If in the expansion of (x3-(2/√x))n a term like x2 exists and n is a double digit number, then least value of n is

Question

If in the expansion of (x3-(2/√x))n a term like x2 exists and n is a double digit number, then least value of n is (A) 10 (B) 11 (C) 12 (D) 13

Tardigrade Admin · Accepted Answer

Let the term is Tr+1= n Cr(x3)n-r((-2/√x))r Term like x2 exists ∴ 3 n-3 r-r / 2=2 ⇒ 3 n=2+(7 r/2) ⇒ n=(4+7 r/6) Hence, least value of n which is double digit is 10.

Q. If in the expansion of $(x^{3} - \frac{2}{x})^{n}$ a term like $x^{2}$ exists and $n$ is a double digit number, then least value of $n$ is

10

11

12

13

Let the term is $T_{r + 1} =^{n} C_{r} (x^{3})^{n - r} (\frac{- 2}{x})^{r}$
Term like $x^{2}$ exists
$∴ 3 n - 3 r - r /2 = 2$
$\Rightarrow 3 n = 2 + \frac{7 r}{2}$
$\Rightarrow n = \frac{4 + 7 r}{6}$
Hence, least value of $n$ which is double digit is $10$ .

Q. If in the expansion of (x3−x​2​)n a term like x2 exists and n is a double digit number, then least value of n is

10

11

12

13

Let the term is Tr+1​=nCr​(x3)n−r(x​−2​)r Term like x2 exists ∴3n−3r−r/2=2 ⇒3n=2+27r​ ⇒n=64+7r​ Hence, least value of n which is double digit is 10.

Q. If in the expansion of $(x^{3} - \frac{2}{x})^{n}$ a term like $x^{2}$ exists and $n$ is a double digit number, then least value of $n$ is

Let the term is $T_{r + 1} =^{n} C_{r} (x^{3})^{n - r} (\frac{- 2}{x})^{r}$
Term like $x^{2}$ exists
$∴ 3 n - 3 r - r /2 = 2$
$\Rightarrow 3 n = 2 + \frac{7 r}{2}$
$\Rightarrow n = \frac{4 + 7 r}{6}$
Hence, least value of $n$ which is double digit is $10$ .