JEE Main 12 Jan 2019 Evening Question 8

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

[JEE Main Online Paper Held On 12-Jan-2019 Evening]

Options:

A) 55

B) 54

C) 48

D) 49

Show Answer

Answer:

Correct Answer: B

Solution:

  • Given expression is $ {{({7^{1/5}}-{3^{1/10}})}^{60}} $
    General term of this expansion is $ {T _{r+1}}={{(-1)}^{r}}{{,}^{60}}C _{r}{7^{\frac{60-r}{5}}}{3^{\frac{r}{10}}} $
    For rational terms, r = 0, 10, 20, 30, 40, 50, 60
    So, number of rational terms = 7.
    $ \therefore $ Number of irrational terms = $ 61-7=54 $ .