R D Sharma Solutions for Chapter: Binomial Theorem, Exercise 3: VERY SHORT ANSWER QUESTIONS (VSAQs)

If the middle term in the expansion of ${\left(x+\frac{1}{x}\right)}^{10}$ is ${}^{a}C_b$ then find the value of $a+b$.

If the coefficient of the middle term in the expansion of $(1+x{)}^{2n}$ is ${}^p{C}_q$, then find the value of $\frac{p}{q}$. $$

Write the number of terms in the expansion of ${\left\{{\left(2x+y^3\right)}^4\right\}}^7$.

The sum of the coefficients of two middle terms in the binomial expansion of $(1+x{)}^{2n-1}$ is ${}^{an}C_{bn}$ where $an+bn=kn$ then find the value of $k$.

Write last two digits of the number $3^{400}$

Find the number of terms in the expansion of $(a+b+c{)}^n$.

Write the total number of terms (only numerical value) in the expansion of $(x+a{)}^{100}+(x-a{)}^{100}$.

If ${\left(1-x+x^2\right)}^n=a_0+a_{1}x+a_2{x}^2+\dots +a_{2n}{x}^{2n}$ then the value of $a_0+a_2+a_4+\dots +a_{2n}$ is of the form $\frac{k^n+1}{2}$. Hence, find the value of $k$.