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A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of \( 10 \, \text{m} \) in \( t \, \text{s} \), the distance travelled by the toy in the next \( t \, \text{s} \) will be:

2.

At what temperature a gold ring of diameter \( 6.230 \, \text{cm} \) be heated so that it can be fitted on a wooden bangle of diameter \( 6.241 \, \text{cm} \)? Both the diameters have been measured at room temperature \( 27^{\circ}\text{C} \).
(Given: coefficient of linear thermal expansion of gold \( \alpha_{L} = 1.4 \times 10^{-5} \, \text{K}^{-1} \).)

3.

Two point charges \( Q \) each are placed at a distance \( d \) apart. A third point charge \( q \) is placed at a distance \( x \) from mid-point on the perpendicular bisector. The values \( x \) at which charge \( q \) will experience the maximum Coulomb’s force is:

4.

The speed of light in media ‘A’ and ‘B’ are \( 2.0 \times 10^{10} \, \text{cm/ s}^{} \) and \( 1.5 \times 10^{10} \, \text{cm/ s}^{} \) respectively. A ray of light enters from the medium \( B \) to \( A \) at an incident angle \( \theta \). If the ray suffers total internal reflection, then

5.

In the following nuclear reaction,

Mass number of \( D \) is \( 182 \) and atomic number is \( 74 \). Mass number and atomic number of \( D_{4} \) respectively will be:

6.

The electric field at a point associated with a light wave is given by \( E = 200 \left[\sin(6 \times 10^{15} )t + \sin(9 \times 10^{15} )t\right] \, \text{V m}^{-1} \)
Given: \( h = 4.14 \times 10^{-15} \, \text{eV s} \)
If this light falls on a metal surface having a work function of \( 2.50 \, \text{eV} \), the maximum kinetic energy of the photoelectrons will be:

7.

A capacitor is discharging through a resistor \( R \). Consider in time \( t_1 \), the energy stored in the capacitor reduces to half its initial value and in time \( t_2 \), the charge stored reduces to one eight of its initial values. The ratio \( t_1 / t_2 \) will be:

8.

Starting with the same initial conditions, an ideal gas expands from volume \( V_1 \) to \( V_2 \) in three different ways. The work done by the gas is \( W_1 \) if the process is purely isothermal, \( W_2 \) if the process is purely adiabatic and \( W_3 \) if the process is purely isobaric. Then, choose the correct option.

9.

Two long current carrying conductors are placed parallel to each other at a distance of \( 8 \ \text{cm} \) between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is \( 300 \ \mu \text{T} \). The equal current flowing in the two conductors is:

10.

The time period of a satellite revolving around earth in a given orbit is \( 7 \ \text{hours} \). If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be:

11.

The TV transmission tower at a particular station has a height of \( 125 \ \text{m} \). For doubling the coverage of its range, the height of the tower should be increased by:

12.

The motion of a simple pendulum executing S.H.M. is represented by the following equation.

\( y = A \sin(\pi t + \phi) \), where time is measured in second. The length of pendulum is:

13.

A vessel contains \( 16 \) \( \text{g} \) of hydrogen and \( 128 \) \( \text{g} \) of oxygen at standard temperature and pressure. The volume of the vessel in \( \text{cm}^3 \) is:

14.

Given below are two statements:
Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.
Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.
In the light of the above statements, choose the most appropriate answer from the options given below:

15.

A block of mass \( 40 \; \text{kg} \) slides over a surface, when a mass of \( 4 \; \text{kg} \) is suspended through an inextensible massless string passing over frictionless pulley as shown below:
The coefficient of kinetic friction between the surface and block is \( 0.02 \). The acceleration of block is. \( \text{(Given } g = 10 \; \text{ms}^{-2}\text{)} \).

16.

In the given figure, the block of mass \( m \) is dropped from the point ‘A’. The expression for kinetic energy of block when it reaches point ‘B’ is:

17.

A block of mass \( M \) placed inside a box descends vertically with acceleration ‘\( a \)’. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ‘\( a \)’ will be:

18.

If the electric potential at any point \( (x, y, z) \, \text{m} \) in space is given by \( V = 3x^{2} \) volt. The electric field at the point \( (1, 0, 3) \, \text{m} \) will be:

19.

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of \( 2 \, \Omega \). The value of internal resistance of each cell is:

20.

A person can throw a ball up to a maximum range of \( 100 \, \text{m} \). How high above the ground he can throw the same ball?

21.

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

22.

A small spherical ball of radius \( 0.1 \, \text{mm} \) and density \( 10^{4} \, \text{kg m}^{-3} \) 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 _______ \( \text{m} \).
(Given \( g = 10 \, \text{m s}^{-2} \), viscosity of water \( = 1.0 \times 10^{-5} \, \text{N -s m}^{-2} \).)

23.

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 \( 20.0 \, \text{cm} \) for a tuning fork of frequency \( 400 \, \text{Hz} \) is used. The velocity of the sound at room temperature is \( 336 \, \text{m s}^{-1} \). The third resonance is observed when the air column has a length of _______ \( \text{cm} \).

24.

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 \( 500 \, \Omega \) resistor, the reading of the voltmeter will be ______ \( \text{V} \).

25.

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

26.

The displacement current of \( 4.425 \, \mu\text{A} \) is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of \( 10^{6} \, \text{V s}^{-1} \). The area of each plate of the capacitor is \( 40 \, \text{cm}^{2} \). The distance between each plate of the capacitor is \( x \times 10^{-3} \, \text{m} \). The value of \( x \) is, (Permittivity of free space, \( E_{0} = 8.85 \times 10^{-12} \, \text{C}^{2}\text{N}^{-1}\text{m}^{-2} \)) ______.

27.

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 ______.

28.

The half-life of a radioactive substance is \( 5 \, \text{years} \). After \( x \) years a given sample of the radioactive substance gets reduced to \( 6.25\% \) of its initial value. The value of \( x \) is ______.

29.

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 \( 5 \times 10^{-2} \, \text{m} \) towards the slits, the change in fringe width is \( 3 \times 10^{-3} \, \text{cm} \). If the distance between the slits is \( 1 \, \text{mm} \), then the wavelength of the light will be _____ \( \text{nm} \).

30.

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

JEE Main 2022 29th June Evening Shift

Physics Chemistry Mathematics

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A block of mass \( M \) placed inside a box descends vertically with acceleration ‘\( a \)’. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ‘\( a \)’ will be:

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