JEE Main 2023 (Online) 24th January Morning Shift

In the circuit shown in the figure, the ratio of the quality factor and the band width is ___________ s.

Consider the following radioactive decay process
$$_{84}^{218}A\buildrel \alpha \over
\longrightarrow {A_1}\buildrel {{\beta ^ - }} \over
\longrightarrow {A_2}\buildrel \gamma \over
\longrightarrow {A_3}\buildrel \alpha \over
\longri...

Assume that protons and neutrons have equal masses. Mass of a nucleon is \(1.6\times10^{-27}\) kg and radius of nucleus is \(1.5\times10^{-15}~\mathrm{A^{1/3}}\) m. The approximate ratio of the nuclear density and water density is $$n\times...

A modulating signal is a square wave, as shown in the figure.

If the carrier wave is given as \(\mathrm{c(t) = 2\sin(8\pi t)}\) volts, the modulation index is :

As shown in the figure, a network of resistors is connected to a battery of 24V with an internal resistance of 3 \(\Omega\). The currents through the resistors R\(_4\) and R\(_5\) are I\(_4\) and I\(_5\) respectively. The values of I\(_4\) ...

A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is \(n\times10^{-3}\Omega\). If the resistivity of the material is $$\mathrm{2.4\times1...

From the photoelectric effect experiment, following observations are made. Identify which of these are correct.
A. The stopping potential depends only on the work function of the metal.
B. The saturation current increases as the intensity o...

A conducting circular loop of radius \(\frac{10}{\sqrt\pi}\) cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s ...

In \(\overrightarrow E\) and \(\overrightarrow K\) represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by :
(\(\omega\) - angular frequency) :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Photodiodes are preferably operated in reverse bias condition for light intensity measurement.
Reason R : The current in the...

If two charges q\(_1\) and q\(_2\) are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

A stream of a positively charged particles having \({q \over m} = 2 \times {10^{11}}{C \over {kg}}\) and velocity \({\overrightarrow v _0} = 3 \times {10^7}\widehat i\,m/s\) is deflected by an electric field \(1.8\widehat j\) kV/m. The elec...

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both...

The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth \(\mathrm{R_e=6400~km}\)) :

1 g of a liquid is converted to vapour at 3 \(\times\) 10\(^5\) Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm\(^3\) during this phase change, then the increase in internal energy in the process will b...

Given below are two statements :
Statement I : The temperature of a gas is \(-73^\circ\)C. When the gas is heated to \(527^\circ\)C, the root mean square speed of the molecules is doubled.
Statement II : The product of pressure and volume o...

A hole is drilled in a metal sheet. At \(\mathrm{27^\circ C}\), the diameter of hole is 5 cm. When the sheet is heated to \(\mathrm{177^\circ C}\), the change in the diameter of hole is \(\mathrm{d\times10^{-3}}\) cm. The value of d wil...

As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g = 10 m/s\(^2\))

Given below are two statements :
Statement I : An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.
Statement II : Force exerted by the floor of an elevator on the foot of a person stan...

Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F\(_1\). If distance between wires is halved and current...

A circular loop of radius \(r\) is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is :

The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :

A 100 m long wire having cross-sectional area \(\mathrm{6.25\times10^{-4}~m^2}\) and Young's modulus is \(\mathrm{10^{10}~Nm^{-2}}\) is subjected to a load of 250 N, then the elongation in the wire will be :

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be \(\sqrt x\) cm. The value of \(x\) is ________.

A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced...

Match List I with List II

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...

Vectors \(a\widehat i + b\widehat j + \widehat k\) and \(2\widehat i - 3\widehat j + 4\widehat k\) are perpendicular to each other when \(3a + 2b = 7\), the ratio of \(a\) to \(b\) is \({x \over 2}\). The value of \(x\) is ____________.

Given below are two statements :
Statement I : If the Brewster's angle for the light propagating from air to glass is \(\mathrm{\theta_B}\), then the Brewster's angle for the light propagating from glass to air is \(\frac{\pi}{2}-\theta_B\)...

A travelling wave is described by the equation
\(y(x,t) = [0.05\sin (8x - 4t)]\) m
The velocity of the wave is : [all the quantities are in SI unit]

A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of \(\mathrm{5^{th}}\) second. The force acted on the body is ________ N.