List of top Mathematics Questions asked in WBJEE

For any complex number $z$, the minimum value of $\left|z\right|+\left|z-1\right|$ is

$\int\limits_{0}^{1000} e^{x-\left[x\right]} dx$ is equal to

In a triangle $ABC$, if sin A sin $B =\frac{ab}{c^{2}}$, then the triangle is

If the $m^{th}$ term and the nth term of an $AP$ are respectively $\frac{1}{n}$ and $\frac{1}{m}$, then the $(mn )^{th}$ term of the $AP$ is

The coefficient of $ x^{-10}$ in $\left(x^{2} - \frac{1}{x^{3}}\right)^{10}$ is

The value of $\left(1-\omega+\omega^{2}\right)^{5} + \left(1+\omega -\omega^{2}\right)^{5}, $ where $\omega$ and $\omega^2$ are the complex cube roots of unity, is

The number of ways four boys can be seated around a round-table in four chairs of different colours is

The function $f(x ) = xe^{1-x}$ is

The differential equation of the family of curves $y = e^{2x} (a \,\cos\, x + b \,\sin\, x)$, where $a$ and $b$ are arbitrary constants, is given by

If the matrix $\begin{bmatrix}a&b\\ c&d\end{bmatrix}$ is commutative with the matrix $\begin{bmatrix}1&1\\ 0&1\end{bmatrix}$, then

One possible condition for the three points $(a, 5), (b, a)$ and $(a^2, - b^2)$ to be collinear is

If $\,^{16}C_{r} =\, ^{16}C_{r+1}$, then the value of $\, ^{r}P_{r-3}$ is

The value of $\cos \frac{\pi}{15}\, \cos \frac{2\pi}{15}\, \cos \frac{4\pi}{15}\, \cos \frac{8\pi}{15} $ is

The order and degree of the following differential equation $\left[1+\left(\frac{dy}{dx}\right)^{2}\right]^{5/2} = \frac{d^{3}y}{dx^{3}}$ are respectively

The differential equation of the family of circles passing through the fixed points $(a, 0)$ and $(-a, 0)$ is

The value of the integral $\int\limits_{-a}^{a} \frac{xe^{x^2}}{1+x^{2}} dx $ is

The value of $\displaystyle\lim_{n\to\infty}\left(\frac{1}{n+1} +\frac{1}{n+2}+... +\frac{1}{6n}\right)$ is

$\frac {3x^2+1}{x^2-6x+8}$ is equal to

If \( n = 1, 2, 3, \dots \), then \( \cos \alpha \cos 2\alpha \cos 4\alpha \dots \cos^{2n - 1} \alpha \) is equal to: 

From a set of 100 cards numbered 1 to 100, one card is drawn at random. Find the probability that the number obtained on the card is divisible by 6 or 8, but not by 24.

The area (in sq. units) enclosed by y = 1, 2x + y = 2 and x + y = 2 is

The line 2x - y = 1 bisects the angle between two lines. If the equation of one line is y = x, then the equation of the other line is

Directions: The following question has four choices, out of which one or more are correct. An infinite current-carrying wire passes through point O and in perpendicular to the plane containing a current-carrying loop ABCD as shown in the figure. Choose the correct option(s).

$$\begin{array}{l}\text{ Given: }\left|\begin{array}{ccc}a& b& a\alpha +b\\ b& c& b\alpha +c\\ ac+b& bc+c& 0\end{array}\right|=0\\ \text{ Applying }{C}_3\to C_3-(\alpha C_1+C_2)\end{array}$$If the determinant $\left|\begin{array}{ccc}a& b& 0\\ b& c& 0\\ a\alpha +b& bc+c& -(a{c}^2+2bc+c)\end{array}\right|=0$$$\Rightarrow -(a{\alpha }^2+2b\alpha +c)(ac-b^2)=0$$$$\Rightarrow a{\alpha }^2+2b\alpha +c=0\text{ or }{b}^2=ac$$$\therefore \alpha$ is root of $a{x}^2+2bx+c$ or $a,b,c$ are in GP.

Directions: The following question has four choices, out of which one or more are correct.A ray of light is incident on a reflecting surface. The ray moves in horizontal direction and is reflected vertically after striking the surface. If the surface is denoted by $y=\frac{2L}{\pi }\sin \left(\frac{\pi }{L}x\right),0\le x\le L,$ what are the coordinates of the point(s) where the ray is incident?