List of top Mathematics Questions asked in JEE Main

Let
A = $\begin{bmatrix} 1 \\ 1 \\ 1 \\ \end{bmatrix}$ and B = $\begin{bmatrix} 9^2 & -10^2 & 11^2 \\ 12^2 & 13^2 & 14^2 \\ -15^2 & 16^2 & 17^2 \\ \end{bmatrix}$
then the value of A'BA is

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 39 and x – y = 3, respectively and P(2, 3) is its circumcentre. Then which of the following is NOT true?

The integral
$\frac{24}{\pi} \int_{0}^{\sqrt{2}} \frac{2 - x^2}{(2 + x^2) \sqrt{4 + x^4}} \, dx$
is equal to _______.

Let the coefficients of the middle terms in the expansion of$\begin{array}{l} \left(\dfrac{1}{\sqrt 6}+ \beta x\right)^4, \left(1 – 3\beta x\right)^2 \text{and}\left(1 – \dfrac{\beta}{2}x\right )^6, \beta > 0,\end{array}$respectively form the first three terms of an A.P. If d is the common difference of this A.P., then $\begin{array}{l} 50-\frac{2d}{\beta^2} \end{array}$is equal to _______.

The value of the integral $∫^{ \frac{π}{2}}_{ \frac{-π}{2}} \frac{dx}{(1+e^x)(sin^6x+cos^6x)}$ is equal to

Let a, b be two non-zero real numbers. If p and r are the roots of the equation x² – 8ax + 2a = 0 and q and s are the roots of the equation x² + 12bx + 6b = 0, such that $\frac{1}{p}$,$\frac{1}{q}$,$\frac{1}{r}$,$\frac{1}{s}$ are in A.P., then a^–1 – b^–1 is equal to _________.

If $\lim_{n\rightarrow \infty}$ $\frac{(n+1)^{k-1}}{n^{k+1}}[(nk+1)+(nk+2)+....+(nk+n)]=33.\lim_{n\rightarrow \infty}\frac{1}{n^{k+1}}.[1^k+2^k+3^k+....+n^k]$
then the integral value of k is equal to _______.

Let P and Q be any points on the curves (x – 1)² + (y + 1)² = 1 and y = x², respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

The number of solutions of |cos x| = sinx, such that –4π ≤ x ≤ 4π is :

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

Let $S ={ (\begin{matrix} -1 & 0 \\ a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}$ and
let $T_n = {A ∈ S : A^{n(n + 1)} = I}. $
Then the number of elements in $\bigcap_{n=1}^{100}$ $T_n $ is

The number of matrices
$A=\begin{pmatrix} a & b \\ c & d \\ \end{pmatrix}$, where a,b,c,d ∈−1,0,1,2,3,…..,10
such that A = A^-1, is ______.

If the sum of solutions of the system of equations 2sin²θ – cos2θ = 0 and 2cos²θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

Let the abscissae of the two points P and Q on a circle be the roots of x² – 4x – 6 = 0 and the ordinates of P and Q be the roots of y² + 2y – 7 = 0. If PQ is a diameter of the circle x² + y² + 2ax + 2by + c = 0, then the value of (a + b – c) is