NTA JEE Main 29th June 2022 Shift 2

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is $$I_1$$. The same rod is bent into a ring and its moment of inertia about a diameter is $$I_2$$. If $$\frac{I_1}{I_2}$$ is $$\frac{x\pi^2}{3}$$, then the value of $$x$$ will be ______.

A small spherical ball of radius 0.1 mm and density $$10^4$$ kg m$$^{-3}$$ falls freely under gravity through a distance $$h$$ before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of $$h$$ will be ______ m. (Given $$g = 10$$ m s$$^{-2}$$, viscosity of water $$= 1.0 \times 10^{-5}$$ N-s m$$^{-2}$$).

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 m s$$^{-1}$$. The third resonance is observed when the air column has a length of ______ cm.

The displacement current of 4.425 $$\mu$$A is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of $$10^6$$ V s$$^{-1}$$. The area of each plate of the capacitor is 40 cm$$^2$$. The distance between each plate of the capacitor is $$x \times 10^{-3}$$ m. The value of $$x$$ is,
(Permittivity of free space, $$\varepsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$ N$$^{-1}$$ m$$^{-2}$$)

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 $$\Omega$$ is used to measure the potential difference across 500 $$\Omega$$ resister, the reading of the voltmeter will be ______ V.

An inductor of 0.5 mH, a capacitor of 200 $$\mu$$F and a resistor of 2 $$\Omega$$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ $$\times 10^2$$ Hz.

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by $$5 \times 10^{-2}$$ m towards the slits, the change in fringe width is $$3 \times 10^{-3}$$ cm. If the distance between the slits is 1 mm, then the wavelength of the light will be ______ nm.

The half life of a radioactive substance is 5 years. After $$x$$ years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of $$x$$ is ______.

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the $$n$$-side with a speed of $$6.0 \times 10^5$$ m s$$^{-1}$$. The speed with which electron enters the $$p$$ side will be $$\frac{x}{3} \times 10^5$$ m s$$^{-1}$$, then the value of $$x$$ is ______.: (Given mass of electron $$= 9 \times 10^{-31}$$ kg, charge on electron $$= 1.6 \times 10^{-19}$$ C.)

The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of ($$-$$0.05 cm). While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be ______ $$\times 10^{-2}$$ cm.