NTA JEE Main 6th April 2023 Shift 1

The length of a metallic wire is increased by 20% and its area of cross-section is reduced by 4%. The percentage change in resistance of the metallic wire is ______.

A particle of mass 10 g moves in a straight line with retardation 2x, where $$x$$ is the displacement in SI units. Its loss of kinetic energy for above displacement is $$\left(\dfrac{10}{x}\right)^{-n}$$ J. The value of $$n$$ will be ______.

Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is ______ $$\times 10^{-3}$$ kg m$$^2$$.

A steel rod has a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young's modulus of steel is $$2.0 \times 10^{11}$$ N m$$^{-2}$$. The longitudinal strain produced in the wire is ______ $$\times 10^{-5}$$.

A person driving car at a constant speed of 15 m s$$^{-1}$$ is approaching a vertical wall. The person notices a change of 40 Hz in the frequency of his car's horn upon reflection from the wall. The frequency of horn is ______ Hz.
(Given: Speed of sound: 330 m s$$^{-1}$$)

A parallel plate capacitor with plate area $$A$$ and plate separation $$d$$ is filled with a dielectric material of dielectric constant $$K = 4$$. The thickness of the dielectric material is $$x$$, where $$x < d$$.

Let $$C_1$$ and $$C_2$$ be the capacitance of the system for $$x = \dfrac{1}{3}d$$ and $$x = \dfrac{2d}{3}$$, respectively. If $$C_1 = 2$$ $$\mu$$F, the value of $$C_2$$ is ______ $$\mu$$F.

Two identical circular wires of radius 20 cm and carrying current $$\sqrt{2}$$ A are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is ______ $$\times 10^{-8}$$ T.

(Take $$\pi = 3.14$$)

An ideal transformer with purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 V. The average rate of energy consumption in the houses served by the transformer is 60 kW. The value of resistive load $$(R_s)$$ required in the secondary circuit will be ______ m$$\Omega$$.

A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of 30° with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water surface in centimeters is $$(n_w = \dfrac{4}{3})$$ ______.

The radius of fifth orbit of Li$$^{++}$$ is ______ $$\times 10^{-12}$$ m. Take: radius of hydrogen atom = 0.51 $$\mathring{A}$$