jee main part test 1

7/28/2019 jee main part test 1

1/13

Time: 3 Hrs 1

Space For Rough Work

1. If the acceleration due to gravity is 210 ms and the

units of length and time are changed in kilometer and

hour respectively, the numerical value of the

acceleration is

(a) 360000 (b) 72,000

(c) 36,000 (d) 129600

2. The pair(s) of physical quantities that do not have the

same dimensions, is

(a) Reynolds number and coefficient of friction

(b) Latent heat and gravitational potential

(c) Curie and frequency of a light wave

(d) Planck's constant and torque

3. A particle moving in a straight line covers half thedistance with speed of 3 m/s. The other half of the

distance is covered in two equal time intervals with

speed of 4.5 m/s and 7.5 m/s respectively. The average

speed of the particle during this motion is

(a) 4.0 m/s (b) 5.0 m/s

(c) 5.5 m/s (d) 4.8 m/s

4. The acceleration of a particle is increasing linearly with

time as bt . The particle starts from the origin with an

initial velocity 0v The distance travelled by the particle

in time t will be

(a) 203

1bttv (b) 30

3

1bttv

(c) 306

1bttv (d) 20

2

1bttv

5. A particle is dropped vertically from rest from a heig

The time taken by it to fall through successive distanc

of 1 meach will then be

(a) All equal, being equal to g/2 second

(b) In the ratio of the square roots of the integers 1, 2

(c) In the ratio of the difference in the square roots of

the integers i.e. )34(),23(),12(,1 ..

(d) In the ratio of the reciprocal of the square roots of

the integers i.e.,.4

1,

3

1,

2

1,

1

1

6. A car starts from rest under constant acceleration then

moves with constant velocity and finally decelerates a

constant rate and comes to rest. If ratio of time for eapart of the journey is 1 : 6 : 2 and max. Speed attaine

is 54 kph then find the average velocity for complete

journey.

(a) 40 kph (b) 45 kph

(c) 50 kph (d) 54 kph

7. The acceleration of a particle moving rectilinearly vari

with the magnitude of its velocity as a v . What the initial speed if it comes to rest after 1 sec from

starting.

(a) 0.25 m/s (b) 0.5 m/s

(c) 0.75 m/s (d) 1 m/s

TEST -I[PHYSICS


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Time: 3 Hrs 2


8. Acceleration (a) displacement (s) graph of a particlemoving in a straight line is as shown in figure.

a

s

The initial velocity of the particle is zero. The v-sgraph of the particle would be

v

s

(A)

v

s

)

v

s

(C)

s

(D)

9. A projectile is given an initial velocity of 2 ji . TheCartesian equation of its path is

(g = 10 m/sec2)

(a)2

y 2 5 x x (b) 2y 5 x x

(c)2

4y 2 5 x x (d) 2y 2 25 x x

10. The speed of a projectile when it is at its greatest heig

is 2/5 times its speed at half the maximum heightthe angle of projection is

(a) 30 (b) 60

(c) 45 (d)1 3tan

4

11. A boat man can row with speed of 10 km/h in still

water. If the river flows at 5 km/h, the direction in wh

the boat man should row to reach a point on the othe

bank directly opposite to the point from where he

started is (width of the river is 2 km)

(a) in a direction inclined at 90 to the direction of riv

flow

(b) in a direction inclined at 60 to the direction of riv

flow

(c) in a direction inclined at 120 to the direction of

river flow

(d) Should row directly along the river flow

12. Air is blowing and is providing a constant horizon

acceleration ax = g to the particle as shown in t

figure. Particle is projected from point P with a velocu in upward direction. Let Q be the highest point

particle. Speed of the particle at highest point Q is


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Time: 3 Hrs 3


u

Q

a =gx

P

(a) 2 u (b) u

(c) u / 2 (d) None of these

13. The linear momentum P of a particle varies with time

as P = + t2, where and are constants. The netforce acting on the particle is

(a) zero (b) constant

(c) proportional to t (d) proportional to t2

14. The condition under which the vectors

and

a b a b are parallel is

(a) ||

a b (b)

a b

(c)

a b (d)

a b .

15. A string of length L is fixed at one end and carries a

mass M at the other end. The string makes 2/revolutions per second around the vertical axis throughthe fixed end as shown in the figure, then tension in thestring is

(a) ML

(b) 2 ML

(c) 4 ML

(d) 16 ML

16. A car is moving with a uniform speed on a level roaInside the car there is a balloon filled with helium aattached to a piece of string tied to the floor. The striis observed to be vertical. The car now takes a left tumaintaining the speed on the level road. The balloonthe car will

(a) Continue to remain vertical

(b) Burst while taking the curve

(c) Be thrown to the right side

(d) Be thrown to the left side

17. A body is revolving with a uniform speed v in a cirof radius r . The tangential acceleration is

(a)r

v(b)

r

v2

(c) Zero (d)2r

v

18. Which of the following numbers has maximum numb

of significant figure?

(a) 1001 (b) 100.1

(c) 100.10 (d) 0.001001

19. A particle has to move in vertical plane from

A to B either by path (i) or (ii) as shown in

figure. If the time taken by the particle in thetwo cases are t1 and t2, then

H

B

A

(i)

H

B

A

(ii)

S

T

M

L

R


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Time: 3 Hrs 4


(a) t1 < t2

(b) t1 > t2

(c) t1 = t2

(d) conclusion depends on the shape of curves

20. A 2m wide truck is moving with a speed of 55 m/salong a straight horizontal road. A man starts crossingthe road with a uniform speed vwhen the truck is 4 maway from him. The minimum value ofv to cross thetruck safely is

(a) 10 m/s (b) 5 m/s

(c) 3 m/s (d)2

55m/s

21. A ball is thrown from the ground to clear a wall 3 m

high at a distance of 6 m and falls 18 m away from thewall, the angle of projection of ball is

(a)

2

3tan 1 (b)

3

2tan 1

(c)

2

1tan 1 (d)

4

3tan 1

22. For the arrangement shown in figure, the masses of the

blocks are mA = 2 kg, mB = 1 kg, mC = 1 kg. The

frictional force between the blocks A and B and thetension in string connecting A and B are respectively

(coefficient of friction between any two surfaces is 0.5)

A

B

C

(a) 0, 5 N (b) 0, 0

(c) 10 N, 5 N (d) 5 N, 0

23.A block of mass 2 kg is hanging with two idenmassless springs as shown in figure. The acceleratiothe block at the moment, the right spring break

(g= 10 m/s2

)

2kg

30 30

(a) 10 m/s2 (b) 5 m/s2

(c) 25 m/s2 (d) 4 m/s2

24.Two blocks M1 and M2 rest upon each other on

an inclined plane. Coefficient of friction between

surfaces are shown. If the angle is slowlyincreased, then (M1 < M2)


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Time: 3 Hrs 5


A

B

M1M2

1=0.5

2=0.2

(a) block A slips first

(b) block B slips first

(c) both slip simultaneously

(d) both remain at rest

25. Two blocks of masses 2m and m are connected as

shown in the figure. Now the string between the blocks

is suddenly broken. The acceleration of the blocks A and

B respectively at that instant are

m

2m A

B

(a) g and g

(b) g and2

g

(c)2

gand g

(d) 2

g

and 2

g

26. Any vector in an arbitrary direction can alwaysbe replaced by two (or three)

(a) Parallel vectors which have the originalvector as their resultant

(b) Mutually perpendicular vectors which havethe original vector as their resultant

(c) Arbitrary vectors which have the originalvector as their resultant

(d) It is not possible to resolve a vector

27. Let BAC then

(a) ||C is always greater then || A

(b) It is possible to have |||| AC and |||| BC

(c) C is always equal to A + B(d) C is never equal to A + B

28. The resultant of BA is .1R On reversing the vec

,B the resultant becomes .2R What is the value 22

21 RR

(a) 22 BA (b) 22 BA

(c) )(2 22 BA (d) )(2 22 BA

29. A physical quantity P is given by P=2

34

2

13

DC

BA

. T

quantity which brings in the maximum percentage erin P is(a) A (b) B(c) C (d) D

30. A physical quantity is given by cba TLMX . Tpercentage error in measurement of LM, and T a

, and respectively. Then maximum percentaerror in the quantity X is(a) cba (b) cba

(c)

cba (d) None of these


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Time: 3 Hrs 6


31. The orbital diagram in which the Aufbau principle is

violated is

32. The exact path of electron 2P orbital cannot be

determined. The above statement in based upon

(a) Hunds rule (b) Bohrs rule

(c) Uncertainty principle (d) Aufbau principle.

33. The ratio of the radii of first orbits of H, He+ and Li2+ is

(a) 1: 2: 3 (b) 6: 3: 2

(c) 1: 4: 9 (d) 9: 4: 1.

34. The ionization energy of hydrogen atom is 13.6 eV. The

third ionization energy of lithium would be

(a) 13.6 eV (b) 27.2 eV

(c) 40.8 eV (d) 122.4 eV.

35.The wavelength of a moving body of mass 0.1 mg is 3.31 1029 m. The kinetic energy of the bodywould

(a) 2 106J (b) 1 103J(c) 4 103J (d) 2 103J.

36. The molecular species having highest bond order is

(a) O2 (b) N2

(c) N2 (d) O2

37. The correct order of bond angles (smallest first) in H

NH3, BF3 and SiH4 is

(a) H2S < NH3 < BF3 < S1H4

(b) NH3 < H2S < SiH4 < BF3(c) H2S < NH3 < SiH4 < BF3(d) H2S < S1H4 < NH3 < BF3.

38. The state of hybridisation of boron and oxygen atoms

boric acid molecule (H3BO3) are respectively

(a) sp3, sp3 (b) sp2 , sp3

(c) sp3 , sp2 (d) sp2 , sp2

39. Which of the following pairs of species have the sam

bond order

(a) CN and NO+ (b) CN and CN+

(c) 2O

and CN

(d) NO+

and CN+

.40. Which of the following overlap of orbitals is/are

Incorrect

(a) I, III (b) II, III

(c) III, IV (d) I, IV.

41. The order of OO bond length in O2,H2O,O3 is(a) O2 > O3 > H2O2 (b) O3 > H2O2 > O2

[CHEMISTRY]


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Time: 3 Hrs 7


(c) H2O2 > O3 > O2 (d) O2 > H2O2 > O3.

42. The molecular orbital shown in the diagram is

(a) * (b) (c) 2Pz (d) *2Pz..

43. The polarisability of halide ion increases in order:

(a) F < I < Br < Cl (b) F < Cl < Br < I

(c) I < Br < Cl < F (d) Br < Cl < F < I.

44. Choose the isoelectronic structures from the following

I. CH3+; II. H3O

+; III. NH3 ; IV. CH3

(a) I and II (b) III and IV

(c) I and III (d) II, III, IV.

45. BCl3 molecule is planer while NCl3 is pyramidal

because

(a) BCl3 does not have Ione pair on B but NCl3 has

(b) B-Cl bond is more polar than NCl bond(c) N atom is smaller than B

(d) NCl bond is more covalent than BCl bond.46. The correct increasing order of CO bond lengths

among Co, CO32 and CO2 is

(a) CO32 < CO2 < CO (b) CO2 < CO3

2 < CO

(c) CO < CO32 < CO2 (d) CO < CO2 < CO3

2.

47. How many OH bonds are present in H3PO4(a) one (b) two

(c) zero (d) three.

48. In 3I

ion the number of Ione pairs and bond pairs

respectively are:

(a) 8, 2 (b) 2, 3

(c) 3, 2 (d) 9, 2.

49.Among the three species shown below, the correct ord

of dipole moments is

(a) I = II = III (b) I > II > III

(c) II < I < III (d) I > III > II.

50. The equivalent weight of phosphoric acid H3PO4 in t

reaction, NaOH + H3PO4 NaH2PO4 + H2O is:(a) 59 (b) 49

(c) 25 (d) 98.

51. Find the value of wave number V in terms of

Rydbergs constant, when transition of electron tak

place between two levels of He+ ion whose sum is 4 a

different is 2:

(a)8

9

R(b)

32

9

R

(c)3

4

R(d) None of these.

52. The correct quantum numbers of 3p-electrons are:

(a) n = 3, l = 2, m= + 2, s= + 1/2

(b) n = 3, l = 1, m= 1, s= 1/2(c) n = 3, l = 2, m= 2, s= + 1/2(d) None of these.

53.In any subshell, the maximum number of electro

having same values of spin quantum number is:

(a) ( 1)l l (b) 2l


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Time: 3 Hrs 8


(c) 2 1l (d) 4 1l .54. The number of radial nodes of 3s and 2p-orbitals are

respectively:

(a) 2,0 (b) 0,2

(c) 1,2 (d) 2,1 .

55. How many d-electrons in Cu+ (At. No.=29) can have the

spin quantum number (1/2)(a) 3 (b) 7

(c) 5 (d) 9.

56. The measurement of the electron position is associated

with an uncertainty in momentum, which is equal to 1 1018 g cm s1. The uncertainty in electron velocity is :

(mass of an electron is 9 1028g)(a) 1 105 cm s1 (b) 1 1011 cm s1

(c) 1 109 cm s1 (d) 1 106 cm s1.

57. The ionization enthalpy of hydrogen atom is 1.312 106

J mol1. The energy required to excite the electron in the

atom from n = 1 ot n = 2 is :.

(a) 9.84 105J mol1 (b) 8.51 105J mol1

(c) 6.56 105J mol1 (d) 7.56 105J mol1.58. The set representing the correct order of first ionization

potential is

(a) K > Na > Li (b) Be > Mg > Ca

(c) B > C > N (d) Ge > Si > C.

59. Element with atomic number 56 belongs to which

block?(a) s (b) p

(c) d (d) f.

60. Which one of the following arrangements represents the

correct order of electron gain enthalpy

(with negative sign) of the given atomic species

(a) F < Cl < O < S (b) S < O < Cl < F

(c) O < S < F < Cl (d) Cl < F < S < O.

61. If 1 2 3 3sin sin sin , then

1 2 3cos cos cos is equal to

(a) 3 (b) 2

(c) 1 (d) 0 .

62. The minimum value of2 29 4tan cot is

(a) 13 (b) 9

(c) 6 (d) 12 .

63. If x lie in IInd quadrant, then1 1

1 1

sinx sinx

sinx sinx

equal to

(a)2

xsin (b)

2

xtan

(c)2

xsec (d)

2

xcosec .

64. The value of tan 20 tan 40 tan 60 tan 80 is equal to(a) 1 (b) 2

(c) 3 (d)3

2.

65. If 23 24

,then cosec cot is equal to

(a) 1 cot (b) 1 cot(c) 1 cot (d) 1 cot .

66. Cos 2 + 2cos is always

[MATHEMATICS]


9/13

Time: 3 Hrs 9


(a) greater then3

2

(b) less than or to3

2

(c) greater than or equal to 32 and less than or

equal to 3

(d) None of these.

67.4 4 4 43 5 7

8 8 8 8sin sin sin sin

is equal to

(a) 1 (b) 3 2/

(c) 2 (d) 1 4/ .

68. If 2tan( / ) and 2tan( / ) are the roots of the

equation28 26 15 0x x then cos( ) is

equal to

(a)627

725 (b)

627

725

(c) 1 (d) None of these.

69. If2 2

3 2 1sin sin and

3 2 2 2sin sin , 02

and 0

2,

then the value of + 2 is

(a) 4

(b) 2

(c) (d) None of these.

70. The set of values of x in ( , ) which satisfied

4 1 5sinx is

(a)10 10

,

(b)

10

(c)3

10 10,

(d) None of these.

71. The number of ordered pairs (x,y) satisfying

2y sinx and 25 2 3y x x is:

(a) 0 (b) 1

(c) 2 (d).

72. The smallest positive root of the equation

tan 0x x is in

(a) 02

,

(b)3

2,

(c)

2

,

(d)3

2

2

,

73. The number of ordered pairs (x,y) whe

0 10x,y [ , ] satisfying

22 1 2 12

sec ysin x sinx .

is

(a) 0 (b) 16

(c) infinite (d) 12

74. The number of solutions of the equation3 2 4 2 0x x x sinx in 0 2x is

(a) zero (b) one(c) two (d) four.

75. The number of solution of10

xsinx is

(a) 4 (b) 6

(c) 8 (d) None of these.


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Time: 3 Hrs 10


76. If, , are the roots of the equation

3 7 7 0x x , then 4 4 41 1 1

is:

(a)7

3

(b)3

7

(c)4

7(d)

7

4.

77. If2p( x ) ax bx c and 2Q( x) ax dx c,

where 0ac , then 0P( x)Q( x) has at least(a) four real roots (b) two real roots

(c) four imaginary roots (d) None of these.

78. If the roots of the given equation21 0(cos p )x (cos p)x sinp are real, then

(a) 0p ( , ) (b)2 2

p ,

(c) 0p ( , ) (d) 0 2p ( , ) .

79. The roots of the equation2

2 1 3 2 1 2 0x x

are

(a)1 1

02 2

, ,

(b)1 3

02 2

, ,

(c)3 1

0 12 2

, , ,

(d)1 3

0 12 2

, ,

80. If a b c d then the roots of the

equation 2 0( x a)( x c ) ( x b)( x d ) are(a) real and distinct (b) real and equal

(c) imaginary (d) None of these.

81.2 2 2

3 2 5 6 2( a a )x ( a a )x a r for

three distinct values of x for some r R, if a + r isequal to

(a) 1 (b) 2

(c) 3 (d) does not exist.

82. If and (


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Time: 3 Hrs 11


(a) (-2, -1)(-1,0) (0,1) (2,)(b) (-2, 0) (0,1) (2,)(c) (-2, -1)(-1,0) (0,)(d) None of these.

88. Solution of the inequality 1 2 21 2/log ( x) log ( x)

(a)

1 5

1 2,

(b)1 5 1 5

1 22 2

, ,

(c) 1 2,(d) None of these.

89.Value of the expression

65

2525

31

3 296781 3 7 125

409

loglogloglog

(a) 2 (b) 2(c) 1 (d) 25 7log

90. In an equilateral triangle, 3 coins of radius 1 unit each akept so that they touch each other and also the sidesthe triangle. Area of the triangle is

(a) 4 2 3 (b) 6 4 3

(c)7 3

124

(d)7 3

34

.


12/13

Time: 3 Hrs 12


JEE- Main (2013)

PART TEST-1

EX. DATE-21-10-2012 (XII-P)Answer Key

Physics Chemistry Mathematics

Q. No. Ans. Q. No. Ans. Q. No. Ans.

1 D 31 B 61 D

2 D 32 C 62 D

3 A 33 B 63 B

4 C 34 D 64 C

5 C 35 D 65 C

6 B 36 C 66 C

7 A 37 C 67 B

8 C 38 B 68 A

9 A 39 A 69 B

10 B 40 B 70 C

11 C 41 C 71 A

12 B 42 D 72 B

13 C 43 B 73 B

14 A 44 D 74 B

15 D 45 A 75 B

16 D 46 D 76 B


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Time: 3 Hrs 13


17 C 47 D 77 B

18 C 48 D 78 C

19 B 49 D 79 D

20 B 50 D 80 A

21 B 51 B 81 B

22 B 52 B 82 B

23 A 53 C 83 C

24 A 54 A 84 C

25 C 55 C 85 D

26 C 56 C 86 B

27 B 57 A 87 A

28 C 58 A 88 B

29 C 59 A 89 C

30 A 60 C 90 B

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