List of top Mathematics Questions

If operation 'o' is defined as \( (a \, o \, b) = a^2 + b^2 - ab \), then \( (1 \, o \, 2) \, o \, 3 \) is?
If \( n(A) = 4 \) and \( n(B) = 2 \), then \( n(A \times B) \) is?
\(\int \frac{x-3}{x^2-9} \, dx\)
\(\int_0^1 x^{99} \, dx \)
\(\int_0^1 (x + 2x + 3x^2 + 4x^3) \, dx \)
\(\int_{-1}^1 \sin x \cos^3 x \, dx \)
\(\int_1^9 \frac{dx}{\sqrt{x}} \)
\(\int \frac{dx}{x \log x} \)
\(\int_0^a e^x \, dx \)
\(\int_0^{\frac{\pi}{2}} \sin x \cos x \, dx \)
\(\int_0^a \frac{dx}{\sqrt{x}} \)
\(\int x^2 \, dx \)
\(\int_0^a \frac{x}{\sqrt{a^2 - x^2}} \, dx \)
\(\int_{-1}^{1} \sin^7 x \cos^{13} x \, dx = ? \)
\(\int_{0}^{\frac{\pi}{2}} \log (\tan x) \, dx = ? \)
\(\int \frac{4 \tan^{-1} x}{1 + x^2} \, dx \)
\(\int_0^{\frac{\pi}{2}} \frac{dx}{\sqrt{\sin x + \cos x}} \)
\(\int \tan \left( \tan^{-1} x \right) \, dx = ? \)
\(\int \frac{\cos 2x}{\cos x + \sin x} dx \)
\(\frac{d}{dx} \left( \cos(\pi x + \sin \pi x) \right) \)
\(\int \log x^2 \, dx \)
\(\int (\sin 3x + 4 \sin^3 x) \, dx \)
\(\int \frac{dx}{e^{-x}} \)
\(\frac{d}{dx} \left[ \log x^2 + \log a^2 \right] \)
\(\frac{d}{dx} \left[ e^{x^2} \right] \)