NTA JEE Main 31st August 2021 Shift 2

A particle is moving with constant acceleration $$a$$. Following graph shows $$v^2$$ versus $$x$$ (displacement) plot. The acceleration of the particle is _________ m s$$^{-2}$$.

A sample of gas with $$\gamma = 1.5$$ is taken through an adiabatic process in which the volume is compressed from 1200 cm$$^3$$ to 300 cm$$^3$$. If the initial pressure is 200 kPa. The absolute value of the workdone by the gas in the process = _________ J.

A parallel plate capacitor of capacitance 200$$\mu$$F is connected to a battery of 200 V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be _________ J.

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.

A long solenoid with 1000 turns m$$^{-1}$$ has a core material with relative permeability 500 and volume $$10^3$$ cm$$^3$$. 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 the core would be approximately $$\frac{x}{499}$$. Find the value of $$x$$.

At very high frequencies, the effective impedance of the given circuit will be _________ $$\Omega$$.

Cross-section view of a prism is the equilateral triangle $$ABC$$ shown in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from P (midpoint of BC) to A is _________ $$\times 10^{-10}$$ s. (Given, speed of light in vacuum = $$3 \times 10^8$$ m s$$^{-1}$$ and $$\cos 30° = \frac{\sqrt{3}}{2}$$)

In a Young's double slit experiment, the slits are separated by 0.3 mm and the screen is 1.5 m away from the plane of slits. Distance between fourth bright fringes on both sides of central bright fringe is 2.4 cm. The frequency of light used is $$x \times 10^{14}$$ Hz.

A bandwidth of 6 MHz is available for A.M. transmission. If the maximum audio signal frequency used for modulating the carrier wave is not to exceed 6 kHz. The number of stations that can be broadcasted within this band simultaneously without interfering with each other will be _________.

The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisions of vernier scale. One main scale division is 1 mm. The main scale reading is 10 mm and 8th division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of 0.04 cm, then the radius of the bob is _________ $$\times 10^{-2}$$ cm.