List of top Questions asked in WBJEE

ABC is an isosceles triangle with an inscribed circle with center O. Let P be the midpoint of BC. If AB=AC=15 and BC=10,then OP equals
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 α,β be the roots of the equation, ax2+bx+c=0.a,b,c are real and sn=αn+βn and \(\begin{vmatrix}3 &1+s_1  &1+s_2\\1+s_1&1+s_2  &1+s_3\\1+s_2&1+s_3  &1+s_4\end{vmatrix}=\frac{k(a+b+c)^2}{a^4}\) then k=

An electric dipole of dipole moment p is placed at the origin of the coordinate system along the z-axis. The amount of work required to move a charge 'q' from the point (a,0,0) to the point (0,0,a) is
If \(\int \frac{dx}{(x+1)(x-2)(x-3)}=\frac{1}{k}log_e\left \{ \frac{|x-3|^3|x+1|}{(x-2)^4}\right \}+c\), then the value of k is 
A rectangle ABCD has its side parallel to the line y=2x and vertices A,B,D are on y=1,x=1 and x=-1 respectively. The coordinate of C can be
Let f(x)=[x2]sinπx, x>0. Then
A thin glass rod is bent in a semicircle of radius R.A charge is non-uniformly distributed along the rod with a linear charge density \(\lambda=\lambda_0sin\theta\) (\(\lambda_0\) is a positive constant). The electric field at the center P of the semicircle is 
Three identical convex lenses each of focal length f are placed in a straight line separated by a distance f from each other. An object is located in \(\frac{f}{2}\) in front of the leftmost lens. Then,
Three identical convex lenses
As shown in the figure, a liquid is at the same levels in two arms of a U-tube of uniform cross-section when at rest. If the U-tube moves with an acceleration 'f' towards the right,the difference in liquid heights between the two arms of the U-tube will be,(acceleration due to gravity=g)
a U-tube of uniform cross-section
The calculated spin-only magnetic moment values in BM for [FeCl4]- and [Fe(CN)6]3- are
\(\lim_{x\rightarrow \infty}\){\(x-\sqrt[n]{(x-a_1)(x-a_2)......(x-a_n)}\)} where a1,a2,.....an are positive rational numbers.The limit
A particle of mass m is projected at velocity at a velocity u, making an angle θ with the horizontal(x-axis). If the angle of projection θ is varied keeping all other parameters same, then magnitude of angular momentum(L) at its maximum height about the point of projection varies with θ as,
In an experiment on a circuit, as shown in the figure, the voltmeter shows 8V reading. The resistance of the voltmeter is 
the voltmeter shows 8V reading
The value of 'a' for which the scaler triple product formed by the vectors \(\vec\alpha=\hat{i}+a\hat{j}+\hat{k}\),  \(\vec{\beta}=\hat{j}+a\hat{k}\)  and  \(\vec{\gamma}=a\hat{i}+\hat{k}\)  is maximum, is
A missile is fired from the ground level rises x meters vertically upwards in t sec, where \(x=100t-\frac{25}{2}t^2\). the maximum height reached is

The equivalent weight of KIO3 in the given reaction is (M=molecular mass) :
2Cr(OH)3 + 4OH + KIO3 → 2CrO42- + 5H2O +KI

A balloon starting from rest ascends from the ground with a uniform acceleration of 4 ft/sec2. At the end of 5 sec, a stone is dropped from it. If t be the time to reach the stone to the ground and H is the height of the balloon when the stone goes to the floor, Then
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?
Let \(cos^{-1}\frac{y}{b}\)=\(log_e (\frac{x}{n})^n\), then Ay2+By1+Cy=0 is possible :  (where y2=\(\frac{d^2y}{dx^2}\), y1=\(\frac{dy}{dx}\))
Suppose f:R\(\rightarrow\)R be given by f(x)={\(e^{(x^{10}-1)}+(x-1)^2sin\frac{1}{1-x},if\,\,\,x\neq1\)}, then
A train is moving along the tracks at a constant speed u. A girl on the train throws a ball of mass m straight ahead along the direction of motion of the train with speed v with respect to herself. Then,
the logic circuit
Consider the logic circuit with inputs A,B,C, and output Y. How many combinations of A, B and C give the output Y=0?
In the interval (-2\(\pi\),0), the function f(x)=sin(\(\frac{1}{x^3}\)).
A body of mass 2 kg moves in a horizontal circular path of radius 5m. In an instant its speed is \(2\sqrt5\) m/s and is increasing at the rate of 3 m/s2.The magnitude of the force acting on the body at the instant is,