List of top Questions asked in JEE Main- 2026

Find the ratio of wave number (\( \nu \)) of the 1st line of Balmer series and Brackett series for Hydrogen-like species.
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 the length of image of rod \(AB\). The rod is placed in front of a concave mirror of focal length \(f = 10\,\text{cm}\). End \(A\) is \(20\,\text{cm}\) from the mirror and the length \(AB = 10\,\text{cm}\).
Resolving power of a telescope is \(5\times10^{-7}\,\text{rad}\). If wavelength of incident light is \(500\,\text{nm}\), find the diameter of the aperture of the telescope.
Let $y = \tan^{-1}\left( \frac{3\cos x - 4\sin x}{4\cos x + 3\sin x} \right) + \tan^{-1}\left( \frac{x}{1 + \sqrt{1 + x^2}} \right)$. Then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{3}}{2}$ is :
A slit of width \(a\) is illuminated by light of wavelength \(\lambda\). The linear separation between the 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance \(D\) from the slit is:
In a screw gauge, when the circular scale is given five complete rotations, it moves linearly by \(2.5\,\text{mm\). If the circular scale has 100 divisions, the least count of the screw gauge is:}
There is a spiral which has \(r_i=3\,\text{cm\), \(r_{ext}=6\,\text{cm}\), \(I=20\,\text{mA}\) and \(N=200\), where \(r_i\) : internal radius \(r_{ext}\) : external radius \(N\) : number of turns \(I\) : current. Find the magnetic moment of the spiral.}
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: \(R=100\Omega\), \(C=0.2\,\mu F\).
If the right plate of a parallel plate capacitor is pulled with constant velocity as shown in the figure, find how the rate of change of energy stored in the capacitor depends on the separation \(x\).
If $Z$ be a complex number such that $|Z + 2| = |Z - 2|$ and $\text{arg} \left( \frac{Z - 3}{Z + 1} \right) = \frac{\pi}{4}$, then the value of $|Z|^2$ is
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
Anion \( X^- \) contains 45 neutrons and 36 electrons. The atomic mass, period number, and state in which "X" exists is:
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
Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{a, b, c\}$ then total number of functions from $A$ to $B$ which are not onto are
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 in a $\triangle ABC$, given that $A \equiv (1, 2)$, mid-point of $AB$ is $(-5, -1)$ and centroid is $(3, 4)$ then circumcentre is $(\alpha, \beta)$, then the value of $21(\alpha + \beta)$ is :
If $f(x)$ is a non-constant polynomial satisfying $f(x) = f'(x)f''(x)$ and $f(0) = 0$. Then the value of $\int_0^2 f(x) dx + f'(2) + f''(2)$ is :
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 \(T_A-T_B\).
An ideal gas is placed in a container at \( (P_1, V_1, T_1) \) and another ideal gas is placed in a different container at \( (P_2, V_2, T_2) \) are mixed at final pressure of \( P \) and final volume of \( V \). Calculate the final temperature.
Statement-1: Heat capacity at constant volume is always greater than heat capacity at constant pressure.
Statement-2: At constant volume as work done is zero, heat given to the chaotic motion is reflected by increase in temperature.
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
The domain of $f(x) = \cos^{-1} \left( \frac{4x + 2[x]}{3} \right)$ (where $[x]$ denotes greatest integer function) is
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 :-
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