JEE Main 2021 (Online) 20th July Morning Shift

Let y = mx + c, m > 0 be the focal chord of y2 = \(-\) 64x, which is tangent to (x + 10)2 + y2 = 4. Then, the value of 4\(\sqrt 2\) (m + c) is equal to _____________.

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsman and 1 wicketkeeper, is ...

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :

The probability of selecting integers a\(\in\)[\(-\) 5, 30] such that x2 + 2(a + 4)x \(-\) 5a + 64 > 0, for all x\(\in\)R, is :

If in a triangle ABC, AB = 5 units, \(\angle B = {\cos ^{ - 1}}\left( {{3 \over 5}} \right)\) and radius of circumcircle of \(\Delta\)ABC is 5 units, then the area (in sq. units) of \(\Delta\)ABC is :

If \(\alpha\) and \(\beta\) are the distinct roots of the equation \({x^2} + {(3)^{1/4}}x + {3^{1/2}} = 0\), then the value of \({\alpha ^{96}}({\alpha ^{12}} - 1) + {\beta ^{96}}({\beta ^{12}} - 1)\) is equal to :

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are :

Let \(\overrightarrow a = 2\widehat i + \widehat j - 2\widehat k\) and \(\overrightarrow b = \widehat i + \widehat j\). If \(\overrightarrow c\) is a vector such that $$\overrightarrow a .\,\overrightarrow c = \left| {\overrightarrow c ...

Let \(\overrightarrow a\), \(\overrightarrow b\), \(\overrightarrow c\) be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle \(\theta\), with the vector \(\overrightarrow a\) + $$\overrightarrow...

If the shortest distance between the lines \(\overrightarrow {{r_1}} = \alpha \widehat i + 2\widehat j + 2\widehat k + \lambda (\widehat i - 2\widehat j + 2\widehat k)\), \(\lambda\) \(\in\) R, \(\alpha\) > 0 and $$\overrightarrow {{r_2}} ...

AC voltage V(t) = 20 sin\(\omega\)t of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is 1 m2. The amplitude of the oscillating displacement current for the applied AC voltag...

In an LCR series circuit, an inductor 30 mH and a resistor 1 \(\Omega\) are connected to an AC source of angular frequency 300 rad/s. The value of capacitance for which, the current leads the voltage by 45\(^\circ\) is $${1 \over x} \times ...

A nucleus of mass M emits \(\gamma\) -ray photon of frequency 'v'. The loss of internal energy by the nucleus is :[Take 'c' as the speed of electromagnetic wave]

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains ? (Take ln 3 = 1.1)

A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular to the rod. The collision is complet...

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30\(^\circ\) banked road at maximum possible speed without skidding is ____________ \(\times\) 103 kg m/s2. [Given cos30\(^\circ\) = 0.87, \(\mu\)s = 0.2]

A carrier wave Vc(t) = 160 sin(2\(\pi\) \(\times\) 106t) volts is made to vary between Vmax = 200 V and Vmin = 120 V by a message signal Vm(t) = Am sin(2\(\pi\) \(\times\) 103t) volts. The peak voltage Am of the modulating signal is _______...

The value of current in the 6 \(\Omega\) resistance is :

A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m2. At every point the direction of current density is at an angle of 60\(^\circ\) with the unit vector of area of cross-section. The magnitude of electri...

The radiation corresponding to 3 \(\to\) 2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. The electrons are passed through a magnetic field of 5 \(\times\) 10\(-\)4 T. Assume that the radius of the largest...

The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the grap...

For the circuit shown below, calculate the value of Iz :

A body having specific charge 8 \(\mu\)C/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally tow...

A certain charge Q is divided into two parts q and (Q \(-\) q). How should the charges Q and q be divided so that q and (Q \(-\) q) placed at a certain distance apart experience maximum electrostatic repulsion?

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is :

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepi...

A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s2 and 4 m/s2 respectively. Identify from the below...

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ___________ \(\pi\)J.

Consider a mixture of gas molecule of types A, B and C having masses mA < mB < mC. The ratio of their root mean square speeds at normal temperature and pressure is :

The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0\(^\circ\) C to 50\(^\circ\) C when no work is done is ___________. (R is the universal gas constant).

The entropy of any system is given by \(S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right]\) where \(\alpha\) and \(\beta\) are the constants. \(\mu\), J, k and R are no. of moles, mechanical equivalent of heat, Bo...

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s2. The normal reaction R' by the floor if mass of the iron cylinde...

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let rd and r\(\alpha\) be their respective radii of circular path. The value of \({{{r_d}} \over {{r_\alpha }}}\) is equal to :

A butterfly is flying with a velocity \(4\sqrt 2\) m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :

The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are l1 and l2 respectively. The actual length of the metal wire is :

A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes time 't1'. When it rolls down the plane, it takes time t2. The value of \({{{t_2}} \over {{t_1}}}\) is $$\sqrt {{3 \over x...

If \(\overrightarrow A\) and \(\overrightarrow B\) are two vectors satisfying the relation \(\overrightarrow A\) . \(\overrightarrow B\) = \(\left| {\overrightarrow A \times \overrightarrow B } \right|\). Then the value of $$\left| {\o...

The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the speed of car is ___________ km/h.

The amplitude of wave disturbance propagating in the positive x-direction is given by \(y = {1 \over {{{(1 + x)}^2}}}\) at time t = 0 and \(y = {1 \over {1 + {{(x - 2)}^2}}}\) at t = 1 s, where x and y are in metres. The shape of wave does ...

In a spring gun having spring constant 100 N/m a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball ...