Question

 If a, b, c are odd positive integers, then number of integral solutions of a + b + c = 13, is 

(a) 14       ,       (b) 21     , (c) 28   ,     (d) 56

Answer 1

The correct answer is  option b) 21 

explaination ::

Let a = 2k + 1, b = 2l + 1, c = 2m + 1

where k, l, m are whole number

a + b + c = 13

2k + 1 + 2l + 1 + 2z + 1 = 13

or,         x + y + z = 5

The number of integrals solutions 

${=}^{5+3-1}{C}_{3-1}{=}^7{C}_2$ 

$=\frac{7.6}{1.2}=21$