Question

What is the number of non-zero terms in the expansion of ${(1+2\sqrt{3}x)}^{11}+{(1-2\sqrt{3}x)}^{11}$ (after simplification)

• A. $4$
• B. $5$
• C. $6$
• D. $11$

Answer 1

The correct option is C $6$

Given : $\stackrel{\left(A\right)}{(1+2\sqrt{3}x{)}^{11}}+\stackrel{\left(B\right)}{(1-2\sqrt{3}x{)}^{11}}$

General term of $A$

$Tr+1{=}^{11}{C}_r\left(1{)}^{11-r}\right(2\sqrt{3}x{)}^r$

General term of $B$

$Tr+1{=}^{11}{C}_r\left(1{)}^{11-r}\right(2\sqrt{3}x{)}^r(-1{)}^x$

All the terms, in which ${}^{\prime }r=od{d}^{\prime }$ will cancel out each other, therefore no. of non-zero terms

$\to T_1,T_3,T_5,T_7,T_9,T_{11}$

$Total=6$.