If the ( r + 1 ) t h term in the expansion of ( 3 √ a √ b + √ b 3 √ a ) 21 has the same power of a and b, then value of r is Options: A . &nbsp 9 B . &nbsp 10 C . &nbsp 8 D . &nbsp 6

Answer: Option A : A We have T r + 1 = 21 C r ( 3 √ a √ b ) 21 − r ( √ b 3 √ a ) r = 21 C r a 7 − ( r 2 ) b 2 3 r − ( 7 2 ) Since the powers of a and b are the same, therefore 7 - r 2 = 2 3 r - 7 2 ⇒ r = 9

If the (r+1)th term in the expansion of (3√a√b+√b3√

Discussion Forum : Binomial Theorem

Question -

If the $(r + 1)^{t h}$ term in the expansion of ${(\sqrt[3]{\frac{a}{\sqrt{b}}} + \sqrt{\frac{b}{\sqrt[3]{a}}})}^{21}$ has the same power of a and b, then value of r is

Options:

A . 9

B . 10

C . 8

D . 6

Answer: Option A
:
A

We have $T_{r + 1}$ = $^{21} C_{r} {(\sqrt[3]{\frac{a}{\sqrt{b}}})}^{21 - r} {(\sqrt{\frac{b}{\sqrt[3]{a}}})}^{r}$

= $^{21} C_{r} a^{7 - (\frac{r}{2})} b^{\frac{2}{3} r - (\frac{7}{2})}$

Since the powers of a and b are the same,

therefore

7 - $\frac{r}{2}$ = $\frac{2}{3}$ r - $\frac{7}{2}$ ⇒ r = 9

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