List of top Questions asked in MET- 2018

The value of $a$ for which $f(x) = a\sin x + \dfrac{1}{3}\sin 3x$ has an extremum at $x = \dfrac{\pi}{3}$ is

If $|f(x)|$ is continuous at $x = a$, then $f(x)$

$\displaystyle\int_{0}^{\pi/2} \dfrac{\sin^{n}\theta}{\sin^{n}\theta + \cos^{n}\theta}\,d\theta$ is equal to

The general solution of $x\sqrt{1+y^{2}}\,dx + y\sqrt{1+x^{2}}\,dy = 0$ is

The area in square units enclosed by the curve $x^{2}y = 36$, the $x$-axis and the lines $x = 6$ and $x = 9$ is

Derivative of $x^{x}$ is

The product of the perpendiculars from $(-1, 2)$ to the pair of lines $2x^{2} - 5xy + 2y^{2} + 3x - 3y + 1 = 0$ is

If $\left(\dfrac{1}{2},\,\dfrac{1}{3},\,n\right)$ are the direction cosines of a line, then the value of $n$ is

If $(3 - x) \equiv (2x - 5) \pmod{4}$, then one of the values of $x$ is

If $\mathbf{a}= -\hat{i} + 2\hat{j} - \hat{k}$, $\mathbf{b} = \hat{i} + \hat{j} - 3\hat{k}$ and $\mathbf{c} = -4\hat{i} - \hat{k}$, then $\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) + (\mathbf{a} \cdot \mathbf{b})\mathbf{c}$ is

The negation of the compound proposition $p \vee (\neg p \vee q)$ is

The value of $\begin{vmatrix} a & a+b & a+2b \\ a+2b & a & a+b \\ a+b & a+2b & a \end{vmatrix}$ is equal to

The statement $P(n) = 9^{n} - 8^{n}$, when divided by 8, always leaves the remainder

The sum to $n$ terms of the series $\dfrac{1}{2} + \dfrac{3}{4} + \dfrac{7}{8} + \dfrac{15}{16} + \cdots$ is}

If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi$, then $x + y + z$ is

In the group $G = \{0,1,2,3,4\}$ under $\times_5$, the inverse of $(2 \times_5 2^{-1})$ is}

Every group of order 7 is

The coefficient of $x^{-9}$ in the expansion of $\left(\dfrac{x^{2}}{2} - \dfrac{2}{x}\right)^{9}$ is}

A parallelogram is constructed on the vectors $\mathbf{a} = 3\alpha - \beta$, $\mathbf{b} = \alpha + 3\beta$. If $|\alpha| = |\beta| = 2$ and the angle between $\alpha$ and $\beta$ is $\dfrac{\pi}{3}$, then the length of a diagonal of the parallelogram is

The minimum value of $x^{2} + \dfrac{1}{1 + x^{2}}$ is at}

Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to

If $P(n): 1 + 3 + 5 + \cdots + (2n-1) = n^2$ is

If uncertainty in position and velocity are equal, then uncertainty in momentum will be

Low spin complexes are generally formed by elements of

The number of amino acids in insulin is