List of top Questions asked in JEE Main- 2026

Select the correct statements : (a) Glucose has 2 anomeric forms.
(b) Both forms have difference in configuration at \(C_1\) carbon.
(c) \(\alpha\)-form has more melting point than \(\beta\)-form.
(d) Specific rotation of \(\alpha\)-form is \(+19^\circ\) and \(\beta\)-form has \(+112^\circ\).
(e) \(\alpha\)-form crystallises at \(307^\circ\) and \(\beta\)-form crystallises at \(371^\circ\).
Find dimensions of \( \dfrac{A}{B} \) if \[ \left( P + \frac{A^2}{B} \right) + \frac{1}{2}\rho V^2 = \text{constant}, \] where \( P \rightarrow \) pressure, \( \rho \rightarrow \) density, \( V \rightarrow \) speed.
An ideal gas has number of moles \(n=2\), initial volume \(V_0\) and pressure \[ P=P_0\left[1+\left(\frac{V_0}{V}\right)^2\right]^{-1}. \] The gas goes from state \(A\) (initial) to \(B\) (final) such that volume becomes \(3V_0\). Find \(T_A-T_B\).
If coefficient of $x^3$ in $(1+x)^3 + (1+x)^4 + \dots + (1+x)^{99} + (1+kx)^{100}$ is $\binom{100}{3} \left( \frac{101}{4} - 43n \right)$, then the value of $(k^3 + 43n)$ is
If $\int_{-2}^2 ([\sin x] + |x \sin x|) dx = 2 \sin 2 - 4 \cos 2 - \beta$, then the value of $|\beta|$ where $[\cdot]$ is GIF is
In an A.P. first term is $\frac{10}{3}$ and first 30 terms are non-negative such that sum of first 30 terms = $(T_{30})^3$, then d is equal to (where $T_n$ is $n^{\text{th}}$ term of A.P., and d is the common difference of A.P.)
Find number of ways of arranging 4 Boys \& 3 Girls such that all girls are not together :
A particle is moving along the \(x\)-axis where the speed varies as \[ v^2 = 100 - x^2 \] Determine the time period.
If $A = \frac{\sin 3^\circ}{\cos 9^\circ} + \frac{\sin 9^\circ}{\cos 27^\circ} + \frac{\sin 27^\circ}{\cos 81^\circ}$ and $B = \tan 81^\circ - \tan 3^\circ$, find $\frac{B}{A}$
Let mean and median of 9 observations 8, 13, a, 17, 21, 51, 103, b, 67 are 40 and 21 respectively where a > b. If mean deviation about median is 26 then 2a is :-
Find the ratio of wave number (\( \nu \)) of the 1st line of Balmer series and Brackett series for Hydrogen-like species.
Two blocks \(A\) and \(B\) are released from rest on two inclined planes of the same inclination. One inclined plane is smooth while the other is rough as shown in the figure. If block \(B\) takes \(50\%\) more time to reach the bottom than block \(A\), find the coefficient of friction \((\mu)\). The inclination of the plane is \(45^\circ\).
If force \( \vec{F}= 2t\,\hat{i} + 3t^2\,\hat{j} \) acts on a particle of mass \(m = 2\,\text{kg}\), find the power at \(t = 2\,\text{s}\) if the particle was initially at rest.
Two projectiles \(A\) and \(B\) are launched with the same speed at angles \(15^\circ\) and \(30^\circ\) respectively. Find the ratio of range \(A\) to range \(B\).
Length of rods are \( \ell \) and \(2\ell\) respectively and their Young's modulus are \( \gamma \) and \(2\gamma\) respectively. Given: \[ \ell = 0.314\,\text{m}, \quad R = 0.2\,\text{mm} \,(\text{same}), \quad \gamma = 2\times10^9 \]
Find the total extension \( \Delta \ell \).
Nuclei \(A\) and \(B\) form a nucleus \(C\). Binding energy per nucleon for \(A, B\) and \(C\) are \(3\,\text{MeV}, 7\,\text{MeV}\) and \(6\,\text{MeV}\) respectively. Find the energy produced in the reaction: \[ 2A^{3} + B^{4} \rightarrow C^{10} \]
In an AC circuit a resistor \(100\Omega\), inductor \(0.1\,\text{mH}\) and a capacitor are connected in series across an AC source of \(220\,\text{V},\,50\,\text{Hz}\). If the power factor of the circuit is \( \frac{1}{2} \) and \( |X_L - X_C| = \alpha\sqrt{3}\,\Omega \), find \(\alpha\).
Consider the differential equation $\frac{dy}{dx} = (x^2 + x + 1)(y^2 - y + 1)$. If $y(0) = \frac{1}{2}$, then the value of $2(y(1)) - 1$ is
If Latus rectum of parabola $y^2 = 4kx$ and ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ coincide then the value of $e^2 + 2\sqrt{2}$ is, where $e$ is eccentricity of ellipse
A circle $x^2 + y^2 + x - 3y = 0$ passes through $P(1, 2)$. If 2 chords (PS \& PR) drawn from P are bisected by $y$-axis, then mid point of RS is $(\alpha, \beta)$, find $6(\alpha + \beta)$
If $S = \{ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}, A^2 - 4A + 3I = \text{Null matrix}, a, b, c, d \in \{0, 1, 2, 3, 4\} \text{ and } \text{Tr}(A) = 4 \}$. Then the number of elements of set $S$ is/are
Let $A$ is a matrix of order 3 such that $|A| = -4$, then the value of $|\text{adj}(\text{adj}(2\text{adj} A)^{-1})|$ is
If \( L_1 : x - y = 0 \), \( L_2 : y = -3x \), \( L_3 \) is the obtuse angle bisector of \( L_1 \) and \( L_2 \), and \( L_4 : x + 3 = 0 \). Let \( A \) be the point of intersection of \( L_4 \) and \( L_1 \), \( B \) be the point of intersection of \( L_4 \) and \( L_2 \), and \( C \) be the point of intersection of \( L_4 \) and \( L_3 \). Then the value of \( \dfrac{(BC)^2}{(AC)^2} \) is:
Two 4-bit binary numbers \(A = 1101\) and \(B = 1010\) are given in the input logic circuit. Find the output \(Y\).
Each diode in the circuit has \(10\Omega\) resistance in forward bias and infinite resistance in reverse bias. Find the time constant of the circuit. Given: \(R=100\Omega\), \(C=0.2\,\mu F\).