JEE Main 2021 (Online) 26th August Morning Shift

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______________.

Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = \({5 \over 9}\), is :

The sum of all integral values of k (k \(\ne\) 0) for which the equation \({2 \over {x - 1}} - {1 \over {x - 2}} = {2 \over k}\) in x has no real roots, is ____________.

The sum of the series \({1 \over {x + 1}} + {2 \over {{x^2} + 1}} + {{{2^2}} \over {{x^4} + 1}} + ...... + {{{2^{100}}} \over {{x^{{2^{100}}}} + 1}}\) when x = 2 is :

If the sum of an infinite GP a, ar, ar2, ar3, ....... is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, ....... is :

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. if \(\alpha\) and \(\sqrt \beta\) are the mean and standard deviatio...

Let ABC be a triangle with A(\(-\)3, 1) and \(\angle\)ACB = \(\theta\), 0 < \(\theta\) < \({\pi \over 2}\). If the equation of the median through B is 2x + y \(-\) 3 = 0 and the equation of angle bisector of C is 7x \(-\) 4y \(-\) 1 = 0, t...

The sum of solutions of the equation \({{\cos x} \over {1 + \sin x}} = \left| {\tan 2x} \right|\), \(x \in \left( { - {\pi \over 2},{\pi \over 2}} \right) - \left\{ {{\pi \over 4}, - {\pi \over 4}} \right\}\) is :

Let \(\overrightarrow a = \widehat i + \widehat j + \widehat k\) and \(\overrightarrow b = \widehat j - \widehat k\). If \(\overrightarrow c\) is a vector such that \(\overrightarrow a \times \overrightarrow c = \overrightarrow b\) an...

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 k\(\Omega\), an inductor of inductive reactance XL = 250 \(\pi\)\(\Omega\) and an unknown capacitor. The value of capacitance to maximize the average p...

A particular hydrogen like ion emits radiation of frequency 2.92 \(\times\) 1015 Hz when it makes transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be :

The material filled between the plates of a parallel plate capacitor has resistivity 200 \(\Omega\)m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then t...

An amplitude modulated wave is represented by Cm(t) = 10(1 + 0.2 cos 12560t) sin(111 \(\times\) 104t) volts. The modulating frequency in kHz will be ................. .

In the given figure, the emf of the cell is 2.2 V and if internal resistance is 0.6\(\Omega\). Calculate the power dissipated in the whole circuit :

What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3\(\Omega\) ?(Given resistivities of iron and copper-nickel alloy wire are 12 \(\mu\)\(\Omega\) a...

In a photoelectric experiment ultraviolet light of wavelength 280 nm is used with lithium cathode having work function \(\phi\) = 2.5 eV. If the wavelength of incident light is switched to 400 nm, find out the change in the stopping potenti...

An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds :

The electric field in a plane electromagnetic wave is given by $$\overrightarrow E = 200\cos \left[ {\left( {{{0.5 \times {{10}^3}} \over m}} \right)x - \left( {1.5 \times {{10}^{11}}{{rad} \over s} \times t} \right)} \right]{V \over m}\wi...

Identify the logic operation carried out by the given circuit :-

Statement I : By doping silicon semiconductor with pentavalent material, the electrons density increases.Statement II : The n-type semiconductor has net negative charge.In the light of the above statements, choose the most appropriate answe...

A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in the figure. The approximate variation electric field \(\overrightarrow E\) as a function of...

Car B overtakes another car A at a relative speed of 40 ms\(-\)1. How fast will the image of car B appear to move in the mirror of focal length 10 cm fitted in car A, when the car B is 1.9 m away from the car A?

Inside a uniform spherical shell :(1) the gravitational field is zero(2) the gravitational potential is zero(3) the gravitational field is same everywhere(4) the gravitational potential is same everywhere(5) all of the aboveChoose the most ...

An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by 2.5 \(\times\) 103 J ?

The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are VH, VO and VC respectively then :

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms-2. The gases come out at a relative speed of 500 ms\(-\)1 with respect to the rocket : [Use g = 10...

The fractional change in the magnetic field intensity at a distance 'r' from centre on the axis of current carrying coil of radius 'a' to the magnetic field intensity at the centre of the same coil is : (Take r < a)

Two short magnetic dipoles m1 and m2 each having magnetic moment of 1 Am2 are placed at point O and P respectively. The distance between OP is 1 meter. The torque experienced by the magnetic dipole m2 due to the presence of m1 is .............

Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3s with the same initial velocity of 35 m/s, then these balls collide at a height of ............... m. ...

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7....

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .........

Consider a badminton racket with length scales as shown in the figure.If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about...

In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular o...

If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M\(-\)5G\(-\)2 are :

The magnitude of vectors \(\overrightarrow {OA}\), \(\overrightarrow {OB}\) and \(\overrightarrow {OC}\) in the given figure are equal. The direction of \(\overrightarrow {OA}\) + \(\overrightarrow {OB}\) \(-\) $$\overrightarrow {OC} $...

White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringes. ...

A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of sourc...

Two travelling waves produces a standing wave represented by equation,y = 1.0 mm cos(1.57 cm\(-\)1) x sin(78.5 s\(-\)1)t. The node closest to the origin in the region x > 0 will be at x = .............. cm.

A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter lying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of k is ................. . (Tak...