List of top Questions asked in WBJEE

The position vectors of two adjacent sides of a rectangle \(OACB\) are \(\vec{a}\) and \(\vec{b}\) respectively, where \(O\) is the origin. If \(16|\vec{a}\times\vec{b}|=3(|\vec{a}|+|\vec{b}|)^{2}\) and \(\theta\) be the acute angle between the diagonals \(OC\) and \(AB\), then the value of \(\tan\left(\frac{\theta}{2}\right)\) is:
If \(a=\lim_{n\rightarrow\infty}\cos^{2n}x\), \((x=n\pi)\) and \(b=\lim_{n\rightarrow\infty}\cos^{2n}x\), \((x\ne m\pi)\), then numerical value of the area of the triangle whose vertices are \((a,b)\), \((-2,1)\) and \((2,1)\) is:
Let \(A=[a,\infty)\) denotes the domain, then \(f:[a,\infty)\rightarrow B\) which is defined by \(f(x)=2x^{3}-3x^{2}+6\) will have an inverse for the smallest real value of \(a\) if:
A mapping is selected at random from all mappings \(f:A\rightarrow A\) where set \(A=\{1,2,3,\dots,n\}\). If the probability that the mapping is injective is \(\frac{3}{32}\), then the value of \(n\) is:
If the locus of mid point of any normal chord of the parabola \(y^{2}=4x\) is \(x-\lambda=\frac{\mu}{y^{2}}+\frac{y^{2}}{\nu}\), \(\lambda,\mu,\nu\in\mathbb{N}\), then \((\lambda+\mu+\nu)\) equals to:
If \(\int\frac{\csc^{2}x-2010}{\cos^{2010}x}dx=-\frac{f(x)}{(g(x))^{2010}}+c\), where \(f\left(\frac{\pi}{4}\right)=1\), then the number of solutions of the equation \(\frac{f(x)}{g(x)}=\{x\}\) in \([0,2\pi]\) is/are (where \(\{\cdot\}\) represents fractional part function):
If \(0<\alpha<\beta<\gamma<\frac{\pi}{2}\) then the equation \(\frac{1}{x-\sin\alpha}+\frac{1}{x-\sin\beta}+\frac{1}{x-\sin\gamma}=0\) has:
Which of the following statements is always true?
If \[ f(x)=\frac{1+x}{1-x} \] and \(A\) is a matrix such that \(A^{3}=0\), then \[ f(A)= \]
Consider the sequence of numbers \[ \{1,2,3,\dots,13\}. \] A person chooses three numbers at random from the sequence. The probability that the chosen three numbers form an A.P. is:
\(t_n\) denotes the nth term of an A.P. and \[ t_p=\frac{1}{q}, \qquad t_q=\frac{1}{p}. \] Then which one of the following options is a root of the equation \[ (p+2q-3r)x^{2}+(q+2r-3p)x+(r+2p-3q)=0? \]
The expression \[ \sum_{K=1}^{32}(3K+2)\left\{\sum_{r=1}^{10}\left(\sin\frac{2r\pi}{11}-i\cos\frac{2r\pi}{11}\right)\right\}^{K} \] represents:
A vector given by \[ \vec{P}=f(t)\hat{i}+g(t)\hat{j}+\hat{k} \] moves in such a way that it is always parallel to the vector \[ \vec{Q}=-f^{\prime\prime}(t)\hat{i}+f^{\prime}(t)\hat{j}+\hat{k}. \] The magnitude of \(\vec{P}\) is:
If \[ \sum_{r=1}^{\infty}\tan^{-1}\left(\frac{1}{2r^{2}}\right)=a, \] then \(\tan a\) is equal to:
Given \(P(x)=x^{4}+ax^{3}+bx^{2}+cx+d\) such that \(x=0\) is the only real root of \(P^{\prime}(x)=0\). If \(P(-1)\)

What are the charges stored in the \( 1\,\mu\text{F} \) and \( 2\,\mu\text{F} \) capacitors in the circuit once current becomes steady? 

One end of a steel wire is fixed to the ceiling of an elevator moving up with an acceleration \( 2\,\text{m/s}^2 \) and a load of \( 10\,\text{kg} \) hangs from the other end. If the cross-section of the wire is \( 2\,\text{cm}^2 \), then the longitudinal strain in the wire is given. (Take \( g=10\,\text{m/s}^2 \) and \( Y=2.0\times10^{11}\,\text{N/m}^2 \)). 

Which logic gate is represented by the following combinations of logic gates?

Figure shows the graph of angle of deviation \( \delta \) versus angle of incidence \( i \) for a light ray striking a prism. The prism angle is 

Three different liquids are filled in a U-tube as shown. Their densities are \( \rho_1, \rho_2, \rho_3 \) respectively. From the figure we may conclude that 

Arrange the following compounds in order of their increasing acid strength. 


Which of the following compounds is most reactive in SN$_1$ reaction? 

Increasing order of the nucleophilic substitution of following compounds is

Which of the following hydrocarbons reacts easily with MeMgBr to give methane? 

The major product (F) in the following reaction is