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Binomial Theorem MATHS - Binomial Theorem

Rajasthan Board (RBSE) - STD 11 Science - MATHS (Rajasthan - English Medium). 216 questions in this chapter.

Question types

Binomial Theorem question types

216 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

216
Questions
7
Question groups
5
Question types
Sample Questions

Binomial Theorem questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 3M.C.Q (1 Marks)1 Mark
The term independent of x in the expansion of $\Big(9\text{x}-\frac{1}{3\sqrt{{x}}2}\Big)18,$ x > 0 , is ‘a’ times the corresponding binomial coefficient. Then ‘a’ is:
  • A
    $3$
  • B
    $\frac{1}{3}$
  • C
    $-\frac{1}{3}$
  • D
    $\text{None of these}$
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Q 4M.C.Q (1 Marks)1 Mark
In the expansion of $\Big(\sqrt[3]4+\frac{1}{\sqrt[4]{6}}\Big)^{20},$
  • A
    The number of rational terms = 4
  • B
    The number of irrational terms = 19
  • C
    The middle term is irrational
  • D
    The number of irrational terms = 17
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Q 9True False[1 Marks ]1 Mark
State which of the statement in True or False.
The sum of the series $\sum\limits_{\text{r}=0}^{10}\ ^{20}\text{C}_\text{r}\ \text{is}\ 2^{19}+\frac{^{20}\text{C}_{10}}{2}$
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Q 10True False[1 Marks ]1 Mark
State which of the statement in True or False.
If the expansion of $\Big(\text{x}-\frac{1}{\text{x}^2}\Big)^{2\text{n}}$ contains a term independent of x, then n is a multiple of 2.
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Q 12Fill In The Blanks[1 Marks ]1 Mark
Fill in the blank.
If the seventh terms from the beginning and the end in the expansion of $\Big(3\sqrt{2}+\frac{1}{3\sqrt{3}}\Big)^\text{n}$ are equal, then n equals _____________.
[Hint: $\text{T}_7=\text{T}_{\text{n}-7+2}\Rightarrow\ ^\text{n}\text{C}_6\Big(2^\frac{1}{3}\Big)^{\text{n}-6}\bigg(\frac{1}{3^\frac{1}{3}}\bigg)^6$ $=\ ^\text{n}\text{C}_{\text{n}-6}\Big(2^\frac{1}{3}\Big)^6\bigg(\frac{1}{3^\frac{1}{3}}\bigg)^{\text{n}-6}$
$\Rightarrow\Big(2^\frac{1}{3}\Big)^{\text{n}-12}=\bigg(\frac{1}{3^{\frac{1}{3}}}\bigg)^{\text{n}-12}\Rightarrow$ only problem when $\text{n}-12=0\Rightarrow\text{n}=12]$
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Q 263 Marks Question3 Marks
Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of ${\left( {\sqrt[4] 2 + \frac{1}{{\sqrt [4]{3} }}} \right)^n}$ is $\sqrt 6 :1$.
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Q 293 Marks Question3 Marks
If a and b are distinct integers, prove that a - b is a factor of an - bn, whenever n is a positive integer.
[Hint write an = (a – b + b)n and expand]
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