JEE Main 2021 (Online) 25th February Morning Shift

The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is _____________.

The total number of positive integral solutions (x, y, z) such that xyz = 24 is :

When a missile is fired from a ship, the probability that it is intercepted is \({1 \over 3}\) and the probability that the missile hits the target, given that it is not intercepted, is \({3 \over 4}\). If three missiles are fired independe...

The coefficients a, b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :

The integer 'k', for which the inequality x2 \(-\) 2(3k \(-\) 1)x + 8k2 \(-\) 7 > 0 is valid for every x in R, is :

Let A1, A2, A3, ....... be squares such that for each n \(\ge\) 1, the length of the side of An equals the length of diagonal of An+1. If the length of A1 is 12 cm, then the smallest value of n for which area of An is less than one, is __...

If \(0 < \theta ,\phi < {\pi \over 2},x = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta } ,y = \sum\limits_{n = 0}^\infty {{{\sin }^{2n}}\phi }\) and \(z = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta .{{\sin }^{2n}}\phi }\) t...

The image of the point (3, 5) in the line x \(-\) y + 1 = 0, lies on :

All possible values of \(\theta\) \(\in\) [0, 2\(\pi\)] for which sin 2\(\theta\) + tan 2\(\theta\) > 0 lie in :

Let \(\overrightarrow a = \widehat i + 2\widehat j - \widehat k\), \(\overrightarrow b = \widehat i - \widehat j\) and \(\overrightarrow c = \widehat i - \widehat j - \widehat k\) be three given vectors. If \(\overrightarrow r\) is a ve...

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

The current (i) at time t = 0 and t = \(\infty\) respectively for the given circuit is :

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 \(\mu\)F is used in the resonant circuit. The self inductance of coil necessary for resonance is __________ \(\times\) 10\(-\)8 H.

Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio \({{{N_1}} \over {{N_2}}}\) will be e...

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ________ m/s. (Take ...

Given below are two statements :Statement I : A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz.Statement II : The side band frequencies are 1002 kHz and 998 kHz.In the...

In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than E1 and E2 as well. For key K1 (closed), the jockey is adjusted to touch the wire at point J1 so that there is no deflection in the galv...

An \(\alpha\) particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are \(\lambda\)\(\alpha\) and \(\lambda\)p respectively. The ratio $${{{{\lambda _p}} \over {{\lambda ...

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is __...

A 5V battery is connected across the points X and Y. Assume D1 and D2 to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point X.

The electric field in a region is given by \(\overrightarrow E = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right){N \over C}\). The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (par...

512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ________ V.

The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is __________ cm.

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively.If TA and TB are the time periods of A and B respectively then the value of TB \(-\) TA :[Given : radius of earth ...

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass.Reason R : The product of their mass and r...

A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now a spherical cavity of radius \(\left( {{R \over 2}} \right)\) is made in the sphere (as shown in figure) and the force becomes ...

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.Assertion A : When a rod lying freely is heated, no thermal stress is developed in it.Reason R : On heating, the length of the rod increas...

In a certain thermodynamical process, the pressure of a gas depends on its volume as kV3. The work done when the temperature changes from 100\(^\circ\)C to 300\(^\circ\)C will be ___________ nR, where n denotes number of moles of a gas.

A diatomic gas, having \({C_p} = {7 \over 2}R\) and \({C_v} = {5 \over 2}R\), is heated at constant pressure. The ratio dU : dQ : dW :

A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R = gas constant) is \({x \over {3R}}\). Value of x is _____...

A proton, a deuteron and an \(\alpha\) particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _________ and their speed is _______, in the ratio.

Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ________.

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is :

If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :

The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaw...

Match List - I with List - II :



List I

List II




(a)
h (Planck's constant)
(i)
\([ML{T^{ - 1}}]\)


(b)
E (kinetic energy)
(ii)
\([M{L^2}{T^{ - 1}}]\)


(c)
V (elec...

In an octagon ABCDEFGH of equal side, what is the sum of \(\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} + \overrightarrow {AG} + \overrightarrow {AH}\),if, $$\overri...

Two coherent light sources having intensity in the ratio 2x produce an interference pattern. The ratio \({{{I_{\max }} - {I_{\min }}} \over {{I_{\max }} + {I_{\min }}}}\) will be :

A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides w...

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as \(U = {\alpha \over {{r^{10}}}} - {\beta \over {{r^5}}} - 3\)where, \(\alpha\) and \(\beta\) are positive constants. The equilibrium di...