NTA JEE Main 10th April 2023 Shift 1

A closed circular tube of average radius 15 cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is 22 m s$$^{-1}$$, when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is _______ J. (Given $$g = 10$$ m s$$^{-2}$$).

If the earth suddenly shrinks to $$\frac{1}{64}$$th of its original volume with its mass remaining the same, the period of rotation of earth becomes $$\frac{24}{x}$$ h. The value of x is _______.

Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is _______ $$\times 10^{-6}$$ m. [Young's modulus for steel $$= 2 \times 10^{11}$$ N m$$^{-2}$$ and $$g = 10$$ m s$$^{-2}$$]

A transverse harmonic wave on a string is given by $$y(x, t) = 5\sin6t + 0.003x$$ where $$x$$ and $$y$$ are in cm and $$t$$ in sec. The wave velocity is _______ m s$$^{-1}$$.

Three concentric spherical metallic shells $$X$$, $$Y$$ and $$Z$$ of radius $$a$$, $$b$$ and $$c$$ respectively $$a < b < c$$ have surface charge densities $$\sigma$$, $$-\sigma$$ and $$\sigma$$, respectively. The shells $$X$$ and $$Z$$ are at same potential. If the radii of $$X$$ & $$Y$$ are 2 cm and 3 cm, respectively. The radius of shell Z is _______ cm.

10 resistors each of resistance 10 $$\Omega$$ can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be _______.

The current required to be passed through a solenoid of 15 cm length and 60 turns in order to demagnetise a bar magnet of magnetic intensity $$2.4 \times 10^3$$ A m$$^{-1}$$ is _______ A.

A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5 $$\Omega$$, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m s$$^{-1}$$ will be _______ $$\times 10^{-3}$$ N.

Unpolarised light of intensity 32 W m$$^{-2}$$ passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is 3 W m$$^{-2}$$, then the angle between pass axis of first two polaroids is _______ $$^\circ$$.

The decay constant for a radioactive nuclide is $$1.5 \times 10^{-5}$$ s$$^{-1}$$. Atomic weight of the substance is 60 g mole$$^{-1}$$, $$N_A = 6 \times 10^{23}$$. The activity of 1.0 $$\mu$$g of the substance is _______ $$\times 10^{10}$$ Bq.