List of top Mathematics Questions

The value of \( \tan^{-1} \left( \frac{1}{2} \right) + \tan^{-1} \left( \frac{1}{3} \right) \) is

The line which passes through the origin and intersects the two lines \[ \frac{x - 1}{2} = \frac{y - 3}{4} = \frac{z - 14}{4} \] is

The area bounded by \( f(x) = x^2, 0 \leq x \leq 1 \), and \( g(x) = x + 2, 1 \leq x \leq 2 \) and x-axis is

Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

The condition that the line \( \frac{x}{p} + \frac{y}{q} = 1 \) be normal to the parabola \( y^2 = 4ax \) is

If \( u_n = \int_0^{\frac{\pi}{4}} \tan \theta d\theta \), then \( u_{n+2} \) is:

If \( x = -\frac{7}{3} \), then \( x^4 \) is

A and B are two independent witnesses (i.e., there is no collision between them) in a case. The probability that A will speak the truth is \( x \) and the probability that B will speak the truth is \( y \). A and B agree in a certain statement. The probability that the statement is true is

A and B are events such that \( P(A \cup B) = 3/4 \), \( P(A) = 1/4 \), and \( P(A \cap B) = 2/3 \). Then the probability that \( P(A \cap B) \) is

The difference between greatest and least value of \[ f(x) = 2 \sin x + \sin 2x, \, x \in \left[ 0, \frac{3\pi}{2} \right] \] is

\[ \int \left[ f'(x) \left( g(x) \right)^2 \right] dx \] is equal to:

Let A be the centre of the circle \( x^2 + y^2 - 2x - 4y - 20 = 0 \), and B(1, 7) and D(4, -2) are points on the circle then, if tangents are drawn at B and D, which meet at C, then area of quadrilateral ABCD is

The value of \( x \) obtained from the equation \[ \frac{x + \alpha}{\gamma} = \frac{x + \beta}{\alpha} = \frac{x + \gamma}{\beta} \] will be

The solution of the differential equation \[ \log x \frac{dy}{dx} + x = \sin 2x \] is

The range of the function \[ f(x) = \frac{1}{2 - \cos 3x} \] is

Value of \[ \int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sin x + \cos x} \, dx \]

\[ \lim_{x \to \infty} \frac{x^2}{3x - 3} = ? \]

The area bounded by \( y = |x| \), \( y = 0 \) and \( |x| = \frac{1}{2} \) will be:

If \( \vec{a} \times \vec{b} \) and \( \vec{c} \times \vec{d} \) are perpendicular, then which of the following is always true?

The acceleration of a sphere falling through a liquid is \( (30 - 3y) \, \text{cm/s}^2 \) where \( y \) is speed in cm/s. The maximum possible velocity of the sphere and the time when it is achieved are

A value of \( c \) for which conclusion of Mean Value Theorem holds for the function \( f(x) = \log x \) on the interval [1, 3] is

The function \( f(x) = \sin x - kx - c \), where \( k \) and \( c \) are constants, decreases always when

Negation of the proposition: If we control population growth, we prosper is

The equation \( z^2 + (2 - 3i)z + (2 + 3i) = 4 = 0 \) represents a circle of radius

Equation \( \frac{1}{8} \sin^3 x = \cos 6x \) represents