List of top Mathematics Questions

The numerically greatest term in the binomial expansion of $(2a - 3b)^{19}$ and $a = \frac{1}{4}$ and $b = \frac{2}{3}$ is

If $\alpha, \beta, \gamma$ are any three angles, then $\cos \, \alpha + \cos \beta - \cos \, \gamma - \cos (\alpha + \beta + \gamma) =$

In triangle ABC. if a = 3 ,b = 4,c = 6, then $\frac{\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}}{\cot A +\cot B + cot C} = $

If $\tan \, \theta = \frac{\cos 25^{\circ} + \sin 25^{\circ} }{\cos 25^{\circ} - \sin 25^{\circ} }$ and $\theta$ is in the third quadrant, then $\theta = $

In $\Delta ABC. a^3 . \cos (B - C) + b^3 . \cos(C - A) + c^3 . \cos (A - B) = $

If $\frac{x^{3}}{\left(2x-1\right)\left(x-1\right)^{2}} = A + \frac{B}{2x-1}+ \frac{C}{x-1}+ \frac{D}{\left(x-1\right)^{2}} $, then $2A - 3B + 4C + 5D = $

The length of the transverse common tangent of the circles $x^2 + y^2 - 2x + 4y + 4 = 0$ and $x^2 + y^2 + 4x - 2y + 1 = 0 $ is

The locus represented by $xy + yz = 0$ is

The probability of happening of an event A is 0.5 and the of B is 0.3 .If A and B are mutually exclusive events, then the probability of neither A nor B is

If $f: R \rightarrow[-1,1]$ and $g: R \rightarrow A$ are two surjective mappings and $\sin \left(g(x)-\frac{\pi}{3}\right)=\frac{f(x)}{2} \sqrt{4-f^{2}(x)}$, then $A=$

The equation of the line parallel to the line $3x - 4y + 2 = 0 $ and passing through $(-2, 3 )$ is

Option : No Option Orientation : Vertical If the angle between the tangents drawn to the circle $x^2 + y^2 -12 x - 16y = 0$ at the points w here the line $5y = 5x + k$ cut the circle is $60^{\circ}$ , then the value of $k$ is

If $A = \begin{bmatrix}k/2&0&0\\ 0&1/3&0\\ 0&0&m/4\end{bmatrix} $ and $A^{-1} = \begin{bmatrix}1/2&0&0\\ 0&1/3&0\\ 0&0&1/4\end{bmatrix}$ then $ k + l + m = $

For the matrix $A = \begin{pmatrix}3&-3&4\\ 2&-3&4\\ 0&-1&1\end{pmatrix}, A^{-1} = $

A random variable X has the following probability distribution The variance of this random variable is

$ \displaystyle \lim_{x \to 0} \frac{a^{\tan \, x} - a^{\sin \, x}}{\tan \, x - \sin \, x}$ is equal to $(a > 0)$

$\lim_{x \to \infty} \frac{3x^3 + 2x^2 - 7x + 9 }{4x^3 + 9x - 2 }$ is equal to

In a triangle ABC if $\cos \, A + \cos \, B + \cos \, C = \frac{3}{2}$ , then the triangle is

The value of the integral $\int^{\pi}_0 \frac{x \tan \, x}{\sec \, x + \tan \, x} dx $ is equal to

The value of $\sin^{4} \frac{\pi}{8} + \sin^{4} \frac{3 \pi}{8} + \sin^{4} \frac{5\pi}{8} + \sin^{4} \frac{7\pi}{8} $ is

If two circles of radii $r_1$ and $r_2$ touch externally then length of a common tangent is

If $I = \int^\limits{\pi/4}_{0} (\sqrt{\tan \, x } + \sqrt{\cot \, x} ) dx $ then value of I is

From the top of a lighthouse, the angles of depression of two stations on the oposite sides of it at a distance d apart are $\alpha$ and $\beta$. The height of the lighthouse is

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3 - 3x^2 + 3x + 7 = 0$, and w is cube root of unity, then the value of $\frac{\alpha-1}{\beta-1} + \frac{\beta-1}{\gamma-1} + \frac{\gamma-1}{\alpha-1}$ is equal to

The perimeter of the locus represented by arg $\left( \frac{z + i}{z-i}\right) = \frac{\pi}{4}$ is equal to