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  4. The number of zero terms in the expansion of (1+3 √2 x)9+(1-3 √2 x)9 is

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

Binomial Theorem

Solution:

Given expression
$=2\left[1+{ }^{9} C_{2}(3 \sqrt{2} x)^{2}+{ }^{9}\right. C_{4}(3 \sqrt{2} x)^{4}
\left.+{ }^{9} C_{6}(3 \sqrt{2} x)^{6}+{ }^{9} C_{8}(3 \sqrt{2} x)^{8}\right]$
$\therefore $the number of non-zero terms is $5$