Binomial Theore...

The value of the term independent of \(x\) in the expansion of \(\left(x^{2}-\frac{1}{x}\right)^{9}\) is:

The coefficient of \(x^{n}\) in the expansion of \(\left(\frac{1+x}{1-x}\right)^{2}\), is:

For positive integers \(\mathrm{r}>1, \mathrm{n}>2\), the coefficient of \((3 \mathrm{r})^{\mathrm{th}}\) and \((\mathrm{r}+2)^{\text {th }}\) terms in the binomial expansion of \((1+\mathrm{x})^{2 \mathrm{n}}\) are equal, then:

The total number of terms in the expansion of \((x+a)^{47}-(x-a)^{47}\) after simplification is:

The number of terms which are free from radical signs in the expansion of \(\left(\mathrm{y}^{\frac{1}{5}}+\mathrm{x}^{\frac{1}{10}}\right)^{55}\) are:

Find the number of terms in the expansion of \((2 \mathrm{x}+3 \mathrm{y}+\mathrm{z})^{7}\).

If the coefficient of \(x\) in the expansion of \(\left(x^{2}+\frac{\lambda}{x}\right)^{5}\) is 270 , then the value of \(\lambda\) is:

Find the middle terms in the expansion of \(\left(1+3 x+3 x^{2}+x^{3}\right)^{2 n}\).

The constant term in the expansion of \(\left(x-\frac{1}{x}\right)^{10}\) is:

Determine the value of \(\mathrm{x}\) in the expression of \((2+\mathrm{x})^{5}\), if the second term in the expansion is 240.