List of top Mathematics Questions asked in JEE Main

If \(å= î+2ĵ + k, b = 3(î - ĵ + k), å · c = 3\) and \(å \times č = b\), then \(å·((xb)-b-č)\)=

Let the system of equations \(x+2y+3z = 5\), \(2x+3y+z = 9\), \(4x+3y+λz = μ\) have an infinite number of solutions. Then \(λ + 2μ\) is equal to

The number of solution of the equation \(4sin^2 x-4cos^3 x+9-4cos x = 0\), \(x ∈ [-2\pi, 2\pi]\)

If \(f(x) = (x - 2)^2 (x - 3)^3\) and \(x ∈ [1, 4]\) and If \(M\) and \(m\) denotes maximum and minimum values respectively, then \(M - m\) is

A = {1, 2, 3, 4} , R = {(1, 2), (2, 3), (2, 4)} R ⊆ S and S is an equivalence relation then the minimum number of elements to be added to R is n, then the value of n is?

An equation of a plane parallel to the plane \(x-2y+2z-5=0\) and at a unit distance from the origin is?

Given data \(60, 60, 44, 58, 68, α, β, 56\) has mean \(58\), variance = \(66.2\), then find \(α^2 + β^2\).

The value of integral \(∫_0^{\frac \pi4} \frac {xdx}{cos^42x+sin^42x}\).

\(3, 7, 1,......., 404\) and \(4, 7, 10,......, 403\). Find sum of common terms.

Number of ways of arranging 5 officers in 4 rooms.

If the coefficient of x⁷ in expansion of \((ax- \frac{1}{bx^2})^{13}\) is equal to the coefficient of x^-5 in expansion of \((ax + \frac{1}{bx^2})13\), then a⁴b⁴ is ______

Let $f$ be a twice differentiable function on $R$. 
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$ 
then $(2 a+1)^5 a^2$ is equal to ______.

The remainder when \((2023)^{2023}\) is divided by \(35\) is _____

Let a₁, a₂, a₃, …. be a G.P. of increasing positive numbers. Let the sum of its 6^th and 8^th terms be 2 and the product of its 3rd and 5th terms be \(\frac{1}{9}\) .Then 6 (a₂ + a₄) (a₄ + a₆) is equal to

If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to

Let $A = \begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{bmatrix}, a , b \in R$. 
If for some $n \in N , A ^{ n }=\begin{bmatrix}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{bmatrix}$ 
then $n + a + b$ is equal to _________.

Let $f(x)= \begin{vmatrix} 1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{vmatrix}, x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right] $ If $\alpha$ and $\beta$ respectively are the maximum and the minimum values of $f$, then

Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$ If $S =\left\{\alpha \in R : y ^2=1- x \right\}$, then $\displaystyle\sum_{\alpha \in S } 16 \alpha^3$ is equal to ______

A light ray emits from the origin making an angle \(30\degree\) with the positive x-axis. After getting reflected by the line \(x + y = 1\), if this ray intersects x-axis at Q, then the abscissa of Q is

Let be a sequence such that a1+a₂+....+ a_n=\(\frac{n^2+3n}{ (n+1 ) (n+2)}\). If  \(28∑^{10}_{k=1}\frac{1}{a_k} =\) P₁P₂P₃ . . . P_m ,  where p1, p2, …..p_m are the first m prime numbers, then m is equal to

A plane $E$ is perpendicular to the two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, and passes through the point $P (1,-1,1)$ If the distance of the plane $E$ from the point $Q(a, a, 2)$ is $3 \sqrt{2}$, then $( PQ )^2$ is equal to

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

The value of $\left(\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)^3$ is