List of top Mathematics Questions

If $A = \begin{bmatrix}5a &-b\\ 3&2\end{bmatrix}$ and $A$ adj $A$ = $AA^T$ , then $5a + b$ is equal to :

If $f(x) = x^2 , g(x) = 2x,0 \leq x \leq 2$ then the value of $I(x) = \int\limits_0^2 max (f(x), g(x))$ is

For what value of $k$, the function defined by $ f(x) = \begin{cases} \frac{log(1+2x)sin\,x^\circ}{x^2} & \text{for } x \ge \text {0}\\ k & \text{for } x = \text{ 0} \end{cases}$ is continuous at $x = 0$ ?

Derivative of $log \left(sec\,\theta +tan \,\theta\right) $ with respect to $sec\, \theta$ at $\theta = \pi/4$ is

If Rolle�s theorem for $f\left(x\right)= e^{x} \left(sinx - cosx\right)$ is verified on $[\pi/4$, $5 \pi/4]$, then the value of $c$ is

If $ 2 \,tan^{-1} (cos\,x) = tan^{-1} (2 \,cosec\,x)$ then $sin\,x + cos\,x $ is equal to

The approximate value of $f\left(x\right)= x^{3}+5x^{2}-7x +9$ at $x=1.1 $ is

$\int \frac{1}{\sqrt{8+2x-x^{2}}} dx$ is equal to

If $A$ and $B$ are foot of perpendicular drawn from point $Q (a, b, c)$ to the planes $yz$ and $zx$, then equation of plane through the points $A, B$ and $O$ is ___________

If $A=\begin{bmatrix}1&1&0\\ 2&1&5\\ 1&2&1\end{bmatrix}$, then $a_{11}A_{21} +a_{12}A_{22}+a_{13}A_{23} $ is equal to

The joint equation of lines passing through the origin and trisecting the first quadrant is ________

The number of surjective functions from $A$ to $B$ where $A = \{1, 2, 3, 4 \}$ and $B = \{a, b\}$ is

The equation of one of the common tangents to the parabola $y^2 = 8x$ and $x^2 + y^2 - 12x + 4 = 0$ is

The value of $ (1 + \omega - \omega^2)^7$ is

If $|\vec{a} | = 3, |\vec{b}| = 2, |\vec{c}| = 1$ then the value of $|\vec{a}. \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}| $ is (given that $\vec{a} + \vec{b} + \vec{c} = 0$)

If the tangent to the function $y = f(x) $ at $(3,4)$ makes an angle of $\frac{3 \pi }{4}$ with the positive direction of x-axis in anticlockwise direction then $f ' (3)$ is

A tetrahedron has vertices at $O (0, 0, 0), A (1, 2, 1) B (2, 1, 3) $ and $C (-1, 1, 2)$. Then the angle between the faces $OAB$ and $ABC$ will be

If $ A$ and $B$ are matrices and $B = ABA^{-1}$ then the value of $(A + B) (A - B)$ is

In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present.

What is the area of a loop of the curve $r = a \sin^3 \theta$ ?

If $e^x = y + \sqrt{ 1 + y^2}$ , then the value of y is

Let $z = 1 + ai$ be a complex number, $a > 0$, such that $z^3$ is a real number. Then the sum $1 + z + z^2 +..... + z^{11}$ is equal to :

If a variable line drawn through the intersection of the lines $\frac{x}{3} + \frac{y}{4} = 1$ and $\frac{x}{4} + \frac{y}{3} = 1$, meets the coordinate axes at $A$ and $B$, $(A \neq B)$, then the locus of the midpoint of $AB$ is :

If all the words (with or without meaning) having five letters, formed using the letters of the word $SMALL$ and arranged as in a dictionary; then the position of the word $SMALL$ is:

If a curve $y = f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation, $y(1 + xy) dx = x \,dy$, then $f \left( - \frac{1}{2} \right)$ is equal to :