List of top Mathematics Questions asked in WBJEE

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

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

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 

From the focus of the parabola y²=12x, a ray of light is directed in a direction making an angle \(tan^{-1}\frac{3}{4}\)  with the x-axis. Then the equation of the line along which the reflected ray leaves the parabola is

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

The tangent at point(a cosθ, b sinθ), 0<θ<\(\frac{\pi}{2}\), to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) meets the x-axis at T and y-axis at T₁, Then the value of \(\min_{\,\,\,0<\theta<\frac{\pi}{2}}\)(OT)(OT₁) is

A, B are fixed points with coordinates (0,a) and (0,b) (a>0,b>0). P is a variable point (x,0) referred to as the rectangular axis. If the angle \(\angle\)APB is maximum, then