List of top Mathematics Questions

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

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

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

For the LPP; maximise $z =x + 4y$ subject to the constraints $x + 2y \leq 2, x +2 y \ge 8, x, y \ge 0$

A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is ___________$\pi$ cm/s

The focus of the curve $y^2 + 4x - 6y + 13 = 0$ is

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

Amplitude of $\frac{1+\sqrt{3}i}{\sqrt{3}+1}$ 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 foci of a hyperbola coincide with the foci of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1 $ If the eccentricity of the hyperbola is 2, then the equation of the tangent to this hyperbola passing through the point (4, 6) is :

Let the orthocenter an centroid of a triangle be $A(-3, 5)$ and $B(3, 3)$ respectively. If $C$ is the circumcentre of this triangle, then the radius of the circle having line segment $AC$ as diameter, is:

Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is :

The locus of the point of intersection of the lines, $\sqrt{2} x-y + 4 \sqrt{2} \, k=0$ and $\sqrt{2} k x+k \, y-4 \sqrt{2} = 0$ (k is any non-zero real parameter), is :

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

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 $A = \begin{bmatrix}\cos\alpha&\sin\alpha\\ - \sin\alpha&\cos\alpha\end{bmatrix}$ , then $AA' = $