NTA JEE Mains 27th Jan 2024 Shift 2

A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is _____ m. Use g = 10 m s$$^{-2}$$

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $$\frac{7}{x}$$, where x is _____.

The reading of pressure metre attached with a closed pipe is $$4.5 \times 10^4$$ N m$$^{-2}$$. On opening the valve, water starts flowing and the reading of pressure metre falls to $$2.0 \times 10^4$$ N m$$^{-2}$$. The velocity of water is found to be $$\sqrt{V}$$ m s$$^{-1}$$. The value of $$V$$ is _____.

A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is _____ m s$$^{-1}$$.

The electric potential at the surface of an atomic nucleus ($$Z = 50$$) of radius $$9 \times 10^{-13}$$ cm is $$\alpha \times 10^6$$ V. What is the value of $$\alpha$$?
(Charge of proton $$1.6 \times 10^{-19}$$ C)

Two charges of $$-4 \mu$$C and $$+4 \mu$$C are placed at the points $$A(1, 0, 4)$$ m and $$B(2, -1, 5)$$ m located in an electric field $$\vec{E} = 0.20\hat{i}$$ V cm$$^{-1}$$. The magnitude of the torque acting on the dipole is $$8\sqrt{\alpha} \times 10^{-5}$$ N m, where $$\alpha$$ = _____.

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $$R_1 = 2\pi$$ m and $$R_2 = 4\pi$$ m carrying current $$I = 4$$ A as per figure given below is $$\alpha \times 10^{-7}$$ T. The value of $$\alpha$$ is _____.
(Centre O is common for all segments)

A series LCR circuit with $$L = \frac{100}{\pi}$$ mH, $$C = \frac{10^{-3}}{\pi}$$ F and $$R = 10$$ $$\Omega$$, is connected across an AC source of 220 V, 50 Hz supply. The power factor of the circuit would be _____.

A parallel beam of monochromatic light of wavelength 5000 $$\mathring{A}$$ is incident normally on a single narrow slit of width 0.001 mm. The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of _____ (degree).

If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be $$\frac{\alpha}{7R}$$, where $$\alpha$$ = _____.