Class 11 Maths Chapter 7: Binomial Theorem MCQs with answers
10 multiple-choice questions on Binomial Theorem, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.
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Answer: (b) 10
(a + b)n has n + 1 terms, so (3x − 5y)9 has 9 + 1 = 10 terms. 9 is the index itself, not the count of terms.
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Answer: (c) 35
Each entry is the sum of the two entries above it; the fourth entry of the next row is 15 + 20 = 35 (that is, ⁷C₃). 21 = 6 + 15 is the third entry.
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Answer: (a) 256
Putting x = 1 in (1 + x)8 gives ⁸C₀ + ⁸C₁ + ... + ⁸C₈ = 28 = 256. 255 forgets the term ⁸C₀ = 1.
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Answer: (d) 270
T₄ = T3+1 = ⁵C₃ y2 33 = 10 × 27 y2 = 270y2. 90 is the coefficient of the third term, which has y3.
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Answer: (a) 11
The index of p falls by 1 as the index of q rises by 1, so their sum stays equal to the index 11 in every term. 12 is the number of terms.
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Answer: (b) 126
The term is ⁹C₄ x5(−y)4 = 126x5y4; an even power of −y is positive. 84 = ⁹C₃ belongs to x6y3.
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Answer: (c) 45
The third term is T2+1, with coefficient ¹⁰C₂ = (10 × 9)/2 = 45. ¹⁰C₃ = 120 belongs to the fourth term.
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Answer: (d) Meru Prastara
Pingla's triangular arrangement of the coefficients is the Meru Prastara; Chhanda shastra is the name of the book in which he gave it.
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Answer: (a) 0
Putting x = 1 in (1 − x)10 = ¹⁰C₀ − ¹⁰C₁x + ¹⁰C₂x2 − ... + ¹⁰C₁₀x10 gives 010 = 0. 1024 is the sum without the signs.
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Answer: (b) 0.0112
The third term is ⁸C₂(0.02)2 = 28 × 0.0004 = 0.0112. 0.16 is the second term, 8 × 0.02; 0.0056 halves ⁸C₂.
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