JEE Main 2022 (Online) 28th July Evening Shift

A transformer operating at primary voltage \(8 \,\mathrm{kV}\) and secondary voltage \(160 \mathrm{~V}\) serves a load of \(80 \mathrm{~kW}\). Assuming the transformer to be ideal with purely resistive load and working on unity power factor...

A radioactive sample decays \(\frac{7}{8}\) times its original quantity in 15 minutes. The half-life of the sample is

A slab of dielectric constant \(\mathrm{K}\) has the same cross-sectional area as the plates of a parallel plate capacitor and thickness \(\frac{3}{4} \mathrm{~d}\), where \(\mathrm{d}\) is the separation of the plates. The capacitance of t...

The distance of centre of mass from end A of a one dimensional rod (AB) having mass density \(\rho=\rho_{0}\left(1-\frac{x^{2}}{L^{2}}\right) \mathrm{kg} / \mathrm{m}\) and length L (in meter) is \(\frac{3 L}{\alpha} \mathrm{m}\). The value...

A FM Broadcast transmitter, using modulating signal of frequency 20 kHz has a deviation ratio of 10. The Bandwidth required for transmission is :

Given below are two statements :
Statement I : A uniform wire of resistance \(80 \,\Omega\) is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be \(5 \,\Omega\).
Statem...

An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about _______ W.

Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, ...

For the given circuit the current through battery of 6 V just after closing the switch 'S' will be _________ A.

Sun light falls normally on a surface of area \(36 \mathrm{~cm}^{2}\) and exerts an average force of \(7.2 \times 10^{-9} \mathrm{~N}\) within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incide...

An n.p.n transistor with current gain \(\beta=100\) in common emitter configuration is shown in figure. The output voltage of the amplifier will be

A uniform electric field \(\mathrm{E}=(8 \mathrm{~m} / \mathrm{e}) \,\mathrm{V} / \mathrm{m}\) is created between two parallel plates of length \(1 \mathrm{~m}\) as shown in figure, (where \(\mathrm{m}=\) mass of electron and e = charge of ...

The power of a lens (biconvex) is \(1.25 \mathrm{~m}^{-1}\) in particular medium. Refractive index of the lens is 1.5 and radii of curvature are \(20 \mathrm{~cm}\) and \(40 \mathrm{~cm}\) respectively. The refractive index of surrounding m...

An object 'O' is placed at a distance of \(100 \mathrm{~cm}\) in front of a concave mirror of radius of curvature \(200 \mathrm{~cm}\) as shown in the figure. The object starts moving towards the mirror at a speed $$2 \mathrm{~cm} / \mathrm...

In an experiment with a convex lens, The plot of the image distance \(\left(v^{\prime}\right)\) against the object distance (\(\left.\mu^{\prime}\right)\) measured from the focus gives a curve \(v^{\prime} \mu^{\prime}=225\). If all the dis...

A vessel contains \(14 \mathrm{~g}\) of nitrogen gas at a temperature of \(27^{\circ} \mathrm{C}\). The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be :
Take $$\mathrm{R}=8.32 \mathrm{~J} \mat...

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _________ J.

A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length 'l' is hanging on one side and rest of its length '\(\mathrm{L}-l\)' is hanging on the other s...

A triangular shaped wire carrying \(10 \mathrm{~A}\) current is placed in a uniform magnetic field of \(0.5 \mathrm{~T}\), as shown in figure. The magnetic force on segment \(\mathrm{CD}\) is
(Given $$\mathrm{BC}=\mathrm{CD}=\mathrm{BD}=5 \...

The magnetic field at the center of current carrying circular loop is \(B_{1}\). The magnetic field at a distance of \(\sqrt{3}\) times radius of the given circular loop from the center on its axis is \(B_{2}\). The value of $$B_{1} / B_{2...

At time \(t=0\) a particle starts travelling from a height \(7 \hat{z} \mathrm{~cm}\) in a plane keeping z coordinate constant. At any instant of time it's position along the \(\hat{x}\) and \(\hat{y}\) directions are defined as $$3 \mathrm...

A ball is thrown vertically upwards with a velocity of \(19.6 \mathrm{~ms}^{-1}\) from the top of a tower. The ball strikes the ground after \(6 \mathrm{~s}\). The height from the ground up to which the ball can rise will be $$\left(\frac{k...

A pressure-pump has a horizontal tube of cross sectional area \(10 \mathrm{~cm}^{2}\) for the outflow of water at a speed of \(20 \mathrm{~m} / \mathrm{s}\). The force exerted on the vertical wall just in front of the tube which stops water...

Consider a cylindrical tank of radius \(1 \mathrm{~m}\) is filled with water. The top surface of water is at \(15 \mathrm{~m}\) from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of \(5 \mathrm{~m}\) from t...

A string of area of cross-section \(4 \mathrm{~mm}^{2}\) and length \(0.5 \mathrm{~m}\) is connected with a rigid body of mass \(2 \mathrm{~kg}\). The body is rotated in a vertical circular path of radius \(0.5 \mathrm{~m}\). The body acqui...

Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s re...

The potential energy of a particle of mass \(4 \mathrm{~kg}\) in motion along the x-axis is given by \(\mathrm{U}=4(1-\cos 4 x)\) J. The time period of the particle for small oscillation \((\sin \theta \simeq \theta)\) is $$\left(\frac{\pi}...

Consider the efficiency of carnot's engine is given by \(\eta=\frac{\alpha \beta}{\sin \theta} \log_e \frac{\beta x}{k T}\), where \(\alpha\) and \(\beta\) are constants. If T is temperature, k is Boltzmann constant, \(\theta\) is angular d...

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of \(0.5 \mathrm{~s}\) is measured from time of 100 oscillation with a watch of \(1 \mathrm{~s}\) resolution. If measured value of length is $$10 \m...

A bullet of mass \(200 \mathrm{~g}\) having initial kinetic energy \(90 \mathrm{~J}\) is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to \(40 \mathrm{~J}\) within \(1 \mathrm{~s}\), the minimum len...