JEE (Main) Mathematics - BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS Multiple Choice Questions (MCQs)
JEE (Main) Mathematics - Binomial Theorem MCQs
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What is the expansion of \( (a + b)^3 \)?
- a) \( a^3 + 3a^2b + 3ab^2 + b^3 \)
- b) \( a^3 + 2a^2b + 3ab^2 + b^3 \)
- c) \( a^3 + 3ab + 3b^2 + b^3 \)
- d) \( a^3 + 3ab + 3b^2 \)
Answer: a) \( a^3 + 3a^2b + 3ab^2 + b^3 \)
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The general term of the binomial expansion of \( (1 + x)^n \) is given by:
- a) \( \binom{n}{r} x^r \)
- b) \( \binom{n}{r} x^{n-r} \)
- c) \( \binom{n}{r} x^r \)
- d) \( \binom{n}{r} x^{n-r} \)
Answer: b) \( \binom{n}{r} x^{n-r} \)
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The number of terms in the expansion of \( (x + y)^{10} \) is:
- a) 10
- b) 11
- c) 12
- d) 20
Answer: b) 11
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What is the coefficient of \( x^4 \) in the expansion of \( (2x + 3)^5 \)?
- a) 240
- b) 160
- c) 120
- d) 180
Answer: a) 240
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What is the sum of the coefficients of the expansion of \( (1 + x)^n \)?
- a) 1
- b) 0
- c) \( 2^n \)
- d) \( n \)
Answer: c) \( 2^n \)
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Which term in the expansion of \( (2x + 3y)^7 \) contains \( x^4y^3 \)?
- a) The 4th term
- b) The 5th term
- c) The 6th term
- d) The 7th term
Answer: b) The 5th term
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The expansion of \( (1 + x)^6 \) will have how many non-zero terms?
- a) 5
- b) 6
- c) 7
- d) 8
Answer: c) 7
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The middle term of the expansion of \( (a + b)^{10} \) is:
- a) \( \binom{10}{5} a^5b^5 \)
- b) \( \binom{10}{6} a^4b^6 \)
- c) \( \binom{10}{4} a^6b^4 \)
- d) \( \binom{10}{3} a^7b^3 \)
Answer: a) \( \binom{10}{5} a^5b^5 \)
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In the expansion of \( (2x - 3y)^5 \), the coefficient of \( x^2y^3 \) is:
- a) -240
- b) 240
- c) -120
- d) 120
Answer: a) -240
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What is the general form of the term \( T_r \) in the expansion of \( (a + b)^n \)?
- a) \( \binom{n}{r} a^{n-r} b^r \)
- b) \( \binom{n}{r} a^r b^{n-r} \)
- c) \( \binom{r}{n} a^r b^n \)
- d) \( \binom{n}{r} a^r b^r \)
Answer: a) \( \binom{n}{r} a^{n-r} b^r \)
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The number of ways to select 2 objects from 5 objects in the expansion of \( (x + 2)^5 \) is:
- a) 10
- b) 20
- c) 15
- d) 25
Answer: c) 15
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Which term is the first non-zero term in the expansion of \( (x - 1)^7 \)?
- a) \( x^7 \)
- b) \( -7x^6 \)
- c) \( 7x^6 \)
- d) \( -1 \)
Answer: b) \( -7x^6 \)
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In the expansion of \( (x + 2)^4 \), the coefficient of \( x^2 \) is:
- a) 8
- b) 6
- c) 12
- d) 4
Answer: b) 6
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The expansion of \( (x - 2)^3 \) has how many terms?
- a) 3
- b) 4
- c) 5
- d) 6
Answer: b) 4
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In the expansion of \( (3x + 2)^5 \), the coefficient of \( x^3 \) is:
- a) 270
- b) 225
- c) 180
- d) 150
Answer: a) 270
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