List of top Mathematics 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 s_n=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=

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

\(\lim_{x\rightarrow \infty}\){\(x-\sqrt[n]{(x-a_1)(x-a_2)......(x-a_n)}\)} where a₁,a₂,.....a_n are positive rational numbers.The limit

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

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

In the interval (-2\(\pi\),0), the function f(x)=sin(\(\frac{1}{x^3}\)).

The locus of points(x,y) in the plane satisfying sin²x + sin²y =1 consists of

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

Let x be a nonvoid set.If ρ1 and ρ2 be the transitive relations of x, then-(° denotes the compositions of relations )

If 4a²+9b²-c²+12ab=0, then the family of straight lines ax+by+c=0 is concurrent at

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

Let \(A=\begin{pmatrix}2&0&3\\4&7&11\\5&4&8\end{pmatrix}\). Then

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

Let f be a strictly decreasing function defined on R such that f(x)>0,∀x∈R. Let \(\frac{x^2}{f(a^2+5a+3)}+\frac{y^2}{f(a+15)}=1\) be an ellipse with a major axis along the y-axis. The value of 'a' can lie in the interval(s)

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

A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, Then

If R and R₁ are equivalence relations on a set A, then so are the relations

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