Class 11 Mathematics · Chapter 8 · Test 3
Binomial Series
36 MCQs Covers the binomial series for a negative integer or fraction index and its condition of validity |x| < 1.
36 questions · 30 min · 36 marks
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Sample questions
The first 5 of 36. Try each one, then tap to see the answer.
Question 1
The binomial series for (1 + x)^n with n a negative integer or a fraction is valid when:
- A|x| > 1
- B|x| = 1
- C|x| < 1
- Dany real x
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Answer: C
The series converges to (1 + x)^n only for |x| < 1.
Question 2
The number of terms in the expansion of (1 + x)^n when n is a negative integer or a fraction is:
- Ainfinite
- Bn + 1
- Cn
- Dn - 1
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Answer: A
The series never terminates because n - r + 1 never becomes zero.
Question 3
The expansion of (1 + x)^-1 is:
- A1 + x + x^2 + ...
- B1 - x - x^2 - ...
- C1 + 2x + 3x^2 + ...
- D1 - x + x^2 - x^3 + ...
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Answer: D
The terms alternate in sign with coefficient 1.
Question 4
The expansion of (1 - x)^-1 is:
- A1 - x + x^2 - ...
- B1 + x + x^2 + x^3 + ...
- C1 + 2x + 3x^2 + ...
- D1 - x - x^2 - ...
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Answer: B
Replacing x by -x in (1+x)^-1 gives 1 + x + x^2 + ....
Question 5
The expansion of (1 + x)^-2 is:
- A1 + 2x + 3x^2 + 4x^3 + ...
- B1 - x + x^2 - ...
- C1 - 2x + 3x^2 - 4x^3 + ...
- D1 - 2x + 4x^2 - 8x^3 + ...
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Answer: C
The general term is (-1)^r (r+1) x^r.
More tests in Mathematical Induction and Binomial Theorem
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