List of top Mathematics Questions asked in WBJEE

In a triangle ABC, tan C < 0. Then

The value(s) of k for which the equations x² - kx - 21 = 0 and x² - 3kx + 35 = 0 will have a common root is/are

If the ratio of the roots of the equation $p{x}^2+qx+r=0$ is $a:b,$ then $\frac{ab}{(a+b{)}^2}=$

The sum of n terms of an AP is n² + n; the common difference will be:

If sum of the coefficients of x⁷ and x⁴ in the expansion of ${(\frac{x^2}{a}-\frac{b}{x})}^{11}$ is zero, then

From a set of 100 cards numbered 1 to 100, one card is drawn at random. Find the probability that the number obtained on the card is divisible by 6 or 8, but not by 24.

If p + q + r = a + b + c = 0, then the determinant $\mathrm{\Delta }=\left|\begin{array}{lll}pa& qb& rc\\ qc& ra& pb\\ rb& pc& qa\end{array}\right|$ equals

Evaluate:$\underset{x\to -2}{lim}\frac{x^5+2x^4+x^2+3x+2}{x^4+2x^3+3x^2-5x-22}$

The forces with magnitudes 5,3 and 1 unit are acting on a particle in the direction of the vectors $6\hat{i}+2\hat{j}+3\hat{k};3\hat{i}-2\hat{j}+6\hat{k}$ and $2i-3\hat{j}-6\hat{k},$ respectively. They remain constant while the particle is displaced from the point $A(2,-1,-3)$ to $B(5,-1,1)$. The work done is

If ¹⁸C15 + 2(¹⁸C16) + ¹⁷C16 + 1 = ⁿC3, then n is equal to

The area (in sq. units) bounded by the parabola y = 2 – x² and the line x + y = 0 is

The solution of $\frac{dy}{dx}=\frac{x\log x^2+x}{\sin y+y\cos y}$

The equation of the plane parallel to the planes x + 2y + 3z – 5 = 0 and x + 2y + 3z – 7 = 0 and equidistant from them is

If $\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{b}=\hat{i}\times (\overrightarrow{a}\times \hat{i})+\hat{j}\times (\overrightarrow{a}\times \hat{j})+\overrightarrow{k}\times (\overrightarrow{a}\times \hat{k})$ then length of $\overrightarrow{b}$ isequal to

$\int \frac{a^{x/2}}{\sqrt{a^{-x}-a^x}}\mathrm{dx}$ is equal to

If fourth term of an A.P. is zero, then $\frac{t_{25}}{t_{11}}$ is, where $t_n$ denotes the $n^{\text{th }}$ term of AP.

If in a triangle ABC, sin A, sin B, sin C are in A.P., then 

The sum of n terms of two AP's are in the ratio of $(3n+8):(7n+15)$. Find the ratio of their ${12}^{\text{th }}$ terms.

The standard deviation of n observations $x_1,x_2,\dots x_n$ is 2 If $\sum _{i=1}^n{x}_i=20$ and $\sum _{i=1}^n{x}_i^2=100,$ then $n$ is equal to

The number of real solutions of the equation |x|² + 5|x| + 4 = 0 is

The coordinates of a moving point p are (2t² + 4, 4t + 6). Then  its locus will be a

$\sqrt{4},\sqrt[4]{4},\sqrt[8]{4},\sqrt[16]{4},\dots \dots \dots$up to ∞ are roots of the equation

The shortest distance from the point (1, 2, -1) to the surface of the sphere x² + y² + z² = 54 is