List of top Mathematics Questions

The number of solutions of the equation $\sin \, 2x + 2 \, \sin \, x - \cos \, x - 1 = 0$ in the range $0 \leq x \leq 2 \pi$ is

If $\cos^{-1} \frac{3}{5} + \cos^{-1} \frac{12}{13} = \cos^{-1} k$, then the value of $k$ is

If $\cos \, 3x \, \cos \, 2x \, \cos \, x = \frac{1}{4} $ and $0 < x < \frac{\pi}{4}$, then the value of $x$ is

If $(1 + \tan \, 1^{\circ})(1 + \tan \, 2^{\circ}) ...... (1 + \tan \, 45^{\circ}) = 2^n$, then n is

The interval in which the function $f\left(x\right) = \frac{4x^{2}+1}{x}$ is decreasing is :

If the parabola $y^2 = 4ax$ passes through the point $(1, -2)$, then the tangent at this point is

If $(27)^{999}$ is divided by $7$, then the remainder is :

The value of $(^{21}C_{1} - ^{10}C_{1}) + (^{21}C_{2} - ^{10}C_{2}) + (^{21}C_{3} - ^{10}C_{3}) +(^{21}C_{4} - ^{10}C_{4}) +....+(^{21}C_{10} - ^{10}C_{10})$ is :

If matrix \( A = \begin{pmatrix} 3 & 2 & 4 \\1 & 2 & -1 \end{pmatrix} \) and

The volume \( V \) and depth \( x \) of water in a vessel are connected by the relation \[ V = 5x - \frac{x^2}{6} \] and the volume of water is increasing, at the rate of 5 cm\(^3\)/sec, when \( x = 2 \) cm. The rate at which the depth of water is increasing is

The set of points of discontinuity of the function \[ f(x) = \sin (2 \sin x) \sin^2 x \] is given by

If vectors \( \mathbf{i} + \mathbf{j} + \mathbf{k} \) and \( \mathbf{i} + \mathbf{j} + \mathbf{k} \) are coplanar, then find

The angle between a pair of tangents drawn from a point \( T \) to the curve \[ x^2 + y^2 + 4x - 6y - 9 = 3x + 1 \] is

The distance of the point \( (1, -2, 3) \) from the plane \( x - y + z = 5 \) measured parallel to the line \[ \frac{x}{2} = \frac{y}{3} = \frac{z - 1}{6} \] is

The conditional \( (P \land Q) \Rightarrow P \) is

If \( f(x) = \cos x + 1 \) and \( f'(x) = 2 \cos x \), then \[ \int_0^\frac{\pi}{2} f(x)dx \] is equal to

If the eccentricity of the hyperbola \[ x^2 - y^2 \cos^2 \alpha = 25 \] is \( \sqrt{5} \), then the eccentricity of the ellipse \[ x^2 \cos^2 \alpha + y^2 = 5 \] is equal to:

The rank of the matrix \[ \begin{pmatrix} 1 & 2 & 5 \\ 2 & 4 & 4 \\ 3 & 6 & 6 \end{pmatrix} \] is

The parabola having its focus at (3, 2) and directrix along the y-axis has its vertex at

The tangent lines to the curve \( y^2 = 4ax \) at points where \( x = a \), are

A random variable \( X \) has the probability distribution \[ P(X) = \{ 0.15, 0.23, 0.12, 0.10, 0.20, 0.07, 0.06, 0.08 \} \] For the events \( E = \{ X \text{ is a prime number} \} \) and \( F = \{ X<4 \} \), then \( P(E \cup F) \) is

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

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

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