JEE Main 2021 (Online) 26th February Morning Shift

The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is :

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is :

The sum of 162th power of the roots of the equation x3 \(-\) 2x2 + 2x \(-\) 1 = 0 is ________.

In an increasing geometric series, the sum of the second and the sixth term is \({{25} \over 2}\) and the product of the third and fifth term is 25. Then, the sum of 4th, 6th and 8th terms is equal to :

The sum of the infinite series \(1 + {2 \over 3} + {7 \over {{3^2}}} + {{12} \over {{3^3}}} + {{17} \over {{3^4}}} + {{22} \over {{3^5}}} + ......\) is equal to :

Let R = {(P, Q) | P and Q are at the same distance from the origin} be a relation, then the equivalence class of (1, \(-\)1) is the set :

The intersection of three lines x \(-\) y = 0, x + 2y = 3 and 2x + y = 6 is a :

If \(\sqrt 3 ({\cos ^2}x) = (\sqrt 3 - 1)\cos x + 1\), the number of solutions of the given equation when \(x \in \left[ {0,{\pi \over 2}} \right]\) is __________.

The number of integral values of 'k' for which the equation \(3\sin x + 4\cos x = k + 1\) has a solution, k\(\in\)R is ___________.

If \(\overrightarrow a\) and \(\overrightarrow b\) are perpendicular, then $$\overrightarrow a \times \left( {\overrightarrow a \times \left( {\overrightarrow a \times \left( {\overrightarrow a \times \overrightarrow b } \right)} \rig...

In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________.

An alternating current is given by the equation i = i1 sin \(\omega\)t + i2 cos \(\omega\)t. The rms current will be :

If \(\lambda\)1 and \(\lambda\)2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of \(\lambda\)1 : \(\lambda\)2 is :

Consider the combination of 2 capacitors C1 and C2 with C2 > C1, when connected in parallel, the equivalent capacitance is \({{15} \over 4}\) times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitor...

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initial...

A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R3. Its time period of revolution will be given by :

The maximum and minimum amplitude of an amplitude modulated wave is 16V and 8V respectively. The modulation index for this amplitude modulated wave is x \(\times\) 10\(-\)2. The value of x is __________.

Five equal resistances are connected in a network as shown in figure. The net resistance between the points A and B is :

In an electrical circuit, a battery is connected to pass 20C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15V. The workdone by the battery is __________J.

Given below are two statements : one is labeled as Assertion A and the other is labelled as Reason R.Assertion A : An electron microscope can achieve better resolving power than an optical microscope.Reason R : The de Broglie's wavelength o...

A radiation is emitted by 1000W bulb and it generates an electric field and magnetic field at P, placed at a distance of 2m. The efficiency of the bulb is 1.25%. The value of peak electric field at P is x \(\times\) 10\(-\)1 V/m. Value of x...

The circuit contains two diodes each with a forward resistance of 50\(\Omega\) and with infinite reverse resistance. If the battery voltage is 6V, the current through the 120\(\Omega\) resistance is ____________ mA.

LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is 1.9 eV. Calculate the wavelength of light emitted and its colour.[h = 6.63 \(\times\) 10\(-\)34 Js and c = 3 \(\times\) 108 ms\(-\)1]

Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = \({{\sqrt 3 } \over 2}L\).

A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value | f | = 40 cm. The image of object produced by the mirror is of height 25 cm and has the same orientation of t...

A planet revolving in elliptical orbit has :A. a constant velocity of revolution.B. has the least velocity when it is nearest to the sun.C. its areal velocity is directly proportional to its velocity.D. areal velocity is inversely proportio...

Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If \(\sqrt 8\)R is the distance between the centres of a ring (of...

The temperature \(\theta\) at the junction of two insulating sheets, having thermal resistances R1 and R2 as well as top and bottom temperatures \(\theta\)1 and \(\theta\)2 (as shown in figure) is given by :

A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at...

A boy pushes a box of mass 2 kg with a force \(\overrightarrow F = \left( {20\widehat i + 10\widehat j} \right)N\) on a frictionless surface. If the box was initially at rest, then ___________ m is displacement along the x-axis after 10s.

A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of 1.8 m/s2 will be ______________ N. [g = 10 m/s2]

As shown in the figure, a block of mass \(\sqrt 3\) kg is kept on a horizontal rough surface of coefficient of friction \({1 \over {3\sqrt 3 }}\). The critical force to be applied on the vertical surface as shown at an angle 60\(^\circ\) w...

The normal density of a material is \(\rho\) and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be :

Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to t...

If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor :

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it wi...

In a typical combustion engine the workdone by a gas molecule is given by \(W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {kT}}}}\), where x is the displacement, k is the Boltzmann constant and T is the temperature. If \(\alpha\) and $$\...

In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :

The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = \(-\) 0.21 sin (x + 30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x \(\times\) ...