mdpcos, narayana, madhapur - class: sz3 jee-main model … · 2020. 12. 27. ·...

Corporate Office: 10th Floor, Melange Tower; No.80-84, Pathrika Nagar; Hitech-City, Madhapur, Hyderabad. Telangana - 500 081.

: 040-45009999(360/341) : [email protected] : http://www.narayanagroup.com

Class: SZ3 JEE-MAIN MODEL Date: 26-12-2020

Time: 3hrs WTM-28 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]

http://www.narayanagroup.com/

SZ3_JEE-MAIN_WTM-28_QP_Exam.Dt.26-12-2020

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. In an elastic collision

1) the initial kinetic energy is equal to the final kinetic energy

2) the final kinetic energy is less than the initial kinetic energy

3) the kinetic energy remains constant and continuous

4) the kinetic energy first increases then decreases.

02. Two blocks of masses 10 kg and 30 kg are placed along a vertical

line. The first block is raised through a height of 7cm. By what

distance should the second mass be moved to raise the centre of

mass by 1 cm ?

1) 1 cm downward 2) 1 cm upward

3) 2 cm downward 4) 2 cm upward

03. A ball of mass 0.50kg moving at a speed of 5.0 m/s collides with

another ball of mass 1.0 kg. After the collision the balls stick

together and remain motionless. What was the velocity of the 1.0kg

block before the collision ?

1) 2.5 m/s opposite to the direction of motion of the first ball

2) 2 m/s opposite to the direction of motion of the first ball

3) 4 m/s opposite to the direction of motion of the first ball

4) 1.5 m/s opposite to the direction of motion of the first ball

04. A 60 kg man skating with a speed of 10 m/s collides with a 40 kg

skater at rest and they cling to each other. Find the loss of kinetic

energy during the collision.

1) 1400J 2) 1200J 3) 1300J 4) 1100J


Narayana CO Schools

3

05. A ball of mass m moving at a speed v makes a head-on collision

with an identical ball at rest. The kinetic energy of the balls after

the collision is three fourths of the original. Find the coefficient of

restitution.

1) 1

2 2)

1

2 3)

1

4 4)

1

3

06. A bullet of mass 'm’ moving at a speed 'v' hits a ball of mass 'M' kept

at rest. A small part having mass 1m breaks from the ball and

sticks to the bullet. The remaining ball is found to move at a speed

2v in the direction of the bullet. Find the velocity of the bullet after

the collision.

1) ( )1

1

mv m m

m m

−

+ 2)

( )1 2

1

mv M m v

m m

− −

+ 3)

( )1 2

2

mv m m v

m m

−

+ 4) None

07. Two bodies of masses 1m and 2m are moving with velocities 11ms−

and 13ms− respectively in opposite directions. If the bodies undergo

one dimensional elastic collision, the body of mass 1m comes to rest.

Find the ratio of 1m and 2m .

1) 7:1 2) 1:7 3) 4:1 4) 5:1

08. Ball 1 collides with an another identical ball 2 at rest as shown in

the figure. For what value of coefficient of restitution e, the velocity

of second ball becomes two times that of first ball after collision?

1) 1

2 2)

1

4 3)

1

3 4)

1

6

09. A pendulum consists of a wooden bob of mass 'm 'and of length l.

A bullet of mass 1m is fired towards the pendulum with a speed 1v

and it emerges out of the bob with a speed 1 .3

v Find the initial speed

of the bullet if the bob just completes the vertical circle.

1) 1

3 5

2

glm

m 2) 1

3 5

2

glm

m 3)

3 5

2

gl 4) None


Narayana CO Schools

4

10. A perfectly elastic ball 1P of mass ‘m’ moving with velocity v collides

elastically with three exactly similar balls 2 3 4, ,P P P lying on a smooth

table. Velocity of the four balls after collision are

1) 0, 0, 0, 0 2) v, v, v, v 3) v, v, v, 0 4) 0, 0, 0, v

11. Consider a two particle system with the particles having masses 1m

and 2m . If the first particle is pushed towards the centre of mass

through a distance d, by what distance should the second particle

be moved, so as to keep the centre of mass at the same position?

1) d 2) 2

1

m d

m 3) 1

1 2

m d

m m+ 4) 1

2

m d

m

12. A 6 kg mass travelling at 12.5ms− collides head on with a stationary

4 kg mass. After the collision the 6 kg mass travels in its original

direction with a speed of 11 .ms− The final velocity of 4 kg mass is

1) 11ms− 2) 12.25ms− 3) 12ms− 4) 10ms−

13. A body of mass m moving at a constant velocity v hits another body

of the same mass moving with a velocity v/2 but in the opposite

direction and sticks to it. The common velocity after collision is

1) v 2) v/4 3) 2v 4) v/2

14. A nonzero external force acts on a system of particles. The velocity

and the acceleration of the centre of mass are found to be 0v and 0a

at an instant t. its possible that

1) 0 00, 0v a= = 2) 0 00, 0v a=

3) 0 00, 0v a = 4) all of these

15. Two particles of equal masses have velocities 1 4v i= and 2 4 .v j= .

First particle has an acceleration ( ) 2

1 5 5a i j ms−= + while the

acceleration of the other particle is zero. The centre of mass of the

two particles moves in a path of

1) Straight line 2) Parabola

3) Circle 4) Ellipse


Narayana CO Schools

5

16. A bomb of mass 4m explodes into two parts of mass ratio 1:3.If the

K.E of smaller fragment is K. Find the K.E. of the larger fragment

1) 4

k 2)

3

k 3) k 4) None

17. A body of mass is dropped and another body of mass M is projected

vertically up with speed 'u' simultaneously from the top of a

tower of height H . If the body reaches the highest point before the

dropped body reaches the ground, then maximum height raised by

the centre of mass of the system from ground is

1) 2

2

uH

g+ 2)

2

2

u

g

3)

21

2

MuH

g m M

+

+ 4)

21

2

muH

g m M

+

+

18. A pulley fixed to the ceiling carries a string with blocks of mass m

and 3m attached to its ends. The masses of string and pulley are

negligible. When the system is released, its center of mass moves

with what acceleration

1) 0 2) / 4g 3) / 2g 4) / 2g−

19. Two bodies pf masses 2kg and 4kg have their velocity 5 2 10i j k− +

and 10 2 3i j k+ + respectively then, the velocity of their centre of

mass is

1) 25 2 16

2

i j k+ + 2)

25 2 16

2

i j k− +

3) 25 2 16

2

i j k− − 4) None

20. Two balls are thrown at same time in air, while they are in air,

acceleration of their centre of mass

1) depends on masses of the balls

2) depends on the direction of motion of the balls

3) depends on speeds of the balls

4) is equal to acceleration due to gravity


Narayana CO Schools

6

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. The coefficient of restitution (e ) for a perfectly elastic collision is

22. A bullet of mass 50g is fired with a speed of 200 m/s from a gun of

mass 2kg. The magnitude of recoil velocity of the gun is

_________m/s.

23. Two bodies of masses 1m and 2m are moving with velocity 1v and 2v

respectively in the same direction. The total momentum of the

system in the frame of reference attached to the centre of mass is

(v is relative velocity between the masses)

24. Two particles A and B initially at rest, move towards each other,

under mutual force of attraction. At an instance when the speed of

A is v and speed of B is 2v,the speed of centre of mass of the system

is

25. An object A is dropped from the top of 30m high building and at the

same moment another object B is projected vertically upwards with

an initial speed of 15 m/s from the base of the building. Mass of

the object A is 2kg while mass of the object B is 4kg. Find the

maximum height above the ground level attained by the centre of

mass of A and B system is_________m. (take 210 /g m s= )


Narayana CO Schools

7

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. How many positional isomers of n-decene will show geometrical

isomerism?

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

27. Which of the following compounds will show geometrical

isomerism?

1) 2-butene 2) propene

3) 2-methyl-2-butene 4) both (1) and (3)

28. Regarding geometrical isomers which is correct?

1) cis and trans isomers differ in solubilities

2) cis and trans isomers differ in dipole moment

3) cis and trans isomers exhibit similar but not identical chemical

properties

4) all the above

29. Which of the following has zero dipole moment?

1) cis-2-butene 2) trnas-2-butene

3) 1-butene 4) 2-methyl-1-propene

30. Which of the following statement(s) is/are true regarding the cis

and trans isomers of an alkene

1) they are configurational isomers

2) the cis-isomer has higher dipole moment than the trans-isomer

3) 2-butene exhibits geometrical isomerism

4) all the above


Narayana CO Schools

8

31. Which compound can show geometrical isomerism?

1) ( )3 3 2CH CH C CH= 2) 3 2CH CH CH=

3) 3 3CH CH CHCH= 4) ( ) ( )3 32 2CH C C CH=

32.

1) Trans 2) Z

3) Not is an isomer 4) E

33. is

1) E-isomer 2) Z-isomer

3) cis-isomer 4) trans-isomer

34. E-isomer is

1) 2)

3) 4)

35. Which of the following pairs of compounds are does show

geometrical isomers?

1) maleic acid and malonic acid

2) ethylene dichloride and ethylidene dichloride

3) maleic acid and fumaric acid

4) all the above

36. The index of hydrogen deficiency of cyclohexane is

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


Narayana CO Schools

9

37. The number of isomeric amines possible for the formula 3 9C H N

1) 4 2) 3 3) 5 4) 6

38. neopentane and isopentane are

1) functional isomers 2) chain isomers

3) geometrical isomers 4) position isomers

39. Among the following the pair that is not a pair of metamers

1) 3 2 2 3 3 2 2 3 and CH OCH CH CH CH CH OCH CH

2) ( )3 2 2 3 3 3 2 and CH OCH CH CH CH OCH CH

3) 3 2 2 3 3 2 3 and CH NHCH CH CH CH NHCH CH

4) 3 2 2 3 3 2 2 3 and CH COCH CH CH CH CH COCH CH

40. Which of the following is an example of ring-chain isomerism

1) propene and cyclopropane

2) propyne and cyclopropane

3) but-1-ene and cyclopropane

4) all the above

41. Which of the following is the correct relationship?

1) I and II are functional isomers 2) II and IV are metamers

3) I and III are chain isomers 4) All the above


Narayana CO Schools

10

42. are

1) position isomers 2) chain isomers

3) functional isomers 4) all

43. Which isomer of 6 14C H has two isopropyl groups

1) 2-methyl pentane 2) 3-methyl pentane

3) 2,3-dimethyl butane 4) 2,2-dimethyl butane

44. The compound which is not isomeric with diethyl ether is

1) n-propylmethyl ether 2) butan-1-ol

3) 2-methyl propan-2-ol 4) butanone

45. Geometrical isomers differ in

1) position substituents

2) position of double bond

3) C –– C

4) spatial arrangement of groups around double bond




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.


Narayana CO Schools

11

46. In the following alkenes how many alkenes can show geometrical

isomerism

47. How many structural isomers (aldehyde + ketone) are possible for

5 10C H O

48. How many of the following are correct properties of

(i) cis trans

(ii) less polar (cis) < more polar (trans)

(iii) melting point (cis) < melting point (trans)

(iv) boiling point (cis) < boiling point (trans)


Narayana CO Schools

12

49. How many of the following does not exhibit a pair of metamers?

50. How many isomers are possible with the formula 2C ClBrFI ?


Narayana CO Schools

13

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 ( ) ( )1

n nf x a x= − then ( ) _________fof x =

1) x 2) a x− 3) nx 4) 1

nx−

52. If ( )f x and ( )g x are two functions with ( )1

g x xx

= − and

( )( ) 3

3

1fog x x

x= − then ( ) ___________f x =

1) 3 3x x+ 2) 2

2

1x

x− 3)

2

11

x+ 4) 2

4

33x

x+

53. Let ( )f x ax b= + and ( ) , 0, 0g x cx d a c= + assume 1, 2.a b= = If

( )( ) ( )( )fog x gof x= for all x what can you say about c and d

1) c and d both arbitrary 2) 1,c d= arbitrary

3) c arbitrary , 1d = 4) 1, 1c d= =

54. If ( ) 2 2sin sin cos cos3 3

f x x x x x

= + + + +

and 5

14

g

=

then

( )( ) _________gof x =

1) 1 2) 0 3) sin x 4) cos x−


Narayana CO Schools

14

55. If ( ), 1

2 , 1

x xf x

x x

=

− then ( )( ) ________f f x =

1)

2 , 1

, 1 1

2 , 1

x x

x x

x x

− −

−

−

2)

, 1

2 , 1 1

2 , 1

x x

x x

x x

−

− −

−

3)

2 , 1

, 1 1

2 , 1

x x

x x

x x

− −

−

−

4) can not say

56. If ( ) 2sinf x x= and the composite functions ( ) sing f x x= then the

function ( ) _________g x =

1) 1x − 2) x 3) 1x + 4) x−

57. Let :g R R→ be given by ( ) 3 4g x x= + . If ( ) ( )....ng x gogo og x= and

( )ng x A Bx= + then A,B are

1) 1 12 ,2n n+ + 2) 4 1,4n n− 3) 3 ,3 1n n + 4) 5 1,5n n+

58. For 0,1 ,x R − If ( )0

1

1f x

x=

− and ( ) ( )( )1 0 , 0,1,2,....n nf x f f x n+ = = then

the value of ( )100 1 2

2 33 ___________

3 2f f f

+ + =

1) 4

3 2)

1

3 3)

5

3 4)

8

3

59. If : 6,6f R− → is defined by ( ) 2 3f x x= − x R then

( )( ) ( )( ) ( )( )1 0 1fofof fofof fofof− + + =_________

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

60. Let ( ) 1g x x x= + − and ( )

1, 0

0, 0

1, 0

x

f x x x

x

−

= =

then

( )( ) __________f g x =

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


Narayana CO Schools

15

61. The function ( )2

2

6 8,

6 8

ax xf x x R

a x x

+ −=

+ − is onto for a in the interval:

1) ( )2,14 2) ( ) ( ), 2 14,−

3) 2,14 4) none of these

62. If ) ): 0, 0,f → and ( )1

xf x

x=

+ then f is :

1) many-one, into 2) one-one, into

3) many-one, onto 4) one-one, onto

63. A function f from the set of natural numbers to integers defined

by ( )

1,

2

,2

nwhen n is odd

f nn

when n is even

−

= −

is

1) onto but not one-one 2) one-one and onto both

3) neither one-one nor onto 4) one-one but not onto

64. Let S be the set of all triangles and R+ be the set of positive real

numbers. Then the function ( ): , ,f S R f area of+→ = where

S is

1) surjective but not injective

2) injective but not surjective

3) injective as well as surjective

4) neither injective nor surjective

65. If 2 2

:5 5

A x x− −

=

, : 1 1B y y= − and ( ) ( )cos 5 2f x x= + then

the mapping :f A B→ is

1) one-one but not onto 2) onto but not one-one

3) both one-one and onto 4) neither one-one nor onto

66. Let ' 'g be a function defined by ( ) 1g x x x= + − where .

denotes the fractional part function then y is ____________

1) one-one function 2) many -one function

3) onto function 4) all of these


Narayana CO Schools

16

67. Let ( ) 2

1 3f x x x= + + − where x x then and :f R R→

1) many one 2) one one

3) onto 4) all of these

68. Which of the following functions from Z to it self are bijections?

1) ( ) 3f x x= 2) ( ) 2f x x= +

3) ( ) 2 1f x x= + 4) ( ) 2f x x x= +

69. If ( )3,81A = and :f A B→ is a surjection defined by ( ) 3logxf x =

then B = ____________

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

70. If ( ) ( )

2

sin

1

xf x

x x

=

+ + where . denotes greatest integer function. Then

1) f is one-one 2) f is not one-one

3) f is a constant function 4) none of these




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 : , :f R R g R R→ → be two functions defined as ( )f x x x= + and

( )g x x x= − for all x R and ( )( )3fog − is k, then ____12

k=


Narayana CO Schools

17

72. Let :f R R→ , :g R R→ be two functions defined as ( )f x x x= + and

( )g x x x x R= − then ( )( ) ___________gof x =

73. Let ( ) ( ), 11

kxf x x

x= −

+ then the value of k for which ( )( )fof x x=

is _________

74. If the function :f R A→ given by ( )2

2 1

xf x

x=

+ is surjection then the

least value in the range of A is ______________

75. If ( ) ( ) ( )2 , tan , logf x x g x x h x x= = = then ( ) _________4

ho gof

=

mdpcos, narayana, madhapur - class: sz3 jee-main model … · 2020. 12. 27. ·...

Documents