List of top Mathematics Questions

If $a$ is a unit vector, then $| a \times \hat{ i }|^{2}+| a \times \hat{ j }|^{2}+| a \times \hat{ k }|^{2}=$

A bag contains $5$ red balls, $3$ black balls and $4$ white balls are drawn at random. The probability that they are not of same colour is

$A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations

If $\frac{x^{2} + 5}{\left(x^{2} + 1 \right)\left(x-2\right)} = \frac{A}{x-2} + \frac{Bx+C}{x^{2} + 1 } , $ then $A + B + C = $

If $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 ,$ then $\frac{d^2 y}{dx^2} = $

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 :

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)

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 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 ?