Question

The coefficient of $x^5$ in the expansion of

$(1+x^2{)}^5$ $(1+x{)}^4$ is

• A. 30
• B. 60
• C. 40
• D. None of these

Answer 1

The correct option is B

60

We have $(1+x^2{)}^5$$(1+x{)}^4$

= (${}^5{C}_0$ + ${}^5{C}_1$x^2 + ${}^5{C}_2$ x^4 +..........)(${}^4{C}_0$ + ${}^4{C}_1$x + ${}^4{C}_2$x^2 +${}^4{C}_3$x^3 + ${}^4{C}_4$x^4)\)

So coefficient of $x^5$ in [$(1+x^2{)}^5$$(1+x{)}^4$]

= ${}^5{C}_2$.${}^4{C}_1$ +${}^4{C}_3$.${}^5{C}_1$ = 60.