List of top Mathematics Questions asked in WBJEE

Let P (4, 3) be a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1.$ If the normal at P intersects the X-axis at (16, 0), then the eccentricity of the hyperbola is

Let a, b, c be real numbers such that $a + b + c < 0$ and the quadratic equation $ax^2 + bx + c = 0$ has imaginary roots. Then

Let $f(x) = x^{4} - 4x^{3} + 4x^{2} +c, c \in \mathbb{R}.$ Then

Let S, T, U be three non-void sets and f : S $\to$ T,g : T $\to$ U is surjective. Then

T$\displaystyle\lim_{x \to 0+}$ $\left(x^{n} \,ln\, x\right), n > 0$

Let A be a square matrix of order 3 whose all entries are 1 and let $I_3$ be the identity matrix of order 3. Then the matrix $A - 3I_3$ is

If $log_{2}\,6+\frac{1}{2x} = log_{2}\left(2^{\frac{1}{x}} + 8\right)$, then the values of x are

$A$ and $B$ each select one number at random from the distinct numbers $1, 2, 3,.....,n$ and the probability that the number selected by $A$ is less than the number selected by $B$ is $\frac{1009}{2019}$ .Now , the probability that the number selected by $B$ is the number immediately next to the number selected by $A$ is

The number of irrational terms in the expansion of $ \left(3^{\frac{1}{8}}+5^{\frac{1}{4}}\right)^{84}$ is

There are 7 greetings cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective colour is,

A variable line passes through the fixed point ($\alpha,\,\beta$). The locus of the foot of the perpendicular from the origin on the line is,

Let $\vec{\alpha} . \vec{\beta} , \vec{\gamma}$ be three unit vectors such that $\vec{\alpha} . \vec{\beta} = \vec{\alpha} . \vec{\gamma} = 0 $ and the angle between $\vec{\beta}$ and $\vec{\gamma}$ is $30^{\circ}$ . Then $\vec{\alpha} $ is

For $0 \leq p \leq 1$ and for any positive $a, b$ let $I(p) = (a + b)^p, J(p) = a^p + b^p$, then

Let $z_1$ and $z_2$ be complex numbers such that $z_1 \neq z_2$ and $| z_1| = | z_2 |$ . If Re $(z_1) > 0$ and $Im (z_2) < 0 $ ,then $\frac{z_1+ z_2}{z_1 - z_2}$ is

The least positive integer $n$ such that $\begin{pmatrix}\cos \frac{\pi}{4}&\sin \frac{\pi}{4}\\ -\sin \frac{\pi}{4}&\cos \frac{\pi}{4}\end{pmatrix} ^{n }$ is an identity matrix of order $2$ is

From a collection of $20$ consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

The value of the integral $I = \int\limits^{2014}_{1/2014} \frac{\tan^{-1} x}{x} dx $ is

On $R$, a relation $\rho$ is defined by $x \rho y$ if and only if $x - y$ is zero or irrational. Then

If $f : R \to R$ be defined by $f(x) = e^x $ and $g : R \to R $ be defined by $g(x) = x^2$. The mapping $g of : R \to R $ be defined by $(g o f ) (x) = g[f(x)] \forall x \in R$ , Then

If $z_1$ and $z_2$ be two non zero complex numbers such that $\frac{z_1 }{z_2 } + \frac{z_2}{z_1} = 1 $, then the origin and the points represented by $z_1$ and $z_2$

If $\int \, f(x) \, \sin \, x \, \cos \, x \, dx = \frac{1}{2(b^2 - a^2)} \log f(x) + c$, where c is the constant of integration , then f(x) =

The approximate value of $\sin \, 31^{\circ}$ is

On the set $R$ of real numbers, the relation $\rho$ is defined by $x \rho y, (x, y) \in R$

Let $\vec{\alpha } = \hat{i} + \hat{j} + \hat{k} , \vec{\beta} = \hat{i} - \hat{j} - \hat{k}$ and $\vec{\gamma} = - \hat{i} + \hat{j} - \hat{k}$ be three vectors. A vector $\vec{\delta} $, in the plane of $\vec{\alpha}$ and $\vec{\beta}$, whose projection on $\vec{\gamma}$ is $\frac{1}{\sqrt{3}}$, is given by

The value of $\displaystyle\lim_{n \to \infty} \frac{1}{n} \left\{ \sec^2 \frac{\pi}{4 n} + \sec^2 \frac{2 \pi }{4n} + ..... \sec^2 \frac{n \pi}{4n} \right\}$ is