List of top Questions asked in MET- 2018

The work done by the force $4\hat{i} - 3\hat{j} + 2\hat{k}$ in moving a particle along a straight line from the point $(3, 2, -1)$ to $(2, -1, 4)$ 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 product of the perpendiculars from $(-1, 2)$ to the pair of lines $2x^{2} - 5xy + 2y^{2} + 3x - 3y + 1 = 0$ is

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

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

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

In the group $G = \{0,1,2,3,4\}$ under $\times_5$, the inverse of $(2 \times_5 2^{-1})$ 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 sum to $n$ terms of the series $\dfrac{1}{2} + \dfrac{3}{4} + \dfrac{7}{8} + \dfrac{15}{16} + \cdots$ is}

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

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

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

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

Every group of order 7 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 equation $3^{3x + 4} = 9^{2x - 2},\ x>0$ has the solution

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

An optically active alkene with the M.F. $\mathrm{C}_6\mathrm{H}_{12}$ which upon hydrogenation gives optically inactive alkane is

Low spin complexes are generally formed by elements of

The number of amino acids in insulin is

Molisch test is given by

Degree of dissociation of an acid HCl is $95%$, $0.192\mathrm{g}$ of the acid is present in $0.5\mathrm{L}$ of solution. The pH of the solution is}