JEE Main 2014_Test 8 (Paper I) Code A

8/10/2019 JEE Main 2014_Test 8 (Paper I) Code A

1/18


2/18

TOPICS OF THE TEST

Test No. 8

Complete Syllabus of Class XI


3/18

Space for Rough Work

Test - 8 All India Aakash Test Series for JEE (Main)-2015

1/14

PART - A (PHYSICS)

SECTION - IStraight Objective Type Questions

This section contains 25 multiple choice questions

numbered 1 to 25. Each question has 4 choices (1), (2),

(3) and (4), out of which ONLY ONE is correct.

Choose the correct answer :

1. A motor boat travels across a river from a point Ato

point Bon the opposite bank along the line AB

making an angle with the direction of flow of the

river. The flag on the mast of the motor boat makes

an angle with direction of motion. Find the speed

of motor boat with respect to ground. Assuming

velocity of wind is u perpendicular to the stream.

Assume2

(1)cos( )

sin

u

(2)

sin2

sin

u

(3)sin

cos( )

u

(4)

sin

cos

u

2. Two intersecting straight lines move translationally,perpendicular to their orientation with speed v1and

v2. If the lines are orthogonal to each other, the

speed of the point of intersection is

(1) 2 21 2

v v (2)2 2

1 2

2

v v

(3)2 2

1 2

2

v v(4) 2 2

1 2 1 2v v v v

TEST - 8Time : 3 Hrs. MM : 360

3. A bus is 2 m long and 3 m wide. The bus moves on a

straight road with speed 10 m/s. A bullet hits it in a

direction making an angle 37 with the direction of

motion of bus as observed from road. The bullet enters

the one edge and comes out from diagonally opposite

edge as shown in the figure. Then time taken by the

bullet to cross the bus and speed of bullet are

respectively

3m

2 m

10 m/s

(1) 2 s, 20 m/s (2) 1 s, 25 m/s

(3) 0.2 s, 25 m/s (4) 2 s, 15 m/s

4. A block of mass mrests on a bracket of mass Mas

shown. The coefficient of friction between the masses

Mandmis s. The bracket rests on a smooth horizontal

surface. The maximum force Fthat can be applied on

the system for no relative motion betweenmandMis

M

m

F

= 0

(1)( )

( 2 )

sMg m M

M m

(2)

( )

smg

M m

(3)( )

sMg

M m

(4)

( )

( 2 )

smg M m

M m


4/18


All India Aakash Test Series for JEE (Main)-2015 Test - 8

2/14

5. A particle of mass mmoves in theXYplane with a

velocity valong the straight line AB. If the angular

momentum of the particle with respect to origin Ois

LA

when it is at Aand LBwhen it is at B, then

Y

X

BA

O

(1) LA> L

B

(2) LA= L

B

(3) The relationship between LA and L

B depends

upon the slope of the line AB

(4) LA< L

B

6. A particle of mass 1 kg is given a velocity 2 m/s

along positivex-axis at origin. A variable force is to

act on particle given by F = 2 3x, where x is

position of particle alongx-axis. If the force continuesto act, the range in which particle oscillates is

y

x

2 m/s

m= 1 kg

(1) 2 2

to3 3

x x

(2) 4 4

to3 3

x x

(3) 2

to 23

x x

(4) x= 6 tox= +6

7. At a certain instant blockAhas a downward velocityof 0.8 m/s. At this instant, velocity of block B is

BA

(1) 1.6 m/s up (2) 1.6 m/s down

(3) 1.2 m/s down (4) 1.2 m/s up

8. The figure shows a uniform cylinder of radius aand

weight 75 N. After drilling a cylindrical cavity in the

cylinder, weight of remaining body is 60 N. The axis

of cavity is parallel to that of solid cylinder. For

equilibrium of body, tension in the string must be

T

2

3

a Rough

(1) 2 N (2) 15 N

(3) 5 N (4) 20 N

9. A block of mass 2 kg is placed on a wedge of mass

9 kg. A force of 210 N is applied on the wedge as

shown in figure. The time after which block leaves

the contact with the wedge is [Neglect friction

everywhere]

9 kg

452 kg

10 m

210 N

(1) 2 s (2) 1

s2

(3) 2 s (4) 4 s

10. Two rods of different materials having coefficients of

thermal expansions 1and

2and Young's moduli

Y1and Y

2respectively are fixed between two rigid

walls. The rods are heated such that they undergo

the same increase in temperature. There is no

bending of rods. If1

2

2

3

and stresses developed

in the two rods are equal, then1

2

Y

Yis


5/18



3/14

(1)3

2(2) 1

(3)2

3(4)

1

2

11. 2 kg of ice at 20C is mixed with 5 kg of water at

20C in an insulating vessel having a negligible heat

capacity. Calculate the final mass of water remaining

in the container. It is given that the specific heats ofwater and ice are 1 kcal/kg/C and 0.5 kcal/kg/C

while the latent heat of fusion of ice is 80 kcal kg1

(1) 7 kg (2) 6 kg

(3) 4 kg (4) 2 kg

12. A solid sphere of uniform density is released from

rest on an inclined plane. If it falls through a height

7 m along the inclined plane without slipping. The

speed of sphere will be [g= 10 m/s2]

(1) 10 m/s (2) 5 m/s

(3) 15 m/s (4) 7.5 m/s

13. Six moles of O2gas are heated from 20C to 35C at

constant volume. If specific heat capacity at constant

pressure is 8 cal mol1K1and R= 8.31 Jmol1K1,

what is change in internal energy of gas ?

(1) 180 cal (2) 300 cal

(3) 360 cal (4) 540 cal

14. If a satellite is moving around a planet in an elliptical

orbit of semi-major axis a0. The time period of

revolution of satellite is

(1)3

02

a

GM

(2)3

02a

GM

(3)3

0a

GM (4)

3

0

2

a

GM

15. A floating raft of mass 600 kg has 7 cm of thickness

submerged in water. When a man stands on the

raft, 8.4 cm are submerged. The mass of man is

(1) 100 kg (2) 60 kg

(3) 120 kg (4) 80 kg

16. A wire of area of cross-section 106m2is stretched to

increase its length by 0.1%. The tension produced in

the wire is 1000 N. The Young's modulus of wire is

(1) 1017N/m2 (2) 1012N/m2

(3) 109N/m2 (4) 1010N/m2

17. When two progressive waves y1= 4 sin(2x 6t) and

2 3 sin 2 62

y x t

are superimposed, the

amplitude of the resultant wave is

(1) 5 (2) 6

(3)5

3(4)

1

2

18. Angular frequency of small oscillation of the system

shown in figure is [Given, there is no slipping

between the string and pulley]

mk

( )IR

(1)2

2

Im

R

k

(2)2

k

Im

R

(3)

2

2

2

Im

R

k

(4) 2

Im

R

19. A hollow cylinder with both sides open generates a

frequency v in air. When the cylinder vertically

immersed into water by half its length the frequency

will be

(1) v (2) 2v

(3)2

v

(4)4

v


6/18



4/14

20. A sound source is moving towards stationary listener

with1

10th of the speed of sound. The ratio of

apparent to real frequency is

(1)

29

10

(2)9

10

(3)11

10(4)

211

10

21. If vsis the speed of sound in a diatomic gas and v

0

is the rms speed of its molecule at same

temperature, which of the following is correct?

(1) vs= 0.68v

0

(2) vs= 0.5v

0

(3) vs= 0.6v

0

(4) vs= 0.75v

0

22. A horizontal wire of length Land mass M is under

tension T. If mass density (linear) of the wire follows

the relation = kX, where X is distance of point

from one end of the rod, find the time taken by wave

pulse to reach fromX= 0 toX= L.

(1) 3 2

2

ML

T(2)

2 2

3

ML

T

(3) 3

2

ML

T(4)

2

3

ML

T

23. The value of initial temperature of an ideal gas

contained in a rigid container, such that increase in

temperature by 1C results in a pressure increment

of 0.4%, is

(1) 250C

(2) 250 K

(3) 17 K

(4) 17C

24. A horizontal tube of length l closed at both ends

contains an ideal gas. The tube is rotated with

constant angular velocity , as shown in figure.

Assuming temperature to be uniform and constant

and n1and n

2be number of molecules of gas per unit

volume in the two regions as shown in figure. Which

of the following is correct?

n1

n2

(1) n1> n

2(2) n

2> n

1

(3) n1= n

2(4) Cannot be decided

25. For an enclosure maintained at 2000 K, the

maximum radiation occurs at wavelength m

. If the

temperature is raised to 3000 K, the peak will shift

to

(1) 0.5m

(2) m

(3) 2

3 m (4)

3

2 m

SECTION - II

Assertion Reason Type Questions

Directions : Questions number 26 to 30 are Assertion-

Reason type questions. Each of these questions

contains two statements. Statement-1 (Assertion) and

Statement-2 (Reason). Each of these questions also has

four alternative choices, only one of which is the correctanswer. You have to select the correct choice.

26. Statement-1 : Emissive power of a body is

dimensionless quantity.

and

Statement-2 : Absorptive power of a body is a

dimensionless quantity.


7/18


8/18


9/18



7/14

36. 120 mL of buffer of pH 8.56 is to be prepared by

mixing 0.10 M NH4OH and 0.25 M NH

4Cl. If pK

bof

NH4OH is 4.74, calculate the volume of NH

4OH

solution required. [Use log 5 = 0.7]

(1) 50 mL

(2) 40 mL

(3) 30 mL(4) 20 mL

37. Glass is a solid solution, which is an optically

transparent fusion product of inorganic materials. The

colour of glass is due to presence of metal ions.

Then which of the following is not correct match?

Column-I Column-II

Colour of glass Metal oxide

(1) Green Fe2O3

(2) Yellow Na2O2

(3) Blue CuO

(4) Red Colloidal Au, Cu

38. Boron and silicon both have similarity due to

diagonal relationship, then which of the following is

not true for them?

(1) Both are semi-conductor

(2) As borate, silicates have tetrahedral structural

unit

(3) Both can dissolve in cold dilute acid

(4) Borides and silicides can be hydrolysed by H2O

39. Which one of the following processes can be used

for removing both types of hardnesses of water?

(1) Permutit process

(2) Washing soda process

(3) Clark's process

(4) Calgon process

40. Certain sample of water was found to contain

68 ppm of CaSO4and 19 ppm of MgCl

2. Then what

will be the total hardness of water in terms of ppm

of CaCO3?

(1) 87 ppm (2) 49 ppm

(3) 70 ppm (4) 80 ppm

41. Water (hydrane) is a type of solvent(1) Protophilic solvent (2) Protogenic solvent

(3) Amphiprotic solvent (4) All of these

42. Which is the correct increasing order of the energy

of hybrid orbital of the central atom?

(1) [PCl6]< [PCl

4]+< NH

4

+< SO2< CO

2

(2) CO2> SO

2> NH

4

+> [PCl4]+> [PCl

6]

(3) CO2< SO

2< NH

4

+< [PCl6]< [PCl

4]+

(4) CO2< SO

2< NH

4

+< [PCl4]+< [PCl

6]

43. The correct relationship among the following pairs of

given compound is

I.

O O

O O

II.

O

O

OO

III.

O

OO

O

Column-I Column-II

(I, II) (II, III)

(1) Functional isomers Metamers

(2) Metamers Functional isomers

(3) Metamers Metamers

(4) Functional isomers Functional isomers


10/18



8/14

44. Which one is incorrect pair of degree of unsaturation

(DU) with the structure?

Column-I Column-II

Compound Degree of

unsaturation

(1) 3

(2)

H C CH CH C = CH3 2 2

CH3

4

(3) 5

(4)

CH CH CH2 32

2

45. Which of the following is most stable?

(1)

CHO

NH2

H

H

H

H

(2)

CHO

H

H

H

H

NH2

(3)

CHO

HH

NH2

H

H(4)

CHO

HH

H

H

NH2

46. How many isomeric alkynes will produce

3-chloro-3-ethylpentane in the following sequence of

reactions?

Cat aly tic P hot oche mical

Hydrogenation Chlor inat ionAlkynes

3-chloro-3-ethylpentane

(1) 4 (2) 3

(3) 2 (4) 1

47. A conjugated alkadiene having molecular formula

C13

H22

on ozonolysis gives butanone, ethanedial and

cyclohexane carbaldehyde. Which of the following is

the correct structural formula of the alkadiene?

(1) C = CH CH = CCH CH

3 2

H CH3

(2) C = CH CH = CH CH

3 2C

H C3

H

(3) C CH = CH CH2CH

3 CH

H C3

(4) CH CH = CH CH CH

3 2C

CH3

H

48. The two equilibria,

AB(aq) A (aq) B (aq)

and2AB(aq) B (aq) AB (aq)

are simultaneously maintained in a solution with

equilibrium constants K1 and K2 respectively. Theratio of concentration of A+to AB2

in the solution is

(1) Directly proportional to the concentration of B

(2) Inversely proportional to the concentration of B

(3) Directly proportional to the square of the

concentration of B

(4) Inversely proportional to the square of the

concentration of B


11/18


12/18



10/14

(1) Statement-1 is True, Statement-2 is True;

Statement-2 is a correct explanation for

Statement-1


Statement-2 is NOT a correct explanation for

Statement-1

(3) Statement-1 is True, Statement-2 is False

(4) Statement-1 is False, Statement-2 is True

57. Statement-1 : Al2(SO

4)3 is used as a mordant in

textile industry.

and

Statement-2 : The process of formation of metallic

hydroxides on the fibres before dyeing is known as

mordanting.

(1) Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for

Statement-1



Statement-1



58. Statement-1 : If the equation for a reaction is

reversed, the equilibrium constant is inverted and if

the equation is multiplied by 2, the equilibrium

constant is squared.

and

Statement-2 : The numerical value of an equilibrium

constant depends on the reaction and reaction

coefficients.



Statement-1



Statement-1



59. Statement-1 : All strong acids in water show almost

same acidic nature.

and

Statement-2 : This is due to levelling effect of water

on account of its high dielectric constant and strong

protons accepting tendency.



Statement-1

(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT a correct explanation for

Statement-1



60. Statement-1 : The presence of excessive nutrients in

a lake due to inflow of nutrients from fertilizers is

called eutrophication.

and

Statement-2 : Eutrophication badly affects the

aquatic life.



Statement-1



Statement-1




13/18



11/14

SECTION - I

Straight Objective Type Questions

This section contains 25 multiple choice questions

numbered 61 to 85. Each question has 4 choices (1), (2),(3) and (4), out of which ONLY ONE is correct.

61. Let f: RRbe the function defined by

24 3, if 2

( )3, if 2

x x xf x

x x

Then the number of real numbers x for which

f(x) = 3 is

(1) 1 (2) 2

(3) 3 (4) 4

62. In a survey it was found that 38% people like

watching Football, 75% like watching Cricket andx%

like both. Then

(1) x= 13 (2) x= 38

(3) 13 38x (4) 13 75x

63. If 6 43 3 35

log 2 7 log 4 2log 2 2

y y

, then

the value of yis

(1) 3 (2) 2

(3) 2 (4) 4

64. If the equation z2+ (a+ ib)z+ (c+ id) = 0, where

a, b, c, dare real and bd0, has real roots, then

the value of d2 abd+ b2cis equal to

(1) 1 (2) 1

(3) 0 (4) 2

PART - C (MATHEMATICS)

65. If (x2+ x+ 2)2 (a 3)(x2+ x+ 2)(x2+ x+ 1) +

(a 4)(x2+ x+ 1)2= 0 has at least one real root,

then

(1) 0 < a< 5 (2)

195

3a

(3) 5 a< 7 (4) a7

66. In a geometric series of real numbers, the first term

is 2 and the sum of the reciprocals of its third and

fourth terms is more than its second term by 2. The

sum of all possible values for its seventh term is

(1)33

16(2)

65

32

(3)17

8(4)

1

8

67. If cos + cos = aand sin + sin = b, then

the value of cos cos equals to

(1)

2 2 2 2

2 2

( ) 4

4( )

a b a

a b(2)

2 2 2 2

2 2

( ) 4

2( )

a b b

a b

(3)

2 2 2 2

2 2 2

( ) 4

2( )

a b a

a b(4)

2 2 2 2

2 2

( ) 4

4( )

a b b

a b

68. The sum

1 1 1

sin 45 s in 46 sin 4 7 sin 48 s in 49 sin 50

1...

sin 133 sin 134

is equal to

(1) sec 1 (2) cosec 1

(3) cot 1 (4) tan 1


14/18



12/14

69. If S= 12+ 32+ 52+ ... + 992, then the value of the

sum 22+ 42+ 62+ ... + 1002 is

(1) S+ 2550 (2) 2S

(3) 4S (4) S+ 5050

70. The constant term in the quadratic expression

1

1 1

1

n

k

x xk k

as n is

(1) 1 (2) 1

(3) 0 (4)1

2

71. The equation (x 1)(x 2)(x 3) = 24 has the real

root equal to aand the complex roots band c. Then

the value ofbc

ais

(1)1

5(2)

1

5

(3)6

5(4)

6

5

72. If10

1025log

1024p

and log

102 = q, then the value of

log10

(4100) in terms of pand qis equal to

(1) p+ 9q (2) p+ 10q

(3) 12p+ q (4) p+ 12q

73. The sum of the infinite series

1 1 1 1 1...

9 18 30 45 63 is

(1)1

3(2)

1

4

(3)1

5(4)

2

3

74. The graphs of y= sin x, y= cos x, y= tan xand

y= cosec xare drawn on the same axes from 0 to

2

. A vertical line is drawn through the point where

the graphs of y = cos x and y = tan x cross,

intersecting the other two graphs at points Aand B.

The length of the line segment ABis

(1) 1 (2) 5 12

(3) 2 (4) 5 1

2

75. Let A(5, 12), B(13 cos , 13 sin ) and C(13 sin ,

13 cos ), where is real, be the vertices of a

ABC. Then, the orthocentre of ABC lies on the

line

(1) x y 7 = 0 (2) x+ y 7 = 0

(3) x y+ 7 = 0 (4) x+ y+ 7 = 0

76. The line 3x + 2y 24 = 0 meets x-axis at A and

y-axis at B. The perpendicular bisector of ABmeets

the line through (0, 1) parallel to x-axis at C. Then,

the area of the ABCis

(1) 91 sq. unit (2) 12 sq. unit

(3) 36 sq. unit (4) 48 sq. unit

77. If the line xcos + ysin = 2 is the equation of a

transverse common tangent to the circles

x2+ y2= 4 and 2 2 6 3 6 20 0x y x y , then

the value of is

(1)3

(2)

6

(3)2

3

(4)

5

6

78. Two circles with centres at A(2, 3) and B(5, 6) and

having equal radii are intersecting orthogonally. Then,

the radius of the circles is

(1) 3 2 (2) 2 2

(3) 3 (4) 2


15/18


16/18



14/14

87. Statement-1 : A chord y = mx + c of the curve

3x2 y2 2x+ 4y = 0, which passes through the

point (1, 2), subtend a right angle at the origin.

and

Statement-2 : Lines represented by the equation

(3c + 2m)x2 2(1 + 2m)xy + (4 c)y2 = 0 are

perpendicular if c+ m+ 2 = 0.



Statement-1



Statement-1



88. Statement-1 : The real roots of the equation

x4 3x3 2x2 3x+ 1 = 0 lie in the interval [0, 4].

and

Statement-2 : The real roots of the equation are

reciprocal to each other.



Statement-1



Statement-1



89. Statement-1 : If a, b, c, d R+and (a+ b + c +

d+ 3)5= 9375abcd, then a+ b+ c+ d= 12.

and

Statement-2 : If for positive real numbers AM = GM,

then numbers are equal.


Statement-2 is a correct explanation forStatement-1



Statement-1



90. Statement-1 : The minimum distance between the

parabola y2= 4xand the circle x2+ y2 54y+ 704

= 0 is 522 .

and

Statement-2 : Shortest distance between these two

curves occurs along the common normal.



Statement-1



Statement-1




17/18

Test Booklet Code

Test No. 7

JEE (Main)-2015

for

SHAK TA EA STAI

SD E

N RI IEL

L SA


18/18

Test - 7 (Answers & Hints) All India Aakash Test Series for JEE (Main)-2015

1/9

ANSWERS

1. (1)

2. (3)

3. (1)

4. (2)

5. (1)

6. (3)

7. (2)

8. (3)

9. (3)

10. (2)

11. (2)

12. (3)

13. (1)

14. (4)

15. (2)

16. (2)

17. (2)

18. (3)

19. (2)

20. (2)

21. (1)

22. (4)

23. (3)

24. (1)

25. (3)

26. (2)

27. (1)

28. (1)

29. (4)

30. (2)

PHYSICS CHEMISTRY MATHEMATICS

31. (3)

32. (3)

33. (3)

34. (3)

35. (4)

36. (2)

37. (1)

38. (3)

39. (2)

40. (2)

41. (1)

42. (3)

43. (3)

44. (3)

45. (2)

46. (1)

47. (1)

48. (3)

49. (3)

50. (4)

51. (1)

52. (1)

53. (4)

54. (4)

55. (3)

56. (2)

57. (2)

58. (2)

59. (3)

60. (4)

61. (2)

62. (4)

63. (1)

64. (3)

65. (3)

66. (4)

67. (3)

68. (2)

69. (4)

70. (4)

71. (1)

72. (3)

73. (1)

74. (4)

75. (2)

76. (3)

77. (3)

78. (4)

79. (1)

80. (3)

81. (4)

82. (2)

83. (1)

84. (3)

85. (2)

86. (4)

87. (1)

88. (4)

89. (1)

90. (3)

TEST - 7

JEE Main 2014_Test 8 (Paper I) Code A

Documents

Transcript of JEE Main 2014_Test 8 (Paper I) Code A