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

Question

If the (r+1) th term in the expansion of (√[3](a/√b)+√(b/√[3]a))21 has the same power of a and b, then the value of r is (A) 9 (B) 10 (C) 8 (D) 6

Tardigrade Admin · Accepted Answer

We have Tr+1= 21 Cr(√[3](a/√b))21-r(√(b/√[3]a))r = 21 Cr a7-(r / 2) b(2 / 3) r-(7 / 2) As the powers of a and d are the same, 7-(r/2)=(2/3) r-(7/2) ⇒ r=9

Q. If the $(r + 1)$ th term in the expansion of $(3 \frac{a}{b} + \frac{b}{3 a})^{21}$ has the same power of $a$ and $b$ , then the value of $r$ is

9

10

8

6

We have $T_{r + 1} =^{21} C_{r} (3 \frac{a}{b})^{21 - r} (\frac{b}{3 a})^{r}$
$=^{21} C_{r} a^{7 - (r /2)} b^{(2/3) r - (7/2)}$
As the powers of $a$ and $d$ are the same, $7 - \frac{r}{2} = \frac{2}{3} r - \frac{7}{2}$
$\Rightarrow r = 9$

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

9

10

8

6

We have Tr+1​=21Cr​(3b​a​​)21−r(3a​b​​)r =21Cr​a7−(r/2)b(2/3)r−(7/2) As the powers of a and d are the same, 7−2r​=32​r−27​ ⇒r=9

Q. If the $(r + 1)$ th term in the expansion of $(3 \frac{a}{b} + \frac{b}{3 a})^{21}$ has the same power of $a$ and $b$ , then the value of $r$ is

We have $T_{r + 1} =^{21} C_{r} (3 \frac{a}{b})^{21 - r} (\frac{b}{3 a})^{r}$
$=^{21} C_{r} a^{7 - (r /2)} b^{(2/3) r - (7/2)}$
As the powers of $a$ and $d$ are the same, $7 - \frac{r}{2} = \frac{2}{3} r - \frac{7}{2}$
$\Rightarrow r = 9$