In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?

Evaluate: \(\int(2x + 1)^3 dx\)

If α and β are the roots of \(7x2 +12x - 4 = 0\),find the value of \(\frac{αβ}{(α + β)^2}\)

If \(3x^2 + p x + 12 = 0\) has equal roots, find the values of p .

Given that \(\frac{3x + 4}{(x - 2)(x + 3)}≡\frac{P}{x + 3}+\frac{Q}{x - 2}\),find the value of Q.