JEE Main 2021 (Online) 25th July Morning Shift

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the ...

Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 balls is \(k{\left( {{3 \over 4}} \right)^9}\) then k lies in the set :

The number of real roots of the equation \({e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0\) is :

If \(\alpha\), \(\beta\) are roots of the equation \({x^2} + 5(\sqrt 2 )x + 10 = 0\), \(\alpha\) > \(\beta\) and \({P_n} = {\alpha ^n} - {\beta ^n}\) for each positive integer n, then the value of $$\left( {{{{P_{17}}{P_{20}} + 5\sqrt 2 {P_...

Let Sn be the sum of the first n terms of an arithmetic progression. If S3n = 3S2n, then the value of \({{{S_{4n}}} \over {{S_{2n}}}}\) is :

If the value of \({\left( {1 + {2 \over 3} + {6 \over {{3^2}}} + {{10} \over {{3^3}}} + ....upto\,\infty } \right)^{{{\log }_{(0.25)}}\left( {{1 \over 3} + {1 \over {{3^2}}} + {1 \over {{3^3}}} + ....upto\,\infty } \right)}}\) is \(l\), the...

Consider the following frequency distribution :
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px...

The sum of all values of x in [0, 2\(\pi\)], for which sin x + sin 2x + sin 3x + sin 4x = 0, is equal to :

Let the vectors\((2 + a + b)\widehat i + (a + 2b + c)\widehat j - (b + c)\widehat k,(1 + b)\widehat i + 2b\widehat j - b\widehat k\) and \((2 + b)\widehat i + 2b\widehat j + (1 - b)\widehat k\), \(a,b,c, \in R\) be co-planar. Then which of ...

Let \(\overrightarrow p = 2\widehat i + 3\widehat j + \widehat k\) and \(\overrightarrow q = \widehat i + 2\widehat j + \widehat k\) be two vectors. If a vector $$\overrightarrow r = (\alpha \widehat i + \beta \widehat j + \gamma \wideha...

An inductor of 10 mH is connected to a 20V battery through a resistor of 10 k\(\Omega\) and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after 1 \(\mu\)s...

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :(where \(\lambda\) is the decay const...

The half-life of \({}^{198}Au\) is 3 days. If atomic weight of \({}^{198}Au\) is 198 g/mol then the activity of 2 mg of \({}^{198}Au\) is [in disintegration/second] :

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as :\(\varepsilon (x) = {\varepsilon _0} + kx\), for...

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and bal...

A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial peed. The speed of the two body centre of mass is $${x...

In amplitude modulation, the message signalVm(t) = 10 sin (2\(\pi\) \(\times\) 105t) volts and Carrier signalVC(t) = 20 sin(2\(\pi\) \(\times\) 107 t) voltsThe modulated signal now contains the message signal with lower side band and upper ...

In the given figure, there is a circuit of potentiometer of length AB = 10 m. The resistance per unit length is 0.1 \(\Omega\) per cm. Across AB, a battery of emf E and internal resistance 'r' is connected. The maximum value of emf measured...

An electric bulb rated as 200 W at 100 V is used in a circuit having 200 V supply. The resistance 'R' that must be put in series with the bulb so that the bulb delivers the same power is _____________ \(\Omega\).

What should be the order of arrangement of de-Broglie wavelength of electron (\(\lambda\)e), an \(\alpha\)-particle (\(\lambda\)a) and proton (\(\lambda\)p) given that all have the same kinetic energy?

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be :

A circular conducting coil of radius 1 m is being heated by the change of magnetic field \(\overrightarrow B\) passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2 \(\mu\)\(\Omega\). The magnetic fi...

A linearly polarized electromagnetic wave in vacuum is \(E = 3.1\cos \left[ {(1.8)z - (5.4 \times {{10}^6})t} \right]\widehat iN/C\)is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

Identify the logic operation carried out.

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If the free charged particle is displaced from its equilibrium position through dista...

A ray of laser of a wavelength 630 nm is incident at an angle of 30\(^\circ\) at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2.42 and that of air is 1. Choose the correct option.

The minimum and maximum distances of a planet revolving around the sun are x1 and x2. If the minimum speed of the planet on its trajectory is v0 then its maximum speed will be :

For a gas CP \(-\) CV = R in a state P and CP \(-\) CV = 1.10 R in a state Q, TP and TQ are the temperatures in two different states P and Q respectively. Then

A monoatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If l1 and l2 are the lengths o...

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :

The value of aluminium susceptibility is 2.2 \(\times\) 10\(-\)5. The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is \({x \over {{{10}^4}}}\). Then the value of x is _________...

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap ? (Take g = 9.8 m/s2)

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire then its Young's modulus is :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Moment of inertia of a circular disc of mass 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis whic...

A particle of mass 'm' is moving in time 't' on a trajectory given by\(\overrightarrow r = 10\alpha {t^2}\widehat i + 5\beta (t - 5)\widehat j\)Where \(\alpha\) and \(\beta\) are dimensional constants.The angular momentum of the particle b...

In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be ...

A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60\(^\circ\) to the vertical will be (g = 10 m/s2) ____________ m/s.

Student A and student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the fi...

Match List - I with List - IIChoose the correct answer from the options given below :

In the Young's double slit experiment, the distance between the slits varies in time as d(t) = d0 + a0 sin\(\omega\)t; where d0, \(\omega\) and a0 are constants. The difference between the largest fringe width and the smallest fringe width ...