NTA JEE Main 12th April 2023 Shift 1

To maintain a speed of $$80$$ km h$$^{-1}$$ by a bus of mass $$500$$ kg on a plane rough road for $$4$$ km distance, the work done by the engine of the bus will be _____ kJ. [The coefficient of friction between tyre of bus and road is 0.04]

For rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $$\frac{x}{5}$$. The value of $$x$$ is _____.

64 identical drops each charged upto potential of $$10$$ mV are combined to form a bigger drop. The potential of the bigger drop will be _____ mV.

Glycerin of density $$1.25 \times 10^3$$ kg m$$^{-3}$$ is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends are $$10$$ cm$$^2$$ and $$5$$ cm$$^2$$ and pressure drop across its length is $$3$$ N m$$^{-2}$$. The rate of flow of glycerine through the pipe is $$x \times 10^{-5}$$ m$$^3$$ s$$^{-1}$$. The value of $$x$$ is _____.

For a certain organ pipe, the first three resonance frequencies are in the ratio of $$1 : 3 : 5$$ respectively. If the frequency of fifth harmonic is $$405$$ Hz and the speed of sound in air is $$324$$ m s$$^{-1}$$, the length of the organ pipe is _____ m.

The current flowing through a conductor connected across a source is $$2$$ A and $$1.2$$ A at $$0°$$C and $$100°$$C respectively. The current flowing through the conductor at $$50°$$C will be _____ $$\times 10^2$$ mA.

A compass needle oscillates 20 times per minute at a place where the dip is $$30°$$ and 30 times per minute where the dip is $$60°$$. The ratio of total magnetic field due to the earth at two places respectively is $$\frac{4}{\sqrt{x}}$$. The value of $$x$$ is _____.

A conducting circular loop is placed in a uniform magnetic field of $$0.4$$ T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $$1$$ mm s$$^{-1}$$. The magnitude of induced emf in the loop at an instant when the radius of the loop is $$2$$ cm will be _____ $$\mu$$V.

Two convex lenses of focal length $$20$$ cm each are placed coaxially with a separation of $$60$$ cm between them. The image of the distant object formed by the combination is at _____ cm from the first lens.

A common example of alpha decay is
$$^{238}_{92}$$U $$\to ^{234}_{90}$$Th $$+ _2$$He$$^4 + Q$$
Given:
$$^{238}_{92}$$U $$= 238.05060$$ u
$$^{234}_{90}$$Th $$= 234.04360$$ u
$$^4_2$$He $$= 4.00260$$ u and $$1$$u $$= 931.5$$ $$\frac{\text{MeV}}{c^2}$$
The energy released $$(Q)$$ during the alpha decay of $$^{238}_{92}$$U is _____ MeV.