List of top Questions asked in JEE Main

If $\frac{dy}{dx} +2y = sin 2x$ and $y(0) = \frac{3}4$ , then $y (\frac{π}{8})$ is equal to:

Let relation defined as $(x_1, y_1) \,R (x_2, y_2)\, x_1 ≤ x_2,\, y_1 ≤ y_2$ and given that
(a) R is reflexive but not symmetric.
(b) R is transitive. then

Let $S$ be the set of all solutions of the equation $\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^2}\right)=\pi$, $x \in\left[-\frac{1}{2}, \frac{1}{2}\right]$ Then $\displaystyle\sum_{x \in S} 2 \sin ^{-1}\left(x^2-1\right)$ is equal to

The value of $∫_0^{\frac{\pi}{4}} \frac{dx}{1+tanx} $

The value of $\frac{1\times 2^2+2\times3^2+...+100\times (101)^2}{1^2 \times 2\times2^2 \times3+...+100^2 \times 101}$

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure Then the electric fields in three different region $E_I, E_{I I}$ and $E_{I I I}$ are:

A wave $y=a\sin (\omega t-kx)$ on a string meets with another wave producing a node at $x=0$. Then the equation of the unknown wave is:

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2$ respectively. If the maximum velocities, during oscillations, are equal, the ratio of amplitudes of $A$ and $B$ is:

A short linear object of length b lies along the axis of a concave mirror of focal length $\mathrm{f}$ at a distance $\mathrm{u}$ from the pole of the mirror. The size of the image is approximately equal to:

At a hydroelectric power plant, the water pressure head is at a height of $300m$ and the water flow available is $100m^3{s}^{-1}$. If the turbine generator efficiency is $60\mathrm{\%}$, estimate the electric power available from the plant. $($Given $g=9.8{ms}^{-2})$

Which of the following is a functional isomer of Dimethyl ether?

Find the numbers of distinct real roots $|x||x + 2| - 5|x + 1| - 1$ =0

Let 'd' be the perpendicular distance from the centre of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}$= 1 to the tangent drawn at a point P on the ellipse. If F1 and F are two foci of the ellipse, then (PF1 - PF)²  is equal to;

Maximum number of orbitals possible when n = 4 and m = 0?

Let $A=\left(\begin{array}{ccc}0& 2q& r\\ p& q& -r\\ p& -q& r\end{array}\right)$. If $A{A}^T=I_3$, then $|p|$ is:

Let A = [1, 2, 3, 4, 5], m be the number of relations such as 4x ≤ 5y XRY and n be the minimum number of elements to be added from A × A to make a symmetric relation. Then the value of n + m.

The resistance \( R = \frac{V}{I} \) where \( V = (200 \pm 5) \, \text{V} \) and \( I = (20 \pm 0.2) \, \text{A} \). The percentage error in the measurement of \( R \) is:

A child stands on the edge of the cliff $10 m$ above the ground and throws a stone horizontally with an initial speed of $5 \,ms ^{-1}$ Neglecting the air resistance, the speed with which the stone hits the ground will be ______$ms ^{-1}$ (given, $g=10 \,ms ^{-2}$ )

Which of the following have undistorted octahedral structures?
1. $S{F}_6$
2. $P{F}_6^{-}$
3. $Si{F}_6^{2-}$
4. $Xe{F}_6$
Select the correct answer using the codes given below:

If sin $5x+\sin 3x+\sin x = 0$, then the value of x other than zero, lying between π$0\le \times \le \frac{\mathrm{\pi }}{2}$ is;

If an be the $n^{\text{th }}$ term of the GP of positive numbers. Let $\sum _{n=100}^{100}{a}_{2n}=\alpha$ and $\sum _{n=1}^{100}{a}_{2n-1}=\beta$ such that $\alpha \ne \beta$ then the common ratio is:

Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$Then $R$ is