NTA JEE Main 27th June 2022 Shift 1 - Physics

A silver wire has a mass $$(0.6 \pm 0.006)$$ g, radius $$(0.5 \pm 0.005)$$ mm and length $$(4 \pm 0.04)$$ cm. The maximum percentage error in the measurement of its density will be

A projectile is launched at an angle $$\alpha$$ with the horizontal with a velocity $$20$$ m s$$^{-1}$$. After $$10$$ s, its inclination with horizontal is $$\beta$$. The value of $$\tan\beta$$ will be : $$(g = 10$$ m s$$^{-2})$$.

A girl standing on road holds her umbrella at $$45°$$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $$15\sqrt{2}$$ km h$$^{-1}$$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is

A system of two blocks of masses $$m = 2$$ kg and $$M = 8$$ kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $$0.5$$. The maximum horizontal force $$F$$ that can be applied to the block of mass $$M$$ so that the blocks move together will be $$(g = 9.8$$ m s$$^{-2})$$

Two blocks of masses $$10$$ kg and $$30$$ kg are placed on the same straight line with coordinates $$(0, 0)$$ cm and $$(x, 0)$$ cm respectively. The block of $$10$$ kg is moved on the same line through a distance of $$6$$ cm towards the other block. The distance through which the block of $$30$$ kg must be moved to keep the position of centre of mass of the system unchanged is

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of $$5$$ times its mass?
(Assume the collision to be head-on elastic collision)

Statement I : The law of gravitation holds good for any pair of bodies in the universe.
Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct answer from the options given below.

The velocity of a small ball of mass $$m$$ and density $$d_1$$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $$d_2$$, then the viscous force acting on the ball will be

A mixture of hydrogen and oxygen has volume $$2000$$ cm$$^3$$, temperature $$300$$ K, pressure $$100$$ kPa and mass $$0.76$$ g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be
[Take gas constant $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$]

The displacement of simple harmonic oscillator after $$3$$ seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is

An observer moves towards a stationary source of sound with a velocity one-fifth of the velocity of sound. The percentage change in the apparent frequency is

A force of $$10$$ N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.

A $$72$$ $$\Omega$$ galvanometer is shunted by a resistance of $$8$$ $$\Omega$$. The percentage of the total current which passes through the galvanometer is

The susceptibility of a paramagnetic material is $$99$$. The permeability of the material in Wb/A - m, is
[Permeability of free space $$\mu_0 = 4\pi \times 10^{-7}$$ Wb/A - m]

The current flowing through an ac circuit is given by $$I = 5\sin(120\pi t)$$ A. How long will the current take to reach the peak value starting from zero?

Match List - I with List - II

Consider a light ray travelling in air is incident into a medium of refractive index $$\sqrt{2n}$$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be

An $$\alpha$$ particle and a carbon 12 atom has same kinetic energy $$K$$. The ratio of their de-Broglie wavelengths $$(\lambda_\alpha : \lambda_{C12})$$ is

A hydrogen atom in its ground state absorbs $$10.2$$ eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of (Given, Planck's constant $$= 6.6 \times 10^{-34}$$ Js).

Identify the correct Logic Gate for the following output ($$Y$$) of two inputs $$A$$ and $$B$$.

A pendulum of length $$2$$ m consists of a wooden bob of mass $$50$$ g. A bullet of mass $$75$$ g is fired towards the stationary bob with a speed $$v$$. The bullet emerges out of the bob with a speed $$\frac{v}{3}$$ and the bob just completes the vertical circle. The value of $$v$$ is ______ m s$$^{-1}$$
(if $$g = 10$$ m s$$^{-2}$$).

The area of cross-section of a large tank is $$0.5$$ m$$^2$$. It has a narrow opening near the bottom having area of cross-section $$1$$ cm$$^2$$. A load of $$25$$ kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is $$40$$ cm above the bottom, will be ______ cm s$$^{-1}$$.
[Take $$g = 10$$ m s$$^{-2}$$]

In a carnot engine, the temperature of reservoir is $$527°$$C and that of sink is $$200$$ K. If the work done by the engine when it transfers heat from reservoir to sink is $$12000$$ kJ, the quantity of heat absorbed by the engine from reservoir is ______ $$\times 10^6$$ J.

A capacitor of capacitance $$50$$ pF is charged by $$100$$ V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ______ nJ.

A $$220$$ V, $$50$$ Hz AC source is connected to a $$25$$ V, $$5$$ W lamp and an additional resistance $$R$$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $$R$$ (in ohm) will be

A cell, shunted by a $$8$$ $$\Omega$$ resistance, is balanced across a potentiometer wire of length $$3$$ m. The balancing length is $$2$$ m when the cell is shunted by $$4$$ $$\Omega$$ resistance. The value of internal resistance of the cell will be ______ $$\Omega$$.

The current density in a cylindrical wire of radius $$4$$ mm is $$4 \times 10^6$$ A m$$^{-2}$$. The current through the outer portion of the wire between radial distances $$\frac{R}{2}$$ and $$R$$ is ______ $$\pi$$ A.

In Young's double slit experiment the two slits are $$0.6$$ mm distance apart. Interference pattern is observed on a screen at a distance $$80$$ cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be ______ nm.

A beam of monochromatic light is used to excite the electron in $$Li^{++}$$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $$x \times 10^{-10}$$ m. The value of $$x$$ is ______.
[Given $$hc = 1242$$ eV nm]

The height of a transmitting antenna at the top of a tower is $$25$$ m and that of receiving antenna is, $$49$$ m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is $$K\sqrt{5} \times 10^2$$ m. The value of $$K$$ is ______.
(Assume radius of Earth is $$64 \times 10^5$$ m) [Calculate upto nearest integer value]