List of top Mathematics Questions asked in MET

A person is permitted to select at least one and at most \(n\) coins from a collection of \((2n+1)\) distinct coins. If the total number of ways in which he can select coins is 255, then \(n\) equals

The least positive integer \(n\) for which \(n!<\left(\frac{n+1}{2}\right)^n\) holds is

Sum of the series to \(n\) terms \(5 + 7 + 13 + 31 + 85 + \ldots\) is

The sum of \(n\) terms of the series \(1 + \frac{4}{5} + \frac{7}{5^2} + \frac{10}{5^3} + \dots\) is

The sum to \(n\) terms of the series \(\sum_{r=1}^n \frac{r}{1+r^2+r^4}\) is

The domain and range of \( f(x) = \sin^{-1}(x) \) are:

If \( S = \sum_{n=0}^{\infty} \frac{(\log x)^{2n}}{(2n)!} \), then \( S \) is equal to

Let \( A = \{(x, y) : y = e^x, x \in \mathbb{R} \} \) and \( B = \{(x, y) : y = e^{-x}, x \in \mathbb{R} \} \). Then,

The function \( f(x) = \max\left\{(1 - x), (1 + x), 2\right\}, \, x \in (-\infty, \infty) \) is equivalent to

If \( \frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3} \), then \( a + b \) is equal to

If \( \lim_{x \to \infty} \left( 1 + \frac{a}{x} + \frac{b}{x^2} \right)^{2x} = e^2 \), then

The value of \( f(0) \), so that the function \( f(x) = \frac{2 - (256 - 7x)^{1/8}}{(5x + 3x)^{1/5} - 2} \), \( x \neq 0 \), is continuous everywhere, is given by

If \( \frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3} \), then \( a + b \) is equal to

If \( \frac{e^x + 2}{(e^x - 1)(2e^x - 3)} = -\frac{3}{e^x - 1} + \frac{B}{2e^x - 3} \), then \( B \) is equal to

Negation of “Ram is in Class X or Rashmi is in Class XII” is

The solution of the differential equation \( \frac{dy}{dx} - \sin x \sin y = 0 \) is

If \( \log_3 2 \), \( \log_3 (2^x - 5) \), and \( \log_3 \left( \frac{2^x - 7}{2} \right) \) are in AP, then \( x \) is equal to

If the roots of the cubic equation \( ax^3 + bx^2 + cx + d = 0 \) are in GP, then

The inverse of the proportion \( (p \wedge q) \Rightarrow r \) is

The least remainder when \( 17^{30} \) is divided by 5, is

In the group \( G = \{ 1, 2, 3, 4, \times_5 \} \), the solution of \( 2^{-1} \times (3 \times 5^x) = 4 \) is

The circle on focal radii of a parabola as diameter touches

\( \frac{\sqrt{3}}{6} + \sqrt{3} + \frac{\sqrt{6}}{3 + \sqrt{2}} \) is equal to

The diameter of \( 16x^2 - 9y^2 = 144 \) which is conjugate to \( x = 2y \) is

The equation of the ellipse whose axes are parallel to the coordinate axes having its centre at the point \( (2, -3) \) and focus at \( (3, -3) \) and one vertex at \( (4, -3) \) is