class: sz3 jee-main model date: 09-01-2021 time: 3hrs wtm … · 2021. 1. 9. ·...

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Class: SZ3 JEE-MAIN MODEL Date: 09-01-2021

Time: 3hrs WTM-30 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-30_QP_Exam.Dt.09-01-2021

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. Let F be force acting on a particle having position vector r . Let

be the torque of this force about the origin, then

1) . 0r = and . 0F = 2) . 0r = but . 0F

3) . 0r but . 0F = 4) . 0r and . 0F

02. A uniform ladder of mass 10kg leans against a smooth vertical wall

making an angle of 53with it. The other end rests on a rough

horizontal floor. The frictional force that the floor exerts on the

ladder is ___________Newton.(Take 29.8 /g m s= )(nearly)

1) 65 2) 60 3) 45 4) 95

03. A ball, moving with a speed of 10 3 / ,m s strikes an identical

stationary ball such that after the collision, the direction of each

ball makes an angle of 030 with the original line of motion. The

speeds of two balls after the collision are, respectively.

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

3) 5m/s, 5m/s 4) 10m/s, 10m/s


Narayana CO Schools

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04. A cube of side ‘a’ is placed on an inclined plane of inclination .

What is the maximum value for which the cube will not topple?

1) 15° 2) 30° 3) 45° 4) None of these

05. The centre of an equilateral triangle is O. Three forces 1 2 3, and F F F

are applied along sides , and AB BC AC respectively. The magnitude

of 3F , so that the total torque about O should be zero is

1) ( )1 2F F+ 2) ( )1 2F F− 3) 1 2

2

F F+ 4) None

06. Two small kids weighing 10 kg and 15 kg respectively are trying to

balance a seesaw of total length 5m, with the fulcrum at the centre.

If one of the kids is Sitting at an end, where should the other

sit ?(nearly)

1) 2.7 m 2) 1.7 m 3) 2.9 m 4) none


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07. The total torque acting on the body shown in figure about the point

O is

1) 0.54 Nm 2) 1.49 Nm 3) 1.69 Nm 4) 0.89Nm

08. A force F is applied on the top of a cube as shown in figure. The

coefficient of friction between the cube and the ground is . If F is

gradually increased, the cube topples before sliding, then should

be

1) 1

2 2)

1

4 3) 1 4)

1

2

09. A Cube is placed on a rough inclined plane of inclination as

shown in figure. The coefficient of friction between the cube and the

plane is . If the angle is gradually increased, the cube Slides before

toppling when

1) 1 2) 1

2 3) 1 4) None


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10. Which of the following is correct in case of variable mass systems

1) It disobeys conservation of momentum

2) ext rel

dv dmF m v

dt dt+ =

3) ext rel

dm dvF v m

dt dt+ =

4) extF ma=

11. Rocket propulsion is based on

1) Newton’s 1st law

2) Newton’s 2nd law

3) Newton’s 3rd law (law of conservation of linear momentum)

4) Newton’s 1st & 2nd laws

12. Find the mass of a rocket as a function of time, if it moves with a

constant acceleration , in the absence of external forces. The gas

escapes with a constant velocity u relative to the rocket and its

mass initially was 0m .

1) ( )/

0

u tm m e

−= 2) ( )

2 /

0

u tm m e

−=

3) ( )/

0

u tm m e

−= 4) ( )

2 /

0

u tm m e

−=

13. A rocket set for vertical firing weighs 50 kg and contains 450 kg of

fuel. It can have a maximum exhaust velocity of 2 km/s. What

should be its minimum rate of fuel consumption to just lift it off the

launching pad? (g=9.8 m/sec2)

1) 2.45 kg/s 2) 5 kg/s

3) 3.5 kg/s 4) 1.5 kg/s

14. A satellite in a force-free space sweeps stationary interplanetary

dust at a rate / ,dM dt v= where M is the mass, v is the velocity of

the satellite and is a constant. What is the deacceleration of the

satellite?

1) 22 /v M− 2) 2 /v M− 3) 2 /v M+ 4) 2v−


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15. A 5000 kg rocket is set for vertical firing. The exhaust speed is 800

m/s. To give an initial upward acceleration of 20 2/m s , the amount

of gas ejected per second to supply the needed thrust will be

( )210 /g m s=

1) 127.5 kg/s 2) 187.5 kg/s 3) 85 kg/s 4) 137.5 kg/s

16. A particle of mass m moving with velocity 0v collides with a sphere

of same mass at rest. as shown. If the surface of contact is smooth

and the collision is elastic. Find the velocities of particle and sphere

after the collision.

1) 0 03

,2 2

v v 2) 0 0

3,

3 2

v v 3) 0 0

5,

3 2

v v 4) 0 0

3 5,

2 2

v v

17. Find the torque of a force 3 5F i j k= − + + acting at the point

7 3r i j k= + +

1) 14 38 16i j k− + 2) 4 4 6i j k+ +

3) 21 4 4i j k+ + 4) 14 34 16i j k− + +

18. A force of ˆFk− acts on O, the origin of the coordinates system. The

torque about the point ( )1, 1− is

1) ( )ˆ ˆF i j− + 2) ( )ˆ ˆF i j+ 3) ( )ˆ ˆF i j− − 4) ( )ˆ ˆF i j−

19. A couple produces

1) purely linear motion 2) purely rotational motion

3) linear and rotational motion 4) no motion

20. Find the torque of a force 3 4 5F i j kN= + + about a point O, whose

position vector is .r i j km= + +

1) 6Nm 2) 7Nm 3) 5Nm 4) 4Nm


Narayana CO Schools

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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 particle of mass m strikes another particle of same mass at rest.

Find the angle between velocities of particles after the collision, if

the collision is elastic is ___________degrees.

22. A rocket is set for a vertical firing. If the exhaust speed is 2000

m/sec, the rate of fuel consumption to just lift of the rocket is

___________kg/sec. 2( 10 / ,g m s= mass of rocket = 6000kg)

23. 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. Include gravity is _______ 2/ .m s

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

then the rate of fuel consumption to give to the rocket an initial

vertical upward acceleration is ____________kg/sec. (Take mass of

rocket = 6000 kg.)

25. The ladder shown in figure has negligible mass and rests on a

frictionless floor. The crossbar connects the two legs of the ladder

at the middle. The angle between the two legs is 060 . . The fat person

sitting on the ladder has a mass of 80kg. The tension in the cross

bar is ___________Newton. (nearly) ( 29.8 /g m s= )


Narayana CO Schools

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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. Calculate the total number of geometrical isomers for the following

compound

1) 2 2) 4 3) 8 4) 16

27. How many geometrical isomers are possible for this compound

2 2CH CH CH CH CH CH= − = − =

1) 2 2) 3 3) 4 4) 8

28. How many geometrical isomers are possible for the below

compound

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

29. Number of geometrical isomers are possible for the below

compound 3 3CH CH CH CH CH CH CH CH− = − = − = −

1) 2 2) 3 3) 6 4) 8

30. The structure of syn-Azobenzene is

1) 2)

3) 4)


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31. Which of the following can exist in ‘syn’ and ‘anti’ forms?

1) 6 5C H N N OH− = − 2) 6 5 6 5C H N N C H− = −

3) 6 5C H CH N OH− = − 4) All the above

32. Which of the following is incorrect matching.

1)

2)

3)

4) All the above

33. The number of geometrical isomers in 3 2 2CH CH CH CH CH CH= − − =

is

1) two 2) three 3) four 4) five

34. Alkali metals are strong reducing agents because

1) these are metals

2) these are monovalent

3) their ionic radii is large

4) of low IP value

35. The solubility of metal halides depends on their nature, Lattice

energy and hydration energy of the individual ions. Amongst

fluorides of alkali metals, the lowest solubility of LiF in water is due

to

1) Ionic nature of LiF

2) High Lattice enthalpy

3) High hydration enthalpy of Li+ ion

4) Low ionisation enthalpy of Li atom


Narayana CO Schools

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36. The alkali metals are low melting which of the following alkali metal

is expected to melt if the room temperature rises to 030 ?C

1) Na 2) K 3) Rb 4) Ca

37. Alkali metals react with water vigorously to form hydroxides and

dihydrogen. Which of the following alkali metals reacts with water

least vigorously

1) Li 2) Na 3) K 4) Cs

38. The order of decreasing ionisation enthalpy in alkali metals is

1) Na>Li>K>Rb 2) RbRb 4) K>Li


Narayana CO Schools

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44. Which of the following is used as fire extinguisher?

1) 3NaHCO 2) NaCl

3) NaOH 4) All the above

45. NaOH is manufactured by the electrolysis of brine solution the

products of reaction are

1) 2&Na Cl 2) 2 2&Cl O 3) 2 2&Cl H 4) 2&Na O



This section contains 5 questions. The answer to each question is a Numerical values comprising of positive or negative decimal numbers (place value


46. How many geometrical isomers of 3CH CH CH CH NOH− = − = exist?

47. The total number of geometrical isomers possible in following

compounds is

48. How many of the following statements is/are correct

I) A typical 70kg man contains about 90 gr of Na and 170 gr of K

compared with only 5 gr of iron and 0.06 gr of copper

II) Sodium carbonate is used in paper, paints and textile industries

III) Sodium chloride is used for the preparation of 2 2 ,Na O NaOH and

2 3Na CO

IV) Both LiCl and 2MgCl are soluble in ethanol

V) The oxides, 2Li O and MgO do not combine with excess oxygen

to give any superoxide

49. 3752 3 2 2 3 2 2.10 .

KNa CO H O Na CO xH O yH O⎯⎯⎯→ + . From the above equation

?y x− =

50. The oxidation state of potassium in 2KO


Narayana CO Schools

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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. The domain of the function ( )( )1

2

sin 3

9

xf x

x

− −=

− is _____________

1) [2,3] 2) [1,2) 3) [1,2] 4) [2,3)

52. The domain of ( ) 12

cos2 sin

f xx

− = +

contained in 0,2 is

____________

1) 0,2

2) ,2

3) 0, 4) ,

2 2

−

53. The range of ( ) 1 21

sin2

f x x−

= +

is __________

( ). . .denotesG I F

1) ,0,2 2

−

2) 0,2

3) 2

4) 0,

54. the range of ( ) 1 1 1sin cos tanf x x x x− − −= + + is __________

1) ( )0, 2) 3

,4 4

3) ,4 4

−

4) 3

0,4

55. If ( ) 21 ....f x x x== + + + for 1x then ( )1f x− = __________

1) 1x

x

− 2)

1x

x

+ 3)

2x

x

− 4)

2x

x

+

56. The domain of ( )( )21 16logsin x

f xe

−

= is____________

1) 1

,44

2) 1 1

4, ,44 4

− −

3) 1

4,4

− −

4) 1

4,4


Narayana CO Schools

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57. The function ( ) ( )( ) ( )1 1 2cos 3 cos 3 1f x x x x x− −= + + + + is defined

on the set ‘S’ then ‘S’ is equal to __________

1) 3,0− 2) 3,0− 3) 0,3 4) ( )3,0−

58. The range of 2

1

2sin

1

xy

x

− = +

is ____________

1) 0,2

2) 0,2

3) 0,

2

4) 0,1

59. The range of 1 2 1 21 1

sin cos2 2

x x− −

+ + −

{Where [.] denotes G.I.F} is_____________

1) ,2

2) 3)

2

4) ,2

60. The range of ( ) 1 1sin secf x x x− −= + is____________

1) ,2 2

−

2) 0,2

−

3)

2

4)

61. If ) ): 2, 1,f → defined by ( )4 242x xf x −= is an invertible

function then ( )1f x− = _______________

1) 22 4 log x+ − 2) 22 4 log x+ +

3) 22 4 log x− + 4) 22 4 log x− −

62. If ( ) 3 5f x x= − then ( )1f x− = ___________

1) is given by 1

3 5x −

2) is given by5

3

x +

3) does not exist because f is not one -one

4) does not exist because f is not one to.


Narayana CO Schools

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63. if :f A B→ be a function defined as ( )1

2

xf x

x

−=

−where 2A R= −

and 1B R= − then f is :

1) invertible and ( )13 1

1

yf y

y

− −=−


1

yf y

y

− −=−


1

yf y

y

− +=−

4) Not invertible

64. assuming that ( )1

1

tf t

t

−=

+ is an invertible function then 1

11f

C

− +

is equal to:

1) ( )2 1C− + 2) 1

2 C+ 3) 2 1C − 4) 2 1C +

65. If ( )3 7

2 4f x x= + − and ( )g x be the inverse function of ( )f x then

the value of ( ) ( )1 1 17f og− − is equal to _________

1) 3 61

2

+ 2) 242 3) 17 4)

3 61

2

−

66. If ) ): 1, 3,f → be defined as ( ) ( ) ( )2

2 2log 2 log 3f x x x= + +

If 1f − is the inverse of the function of f then ( )1f x− is equal

to___________

1) 1 22 x− − − 2) 32 x−

3) 2 32 x− 4) 1 22 x− + −

67. Consider all functions : 1,2,3,4 1,2,3,4f → which are one – one,

on to and satisfy the property if ( )f k is add then ( )1f k + is even,

1,2,3k = . If number of such solutions is P then P-7 =___________

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


Narayana CO Schools

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68. The polynomial ( )p x is such that for any polynomial ( )q x we have

( )( ) ( )( )p q x q p x= then ( )p x is____________

1) even 2) odd

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

69. if ( )4 1

4 1 0

For xf x

x For x

−=

− −

If ( )f x is an even function on R then the definition of ( )f x on

( )0, is____________

1) ( )4 ,0 1

4 , 1

x xf x

x

=

2) ( )

4 ,0 1

4 , 1

x xf x

x

=

−

3) ( )4 ,0 1

4 , 1

xf x

x x

=

4) ( )

4 , 1

4 , 1 0

xf x

x x

−=

− −

70. If then ( )2 1,sin

21,

xxx

f xxx x

=

is__________

1) an even function 2) an odd function

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



This section contains 5 questions. The answer to each question is a Numerical values comprising of positive or negative decimal numbers (place value


71. In the domain of 1 3sin log3

x−

the maximum value is ___________

72. In the domain of the function ( ) ( )1sin 26

f x x−

= +

for real

valued x the maximum value =___________


Narayana CO Schools

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73. If : 0,f a s→ be a function defined by ( )f x = 3cos2

x if the largest

value of ‘a’ far which ( )f x has an inverse function ( )1f x− is K

then the Value of K is ___________

74. If ( )f x is an even function defined on the interval ( )5,5− then the

total no of real valued of x satisfying the equation ( )1

2

xf x f

x

+ =

+

are___________

75. The largest interval lying in ,2 2

−

for which the function is

( )2 1cos 1 log cos

2

x xf x e x− −

= + − +

Defined is ),k l then k=_____________

class: sz3 jee-main model date: 09-01-2021 time: 3hrs wtm … · 2021. 1. 9. ·...

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