class: sz3 jee-main model date: 09-01-2021 time: 3hrs wtm … · 2021. 1. 9. ·...
TRANSCRIPT
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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
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-30_QP_Exam.Dt.09-01-2021
Narayana CO Schools
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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. 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
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
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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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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
Narayana CO Schools
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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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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
Narayana CO Schools
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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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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
Narayana CO Schools
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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
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
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= )
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
Narayana CO Schools
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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. 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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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
Narayana CO Schools
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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
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
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
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
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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
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. 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
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
Narayana CO Schools
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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. 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
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
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.
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
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
− −=−
2) invertible and ( )12 1
1
yf y
y
− −=−
3) invertible and ( )12 1
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
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
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
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. 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 =___________
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SZ3_JEE-MAIN_WTM-30_QP_Exam.Dt.09-01-2021
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=_____________