Practice Questions

Q66.The area (in sq. units) of the region {(x, y) ∈R2 : x2 ≤y ≤3 −2x}, is. (1) 32 (2) 34 3 3 (3) 29 (4) 31 3 3 JEE Main 2020 (08 Jan Shift 2) JEE Main Previous Year Paper

Q67.The area (in sq. units) of the region enclosed by the curves y = x2 −1 and y = 1 −x2 is equal to: (1) 4 (2) 8 3 3 (3) 7 (4) 16 2 3 x cosec x is the solution of the differential equation, dxdy + p(x)y = −2π cosec x, 0 < x < 2π ,

Q70.A random variable X has the following probability distribution: X : 1 2 3 4 5 P(X) : k2 2k k 2k 5k2 Then, P(X > 2) is equal to: (1) 7 (2) 1 12 36 (3) 1 (4) 23 6 36

Q70.Let A and B be two independent events such that P(A) = 13 and P(B) = 16 . Then, which of the following is true? (1) P( BA ) = 32 (2) P( B'A ) = 13 = 14 (3) P( B'A' ) = 13 (4) P( (A∪B) A )

Q1. The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is: (1) 37.03 cm2 (2) 37.030 cm2 (3) 37.0 cm2 (4) 37 cm2

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%

Q2. The position of a particle as a function of time t, is given by x(t) = at + bt2 −ct3 where a, b and c are constants. When the particles zero acceleration, then its velocity will be: b2 (1) a + 3cb2 (2) a + 2c (3) a + b2c (4) a + 4cb2

Q3. The stream of a river is flowing with a speed of 2 km h−1 . A swimmer can swim at a speed of 4 km h−1 . The direction of the swimmer with respect to the flow of the river, to cross the river straight, is (1) 150° (2) 90° (3) 120° (4) 60° part is hanging

Q3. Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is: (1) 1 : 16 (2) 1 : 2 (3) 1 : 4 (4) 1 : 8

Q3. A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = k t acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is (1) 2√kp (2) 2√pk (3) √2kp (4) √2pk

Q4. The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians): (1) π (2) π 6 3 (3) π (4) π 8 4

Q5. A particle which is experiencing a force, given by F = 3ˆi −12ˆj, undergoes a displacement of d = 4ˆi. If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement? (1) 9 J. (2) 15 J. (3) 12 J. (4) 10 J.

Q5. Four particles A, B, C and D with masses mA = m, mB = 2m, mC = 3m and mD = 4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is: (1) a ^i + ^j (2) a ^i - ^j (3) a^i + ^j (4) Zero 5 5

Q6. The value of acceleration due to gravity at Earth's surface is 9.8 m s−2 . The altitude above its surface at which the acceleration due to gravity decreases to 4.9 m s−2 , is close to: (Radius of earth = 6.4 × 106 m ) (1) 1.6 × 106 m (2) 2.6 × 106 m (3) 6.4 × 106 m (4) 9.0 × 106 m

Q8. Two rods A and B of identical dimensions are at temperature 30∘C. If A is heated upto 180∘C and B upto T∘C, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is (1) 230∘C (2) 270∘C (3) 200∘C (4) 250∘C

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: (1) 𝐿 (2) 4𝐿 𝑚 𝑚 𝐿 2𝐿 (3) (4) 2𝑚 𝑚

Q9. If 'M' is the mass of water that rises in a capillary tube of radius 'r' , then mass of water which will rise in a capillary tube of radius '2r' is: (1) 4 M (2) 2 M (3) M (4) M 2

Q9. The elastic limit of brass is 379 MPa. The minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit will be (1) 1.00 mm (2) 1.36 mm (3) 1.16 mm (4) 0.90 mm

Q9. A steel wire having a radius of 2.0 mm , carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1π m s-2, what will be the tensile stress that would be developed in the wire? (1) 5.2 × 106 N m-2 (2) 6.2 × 106 N m-2 (3) 4 . 8 × 106 N m-2 (4) 3.1 × 106 N m-2

Q9. A cylinder with fixed capacity of 67.2 litre contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is: [Given that R = 8.31 J mol−1 K−1] (1) 748 J (2) 700 J (3) 350 J (4) 374 J

Q9. For the given cyclic process CAB as shown for a gas, the work done is: (1) 10 J (2) 5 J (3) 1 J (4) 30 J

Q9. Half mole of an ideal monoatomic gas is heated at a constant pressure of 1 atm from 20° C to 90° C . Work done by the gas is (Gas constant, R = 8.21 J mol−1 K−1 ) (1) 73 J (2) 581 J (3) 291 J (4) 146 J

Q10.An ideal gas occupies a volume of 2 m3 at a pressure of 3 × 106 Pa. The energy of the gas is: (1) 108J (2) 9 × 106J (3) 3 × 102J (4) 6 × 104J

Q10.A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0 .1 W K−1 m−1 , the energy flux through it in the steady-state is: (1) 65 W m−2 (2) 120 W m−2 (3) 90 W m−2 (4) 200 W m−2

Q11.The displacement of a damped harmonic oscillator is given by x(t) = e−0.1t cos(10πt + φ). Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to: (1) 27 s (2) 4 s (3) 13 s (4) 7 s