List of top Questions asked in JEE Main

For the AC circuit shown in the figure, $ R = 100 \, \text{k}\Omega $ and $ C = 100 \, \text{pF} $, and the phase difference between $ V_{\text{in}} $ and $ (V_B - V_A) $ is 90°. The input signal frequency is $ 10^x $ rad/sec, where $ x $ is:

A, B and C are disc, solid sphere and spherical shell respectively with the same radii and masses. These masses are placed as shown in the figure.

The moment of inertia of the given system about PQ is $ \frac{x}{15} I $, where $ I $ is the moment of inertia of the disc about its diameter. The value of $ x $ is:

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727°C and power radiated by the wire is 94.2 W. Its emissivity is $ \frac{x}{8} $, where $ x = \ldots $

A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as 1.28)

Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:

The percentage increase in magnetic field $ B $ when space within a current-carrying solenoid is filled with magnesium (magnetic susceptibility $ \chi_{mg} = 1.2 \times 10^{-5} $) is:

If $ \epsilon_0 $ denotes the permittivity of free space and $ \Phi_E $ is the flux of the electric field through the area bounded by the closed surface, then the dimension of $ \epsilon_0 \frac{d\Phi_E}{dt} $ are that of:

A rod of length $ 5L $ is bent at a right angle, keeping one side length as $ 2L $. The position of the centre of mass of the system (Consider $ L = 10 $ cm):

Two plane polarized light waves combine at a certain point whose electric field components are $ E_1 = E_0 \sin(\omega t) $ $ E_2 = E_0 \sin(\omega t + \frac{\pi}{3}) $ Find the amplitude of the resultant wave.

Two harmonic waves moving in the same direction superimpose to form a wave $ x = a \cos(1.5t) \cos(50.5t) $ where $ t $ is in seconds. Find the period with which they beat (close to the nearest integer):

The number of points of discontinuity of the function $ f(x) = \left\lfloor \frac{x^2}{2} \right\rfloor - \left\lfloor \sqrt{x} \right\rfloor, \quad x \in [0, 4], $ where $ \left\lfloor \cdot \right\rfloor $ denotes the greatest integer function, is:

Let $ ABC $ be the triangle such that the equations of lines $ AB $ and $ AC $ are: $ 3y - x = 2 \quad \text{and} \quad x + y = 2, $ respectively, and the points $ B $ and $ C $ lie on the x-axis. If $ P $ is the orthocentre of the triangle $ ABC $, then the area of the triangle $ PBC $ is equal to:

Let $ x_1, x_2, x_3, x_4 $ be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from $ x_1, x_2, x_3, x_4 $, then the resulting numbers are in an arithmetic progression. Then the value of $ \frac{1}{24} (x_1 x_2 x_3 x_4) $ is:

The integral $ \int_0^\pi \frac{(x + 3) \sin x}{1 + 3 \cos^2 x} \, dx $ is equal to:

Let $ C_1 $ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let $ C_2 $ be the circle with center $ (1, 3) $ that touches $ C_1 $ externally at the point $ (\alpha, \beta) $. If $ (\beta - \alpha)^2 = \frac{m}{n} $, and $ \gcd(m, n) = 1 $, then $ m + n $ is equal to:

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include at least 4 batsmen and at least 4 bowlers. One batsman and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is:

Let $ x = -1 $ and $ x = 2 $ be the critical points of the function $ f(x) = x^3 + ax^2 + b \log|x| + 1 $, where $ x \neq 0 $. Let $ m $ and $ M $ be the absolute minimum and maximum values of $ f $ in the interval $ \left[-2, -\frac{1}{2}\right] $. Then, $ |M + m| $ is equal to:

The remainder when $ \left( (64)^{64} \right)^{64} $ is divided by 7 is equal to:

The remainder when $ 64^{64} $ is divided by 7 is equal to:

The sum of the infinite series $ \cot^{-1} \left( \frac{7}{4} \right) + \cot^{-1} \left( \frac{19}{4} \right) + \cot^{-1} \left( \frac{39}{4} \right) + \cot^{-1} \left( \frac{67}{4} \right) + ... $ is:

If $ \alpha $ is a root of the equation $ x^2 + x + 1 = 0 $ and $$ \sum_{k=1}^{n} \left( \alpha^k + \frac{1}{\alpha^k} \right)^2 = 20$$, then n is equal to _______

x mg of Mg(OH)$_2$ (molar mass = 58) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ____ mg. (Nearest integer) (Given: Mg(OH)$_2$ is assumed to dissociate completely in H$_2$O)

The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is _______ kg. (Nearest integer)
Given: Molar mass (in g mol$^{-1}$) of Ca-40, O-16, C-12

A metal complex with a formula MC$\ell_4$3NH$_3$ is involved in sp$^3$d$^2$ hybridisation. It upon reaction with excess of AgNO$_3$ solution gives ‘x’ moles of AgCl. Consider ‘x’ is equal to the number of lone pairs of electron present in central atom of BrF$_5$. Then the number of geometrical isomers exhibited by the complex is ________

The molar conductance of an infinitely dilute solution of ammonium chloride was found to be 185 S cm$^{-1}$ mol$^{-1}$ and the ionic conductance of hydroxyl and chloride ions are 170 and 70 S cm$^{-1}$ mol$^{-1}$, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is 85.5 S cm$^{-1}$ mol$^{-1}$, its degree of dissociation is given by x $\times$ 10$^{-1}$. The value of x is ______. (Nearest integer)