty of 1 mark 3 x 4 = 12

(A) If both Assertion and Reason are true and Reason is correct explanation of Assertion.

(B) If both Assertion and Reason are true but Reason is not the correct explanation of assertion.

(C) If Assertion is true but Reason is false.

(D) If Assertion is false but Reason is true.

28.

Assertion (A): Benzoic acid does not give Friedel-Craft’s reaction

Reason (R): Benzoic acid is obtained by catalytic oxidation of toluene with air in presence of Co-Mn

catalyst

(a) A (b) B (c) C (d) D

CH3 CH CH2 CN

OH

(a) CH3 CH CH2 NO2

OH

(b)

CH3 CH CH2 COCH3

OH

(c) CH3 CH CH2 CHO

OH

(d)


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29.

Assertion (A): Cycloalkenes decolourise the purple colour of dilute and cold 4 KMnO or colour of

bromine in carbon tetrachloride

Reason (R): Cycloalkenes undergo the electrophilic addition reactions which are characteristic of

alkenes

(a) A (b) B (c) C (d) D

30. Assertion (A): Ozone is a powerful oxidizing agent in comparison to 2O

Reason (R): Ozone is diamagnetic but 2O is paramagnetic

(a) A (b) B (c) C (d) D


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Mathematics

Part –

A



31.

The number of solution of tan sec 2cos x x x in [0,2 ) is

(a) 2 (b) 3 (c) 0 (d) 1

32. If 0 x and1

cos sin ,2

x x then tan x is

(a) 1 7

4

(b)

4 7

3

(c)

4 73

(d) 1 7

4

33. z and w are two nonzero complex numbers such that z w and Arg z Arg w then z equals

(a) (b) (c) (d)

34.

Let z and w be complex numbers such that 0 z iw and arg zw . Then arg z equals

(a)5

4

(b)

2

(c)3

4

(d)

4

35. If one root of the equation 2 12 0 x px is 4, while the equation 2 0 x px q has equal roots, then

the value of ' 'q is

(a) 4 (b) 12 (c) 3 (d)49

4

36. If the roots of the equation 2 0bx cx a be imaginary then for all real values of , x then expression

2 2 23 6 2b x bcx c is:

(a) less than 4ab (b) greater than 4ab

(c) less than 4ab (d) greater than 4ab


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37. The number of ways in which 6 men and 5 women can dine at a round table if no two women are to

sit together is given by

(a) 7 ! 5 ! (b) 6 ! 5 ! (c) 30 ! (d) 5 ! 4 !

38.

Total number of four digit odd numbers that can be formed using 0,1, 2,3,5,7 (using repetition is

allowed) are

(a) 216 (b) 375 (c) 400 (d) 720

39.

If x is positive, the first negative term in the expansion of 27 5

1 x is

(a) 6th term (b) 7th term (c) 5th term (d) 8th term

40.

The coefficient of the middle term in the binomial expansion in powers of x of 4

1 x and of

6

1 x is the same if equals

(a)3

5 (b)

10

3 (c)

3

10

(d)

5

3

41.

Let r T be the rth term of an A.P. whose first term is ‘a’ and common difference is ‘ '.d If for some

positive integers 1 1, , , ,m nm n m n T and T then a d n m

equals

(a)1 1

m n (b) 1 (c)

1

mn (d) 0

42.

The sum of the first n terms of the series 2 2 2 2 2 61 2.2 3 2.4 5 2.6 ..... is

21

2

n n when n is

even. When n is odd the sum is

(a)

21

2

n n

(b) 2 1

2

n n (c)

2

1

4

n n (d)

3 1

2

n n


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50. Angle between the tangents to the curve 2 5 6 y x x at the points 2,0 and 3,0 is

(a) (b)2

(c)6

(d)4

51.

If : f R S , defined by sin 3 cos 1, f x x x is onto, then the interval of S is

(a) 1,3 (b) 1,1 (c) 0,1 (d) 0,3

52.

The domain of the function 1

2

sin 3

9

x f x

x

is

(a) 1, 2 (b) [2,3) (c) 1, 2 (d) 2,3

53.

The value of

2

2

0

0

sec

limsin

x

x

tdt

x x

is

(a) 0 (b) 3 (c) 2 (d) 1

54.

If f is a real valued differentiable function satisfying 2

, , f x f y x y x y R and 0 0, f

then 1 f equals

(a) 1 (b) 0 (c) 2 (d) 1

55.

Let

11 sin 1

1

0 1

x if x f x x

ifx

Then which one of the following is true?

(a) f is neither differentiable at 0 x nor at 1 x

(b) f is differentiable at 0 x and at 1 x

(c) f is differentiable at 0 x but not at 1 x

(d) f is differentiable at 1 x but not at 0 x


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56. If the roots of the equation 2 0 x bx c be two consecutive integers, then 2 4b c equals

(a) 2 (b) 3 (c) 2 (d) 1

57.

Let : 1,1 f R be a differentiable function with 0 1 f and ' 0 1. f Let

2

2 2 g x f f x . Then ' 0 g

(a) 4 (b) 0 (c) 2 (d) 4

Part – B







58. Let A be a 2 2 matrix

Assertion (A): adj (adj A) = A

Reason (R): adj A A

(a) A (b) B (c) C (d) D

59.

Let : f R R be a continuous function defined by 1

2 x x

f xe e

Assertion (A): 1

,3

f c for some x R

Reason (R): 1

0 ,2 2

f x for all x R

(a) A (b) B (c) C (d) D


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60. Consider the planes 3 6 2 15 x y z and 2 2 5 x y z

Assertion (A): The parametric equations of the line of intersection of the given planes are

3 14 , 1 2 , 15 x t y t z t . because

Reason (R): The vector ˆˆ ˆ14 2 15i j k is parallel to the line of intersection of given planes

(a) A (b) B (c) C (d) D


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Physics

Part –

A



61. In CE transistor amplifier, we can measure the AC variations across the input and output terminals

by

(a) blocking the AC voltage by large inductors

(b) blocking the AC voltage by large capacitors

(c) blocking the DC voltage by large inductors

(d) blocking the DC voltage by large capacitors

62.

In amplitude modulation, the value of modulation index should be

(a) 1 (b) 1 (c) 1 (d) 1

63. From what minimum height h must the system be released when spring is

unstretched so that after perfectly inelastic collision 0e with ground, B may

be lifted off the ground (spring constant k )?

(a) / 4mg k (b) 4 /mg k

(c) / 2mg k (d) none of these


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64.

A mass m is moving at speed v perpendicular to a rod of length d

and mass 6 M m which pivots around a frictionless axle running

through its center. It strikes and sticks to the end of the rod. The

moment of inertia of the rod about its center is 2 /12 Md . Then the

angular speed of the system just after the collision is

(a)2

3

v

d (b)

2v

d

(c)v

d (d)

3

2

v

d

65.

A uniform solid brass sphere is rotating with angular speed 0 about a diameter. If its temperature is

now increased by100 C . What will be its new angular speed? (Given 52.0 10 B per C )

(a) 1.1 0 (b) 1.01 0 (c) 0.996 0 (d) 0.824 0

66.

One mole of an ideal monoatomic gas undergoes process 2T V and temperature of gas changes

from 300 K to 1200 K then work done by the gas is

(a) 400 R (b) 450 R (c) 900 R (d) 600 R

67.

A physical pendulum is positioned so that its center of gravity is above the suspension point. When

the pendulum is released it passes the point of stable equilibrium with an angular velocity . The

period of small oscillations of the pendulum is

(a)4

(b)

2

(c)

(d)2

68.

Two canoes are 10 m apart on a lake. Each bobs up and down with a period of 4.0 s. When one canoe

is at its highest point, the other canoe is at its lowest point. Both canoes are always within a single

cycle of the waves. Determine the speed of the wave.

(a) 2.5 m/s (b) 5 m/s (c) 40 m/s (d) 4 m/s


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69. A sound wave of wavelength 0.40 m enters the tube

at .S The smallest radius r of the circular segment

to hear minimum at detector D must be:

(a) 1.75 m (b) 0.175 m

(c) 0.93 m (d) 9.3 m

70.

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and ,b

respectively. When a current i passes through the coil, the magnetic field at the center is

(a) 0 NI

b

(b) 0

2 NI

a

(c)

02

NI b In

a b a

(d) 0

2

N I b

Inb a a

71. Two identical bar magnets each having length L and magnetic moment

M are arranged in such a way that one of them is bent in the form a

semicircle and placed over the other as shown in the figure. The net

magnetic moment of the system is?

(a)2

1 M

(b) 2 1 M (c) 2 M (d) 0

72. A particle of the charge per unit mass is released from origin with a velocity 0 ˆv v i in a uniform

magnetic field 0ˆ B B k . If the particle passes through 0, , 0 y , then y is equal to

(a) 0

0

2v

B (b) 0

0

v

B (c) 0

0

2v

B (d) 0

0

v

B

N

N S

S


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73. The charge on the capacitor in steady

state in the circuit shown in figure is

(a) 0.5 C

(b) 1 C

(c) 2 C

(d) 4 C

74.

A parallel plate capacitor is constructed using three

different dielectric materials as shown. What is the

capacitance across P are Q ?

(a) 2 3 01

2 32

K K A K

K K t

(b) 2 3 012 3

K K A K

K K t

(c) 2 3 012 3

2 K K A K

K K t

(d) 2 3 0

12 32

K K A

K K K t

75. Energy levels, A, B, C of a certain atom correspondence to increasing values of energy

. . . A B C

i e E E E If 1 2 3, , are the wavelengths of radiations corresponding to the transitions C to B, B

to A and C to A respectively, which of the following relations is correct?

(a)3 1 2

(b) 1 231 2

(c)

1 2 3 0 (d)3 2 2

3 1 2


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76. A nozzle throws a stream of gas against a wall with a velocity v

much larger than the thermal agitation of the molecules. The wall

deflects the molecules without changing the magnitude of their

velocity. Also, assume that the force exerted on the wall by the

molecules is perpendicular to the wall. (This is not strictly true

for a rough wall). Find the force exerted on the wall.

(a) 2 2 Anmv cos (b) 2 22 Anmv cos (c) 2 22 sin Anmv (d) 2 cos Anmv

77. A double-slit arrangement produces fringes for light 5890 A which are apart. If the whole

arrangement is fully dipped in a liquid of4

3 , the angular fringe separation is

(a) 0.15 (b) 0.30 (c) 0.10 (d) 0.25

78.

A fish rising vertically up toward the surface of water with speed 3

1ms

observes a bird diving vertically down towards it with speed 9

1ms

. The actual velocity of bird is

(a) 4.5 1ms (b) 5.4 1ms

(c) 3.01

ms

(d) 3.41

ms

79.

A particle revolves in clockwise direction (as seen from point ) A in a

circle C of radius 1 cm and completes one revolution in 2 sec. The axis

of the circle and the principal axis of the mirror M coincide, call it . AB

The radius of curvature of the mirror is 20 cm. Then, the direction of

revolution (as seen from A ) of the image of the particle and its speed is

(a) Clockwise, 1.57 1cms (b) Clockwise, 3.14 1cms

(c) Anticlockwise, 1.57 1cms (d) Anticlockwise, 3.14 1cms


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80. A transparent cylinder has its right half polished so as to act as a

mirror. A paraxial light ray incident from left, that is parallel to the

principal axis, exits parallel to the incident ray as shown. The

refractive index n of the material of the cylinder is

(a) 1.2 (b) 1.5

(c) 1.8 (d) 2.0

81. Two identical sonometer wires have a fundaments frequency of 500 Hz when kept under the same

tension. The percentage change in tension of one of the wires that would cause an occurrence of 5

beats per second, when both wires vibrate to together is

(a) 0.5% (b) 1% (c) 2% (d) 4%

82. An inclined plane makes an angle 30 with the horizontal. A groove OA of length 5 m cut, in the

plane makes an angle 30 with .OX A short smooth

cylinder is free to slide down the influence of

gravity. The time taken by the cylinder to reach

from A to O is 210 / g m s

(a) 4 s (b) 2 s (c) 3 s (d) 1 s

83.

A projectile can have the same range R for two angles of projection. It 1t and 2t be the times of flight

in the two cases, then what is the product of two times of fight?

(a) 21 2t t R (b) 1 2t t R (c) 1 21

t t R

(d) 1 2 21

t t R


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84. A block A of mass 2 kg is placed over another block B of mass 4

kg which is placed over a smooth horizontal floor. The

coefficient of the friction between A and B is 0.4. When a

horizontal force of magnitude 10 N is applied on A , the

acceleration of blocks A and B are

(a) 1 2ms and 2 2ms , respectively

(b) 5 2ms and 2.5 2ms , respectively

(c) both the blocks will moves together with acceleration 1/3 2ms

(d) both the blocks will moves together with acceleration 5/3 2ms

85. A uniform ball of radius r rolls without slipping down from the top of a sphere of radius . R The

angular velocity of the ball when it breaks from the sphere

(a)

2

5

17

g R r

r

(b)

2

10

17

g R r

r

(c)

2

5

10

g R r

r

(d)

2

10

7

g R r

r

86. In the electrical network at 0,t key was placed on (1) till the

capacitor got fully charged. Key is placed on (2) at 0.t Time

when the energy in both the capacitor and the inductor will be

same for the first time is

(a)4

LC

(b)3

4 LC

(c)3

LC

(d)2

3 LC

87. A hollow equiconvex lens made of a very thin glass sheet has one of its curved surfaces silvered. It

converges a parallel beam of light at a distance of 0.2 m in front of it. Where will it converge the same

rays if filled with water, refractive index 4 / 3 ?wn

(a) 5.7 cm, right (b) 12 cm, left (c) 22 cm, left (d) 15.5 cm, right


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Part – B







88.

Assertion (A): A body in equilibrium has to be at rest only

Reason (R): A body in equilibrium may be moving with a constant speed along a straight line path

(a) A (b) B (c) C (d) D

89. Assertion (A): A body of mass 1m collides head on elastically with another stationery body of mass

2m . After the collision, velocity of mass 2m is maximum, when 1 2m m

Reason (R): Velocity of second body is always maximum, when the mass 2m is greater than mass of

the hitting body

(a) A (b) B (c) C (d) D

90.

Assertion (A): A body that is a good radiator is also a good absorbed of radiation at a givenwavelength

Reason (R): According to Kirchhoff’s Law the absorptivity of a body is equal to its emissivity at a

given wavelength

(a) A (b) B (c) C (d) D

04-jee main full length test-04!28!03-2016

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