List of top Questions asked in JEE Main- 2024

Let \( f : \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] \rightarrow \mathbb{R} \) be a differentiable function such that \( f(0) = \frac{1}{2} \). If the \( \lim_{x \to 0} \frac{\int_{0}^{x} f(t) \, dt}{e^{x^2} - 1} = \alpha \), then \( 8\alpha^2 \) is equal to:

If \( 2 \sin^3 x + \sin 2x \cos x + 4 \sin x - 4 = 0 \) has exactly 3 solutions in the interval \( \left[ 0, \frac{n \pi}{2} \right] \), \( n \in \mathbb{N} \), then the roots of the equation \( x^2 + nx + (n - 3) = 0 \) belong to:

Let \( A (2, 3, 5) \) and \( C(-3, 4, -2) \) be opposite vertices of a parallelogram \( ABCD \). If the diagonal \( \overrightarrow{BD} = \hat{i} + 2 \hat{j} + 3 \hat{k} \), then the area of the parallelogram is equal to

If \[ f(x) = \begin{vmatrix} 2 \cos^4 x & 2 \sin^4 x & 3 + \sin^2 2x \\ 3 + 2 \cos^4 x & 2 \sin^4 x & \sin^2 2x \\ 2 \cos^4 x & 3 + 2 \sin^4 x & \sin^2 2x \end{vmatrix} \] then \( \frac{1}{5} f'(0) \) is equal to

Consider the system of linear equations \( x + y + z = 4\mu \), \( x + 2y + 2\lambda z = 10\mu \), \( x + 3y + 4\lambda^2 z = \mu^2 + 15 \), where \( \lambda, \mu \in \mathbb{R} \). Which one of the following statements is NOT correct?

Let \(y = y(x)\) be the solution of the differential equation \(\sec(x) \frac{dy}{dx} + [2(1 - x) \tan(x) + x(2 - x)] = 0\) such that \(y(0) = 2\). Then \(y(2)\) is equal to:

The area (in square units) of the region bounded by the parabola \(y^2 = 4(x - 2)\) and the line \(y = 2x - 8\) is:

Let \( g : \mathbb{R} \rightarrow \mathbb{R} \) be a non-constant twice differentiable function such that \( g'\left(\frac{1}{2}\right) = g'\left(\frac{3}{2}\right) \). If a real-valued function \( f \) is defined as \[ f(x) = \frac{1}{2} \left[ g(x) + g(2 - x) \right], \] then

Calculate the Molarity of a Solution having density = \(1.5\) \(g/ml\). \(\%(w/w)\) of Solute is \(36\%\) and Molecular weight of Solute is \(36\) \(g/mol\)

How many of the following vitamins are stored in Human Body?
A, B, C, D, E, K?

Match the following : 

(a) \([Cr(H_2O)_6]^{+3}\)	(i) \(t^2_{2g}eg^0\)
(b) \([Fe(H_2O)_6]^{+3}\)	(ii) \(t^3_{2g}eg^0\)
\((c) [Ni(H_2O)_6]^{+2}\)	(iii) \(t^3_{2g}eg^2\)
(d) \([V(H_2O)_6]^{+3}\)	(iv) \(t^6_{2g}eg^2\)

Number of moles of \(H^+\) required by \(1\) mole \(MnO_4^-\) to oxidize oxalate ion to \(CO_2\) is ____ .

What will be the reactivity order of following compounds towards electrophilic substitution reaction ?

Choose the correct answers. 

1. \(Mn_2O_7 \) is a oil at room temperature. 
2. \(V_2O_4\) react with acid to give \(VO^{2+}\).
3. \(CrO\) is a basic oxide.
4. \(V_2O_5\) does not react with acids.

Quantum number for outermost electron of K-atom are given by

Which of the following has maximum ionic character?

Statement-I : Among \(15^{th}\) group hydrides reducing character decreases from
\(NH_3\) to \(BiH_3\).
Statement-II : \(E_2O_3\) and \(E_2O_5\) are always basic. [Where \(E\) is group \(15\) element]

The number of solution of equation \(e^{sinx} - 2e ^{-sinx} = 2\) is

If \(A = {1, 2, 3, … 100}\), \(R = {(x, y) | 2x = 3y, x, y ∈ A}\) is symmetric relation on \(A\) and the number of elements in \(R\) is \(n\), the smallest integer value of \(n\) is

The value of \(\frac {120}{\pi^3}|∫_0^\pi\frac {x^2sinx.cosx}{(sinx)^4+(cosx)^4}dx|\) is

A parabola has vertex \((2, 3)\), equation of directrix is \(2x – y = 1\) and equation of ellipse is \(\frac {x^2}{a^2} +\frac {y^2}{b^2} =1\), \(e=\frac {1}{\sqrt 2}\) and ellipse passing through focur of parabola then square of length of latus rectum of ellipse is

If \((α, β, γ)\) is mirror image of the point \((2, 3, 4)\) with respect to the line \(\frac {(x-1)}{2}=\frac {(y-2)}{3}=\frac {(z-3)}{4}\). Then \(2α + 3β + 4γ\) is

The line passes through the centre of circle \(x^2 + y^2 – 16x – 4y = 0\), it interacts with the positive coordinate axis at A & B. Then find the minimum value of OA + OB, where O is origin.

Half life of a first order reaction is \(36\;hr\). Find out time (in hour) required for concentration of reactant to get reduced by \(90\%\).

A compound \((x)\) with molar mass \(108\) \(g\) \(mol^{-1}\) undergoes acetylation to give product with molar mass \(192\) \(g\) \(mol^{-1}\)