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Q.
The number of dissimilar terms in the expansion of $\left(1+x+x^3\right)^{10}$ is
Binomial Theorem
Solution:
$\left(1+ x + x ^3\right)^{10}={ }^{10} C _0+{ }^{10} C _1\left( x + x ^3\right)+{ }^{10} C _2 x ^2\left(1+ x ^2\right)^2+{ }^{10} C _3 x ^3\left(1+ x ^2\right)^3+\ldots \ldots \ldots . .{ }^{10} C _9 x ^9\left(1+ x ^2\right)^9+{ }^{10} C _{10} x ^{10}\left(1+ x ^2\right)^{10}$
The expansion does not contain any term of $x^{29}$
$\therefore$ Number of different terms is 30
