List of top Mathematics Questions asked in WBJEE

\(\int_{0}^{2\pi}\theta sin^6\theta cos\theta\,d\theta\) is equal to

Let A be the point (0,4) in the xy-plane and B be the point (2t,0). Let L be AB's midpoint and let AB's perpendicular bisector meet the y-axis M. Let N be the midpoint of LM. The locus of N is

The equation \(r^2=cos^2(\theta-\frac{\pi}{3})=2\) represents

The average length of all vertical chords of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\),  \(a \leq x\leq 2a\), is

Let A be a set containing n elements, A subset P of A is chosen and set A is reconstructed by replacing the elements of P. A subset Q of A is chosen again. The number of ways of choosing P and Q such that Q contains just one element more than P is

If f(x)=3\(\sqrt[3]{x^2}-x^2\), then

Let a₁, a₂, a₃,.....,a_n be positive real numbers.Then the minimum value of \(\frac{a_1}{a_2}+\frac{a_2}{a_3}+....+\frac{a_n}{a_1}\) is

Let A=\(\begin{pmatrix}  0&0  &1 \\   1&0  &0 \\   0&0  &0  \end{pmatrix}\), B=\(\begin{pmatrix}  0&1  &0 \\   0&0  &1 \\   0&0  &0  \end{pmatrix}\) and P=\(\begin{pmatrix}  0&1  &0 \\   x&0  &0 \\   0&0  &y  \end{pmatrix}\) be an orthogonal matrix such that B=PAP^-1 holds. Then

Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and E_k={(a,b)∈S:ab=k}. If P_k=P(E_k), then the correct among the following is 

Let f(x)=[x²]sinπx, x>0. Then

Let A and B be orthogonal and det A+det B=0. Then

If I=∫\(\frac{x^2dx}{(x\,sin\,x+cos\,x)^2}\)=f(x)+tan x+c, then f(x) is

The expression \(\frac{\int_{0}^{n}[x]dx}{\int_{0}^{n}\left \{ x\right \}dx}\), where [x] and {x} are respectively integral and fractional part of x and n∈N, is equal to

Reflection of the line \(\bar{a}z\)+\(a\bar{z}\)=0 in the real axis is given by

If the distance between the plane αx-2y+z=k and the plane containing the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\) is \(\sqrt{6}\), then|k| is :

If the volume of the parallelopiped with \(\vec a\times \vec b\), \(\vec b\times \vec c\)  and  \(\vec c\times \vec a\) as coterminous edges is 9 cu. units,then the volume of the parallelopiped with (\(\vec a\times \vec b\))×(\(\vec b\times \vec c\)), (\(\vec b\times \vec c\))×(\(\vec c\times \vec a\)) and (\(\vec c\times \vec a\))×(\(\vec a\times \vec b\)) as coterminous edges is

Given \(\frac{d^2y}{dx^2}=cot\,x\frac{dy}{dx}+4y\,cosec^2x=0\). Changing the independent variable x to z by the substitution z=log tan \(\frac{x}{2}\), the equation is changed to 

Let A(2 secθ, 3 tanθ) and B(2 secΦ, 3 tanΦ) where \(\theta+\phi=\frac{\pi}{2}\) be two parts of the hyperbola \(\frac{x^2}{4}-\frac{y^2}{9}=1\). If (α,β) is the point of intersection of normals of the hyperbola at A and B, then β is equal to

If the lines joining the focii of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)  where a>b and an extremity of its minor axis is inclined at an angle 60°, then the eccentricity of the ellipse is

The angle between a normal to the plane 2x-y+2z-1=0 and the X-axis is 

Let \(\rho\) be a relation defined on a set of natural numbers N, as \(\rho\)={(x,y)∈N×N:2x+y=4}, then domain A and range B are 

Which of the following statements are true?

Let f(x)=x^m, m being a non-negative integer. The value of m so that the equality f'(a+b)=f'(a)+f'(b) is valid for all a,b>0 is

The value of \(\int_{0}^{\frac{1}{2}}\frac{dx}{\sqrt{1-x^{2n}}}\) is (n∈N)

If the vertices of a square z₁,z₂,z₃ and z₄ taken in the anti-clockwise order, then z₃=