JEE Main 2022 (Online) 30th June Morning Shift

The number of 6-digit numbers made by using the digits 1, 2, 3, 4, 5, 6, 7, without repetition and which are multiple of 15 is ____________.

If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then \({{P(X = 2)} \over {P(X = 3)}}\) is equal to :

The probability distribution of X is :

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Let \({S_1} = \left\{ {x \in R - \{ 1,2\} :{{(x + 2)({x^2} + 3x + 5)} \over { - 2 + 3x - {x^2}}} \ge 0} \right\}\) and \({S_2} = \left\{ {x \in R:{3^{2x}} - {3^{x + 1}} - {3^{x + 2}} + 27 \le 0} \right\}\). Then, \({S_1} \cup {S_2}\) is equ...

Let S be the set of all integral values of \(\alpha\) for which the sum of squares of two real roots of the quadratic equation \(3{x^2} + (\alpha - 6)x + (\alpha + 3) = 0\) is minimum. Then S :

The value of \(1 + {1 \over {1 + 2}} + {1 \over {1 + 2 + 3}} + \,\,....\,\, + \,\,{1 \over {1 + 2 + 3 + \,\,.....\,\, + \,\,11}}\) is equal to:

Let for \(f(x) = {a_0}{x^2} + {a_1}x + {a_2},\,f'(0) = 1\) and \(f'(1) = 0\). If a0, a1, a2 are in an arithmatico-geometric progression, whose corresponding A.P. has common difference 1 and corresponding G.P. has common ratio 2, then f(4) i...

Let \(\alpha\)1, \(\alpha\)2 (\(\alpha\)1 < \(\alpha\)2) be the values of \(\alpha\) fo the points (\(\alpha\), \(-\)3), (2, 0) and (1, \(\alpha\)) to be collinear. Then the equation of the line, passing through (\(\alpha\)1, \(\alpha\)2) a...

Let \({S_1} = \{ x \in [0,12\pi ]:{\sin ^5}x + {\cos ^5}x = 1\}\)
and \({S_2} = \{ x \in [0,8\pi ]:{\sin ^7}x + {\cos ^7}x = 1\}\)
Then \(n({S_1}) - n({S_2})\) is equal to ______________.

Let a vector \(\overrightarrow c\) be coplanar with the vectors \(\overrightarrow a = - \widehat i + \widehat j + \widehat k\) and \(\overrightarrow b = 2\widehat i + \widehat j - \widehat k\). If the vector \(\overrightarrow c\) also ...

In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency (f2) and new quality factor (Q2) will be :
(f1 = original resonant frequency, Q1 = original quality factor)

A series LCR circuit with \(R = {{250} \over {11}}\,\Omega\) and \({X_L} = {{70} \over {11}}\,\Omega\) is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be _______...

A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by :

A hydrogen atom in its first excited state absorbs a photon of energy x \(\times\) 10\(-\)2 eV and excited to a higher energy state where the potential energy of electron is \(-\)1.08 eV. The value of x is ______________.

Co is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity \(\varepsilon\)r (as shown in Fig. 2), ...

Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :

A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The a...

A speech signal given by 11 sin(2200 \(\pi\)t) V is used for amplitude modulation with a carrier signal given by 44 sin(6600 \(\pi\)t) V. The minimum amplitude of modulated wave will be :

An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 \(\Omega\). If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, the...

The circuit diagram of potentiometer used to measure the internal resistance of a cell (E) is shown in figure. The key 'K' is kept closed so as to send constant current through potentiometer wire. When key 'K1' is kept open the null point i...

A source of monochromatic light liberates 9 \(\times\) 1020 photon per second with wavelength 600 nm when operated at 400 W. The number of photons emitted per second with wavelength of 800 nm by the source of monochromatic light operating a...

An expression for oscillating electric field in a plane electromagnetic wave is given as Ez = 300 sin(5\(\pi\) \(\times\) 103x \(-\) 3\(\pi\) \(\times\) 1011t) Vm\(-\)1
Then, the value of magnetic field amplitude will be :
(Given : speed of...

The circuit diagram used to study the characteristic curve of a zener diode is connected to variable power supply (0 \(-\) 15 V) as shown in figure. A zener diode with maximum potential Vz = 10 V and maximum power dissipation of 0.4 W is co...

Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be ____________ E. Where E is the potential energy of a single smaller drop.

The refractive index of an equilateral prism is \(\sqrt 2\). The angle of emergence under minimum deviation position of prism, in degree, is ___________.

The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3\(\rho\) and 5\(\rho\) respectively. The ratio of their acceleration due to gravity is :

The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is :
(Given 0$$^\c...

A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm3 to 150 cm3 adiabatically. In this process, the value of workdone on the gas will be :

A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static friction between the block and the wall is 0.5. A force F is also applied on the block vertically upward (as shown in figure). ...

A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii r1 and r2 respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be :

A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be :
(Take : e = 1.6 \(\times\) 10\(-\)19 C, mp = 1.67 \(\times\) 10\(-\)27 kg)

At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms\(-\)2. At t = 20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of t...

Two projectiles P1 and P2 thrown with speed in the ratio \(\sqrt3\) : \(\sqrt2\), attain the same height during their motion. If P2 is thrown at an angle of 60\(^\circ\) with the horizontal, the angle of projection of P1 with horizontal wil...

An air bubble of negligible weight having radius r rises steadily through a solution of density \(\sigma\) at speed v. The coefficient of viscosity of the solution is given by :

The excess pressure inside a liquid drop is 500 Nm\(-\)2. If the radius of the drop is 2 mm, the surface tension of liquid is x \(\times\) 10\(-\)3 Nm\(-\)1. The value of x is _____________.

Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure). The moment of inertia of the system, about an axis passing through the point O and perpendicular to the ...

If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is divided into five equal parts, will be :

Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits in Young's experiment are in the ratio of 9 : 16. (Assuming intensity of light is directly proportional to the width of ...

Which of the following equations correctly represents a travelling wave having wavelength \(\lambda\) = 4.0 cm, frequency v = 100 Hz and travelling in positive x-axis direction?

An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh\(-\)1 in the direction of wind which is blowing at 72 kmh\(-\)1 speed. Frequency of siren is 720 ...