List of top Mathematics Questions

The maximum value of \( f(x) = \frac{x}{1 + 4x + x^2} \) is
The set of all \( x \) for which \( \sin x \leq x \) is:
The normal to the curve y = f(x) at the points (3, 4) makes an angle \( \frac{3\pi}{4} \) with positive x-axis then \(f'(3) = \)
\( \int \frac{dx}{(1+\sqrt{x})^{2022}} = \)
Evaluate the integral \( \int \frac{1 - k \cos^2 x}{\sin^k x \cos^2 x} dx \).
The function \( f(x) = 2x^3 - 9ax^2 + 12a^2x + 1 \ (a>0) \) attains its maximum and minimum at \( p \) and \( q \) respectively and \( p^2 = q \). Then the value of \( a \) is:
If \( f(x) = \max(\sin x, \cos x) \) and \( g(x) = \min(\sin x, \cos x) \), then \[ \int_0^{\pi/2} f(x) dx + \int_0^{\pi/2} g(x) dx = \]
Assertion (A) : \( f(x)=|x| \) is differentiable at \( x=a \neq 0 \) and continuous but not differentiable at \( x=0 \) Reason (R) : If a function is differentiable at a point then it is continuous at that point. But converse is not true. .
Let \( \alpha, \beta \) be real numbers such that \( \pi<(\alpha - \beta)<3\pi \). If: \[ \sin \alpha + \sin \beta = \frac{-21}{65}, \quad \cos \alpha + \cos \beta = \frac{-2}{65} \] then the value of \( \cos\left( \frac{\beta - \alpha}{2} \right) \) is:
If \( \cos\theta - \sin\theta = \sqrt{5} \sin\theta \), then the value of \( \cos\theta + 4\sin\theta \) is:
Evaluate: \( 1 + \cot^2 30^\circ - \sec^2 45^\circ \)
A true statement among the following identities is:
Simplify the expression: \[ \sec^2 x + 5 \tan x + 5 \]
The value of $\tan\left(\dfrac{7\pi}{8}\right)$ is
The value of $\dfrac{\sin\theta + \sin3\theta}{\cos\theta + \cos3\theta}$ is:
Simplify: $\dfrac{\cos\theta}{1 - \tan\theta} + \dfrac{\sin\theta}{1 - \cot\theta}$
If $A + B + C = \pi$, $\cos B = \cos A \cos C$, then $\tan A \tan C =$
Simplify: \( \sin(x + y) \sec x \sec y = \)
Evaluate: \( \int_{0}^{4} \frac{x + 2}{\sqrt{4x - x^2}}\, dx \)
Given: $$ \int \frac{3x + 4}{x^3 - 2x + 4} \, dx = \log f(x) + C $$ Then: $$ f(3) = ? $$
If $$ \int_1^3 x^n \sqrt{x^2 - 1} \, dx = 6 $$ Then find the value of $ n $.
Evaluate the integral \( \int \frac{x^2 - 2}{x^3 \sqrt{x^2 - 1}} \, dx \)
Evaluate \( \int \frac{dx}{1 + a \cos x} \), given \( a>|\sec \theta| \)
Let \( f(x) = \int \frac{e^{3x}}{4 + 8e^{2x} + e^{4x}} \, dx \), and \( g(x) = \int \frac{2\, dx}{e^{3x} + 8e^x + 4e^{-x}} \), then \( f(x) - g(x) = \) ?
Let $$ I_n = \int (\cos^n x + \sin^n x) \, dx,\quad \text{and} \quad \frac{n - 1}{n} I_{n - 2} = \frac{\sin x \cos x}{n} f(x) $$ Then, what is $ f(x) $?