Question

If ${}^n{C}_0$ + 3${}^n{C}_1$ + $3^2$${}^n{C}_2$ + .................$3^n$${}^n{C}_n$ = $a^n$, then a =

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is B

4

$(1+x{)}^n$ = ${}^n{C}_0$ + ${}^n{C}_1$x + ${}^n{C}_2$$x^2$ - .....................${}^n{C}_n$$x^n$

If we put x = 3, we get the required expression

⇒ $(1+3{)}^n$ = ${}^n{C}_0$ + ${}^n{C}_1$3 + ${}^n{C}_2$$3^2$............${}^n{C}_n$$3^n$

= $4^n$

⇒ a = 4