List of top Questions asked in MET- 2018

Science of printing

Scientific psychology recognises a ...6... truth that no two individuals are ...7... in this world even through equality is a fostered norm of civil society, the truth is that men ...8... unequals in varying hues or degrees.

A cigarette shop on a busy road was bound to be profitable because

Scientific psychology recognises a ...6... truth that no two individuals are ...7... in this world even through equality is a fostered norm of civil society, the truth is that men ...8... unequals in varying hues or degrees.

If $f(x) = \sec x - \cot x$, then $f'\!\left(\dfrac{\pi}{6}\right)$ 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

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 $a$, $b$, $c$ 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

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

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 the coefficients of the $r$th term and the $(r+1)$th term in the expansion of $(1+x)^{20}$ are in the ratio $1:2$, then $r$ equals

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

If $(\sqrt{3} - i)^{50} = 2^{48}(x - iy)$, then $x^{2} + y^{2}$ equals

The area of a parallelogram with diagonals $\mathbf{a} = 3\mathbf{i} + \mathbf{j} - 2\mathbf{k}$ and $\mathbf{b} = \mathbf{i} - 3\mathbf{j} + 4\mathbf{k}$ is

If $A + B + C = \pi$, then $\begin{vmatrix} \sin(A+B+C) & \sin B & \cos C \\ \sin B & 0 & \tan A \\ \cos(A+B) & \tan A & 0 \end{vmatrix}$ equals

The equation of the curve passing through the origin and satisfying $\dfrac{dy}{dx} = (x - y)^{2}$ is

If $\displaystyle\int_{-1}^{4} f(x)\,dx = 4$ and $\displaystyle\int_{2}^{4} [3 - f(x)]\,dx = 7$, then $\displaystyle\int_{-1}^{2} f(x)\,dx$ equals

If $f''(0) = k$, then $\displaystyle\lim_{x\to 0} \dfrac{2f(x) - 3f(2x) + f(4x)}{x^{2}}$ equals

The minimum value of $x\log x$ is equal to

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

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

If $\omega$ is a cube root of unity, then $(1 + \omega - \omega^{2})(1 - \omega + \omega^{2})$ is

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

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