Sample QuestionsBinomial Theorem questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If in the expansion of $\Big(\text{x}-\frac{1}{3\text{x}^{3}}\Big)^{9},$ the term independent of $x$ is:
- A
$\text{T}_{3}$
- ✓
$\text{T}_{4}$
- C
$\text{T}_{5}$
- D
Answer: B.
View full solution →The number of terms with integral coefficients in the expansion of $\Big(17^{\frac{1}{3}}+35^{\frac{1}{2}}\text{x}\Big)^{600}$ is:
Answer: D.
View full solution →If in the expansion of $(1+\text{x})^{20},$ the coefficients of rth and (r + 4) terms are equal, then r is equal to:
Answer: C.
View full solution →If the sum of the binomial coefficients of the expansion $\Big(2\text{x}+\frac{1}{\text{x}}\Big)^{\text{n}}$ is equal to $256,$ then the term independent of $x$ is:
Answer: A.
View full solution →If the coefficients of $2^{nd}, 3^{rd}$ and $4^{th}$ terms in the expansion of $(1+\text{x})^{\text{n}}, \text{n}\in\text{N}$ are in $A.P. $ then $n =$
Answer: A.
View full solution →Write the number of terms in the expansion of $(1-3\text{x}+3\text{x}^{2}-\text{x}^{3})^{8}.$
View full solution →Write the number of terms in the expansion of $(2+\sqrt{3}\text{x})^{10}+(2-\sqrt{3}\text{x})^{10}.$
View full solution →Write the total number of terms in the expansion of $(\text{x}+\text{a})^{100}+(\text{x}-\text{a})^{100}.$
View full solution →Find the ratio of the coefficients of $x^p$ and $x^q$ in the expansion of $(1+\text{x})^{\text{p}+\text{q}}.$
View full solution →Write last two digits of the number $3^{400}.$
View full solution →Find the coefficient of:
x in the expansion of $(1-2\text{x}^3+3\text{x}^5)\Big(1+\frac{1}{\text{x}}\Big)^8.$
View full solution →Find the middle term in the expansion of:
$\Big(\frac{\text{x}}{\text{a}}-\frac{\text{a}}{\text{x}}\Big)^{10}$
View full solution →Find the 11th term from the beginning and the 11th term from the end in the expansion of $\Big(2\text{x}-\frac{1}{\text{x}^2}\Big)^{25}$
View full solution →Find the 4th term from the beginning and 4th term from the end in the expansion of $\Big(\text{x}+\frac{2}{\text{x}}\Big)^9.$
View full solution →Find the 7th term in the expansion of $\Big(3\text{x}^2-\frac{1}{\text{x}^3}\Big)^{10}$
View full solution →Using binomial theorem, write down the expansions of the following:
$\Big(\text{x}-\frac{1}{\text{x}}\Big)^6$
View full solution →Find the coefficient of:
x in the expansion of $(1+3\text{x}+7\text{x}^2)(1-\text{x})^{16}.$
View full solution →If in the expansion of $(1+\text{x})^{\text{n}}$ the coefficients of three consecutive terms are 56, 70 and 56, then find n and the position of the terms of these coefficients.
View full solution →Find the middle terms(s) in the expansion of:
$\Big(\frac{\text{p}}{\text{x}}+\frac{\text{x}}{\text{p}}\Big)^{9}$
View full solution →Evaluate the following:
$(2+\sqrt3)^7+(2-\sqrt3)^7$
View full solution →If the $2^{nd}, 3^{rd}$ and $4^{th}$ terms in the expansion of $(\text{x}+\text{a})^{\text{n}}$ are $240, 729$ and $1080$ respectively find $x, a, n.$
View full solution →Evaluate the following:
$\Big\{\text{a}^2+\sqrt{\text{a}^2-1}\Big\}^4+\Big\{\text{a}^2-\sqrt{\text{a}^2-1}\Big\}^4$
View full solution →If n is a positive integer, prove that $3^{3\text{n}}-26\text{n}-1$ is divisible by 676.
View full solution →Find the term independent of $x$ in the expansion of the following expressions:
$(1+\text{x}+2\text{x}^{3})\Big(\frac{3}{2}\text{x}^{2}-\frac{1}{3\text{x}}\Big)^{9}$
View full solution →Find the sixth term in the expansion $\Big(\text{y}^{\frac{1}{2}}+\text{x}^{\frac{1}{3}}\Big)^{\text{n}},$ if the binomial coefficient of the term from the end is $45.$
View full solution →