List of top Mathematics Questions

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 equation of the hyperbola with vertices (3,0), (-3,0) and semi-latus rectum 4 is given by:

The eccentricity of the ellipse whose major axis is three times the minor axis is:

If A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. then, I. P(not A) = 0.58 II. P(not B) = 0.52 III. P(A or B) = 0.47

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

If $A = \begin{bmatrix}2&-2\\ -2&2\end{bmatrix}$ then $A^n = 2^k A,$ where k =

The no. of points of discontinuity of the function f (x) = x - [x] in the interval (0, 7) are

Amplitude of $\frac{1+\sqrt{3}i}{\sqrt{3}+1}$ is :

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

The combined equation of the asymptotes of the hyperbola $2x^2 + 5xy + 2y^2 + 4x + 5y = 0$ is -

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

The principal value of $sin^{-1} \left(sin \frac{5\pi}{3}\right)$ is

The vector equation of the symmetrical form of equation of straight line $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$ is

The set of all $\alpha \epsilon R$, for which $w = \frac{1 + (1 - 8 \alpha)z}{1 - z}$ is a purely imaginary number, for all $z \neq 1$, 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 :

From a point A with position vector $p(\hat{i} + \hat{j} + \hat{k})$, AB and AC are drawn perpendicular to the lines $\vec{r} = \hat{k} + \lambda (\hat{i} + \hat{j})$ and $\vec{r} = - \hat{k} + \mu (\hat{i} - \hat{j})$, respectively. A value of p is equal to :

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 :

If the system of linear equations : $x + 3y + 7z = 0 $ $-x + 4y + 7z = 0$ $(\sin 3 \theta ) x + (\cos 2 \theta) y + 2z = 0 $ has a non-trivial solution, then the number of values of 6 lying in the interval $[0, \pi ]$, is :

The number of solutions of $\sin \, 3x = \cos \, 2x$, in the interval $\left( \frac{\pi}{2} , \pi \right)$ is :