List of top Questions asked in MET- 2017

$\lim_{n \to \infty} \left[ \frac{1}{n+1} + \frac{1}{n+2} + \frac{1}{n+3} + \ldots + \frac{1}{n+6n} \right]$ is

The degree of the differential equation $5\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^3y}{dx^3}\right)^2 = x\left(\frac{d^2y}{dx^2}\right)^5$ is

$\int_{-1/2}^{1/2} \frac{dx}{\sqrt{1-x^2}}$ is equal to

If $\alpha, \beta, \gamma$ are the angles which a half ray makes with the positive direction of the axes, then $\sin^2\alpha + \sin^2\beta + \sin^2\gamma$ is equal to

The middle term of $\left(x - \frac{1}{x}\right)^6$ is

The number of ways in which a team of 11 players can be selected from 22 players including 2 of them and excluding 4 of them is

If $P(n)$ is a statement such that $P(3)$ is true. Assuming $P(k)$ is true $\Rightarrow P(k+1)$ is true for all $k \ge 3$, then $P(n)$ is true

If $\Delta_1 = \begin{vmatrix} x & a & b \\ b & x & a \\ a & b & x \end{vmatrix}$ and $\Delta_2 = \begin{vmatrix} x & b \\ a & x \end{vmatrix}$ are the given determinants, then}

If $\Delta = \begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix} = k(a-b)(b-c)(c-a)$, then $k$ is equal to

If every element of a group G is its own inverse, then G is

If $\log_3 2$, $\log_3 (2^x - 5)$ and $\log_3 \left(2^x - \frac{7}{2}\right)$ are in AP, the value of $x$ is

If $\cos^{-1}x + \cos^{-1}y = 2\pi$, then the value of $\sin^{-1}x + \sin^{-1}y$ is equal to

The line $\frac{x}{a} - \frac{y}{b} = 1$ cuts the x-axis at P. The equation of the line through P perpendicular to the given line is

$\int_0^1 x^{12} (1-x)^{10} dx$ is equal to

If $f(x+y) = f(x) \cdot f(y)$, $f(3) = 3$, $f'(0) = 11$, then $f'(3)$ is equal to

$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n(n+1)}$ is equal to

The coefficient of $x$ in the expansion of $(1+x+x^2+x^3)^{-1}$ is

$(p \land q) \lor (\sim p \land \sim q)$ is

If $4\sin^{-1}x + \cos^{-1}x = \pi$, then $x$ is equal to

$\frac{d}{dx} \left[ \int_0^{x^2} \sin^{-1} \left( \frac{1}{1+t} \right) dt \right]$ is equal to

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

K\(_2\)Cr\(_2\)O\(_7\) on heating with aqueous caustic soda gives

If the roots of $x^2 + ax + 9 = 0$ are complex, then

The first compound of noble gas prepared by Bartlett was

If the projection of $\overrightarrow{PQ}$ on OX, OY, OZ are respectively 12, 3 and 4, then the magnitude of $\overrightarrow{PQ}$ is