List of top Mathematics Questions

The maximum value of $\sin(x + \pi/6) + \cos(x + \pi/6)$ is attained at $x =$

The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is

The mean and standard deviation of 100 items are 50 and 4, respectively then the sum of all squares of the items is

Probability of occurrence of an event A is 1/2 and that of B is 3/10. If A and B are mutually exclusive, then the probability of occurrence of neither A nor B is

Let R be the relation in the set N given by $R = \{(a, b) : a = b - 2, b>6\}$. Which of the following is the correct answer?

$f(x) = (x + 1)^2$ for $x \ge 1$. $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y = x$, then $g(x)$ is

If $\sin^{-1} x + \sin^{-1} y = \pi/2$, then $x^2$ is equal to

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 \(|adj(A)|\).

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

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

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

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

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

$\int\frac{x\cos x-\sin x}{x^{2}}dx$ 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.

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

$\int x(1+2\log x)dx$ 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 function $f(x)=2x^{3}-15x^{2}+36x-24$ is strictly decreasing in the interval is

$\int\frac{\tan x+\cot x}{1+\tan^{2}x}dx$ is equal to