Question

the $7th$ term in ${(\frac{1}{y}+y^2)}^{10}$, when expanded in descending power of $y$, is

• A. $\frac{210}{y^2}$
• B. $\frac{y^2}{210}$
• C. $210y^2$
• D. None of these

Answer 1

The correct option is C $210y^2$

When ${(\frac{1}{y}+y^2)}^{10}$ is expanded, the power of $y$ go on increasing as the terms proceed.

Hence it is expanded in ascending powers of $y$.

So ${(y^2+\frac{1}{y})}^{10}$, when expanded will be in descending power of $y$.

Hence $t_7{=}^{10}{C}_6{\left(y^2\right)}^4{\left(\frac{1}{y}\right)}^6=\frac{10\times 9\times 8\times 7}{4\times 3\times 2\times 1}{y}^2=210y^2$