List of top Questions asked in JEE Main- 2026

Evaluate: \[ \frac{6}{3^{26}}+\frac{10\cdot1}{3^{25}}+\frac{10\cdot2}{3^{24}}+\frac{10\cdot2^{2}}{3^{23}}+\cdots+\frac{10\cdot2^{24}}{3}. \]

If \(x^2+x+1=0\), then the value of \(\left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 + \dots + \left(x^{25} + \frac{1}{x^{25}}\right)^2\) is:

Let PQ and MN be two straight lines touching the circle \(x^2+y^2-4x-6y-3=0\) at the points A and B respectively. Let O be the centre of the circle and \(\angle AOB = \pi/3\). Then the locus of the point of intersection of the lines PQ and MN is:

Let the foci of a hyperbola coincide with the foci of the ellipse \(\frac{x^2}{36} + \frac{y^2}{16} = 1\). If the eccentricity of the hyperbola is 5, then the length of its latus rectum is:

The sum of all the roots of the equation \((x-1)^2 - 5|x-1| + 6 = 0\), is:

The value of \(\text{cosec}10^\circ - \sqrt{3} \sec10^\circ\) is equal to:

If the domain of the function \(f(x) = \cos^{-1}\left(\frac{2x-5}{11-3x}\right) + \sin^{-1}(2x^2-3x+1)\) is the interval \([\alpha, \beta]\), then \(\alpha + 2\beta\) is equal to:}

Let \[ I(x) = \int \frac{3\,dx}{(4x+6)\sqrt{4x^2 + 8x + 3}} \] and \[ I(0) = \frac{\sqrt{3}}{4} + 20. \] If \[ I\left(\frac{1}{2}\right) = \frac{a\sqrt{2}}{b} + c, \] where \(a, b, c \in \mathbb{N}\) and \(\gcd(a,b)=1\), then find the value of \[ a + b + c. \]

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is picked from B and put in A. Then a ball is drawn from A. Probability it is white is $p/q$. Find $p+q$.

Let \( \dfrac{\pi}{2} < \theta < \pi \) and \( \cot \theta = -\dfrac{1}{2\sqrt{2}} \). Then the value of \[ \sin\!\left(\frac{15\theta}{2}\right)(\cos 8\theta + \sin 8\theta) + \cos\!\left(\frac{15\theta}{2}\right)(\cos 8\theta - \sin 8\theta) \] is equal to

Consider two sets \[ A = \{ x \in \mathbb{Z} : |(|x-3|-3)| \le 1 \} \] and \[ B = \left\{ x \in \mathbb{R} - \{1,2\} : \frac{(x-2)(x-4)}{x-1}\,\log_e(|x-2|) = 0 \right\}. \] Then the number of onto functions \( f : A \to B \) is equal to

Let \[ \sum_{k=1}^{n} a_k = \alpha n^2 + \beta n. \] If \( a_{10} = 59 \) and \( a_6 = 7a_1 \), then \( \alpha + \beta \) is equal to

Let $P=[p_{ij}]$ and $Q=[q_{ij}]$ be two square matrices of order $3$ such that $q_{ij}=2^{(i+j-1)}p_{ij}$ and $\det(Q)=2^{10}$. Then the value of $\det(\operatorname{adj}(\operatorname{adj} P))$ is

The letters of the word ``UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word ``UDAYPUR'' is

Let $f$ be a function such that $3f(x)+2f\!\left(\dfrac{m}{19x}\right)=5x$, $x\ne0$, where $m=\displaystyle\sum_{i=1}^{9} i^2$. Then $f(5)-f(2)$ is equal to

Let $y=y(x)$ be a differentiable function in the interval $(0,\infty)$ such that $y(1)=2$, and \[ \lim_{t\to x}\left(\frac{t^2y(x)-x^2y(t)}{x-t}\right)=3 \text{ for each } x>0. \] Then $2y(2)$ is equal to

$A_1$ is the area bounded by $y=x^2+2$, $x+y=8$, and the $y$-axis in the first quadrant, and $A_2$ is the area bounded by $y=x^2+2$, $y^2=x$, $x=0$ and $x=2$ in the first quadrant. Find $(A_1-A_2)$.

Consider an A.P. $a_1,a_2,\ldots,a_n$ with $a_1>0$, $a_2-a_1=-\dfrac{3}{4}$ and $a_n=\dfrac{a_1}{4}$. If \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then find $\sum_{i=1}^{17} a_i$.

Given that \[ \vec a=2\hat i+\hat j-\hat k,\quad \vec b=\hat i+\hat j,\quad \vec c=\vec a\times\vec b, \] \[ |\vec d\times\vec c|=3,\quad \vec d\cdot\vec c=\frac{\pi}{4},\quad |\vec a-\vec d|=\sqrt{11}, \] find $\vec a\cdot\vec d$.

If \(\alpha, \beta\) are roots of the quadratic equation \[ \lambda x^2 - (\lambda+3)x + 3 = 0 \] and \(\alpha<\beta\) such that \[ \frac{1}{\alpha} - \frac{1}{\beta} = \frac{1}{3}, \] then find the sum of all possible values of \(\lambda\).

If all the letters of the word 'UDAYPUR' are arranged in all possible permutations and these permutations are listed in dictionary order, then the rank of the word 'UDAYPUR' is

Let a function $f(x)$ satisfy \[ 3f(x)+2f\!\left(\frac{m}{19x}\right)=5x \] where $m=\sum_{i=1}^{9} i^2$. Find $f(5)+f(2)$.

If \(f(x^2 + 1) = x^4 + 5x^2 + 1\), then find \(\int_{0}^{3} f(x) dx\) :

Let \(x \frac{dy}{dx} - \sin 2y = x^3(2 - x^3) \cos^2 y ; y(2) = 0\), then find \(\tan(y(1))\) :