List of top Questions asked in WBJEE

A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, Then 

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

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 

From the focus of the parabola y²=12x, a ray of light is directed in a direction making an angle \(tan^{-1}\frac{3}{4}\)  with the x-axis. Then the equation of the line along which the reflected ray leaves the parabola is

Consider a quadratic equation ax²+2bx+c=0 where a,b,c are positive real numbers. If the equation has no real root, then which of the following is true?

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 f(x) = e^sinx+e^cosx, The global maximum value of f(x)

The average ordinate of y=sin x over [0,\(\pi\)] is

If x=sinθ and y=sin kθ, then (1-x²)y₂-xy₁-αy=0, for α=

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

In the interval (-2\(\pi\),0), the function f(x)=sin(\(\frac{1}{x^3}\)).

The value of \(\lim_{n\rightarrow\infty}[(\frac{1}{2.3}+\frac{1}{2^2.3})+(\frac{1}{2^2.3^2}+\frac{1}{2^3.3^2})+.....+(\frac{1}{2^n.3^n}+\frac{1}{2^{n+1}.3^n})]\)

The family of curves y=e^{asin x}, where a is an arbitrary constant, is represented by the differential equation

Let x be a nonvoid set.If ρ1 and ρ2 be the transitive relations of x, then-(° denotes the compositions of relations )

Let A and B be two independent events. The probability that both A and B happens is \(\frac{1}{12}\) and the probability that neither A nor B happens is \(\frac{1}{2}\). Then

If the matrix M_r is given by M_r=\(\begin{pmatrix}r &r-1 \\ r-1&r \end{pmatrix}\) for r=1,2,3....then det(M₁)+det(M₂)+.......+det(M₂₀₀₈)=

Let \(A=\begin{pmatrix}2&0&3\\4&7&11\\5&4&8\end{pmatrix}\). Then

Let \(P(n)=3^{2n+1}+2^{n+2}\) where n∈N. Then

If one root of \(x^2+px-q^2=0\), p and q are real, be less than 2, and other be greater than 2. Then 

n objects are distributed at random among n persons. The number of ways in which this can be done so that at least one of them will not get any object is

If 1,\(log_9\)(\(3^{1-x}+2\)).\(log_3\)(\(4.3^x-1\)) are in A.P. then \(x\) equals 

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

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

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

A, B are fixed points with coordinates (0,a) and (0,b) (a>0,b>0). P is a variable point (x,0) referred to as the rectangular axis. If the angle \(\angle\)APB is maximum, then