JEE Main 2022 (Online) 26th June Morning Shift

Let the common tangents to the curves \(4({x^2} + {y^2}) = 9\) and \({y^2} = 4x\) intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and l ...

There are ten boys B1, B2, ......., B10 and five girls G1, G2, ........, G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group, is...

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is :

The sum of the cubes of all the roots of the equation \({x^4} - 3{x^3} - 2{x^2} + 3x + 1 = 0\) is _________.

Let A = {n \(\in\) N : H.C.F. (n, 45) = 1} and
Let B = {2k : k \(\in\) {1, 2, ......., 100}}. Then the sum of all the elements of A \(\cap\) B is ____________.

Let \(A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } }\) and \(B = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\max \,\{ i,j\} } }\). Then A + B is equal to _____________.

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to :

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle. Then the area of \(\Delta\)PQR is :

If \({\sin ^2}(10^\circ )\sin (20^\circ )\sin (40^\circ )\sin (50^\circ )\sin (70^\circ ) = \alpha - {1 \over {16}}\sin (10^\circ )\), then \(16 + {\alpha ^{ - 1}}\) is equal to __________.

If \(\overrightarrow a \,.\,\overrightarrow b = 1,\,\overrightarrow b \,.\,\overrightarrow c = 2\) and \(\overrightarrow c \,.\,\overrightarrow a = 3\), then the value of $$\left[ {\overrightarrow a \times \left( {\overrightarrow b \ti...

A 110 V, 50 Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance 55 \(\Omega\), at resonance in the circuit, will be __________ A.

How many alpha and beta particles are emitted when Uranium 92U238 decays to lead 82Pb206 ?

Two capacitors having capacitance C1 and C2 respectively are connected as shown in figure. Initially, capacitor C1 is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C1 is now con...

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is \(\alpha\) with respect ...

Choose the correct statement for amplitude modulation :

An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is :

An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are Ee and pe and that of photon are Eph and pph respectively. Which of the following is correct?

The magnetic flux through a coil perpendicular to its plane is varying according to the relation \(\phi = (5{t^3} + 4{t^2} + 2t - 5)\) Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will...

A 10 \(\Omega\), 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 \(\mu\)s. The average e.m.f. induced in the coil is ____________ V.

If Electric field intensity of a uniform plane electromagnetic wave is given as \(E = - 301.6\sin (kz - \omega t){\widehat a_x} + 452.4\sin (kz - \omega t){\widehat a_y}{V \over m}\). Then magnetic intensity 'H' of this wave in Am\(-\)1 wi...

In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size \({\lambda \over {100}}\), where \(\lambda\) is the wavelength of the wave in free space. The phenomenon, which happens there will be :

The I-V characteristics of a p-n junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltage of 2 V and 4 V respectively, is :

As per the given circuit, the value of current through the battery will be ____________ A.

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Non-polar materials do not have any permanent dipole moment.
Reason (R) : When a non-polar material is placed in an electric ...

A light ray is incident, at an incident angle \(\theta\)1, on the system of tow plane mirrors M1 and M2 having an inclination angle 75\(^\circ\) between them (as shown in figure). After reflecting from mirror M1 it gets reflected back by th...

The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by :
(Given R = radius of earth)

The efficiency of a Carnot's engine, working between steam point and ice point, will be :

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the...

A person is standing in an elevator. In which situation, he experiences weight loss?

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is :

A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms\(-\)1. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle \(\theta\) with the horizontal, to hit the jet. If t...

A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ________ m. [Use g = 10 m/s2]

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 \(\times\) 10\(-\)4 is __________ kJ/m3. Assume that material is elastic upto the linear strain of 5 ...

The elongation of a wire on the surface of the earth is 10\(-\)4 m. The same wire of same dimensions is elongated by 6 \(\times\) 10\(-\)5 m on another planet. The acceleration due to gravity on the planet will be ____________ ms\(-\)2. (Ta...

An ideal fluid of density 800 kgm\(-\)3, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to \({a \over 2}\). The pressure difference between the wide and narrow sections of pipe is 4100 Pa....

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads\(-\)1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two
objects each of mass m be att...

Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with \({g \over 6}\) vertically upwards then the time period will be :
(Where g = acceleration due to gravity)

An expression for a dimensionless quantity P is given by \(P = {\alpha \over \beta }{\log _e}\left( {{{kt} \over {\beta x}}} \right)\); where \(\alpha\) and \(\beta\) are constants, x is distance; k is Boltzmann constant and t is the tempe...

In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be _________ \(\times\) 10\(-\)2 mm.