List of top Questions asked in JEE Main

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be:

The free space inside a current carrying toroid is filled with a material of susceptibility \( 2 \times 10^3 \). The percentage increase in the value of magnetic field inside the toroid will be:

The critical angle for a denser refractive index is 45°. The speed of light in water medium is \( 3 \times 10^8 \) m/s. The speed of light in the denser medium is:

On a temperature scale X, the boiling point of water is 65° X and the freezing point is 15° X. Assume that the X scale is linear. The equivalent temperature corresponding to 95° X on the Fahrenheit scale would be:

A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is E. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is E₅. The ratio \( E_5 / E_1 \) is:

An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m/s to keep it in position. The number of bullets fired per second by the machine gun is:

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (x) starting from mean position to extreme position (A) is given by:

From the v - t graph shown, the ratio of distance to displacement in 25 s of motion is:

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and the third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed (\( V_{\text{rms}} \)) and choose the correct answer from the options given below:

Two radioactive elements A and B initially have the same number of atoms. The half-life of A is the same as the average life of B. If \( \lambda_A \) and \( \lambda_B \) are the decay constants of A and B respectively, then choose the correct relation from the given options:

As per the given graph, choose the correct representation for curve A and curve B.

(Where \( X_L = \) reactance of pure inductive circuit connected with A.C. source, \( X_C = \) reactance of pure capacitive circuit connected with A.C. source, \( R = \) impedance of pure resistive circuit connected with A.C. source, and \( Z = \) impedance of the LCR series circuit)

A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at 4 km distance from it is \( x \times 10^{-2} \) m. The value of \( x \) is:

The electric field in an electromagnetic wave is given as \[ \vec{E} = 20 \sin \left( \omega t - \frac{x}{c} \right) \, \hat{j} \, \text{N/C} \] where \( \omega \) and \( c \) are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of \( 5 \times 10^4 \, \text{m}^3 \) will be (Given \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 / \text{Nm}^2 \)):

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

The mean of the coefficients of \( x^n, x^{n+1}, \dots, x^r \) in the binomial expansion of \( (2 + x)^r \) is:

If \( a \) and \( b \) are the roots of the equation \( x^2 - 7x - 1 = 0 \), then the value of \( a^2 + b^2 + a^3 + b^3 is equal to:}

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sit on the allotted seat, is:

Let a line \( l \) pass through the origin and be perpendicular to the lines \[ l_1: \vec{r}_1 = i + j + 7k + \lambda(i + 2j + 3k), \quad \lambda \in \mathbb{R} \] \[ l_2: \vec{r}_2 = -i + j + 2k + \mu(i + 2j + k), \quad \mu \in \mathbb{R} \] If \( P \) is the point of intersection of \( l_1 \) and \( l_2 \), and \( Q (a, b, \gamma) \) is the foot of perpendicular from P on \( l \), then \( (a + b + \gamma) \) is equal to:

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are \( \rho \) and \( \frac{\rho}{3} \) respectively. The ratio of acceleration due to gravity at their surfaces (i.e. \( g_A : g_B \)) will be:

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of ----- from the centre:

The number of integral terms in the expansion of \left( 3^{\frac{1}{2}} + 5^{\frac{1}{4}} \right)^{680} \text{ is equal to:}

The number of ordered triplets of the truth values of \( p, q, r \) and such that the truth value of the statement \[ (p \lor q) \land (p \lor r) \implies (q \lor r) \text{ is True, is equal to:} \]

Let \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 0 & 3 \\ 1 & 0 & 0 \end{bmatrix} \), where \( a, c \in \mathbb{R} \). If \( A^n = A \) and the positive value of \( a \) belongs to the interval \( (n-1, n] \), where \( n \in \mathbb{N} \), then \( n \) is equal to:

For \( m, n>0 \), let \( \alpha(m,n) = \int_{0}^{1} (1 + 3t)^{n} \, dt \). If \( \alpha(10,6) = \int_{0}^{1} (1 + 3t)^{6} \, dt \) and \( \alpha(11,5) = p(14)^{5} \), then \( p \) is equal to:

Let \( S = 109 + \frac{108}{5} + \frac{107}{5^2} + \frac{106}{5^3} + \cdots \). Then the value of \( (16S - (25)^{3}) \) is equal to: