List of top Mathematics Questions

If a polygon has 54 diagonals, find the number of sides of the polygon.

If \( \sin x \cos x = \frac{1}{4} \), then the general solution is:

If $\cot x=\dfrac{5}{12}$ for some $x\in\left(\pi,\dfrac{3\pi}{2}\right)$, then \[ \sin 7x\left(\cos\frac{13x}{2}+\sin\frac{13x}{2}\right) +\cos 7x\left(\cos\frac{13x}{2}-\sin\frac{13x}{2}\right) \] is equal to:

If $A=\{1,2,3,4\}$. A relation from set $A$ to $A$ is defined as $(a,b)\,R\,(c,d)$ such that $2a+3b=3c+4d$. Find the number of elements in the relation.

The differential equation is \[ \frac{dy}{dx}+\frac{y}{x}=0 \] and \(y(1)=2\). Then the value of \(y(3)\) is

A retailer buys a TV from a wholesaler for ₹20,000 and sells it to a consumer at a 10% profit. If the GST rate is 18%, calculate the total tax paid by the retailer to the Government.

\[ \int \frac{dx}{\sqrt{x+1}+\sqrt{x}}= \]

If \( \begin{bmatrix} 1 & 3 \\ 4 & 5 \end{bmatrix} \begin{bmatrix} x \\ 2 \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \end{bmatrix} \), then value of \( x \) is :

The letters of the word ``UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word ``UDAYPUR'' is

If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:

The roots of the equation $\begin{vmatrix} 2 & -2 & 4 \\ -5 & x+2 & -10 \\ -1 & 1 & x+1 \end{vmatrix} = 0$, are

Let $A = \begin{bmatrix} 2 & x \\ 3 & 1 \end{bmatrix}, B = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$ and $C = \begin{bmatrix} 3x+2 & 10 \\ 14-x & 10 \end{bmatrix}$. If $B^T A^T = C$, then the value of $x$ is equal to

A system of equations is given in the matrix form as $\begin{bmatrix} \alpha & 2 & 3 \\ 2 & 3 & -\alpha \\ 3 & 5 & \alpha+1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \\ 5 \end{bmatrix}$ where $\alpha$ is an integer. If the system of equations does not have a unique solution, then the value of $\alpha$ is equal to

The minimum of the following linear programming problem occurs at:
Minimize $C = 7x + 10y$
subject to $x + y \geq 3$, $x + 2y \geq 4$, $x, y \geq 0$

The integrating factor of the differential equation $2dy = (y + \cos x) dx$ is

The general solution of the differential equation $x^3 \frac{dy}{dx} + 3x^2 y = \cos x$ is

The value of the integral $\int_{0}^{\pi / 2} \sqrt{\cos x \sin 2x} dx$ is equal to

A curve with equation $y = x^3 - 8x^2 + 16x$ meets the $x$-axis at the origin $O$ and at a point $A$. Then the area of the region, bounded by the curve and the straight-line segment $OA$, is

Let $f(x) = \frac{1}{20}(x - 5)^2, x \in \mathbb{R}$. If $\int_{-5}^{5} f(x) dx = \int_5^{a} f(x) dx$, where $a > 5$ is a real constant, then the value of $a$ is equal to

The value of $\int_{-1}^{1} \frac{\log_e(1 + |x|)}{1 + |x|} dx$ is equal to

$\int \frac{\sqrt{\sqrt{x} + 1}}{\sqrt{x}} dx = $}

$\int \frac{x^2 + 6x + 1}{(x+3)^2} dx = $}