In the expansion of (5(1/6)+2(1/8))100, which of the following hold(s) good?

Question

In the expansion of (5(1/6)+2(1/8))100, which of the following hold(s) good? (A) The number of irrational terms are 97 . (B) The number of rational terms are 5. (C) The binomial coefficient of the term in which exponent of ' 5 ' is 15 is 100 C 90. (D) The term in which the exponent of 2 and 5 will be equal is the 58 text th term from the beginning.

Tardigrade Admin · Accepted Answer

Tr+1= 100 Cr 5(100-/6) 2(r/8) text For (r/8) ∈ Q r=0,8,16,24, ldots ldots ldots ldots . .96 For (100-r/6) to be rational r =16,40,64,88 4 terms are rational (100-r/6)=15 (C) r =10

Q. In the expansion of $(5^{\frac{1}{6}} + 2^{\frac{1}{8}})^{100}$ , which of the following hold(s) good?

The number of irrational terms are 97 .

The number of rational terms are 5.

The binomial coefficient of the term in which exponent of ' 5 ' is 15 is $^{100} C_{90}$ .

The term in which the exponent of 2 and 5 will be equal is the $5 8^{th}$ term from the beginning.

$T_{r + 1} =^{100} C_{r} 5^{\frac{100 -}{6}} 2^{\frac{r}{8}}$
$For \frac{r}{8} \in Q$
$r = 0, 8, 16, 24, \dots\dots\dots\dots ..96$
For $\frac{100 - r}{6}$ to be rational
$r = 16, 40, 64, 88$
4 terms are rational
$\frac{100 - r}{6} = 15$
(C) $r = 10$

Q. In the expansion of (561​+281​)100, which of the following hold(s) good?

The number of irrational terms are 97 .

The number of rational terms are 5.

The binomial coefficient of the term in which exponent of ' 5 ' is 15 is 100C90​.

The term in which the exponent of 2 and 5 will be equal is the 58th term from the beginning.

Tr+1​=100Cr​56100−​28r​ For 8r​∈Q r=0,8,16,24,…………..96 For 6100−r​ to be rational r=16,40,64,88 4 terms are rational 6100−r​=15 (C) r=10

Q. In the expansion of $(5^{\frac{1}{6}} + 2^{\frac{1}{8}})^{100}$ , which of the following hold(s) good?

The binomial coefficient of the term in which exponent of ' 5 ' is 15 is $^{100} C_{90}$ .

The term in which the exponent of 2 and 5 will be equal is the $5 8^{th}$ term from the beginning.

$T_{r + 1} =^{100} C_{r} 5^{\frac{100 -}{6}} 2^{\frac{r}{8}}$
$For \frac{r}{8} \in Q$
$r = 0, 8, 16, 24, \dots\dots\dots\dots ..96$
For $\frac{100 - r}{6}$ to be rational
$r = 16, 40, 64, 88$
4 terms are rational
$\frac{100 - r}{6} = 15$
(C) $r = 10$