JEE Main 2021 (Online) 31st August Evening Shift

A tangent line L is drawn at the point (2, \(-\)4) on the parabola y2 = 8x. If the line L is also tangent to the circle x2 + y2 = a, then 'a' is equal to ___________.

Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is :

The sum of the roots of the equation \(x + 1 - 2{\log _2}(3 + {2^x}) + 2{\log _4}(10 - {2^{ - x}}) = 0\), is :

Let a1, a2, a3, ..... be an A.P. If \({{{a_1} + {a_2} + .... + {a_{10}}} \over {{a_1} + {a_2} + .... + {a_p}}} = {{100} \over {{p^2}}}\), p \(\ne\) 10, then \({{{a_{11}}} \over {{a_{10}}}}\) is equal to :

The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is ____________.

If \(S = {7 \over 5} + {9 \over {{5^2}}} + {{13} \over {{5^3}}} + {{19} \over {{5^4}}} + ....\), then 160 S is equal to ________.

The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :

Let A be the set of all points (\(\alpha\), \(\beta\)) such that the area of triangle formed by the points (5, 6), (3, 2) and (\(\alpha\), \(\beta\)) is 12 square units. Then the least possible length of a line segment joining the origin to...

The number of solutions of the equation \({32^{{{\tan }^2}x}} + {32^{{{\sec }^2}x}} = 81,\,0 \le x \le {\pi \over 4}\) is :

Let \(\overrightarrow a ,\overrightarrow b ,\overrightarrow c\) three vectors mutually perpendicular to each other and have same magnitude. If a vector \({ \overrightarrow r }\) satisfies.
$$\overrightarrow a \times \{ (\overrightarro...

At very high frequencies, the effective impendence of the given circuit will be ________________ \(\Omega\).

A parallel plate capacitor of capacitance 200 \(\mu\)F is connected to a battery of 200 V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change ...

A bandwidth of 6 MHz is available for A.M. transmission. If the maximum audio signal frequency used for modulating the carrier wave is not to exceed 6 kHz. The number of stations that can be broadcasted within this band simultaneously witho...

The equivalent resistance of the given circuit between the terminals A and B is :

A resistor dissipates 192 J of energy in 1s when a current of 4A is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in 5s in _________ J.

A free electron of 2.6 eV energy collides with a H+ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (h = 6.6 \(\times\) 10\(-\)34 Js)

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportio...

A coil is placed in a magnetic field \(\overrightarrow B\) as shown below :A current is induced in the coil because \(\overrightarrow B\) is :

The magnetic field vector of an electromagnetic wave is given by \(B = {B_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos (kz - \omega t)\); where \(\widehat i,\widehat j\) represents unit vector along x and y-axis respectively. At t = 0...

If VA and VB are the input voltages (either 5V or 0V) and V0 is the output voltage then the two gates represented in the following circuit (A) and (B) are :-

Statement - I :To get a steady dc output from the pulsating voltage received from a full wave rectifier we can connect a capacitor across the output parallel to the load RL.Statement - II :To get a steady dc output from the pulsating voltag...

Choose the incorrect statement :(1) The electric lines of force entering into a Gaussian surface provide negative flux.(2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same.(3) In a uniform elec...

Cross-section view of a prism is the equilateral triangle ABC in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from P (midpoint of B...

If RE be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 'r' below and a height 'r' above the earth surface is : (Given : r < RE)

Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $$\theta$...

A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

A sample of gas with \(\gamma\) = 1.5 is taken through an adiabatic process in which the volume is compressed from 1200 cm3 to 300 cm3. If the initial pressure is 200 kPa. The absolute value of the workdone by the gas in the process = _____...

Statement : 1If three forces \({\overrightarrow F _1},{\overrightarrow F _2}\) and \({\overrightarrow F _3}\) are represented by three sides of a triangle and \({\overrightarrow F _1} + {\overrightarrow F _2} = - {\overrightarrow F _3}\), ...

A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle is :(Assume that the current is flowing in the clockwise direction.)

A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 103 cm3. If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of 0...

A particle is moving with constant acceleration 'a'. Following graph shows v2 versus x(displacement) plot. The acceleration of the particle is ___________ m/s2.

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 \(\times\) 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the com...

A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis perpendicula...

A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density \({1 \over 4}\) times that of the bob and the length of the thread is increas...

For a body executing S.H.M. :(1) Potential energy is always equal to its K.E.(2) Average potential and kinetic energy over any given time interval are always equal.(3) Sum of the kinetic and potential energy at any point of time is constant...

If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :

The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisions of vernier scale. One main scale division is 1 mm. The main scale reading is 10 mm and...

Statement I :Two forces \(\left( {\overrightarrow P + \overrightarrow Q } \right)\) and \(\left( {\overrightarrow P - \overrightarrow Q } \right)\) where \(\overrightarrow P \bot \overrightarrow Q\), when act at an angle \(\theta\)1 to ...

In a Young's double slit experiment, the slits are separated by 0.3 mm and the screen is 1.5 m away from the plane of slits. Distance between fourth bright fringes on both sides of central bright is 2.4 cm. The frequency of light used is __...

A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1 : 2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is :-