Chapter Exam

Chapter-7 Binomial Theorem — Online MCQ Test

Q: In Pascal's Triangle, which row represents the binomial coefficients for (a+b)³?

Answer: B. Row 3 — Pascal's Triangle row n contains the binomial coefficients for (a+b)ⁿ. Row 3 corresponds to (a+b)³.

Q: What is the general formula for the (r+1)th term in the binomial expansion of (a+b)ⁿ?

Answer: A. Tr+1 = nCr × aⁿ⁻ʳ × bʳ — The general term Tr+1 = nCr × aⁿ⁻ʳ × bʳ is the standard formula where the power of a decreases and power of b increases.

Q: What is the relationship between nCr and nC(n-r)?

Answer: B. nCr = nC(n-r) — By the symmetry property of binomial coefficients: nCr = nC(n-r) = n!/(r!(n-r)!).

Q: How many terms are there in the binomial expansion of (x+y)⁷?

Answer: C. 8 — The binomial expansion of (x+y)ⁿ contains (n+1) terms. For n=7, there are 8 terms.

Q: Find the middle term in the binomial expansion of (2x+3y)⁶.

Answer: B. T₄ — For even n=6, there are 7 terms total, so the middle term is the 4th term (T₄) which occurs at r=3.

Q: In the expansion of (1+x)¹⁰, what is the coefficient of x³?

Answer: C. 120 — The coefficient of x³ is 10C3 = 10!/(3!×7!) = (10×9×8)/(3×2×1) = 720/6 = 120.

Q: In the expansion of (1+x)ⁿ, if the coefficient of x² is 45, what is n?

Answer: B. 10 — Coefficient of x² is nC2 = 45. So n(n-1)/2 = 45, giving n(n-1) = 90. Solving: n = 10.

Q: In (2x + 3y)⁵, the coefficient of x²y³ is:

Answer: B. 1080 — General term: 5Cr × (2x)⁵⁻ʳ × (3y)ʳ. For x²y³: r=3, so T₄ = 5C3 × 2² × 3³ × x² × y³ = 10 × 4 × 27 = 1080.

Q: In the binomial expansion, if Tr = 5C2 × a³ × b², then Tr equals:

Answer: B. T₃ — Since the term is nCr × aⁿ⁻ʳ × bʳ and here n=5, r=2, this is the (r+1)th = 3rd term = T₃.

Q: In (x+y)ⁿ, if 8 times the 3rd term equals 9 times the 2nd term, and both contain equal powers of x and y, then n is:

Answer: C. 14 — Given: 8×T₃ = 9×T₂ and equal powers of x,y means we're at the middle. This requires solving 8×nC2/9×nC1 = 1 with middle term condition, yielding n = 14.

MATHS · Grade 11 · CBSE(NCERT)

Practice Chapter-7 Binomial Theorem with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 11 MATHS. This chapter covers: Binomial expansion - Pascal's Triangle - Binomial coefficients (nCk) - General term (Tr+1) - Middle term. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-7 Binomial Theorem — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 11 MATHS — Chapter-7 Binomial Theorem, with answers and explanations. These are sample questions; the exam has its own separate question set.

In Pascal's Triangle, which row represents the binomial coefficients for (a+b)³?

A. Row 2
B. Row 3 ✓
C. Row 4
D. Row 5

Answer: B. Row 3
Pascal's Triangle row n contains the binomial coefficients for (a+b)ⁿ. Row 3 corresponds to (a+b)³.

What is the general formula for the (r+1)th term in the binomial expansion of (a+b)ⁿ?

A. Tr+1 = nCr × aⁿ⁻ʳ × bʳ ✓
B. Tr+1 = nCr × aʳ × bⁿ⁻ʳ
C. Tr+1 = (n-r)C(n-r) × aⁿ × bʳ
D. Tr+1 = nCr × aⁿ × bʳ

Answer: A. Tr+1 = nCr × aⁿ⁻ʳ × bʳ
The general term Tr+1 = nCr × aⁿ⁻ʳ × bʳ is the standard formula where the power of a decreases and power of b increases.

What is the relationship between nCr and nC(n-r)?

A. nCr > nC(n-r)
B. nCr = nC(n-r) ✓
C. nCr < nC(n-r)
D. nCr + nC(n-r) = 2n

Answer: B. nCr = nC(n-r)
By the symmetry property of binomial coefficients: nCr = nC(n-r) = n!/(r!(n-r)!).

How many terms are there in the binomial expansion of (x+y)⁷?

A. 6
B. 7
C. 8 ✓
D. 9

Answer: C. 8
The binomial expansion of (x+y)ⁿ contains (n+1) terms. For n=7, there are 8 terms.

Find the middle term in the binomial expansion of (2x+3y)⁶.

A. T₃ and T₄
B. T₄ ✓
C. T₃
D. T₂ and T₃

Answer: B. T₄
For even n=6, there are 7 terms total, so the middle term is the 4th term (T₄) which occurs at r=3.

In the expansion of (1+x)¹⁰, what is the coefficient of x³?

A. 100
B. 110
C. 120 ✓
D. 140

Answer: C. 120
The coefficient of x³ is 10C3 = 10!/(3!×7!) = (10×9×8)/(3×2×1) = 720/6 = 120.

In the expansion of (1+x)ⁿ, if the coefficient of x² is 45, what is n?

A. 9
B. 10 ✓
C. 8
D. 12

Answer: B. 10
Coefficient of x² is nC2 = 45. So n(n-1)/2 = 45, giving n(n-1) = 90. Solving: n = 10.

In (2x + 3y)⁵, the coefficient of x²y³ is:

A. 540
B. 1080 ✓
C. 2160
D. 4320

Answer: B. 1080
General term: 5Cr × (2x)⁵⁻ʳ × (3y)ʳ. For x²y³: r=3, so T₄ = 5C3 × 2² × 3³ × x² × y³ = 10 × 4 × 27 = 1080.

In the binomial expansion, if Tr = 5C2 × a³ × b², then Tr equals:

A. T₂
B. T₃ ✓
C. T₄
D. T₅

Answer: B. T₃
Since the term is nCr × aⁿ⁻ʳ × bʳ and here n=5, r=2, this is the (r+1)th = 3rd term = T₃.

In (x+y)ⁿ, if 8 times the 3rd term equals 9 times the 2nd term, and both contain equal powers of x and y, then n is:

A. 16
B. 15
C. 14 ✓
D. 17

Answer: C. 14
Given: 8×T₃ = 9×T₂ and equal powers of x,y means we're at the middle. This requires solving 8×nC2/9×nC1 = 1 with middle term condition, yielding n = 14.

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