List of top Mathematics Questions

Let $y^{2}=8x$ be the equation of a parabola. Which one of the following is an arbitrary point on the parabola?

If two diameters of a circle are along the lines $2x-3y=5$ and $3x-4y=7$, then the centre is at

Let $ax+by+c=0$ be the equation of a straight line such that $3a+2b+4c=0$. Which one of the following points lies on the line?

Two sides of a parallelogram are along the lines $x+y=5$ and $x-y=-5.$ If the diagonals of the parallelogram intersect at (3, 6) then one of its vertices is at

If the distance of the line $4x-3y+k=0$ from the point (1, 2) is 5 units, then the values of k are

If $\tan^{-1}x = \tan^{-1}(3) - \frac{\pi}{4}$, then $x$ is equal to:

If $\sin^{-1}\left(\frac{x}{1+x}\right) = \frac{\pi}{2} - \cos^{-1}\left(\frac{1}{2}\right)$, then $x$ is equal to:

$\frac{(2 \sin \alpha)(1 + \sin \alpha)}{(1 + \sin \alpha + \cos \alpha)(1 + \sin \alpha - \cos \alpha)} =$

$\frac{\cos 75^{\circ} - \cos 15^{\circ}}{\cos 75^{\circ} + \cos 15^{\circ}} =$

$2^2 \sin(\frac{x}{2^2}) \cos(\frac{x}{2}) \cos(\frac{x}{2^2}) =$

If $\sin \theta = \frac{1}{5}$ and the angle $\theta$ is in the second quadrant, then $\sec \theta$ is equal to:

$\sin 15^{\circ} \sin 45^{\circ} \sin 75^{\circ} =$

Let $x$ be a real number such that $\frac{3(x+3)}{7} \le \frac{6(x-1)}{5}$. Then the solution set of the inequality is:

Let $x$ be a real number such that $7x+4 < 9x+8$. Then the solution set of the inequality is:

$\sec^{2}x + \csc^{2}x - \sec^{2}x \csc^{2}x =$

Let $A=\begin{pmatrix}1 & 3 & 5 \\ -6 & 8 & 3 \\ -4 & 6 & 5\end{pmatrix}$ and $P=\frac{1}{2}(A + A^T)$. Then:

Let $P=\begin{pmatrix}1 & 1 & 1 \\ 0 & 2 & 2 \\ 0 & 0 & 3\end{pmatrix}$ and $Q=\begin{pmatrix}2 & 1 & \frac{2}{3} \\ 0 & 4 & \frac{4}{3} \\ 0 & 0 & 6\end{pmatrix}$. Then $\det(QPQ^{-1})$ is equal to:

Let $B$ be a matrix of order $3 \times 2$ and $C$ be a matrix of order $3 \times 3$. If $A$ is a matrix such that $BA = C$, then the order of $A$ is

The constant term in $\left(\frac{\sqrt{x}}{2} + \frac{1}{3x^2}\right)^{10}$ is:

${}^{21}C_1 + {}^{21}C_2 + \dots + {}^{21}C_{10} =$

The coefficient of $x^{10}$ in $(1-x^2)(1-x^3)^9$ is:

$1 + {}^{100}C_1 + {}^{100}C_2 + \dots + {}^{100}C_{99} + 1 =$

25 distinct objects are divided into 5 groups and each group consists of exactly 5 objects. Then the number of ways of forming such groups, is

Let $G_1, G_2, G_3$ be geometric means between $l$ and $n$, where $l$ and $n$ are positive real numbers. Then the common ratio is

The sum of first $n$ terms of a G.P. is 1023. If the first term is 1 and the common ratio is 2, then the value of $n$ is