The total number of irrartional terms in the binomial expansion of ${(7^{1 / 5} - 3^{1 / 10})}^{60}$ is :

48

No worries! We‘ve got your back. Try BYJU‘S free classes today!

49

No worries! We‘ve got your back. Try BYJU‘S free classes today!

54

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

55

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $54$
${(7^{1 / 5} - 3^{1 / 10})}^{60}$
General term : $T_{r + 1} =^{60} C_{r} (- 1)^{r} (7^{1 / 5})^{60 - r} (3^{1 / 10})^{r}$

A term will be rational if its power is a multiple of $LCM (5, 10) = 10$
$∴ r = 0, 10, 20, 30, 40, 50, 60$ for rational terms.
$∴$ No. of irrational terms $= 61 - 7 = 54$

Suggest Corrections

Similar questions

(7^{\frac{1}{5}} - 3^{\frac{1}{10}})^{60}

(3^{1 / 5} + 7^{1 / 3})^{100}

{(3^{1 / 5} - \frac{1}{\sqrt[3]{3}})}^{n}

{(\frac{1}{5^{6 / 5}})}^{{log}_{5} 243}

{⎛ ⎜ ⎝ 3^{\frac{1}{4}} + 7^{\frac{1}{6}} ⎞ ⎟ ⎠}^{144}

{(1 + 3^{1 / 3} + 7^{1 / 2})}^{10}

Join BYJU'S Learning Program