List of top Mathematics Questions

If vector $\vec{r}$ with d.c.s. $l, m, n$ is equally inclined to the co-ordinate axes, then the total number of such vectors is

The value of $\cos^{-1} \left(\cot\left(\frac{\pi}{2}\right)\right) + \cos^{-1} \left(\sin\left(\frac{2\pi}{3}\right)\right) $ is

The equation of the plane through $(-1, 1 , 2 ) $ whose normal makes equal acute angles with co-ordinate axes is

A square is drawn on 1^st quadrant of XY plane having consecutive coordinates (counter - clockwise, starting from left bottom) as P(2,3), Q(7,3), R(7,8), S(2,8) respectively. Thereafter, each side of the square is doubled considering P as a fixed point and the new square becomes PQ'R'S'. Now this new square is mirrored with respect to X axis. What will be the coordinates for the image of R'?

The characteristic equation of a matrix A is λ³ - 5λ² - 3λ + 2I = 0 then |adj A| =

The equation $5x^2 + y^2 + y = 8$ represents

$\quad\int_{0}^{1} \left[f \left(x\right)g'' \left(x\right)-f''\left(x\right)g \left(x\right)\right]$ dx is equal to : [Given f(0) = g(0) = 0]

The volume V and depth x of water in a vessel are connected by the relation $V=5x-\frac{x^{2}}{6} $ and the volume of water is increasing, at the rate of $5 cm^{3}/sec,$ when x = 2 cm. The rate at which the depth of water is increasing, is

The area bounded by f (x) $=x^{2}, 0 \le x \le 1, g\left(x\right)=x+2,1\le x\le2$ and x- axis is

A straight line parallel to the line 2x - y + 5 = 0 is also a tangent to the curve $y^{2}=4x+5.$ Then the point of contact is

Equation $\frac{1}{r}=\frac{1}{8}+\frac{3}{8} cos\, \theta represents$

Let A be the centre of the circle $x^{2}+y^{2}-2x-4y-20=0,$ and B( 1,7) andD(4,-2) are points on the circle then, if tangents be drawn at B and D, which meet at C, then area of quadri 1 ateral A BCD is-

Value of $\int\limits_{0}^{\pi /2} \frac{\sqrt{sin x}}{\sqrt{sin x}\sqrt{cos x}} $ dx is

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in $s m$) of the flower-bed, is :

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

Let $a, b, c \, \in \, R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f (x + y) = f (x) + f (y) + xy, \forall \, x, y \, \in \, R,$ then $\displaystyle\sum^{10}_{n = 1} f(n)$ is equal to :

If for $x \epsilon \left(0, \frac{1}{4}\right) ,$ the derivative of $ \tan^{-1} \left(\frac{6x \sqrt{x}}{1-9x^{3}}\right) $ is $\sqrt{x} . g(x)$, then $g(x)$ equals :

The integral $\int \sqrt{ 1 + 2 \cot \, x (cosec \, x + \cot \, x) } dx \, \left( 0 < x < \frac{\pi}{2} \right)$ is equal to : (where $C$ is a constant of integration)

The total number of terms in the expansion of ${(x+a)^{47} - (x-a)^{47}}$ after simplification is

A focal chord of the parabola y² = 8x in inclined to x-axis at an angle tan^-13. Then its length is equal to:

The equation of a circle passing through the point (1, 1) and the point of intersection of the circles x² + y² + 13x - 3y = 0 and 2x² + 2y² + 4x - 7y -25 = 0 is

If \(\Delta=\begin{vmatrix} 1&2&3\\2&5&7\\3&9&13 \end{vmatrix}\) and \(\Delta'=\begin{vmatrix} 7&20&29\\2&5&7\\3&9&13 \end{vmatrix}\) then

The geometric mean 3,3² ..... 3ⁿ is

what is the product of three Geometric mean between 4 and 1/4 ?