List of top Mathematics Questions

The number of three digit numbers in which $9$ appears only in one place is

If the petrol burnt in driving a motor boat varies as the cube of the velocity, then the speed (in km hom ) of the boat going against a water flow of C kms hour so that the quantity of petrol burnt is minimum is

Let $z = x + iy$ and a point $P$ represent $z$ in the Argand plane. If the real part of $\frac{z - 1}{z + i}$ is 1. then a point that lies on the locus of $P$ is

If A and B are the two real values of k for which the system of equations $x + 2y + z = 1,x + 3y + 4r = k.x + 5v + 10z = k^2 $ is consistent, then $A + B = $

The number of rational terms in the binomial expansion of $\left(\sqrt[4]{5} + \sqrt[5]{4}\right)^{100} $ is

If a circle touches the lines $3x - 4y - 10 = 0$ and $3x - 4y + 30 = 0$ and its centre lies on the line $x + 2y = 0$ then the equation of the equation of the circle is

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

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 = $

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