If n is the number of irrational terms in the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The general term in the expansion of $(3^{1/4} + 5^{1/8})^{60}$ is given by $T_{r+1} = {}^{60}C_r (3^{1/4})^{60-r} (5^{1/8})^r = {}^{60}C_r (3)^{(

Vedclass · Accepted Answer

$26$

Vedclass · Answer

(A) The general term in the expansion of $(3^{1/4} + 5^{1/8})^{60}$ is given by $T_{r+1} = {}^{60}C_r (3^{1/4})^{60-r} (5^{1/8})^r = {}^{60}C_r (3)^{(60-r)/4} (5)^{r/8}$.For the term to be rational,the exponents of $3$ and $5$ must be integers.Thus,$r$ must be a multiple of $8$ such that $0 \leq r \leq 60$.The possible values for $r$ are $0, 8, 16, 24, 32, 40, 48, 56$.There are $8$ rational terms.The total number of terms in the expansion is $60 + 1 = 61$.Therefore,the number of irrational terms $n = 61 - 8 = 53$.We need to check divisibility for $(n - 1) = 53 - 1 = 52$.Since $52 = 26 	imes 2$,$(n - 1)$ is divisible by $26$.

If $n$ is the number of irrational terms in the expansion of $(3^{1/4} + 5^{1/8})^{60}$,then $(n - 1)$ is divisible by

Similar Questions

The total number of terms in the expansion of $(x + a)^{100} + (x - a)^{100}$ after simplification will be

In the binomial expansion of $(1+x)^{2k}$,if its middle term is the only numerically greatest term,then $x$ lies in the interval

In the expansion of $(1 + x)^{43}$,if the coefficients of the $(2r + 1)^{th}$ and the $(r + 2)^{th}$ terms are equal,the value of $r$ is:

Write the general term in the expansion of $(x^{2}-y)^{6}$.

The coefficient of $\frac{1}{x}$ in the expansion of $(1 + x)^n (1 + \frac{1}{x})^n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module