class: sz3 jee-main model date: 02-01-2021 time: 3hrs wtm … · 2021. 2. 1. ·...

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Class: SZ3 JEE-MAIN MODEL Date: 02-01-2021

Time: 3hrs WTM-29 Max. Marks: 300

IMPORTANT INSTRUCTIONS

PHYSICS Section Question Type

+Ve Marks

- Ve Marks

No.of Qs

Total marks

Sec – I(Q.N : 1 – 20) Questions with Single Answer Type 4 -1 20 80

Sec – II(Q.N : 21 – 25) Questions with Numerical Answer Type

(+/ - Decimal Numbers) 4 0 5 20

Total 25 100

CHEMISTRY Section Question Type

+Ve Marks

- Ve Marks

No.of Qs

Total marks




Total 25 100

MATHEMATICS Section Question Type

+Ve Marks

- Ve Marks

No.of Qs

Total marks




Total 25 100

mailto:[email protected]://www.narayanagroup.com/

SZ3_JEE-MAIN_WTM-29_QP_Exam.Dt.02-01-2021

Narayana CO Schools

2

SECTION-I (1 TO 20)

(Single Answer Type)

This section contains 20 multiple choice questions. Each question has 4 options

(1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.

01. About a collision which is not correct

1) physical contact is must

2) colliding particles can change their direction of motion

3) the effect of the external force is not considered

4) linear momentum is conserved

02. A ball of mass 'm' moving with speed 'u' undergoes a head-on elastic

collision with a ball of mass 'nm' initially at rest. Find the fraction

of the incident energy transferred to the second ball.

1) 1

n

n + 2)

( )2

1

n

n+ 3)

( )2

2

1

n

n+ 4)

( )2

4

1

n

n+

03. A block of mass m and a pan of equal mass are connected by a

string going over a smooth light pulley. Initially the system is at

rest when a particle of mass m falls on the pan and sticks to it. If

the particle strikes the pan with a speed v then the speed with

which the system moves after the collision is

1) 3

v 2) v 3)

2

v 4)

2

3

v


Narayana CO Schools

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04. A ball of mass 1 kg is attached to an inextensible string. The ball

is released from the position shown in figure. The impulse

imparted by the string to the ball immediately after the string

becomes taut is ( )210 /g m s=

1) 40 /seckg m 2) 20 /seckg m

3) 10 /seckg m 4) 0 /seckg m

05. Two particles A and B of equal mass m are attached by a string of

length 2l and initially placed over a smooth horizontal table in the

position shown in Figure. Particle B is projected across the table

with speed u perpendicular to AB as shown in the figure. Find the

velocities of each particle after the string becomes taut

1) 3 7

,4 4

u u 2)

5 7,

4 4

u u

3) 2 3

,4 4

u u 4)

7 2,

4 4

u u

06. A rubber ball drops from a height 'h'. After rebounding twice from

the ground, it rises to h/2. The co - efficient of restitution is

1) 1

2 2)

1

21

2

3)

1

41

2

4)

1

61

2


Narayana CO Schools

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07. A body of mass 5kg moving with a speed of 13ms− collides head on

with a body of mass 3kg moving in the opposite direction at a

speed of 12ms− . The first body stops after the collision. The final

velocity of the second body is

1) 13ms− 2) 15ms− 3) 19ms−− 4) 130ms−

08. A steel ball of radius 2cm is initially at rest. It is struck head on by

another steel ball of radius 4cm travelling with a velocity of

81cm/s. The common velocity if it is perfectly inelastic collision

1)144 cm/s 2) 61 cm/s 3)81 cm/s 4) 72 cm/s

09. A ball is dropped from a height ‘h’ on to a floor of coefficient of

restitution ‘e’. The total distance covered by the ball just before

second hit is

1) ( )21 2h e− 2) ( )21 2h e+ 3) ( )21h e+ 4) 2he

10. A block of wood of mass 3M is suspended by a string of length 10

.3

m

A bullet of mass M hits it with a certain velocity and gets embedded

in it. The block and the bullet swing to one side till the string makes

0120 with the initial position. The velocity of the bullet is ( )210g ms−=

1) 140

3ms− 2)

120ms− 3) 130ms− 4)

140ms−

11. Two identical bodies moving in opposite direction with same speed,

collide with each other. If the collision is perfectly elastic then

1) after the collision both comes to rest

2) after the collision first comes to rest and second moves in the

opposite direction with same speed

3) after collision they recoil with same speed

4) both 1 and 2


Narayana CO Schools

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12. A ball hits the floor and rebounds after an inelastic collision. In this

case

1) the momentum of the ball just after collision is same as that

just before the collision

2) the mechanical energy of the ball remains the same in collision

3) the total momentum of the ball and the earth is conserved

4) the total kinetic energy of the ball and the earth is conserved

13. A ball strikes a horizontal floor at an angle 045 = with the normal

to floor. The coefficient of restitution between the ball and the floor

is e = 1/2 . The fraction of its kinetic energy lost in the collision is

1) 3

8 2)

8

3 3)

4

3 4)

5

3

14. After perfectly inelastic collision between two identical particles

moving with same speed in different directions, the speed of the

combined particle becomes half the initial speed of either particle .

The angle between the velocities of the two before collision is

1) 060 2)

045 3) 030 4) 0120

15. Two billiard balls of same size (radius r) and same mass are in

contact on a billiard table. A third ball also of the same size and

mass strikes them symmetrically and remains at rest after the

impact. The coefficient of restitution between the balls is

1) 2

3 2)

3

2 3)

1

2 4) None


Narayana CO Schools

6

16. Consider the collision depicted in figure to be between two billiard

balls with equal masses 1 2.m m= The first ball is called the target.

The billiard player wants to ‘sink’ the target ball in a corner

pocket, which is at an angle 02 37 . = Assume that the collision is

elastic and that friction and rotational motion are not important,

then 1 is

1) 037 2)

090 3) 045 4)

053

17. A ball of mass m collides with the ground at an angle with the

vertical . If the collision lasts for time t, the average force exerted

by the ground on the ball is : (e=coefficient of restitution between

the ball and the ground)

1) ( )cos 1mu e

Ft

+= 2)

( )sin 1mu eF

t

+=

3) ( )cos 1mu e

Ft

−= 4) None


Narayana CO Schools

7

18. A rocket of initial mass 6000kg ejects gases at constant rate of 20

kg/s with constant relative speed of 8 km/s. What is the

acceleration of the rocket after 100s. Neglect gravity is

1) 240 /m s 2) 245 /m s

3) 255 /m s 4) 260 /m s

19. A rocket is set for a vertical firing. If the exhaust speed is 2000 m/s,

then the rate of fuel consumption to just lift off the rocket . Take

mass of rocket = 6000 kg.

1) 30 /kg s 2) 35 /kg s

3) 45 /kg s 4) 40 /kg s

20. A body X with a momentum p collides with identical stationary

body Y one dimensionally. During collision. Y gives an impulse J to

body X. coefficient of restitution is

1) 2

1J

p− 2) 1

J

p+ 3) 1

J

p− 4) 1

2

J

p−

SECTION-II (21 TO 25)

(Numerical Value Answer Type)

This section contains 5 questions. The answer to each question is a Numerical

values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -

123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases.

21. A body of mass 10 kg moving with a velocity of 15ms− hits a body of

1 gm at rest. The velocity of the second body after collision,

assuming it to be perfectly elastic is __________1.ms−


Narayana CO Schools

8

22. A marble going at a speed of 12ms− hits another marble of equal

mass at rest. If the collision is perfectly elastic. then the velocity of

the first marble after collision is ________ 1.ms−

23. An 8 gm bullet is fired horizontally into a 9 kg block of wood and

sticks in it. The block which is free to move, has a velocity of

40cm/s after impact. The initial velocity of the bullet is ______m/s

24. Two balls with masses 1 3m kg= and 2 5m kg= have identical velocity

V = 5 m/s in the direction shown in figure. They collide at origin.

Find the distance of position of C.M. from the origin 2sec after the

collision is __________m.

25. Two Particle of equal masses 4 M are initially at rest. A particle of

mass M moving at speed u collide elastically with one of the larger

balls. How many collisions occur?


Narayana CO Schools

9

SECTION-I (26 TO 45)


This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be

correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.

26. Which will show geometrical isomerism?

1) N

CH3

OH 2)

HO N

N OH

3)

N

H3C

H3C

OH

4) Both (1) and (2)

27. Number of geometrical isomers possible for the compound

3 2 5CH CH CH CH CH C H− = − = −

1) 2 2) 3 3) 4 4) 5

28. Geometrical isomerism is not shown by

1) ( ) = −3

3 2 2 32 |CH

CH CH C CH CH

2) 2 5 2| |H H

C H C C CH I− = −

3) =3 3CH CH CClCH

4) 3 2CH CH CH CH CH− = − =

29. Which of the following compounds exhibit geometrical isomerism?

A) 2 3CH CH CH= −

B) 3 3CH CH CH CH− = −

C) 3 3CH CH C CH CH− = = −

D) 3 3CH CH C C CH CH− = = = −

1) B,D 2) B,C,D 3) B,C 4) only B


Narayana CO Schools

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30. Which of the following compounds will exhibit geometrical

isomerism

1) 3CH CH CH COOH− = − 2) Br CH CH Br− = −

3) − = −2 5C H CH N OH 4) All the above

31. Which of the following will have a trans isomer

1)

C

H

C

H

H

H3C

2)

C

H

C

Cl

H

Cl

3)

C

H

C

CH3

H

H3C

4) Both (2) and (3)

32. The ‘Z’ isomer among the following is

1)

C C

COOH

H

C6H5

Cl 2)

C C

CH2OH

CHO

CH3

H

3)

C C

CH2CH3

Br

CH3

Cl 4)

C

N

CH3C6H5

OH

33. 3 3| |Br Br

CH CH C C CH CH− = − = − How many geometrical isomers of this

compound are possible?

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


Narayana CO Schools

11

34.

CH3

Br How many geometrical isomers are possible for the above

compound

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

35.

CH3

CH3

CH3 How many geometrical isomers are possible for

the above compound

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

36. Which of the following can exhibit cis-trans isomerism?

1) HC CH 2) ClCH CHCl=

3) 3CH CHClCOOH 4) 2 2ClCH CH Cl−

37. The Z-configuration in the following is

1)

C C

C2H5

C3H7

H

H3C 2)

3)

C C

Cl

Br

F

H 4)

C C

Br

F

F

F


Narayana CO Schools

12

38. Write the structure of (E, Z)–Nona–2,4–diene

1)

C4H9

2)

H9C4

3)

C4H9

4) All the above

39. The IUPAC name of the compound

CH3

CH3

1) ( )2 ,4 .6E E Z − octa–2,4,6,–triene

2) ( )2 ,4 .6E E E − octa–2,4,6,–triene

3) ( )2 ,4 .6Z E Z − octa–2,4,6,–triene

4) ( )2 ,4 .6Z Z Z − octa–2,4,6,–triene

40. IUPAC name of the following compound is

1) ( ) − 2 , 4Z E 3–methyl hexa–2,4–diene

2) ( ) 2 ,4E Z −4–methyl hexa–2,4–diene

3) ( ) 2 ,4E Z −3–methyl hexa–2,4–diene

4) All the above


Narayana CO Schools

13

41. Which of the following will not show Cis–trans isomerism

1)

3

3 2 3|CH

CH C CH CH CH− = − −

2)

3

3 2 3|CH

CH CH CH CH CH CH− − = − −

3) 3 3CH CH CH CH− = −

4) 3 2 2 3CH CH CH CH CH CH− − = − −

42. The ‘E’–isomer is .

1)

C C

H

Br

F

Cl 2)

C C

CH3

H

H3C

H

3) 4) All

43. Which one of the following will show geometrical isomerism

1) 2)

3) 4) 3 2 2 3CH CH CH CHCH CH=

44. Which of the following does not show geometrical isomerism

1) 1,2–dichloro–1–Pentene 2) 1,3–dichloro–2–Pentene

3) 1,1–dichloro–1– Pentene 4) 1,4–dichloro–2–Pentene


Narayana CO Schools

14

45. IUPAC name of the compound

C C

CH2CH3

I

Cl

CH3

1) E–2–chloro–3–iodo–2–Pentene

2) Z–2–chloro–3–iodo–2–Pentene

3) E–3–iodo–4–chloro–3–Pentene

4) Z–3–iodo–4–chloro–3–Pentene




values comprising of positive or negative decimal numbers (place value

ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -

123.45, -1234.56, -0.12, 0.12 etc.

Marking scheme: +4 for correct answer, 0 in all other cases.

46. Number of the geometrical isomers for the molecule

C C

H

C

R

H C

H

CH

C

R

HH

47. Number of possible geometrical isomers for


Narayana CO Schools

15

48. How many of the following shows geometrical isomerism

1)

2) CHCl CHBr=

3)

4)

5)

6) 3 2 5CH CH C CH C H− = = −

7) 3 2 5CH CH C CH CH CH C H− = = − = −

49.

a)

H3C

H

b)

Number of geometrical isomers in (a) and (b) are x and y. Then

?x y+ =

50. Number of geometrical isomers in 2 2CH C CH CH CH= = − =


Narayana CO Schools

16

SECTION-I (51 TO 70)


This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be

correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.

51. If the function ) ): 1, 1,f → is defined by ( ) ( )12x xf x −= then ( )1f x−

is _________

1) ( )1

1

2

x x−

2) ( )21 1 1 4log2

x+ +

3) ( )21 1 1 4log2

x− + 4) ( )21

1 1 4log2

x +

52. If ; 1,2,3,.... 0, 1, 2,....f → is defined by ( )( )

2

1

2

nif n is even

f nn

if n is add

= − −

then ( )1 100f − − is ________

1) 202 2) 200 3) 201 4) –201

53. Let ' 'f be an injective function with domain , ,x y z and range

1,2,3 such that exactly one of the following statements is correct

and the remaining are false ( ) ( ) ( )1, 1, 2f x f y f z= . The value of

( )1 1f − is ________

1) x 2) y 3) z 4) ( )x or z

54. If ( )2 sin , 1

2

, 1

xx x

f x

x x x

=

then ( )f x is ______

1) an even function 2) an odd function

3) both odd and even 4) neither odd nor even


Narayana CO Schools

17

55. ( )cos

1

2

xf x

x=

+

where x is NOT an integral multiple of and

denotes the greatest integer function is

1) an odd function 2) even function

3) neither odd nor even 4) both even and odd

56. Let : 3,3f R− → where ( )2

3 2sinx

f x x xa

+= + +

be an odd function

(where . represents greatest integer function). Then the value of a

is

1) less than 11 2) 11 3) greater than 11 4) 12

57. Let ( )( )2 sin tan

,21

2 41

x x xf x x n

x

+=

+ −

then f is ( where . represents

greatest integer function)

1) an odd function 2) an even function

3) both odd and even 4) neither odd nor even

58. The inverse of the function ( ) 2x x

x x

e ef x

e e

−

−

−= +

+ is given by

1)

21

log1

e

x

x

−−

+

2)

1

22log

1e

x

x

−

−

3)

1

2log

2e

x

x

− 4)

1

21log

3e

x

x

−

−

59. If :f R R→ is an invertible function such that ( )f x and ( )1f x− are

symmetric about the line y x= − then

1) ( )f x is odd

2) ( )f x and ( )1f x− may NOT be symmetric about the line y x=

3) ( )f x may NOT be odd

4) ( )1f x− may be odd


Narayana CO Schools

18

60. Let the function ( ) ( )23 4 8log 1f x x x x= − + + be defined on the

interval 0,1 . The even extension of ( )f x of the interval 1,1− is

1) ( )23 4 8log 1x x x− + + 2) ( )23 4 8log 1x x x− + +

3) ( )23 4 8log 1x x x+ − + 4) ( )23 4 8log 1x x x− − +

61. If ( )21

xf x

x=

+ then ( ) ________fofof x =

1) 21 3

x

x+ 2)

21

x

x− 3)

2

2

1 2

x

x+ 4)

21

x

x+

62. Let ( ) 102 . 1f x x= + and ( ) 103 1.g x x= − If ( )( )fog x x= then x is equal

to _____

1) 10

10 10

3 1

3 2−−

− 2)

10

10 10

2 1

2 3−−

− 3)

10

10 10

1 3

2 3−−

− 4)

10

10

1 2

1 6

−

−

63. If ( ) 2 2g x x x= + − and ( ) 21

2 5 22

gof x x x= − + then ( ) _______f x =

1) 2 3x− 2) 2 3x− − 3) 4x− 4) 3x+

64. If ( )2

,1

xf x

x=

− ( )

21

xg x

x=

+ then ( )( ) _________fog x =

1) x 2) 21

x

x+ 3) 21 x+ 4) 2x

65. If ( ) 1f x x= − and ( ) ( )logg x x= then the domain of

( )( ) ________gof x =

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


Narayana CO Schools

19

66. If ( ) 2 1f x x= + , ( ) 2 1g x x= + then ( )( )2go fof =

1) 112 2) 122 3) 12 4) 124

67. ( )1, if rational

0, if is irrational

xf x

x

=

, then ( )

( )( )

15

2

3

f f

fof

+

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

2

68. If : , :f R R g R R⎯⎯→ ⎯⎯→ are defined by ( ) 2 3f x x= + and

( ) 2 7g x x= + then the values of x such that ( )( ) 8g f x = are

1) 1, 2 2) –1, 2 3) –1, –2 4) 1, –2

69. If ( ) ( ) ,f x x g x x x= = − , then which of the following functions is

the zero function. [.] denotes G.I.F.

1) ( )( )f g x+ 2) ( )2 f x 3) ( )3 f x 4) ( )( )fog x

70. If : , :f R R g R R⎯⎯→ ⎯⎯→ are defined by ( ) ( ) 23 2, 1f x x g x x= − = + ,

then ( )( )1 2gof − =

1) 25

9 2)

111

25 3)

9

25 4)

25

111




values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -

123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases.

71. Let ( ) 21

1,2

f x x x x= − + then the solution of the equation

( ) ( )1f x f x− = is then 1+ =_____________


Narayana CO Schools

20

72. If the real valued function ( )( )

1

1

x

n x

af x

x a

−=

+ is even then

__________n =

73. If f is an even function defined on the internal ( )5,5− then the total

number of real values of x satisfying the equation ( )1

2

xf x f

x

+ =

+

are _______

74. If :f R R→ and :g R R→ are defined by ( ) ( )3 4, 2 3f x x g x x= − = +

then ( )( ) 1 13 5 __________g of− − =

75. If ( ) 1f x x= + and ( ) 2 1g x x= + then ( )( )1 _________gof =

class: sz3 jee-main model date: 02-01-2021 time: 3hrs wtm … · 2021. 2. 1. ·...

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