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 . &nbsp9 B . &nbsp10 C . &nbsp8 D . &nbsp6

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√a

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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