Question

The number of non-zero terms in the expansion of ${(1+3\sqrt{2}x)}^9+{(1-3\sqrt{2}x)}^9$ is

• A. 9
• B. 0
• C. 5
• D. 10

Answer 1

The correct option is C 5

In the expansion of ${(1+3\sqrt{2}x)}^9+{(1-3\sqrt{2}x)}^9$

$2nd,4th,6th,8th$ and $10th$ terms get cancelled.

$\therefore$ Number of non-zero terms in

$2[{}^9{C}_0{+}^9{C}_2{\left(3\sqrt{2}x\right)}^2+...{+}^9{C}_8{\left(3\sqrt{2}x\right)}^8]$ is $5$