List of top Questions asked in JEE Main

The major product obtained in the following reaction is :

Given the equilibrium constant:
\(K_C\) of the reaction :
\(\mathrm{Cu(s) + 2Ag^{+}(aq) \rightarrow Cu^{2+}(aq) + 2Ag(s)}\) is \(10\times10^{15}\), calculate the \(E^{0}_{cell}\) of this reaction at 298 K
\(\left[2.303\,\frac{RT}{F}\ \text{at 298 K} = 0.059\ \mathrm{V}\right]\)

A particle of mass m and charge q is in an electric and magnetic field given by
\(\vec{E} = 2\hat{i} + 3\hat{j};\ \vec{B} = 4\hat{j} + 6\hat{k}\).
The charged particle is shifted from the origin to the point P(x = 1; y = 1) along a straight path. The magnitude of the total work done is :

The coordination number of Th in \(\mathrm{K_4[Th(C_2O_4)_4(OH_2)_2]}\) is :
\(\left(\mathrm{C_2O_4^{2-}} = \text{Oxalato}\right)\)

The major product of the following reaction is :

A pendulum is executing simple harmonic motion and its maximum kinetic energy is \(K_1\). If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is \(K_2\). Then :

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is \(\sqrt{3}\), then the angle of incidence is:

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to: ( \( \frac{hc}{e} = 1240 \) nm eV)

In a double-slit experiment, green light (5303 Å) falls on a double slit having a separation of \(19.44\ \mu\mathrm{m}\) and a width of \(4.05\ \mu\mathrm{m}\). The number of bright fringes between the first and the second diffraction minima is :

A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is :

A galvanometer having a resistance of \(20\ \Omega\) and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is:

Two rods A and B of identical dimensions are at temperature \( 30^\circ\mathrm{C} \). If A is heated upto \( 180^\circ\mathrm{C} \) and B upto \( T^\circ\mathrm{C} \), then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is

An electric field of 1000 V/m is applied to an electric dipole at angle of \( 45^\circ \). The value of electric dipole moment is \( 10^{-29} \) C.m. What is the potential energy of the electric dipole?

A particle moves from the point \( (2.0\hat{i} + 4.0\hat{j}) \) m, at t = 0, with an initial velocity \( (5.0\hat{i} + 4.0\hat{j}) \) \( \mathrm{ms^{-1}} \). It is acted upon by a constant force which produces a constant acceleration \( (4.0\hat{i} + 4.0\hat{j}) \) \( \mathrm{ms^{-2}} \). What is the distance of the particle from the origin at time 2 s?

The region between \( y = 0 \) and \( y = d \) contains a magnetic field \( \overrightarrow{B} = B\hat{z} \). A particle of mass m and charge q enters the region with a velocity \( \overrightarrow{v} = v\hat{i} \). If \( d = \frac{mv}{2qB} \), the acceleration of the charged particle at the point of its emergence at the other side is :

In the circuit shown, the potential difference between A and B is :

The circuit shown below contains two ideal diodes, each with a forward resistance of \( 50\ \Omega \). If the battery voltage is 6 V, the current through the \( 100\ \Omega \) resistance (in Amperes) is :

If the point \( (2, \alpha, \beta) \) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane \( 2x - 5y = 15 \), then \( 2\alpha - 3\beta \) is equal to

Let \( S_n = 1 + q + q^2 + \ldots + q^n \) and \( T_n = 1 + \left(\frac{q+1}{2}\right) + \left(\frac{q+1}{2}\right)^2 + \ldots + \left(\frac{q+1}{2}\right)^n \) where q is a real number and \( q \ne 1 \). If \( {}^{101}C_1 + {}^{101}C_2 \cdot S_1 + \ldots + {}^{101}C_{101}\cdot S_{100} = \alpha T_{100} \) then \( \alpha \) is equal to

Two lines \( \frac{x-3}{1} = \frac{y+1}{3} = \frac{z-6}{-1} \) and \( \frac{x+5}{7} = \frac{y-2}{-6} = \frac{z-3}{4} \) intersect at the point R. The reflection of R in the xy-plane has coordinates :

Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is :

Let \( f(x) = \frac{x}{\sqrt{a^2+x^2}} - \frac{d-x}{\sqrt{b^2+(d-x)^2}} \), \( x \in R \), where a, b and d are non-zero real constants. Then :

If 19^th term of a non-zero A.P. is zero, then its (49^th term) : (29^th term) is :

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :

If \(\begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix} = (a+b+c)(x + a + b + c)^2\), \(x \ne 0\), then x is equal to :