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WARANGAL SCHOOL OF MATHEMATICS
JEE MAINS MODEL TEST - 3
JEE MAINS MODEL TEST – 3 :: 2021-22
Class : VIII–Spark 1
SERIES - A
Time : 3 hrs
Date : 01-08-2021
Marks : 300
MATHS (1-25)
1.
If three coins are tossed simultaneously , then the probability of getting at least two heads,
is
A)
2.
B)
3
8
C)
1
2
1
2
B)
1
3
C)
1
6
x
. If the
12
2
, then x =
3
1
4
B)
1
3
C)
4
9
D)
7
9
1
10
B)
3
10
C)
7
10
D)
9
10
The probability of throwing a number greater than 2 with a fair dice is
A)
7.
2
3
A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9. The
probability that the selected number is their average is
A)
6.
D)
A) 2
B) 3
C) 4
D) 6
A bag contains three green marbles, four blue marbles, and two orange marbles. If a
marble is picked at random, then the probability that it not an orange marble is
A)
5.
1
4
The probability of guessing the correct answer to a certain test question is
probability of not guessing the correct answer to this question is
4.
D)
In a single throw of a die, the probability of getting a multiple of 3 is
A)
3.
1
4
3
5
B)
2
5
C)
2
3
D)
1
3
A card is accidently dropped from a pack of 52 playing cards. The probability that it is an
ace is
A)
1
4
B)
1
13
C)
1
52
D)
12
13
CLASS : 8–S1; SERIES - A WARANGAL SCHOOL OF MATHEMATICS
1
WARANGAL SCHOOL OF MATHEMATICS
8.
JEE MAINS MODEL TEST - 3
A number is selected from number 1 to 25. The probability that it is prime is
A)
2
3
B)
1
6
C)
1
3
9.
Which of the following cannot be the probability of an event?
10.
2
B) – 1.5
3
If P  E   0.05 , then P  not E  =
A)
11.
12.
B) 1
C)
1
2
D) non existent
19
20
B)
1
25
C)
1
20
D)
17
20
13
25
B)
21
50
C)
12
25
D)
23
50
1
12
B)
1
6
C)
3
4
D) None of these
1
3
B)
3
7
C)
1
6
D)
1
2
D)
1
6
A die is thrown once. The probability of getting a prime number is
A)
19.
D) non existent
From the letters of the word “MOBILE”, a letter is selected. The probability that the lette
is a vowel, is
A)
18.
1
2
A month is selected at random in a year. The probability that it is March or October, is
A)
17.
C)
A number is selected from first 50 natural numbers. What is the probability that it is a
multiple of 3 or 5 ?
A)
16.
B) 1
Aarushi said 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket,
what is the probability of Priya winning a prize?
A)
15.
D) 0.7
The probability of an impossible event is
A) 0
14.
5
6
A) – 0.05
B) 0.5
C) 0.9
D) 0.95
Which of the following cannot be the probability of occurrence of an event?
A) 0.2
B) 0.4
C) 0.8
D) 1.6
The probability of a certain event is
A) 0
13.
C) 15%
D)
2
3
B)
1
3
C)
1
2
The probability of getting an even number, when a die is thrown once is
A)
1
2
B)
1
3
C)
1
6
D)
5
6
CLASS : 8–S1; SERIES - A WARANGAL SCHOOL OF MATHEMATICS
2
WARANGAL SCHOOL OF MATHEMATICS
20.
A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the
box, the probability that it bears a prime number less than 23, is
A)
21.
C)
4
45
D)
9
89
4
15
B)
2
15
C)
1
5
D)
1
3
1
4
B)
1
8
C)
3
4
D)
7
8
1
36
B)
1
2
C)
1
6
D)
1
4
A number is selected at random from the numbers 1 to 30. The probability that it is a
prime number is
A)
25.
10
90
If two different dice are rolled together, the probability of getting an even number on both
dice , is
A)
24.
B)
Two different coins are tossed simultaneously. The probability of getting at least one head
is
A)
23.
7
90
The probability that a number selected at random from the numbers 1, 2, 3, .,.. 15 is a
multiple of 4, is
A)
22.
JEE MAINS MODEL TEST - 3
2
3
B)
1
6
C)
1
3
D)
11
30
A card is drawn at random from a pack of 52 cards. The probability that the drawn card is
not an ace is
A)
1
13
B)
9
13
C)
4
13
D)
12
13
PHYSICS (26-50)
26.
27.
28.
29.
The pressure of air in the bulb of constant volume air thermometer is 75 cm of mercury at
0oC and 100 cm at 100oC. If the pressure is 80 cm of Hg column at room temperature, find
the room temperature?
B) 40oC
C) 27oC
D) 30oC
A) 20oC
The resistance of a resistance thermometer at 0oC is 3.50  and 100oC is 3.66  . At what
temperature will its resistance be 4.30  ?
B) 290.4oC
C) 419oC
D) 500oC
A) 400oC
A faulty thermometer reads 5oC in melting ice and 99oC in steam. When faulty
thermometer reads 52oC, the correct temperature is
B) 122oC
C) 104oC
D) 48oC
A) 50oC
Normal temperature of the human body is 98.4oF. It is equal to
D) Both A, C are correct
A) 310.03 K
B) 313.03 K
C) 36.88oC
CLASS : 8–S1; SERIES - A WARANGAL SCHOOL OF MATHEMATICS
3
WARANGAL SCHOOL OF MATHEMATICS
30.
31.
32.
33.
JEE MAINS MODEL TEST - 3
Railway lines are laid with gaps to allow for expansion. If the gap between steel rails 66m
long be 3.63 cm at 10oC, then at what temperature will the lines just touch (Coefficient of
linear expansion of steel is 11 106 /oC)
B) 60oC
C) 40oC
D) 70oC
A) 50oC
If boiling point of a liquid is 95oF, What will be the reading at Celsius scale?
B) 65oC
C) 63oC
D) 35oC
A) 7oC
A bimetallic strip consists of metals X and Y. It is mounted rigidly at the base as shown in
figure. The metal X has a higher coefficient of expansion compared to that for Y. When
the bimetallic strip is placed in cold bath.
A) It will bend towards right
B) It will bend towards left
C) It will not bend but shrinks
D) It will neither bend nor shrinks
The coefficients of linear expansion of brass and steel are 1 and  2 respectively. If we
take a brass rod of length l1 and steel rod of length l2 at 0oC, the difference in their lengths
(l1 and l2) will remain the same at all temperatures, if
34.
35.
36.
37.
A) 1l1   2l2
B) 1l2   2l1
C) 12l2   2 2l1
D) 1l2 2   2 2l1
If absolute zero is – 273.15oC on Celsius temperature scale, then the absolute zero on the
Fahrenheit scale is
B) –453.15oF
C) –459.67oF
D) –491.67oF
A) –273.15oF
When a body is heated , then maximum rise will be in its
A) length
B) surface area
C) volume
D) density
At which temperature, the centigrade and Fahrenheit scales are equal?
B) – 40o
C) 574.25o
D) 37o
A) 40o
If two rods of lengths L and 2L having coefficient of linear expansion  and 2 
respectively, are connected end-on-end, the average coefficient of linear expansion of the
composite rod equals
A)
38.
39.
3

2
B)
5

2
C)
5

3
D)

2
On which of the following scales of temperature, the temperature is never negative
A) Celsius
B) Fahrenheit
C) Reamur
D) Kelvin
o
An aluminium sphere of 20 cm diameter is heated from 0 C to 100oC. Its volume changes
by ___ [Given coefficient of linear expansion of Al is 23  106 / C]
A) 28.9 cc
B) 2.89 cc
C) 9.28 cc
D) 4.98 cc
o
40.
Two temperature scales A and B are related by
two scales have the same reading?
A) –42oC
B) –72oC
A  42 B  72
. At which temperature

110
220
C) 12oC
D) 40oC
CLASS : 8–S1; SERIES - A WARANGAL SCHOOL OF MATHEMATICS
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WARANGAL SCHOOL OF MATHEMATICS
41.
42.
JEE MAINS MODEL TEST - 3
The steel wire of cross sectional area 2 mm2 and Young’s modulus Y  2  109 Nm-2 is
stretched and tied firmly between two rigid supports at temperature 20oC. Coefficient of
linear expansion of material is 105 /oC. The tension in the wire is 200 N. At what
temperature will the tension becomes zero?
B) 40oC
C) 50oC
D) 30oC
A) 70oC
A steel rod of cross sectional area 5 mm2 is held between two fixed supports. If the rod is
unstrained at 10oC, find the force exerted by rod on the supports if temperature increases
to 25oC _______ [ s  1.2  106 / o C , Y  2  1011 N/m2]
43.
44.
A) 12 N
B) 4 N
C) 18 N
D) 16 N
o
The temperature of a body is charged by 80 C. The corresponding charge is
B) 144oF
C) 104oF
D) 200oF
A) 140oF
A metal rod of Young’s modulus Y and coefficient of thermal expansion  is held at its
two ends such that its length remains same. If its temperature is raised by toC, the stress
developed in it is
A)
45.
46.
47.
t
Y
B)
Y
t
C) Yt
D)
1
Y t
If solid ball of metal has a spherical cavity inside it. If the ball is heated, the volume of the
cavity will
A) increase
B) decrease
C) remains unchangedD) None
In a mercury thermometer the ice point is marked as 10oC and the steam point is marked as
130oC. At 40oC temperature, what will this thermometer read?
B) 66oC
C) 67oC
D) 58oC
A) 78oC
An iron tyre 100 cm in diameter is to be fitted on to a wooden wheel 100.4 cm in
diameter. If coefficient of linear expansion of iron is 105 / o C , what should be the
minimum increase in temperature of iron tyre
B) 200oC
C) 450oC
D) 400oC
A) 300oC
48.
A brass rod and iron rod differ 5 cm in length at all temperatures. If  b  18  10 6 / o C ,
i  11 106 / o C , then length of iron rod at 0oC is
A) 7.85 cm
49.
B) 12.85 cm
C) 20.7 cm
D) 5 cm
A crystal has coefficient of linear expansion 10  107 / o C in one direction and
220  107 / o C in every direction at right angles to it. Then coefficient of cubical
expansion of that material is
50.
A) 45  107 / o C
B) 45  106 / o C
C) 45  105 / o C
D) 45  104 / o C
On heating area of a plate increases by 0.08%. If the rise in its temperature in this case is
80oC, coefficient of cubical expansion of that material is
A) 15  106 / o C
B) 15  105 / o C
C) 15  104 / o C
D) 2  106 / o C
CLASS : 8–S1; SERIES - A WARANGAL SCHOOL OF MATHEMATICS
5
WARANGAL SCHOOL OF MATHEMATICS
JEE MAINS MODEL TEST - 3
CHEMISTRY (51-75)
51.
52.
A quantity of 10g of a hydrocarbon exactly requires 40g oxygen for complete combustion.
The products formed are CO2 and water. When CO2 gas formed is absorbed completely in
lime water, the mass of solution increases by 27.5g. What is the mass of water formed
simultaneously in the combustion?
A) 22.5g
B) 27.5g
C) 50g
D) 10g
A person needs an average of 2.0 mg of riboflavin (vitamin B2) per day. How many grams
of butter should be taken by the person per day if it is the only source of riboflavin? Butter
contains 5.5 g riboflavin per g.
A) 363.6g
53.
B) 2.75mg
C) 11g
D) 19.8g
The mass of 3.2  105 atoms of an element is 8.0  1018 g. The atomic mass of the
element is about (NA = 6  1023 )
A) 2.5  1022
54.
B) 15
C) 8.0  1018
D) 30
If ‘NEERAJ KUAMR’ is written by a graphite pencil, it weighs 3.0  1010 g. How
many carbon atoms are present in it? (NA = 6  1023 )
A) 1.5  1013
55.
56.
57.
58.
59.
60.
B) 5  1012
C) 2  1033
D) 1.5  1010
The atomic masses of two elements P and Q are 20 and 40, respectively. If ‘a’ g of P
contains ‘b’ atoms, then how many atoms are present in ‘2a’ g of Q?
A) a
B) b
C) 2a
D) 2b
The molecular formula of a compound is X4O9. If the compound contains 40% X by mass,
then what is the atomic mass of X?
A) 24
B) 12
C) 26
D) 13
A quantity of 1g of metallic carbonate XCO3 is completely converted into a chloride XCl2
weighing 1.11g. The atomic mass of the element ‘X’ is
A) 10
B) 20
C) 30
D) 40
20
21
22
An element X has three isotopes X , X and X . The percentage abundance of X20 is
90% and average atomic mass of the element is 20.18. The percentage abundance of X21
should be
A) 2%
B) 8%
C) 10%
D) 0%
35
The fractional abundance Cl in a sample of chlorine containing only Cl35 (atomic weight
= 34.9) and Cl37 (atomic weight = 36.9) isotopes is 0.6. The average mass number of
chlorine is
A) 35.7
B) 35.8
C) 18.8
D) 35.77
Twenty molecules of SO3 will weigh as much as ….molecules of oxygen
A) 100
B) 50
C) 15
D) 8
CLASS : 8–S1; SERIES - A WARANGAL SCHOOL OF MATHEMATICS
6
WARANGAL SCHOOL OF MATHEMATICS
61.
JEE MAINS MODEL TEST - 3
A mixture of 2  1021 molecules of P and 3  1021 molecules of Q weighs 0.60g. If
the molecular mass of P is 45, then the molecular mass of Q will be (NA = 6  1023 )
A) 45
62.
B) 180
C) 90
D) 270
A compound contains 7 carbon atoms. 2 oxygen atoms and 9.96  1024 g of other
elements. The molecular mass of compound is (NA = 6  1023 )
63.
64.
65.
A) 122
B) 116
C) 148
D) 154
If the mass of neutron is doubled and that of proton is halved, the molecular mass of H2O
containing only H1 and O16 atoms will
Out of 1.0g dioxygen, 1.0g atomic oxygen and 1.0g ozone, the maximum number of
oxygen atoms are contained in
A) 1.0g of atomic oxygen
B) 1.0g of ozone
C) 1.0g of oxygen gas
D) All contains the same number of atoms

A) 0.2NA
66.
67.

Total number of valence electrons present in 6.4g peroxides ion O 22 is
B) 3.2NA
C) 3.6NA
D) 2.8NA
Dopamine is a neurotransmitter., a molecule that serves to transmit message in the brain.
The chemical formula of dopamine is C8H11O2N. How many moles are there in 1g of
dopamine?
A) 0.00654
B) 153
C) 0.0654
D) None of these
The volume of one mole of water at 277K is 18ml. One ml of water contains 20 drops.
The number of molecules in one drop of water will be (NA = 6  1023 )
A) 1.07  1021
68.
69.
70.
C) 2.67  1021
D) 1.67  1020
Number of gas molecules present in 1ml of gas at 00C and 1 atm is called Loschmidt
B) 6  1023
C) 2.7  1022
A) 2.7  1019
An amount of 6 moles of Cl atoms at STP occupies a volume of
A) 134.4 L
B) 67.2L
C) 68.1L
D) 1.3  1028
D) 136.2L
The number of g-molecules of oxygen in 6.023  1024 CO molecules is
A) 1g-molecule
71.
B) 1.67  1021
B) 0.5g-molecule
C) 5g-molecule
D) 10g-molecules
Equal masses of oxygen, hydrogen and methane are taken in identical conditions. What is
the ratio of the volumes of the gases under identical conditions
A) 16 : 1 : 8
B) 1 : 16 : 2
C) 1 : 16 : 8
D) 2 : 16 : 1
CLASS : 8–S1; SERIES - A WARANGAL SCHOOL OF MATHEMATICS
7
WARANGAL SCHOOL OF MATHEMATICS
72.
A pre-weighed vessel was filled with oxygen at NTP and weighed. It was then evacuated,
filled with SO2 at the same temperature and pressure, and again weighed. The weight of
oxygen is
A) the same as that of SO2
C) twice that of SO2
73.
74.
75.
JEE MAINS MODEL TEST - 3
1
that of SO2
2
1
D) that of SO2
4
B)
The commonly used pain reliever, aspirin has the molecular formula C9H8O4. If a sample
of aspirin contains 0.968g of carbon, then what is the mass of hydrogen in the sample?
A) 0.717g
B) 0.0717g
C) 8.000g
D) 0.645g
The percentage of Fe(III) present in iron ore Fe0.93O1.00 is (Fe = 56)
A) 94
B) 6
C) 21.5
D) 15
An organic compound contains 40% carbon and 6.67% hydrogen by mass. Which of the
following represents the empirical formula of the compound?
B) CH2O
C) C2H4O
D) CH3O
A) CH2
***
CLASS : 8–S1; SERIES - A WARANGAL SCHOOL OF MATHEMATICS
8
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