NTA JEE Main 31st January 2023 Shift 2

Two bodies are projected from ground with same speeds 40 m s$$^{-1}$$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60°, with horizontal then sum of the maximum heights, attained by the two projectiles, is ______ m. (Given $$g = 10$$ m s$$^{-2}$$)

A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball and floor is 0.5, after hitting the floor, the ball rebounds to a height of ______ m.

Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0.5 cm respectively. The densities of materials are in the ratio 3 : 5. The moment of inertia of these discs respectively about their diameters will be in the ratio of $$\dfrac{x}{6}$$. The value of $$x$$ is ______.

A water heater of power 2000 W is used to heat water. The specific heat capacity of water is 4200 J kg$$^{-1}$$ K$$^{-1}$$. The efficiency of heater is 70%. Time required to heat 2 kg of water from 10°C to 60°C is ______ s. (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

The displacement equations of two interfering waves are given by $$y_1 = 10 \sin\left(\omega t + \dfrac{\pi}{3}\right)$$ cm, $$y_2 = 5\left[\sin(\omega t) + \sqrt{3}\cos(\omega t)\right]$$ cm respectively. The amplitude of the resultant wave is ______ cm.

Two parallel plate capacitors $$C_1$$ and $$C_2$$ each having capacitance of 10 $$\mu$$F are individually charged by a 100 V D.C. source. Capacitor $$C_1$$ is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor $$C_2$$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor $$C_1$$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ______ V.
(Assuming Dielectric constant = 10)

For the given circuit, in the steady state, $$|V_B - V_D|$$ = ______ V.

A series LCR circuit consists of $$R = 80$$ $$\Omega$$. $$X_L = 100$$ $$\Omega$$, and $$X_C = 40$$ $$\Omega$$. The input voltage is 2500 $$\cos(100\pi t)$$ V. The amplitude of current, in the circuit, is ______ A.

Two light waves of wavelengths 800 and 600 nm are used in Young's double slit experiment to obtain interference fringes on a screen placed 7 m away from plane of slits. If the two slits are separated by 0.35 mm, then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ______ mm.

If the binding energy of ground state electron in a hydrogen atom is 13.6 eV, then, the energy required to remove the electron from the second excited state of Li$$^{2+}$$ will be: $$x \times 10^{-1}$$ eV. The value of $$x$$ is ______.