List of top Questions asked in JEE Main- 2026

Consider a geometric sequence $729,\,81,\,9,\,1,\ldots$ If $P_n$ denotes the product of first $n$ terms of the G.P. such that \[ \sum_{n=1}^{40} (P_n)^{\frac{1}{n}}=\frac{3^{\alpha}-1}{2\times 3^{\beta}}, \] then find the value of $(\alpha+\beta)$.
If the domain of \[ f(x)=\log_{(10x^2-17x+7)}\,(18x^2-11x+1) \] is $(-\infty,a)\cup(b,c)\cup(d,\infty)-\{e\}$, then find $90(a+b+c+d+e)$.
Maximum value of $n$ for which $40^n$ divides $60!$ 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 $2f(2)$.
Evaluate \[ \left(\frac{4}{7}+\frac{1}{3}\right)+\left(\frac{4}{7}+\frac{4}{3}\right)\left(\frac{1}{3}\right) +\left(\frac{4}{7}+\frac{4}{3}\right)^2\left(\frac{1}{3}\right)^2+\cdots \]
If the equation \[ x^4-ax^2+9=0 \] has four real and distinct roots, then the least possible integral value of $a$ is
If dataset $A=\{1,2,3,\ldots,19\}$ and dataset $B=\{ax+b;\,x\in A\}$. If mean of $B$ is $30$ and variance of $B$ is $750$, then sum of possible values of $b$ is
In \(\Delta ABC\) if \(\frac{\tan(A-B)}{\tan A} + \frac{\sin^2 C}{\sin^2 A} = 1\) where \(A, B, C \in (0, \frac{\pi}{2})\) then
Consider the 10 observations 2, 3, 5, 10, 11, 13, 15, 21, a and b such that mean of observation is a and variance is 34.2. Then the mean deviation about median, is :
Let \(\tan \left( \frac{\pi}{4} + \frac{1}{2} \cos^{-1} \frac{2}{3} \right) + \tan \left( \frac{\pi}{4} - \frac{1}{2} \sin^{-1} \frac{2}{3} \right) = k\). Then number of solution of the equation \(\sin^{-1}(kx - 1) = \sin x - \cos^{-1} x\) is/are :
Given \(\frac{1}{\alpha} - \frac{1}{\beta} = \frac{1}{3}\) such that roots of the quadratic equation \(\lambda x^2 + (\lambda+1)x + 3 = 0\) are \(\alpha\) & \(\beta\), then sum of values of \(\lambda\) is equal to :
The value of \(S = \sum_{r=1}^{20} \sqrt{\pi \int_{0}^{r} x |\sin \pi x| dx}\) is :
Let \(\int \frac{1 - 5 \cos^2 x}{\sin^5 x \cos^2 x} dx = f(x) + c\) then find \(f\left(\frac{\pi}{4}\right) - f\left(\frac{\pi}{6}\right)\) :
Given conic \(x^2 - y^2 \sec^2 \theta = 8\) whose eccentricity is '\(e_1\)' & length of latus rectum '\(l_1\)' and for conic \(x^2 + y^2 \sec^2 \theta = 6\), eccentricity is '\(e_2\)' & length of latus rectum '\(l_2\)'. If \(e_1^2 = e_2^2 (1 + \sec^2 \theta)\) then value of \(\frac{e_1 l_1}{e_2 l_2} \tan \theta\)
The sum of coefficients of \(x^{499}\) and \(x^{500}\) in the expression: \[ (1+x)^{1000} + x(1+x)^{999} + x^2(1+x)^{998} + \cdots + x^{1000} \] is:
If \( y = \operatorname{sgn}(\sin x) + \operatorname{sgn}(\cos x) + \operatorname{sgn}(\tan x) + \operatorname{sgn}(\cot x) \), where \(\operatorname{sgn}(p)\) denotes the signum function of \(p\), then the sum of elements in the range of \(y\) is:
Let matrix \[ A=\begin{pmatrix} 3 & -4\\ 1 & -1 \end{pmatrix} \] and \(A^{100} = 100B + I\). Find the sum of all the elements in \(B^{100}\).
Statement 1 : The function \(f:\mathbb{R}\to\mathbb{R}\) defined by \[ f(x)=\frac{x}{1+|x|} \] is one–one.
Statement 2 : The function \(f:\mathbb{R}\to\mathbb{R}\) defined by \[ f(x)=\frac{x^2+4x-30}{x^2-8x+18} \] is many–one.
Which of the following is correct?
If \[ \sum_{r=1}^{25}\frac{r}{r^4+r^2+1}=\frac{p}{q}, \] where \(p\) and \(q\) are coprime positive integers, then \(p+q\) is equal to:
If the image of a point \(P(3,2,1)\) in the line \[ \frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1} \] is \(Q\), then the distance of \(Q\) from the line \[ \frac{x-9}{3}=\frac{y-9}{2}=\frac{z-5}{-2} \] is:
If the arithmetic mean of \(\dfrac{1}{a}\) and \(\dfrac{1}{b}\) is \(\dfrac{5}{16}\) and \(a,\,4,\,\alpha,\,b\) are in increasing A.P., then both the roots of the equation \[ \alpha x^2-ax+2(\alpha-2b)=0 \] lie between:
Let \(L\) be the distance of point \(P(-1,2,5)\) from the line \[ \frac{x-1}{2}=\frac{y-3}{2}=\frac{z+1}{1} \] measured {parallel to a line having direction ratios \(4,\,3,\,-5\). Then \(L^2\) is equal to: }
Let \(f:[-2a,2a]\to\mathbb{R}\) be a thrice differentiable function and define \[ g(x)=f(a+x)+f(a-x). \] If \(m\) is the minimum number of roots of \(g'(x)=0\) in the interval \((-a,a)\) and \(n\) is the minimum number of roots of \(g''(x)=0\) in the interval \((-a,a)\), then \(m+n\) is equal to:
The function \[ f(x)=\sin 2x+2\cos x,\qquad x\in\left(-\frac{3\pi}{4},\frac{3\pi}{4}\right) \] has:
Let the solution curve of the differential equation \[ x\,dy - y\,dx = \sqrt{x^2+y^2}\,dx,\quad x>0, \] with $y(1)=0$, be $y=y(x)$. Then $y(3)$ is equal to