List of top Questions asked in JEE Main- 2024

A particle connected with light thread is performing vertical circular motion. Speed at point B (Lowermost point) is sufficient, so that it is able to complete its circular motion. Ignoring air friction, find the ratio of kinetic energy at A to that at B. (A being top-most point)

Alternating voltage and current in circuit is given as \(V = (100 \;sin \;ωt)\) volt 
\(I = 100\;sin\bigg(ωt+\frac{π}{3}\bigg)mA\)
Find average power dissipated in circuit.

A liquid drop of radius R is divided into 27 identical drops. If the surface tension of the drops is T, then find work done in this process.

Two charged particles A and B have charge q each while masses are \(m_1\) & \(m_2\). Both have the same velocity v and enter into a transverse magnetic field B such that their radii are \(r_1\) & \(r_2\). Then the ratio \(m_1 : m_2\) is

The intensity at each slit is equal for a YDSE and it is maximum \(I_{max}\) at \(7π\) central maxima. If I is intensity for phase difference \(\frac{7π}{2}\) between two waves on screen. Then \(\frac{I}{I_{max}}\) is?

In a simple pendulum of length 10 m, the string is initially kept horizontal and the bob is released. 10% of energy is lost till the bob reaches the lowest position. Then find the speed of the bob at the lowest position.

Two forces \(F_1\) and \(F_2\) are applied on two rods \(P\) and \(Q\) of same materials such that elongation in rods are same. If ratio of their radii is \(x : y\) and ratio of length is \(m : n\), then ratio of \(F_1 : F_2\) is

A uniform wire has length L and radius r. It is acted on by a force F as shown. The elongation is l. If F and r are both halved, the new elongation will be :

The truth table for the combination of logical gates

A planet at distance r from the sun takes 200 days to complete one revolution around the sun. What will be the time period for a planet at distance \(\frac{r}{4}\) from the sun?

Let \(a_1,a_2,a_3\), ..., an, be in A. P. and \(S_n\) denotes the sum of first \(n\) terms of this A. P. is \(S_{10}\) =\(390, \frac{a_{10}}{a_{50}} =\frac{15}{7}\), then \(S_{15} -S_5 =\) _________.

The ratio of magnitude of potential energy and kinetic energy for \(5^{th}\) excited state of hydrogen atom is

\(∫^{\frac{π}{3}} _0\) \(cos^4x\) \(dx\) is equal to a \(\pi + b\sqrt3\), then \(a^2 + b\) is equal to:

The value of integrate \(∫^1_0 (2x^3 - 3x^2 - x + 1)^\frac{1}{3}dx\) is :

Let the system of equations \(x+2y+3z = 5\), \(2x+3y+z = 9\), \(4x+3y+λz = μ\) have an infinite number of solutions. Then \(λ + 2μ\) is equal to

If the domain of the function \(f(x)\) = \(\frac{\sqrt{x^2-25}}{(4-x^2)}+ \log(x^2+2x-15)\) is \((-∞, α) ∪ (β, ∞)\), then \(α^2+β^2\) is equal to \(b\)

The number of solution of the equation \(4sin^2 x-4cos^3 x+9-4cos x = 0\), \(x ∈ [-2\pi, 2\pi]\)

If the mirror image of the point \(P(3,4,9)\) in the Line 
\(\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}\) is \((α,β,γ)\) then find \(14(a+ẞ+y)\) is:

Let \(α\) and \(β\) the roots of equation \(px^2 + qx - r = 0\), where \(P≠ 0\). If \(p,q,r\) be the consecutive term of non constant G.P and \(\frac{1}{α} + \frac{1}{β} = \frac{3}{4}\) then the value of \((α - β)^2\) is:

Let m and n be the coefficient of \(7^{th}\) and \(13^{th}\) term in expansion of \(\bigg(\frac{1}{3x^{\frac{1}{3}}} +\frac{1}{2x^{\frac{2}{5}}}\bigg)^{18}\), then \(\bigg(\frac{m}{n}\bigg)^{\frac{1}{3}}\) is:

The minimum value of \(| z+ \frac{3+4i}{2}|, |z| \leq 1\) is,

Let vertex \(A(2, 3, 1), B(3, 2, -1), C(-2, 1, 3)\). If \(AD\) is angle bisector of angle \(A\), then projection of \(\overrightarrow{AD}\) on \(\overrightarrow{AC}\) is equal to:

Find out charge (in C) required for electrolysis of \(1\) mole of \(H_2O\) to produce \(O_2\) on one of the electrodes. \((F = 96500 \;C)\)

Ethylene glycol of \(x\) \(kg\) is mixed with \(18.6\) \(kg\) of solvent, \(24 °C\) depression in freezing point takes place. Calculate value of \(x\). (Given: \(K_1\) = \(1.6 °C/molal\) M.W. of ethylene glycol = \(62\) \(g/mol\))