The largest coefficient in the expansion of \((1 + x)^{30}\) is ________.
\(^{30}C_{15}\)
The number of terms in the expansion of \((x + y + z)^n\) is ________.
\(\dfrac{(n+1)(n+2)}{2}\)
In the expansion of \(\left(x^2 - \dfrac{1}{x^2}\right)^{16}\), the value of constant term is ________.
\(^{16}C_{8}\)
If the seventh terms from the beginning and the end in the expansion of \(\left(\sqrt[3]{2} + \dfrac{1}{\sqrt[3]{3}}\right)^n\) are equal, then \(n\) equals ________.
12
The coefficient of \(a^{-6} b^{4}\) in the expansion of \(\left(\dfrac{1}{a} - \dfrac{2b}{3}\right)^{10}\) is ________.
\(\dfrac{1120}{27} a^{-6} b^{4}\)
Middle term in the expansion of \((a^3 + ba)^{28}\) is ________.
\(^{28}C_{14} a^{56} b^{14}\)
The ratio of the coefficients of \(x^p\) and \(x^q\) in the expansion of \((1 + x)^{p+q}\) is ________.
1
The position of the term independent of \(x\) in the expansion of \(\left(\dfrac{x}{3} + \dfrac{3}{2x^2}\right)^{10}\) is ________.
Third term
If \(25^{15}\) is divided by 13, the remainder is ________.
12