List of top Mathematics Questions

If the rate of change in the circumference of a circle is $0.3$ cm/s, then the rate of change in the area of the circle when the radius is $5$ cm is

$\displaystyle\int \frac{2\,dx}{(e^{x} + e^{-x})^{2}}$ is equal to

$\displaystyle\lim_{x\to 0}\frac{(2+x)\sin(2+x) - 2\sin 2}{x}$ is equal to

If $|\mathbf{a} + \mathbf{b}| = |\mathbf{a} - \mathbf{b}|$, then $\mathbf{a}$ and $\mathbf{b}$ are

If $A \cdot \mathrm{adj}(A) = O$, then $|A|$ is}

The area included between the curves $y^{2} = 2x$ and $x^{2} = 2y$ is

The differential equation of the family of curves $y = a\cos\mu x + b\sin\mu x$, where $a$ and $b$ are arbitrary constants, is

The function $f(x) = \sin x(1 + \cos x)$, $0 \le x \le \dfrac{\pi}{2}$, has a maximum value when $x$ equals

The product of $n$ positive numbers is unity. Then their sum is

If $a$, $b$ and $c$ are negative and different real numbers, then $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$ is}

If $a$, $b$, $c$ are different integers such that $(a,b) = c$, which of the following statements is true?

$\displaystyle\int_{0}^{1} x\sin(\pi x)\,dx$ is equal to

$A(-1,2)$, $B(5,1)$, $C(6,5)$ are the vertices of a parallelogram $ABCD$. The equation of the diagonal through $B$ is

If $f(x) = \dfrac{x + \cos x}{x - \cos x}$, then $f'\!\left(\dfrac{\pi}{2}\right)$ equals

If $x(1+y^{2})\,dx + y(1+x^{2})\,dy = 0$ and $y(0) = 1$, then $x^{2}y^{2} + x^{2} + y^{2}$ equals

The value of $\displaystyle\sum_{r=1}^{\infty}\left[3\cdot 2^{-r} - 2\cdot 3^{1-r}\right]$ is

The condition that one root of the equation $ax^{2} + bx + c = 0$ may be the square of the other is

Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The number of persons in the room is

The area bounded by $y = 1 + \dfrac{8}{x^2}$ and the ordinates $x = 2$ and $x = 4$ is

If $f(x) = \begin{cases} x+1, & x \le 1 \\ 3 - ax^2, & x>1 \end{cases}$ is continuous at $x = 1$, then $a$ is

If $\sin(\pi \cos \theta) = \cos(\pi \sin \theta)$, then which of the following is correct?

If $3\sin^{-1}\!\left(\dfrac{2x}{1+x^{2}}\right) - 4\cos^{-1}\!\left(\dfrac{1-x^{2}}{1+x^{2}}\right) + 2\tan^{-1}\!\left(\dfrac{2x}{1-x^{2}}\right) = \dfrac{\pi}{3}$, then $x$ equals

The equation $(\cos p - 1)x^{2}+ (\cos p)\,x + \sin p = 0$ in the variable $x$ has real roots. Then $p$ can take values in the interval

By eliminating the arbitrary constants $A$ and $B$ from $y = Ax^{2} + Bx$, the differential equation obtained is

The least positive remainder when $123 \times 125 \times 127$ is divided by 124 is