List of top Questions asked in MET- 2017

If the product of roots of the equation $mx^2 + 6x + (2m-1) = 0$ is $-1$, then the value of m is

The equation of the circle circumscribing the triangle formed by the lines $x+y=6$, $2x+y=4$ and $x+2y=5$ is

$\lim_{x\to 0} \frac{\sin x - \sin x}{x^3}$ is

If $C(n,2) : C(n,3) = 2 : 44 : 3$, then n is equal to

If $\omega$ is an imaginary cube root of 1, then $(1+\omega-\omega^2)^5 + (1-\omega+\omega^2)^5$ is equal to

$0.2 + 0.22 + 0.222 + \ldots$ to n terms is equal to

If $f(x) = \frac{\tan(3x)}{x} + \frac{x}{2}$ is continuous at $x = 0$, then $f(0)$ is equal to

If the nth term of the geometric progression, $5, -\frac{5}{2}, \frac{5}{4}, -\frac{5}{8}, \ldots$ is $\frac{5}{1024}$, then the value of n is

If $77 \equiv 88x \pmod{5}$, then x is equal to

The area between $y^2 + 4x - 8 = 0$, the x-axis and the line $x = 1$ is

If the position vectors of A, B, C are respectively $\hat{i} + \hat{j} - \hat{k}$, $2\hat{i} + 3\hat{j} + \hat{k}$ and $2\hat{i} - \hat{k}$, then the projection of $\overrightarrow{AB}$ on $\overrightarrow{BC}$ is equal to

The solution of the equation $(2y-1)dx + (2x-3)dy = 0$ is

Negation of "Paris is in France and London is in England" is

Consider the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the area of the triangle formed by the asymptotes and the tangent drawn to it at $(a,0)$ is

If $x^2 + px + q = 0$ is the quadratic equation whose roots are $a - 2$ and $b - 2$, where $a$ and $b$ are the roots of $x^2 - 3x + 1 = 0$, then

If $P = \begin{bmatrix} 0 & i & i \\ -i & 0 & i \\ -i & -i & 0 \end{bmatrix}$ and $Q = \begin{bmatrix} 0 & 0 & -i \\ 0 & 0 & -i \\ i & i & 0 \end{bmatrix}$, then $PQ$ is equal to

If $x = \sin^{-1}(3t - 4t^3)$ and $y = \cos^{-1}(2t - 1)$, then $\frac{dy}{dx}$ is equal to

The differential equation of the family of lines passing through the origin is

$\int \log_e (a^x + x^a) dx$ is equal to

The locus of the point of intersection of two perpendicular tangents to a circle is called

$\lim_{n \to \infty} \left( \frac{1}{4n^2 - 1} + \frac{1}{4n^2 - 4} + \frac{1}{4n^2 - 9} + \ldots + \frac{1}{4n^2 - n^2} \right)$ is equal to

$\int \frac{dx}{x^2 + 4x + 13}$ is equal to

$\vec{a} = \frac{1}{7}(2\hat{i} + 3\hat{j} + 6\hat{k})$, $\vec{b} = \frac{1}{7}(3\hat{i} - 2\hat{j} + \lambda \hat{k})$. If $\vec{a}$ and $\vec{b}$ are mutually perpendicular, then value of $\lambda$ is

The area bounded by the curve $y = 4x^3 - 3x^2 + 2x + 3$ with x-axis and ordinates corresponding to the minima of y is

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