List of top Questions asked in JEE Main- 2026

Consider the 10 observations \(2, 3, 5, 10, 11, 13, 15, 21, a\) and \(b\) such that the mean of observations is \(9\) and variance is \(34.2\). Then the mean deviation about median is:
Considering the principal values of inverse trigonometric functions, the value of \[ \tan\!\left(2\sin^{-1}\!\frac{2}{\sqrt{13}}-2\cos^{-1}\!\frac{3}{\sqrt{10}}\right) \] is equal to:
Let $a_1, \frac{a_2}{2}, \frac{a_3}{2^2}, \dots, \frac{a_{10}}{2^9}$ be a G.P. of common ratio $\frac{1}{\sqrt{2}}$. If $a_1 + a_2 + \dots + a_{10} = 62$, then $a_1$ is equal to :

The number of strictly increasing functions \(f\) from the set \(\{1, 2, 3, 4, 5, 6\}\) to the set \(\{1, 2, 3, ...., 9\}\) such that \(f(i)>i\) for \(1 \le i \le 6\), is equal to:

The number of solutions of \[ \tan^{-1}(4x) + \tan^{-1}(6x) = \frac{\pi}{6}, \] where \[ -\frac{1}{2\sqrt{6}}<x<\frac{1}{2\sqrt{6}}, \] is equal to
Let 4 integers $a_1, a_2, a_3, a_4$ are in A.P. with integral common difference $d$ such that $a_1+a_2+a_3+a_4=48$ and $a_1a_2a_3a_4+d^4=361$. Then the greatest term in this A.P. is
The vertices B and C of a triangle ABC lie on the line \( \frac{x}{1} = \frac{1-y}{2} = \frac{z-2}{3} \). The coordinates of A and B are (1, 6, 3) and (4, 9, 6) respectively and C is at a distance of 10 units from B. The area (in sq. units) of \( \triangle ABC \) is:
Find the maximum distance between the two curves: \[ |z-2| = 4 \quad \text{and} \quad |z-2| + |z+2| = 5 \]

Let \[ f(x)=\int \frac{7x^{10}+9x^8}{(1+x^2+2x^9)^2}\,dx \] and $f(1)=\frac14$. Given that 

and $B=\operatorname{adj}(\operatorname{adj}A)$, if $|B|=81$, find the value of $\alpha^2$ (where $\alpha\in\mathbb{R}$). 
 

Let the ellipse \[ E=\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] have eccentricity equal to the greatest value of the function \[ f(t)=-\frac34+2t-t^2 \] and the length of its latus rectum is $30$. Find the value of $a^2+b^2$.
Let $P$ and $Q$ be any two $3\times3$ matrices where $P=[p_{ij}]_{3\times3}$, $Q=[q_{ij}]_{3\times3}$ such that $q_{ij}=2^{\,i+j-1}p_{ij}$. Find $|\operatorname{adj}(\operatorname{adj}P)|$.
Let \(f\) be a differentiable function satisfying \[ f(x+y)=f(x)+f(y)-xy \quad \text{for all } x,y\in\mathbb{R}. \] If \[ \lim_{h\to 0}\frac{f(h)}{h}=3, \] then the value of \[ \sum_{n=1}^{10} f(n) \] is equal to:
If the function \[ f(x)=\frac{e^x\left(e^{\tan x - x}-1\right)+\log_e(\sec x+\tan x)-x}{\tan x-x} \] is continuous at $x=0$, then the value of $f(0)$ is equal to

Let 

be a continuous function at $x=0$, then the value of $(a^2+b^2)$ is (where $[\ ]$ denotes greatest integer function). 
 

Let \(x=x(t)\) be the solution curve of the differential equation \[ \frac{dx}{dt}=-kx, \] with \[ x(0)=100,\quad x\!\left(\frac{1}{2}\right)=80. \] If \(x(t_\alpha)=5\), then \(t_\alpha\) is equal to:
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
Let \(y=y(x)\) be the solution curve of the differential equation \((1+x^2)dy+(y-\tan^{-1}x) dx=0\), \(y(0) = 1\). Then the value of \(y(1)\) is:
Let $y = y(x)$ be the solution of the differential equation $\sec x \frac{dy}{dx} - 2y = 2 + 3\sin x, x \in (-\frac{\pi}{2}, \frac{\pi}{2})$. If $y(0) = -\frac{7}{4}$, then $y(\frac{\pi}{6})$ is equal to :
Let \(\alpha,\beta,\gamma\ (0<\alpha,\beta,\gamma<\tfrac{\pi}{2})\) be the angles between non–zero vectors \(\vec a\) and \(\vec b\), \(\vec b\) and \(\vec c\), \(\vec c\) and \(\vec a\) respectively. If \(\theta\) is the angle that the vector \(\vec a\) makes with the plane containing \(\vec b\) and \(\vec c\), then:
Let \((\alpha, \beta, \gamma)\) be the co-ordinates of the foot of the perpendicular drawn from the point (5, 4, 2) on the line \(\vec{r}=(-\hat{i}+3\hat{j}+\hat{k})+\lambda(2\hat{i}+3\hat{j}-\hat{k})\). Then the length of the projection of the vector \(\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}\) on the vector \(6\hat{i}+2\hat{j}+3\hat{k}\) is:
Consider two parabolas \(P_1,\ P_2\) and a line \(L\):
\[ P_1:\ y=4x^2,\qquad P_2:\ y=x^2+27,\qquad L:\ y=\alpha x \] If the area bounded by \(P_1\) and \(P_2\) is six times the area bounded by \(P_1\) and \(L\), find \(\alpha\).
Let the locus of the mid-point of the chord through the origin \(O\) of the parabola \(y^2 = 4x\) be the curve \(S\). Let \(P\) be any point on \(S\). Then the locus of the point, which internally divides \(OP\) in the ratio \(3:1\), is
If shortest distance between the lines \[ \frac{x+1}{\alpha}=\frac{y-2}{-2}=\frac{z-4}{-2\alpha} \quad \text{and} \quad \frac{x}{\alpha}=\frac{y-1}{1}=\frac{z-1}{\alpha} \] is $\sqrt{2}$, then find the sum of all possible values of $\alpha$.
Among the statements :
I: If the given determinants are equal, then \( \cos^2\alpha + \cos^2\beta + \cos^2\gamma = \frac{3}{2} \), and
II: If the polynomial determinant equals \( px + q \), then \( p^2 = 196q^2 \), identify the truth value.
Let $z = (1+i)(1+2i)(1+3i)\cdots(1+ni)$ and $|z|^2 = 44200$. Find the value of $n$.