Explanation

(b)
We have, $\left( 1 + x^{2} \right)^{5}(1 + x)^{4}$
$= \left( \ ^{5}C_{0} + \ ^{5}C_{1}x^{2} + \ ^{5}C_{2}x^{4} + ... \right)(\ ^{4}C_{0} + \ ^{4}C_{1}x + {\ ^{4}C_{2}x}^{2} + \ ^{4}C_{3}x^{3} + \ ^{4}C_{4}x^{4})$
The coefficient of $x^{5}$ in $\lbrack\left( 1 + x^{2} \right)^{5}(1 + x)^{4}\rbrack$
$= {\ ^{5}C_{2}.\ }^{4}C_{1} + \ ^{4}C_{3}.\ ^{5}C_{1} = 10.4 + 4.5 = 60$