List of top Mathematics Questions

If \( P \) is a non-singular matrix of order \( 5 \times 5 \) and the sum of the elements of each row is 1, then the sum of the elements of each row in \( P^{-1} \) is:
If \( f(x) = \int_{0}^{\sin^2 x} \sin^{-1} \sqrt{t} \, dt \) and \( g(x) = \int_{0}^{\cos^2 x} \sin^{-1} \sqrt{t} \, dt \), then the value of \( f(x) + g(x) \) is:
The population \( p(t) \) at time \( t \) of a certain mouse species follows the differential equation \( \frac{dp(t)}{dt} = 0.5p(t) - 450 \). If \( p(0) = 850 \), then the time at which the population becomes zero is:
The solution set of the equation \( \tan(\pi \tan x) = \cot(\pi \cot x) \), \( x \in \left(0, \frac{\pi}{2}\right) \), is:
If the equation \( \sin^4 x - (p + 2)\sin^2 x - (p + 3) = 0 \) has a solution, then \( p \) must lie in the interval:
Let \( f(x) = x^2 \), \( x \in [-1, 1] \). Then which of the following are correct?
Three numbers are chosen at random without replacement from \( \{1, 2, \dots, 10\} \). The probability that the minimum of the chosen numbers is 3 or their maximum is 7, is:
The value of \( \int_{-100}^{100} \frac{x + x^3 + x^5}{1 + x^2 + x^4 + x^6} dx \) is:
If \( f(x) \) and \( g(x) \) are two polynomials such that \( \phi(x) = f(x^3) + xg(x^3) \) is divisible by \( x^2 + x + 1 \), then:
Let \( f(x) = |x - \alpha| + |x - \beta| \), where \( \alpha, \beta \) are the roots of the equation \( x^2 - 3x + 2 = 0 \). Then the number of points in \( [\alpha, \beta] \) at which \( f \) is not differentiable is:
Let \( x - y = 0 \) and \( x + y = 1 \) be two perpendicular diameters of a circle of radius \( R \). The circle will pass through the origin if \( R \) is equal to:
Let \( a_n \) denote the term independent of \( x \) in the expansion of \( \left[ x + \frac{\sin(1/n)}{x^2} \right]^{3n} \). Then \( \lim_{n \to \infty} \frac{(a_n) n!}{3^n n^n} \) equals:
If \( f(x) = \frac{3x - 4}{2x - 3} \), then \( f(f(f(x))) \) will be:
Let \( u + v + w = 3 \), \( u, v, w \in \mathbb{R} \) and \( f(x) = ux^2 + vx + w \) be such that \( f(x + y) = f(x) + f(y) + xy \) for all \( x, y \in \mathbb{R} \). Then \( f(1) \) is equal to:
The maximum number of common normals of \( y^2 = 4ax \) and \( x^2 = 4by \) is equal to:
If \( |z_1| = |z_2| = |z_3| = 1 \) and \( z_1 + z_2 + z_3 = 0 \), then the area of the triangle whose vertices are \( z_1, z_2, z_3 \) is:
The probability that a non-leap year selected at random will have 53 Sundays or 53 Saturdays is:
The number of solutions of \( \sin^{-1} x + \sin^{-1} (1 - x) = \cos^{-1} x \) is:
The number of common tangents to the circles \( x^2 + y^2 - 4x - 6y - 12 = 0 \) and \( x^2 + y^2 + 6x + 18y + 26 = 0 \) is:
If \( \cos(\theta + \phi) = \frac{3}{5} \) and \( \sin(\theta - \phi) = \frac{5}{13} \), \( 0<\theta, \phi<\frac{\pi}{4} \), then \( \cot(2\theta) \) has the value:
Let \( f(x) \) be continuous on \( [0, 5] \) and differentiable in \( (0, 5) \). If \( f(0) = 0 \) and \( |f'(x)| \leq \frac{1}{5} \) for all \( x \) in \( (0, 5) \), then for all \( x \) in \( [0, 5] \):
Let \( f(x) = \max\{x + |x|, x - |x|, x - [x]\} \), where \( [x] \) stands for the greatest integer not greater than \( x \). Then \( \int_{-3}^{3} f(x) \, dx \) has the value:
If the sum of \( n \) terms of an A.P. is \( 3n^2 + 5n \) and its \( m^{th} \) term is \( 164 \), then the value of \( m \) is:
The value of the integral \( \int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9 - x} + \sqrt{x}} \, dx \) is:
The value of the expression \( {}^{47} C_4 + \sum_{j=1}^{5} {}^{52-j} C_3 \) is: