List of top Mathematics Questions asked in WBJEE

Which of the following statements are true?

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=

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

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

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

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 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 

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

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 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 

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 \(\lim_{h\rightarrow0}\frac{f(2+2h+h^2)-f(2)}{f(1+h-h^2)-f(1)}\)

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

If a hyperbola passes through the point P(\(\sqrt{2},\sqrt{3}\)) and has foci at (±2,0), then the tangent to this hyperbola at P is

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

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

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

If y=\(\frac{x}{log_e|cx|}\) is the solution of the differential equation \(\frac{dy}{dx}=\frac{y}{x}+\phi(\frac{x}{y})\), then \(\phi (\frac{x}{y})\) is given by 

Let f:[1,3]\(\rightarrow\)R be continuous and be derivable in (1,3) and f'(x)=[f(x)]²+4∀x∈(1,3). Then

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

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 P (4, 3) be a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1.$ If the normal at P intersects the X-axis at (16, 0), then the eccentricity of the hyperbola is