List of top Mathematics Questions

The length of the projection of the line segment joining the points $ (5, -1, 4)$ and $(4, -1, 3)$ on the plane, $x + y + z = 7$ is:

If sum of all the solutions of the equation $8 \cos x.\left(\cos \left(\frac{\pi}{6} + x\right). \cos\left(\frac{\pi}{6} - x\right) - \frac{1}{2}\right)= 1 $ in $\left[0, \pi\right]$ is $ k \pi $, then $k$ is equal to :

If $f : R - \{2\} \to R$ is a function defined by $f(x) = \frac{x^2 - 4}{x - 2}$ , then its range is

The sum of the first 10 terms of the series 9 + 99 + 999 + ?., is

The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is

If $f(x) = \begin{cases} x^2 + \alpha & \text{for } x \ge 0 \\[2ex] 2\sqrt{x^2 + 1} + \beta & \text{for} x < 0 \end{cases}$ is continuous at x = 0 and $f \left(\frac{1}{2} \right) = 2 $ then $\alpha^2+ \beta^2$ is

Letters in the word HULULULU are rearranged. The probability of all three L being together is

If A, B, C are the angles of $\Delta ABC$ then $\cot \, A. \cot \, B + \cot \, B. \cot \, C + \cot \, C. \cot \, A =$

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) =

If $\log_{10} \left(\frac{x^{3} - y^{3} }{x^{3} + y^3} \right) = 2$ then $ \frac{dy}{dx} = $

If $y = \left(\tan^{-1} x\right)^{2}$ then $ \left(x^{2} + 1\right)^{2} \frac{d^{2}y}{dx^{2} } + 2x \left(x^{2} + 1 \right) \frac{dy}{dx} = $

For $0 \leq p \leq 1$ and for any positive $a, b$ let $I(p) = (a + b)^p, J(p) = a^p + b^p$, then

Let $\vec{\alpha} . \vec{\beta} , \vec{\gamma}$ be three unit vectors such that $\vec{\alpha} . \vec{\beta} = \vec{\alpha} . \vec{\gamma} = 0 $ and the angle between $\vec{\beta}$ and $\vec{\gamma}$ is $30^{\circ}$ . Then $\vec{\alpha} $ is

Let $z_1$ and $z_2$ be complex numbers such that $z_1 \neq z_2$ and $| z_1| = | z_2 |$ . If Re $(z_1) > 0$ and $Im (z_2) < 0 $ ,then $\frac{z_1+ z_2}{z_1 - z_2}$ is

The least positive integer $n$ such that $\begin{pmatrix}\cos \frac{\pi}{4}&\sin \frac{\pi}{4}\\ -\sin \frac{\pi}{4}&\cos \frac{\pi}{4}\end{pmatrix} ^{n }$ is an identity matrix of order $2$ is

What is the length of the projection of $3\hat{i}+4\hat{j}+5\hat{k}$ on the xy-plane ?

The solution of $\frac{dv}{dt} +\frac{k}{m}v = -g$ is

If for a matrix A, |A| = 6 and adj $A = \begin{bmatrix}1&-2&4\\ 4&1&1\\ -1&k&0\end{bmatrix}$ , then k is equal to :

The negation of $A \to (A \vee \sim B)$ is :

The solution of the differential equation $\frac{y dx + x dy}{y dx - x dy} = \frac{x^{2} e^{xy}}{y^{4}} $ satisfying $y(0) = 1$, is :

If $L_1$ is the line of intersection of the planes $2x - 2y + 3z - 2 =0, x - y + z + 1 = 0$ and $L_2$ is the line of intersection of the planes $x + 2y - z - 3 = 0, 3x - y + 2z - 1 = 0,$ then the distance of the origin from the plane, containing the lines $L_1$ and $L_2$, is:

$\displaystyle\lim_{x \to0} \frac{x \tan2x - 2x \tan x}{\left(1-\cos2x\right)^{2}} $ equals :

The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point $(0, 3)$ is :

If the tangents drawn to the hyperbola $4y^2 = x^2 + 1$ intersect the co-ordinate axes at the distinct points $A$ and $B$ , then the locus of the mid point of $AB$ is :

The sum of the series $S = \frac{1}{19! } + \frac{1}{3!7!} + \frac{1}{5! 5!} + ... $ to 10 terms is equal to :