D.K. Ramesh Kumar and C. V. Jayanna Solutions for Chapter: Binomial Theorem, Exercise 1: Exercise 1

In the expansion of ${\left(x -\frac{ 3}{x^2}\right)}^n$, the term independent of $x$ is?

How many nine-digit numbers can be formed using the digits $2, 2, 3, 3, 5, 5, 8, 8, 8$ so that the odd digits occupy even position?

There are n points in a plane of which p points are colinear. How many lines can be formed from these points?

The number of words that can be formed out of the letters of the word “ARTICLE” so that vowels occupy even places is?

The sum of coefficients in the expansion of $(1 + x – 3x^2{)}^{3148}$ is?

The coefficient of $x^{32}$ in the expansion of ${\left(x^4-\frac{1}{x^3}\right)}^{15}$ is ?

If ${}^n{C}_{12}{=}^n{C}_6$ then ${}^n{C}_2 =$?

The middle term in the expansion of ${\left(x - \frac{1}{x}\right)}^{18}$ is