If the r -1th term in the expansion of - a - b - b - a 21 has the same power of a and b- then value of r isA- 10B- 6C- 9D- 8

The correct option is C 9 We have T_r+1 = ^21 C _r ( √(a/√(b)))^21 r(√(b/√(a)))^r = ^21 C _r a^7 ( r/2)b^2/3r ( 7/2) Since the powers of a and b are the same ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Numerically Greatest Term

If the r +1th...

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
9

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

Suggest Corrections

Similar questions

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

In the expansion of ${(3 \sqrt{\frac{a}{b}} + 3 \sqrt{\frac{b}{\sqrt{a}}})}^{21}$ the terms cantaining same powers of a and b is

Q. If an the expansion of

{(1 + x)}^{15}

, the coefficients of

{(2 r + 3)}^{th} and {(r - 1)}^{th}

terms are equal, then the value of r is
(a) 5
(b) 6
(c) 4
(d) 3

Q. Find the term in

{(\sqrt[3]{\frac{a}{\sqrt{b}}} + \sqrt{\frac{b}{\sqrt[3]{a}}})}^{21}

which has the same power of a and b.

Q. If the coefficients of the (n + 1)^th term and the (n + 3)^th term in the expansion of (1 + x)²⁰ are equal, then the value of n is
(a) 10
(b) 8
(c) 9
(d) none of these

Join BYJU'S Learning Program

If the (r+1)th term in the expansion of (3√a√b+√b3√a)21 has the same power of a and b, then value of r is

The correct option is A 9 We have Tr+1 = 21Cr(3√a√b)21−r(√b3√a)r = 21Cra7−(r2)b23r−(72) Since the powers of a and b are the same, therefore 7 - r2 = 23r - 72 ⇒ r = 9

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