$\begin{array}{1 1}(A)\;\large\frac{n+1}{2}\\(B)\;\large\frac{n+2}{2}\\(C)\;(\large\frac{n+1}{2})(\large\frac{n+2}{2})\\(D)\;\text{None of these}\end{array} $

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- $(x+a)^n=nC_0x^n a^0+nC_1x^{n-1}a^1+nC_2 x^{n-2} a^2+nC_nx^0 a^n$

No. of terms in $(x+y+z)^n$

$\Rightarrow [x+(y+z)]^n$

$\Rightarrow [x+(y+z)]^n=nC_0x^n (y+z)^0+nC_1 x^{n-1}(y+z)^1+nC_2x^{n-2}(y+z)^2+.....nC_n x^0(y+z)^n$

$\therefore$ No. of terms in $(x+y+z)^n$

$\Rightarrow \large\frac{n+1}{2}[\frac{n+2}{2}]$

$\Rightarrow (\large\frac{n+1}{2})(\frac{n+2}{2})$

Hence (C) is the correct answer.

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