List of top Questions asked in JEE Main- 2026

If probability distribution is given by \[ P(x) = \begin{array}{c|c|c|c|c|c|c|c} x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline P(x) & k & 2k^2 & 6k^2 & 2k^2 + k & 4k & k & k \\ \end{array} \] Then, the value of \( P(3<x \leq 6) \) is:
If two numbers \( a \) and \( b \) are selected from \( S = \{1, 2, 3, \dots, 100\} \), then the probability that \( |a - b| \geq 10 \) is:
Bag \( A \) contains 9 white and 8 black balls and bag \( B \) contains 6 white and 4 black balls. A ball is randomly transferred from bag \( B \) to bag \( A \), then a ball is drawn from bag \( A \). If the probability that the drawn ball is white is \( \dfrac{p}{q} \) (where \( p \) and \( q \) are coprime), then find \( p + q \):
There are 10 defective and 90 non-defective balls in a bag. 8 balls are taken one by one with replacement. Find the probability that at least 7 defective balls are selected.
Let $S$ has 5 elements and $P(S)$ is the power set of $S$. Let an ordered pair $(A,B)$ is selected at random from $P(S)\times P(S)$. If the probability that $A\cap B=\varnothing$ is $\dfrac{3^m}{2^n}$, then the value of $(m+n)$ is
If \( y = y(x) \) and \[ (1 + x^2)\,dy + (1 - \tan^{-1}x)\,dx = 0 \] and \( y(0) = 1 \), then \( y(1) \) is equal to:
The solution of the differential equation \[ x\,dy - y\,dx = \sqrt{x^2 + y^2}\,dx \] (where \(c\) is the constant of integration) is

If xdy - ydx = \(\sqrt{x^2 + y^2}\) dx. If y = y(x) \(\&\) y(1) = 0 then y(3) is :

If \[ \sec x \frac{dy}{dx} - 2y = 2 + 3\sin x \] and \[ y(0) = -\frac{7}{4}, \] then \( y\left( \frac{\pi}{6} \right) \) is:
The solution of the differential equation \[ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx \] is (where \( c \) is the integration constant):
If \( y = y(x) \) and \( (1 + x^2) \frac{dy{dx} + (1 - \tan^{-1}x)dx = 0 \) and \( y(0) = 1 \), then \( y(1) \) is}
If \( x^4 \, dy + (4x^3 y + 2 \sin x) \, dx = 0 \) and \( f\left( \frac{\pi}{2} \right) = 0 \), then find the value of \( \pi^4 f\left( \frac{\pi}{3} \right) \) (where \( y = f(x) \)):
Given \[ f(t)=\left|\frac{t+1}{t^2}\right|,\ (t<0) \] is strictly decreasing in the interval $(2\alpha,\alpha)$, then the maximum value of \[ g(x)=2\log_e(x-2)+\alpha x^2+4x-\alpha \] is:
If $y = y(x)$ satisfies
$(1+x^2)\frac{dy}{dx} + (2 - \tan^{-1}x) = 0$
and $y(0) = 0$, then the value of $y(1)$ is:
Let $f(x)$ be a differentiable function satisfying the equations $\lim_{t \to x} \dfrac{t^2 f(x)-x^2 f(t)}{t-x} = 3$ and $f(1)=2$. Find the value of $2f(2)$.
The minimum value of \( \cos^2\theta + 6\sin\theta\cos\theta + 3\sin^2\theta \) is:

Two lenses one biconvex and other plano concave have same magnitude of power. The refractive indices of their materials are 1.5 and 1.7 respectively. If the radii of curvature of the lenses are as shown. find the ratio : \(\frac{R_1}{R_2}\) : 

300 J of energy is given to a gas at constant volume which increases its temperature from $20^\circ$C to $50^\circ$C. If $R = 8.3$ S.I. units and $C_v = \dfrac{5R}{2}$, find mass of gas.
Cycloalkene (X) reacts with bromine. During the reaction, 1 mole of cycloalkane consumes 1 mole of Br$_2$ to form a product (Y). The product (Y) has C:Br ratio of 3:1. The percentage of bromine in product (Y) is:
An ideal gas in a closed rigid container is at 50$^\circ$C and pressure 3.23 kPa. If temperature is doubled, find new pressure in Pa :
Let \(O\) be the vertex of the parabola \(y^{2}=16x\). The locus of the centroid of \(\triangle OPA\), when point \(P\) lies on the parabola and point \(A\) lies on the \(x\)-axis such that \(\angle OPA = 90^\circ\), is:
Which of the following resonating structures is the most stable?
A wave propagates whose electric field is given by \[ \vec{E} = 69 \sin(\omega t - kx)\,\hat{j}. \] Find the direction of the magnetic field.
Ellipse \( E:\; \dfrac{x^2}{36} + \dfrac{y^2}{16} = 1 \). A hyperbola is confocal with the ellipse and the eccentricity of the hyperbola is equal to \(5\). If the principal axis of the hyperbola is the \(x\)-axis, then the length of the latus rectum of the hyperbola is:
If \( O \) is the vertex of the parabola \( x^2 = 4y \), \( Q \) is a point on the parabola. If \( C \) is the locus of the point which divides \( OQ \) in the ratio \( 2:3 \), then the equation of the chord of \( C \) which is bisected at the point \( (1,2) \) is: