List of top Questions asked in MET

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

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

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

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

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

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

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

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

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

$\int_0^{2a} \frac{f(x)}{f(x)+f(2a-x)} dx$ is equal to

$\int \frac{\tan x}{\sin x \cos x} dx$ is equal to

The equation of the tangent to the curve $(1+x^2)y = 2 - x$, where it crosses the x-axis, is

$\lim_{x\to 0} \frac{1-\cos mx}{1-\cos nx}$ is equal to

If $\vec{a}, \vec{b}, \vec{c}$ are any three mutually perpendicular vectors of equal magnitude a, then $|\vec{a} + \vec{b} + \vec{c}|$

For what values of n is the graph $K_n$ Eulerian?

When $5^{20}$ is divided by 7, the remainder is

If $a * b$ denote the bigger among a and b and $a \cdot b = a + b + 3(a*b)$, then $4 \cdot 7$ is equal to

In a tree on a vertices there is exactly one vertex with degree 2 and remaining vertices are of degree either 1 or 3. Then the number of pendant vertices is

$\frac{1}{\log_{10} 25} + \frac{1}{\log_{10} 4} + \frac{1}{\log_{10} 10} + \frac{1}{\log_{10} 2} + \frac{1}{\log_{10} 5}$ is equal to