List of top Mathematics Questions asked in WBJEE

The variance of first $20$ natural numbers is

If $\omega$ is an imaginary cube root of unity, then the value of the determinant $\begin{vmatrix}1+\omega&\omega^{2}&-\omega\\ 1+\omega^{2}&\omega&-\omega^{2}\\ \omega+\omega^2&\omega&-\omega^{2}\end{vmatrix}$

The value of $2 \cot ^{-1} \frac{1}{2}-\cot ^{-1} \frac{4}{3}$ is

In a certain town, $60\%$ of the families own a car, $30\%$own a house and $20\%$ own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both ?

The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is

If the four points with position vectors $-2\hat{i}+\hat{j}+k, \hat{i} +\hat{j}+\hat{k}, \hat{j}-\hat{k}, $ and $\lambda\hat{j}+\hat{k}$ are coplanar, then $\lambda=$

For all real values of \(a_0, a_1, a_2, a_3\) satisfying \(a_{0}+\frac{a_{1}}{2}+\frac{a_{2}}{3}+\frac{a_{3}}{4}=0\), the equation \(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}=0\) has a real root in the interval

The area of the region bounded by the curve $y = x^3$, its tangent at $(1, 1)$ and $x-axis$ is

A fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

If $\sin^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\frac{x^{4}}{8}+...\right)-\frac{\pi}{6}$ where $\left|x\right| < 2$ then the value of $x$ is

If $f \left(x\right)=\begin{vmatrix}1&x&x+1\\ 2x&x\left(x-1\right)&\left(x-1\right)x\\ 3x\left(x-1\right)&x\left(x-1\right)\left(x-2\right)&\left(x-1\right)\end{vmatrix}$ Then $f (100)$ is equal to

The value of \(\lambda\), such that the following system of equations \(2x - y - 2z = 2\); \(x - 2y + z = -4\); \(x + y + \lambda z = 4\) has no solution, is

Area of the region bounded by $y = |x|$ and $y = -|x| + 2$ is

If $f:[0, \pi / 2) \rightarrow R$ is defined as $f(\theta)=\begin{vmatrix}1 & \tan \theta & 1 \\ -\tan \theta & 1 & \tan \theta \\ -1 & -\tan \theta & 1\end{vmatrix}$. Then, the range of $f$ is

The trigonometric equation $\sin^{-1}x = 2 \sin^{-1}2a$ has a real solution if

The number of real solutions of the equation $(\sin x-x)\left(\cos x-x^{2}\right)=0$ is

If $\sqrt{y}=cos^{-1}x,$ then it satisfies the differential equation $\left(1-x^{2}\right)-x \frac{dy}{dx}=c,$ where $c$ is equal to

A fair six-faced die is rolled $12$ times. The probability that each face turns up twice is equal to

Let $X_{n}=\left\{z=x+i y:|z|^{2} \leq \frac{1}{n}\right\}$ for all integers $n \geq 1$. Then, $\overset{\infty}{\underset{n=1}{\cap}}$ is

Let $n\ge2$ be an integer, $A=\begin{pmatrix}\cos\left(2\pi/ n\right)&\sin \left(2\pi / n\right)&0\\ -\sin\left(2\pi / n\right)&\cos\left(2\pi / n\right)&0\\ 0&0&1\end{pmatrix}$ and $?$ is the identity matrix of order $3$. Then

Out of $7$ consonants and $4 $ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2 $ vowels, is

Suppose $M=\int\limits_{0}^{\pi / 2} \frac{\cos x}{x+2} d x$, $N=\int\limits_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x$ Then, the value of $(M-N)$ equals

The angle of intersection between the curves $y=\left[\left|\sin\,x\right|+\left|\cos\,x\right|\right]$ and $x^{2}+y^{2}=10, $ where $[x]$ denotes the greatest integer $= x,$ is

The minimum value of $2^{\sin\, x} + 2^{\cos\, x}$ is