List of top Mathematics Questions

$\int \frac{1}{x \left(6(\log x)^2 + 7\log x + 2\right)} \, dx =$

If $f(x) = \begin{vmatrix} x - 3 & 2x^2 - 18 & 2x^3 - 81 \\ x - 5 & 2x^2 - 50 & 4x^2 - 500 \\ 1 & 2 & 3 \end{vmatrix}$, then $f(1) \cdot f(3) \cdot f(5) + f(5) \cdot f(1)$ is:

Corner points of the feasible region for an LPP are $(0, 2), (3, 0), (6, 0), (6, 8)$ and $(0, 5)$. Let $z = 4x + 6y$ be the objective function. The minimum value of $z$ occurs at:

$\lim_{x \to \frac{\pi}{4}} \frac{\sqrt{2}\cos x - 1}{\cot x - 1}$ is equal to:

$\lim_{n \to \infty} \left(\frac{n}{n^2 + 1^2} + \frac{n}{n^2 + 2^2} + \dots + \frac{n}{n^2 + 3^2 + \dots + \frac{1}{5n}} \right) =$

If in two circles, arcs of the same length subtend angles $30^\circ$ and $78^\circ$ at the centre, then the ratio of their radii is:

The function $f(x) = |\cos x|$ is:

Let $f : \mathbb{R} \to \mathbb{R}$ be given by $f(x) = \tan x$. Then $f^{-1}(1)$ is:

If $2\sin^{-1} x - 3\cos^{-1} x = 4x$, $x \in [-1, 1]$, then $2\sin^{-1} x + 3\cos^{-1} x$ is equal to:

If $\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = 3\pi$, then $x(y + z) + y(z + x) + z(x + y)$ equals to:

If $A$ is a square matrix such that $A^2 = A$, then $(I + A)^3$ is equal to:

$\int_{-\pi}^\pi (1 - x^2)\sin x \cos^2 x \, dx =$

The distance between the two planes $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is:

If a random variable $X$ follows the binomial distribution with parameters $n = 5$, $p$, and $P(X = 2) = 9P(X = 3)$, then $p$ is equal to:

$\int \frac{\sin x}{3 + 4\cos^2 x} \, dx =$

Let $(g \circ f)(x) = \sin x$ and $(f \circ g)(x) = \left(\sin \sqrt{x}\right)^2$. Then:

The real value of $\alpha$ for which $\frac{1 - i \sin \alpha}{1 + 2i \sin \alpha}$ is purely real is:

If $[x]^2 - 5[x] + 6 = 0$, where $[x]$ denotes the greatest integer function, then:

Which one of the following observations is correct for the features of the logarithm function to any base $b > 1$?

The maximum volume of the right circular cone with slant height $6$ units is:

The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is $180$ cm, then:

The vectors $\overrightarrow{AB} = 3\hat{i} + 4\hat{k}$ and $\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a $\triangle ABC$. The length of the median through $A$ is:

For the function $f(x) = x^3 - 6x^2 + 12x - 3$, $x = 2$ is:}

The function $x^x$, $x > 0$ is strictly increasing at: