JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper
Question Paper MathonGo
𝑥2
Q1. The work done by a gas molecule in an isolated system is given by, 𝑊 = 𝛼𝛽2 𝑒- 𝛼𝑘 𝑇 , where 𝑥 is the
displacement, 𝑘 is the Boltzmann constant and 𝑇 is the temperature. 𝛼 and 𝛽 are constants. Then the dimensions
of 𝛽 will be:
(1) M2 L T2 (2) ML2 T-2
(3) MLT-2 (4) M0 L T0
Q2. If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time
graph?
(1) (2)
(3) (4)
Q3. Moment of inertia M . I . of four bodies, having same mass and radius, are reported as;
𝐼1 = M . I . of thin circular ring about its diameter,
𝐼2 = M . I . of circular disc about an axis perpendicular to disc and going through the centre,
𝐼3 = M . I . of solid cylinder about its axis and
𝐼4 = M . I . of solid sphere about its diameter.
Then:
5
(1) 𝐼1 + 𝐼2 = 𝐼3 + 2 𝐼4 . (2) 𝐼1 + 𝐼3 < 𝐼2 + 𝐼4
(3) 𝐼1 = 𝐼2 = 𝐼3 > 𝐼4 (4) 𝐼1 = 𝐼2 = 𝐼3 < 𝐼4
Q4. Consider two satellites 𝑆1 and 𝑆2 with periods of revolution 1hr and 8hr respectively revolving around a planet
in circular orbits. The ratio of angular velocity of satellite 𝑆1 to the angular velocity of satellite 𝑆2 is:
(1) 8: 1 (2) 2: 1
(3) 1: 4 (4) 1: 8
Q5. Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m
under the action of their own mutual gravitational attraction. The speed of each particle will be:
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,JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper
Question Paper MathonGo
(1) √𝐺1 + 2√2 (2) √ 𝐺 1 + 2√2
2
(3) √ 𝐺 2√2 - 1 (4) √1 + 2√2 𝐺
2 2
Q6. Two stars of masses 𝑚 and 2𝑚 at a distance 𝑑 rotate about their common centre of mass in free space. The
period of revolution is
(1) 𝑑
3
(2) 2𝜋√ 3𝐺𝑚
2𝜋√ 3𝐺𝑚 3
𝑑
1 3𝐺𝑚
(3) (4) 1 𝑑3
2𝜋 √ 𝑑3 √
2𝜋 3𝐺𝑚
Q7. If 𝑌, 𝐾 and 𝜂 are the values of Young's modulus, bulk modulus and modulus of rigidity of any material
respectively. Choose the correct relation for these parameters.
9 𝐾𝜂 3𝑌𝐾
(1) 𝑌 = 3 𝐾-𝜂
N m-2 (2) 𝜂 = 9𝐾 + 𝑌
N m-2
𝑌𝜂 9 𝐾𝜂
(3) 𝐾 = 9𝜂 - 3𝑌
N m-2 (4) 𝑌 = 2𝜂 + 3 𝐾
N m-2
Q8. Each side of a box made of metal sheet in cubic shape is 𝑎 at room temperature 𝑇, the coefficient of linear
expansion of the metal sheet is 𝛼. The metal sheet is heated uniformly, by a small temperature 𝛥𝑇, so that its
new temperature is 𝑇 + 𝛥𝑇. Calculate the increase in the volume of the metal box.
(1) 4𝑎3 𝛼𝛥𝑇 (2) 3𝑎3 𝛼𝛥𝑇
4
(3) 4𝜋𝑎3 𝛼𝛥𝑇 (4) 𝜋𝑎3 𝛼𝛥𝑇
3
Q9. Match List I with List II .
List I List II
(a) Isothermal (i) Pressure constant
(b) Isochoric (ii) Temperature constant
(c) Adiabatic (iii) Volume constant
(d) Isobaric (iv) Heat content is constant
Choose the correct answer from the options given below:
(1) ( a ) → ( ii ) , ( b ) → ( iii ) , ( c ) → ( iv ) , ( d ) → ( i )
(2) ( a ) → ( iii ) , ( b ) → ( ii ) , ( c ) → ( i ) , ( d ) → ( iv )
(3) ( a ) → ( i ) , ( b ) → ( iii ) , ( c ) → ( ii ) , ( d ) → ( iv )
(4) ( a ) → ( ii ) , ( b ) → ( iv ) , ( c ) → ( iii ) , ( d ) → ( i )
Q10. 𝑛 mole of a perfect gas undergoes a cyclic process 𝐴𝐵𝐶𝐴 (see figure) consisting of the following processes.
𝐴 → 𝐵: Isothermal expansion at temperature 𝑇 so that the volume is doubled from 𝑉1 to 𝑉2 = 2𝑉1 and
pressure changes from 𝑃1 to 𝑃2
𝐵 → 𝐶: Isobaric compression at pressure 𝑃2 to initial volume 𝑉1 .
𝐶 → 𝐴: Isochoric change leading to change of pressure from 𝑃2 to 𝑃1
Total work done in the complete cycle 𝐴𝐵𝐶𝐴 is:
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Question Paper MathonGo
1
(1) 𝑛𝑅𝑇ln2 - 2 (2) 𝑛𝑅𝑇ln2
1
(3) 𝑛𝑅𝑇ln2 + (4) 0
2
Q11. In the given figure, a mass 𝑀 is attached to a horizontal spring which is fixed on one side to a rigid support.
The spring constant of the spring is 𝑘 . The mass oscillates on a frictionless surface with time period 𝑇 and
amplitude 𝐴 . When the mass is in equilibrium position, as shown in the figure, another mass 𝑚 is gently fixed
upon it. The new amplitude of oscillation will be:
(1) 𝐴√ 𝑀 + 𝑚 (2) 𝐴√ 𝑀
𝑀 𝑀-𝑚
(3) 𝐴√ 𝑀 - 𝑚 (4) 𝐴√ 𝑀
𝑀 𝑀+𝑚
Q12. A cube of side 𝑎 has point charges +Q located at each of its vertices except at the origin where the charge is
-Q . The electric field at the centre of cube is:
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Question Paper MathonGo
𝑥2
Q1. The work done by a gas molecule in an isolated system is given by, 𝑊 = 𝛼𝛽2 𝑒- 𝛼𝑘 𝑇 , where 𝑥 is the
displacement, 𝑘 is the Boltzmann constant and 𝑇 is the temperature. 𝛼 and 𝛽 are constants. Then the dimensions
of 𝛽 will be:
(1) M2 L T2 (2) ML2 T-2
(3) MLT-2 (4) M0 L T0
Q2. If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time
graph?
(1) (2)
(3) (4)
Q3. Moment of inertia M . I . of four bodies, having same mass and radius, are reported as;
𝐼1 = M . I . of thin circular ring about its diameter,
𝐼2 = M . I . of circular disc about an axis perpendicular to disc and going through the centre,
𝐼3 = M . I . of solid cylinder about its axis and
𝐼4 = M . I . of solid sphere about its diameter.
Then:
5
(1) 𝐼1 + 𝐼2 = 𝐼3 + 2 𝐼4 . (2) 𝐼1 + 𝐼3 < 𝐼2 + 𝐼4
(3) 𝐼1 = 𝐼2 = 𝐼3 > 𝐼4 (4) 𝐼1 = 𝐼2 = 𝐼3 < 𝐼4
Q4. Consider two satellites 𝑆1 and 𝑆2 with periods of revolution 1hr and 8hr respectively revolving around a planet
in circular orbits. The ratio of angular velocity of satellite 𝑆1 to the angular velocity of satellite 𝑆2 is:
(1) 8: 1 (2) 2: 1
(3) 1: 4 (4) 1: 8
Q5. Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m
under the action of their own mutual gravitational attraction. The speed of each particle will be:
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,JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper
Question Paper MathonGo
(1) √𝐺1 + 2√2 (2) √ 𝐺 1 + 2√2
2
(3) √ 𝐺 2√2 - 1 (4) √1 + 2√2 𝐺
2 2
Q6. Two stars of masses 𝑚 and 2𝑚 at a distance 𝑑 rotate about their common centre of mass in free space. The
period of revolution is
(1) 𝑑
3
(2) 2𝜋√ 3𝐺𝑚
2𝜋√ 3𝐺𝑚 3
𝑑
1 3𝐺𝑚
(3) (4) 1 𝑑3
2𝜋 √ 𝑑3 √
2𝜋 3𝐺𝑚
Q7. If 𝑌, 𝐾 and 𝜂 are the values of Young's modulus, bulk modulus and modulus of rigidity of any material
respectively. Choose the correct relation for these parameters.
9 𝐾𝜂 3𝑌𝐾
(1) 𝑌 = 3 𝐾-𝜂
N m-2 (2) 𝜂 = 9𝐾 + 𝑌
N m-2
𝑌𝜂 9 𝐾𝜂
(3) 𝐾 = 9𝜂 - 3𝑌
N m-2 (4) 𝑌 = 2𝜂 + 3 𝐾
N m-2
Q8. Each side of a box made of metal sheet in cubic shape is 𝑎 at room temperature 𝑇, the coefficient of linear
expansion of the metal sheet is 𝛼. The metal sheet is heated uniformly, by a small temperature 𝛥𝑇, so that its
new temperature is 𝑇 + 𝛥𝑇. Calculate the increase in the volume of the metal box.
(1) 4𝑎3 𝛼𝛥𝑇 (2) 3𝑎3 𝛼𝛥𝑇
4
(3) 4𝜋𝑎3 𝛼𝛥𝑇 (4) 𝜋𝑎3 𝛼𝛥𝑇
3
Q9. Match List I with List II .
List I List II
(a) Isothermal (i) Pressure constant
(b) Isochoric (ii) Temperature constant
(c) Adiabatic (iii) Volume constant
(d) Isobaric (iv) Heat content is constant
Choose the correct answer from the options given below:
(1) ( a ) → ( ii ) , ( b ) → ( iii ) , ( c ) → ( iv ) , ( d ) → ( i )
(2) ( a ) → ( iii ) , ( b ) → ( ii ) , ( c ) → ( i ) , ( d ) → ( iv )
(3) ( a ) → ( i ) , ( b ) → ( iii ) , ( c ) → ( ii ) , ( d ) → ( iv )
(4) ( a ) → ( ii ) , ( b ) → ( iv ) , ( c ) → ( iii ) , ( d ) → ( i )
Q10. 𝑛 mole of a perfect gas undergoes a cyclic process 𝐴𝐵𝐶𝐴 (see figure) consisting of the following processes.
𝐴 → 𝐵: Isothermal expansion at temperature 𝑇 so that the volume is doubled from 𝑉1 to 𝑉2 = 2𝑉1 and
pressure changes from 𝑃1 to 𝑃2
𝐵 → 𝐶: Isobaric compression at pressure 𝑃2 to initial volume 𝑉1 .
𝐶 → 𝐴: Isochoric change leading to change of pressure from 𝑃2 to 𝑃1
Total work done in the complete cycle 𝐴𝐵𝐶𝐴 is:
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, JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper
Question Paper MathonGo
1
(1) 𝑛𝑅𝑇ln2 - 2 (2) 𝑛𝑅𝑇ln2
1
(3) 𝑛𝑅𝑇ln2 + (4) 0
2
Q11. In the given figure, a mass 𝑀 is attached to a horizontal spring which is fixed on one side to a rigid support.
The spring constant of the spring is 𝑘 . The mass oscillates on a frictionless surface with time period 𝑇 and
amplitude 𝐴 . When the mass is in equilibrium position, as shown in the figure, another mass 𝑚 is gently fixed
upon it. The new amplitude of oscillation will be:
(1) 𝐴√ 𝑀 + 𝑚 (2) 𝐴√ 𝑀
𝑀 𝑀-𝑚
(3) 𝐴√ 𝑀 - 𝑚 (4) 𝐴√ 𝑀
𝑀 𝑀+𝑚
Q12. A cube of side 𝑎 has point charges +Q located at each of its vertices except at the origin where the charge is
-Q . The electric field at the centre of cube is:
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