List of top Mathematics Questions asked in WBJEE

The value of $1000\left[\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...... +\frac{1}{999\times1000}\right]$ is equal to

The sum $1\times 1! + 2 \times 2! + ... + 50 \times 50!$ equals

The line $x=2 y$ intersects the ellipse $\frac{x^{2}}{4}+y^{2}=1$ at the points $P$ and $Q$. The equation of the circle with $P Q$ as diameter is

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

There are $100$ students in a class. In an examination, $50$ of them failed in Mathematics, $45$ failed in Physics, $40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.

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

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

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

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

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

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