If \(y = \frac{1+x}{1-x}\), find \(\frac{dy}{dx}\).

Evaluate \(\int_{-1}^{0} (x+1)(x-2) \mathrm{d}x\)

Simplify \(\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}}\)

There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys

The 3rd and 7th term of a Geometric Progression (GP) are 81 and 16. Find the 5th term.