List of top Mathematics Questions

Evaluate \( \displaystyle \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx \).

If \(A\) is a square matrix of order \(3\) and \(|A| = 5\), find \(|adj(A)|\).

Evaluate the integral \[ \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx. \]

Find \(x\): \(2x + 3 = 7x - 8\).

Find \(x\): \(4(x - 2) = 3(x + 5)\).

Given that \(\sqrt{5}\) is an irrational number, prove that \(3 + 2\sqrt{5}\) is also an irrational number.

If \( f(x) = \int_0^x t(\sin x - \sin t)dt \) then :

For any natural number n, \( 5^n \) ends with the digit :

The order and the degree of the differential equation $2\frac{dy}{dx}-3x=\left(2y-x\frac{dy}{dx}\right)^{-3}$ respectively, are

Consider the Linear Programming Problem: Maximize $Z=x+2y$ Subject to $2x+3y\le12, x\ge0, y\ge0$. The optimal value is} \textit{Note: A stray '0.' from the original document has been removed for clarity.

The value of $\int_{0}^{3}x^{2}[x]dx$ is equal to

The value of $\int_{0}^{\frac{\pi}{2}}\frac{\cos^{11}x}{\cos^{11}x+\sin^{11}x}dx$ is equal to} \textit{Note: The original exam paper contained a typographical error ($c\hat{D}$ instead of $dx$). It has been corrected here to permit a valid solution.

The solution of the differential equation $(y+x^{2})dx=xdy, x>0$ is a curve which passes through the point (1,0). The equation of the curve is

$\int\frac{x\cos x-\sin x}{x^{2}}dx$ is equal to

The value of $\int_{-2}^{1}\frac{|x|}{x}dx$ is equal to

The value of $\int_{0}^{\pi}\frac{\sin x}{1+\sin x}dx$ is equal to} \textit{Note: The upper limit in the integral from the original paper contains a typo ($x$ instead of $\pi$). It has been corrected here to yield the valid options provided.

$\int x(1+2\log x)dx$ is equal to

$\int\frac{2+3x}{2\sqrt{1+x}}dx$ is equal to} \textit{Note: The original exam paper contained a typographical error in the denominator ($1+c$ instead of $1+x$). It has been corrected here to match the given solutions.

The distance $s$ in meters travelled by a particle in $t$ seconds is given by $s=e^{t}(4\cos 3t+5\sin 3t)$. Then the velocity of the particle at time $t$ is given by

Let $f(x)=x^{2}-10x+16$, $x\in\mathbb{R}.$ If $f^{\prime}(c)$ is equal to slope of the straight line joining the points (2,0) and (8,0), then the value of $c$ is

The function $f(x)=2x^{3}-15x^{2}+36x-24$ is strictly decreasing in the interval is

$\int e^{-x}(1+(1-x)\log x)dx$ is equal to