Question

Number of irrational terms in the binomial expansion of $(3^{1/5}+7^{1/3}{)}^{100}$ is

• A. $94$
• B. $88$
• C. $93$
• D. $95$

Answer 1

The correct option is A $94$

As $n=100$ hence there are $101$ terms

The genral term for expansion is given as

$T_{r+1}$=${}^{100}{C}_r$.$3^{\frac{100-r}{5}}$.$7^{\frac{r}{3}}$

So,we need to find such values of r for which $\frac{100-r}{5}$ and $\frac{r}{3}$ is a natural number.

For such value we find value of r i.e $r=0,15,30,45,60,75,90$

hence there are 7 values for which it is rational .So there are $101-7=94$ irrational terms.