List of top Mathematics Questions

Find \( \cos^{-1} \left( \cos \frac{8\pi}{5} \right) \).
What is \( \tan \left( \frac{1}{2} \left( \tan^{-1} x + \tan^{-1} \frac{1}{x} \right) \right) \)?
Find \( \tan^{-1} (-\sqrt{3}) \).
What is \( \cos^{-1} x + \sec^{-1} 1 \)?
If \( n(A) = 4 \) and \( n(B) = 2 \), then \( n(A \times B) \) is?
If \( f: \mathbb{R} \to \mathbb{R} \) such that \( f(x) = 3x - 4 \), then which of the following is \( f^{-1}(x) \)?
If operation 'o' is defined as \( (a \, o \, b) = a^2 + b^2 - ab \), then \( (1 \, o \, 2) \, o \, 3 \) is?
If \( f : A \to B \) is an onto function, then
Let \( A = \{ 1, 2, 3, ..., n \} \), how many bijective functions \( f: A \to A \) can be defined?
\(\int \frac{x-3}{x^2-9} \, dx\)
If the operation 'o' is defined as \( (a \, o \, b) = a^3 + b^3 \), then what is \( 4 \, o \, (1 \, o \, 2) \)?
\(\int_{-1}^1 \sin x \cos^3 x \, dx \)
\(\int_0^1 (x + 2x + 3x^2 + 4x^3) \, dx \)
\(\int_0^1 x^{99} \, dx \)
\(\int \frac{dx}{x \log x} \)
\(\int_1^9 \frac{dx}{\sqrt{x}} \)
\(\int_0^a e^x \, dx \)
\(\int_0^{\frac{\pi}{2}} \sin x \cos x \, dx \)
\(\int_{-1}^{1} \sin^7 x \cos^{13} x \, dx = ? \)
\(\int \frac{4 \tan^{-1} x}{1 + x^2} \, dx \)
\(\int x^2 \, dx \)
\(\int_{0}^{\frac{\pi}{2}} \log (\tan x) \, dx = ? \)
\(\int_0^a \frac{x}{\sqrt{a^2 - x^2}} \, dx \)
\(\int_0^a \frac{dx}{\sqrt{x}} \)
\(\int_0^{\frac{\pi}{2}} \frac{dx}{\sqrt{\sin x + \cos x}} \)