List of top Mathematics Questions asked in MET

The sum of infinite terms of the GP $\dfrac{\sqrt{2}+1}{\sqrt{2}-1},\;\dfrac{1}{2-\sqrt{2}},\;\dfrac{1}{2},\;\ldots$ is

The first three terms in the expansion of $(1 + ax)^{n}$ $(n \neq 0)$ are $1$, $6x$ and $16x^{2}$. Then the values of $a$ and $n$ are respectively

If $f(x) = \begin{cases} \dfrac{x^{2} - 9}{x - 3}, & x \neq 3 \\ 2x + k, & x = 3 \end{cases}$ is continuous at $x = 3$, then $k$ equals

The area of the region $\{(x,y): x^{2} + y^{2} \le 1 \le x + y\}$ is

$\left|\dfrac{x}{2} - 1\right|<3$ implies that $x$ lies in the interval

$\sin^{-1}\dfrac{1}{\sqrt{5}} + \cos^{-1}\dfrac{3}{\sqrt{10}}$ is equal to

If $a$, $b$, $c$ are the position vectors of $A$, $B$, $C$ respectively such that $3\mathbf{a} + 4\mathbf{b} - 7\mathbf{c} = \mathbf{0}$, then $C$ divides $AB$ in the ratio

If $\begin{bmatrix} a & 2 & 3 \\ b & 5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ -1 & 1 \end{bmatrix} = \begin{bmatrix} 4 & 13 \\ 12 & 11 \end{bmatrix}$, then $(a, b)$ is}

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