List of top Mathematics Questions asked in JEE Main

$\alpha, \alpha + 2 \in Z$ and $n \in N$, where $\alpha, \alpha+2$ are roots of equation $x(x + 2) + (x + 1) (x + 3) + ... + (x + n-1) (x + n+1) = 4n$ then $\alpha + n =$

If eccentricity of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, which passes through the point $(3, 4)$ is $\frac{\sqrt{5}}{3}$, then length of latus rectum of ellipse, is :

Consider $f(x) = \begin{cases} \frac{\sin x}{x}, & x \neq 0 \\ 1, & x = 0 \end{cases}$
Number of critical points of $f(x)$ in the interval $(-2\pi, 2\pi)$ is:

If probability that $ax^2 + 2\sqrt{2}bx + c > 0 \, \forall x \in R$ where $a, b, c \in {1, 2, 3, 4}$ is $\frac{m}{n}$ where $m$ & $n$ are coprime, then $(m + n)$ is:

Let $|a| = 2, |b| = 3$, then maximum value of $3|3a + 2b| + 4|3a - 2b|$ is :

A circle meets coordinate axes at 3 points and cuts equal intercepts. If it cuts a chord of length $\sqrt{14}$ unit on $x + y = 1$, then square of its radius is (centre lies in first quadrant):

Let $x \in [-\pi, \pi]$ & $S = \{ x : \sin x (\sin x + \cos x) = a, a \in I \}$, then number of elements in set $S$ is equal to :

The Range of $f(x) = \sin^{-1} \left( \frac{1}{x^2 - 2x + 2} \right)$ is:

Number of seven digits numbers which can be formed by using all the digits 1, 2, 3, 4, 5 with at least one digit repeated is _____.

The value of $\int_{0}^{3} \frac{e^x + e^{-x}}{[x]!} dx$ is equal to (where $[\, \cdot \,]$ denotes greatest integer function):

If $y = f(x)$ is the solution of the differential equation $(1 + \sin x) \frac{dy}{dx} + \cos x = 0$, such that $f(0) = 0$, then $f\left(\frac{\pi}{2}\right)$ is:

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 $P=[p_{ij}]$ 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 value of $ \int_0^{2\pi} (\sin^4 x + \cos^4 x) \, dx $ is equal to:

$ f(x) $ is a 5 degree polynomial that has extremes at $ x = \pm 1 $ and $ \lim_{x \to 0} \frac{f(x)}{x^3} = 5 $, then $ f(2) - f(-2) $ is:

If for $ 3 \leq r \leq 30 $, $ ^{30}C_{30-r} + 3 \left( ^{30}C_{31-r} \right) + 3 \left( ^{30}C_{32-r} \right) + ^{30}C_{33-r} = ^m C_r $, then $ m $ equals to_________

Let $ f(x) = \begin{cases} \frac{ax^2 + 2ax + 3}{4x^2 + 4x - 3}, & x \neq -\frac{3}{2}, \frac{1}{2} \\ b, & x = -\frac{3}{2}, \frac{1}{2} \end{cases} $ be continuous at $ x = -\frac{3}{2} $. If $ f(x) = \frac{7}{5} $, then $ x $ is equal to :

Let $ f(x) = \int \frac{(2 - x^2) \cdot e^x \cdot \sqrt{1 + x} \cdot (1 - x)^{3/2}}{dx} $. If $ f(0) = 0 $, then $ f\left(\frac{1}{2}\right) $ is equal to:

The sum of the coefficients of $x^{499}$ and $x^{500}$ in \[ (1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+\cdots+x^{1000} \] is:

Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to

The largest value of $n$, for which $40^n$ divides $60!$, is

If $ y = f(x) $ is the solution of the differential equation $ (1 + \sin x) \frac{dy}{dx} + \cos x = 0 $, such that $ f(0) = 0 $, then $ f\left( \frac{\pi}{2} \right) $ is equal to