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 $ .
