Practice Questions

Q24.A rod CD of thermal resistance 10. 0 KW−1 is joined at the middle of an identical rod AB as shown in figure. The ends A, B and D are maintained at 200°C, 100°C and 125°C respectively. The heat current in CD is JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper P W. The value of P is

Q24.A hydraulic press can lift 100 kg when a mass 𝑚 is placed on the smaller piston. It can lift kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass 𝑚 on the smaller piston.

Q24.A 2 kg steel rod of length 0 . 6 m is clamped on a table vertically at its lower end and is free to rotate in the vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due to clamping at its lower end, the speed of the free end of the rod when it passes through its lowest position is _______m s-1 . (Take 𝑔= 10 m s-2 )

Q24.A circular disc reaches from top to bottom of an inclined plane of length L. When it slips down the plane, it . The value of x will be takes time t1 . When it rolls down the plane, it takes time t2 . The value of t2t1 is √3x

Q24.A container is divided into two chambers by a partition. The volume of first chamber is 4. 5 litre and second chamber is 5. 5 litre. The first chamber contain 3. 0 moles of gas at pressure 2. 0 atm and second chamber contain 4. 0 moles of gas at pressure 3. 0 atm . After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is x × 10−1 atm . Value of x (nearest integer) is

Q24.A particle executes S.H.M. with amplitude A and time period T . The displacement of the particle when its speed is half of maximum speed is √xA 2 . The value of x is

Q24.A solid disc of radius a and mass m rolls down without slipping on an inclined plane making an angle θ with the horizontal. The acceleration of the disc will be 2 b g sin θ, where b is _______. (Round off to the Nearest Integer) ( g = acceleration due to gravity) ( θ = angle as shown in figure) JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper

Q24.A soap bubble of the radius 3 cm is formed inside another soap bubble of radius, 6 cm . The radius of an equivalent soap bubble that has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is____ cm.

Q24.In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times that of Q. In the case of the same rotational kinetic energy, the ratio of rotational inertias ( I2I1 ) will be x : 1 . The value of x will be ______.

Q24.A 16 Ω wire is bent to form a square loop. A 9 V supply having an internal resistance of 1 Ω is connected across one of its sides. The potential drop across the diagonals of the square loop is __________ ×10−1 V .

Q24.A ball of mass 10 kg moving with a velocity 10√3 m s−1 along the x -axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y -axis with a speed of 10 m s−1. The second piece starts moving at an angle of 30° with respect to the x -axis. The velocity of the ball moving at 30° with x -axis is x m s−1. The configuration of pieces after the collision is shown in the figure below. The value of x to the nearest integer is JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper

Q24.A resistor dissipates 192 J of energy in 1 s when a current of 4 A is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in 5 s is _____________ J .

Q25.A prism of refractive index n1 and another prism of refractive index n2 are stuck together (as shown in the figure). n1 and n2 depend on λ, the wavelength of light, according to the relation n1 = 1. 2 + 10.8×10−14λ2 and 1.8×10−14 n2 = 1. 45 + λ2 The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be ____ nm.

Q25.The electric field intensity is produced by the radiation coming from a 100 W bulb at a distance of 3 m is E . E . Where The electric field intensity produced by the radiation coming from 60 W at the same distance is √x5 the value of x =_________ . → 2 3 with E0 = 4. 0 × 103 N C−1. The flux of this

Q25.A wire having a linear mass density 9. 0 × 10−4 kg m−1 is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ___________ m.

Q25.Two travelling waves produces a standing wave represented by equation. y = (1. 0 mm) cos[(1. 57 cm−1)x] sin[(78. 5 s−1) t]. The node closest to the origin in the region x > 0 will be at x =. . . . . . (in cm).

Q25.Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then ab can be expressed as x1 , where x is _____.

Q25.Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is Tb = √x, where value of x is ______. Ta (Round off to the Nearest Integer)

Q25.A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be _____ cm. (Take speed of sound in air as 340 m s−1 )

Q25.In the figure given, the electric current flowing through the 5 kΩ resistor is x mA . The value of x to the nearest integer is ________.

Q25.The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4% , will be ___ % .

Q25.Two cars X and Y are approaching each other with velocities 36 km h−1 and 72 km h−1 respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is 340 ms−1, the actual frequency of the whistle sound produced is ________ Hz.

Q25.A long solenoid with 1000 turns m-1 has a core material with relative permeability 500 and volume 103 cm3 . If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of 0 . 75 A in the solenoid, the fractional change in the magnetic moment of 𝑥 the core would be approximately . Find the value of 𝑥. 499

Q25.Two cars are approaching each other at an equal speed of 7. 2 km hr−1. When they see each other, both blow horns having a frequency of 676 Hz. The beat frequency heard by each driver will be _______ Hz. [Velocity of sound in air is 340 m s−1.

Q25.A common transistor radio set requires 12 V D . C . for its operation. The D . C . source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V A . C . on standard domestic A . C . supply. The number of turns of secondary coil are 24, then the number of turns of primary are