List of top Questions asked in WBJEE

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 :

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?

Structure of M is

Nickel combines with a uninegative monodentate ligand (X^-) to form a paramagnetic complex [NiX4]^2-.The hybridization involved and number of unpaired electrons present in the complex and respectively

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

Let O be the vertex, Q be any point on the parabola x²=8y. If point P divides the line segment OQ internally in the ratio 1:3, then the locus of P is 

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

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

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

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

 
'L' in the above sequence of reaction is/are(where L≠M≠N)

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 

The root mean square(rms) speed of X₂ gas is x m/s at a given temperature. When the temperature is doubled, the X₂ molecules dissociated completely into atoms. The root mean square speed of the sample of gas then becomes (in m/s)

Let A,B,C are subsets of set X. Then consider the validity of the following set theoretic statement:

If the n terms a₁,a₂........a_n are in A.P. with increment r, then the difference between the mean of their squares and square of their mean is 

Select the molecule in which all the atoms may lie on a single plane is 

Let f(x)=\(\begin{Bmatrix}  x+1&\,\,\,-1\leq x\leq 0\\   -x&\,\,\,\,\,0<x\leq1    \end{Bmatrix}\)

The straight lines x+2y-9=0, 3x+5y-5=0, and ax+by-1=0 are concurrent if the straight line 35x-22y+1=0 passes through the point:

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