JEE (Main) Mathematics - Binomial Theorem MCQs (Questions 16-30)
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What is the general form of the binomial expansion of \( (a + b)^n \)?
- a) \( a^n + b^n \)
- b) \( \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r \)
- c) \( \sum_{r=0}^{n} \binom{r}{n} a^r b^r \)
- d) \( \sum_{r=0}^{n} \binom{n-r}{r} a^r b^{n-r} \)
Answer: b) \( \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r \)
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What is the number of terms in the expansion of \( (x + 3)^6 \)?
- a) 7
- b) 8
- c) 9
- d) 6
Answer: b) 8
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What is the middle term in the expansion of \( (x + y)^8 \)?
- a) \( \binom{8}{4} x^4 y^4 \)
- b) \( \binom{8}{5} x^3 y^5 \)
- c) \( \binom{8}{3} x^5 y^3 \)
- d) \( \binom{8}{4} x^5 y^3 \)
Answer: a) \( \binom{8}{4} x^4 y^4 \)
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The term containing \( x^2 y^3 \) in the expansion of \( (x + y)^5 \) is:
- a) \( \binom{5}{3} x^2 y^3 \)
- b) \( \binom{5}{2} x^3 y^2 \)
- c) \( \binom{5}{4} x^1 y^4 \)
- d) \( \binom{5}{1} x^4 y^1 \)
Answer: a) \( \binom{5}{3} x^2 y^3 \)
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In the expansion of \( (2x + 3)^4 \), the coefficient of \( x^2 \) is:
- a) 54
- b) 108
- c) 81
- d) 36
Answer: b) 108
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What is the expansion of \( (a + b)^2 \)?
- a) \( a^2 + 2ab + b^2 \)
- b) \( a^2 + b^2 \)
- c) \( 2a^2 + 2b^2 \)
- d) \( a^2 + 2b^2 \)
Answer: a) \( a^2 + 2ab + b^2 \)
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In the expansion of \( (x + 2)^5 \), the coefficient of \( x^3 \) is:
- a) 40
- b) 80
- c) 10
- d) 20
Answer: a) 40
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The binomial expansion of \( (x - 1)^3 \) results in how many terms?
- a) 3
- b) 4
- c) 5
- d) 6
Answer: b) 4
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What is the value of the coefficient of \( x^4 \) in the expansion of \( (2x + 1)^6 \)?
- a) 32
- b) 80
- c) 150
- d) 200
Answer: b) 80
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In the expansion of \( (a + b)^7 \), the term involving \( a^4 b^3 \) is:
- a) \( \binom{7}{4} a^4 b^3 \)
- b) \( \binom{7}{3} a^3 b^4 \)
- c) \( \binom{7}{2} a^5 b^2 \)
- d) \( \binom{7}{5} a^2 b^5 \)
Answer: a) \( \binom{7}{4} a^4 b^3 \)
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In the expansion of \( (x + 5)^4 \), the constant term is:
- a) 625
- b) 25
- c) 125
- d) 1
Answer: a) 625
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The number of terms in the expansion of \( (x + y)^7 \) is:
- a) 6
- b) 7
- c) 8
- d) 9
Answer: c) 8
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The term containing \( x^3 y^2 \) in the expansion of \( (x + y)^5 \) is:
- a) \( 10 x^3 y^2 \)
- b) \( 20 x^3 y^2 \)
- c) \( 5 x^3 y^2 \)
- d) \( 15 x^3 y^2 \)
Answer: d) 10
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In the expansion of \( (x - 3)^5 \), the term involving \( x^2 \) is:
- a) \( -15 x^2 \)
- b) \( 15 x^2 \)
- c) \( 45 x^2 \)
- d) \( -45 x^2 \)
Answer: d) \( -45 x^2 \)
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