Class: SZ3 JEE-MAIN MODEL Date: 02-01-2021 Time: 3hrs WTM … · 2021. 2. 1. ·...
Transcript of 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
Sec – I(Q.N : 26 – 45) Questions with Single Answer Type 4 -1 20 80
Sec – II(Q.N : 46 – 50) Questions with Numerical Answer Type
(+/ - Decimal Numbers) 4 0 5 20
Total 25 100
MATHEMATICS Section Question Type
+Ve Marks
- Ve Marks
No.of Qs
Total marks
Sec – I(Q.N : 51 – 70) Questions with Single Answer Type 4 -1 20 80
Sec – II(Q.N : 71 – 75) Questions with Numerical Answer Type
(+/ - Decimal Numbers) 4 0 5 20
Total 25 100
mailto:[email protected]://www.narayanagroup.com/
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SZ3_JEE-MAIN_WTM-29_QP_Exam.Dt.02-01-2021
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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
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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
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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
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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
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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
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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−
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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?
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SECTION-I (26 TO 45)
(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.
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
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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
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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
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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
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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
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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
SECTION-II (46 TO 50)
(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.
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
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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= = − =
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SECTION-I (51 TO 70)
(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.
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
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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
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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−
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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
SECTION-II (71 TO 75)
(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.
71. Let ( ) 21
1,2
f x x x x= − + then the solution of the equation
( ) ( )1f x f x− = is then 1+ =_____________
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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 =