List of top Mathematics Questions asked in MET

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 $f(x) = \sec x - \cot x$, then $f'\!\left(\dfrac{\pi}{6}\right)$ equals

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

If \( f(x) = \begin{cases} x^3 - 3x^2 - 12x + 1, & -1 \le x \le 2 \\ 37 - 2x, & 2 < x \le 3 \end{cases} \), then

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 difference of the focal distances of any point on the hyperbola is equal to its

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

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

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

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}

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

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

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

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