NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter 8: BINOMIAL THEOREM

True or False

The sum of the series \(\sum_{r=0}^{10} \binom{20}{r}\) is \(2^{19} + \dfrac{\binom{20}{10}}{2}\).

The expression \(7^9 + 9^7\) is divisible by 64.

The number of terms in the expansion of \([(2x + y^3)^4]^7\) is 8.

The sum of coefficients of the two middle terms in the expansion of \((1 + x)^{2n - 1}\) is equal to \(\binom{2n - 1}{n}\).

The last two digits of the number \(3^{400}\) are 01.

If the expansion of \((x - \dfrac{1}{x^2})^{2n}\) contains a term independent of \(x\), then \(n\) is a multiple of 2.

The number of terms in the expansion of \((a + b)^n\) where \(n \in \mathbb{N}\) is one less than the power \(n\).