JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper
Question Paper MathonGo
Q1. A particle is moving with a velocity →
𝑣 = 𝐾𝑦^𝑖 + 𝑥^𝑗, where 𝐾 is a constant.
The general equation for its path is:
(1) 𝑦2 = 𝑥 + constant (2) 𝑥𝑦 = constant
(3) 𝑦 = 𝑥2 + constant (4) 𝑦2 = 𝑥2 + constant
Q2. A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its
volume remains unchanged is:
(1) 2.5% (2) 1.0%
(3) 2.0% (4) 0.5%
Q3. A block of mass 10 𝑘𝑔 is kept on a rough inclined plane as shown in the figure. A force of 3 𝑁 is applied on the
block. The coefficient of static friction between the plane and the block is 0.6 . What should be the minimum
value of force 𝑃, such that the block does not move downward? (take 𝑔 = 10 𝑚𝑠-2 )
(1) 23 𝑁 (2) 25 𝑁
(3) 18 𝑁 (4) 32 𝑁
Q4. A block of mass 𝑚, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring
constant 𝑘 . The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its
equilibrium position. If now the block is pulled with a constant force 𝐹, the maximum speed of the block is:
𝐹 2𝐹
(1) (2)
√𝑚𝑘 √𝑚𝑘
𝜋𝐹 𝐹
(3) (4)
√𝑚𝑘 𝜋√𝑚𝑘
Q5. Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal
masses, 𝑚 while C has mass 𝑀 . Block A is given an initial speed 𝑣 towards B due to which it collides with B
5
perfectly inelastically. The combined mass collides with 𝐶, also perfectly inelastically . th of the initial kinetic
6
energy is lost in the whole process. What is the value of 𝑀 / 𝑚?
(1) 3 (2) 4
(3) 5 (4) 2
𝑚
Q6. Two masses 𝑚 and 2
are connected at the two ends of a massless rigid rod of length 𝑙 . The rod is suspended by
a thin wire of torsional constant 𝑘 at the centre of mass of the rod-mass system (see figure). Because of torsional
constant 𝑘, the restoring torque is 𝜏 = 𝑘𝜃 for angular displacement 𝜃 . If the rod is rotated by 𝜃0 and released,
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, JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper
Question Paper MathonGo
the tension in it when it passes through its mean position will be:
2
(1) 𝑘𝜃20 (2) 3𝑘𝜃0
𝑙
(3) 2𝑘𝜃02 (4) 𝑘𝜃02
𝑙 𝑙
Q7. An 𝐿 -shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure.
If 𝐴𝐵 = 𝐵𝐶, and the angle made by 𝐴𝐵 with downward vertical is 𝜃, then:
2 1
(1) tan𝜃 = (2) tan𝜃 =
√3 3
1 1
(3) tan𝜃 = (4) tan𝜃 =
2 2√3
Q8. If the angular momentum of a planet of mass 𝑚, moving around the Sun in a circular orbit is 𝐿, about the center
of the Sun, its areal velocity is:
𝐿 4𝐿
(1) (2)
𝑚 𝑚
𝐿 2𝐿
(3) 2𝑚
(4) 𝑚
Q9. A heavy ball of mass 𝑀 is suspended from the ceiling of a car by a light string of mass 𝑚 𝑚 ≪ 𝑀 . When the
car is at rest, the speed of transverse waves in the string is 60 ms-1 . When the car has acceleration 𝑎, the wave-
speed increases to 60.5 ms-1 . The value of 𝑎, in terms of gravitational acceleration 𝑔, is closed to
𝑔 𝑔
(1) 10
(2) 20
𝑔 𝑔
(3) (4)
5 30
Q10. A rod, of length 𝐿 at room temperature and uniform area of cross section 𝐴, is made of a metal having
coefficient of linear expansion 𝛼 / °𝐶 It is observed that an external compressive force 𝐹 is applied on each
of its ends, prevents any change in the length of the rod when its temperature rises by ∆𝑇 K Young's modulus,
𝑌 for this metal is:
𝐹 2𝐹
(1) 𝐴𝛼∆𝑇 - 273
(2) 𝐴𝛼∆𝑇
𝐹 𝐹
(3) 𝐴𝛼∆𝑇
(4) 2𝐴 𝛼∆𝑇
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Question Paper MathonGo
Q1. A particle is moving with a velocity →
𝑣 = 𝐾𝑦^𝑖 + 𝑥^𝑗, where 𝐾 is a constant.
The general equation for its path is:
(1) 𝑦2 = 𝑥 + constant (2) 𝑥𝑦 = constant
(3) 𝑦 = 𝑥2 + constant (4) 𝑦2 = 𝑥2 + constant
Q2. A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its
volume remains unchanged is:
(1) 2.5% (2) 1.0%
(3) 2.0% (4) 0.5%
Q3. A block of mass 10 𝑘𝑔 is kept on a rough inclined plane as shown in the figure. A force of 3 𝑁 is applied on the
block. The coefficient of static friction between the plane and the block is 0.6 . What should be the minimum
value of force 𝑃, such that the block does not move downward? (take 𝑔 = 10 𝑚𝑠-2 )
(1) 23 𝑁 (2) 25 𝑁
(3) 18 𝑁 (4) 32 𝑁
Q4. A block of mass 𝑚, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring
constant 𝑘 . The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its
equilibrium position. If now the block is pulled with a constant force 𝐹, the maximum speed of the block is:
𝐹 2𝐹
(1) (2)
√𝑚𝑘 √𝑚𝑘
𝜋𝐹 𝐹
(3) (4)
√𝑚𝑘 𝜋√𝑚𝑘
Q5. Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal
masses, 𝑚 while C has mass 𝑀 . Block A is given an initial speed 𝑣 towards B due to which it collides with B
5
perfectly inelastically. The combined mass collides with 𝐶, also perfectly inelastically . th of the initial kinetic
6
energy is lost in the whole process. What is the value of 𝑀 / 𝑚?
(1) 3 (2) 4
(3) 5 (4) 2
𝑚
Q6. Two masses 𝑚 and 2
are connected at the two ends of a massless rigid rod of length 𝑙 . The rod is suspended by
a thin wire of torsional constant 𝑘 at the centre of mass of the rod-mass system (see figure). Because of torsional
constant 𝑘, the restoring torque is 𝜏 = 𝑘𝜃 for angular displacement 𝜃 . If the rod is rotated by 𝜃0 and released,
Join the Most Relevant Test Series for JEE Main with Most Detailed & Advanced Analysis here: https://links.mathongo.com/mWN
, JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper
Question Paper MathonGo
the tension in it when it passes through its mean position will be:
2
(1) 𝑘𝜃20 (2) 3𝑘𝜃0
𝑙
(3) 2𝑘𝜃02 (4) 𝑘𝜃02
𝑙 𝑙
Q7. An 𝐿 -shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure.
If 𝐴𝐵 = 𝐵𝐶, and the angle made by 𝐴𝐵 with downward vertical is 𝜃, then:
2 1
(1) tan𝜃 = (2) tan𝜃 =
√3 3
1 1
(3) tan𝜃 = (4) tan𝜃 =
2 2√3
Q8. If the angular momentum of a planet of mass 𝑚, moving around the Sun in a circular orbit is 𝐿, about the center
of the Sun, its areal velocity is:
𝐿 4𝐿
(1) (2)
𝑚 𝑚
𝐿 2𝐿
(3) 2𝑚
(4) 𝑚
Q9. A heavy ball of mass 𝑀 is suspended from the ceiling of a car by a light string of mass 𝑚 𝑚 ≪ 𝑀 . When the
car is at rest, the speed of transverse waves in the string is 60 ms-1 . When the car has acceleration 𝑎, the wave-
speed increases to 60.5 ms-1 . The value of 𝑎, in terms of gravitational acceleration 𝑔, is closed to
𝑔 𝑔
(1) 10
(2) 20
𝑔 𝑔
(3) (4)
5 30
Q10. A rod, of length 𝐿 at room temperature and uniform area of cross section 𝐴, is made of a metal having
coefficient of linear expansion 𝛼 / °𝐶 It is observed that an external compressive force 𝐹 is applied on each
of its ends, prevents any change in the length of the rod when its temperature rises by ∆𝑇 K Young's modulus,
𝑌 for this metal is:
𝐹 2𝐹
(1) 𝐴𝛼∆𝑇 - 273
(2) 𝐴𝛼∆𝑇
𝐹 𝐹
(3) 𝐴𝛼∆𝑇
(4) 2𝐴 𝛼∆𝑇
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