Question

Number of rational terms in expansion of $(\sqrt{2},\sqrt{3},\sqrt[3]{35}{)}^{20}$ is a two digit number $ab$, then $a+b=$

• A. $3$
• B. $6$
• C. $8$
• D. $9$

Answer 1

The correct option is C $8$

$(\sqrt{2}+\sqrt{3}+\sqrt[3]{35}{)}^{20}$

In General term of Expansion

$T_n=\frac{20!}{\alpha !\beta !\gamma !}$

$\left(2{)}^{\alpha /2}\right(3{)}^{\beta /2}(5{)}^{\gamma /3}.$

$\alpha +\beta +\gamma =20$

for Rational term $\beta /2.$ & $\gamma /3$ should be Integer

$2^{\alpha /2}{3}^{\beta /2}{5}^{\gamma /3}$

$\beta 0246$ $\beta +\gamma ⩽20$

$\gamma 0000$

$333,3$

$6666$

$9999$

$12121212$

$151515$

$1818$

$20$

Total No. of rational term $26$

Digit no ab

$a=2$

$b=6$

$a+b=8.$