List of top Mathematics Questions

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

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

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

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

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

The circle on focal radii of a parabola as diameter touches

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

The set of points where the function \( f(x) = |x| \) is differentiable, is

If \( f(x) = |x| \sin |x| \), then \( f'(x) \) is equal to

The area bounded by the curve \( y^2 = 2x + 1 \) and the straight line \( x - y - 1 = 0 \) is given by

A circle touches the x-axis and also touches the circle which centre at \( (0, 3) \) and radius 2. The locus of the center of the circle is

One diagonal of a square is along the line \( 8x - 15y = 0 \) and one of its vertices is \( (1, 2) \). Then, the equation of the sides of the square passing through this vertex are

The limit \( \lim_{n \to \infty} \left[ \sec^2 \frac{\pi}{4n} + \sec^2 \frac{2\pi}{4n} + \dots + \sec^2 \frac{n\pi}{4n} \right] \) is equal to

If \( f(x) = |\cos x| \) and \( g(x) = [x] \), then \( g \circ f(x) \) is equal to