1.

Find the term independent of x in \((x^2 - \frac{2}{x^3})^5\)

Answer»

 \((x^2 - \frac{2}{x^3})^5\)

Here x → x2 a → \(\frac{-2}{x^3}\) = 5r(x2)5 – r .\((\frac{-2}{x^3})^r\) = 5r.x10-2r.(-2)r 

= 5Cr(-2)r .x10-5r 

We have 10 – 5r = 0 ⇒ r = 2 

T2+1 = T3 = 5C2(-2)2 .x0 = 4. \(\frac{5.4}{2.1}\) = 40 

∴ The term independent of x is 40


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