If the constant term in the expansion of \({\left( {\sqrt x - \frac{k}{{{x^2}}}} \right)^{10}}\) is 405, then what can be the values of k?

In the expansion of \({\left( {\sqrt {\rm{x}} + \frac{1}{{3{{\rm{x}}^2}}}} \right)^{10}}\) the value of constant term (independent of x) is

In the expansion of \(\left(x + \frac{1}{x}\right)^{2n} \) , what is the (n + 1)th term from the end (when arranged in descending powers of x) ?

If the coefficient of x ^rand x ^r+1 are equal in the expansion, then r is equal to

The average of the coefficients of the two middle terms in the expansion is

The sum of the coefficients of all the terms in the expansion is

The coefficient of x ⁹⁹ in the expansion of (x - 1)(x - 2)(x - 3) … (x - 100) is

Consider the following statements in respect of the expansion of (x + y) ¹⁰

1. Among all the coefficients of the terms, the coefficient of the 6th term has the highest value

2. The coefficient of the 3rd term is equal to coefficient of the 9th term

Which of the above statements is /are correct ?

The term independent of x in the binomial expansion of \(\rm \left( \frac {2}{x^2} - \sqrt x \right)^{10}\)  is equal to

If the constant term in the expansion of \({\left( {\sqrt x - \frac{k}{{{x^2}}}} \right)^{10}}\) is 405, then what can be the values of k?

What is the expansion of (x + 11) (x - 11)?  

The middle term in the expansion of \((x^2 + \frac{1}{x^2} + 2)^n\) is

In the expansion of \({\left( {\sqrt {\rm{x}} + \frac{1}{{3{{\rm{x}}^2}}}} \right)^{10}}\) the value of constant term (independent of x) is