NTA JEE Mains 31th Jan 2024 Shift 1

A body starts falling freely from height $$H$$ hits an inclined plane in its path at height $$h$$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $$\frac{H}{h}$$ for which the body will take the maximum time to reach the ground is _____.

A solid circular disc of mass $$50$$ kg rolls along a horizontal floor so that its center of mass has a speed of $$0.4 \text{ m s}^{-1}$$. The absolute value of work done on the disc to stop it is ______ J.

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $$0.02\%$$ is _____ m. (Take density of sea water $$= 10^3 \text{ kg m}^{-3}$$, Bulk modulus of rubber $$= 9 \times 10^8 \text{ N m}^{-2}$$, and $$g = 10 \text{ m s}^{-2}$$)

A particle performs simple harmonic motion with amplitude $$A$$. Its speed is increased to three times at an instant when its displacement is $$\frac{2A}{3}$$. The new amplitude of motion is $$\frac{nA}{3}$$. The value of $$n$$ is _____.

A parallel plate capacitor with plate separation $$5$$ mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $$2$$ mm, while keeping the battery connections intact, the capacitor draws $$25\%$$ more charge from the battery than before. The dielectric constant of the sheet is ____.

Equivalent resistance of the following network is ______ $$\Omega$$.

An electron moves through a uniform magnetic field $$\vec{B} = B_0\hat{i} + 2B_0\hat{j}$$ T. At a particular instant of time, the velocity of electron is $$\vec{u} = 3\hat{i} + 5\hat{j} \text{ m s}^{-1}$$. If the magnetic force acting on electron is $$\vec{F} = 5e\hat{k}$$ N, where $$e$$ is the charge of electron, then the value of $$B_0$$ is ____ T.

A small square loop of wire of side $$l$$ is placed inside a large square loop of wire of side $$L(L = l^2)$$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $$\sqrt{x} \times 10^{-7}$$ H, where $$x$$ = ______.

Two waves of intensity ratio $$1 : 9$$ cross each other at a point. The resultant intensities at the point, when (a) Waves are incoherent is $$I_1$$ (b) Waves are coherent is $$I_2$$ and differ in phase by $$60°$$. If $$\frac{I_1}{I_2} = \frac{10}{x}$$, then $$x$$ = _________.

The mass defect in a particular reaction is $$0.4$$ g. The amount of energy liberated is $$n \times 10^7$$ kW h, where $$n$$ = _____. (speed of light $$= 3 \times 10^8 \text{ m s}^{-1}$$)