Question

The coefficients of xp and xq in the expression of (1 + x)p + q are
1. Equal
2. Equal with opposite signs
3. Reciprocals of each other
4. None of these

Answer 1

Correct Answer - Option 1 : Equal

Calculation:

The coefficients of xp and xq in the expression of (1 + x)p + q

We know, yp+1 = p + qCp xp and yq + 1 = p + qCq xq

Coefficient of xp = p + qCp = [p + q]!/p!q!

and

Coefficient of xq = p + qCq = [p + q]!/p!q!

∴ Coefficients of xp and xq in the expression of (1 + x)p + q are equal.