Question

The term independent of x in the expansion of `(root(6)(x) - 1/root(3)(x))^9` is ______.

विकल्प

• – ⁹C₃

• – ⁹C₄

• – ⁹C₅

• – ⁸C₃

Answer 1

The term independent of x in the expansion of `(root(6)(x) - 1/root(3)(x))^9` is `underlinebb(- ""^9C_3)`.

Explanation:

T_{r + 1} = `""^9C_r (root(6)(x))^(9 - r) (-1/root(3)(x))^r`

= `""^9C_r (-1)^r . x^((9 - r)/6 - r/3)`

= `""^9C_r . x^(((9 - 3r)/6))`

Now `(9 - 3r)/6` = 0 `\implies` r = 3 ;

Thus, term independent of x = – ⁹C₃