NTA JEE Mains 1st Feb 2024 Shift 2

A particle initially at rest starts moving from reference point $$x = 0$$ along x-axis, with velocity $$v$$ that varies as $$v = 4\sqrt{x}$$ m s$$^{-1}$$. The acceleration of the particle is ______ m s$$^{-2}$$.

A uniform rod AB of mass 2 kg and length 30 cm at rest on a smooth horizontal surface. An impulse of force 0.2 N s is applied to end B. The time taken by the rod to turn through at right angles will be $$\frac{\pi}{x}$$ s, where $$x$$ = ______.

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be [Area of cross section of wire = $$0.005 \text{ cm}^2$$, $$Y = 2 \times 10^{11} \text{ N m}^{-2}$$ and $$g = 10 \text{ m s}^{-2}$$]

A mass $$m$$ is suspended from a spring of negligible mass and the system oscillates with a frequency $$f_1$$. The frequency of oscillations if a mass $$9m$$ is suspended from the same spring is $$f_2$$. The value of $$\frac{f_1}{f_2}$$ is ______.

Suppose a uniformly charged wall provides a uniform electric field of $$2 \times 10^4 \text{ N C}^{-1}$$ normally. A charged particle of mass 2 g being suspended through a silk thread of length 20 cm and remain stayed at a distance of 10 cm from the wall. Then the charge on the particle will be $$\frac{1}{\sqrt{x}} \mu C$$ where $$x$$ = ______ [use $$g = 10 \text{ m s}^{-2}$$]

In an electrical circuit drawn below the amount of charge stored in the capacitor is ______ $$\mu C$$

A moving coil galvanometer has 100 turns and each turn has an area of $$2.0 \text{ cm}^2$$. The magnetic field produced by the magnet is 0.01 T and the deflection in the coil is 0.05 radian when a current of 10 mA is passed through it. The torsional constant of the suspension wire is $$x \times 10^{-5}$$ N-m/rad. The value of $$x$$ is ______.

A coil of 200 turns and area $$0.20 \text{ m}^2$$ is rotated at half a revolution per second and is placed in uniform magnetic field of 0.01 T perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is $$\frac{2\pi}{\beta}$$ volt. The value of $$\beta$$ is ______.

In Young's double slit experiment, monochromatic light of wavelength 5000 Å is used. The slits are 1.0 mm apart and screen is placed at 1.0 m away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is ______ $$\times 10^{-6}$$ m.

A particular hydrogen-like ion emits the radiation of frequency $$3 \times 10^{15}$$ Hz when it makes transition from $$n = 2$$ to $$n = 1$$. The frequency of radiation emitted in transition from $$n = 3$$ to $$n = 1$$ is $$\frac{x}{9} \times 10^{15}$$ Hz, when $$x$$ = ______.