List of top Mathematics Questions asked in WBJEE

If $A, B$ are two events such that $P\left(A\cup B\right) \ge \frac{3}{4}$ and $\frac{1}{8}\le P\left(A\cap B\right) \le\frac{3}{8}$ then

Standard Deviation of n observations $a_{1}, a_{2}, a_{3} ..... a_{n}$ is $\sigma$. Then the standard deviation of the observations $\lambda a_{1},\lambda a_{2}, .... \lambda a_{n}$ is

Let $R$ be a relation defined on the set $Z$ of all integers and $xRy$ when $x + 2y$ is divisible by $3$. Then

The locus of the midpoints of all chords of the parabola $y^2 = 4ax$ through its vertex is another parabola with directrix

The sum of n terms of the following series; $1^3 + 3^3 + 5^3 + 7^3 + ....$ is

The number of values of $k$ for which the equation $x^2 - 3x + k = 0$ has two distinct roots lying in the interval $(0, 1)$ are

The points of the ellipse $16x^2 + 9y^2 = 400$ at which the ordinate decreases at the same rate at which the abscissa increases is/are given by

The number of points at which the function $f \left(x\right)=max \left\{a-x, a+x, b\right\}, -\infty, 0 < a < b$ cannot be differentiable

If $\frac{1}{^{5}C_{r}}+\frac{1}{^{6}C_{r}} =\frac{1}{^{4}C_{r}}$, then the value of $r$ equals to

If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int\limits^{{2}}_{{0}}x^2 [x] dx$

The letters of the word COCHIN are permuted and all permutation are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

If the matrix $A=\begin{pmatrix}2&0&0\\ 0&2&0\\ 2&0&2\end{pmatrix},$ then $A^{n}=\begin{pmatrix}a&0&0\\ 0&a&0\\ b&0&a\end{pmatrix}, n\,\in\,N$ where

For non-zero vectors $\vec{a} $ and $\vec{b} $ if $\left|\vec{a}+\vec{b}\right|

General solution of $y \frac{dy}{dx}+by^{2}=a\,cos\,x, 0 < x< 1$ is

The value of cos $15^{\circ}\, cos 7 \frac{1^{\circ}}{2}\, sin 7 \frac{1^{\circ}}{2}$ is

If the equation $x^2 + y^2 -10x + 21 = 0$ has real roots $x = a$ and $y=\beta$ then

If $\log _{0.2}(x-1)>\log _{0.04}(x+5)$, then

The quadratic expression $\left(2x+1\right)^{2}-px+q\ne0$ for any real $x$ if

If $\theta \in\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)$, then the value of $\sqrt{4 \cos ^{4} \theta+\sin ^{2} 2 \theta}+4 \cot \theta \cos ^{2}\left(\frac{\pi}{4}-\frac{\theta}{2}\right)$

It $\displaystyle \lim_{x \to 0}$$\frac{axe^{x}-b\, \log\left(1+x\right)}{x^{2}}=3$ then the values of $a, b$ are respectively

Let $f: R \rightarrow R$ be a continuous function which satisfies $f(x)=\int\limits_{0}^{x} f(t) d t$. Then, the value of $f\left(\log _{e} 5\right)$ is

The integrating factor of the differential equation $\frac{d y}{d x}+\left(3 x^{2} \tan ^{-1} y-x^{3}\right)\left(1+y^{2}\right)=0$is

The least value of $2x^2 + y^2 + 2xy + 2x - 3y + 8$ for real numbers $x$ and y is

Given that $x$ is a real number satisfying $\frac{5x^{2}-26x+5}{3x^{2}-10x+3} < 0 ,$ then

Let $x_{n}=\left(1-\frac{1}{3}\right)^{2}\left(1-\frac{1}{6}\right)^{2}\left(1-\frac{1}{10}\right)^{2} ........ \left(1-\frac{1}{\frac{n\left(n+1\right)}{2}}\right)^2, n \ge 2.$ Then the value of $\displaystyle \lim_{n \to \infty} x_n$ is