Question

The coefficients of ap and aq in the expression of (1 + a)p+q are

(i) Equal

(ii) Equal with opposite signs

(iii) Reciprocals of each other

(iv) None of these

A i Correct Answer Incorrect Answer
B iii Correct Answer Incorrect Answer
C iv Correct Answer Incorrect Answer
D ii Correct Answer Incorrect Answer

Solution

The coefficients of ap and aq in the expression of (1 + a) p+q We know, bp+1 = p+qCp × p and bq+1 = p+qCq × q Coefficient of ap = p+qCp = [p+q]!/p!q! and Coefficient of aq = p+qCq = [p+q]!/p!q! Therefore, coefficients of ap and aq in the expression of (1 + a)p+q are equal.

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