List of top Questions asked in WBJEE

If
\[ \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix} \cdot A \cdot \begin{pmatrix} -3 & 2 \\ 5 & -3 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \]
then \(A\) is:

If \( a_1, a_2, \dots, a_n \) are in A.P. with common difference \( \theta \), then the sum of the series:
\[ \sec a_1 \sec a_2 + \sec a_2 \sec a_3 + \dots + \sec a_{n-1} \sec a_n = k (\tan a_n - \tan a_1), \]
where \( k = ? \)

The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = e^x + e^{-x} \) is:

Chords AB CD of a circle intersect at right angle at the point P. If the lengths of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is:

Let \( \Gamma \) be the curve \( y = b e^{-x/a} \) and \( L \) be the straight line:
\[ \frac{x}{a} + \frac{y}{b} = 1, \quad a, b \in \mathbb{R}. \]
Then:

Consider the function f(x) = (x−2)logx. Then the equation xlogx = 2−x has:

If \(U_n (n = 1, 2)\) denotes the \(n\)-th derivative (\(n = 1, 2\)) of \(U(x) = \frac{Lx + M}{x^2 - 2Bx + C}\) (\(L, M, B, C\) are constants), then \(PU_2 + QU_1 + RU = 0\) holds for:

The function \(y=e^{kr}\) satisfies \((\frac{d^2y}{dx^2}+\frac{dy}{dx})(\frac{dy}{dx}-y)=y\frac{dy}{dx}\). It is valid for 

In an experiment on a circuit, as shown in the figure, the voltmeter shows 8V reading. The resistance of the voltmeter is 

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

A charged particle in a uniform magnetic field \(\vec{B}=B_0\hat{k}\) starts moving from the origin with velocity \(v=3\hat{i}+4\hat{k}\) m/s.The trajectory of the particle and the time \(t\) at which it reaches 2m above the x-y plane are 

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

Let f be a non-negative function defined on [\(0,\frac{\pi}{2}\)]. If \(\int_{0}^{x}(f'(t)-sin\,2t)dt=\int_{0}^{x}f(t)tan\,t\,dt\). \(f(0)=1\), then \(\int_{0}^{\frac{\pi}{2}}f(x)dx\) is

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

If \(\frac{1}{6}\)sinθ.cosθ.tanθ are in G.P, then the solution set θ is

If z₁ and z₂ are two complex numbers satisfying the equation\(|\frac{z_1+z_2}{z_1-z_2}|=1\), then \(\frac{z_1}{z_2}\) may be

The number of ways in which the letter of the word 'VERTICAL' can be arranged without changing the order of the vowels is 

63g of a compound (Mol.Wt.=126) was dissolved in 500g of distilled water.The density of the resultant solution is 1.126g/ml. The molarity of the solution is

f(x) is differentiable function and given f'(2)=6, f'(1)=4, then \(\lim_{h\rightarrow0}\frac{f(2+2h+h^2)-f(2)}{f(1+h-h^2)-f(1)}\)

If \(I_n=\int_{0}^{\frac{\pi}{2}}cos^nxcos\,nxdx\), then \(I_1,I_2,I_3\).....are in