List of top Mathematics Questions asked in WBJEE

The general solution of the different equation $100\frac{d^{2}y}{dx^{2}}-20 \frac{dy}{dx}+y = 0 $ is

The degree of the differential equation $x = 1+\left(\frac{dy}{dx}\right)+\frac{1}{2!}\left(\frac{dy}{dx}\right)^{2}+\frac{1}{3!}\left(\frac{dy}{dx}\right)^{3} + .........$

$\int\sqrt{1+\cos\,x}\,dx$ is equal to

The value of $\frac{2}{3!}+\frac{4}{5!}+\frac{6}{7!}+........$ is

If $y'' - 3y' + 2y = 0$ where $y(0) = 1$, $y'(0) = 0$, then the value of $y$ at $x \,= log_e \,2$ is

If $z = \frac{4}{1-i}$, then $\bar{z}$ is (where $\bar{z}$ is complex conjugate of $z$ )

If $\frac{d}{dx} \left\{f\left(x\right)\right\} = g\left(x\right)$, then $\int\limits^{b}_{a}$ $f (x)g(x)dx$ is equal to

If $I_{1} = \int\limits^{3\pi}_{0}f\left(\cos^{2}\,x\right)dx$ and $I_{2} = \int\limits^{\pi}_{0} f\left(\cos^{2}\,x\right)dx$, then

The equation of one of the curves whose slope at any point is equal to $y + 2x$ is

The value of integral $\int\limits_{-1}^{1} \frac{\left|x+2\right|}{x+2} dx$ is

The equation $\sqrt{3}\, \sin \,x+\cos\,x = 4$ has

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is $90^{\circ}$ The eccentricity of the ellipse is

The value of $ \displaystyle\lim_{n\to\infty} \left[\frac{n}{n^{2}+1^{2}}+\frac{n}{n^{2}+2^{2}}+\ldots+\frac{1}{n^{2}+2n}\right] $ is

The modulus of $\frac{1-i}{3+i}+\frac{4i}{5}$ is

A line through the point $A(2, 0)$ which makes an angle of $30^{\circ}$ with the positive direction of $x$-axis is rotated about $A$ in clockwise direction through an angle $15^{\circ}$. Then, the equation of the straight line in the new position is

The value of $\int\limits_{0}^{\infty} \frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)}$ is

For any two sets $A$ and $B$, $A-(A-B)$ equals

For what value of $m$, $\frac{a^{m+1}+b^{m+1}}{a^{m}+b^{m}}$ is the arithmetic mean of $�a�$ and $�b�$ ?

If $C_{0}, C_{1}, C_{2}, \ldots, C_{n}$ denote the coefficients in the expansion of $(1+x)^{n}$, then the value of $C_{1}+2C_{2}+3C_{3}+\ldots+nC_{n}$ is

$A$ and $B$ are two independent events such that $P\left(A\cup B'\right)=0.8$, and $P\left(A\right)=0.3$ Then, $P(B)$ is

If $\alpha, \beta $ be the roots of $x^{2}-a(x-1)+b=0$, then the value of $\frac{1}{\alpha^{2}-a\alpha}+\frac{1}{\beta^{2}-a\beta}+\frac{2}{a+b}$ is

The equation of the tangent to the conic $x^{2}-y^{2}-8x+2y+11=0$ at $(2,1)$ is

The slope at any point of a curve $y = f(x )$ is given by $\frac{d y}{d x}=3x^{2}$ and it passes through $(-1 ,1 )$ The equation of the curve is

The coordinates of the foot of the perpendicular from $(0,0)$ upon the line $x + y = 2$ are

Angle between $y^{2}=x$ and $x^{2}=y$ at the origin is