WB JEE 2021

Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while \(\log \left( {{{5c} \over {2a}}} \right),\log \left( {{{7b} \over {5c}}} \right),\log \left( {{{2a} \over {7b}}} \right)\) are in A.P. Then a, b, c are the leng...

Let A, B, C be three non-void subsets of set S. Let (A \(\cap\) C) \(\cup\) (B \(\cap\) C') = \(\phi\) where C' denote the complement of set C in S. Then

Let R be the real line. Let the relations S and T or R be defined by \(S = \{ (x,y):y = x + 1,0 < x < 2\} ,T = \{ (x,y):x - y\) is an integer}. Then

The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of exactly two successes is

If a > 0, b > 0 then the maximum area of the parallelogram whose three vertices are O(0, 0), A(a cos\(\theta\), b sin\(\theta\)) and B(a cos\(\theta\), \(-\) b sin\(\theta\)) is

Let A be the fixed point (0, 4) and B be a moving point on X-axis. Let M be the midpoint of AB and let the perpendicular bisector of AB meets the Y-axis at R. The locus of the midpoint P of MR is

A moving line intersects the lines x + y = 0 and x \(-\) y = 0 at the points A, B respectively such that the area of the triangle with vertices (0, 0), A and B has a constant area C. The locus of the mid-point AB is given by the equation

A ray of light along \(x + \sqrt 3 y = \sqrt 3\) gets reflected upon reaching X-axis, the equation of the reflected ray is

If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-planes respectively, then the equation of the plane OAB is

A line with positive direction cosines passes through the point P(2, \(-\)1, 2) and makes equal angle with co-ordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals.

The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle \(\alpha\). The equation changes to

A plane meets the co-ordinate axes t the points A, B, C respectively such a way that the centroid of \(\Delta\)ABC is (1, r, r2) for some real r. If the plane passes through the point (5, 5, \(-\)12) then r =

The equation 6x + 8x = 10x has

let \(\alpha\), \(\beta\), \(\gamma\) be three non-zero vectors which are pairwise non-collinear. if \(\alpha\) + 3\(\beta\) is collinear with \(\gamma\) and \(\beta\) + 2\(\gamma\) is collinear with \(\alpha\) then \(\alpha\) + 3\(\beta\) ...

If a(\(\alpha\) \(\times\) \(\beta\)) + b(\(\beta\) \(\times\) \(\gamma\)) + c(\(\gamma\) + \(\alpha\)) = 0, where a, b, c are non-zero scalars, then the vectors \(\alpha\), \(\beta\), \(\gamma\) are

The rms value of potential difference V shown in the figure is

Consider a pure inductive AC circuit as shown in the figure. If the average power consumed is P, then

A 12.5 eV electron beam is used to bombard gaseous hydrogen at ground state. The energy level upto which the hydrogen atoms would be excited is

Let r, v, E be the radius of orbit, speed of electron and total energy of electron respectively in H-atom. Which of the following quantities according to Bohr theory, is proportional to the quantum number n ?

A uniform thin rod of length L, mass m is lying on a smooth horizontal table. A horizontal impulse P is suddenly applied perpendicular to the rod at one end. The total energy of the rod after the impulse is

Centre of mass (CM) of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1, 2, 3) and CM of another system of particles of 3 kg and 2 kg lies at the point (\(-\)1, 3, \(-\)2). Where should we put a particle of mass 5 kg, so t...

The carbon resistor with colour code is shown in the figure. There is no fourth band in the resistor. The value of the resistance is

Two metal wires of identical dimensions are connected in series. If \(\sigma\)1 and \(\sigma\)2 are the electrical conductivities of the metal wires respectively, the effective conductivity of the combination is

Electric field component of an EM radiation varies with time as E = a (cos\(\omega\)0t + sin\(\omega\)t cos\(\omega\)0t), where a is a constant and \(\omega\) = 1015 s\(-\)1, \(\omega\)0 = 5 \(\times\) 1015 s\(-\)1. This radiation falls on ...

For a plane electromagnetic wave, the electric field is given by\(\overrightarrow{E} = 90\sin (0.5 \times {10^3}x + 1.5 \times {10^{11}}t)\widehat k\) V/m. The corresponding magnetic field B will be

A particle of mass m and charge q moving with velocity v enters region-b from region-a along the normal to the boundary as shown in the figure. Region-b has a uniform magnetic field B perpendicular to the plane of the paper. Also, region-b ...

What is the value of current through the diode in the circuit given?

For the given logic circuit, the output Y for inputs (A = 0, B = 1) and (A = 0, B = 0) respectively are

The variation of electric field along the Z-axis due to a uniformly charged circular ring of radius a in XY-plane as shown in the figure. The value of coordinate M will be

A metal sphere of radius R carrying charge q is surrounded by a thick concentric metal shell of inner and outer radii a and b, respectively. The net charge on the shell is zero. The potential at the centre of the sphere, when the outer surf...

Three infinite plane sheets carrying uniform charge densities \(-\) \(\sigma\), 2\(\sigma\), 4\(\sigma\) are placed parallel to XZ-plane at Y = a, 3a, 4a respectively. The electric field at the point (0, 2a, 0) is

Two point charges +q1 and +q2 are placed a finite distance d apart. It is desired to put a third charge q3 in between these two charges, so that q3 is in equilibrium. This is

A spherical convex surface of power 5 D separates object and image space of refractive indices 1.0 and \(4\over3\) , respectively. The radius of curvature of the surface is

The cross-section of a reflecting surface is represented by the equation x2 + y2 = R2 as shown in the figure. A ray travelling in the positive x-direction is directed toward positive y-direction after reflection from the surface at point M....

An ideal gas of molar mass M is contained in a very tall vertical cylindrical column in the uniform gravitational field. Assuming the gas temperature to be T, the height at which the centre of gravity of the gas is located is (R\(\to\)unive...

In the given figure, 1 represents isobaric, 2 represents isothermal and 3 represents adiabatic processes of an ideal gas. If \(\Delta\)U1, \(\Delta\)U2 and \(\Delta\)U3 be the changes in internal energy in these processes respectively, then

If pressure of real gas O2, in a container is given by \(p = {{RT} \over {2V - b}} - {a \over {4{b^2}}}\), then the mass of the gas in the container is

300 g of water at 25\(^\circ\)C is added to 100 g of ice at 0\(^\circ\)C. The final temperature of the mixture is

Consider the p - V diagram for 1 mole of an ideal monatomic gas shown in the figure. Which of the following statements is/are true?

Three blocks are pushed with a force F across a frictionless table as shown in figure above. Let N1 be the contact force between the left two blocks and N2 be the contact force between the right two blocks. Then,

Consider two infinitely long wires parallel to Z-axis carrying same current I in the positive z-direction. One wire passes through the point L at coordinates (\(-\)1, +1) and the other wire passes through the point M at coordinates (\(-\)1,...

A thin charged rod is bent into the shape of a small circle of radius R, the charge per unit length of the rod being \(\lambda\). The circle is rotated about its axis with a time period T and it is found the magnetic field at a distance d a...

For two types of magnetic materials A and B, variation of \(1\over\chi\) (\(\chi\) : susceptibility) versus temperature T is shown in the figure. Then,

A small bar magnet of dipole moment M is moving with speed v along x-direction towards a small closed circular conducting loop of radius a with its centre O at x = 0 (see figure). Assume x >> a and the coil has a resistance R. Then, which o...

The acceleration versus distance graph for a particle moving with initial velocity 5 m/s is shown in the figure. The velocity of the particle at x = 35 m will be

In case of projectile motion, which one of the following figures represent variation of horizontal component of velocity (ux) with time t? (Assume that air resistance is negligible)

A body of density 1.2 \(\times\) 103 kg/m3 is dropped from rest from a height 1 m into a liquid to density 2.4 \(\times\) 103 kg/m3. Neglecting all dissipative effects, the maximum depth to which the body sinks before returning to float on ...

Two solid spheres S1 and S2 of same uniform density fall from rest under gravity in a viscous medium and after sometime, reach terminal velocities v1 and v2, respectively. If ratio of masses \({{{m_1}} \over {{m_2}}} = 8\), then $${{{v_1}} ...

Under isothermal conditions, two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If the external pressure is p, then surface tension of the bubbles is

A uniform rod of length L pivoted at one end P is freely rotated in a horizontal plane with an angular velocity \(\omega\) about a vertical axis passing through P. If the temperature of the system is increased by \(\Delta\)T, angular veloci...