List of top Mathematics Questions asked in WBJEE

If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}$ is equal to

The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer, is

Rolle's theorem is applicable in the interval $[-2, 2]$ for the function

If $\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)$, then

Let $A$ and $B$ be two events with $P\left(A^{c}\right)=0.3, P\left(B\right)=0.4$ and $P\left(A\cap B^{c}\right)=0.5$ Then $P\left(B|A \cup B^{c} \right) $ is equal to

The incentre of an equilateral triangle is $(1,1)$ and the equation of one side is $3 x+4 y+3=0$ Then, the equation of the circumcircle of the triangle is

The coefficient of $x^{10}$ in the expansion of $1+\left(1+x\right)+\ldots+\left(1+x\right)^{20}$ is

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then the probability that balls of both colours are drawn is

The eccentric angle in the first quadrant of a point on the ellipse $\frac{x^{2}}{10}+\frac{y^{2}}{8}=1$ at a distance $3$ units from the centre of the ellipse is

The value of $\displaystyle \lim_{n \to \infty}\frac{\left(n!\right)^{\frac{1}{n}}}{n}$ is

Let $p, q$ and $r$ be the side4s opposite to the angles $P, Q$ and $R$, respectively in a $\Delta P Q R$. Then, $2 p r \sin \left(\frac{P-Q+R}{2}\right)$ equals

The area of the region bounded by the curves $y=x^{3}, y=\frac{1}{x}, x=2$ is

The solution of $25\frac{d^{2}y}{dx^{2}}-10 \frac{dy}{dx}+y=0, \, y\left(0\right) =1, \, y\left(1\right)=2e^{\frac{1}{5}} $ is

The value of the integral $\int\limits_{0}^{\pi / 2} \frac{1}{1+(\tan x)^{101}} d x$ is equal to

Let $p, q$ and $r$ be the sides opposite to the angles $P, Q$ and $R$, respectively in a $\Delta P Q R$. If $r^{2} \sin P \sin Q=p q$, then the triangle is

The number of diagonals in a regular polygon of $100$ sides is

If $\frac{z-1}{z+1}$ is purely imaginary, then

If $\left(\frac{3}{2}+i\frac{\sqrt{3}}{2}\right)^{50} \, =3^{25} \left(x+iy\right),$ where $x$ and $y$ are real, then the ordered pair $(x,y)$ is

The intercept on the line $y = x$ by the circle $x^2 + y^2 - 2x = 0$ is $AB$. Equation of the circle with $AB$ as diameter is

If the coordinates of one end of a diameter of the circle $x^2+y^2+4x-8y+5=0$, is (2,1), the coordinates of the other end is

The coordinates of the two points lying on $x + y = 4$ and at a unit distance from the straight line $4x + 3y = 10$ are

The sequence $\log \,a$, $\log \frac{a^{2}}{b}, \,\log \frac{a^{3}}{b^{2}}, ...........$ is

$^{15}C_{3} +\,^{15}C_{5} + .. ...+\,^{15}C_{15} $ will be equal to

If $A = \begin{bmatrix}3&x-1\\ 2x+3&x+2\end{bmatrix}$ is a symmetric matrix, then the value of $x$ is