Binomial Theorem MCQs with Explanations for Class 11

Class: CBSE Class 11 Mathematics
Subject: Mathematics
Section: Algebra
Topic: Binomial Theorem
Board: CBSE Board Examinations

Instructions: These Multiple Choice Questions (MCQs) are designed strictly as per the NCERT syllabus, making them ideal for CBSE Class 11 Board Examination standards. Each question includes a detailed explanation for concept clarity.

1. The number of terms in the expansion of (a + b)¹⁰ is:

A) 9
B) 10
C) 11
D) 12

Answer: C) 11
Explanation: In (a + b)ⁿ, total terms = n + 1. Here n = 10, so terms = 11.

2. The coefficient of x³ in (1 + x)⁵ is:

A) 5
B) 10
C) 15
D) 20

Answer: B) 10
Explanation: General term = ⁵C₃x³ = 10x³.

3. The middle term in (a + b)⁸ is:

A) 4th
B) 5th
C) 4th & 5th
D) 3rd

Answer: B) 5th
Explanation: Middle term = (n/2 + 1)th = (8/2 + 1) = 5th.

4. Sum of coefficients of (1 + x)ⁿ is:

A) 0
B) 1
C) 2ⁿ
D) n

Answer: C) 2ⁿ
Explanation: Put x = 1 → (1+1)ⁿ = 2ⁿ.

5. Coefficient of x² in (2 + x)⁴ is:

A) 12
B) 24
C) 48
D) 6

Answer: B) 24
Explanation: Term = ⁴C₂·2² = 6×4 = 24.

6. General term of (a + b)ⁿ is:

A) ⁿCᵣaⁿbʳ
B) ⁿCᵣaⁿ⁻ʳbʳ
C) ⁿCᵣaʳbⁿ
D) ⁿCᵣab

Answer: B
Explanation: Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ.

7. Constant term in (x + 1/x)⁴ is:

A) 4
B) 6
C) 1
D) 0

Answer: B
Explanation: Middle term gives constant = ⁴C₂ = 6.

8. Coefficient of x in (1 + x)⁷:

A) 7
B) 21
C) 35
D) 1

Answer: A
Explanation: ⁷C₁ = 7.

9. Value of ⁵C₂ is:

A) 5
B) 10
C) 20
D) 25

Answer: B
Explanation: 5!/(2!3!) = 10.

10. The expansion of (1 + x)⁰ is:

A) 0
B) 1
C) x
D) 1+x

Answer: B
Explanation: Any number power 0 = 1.

11. Number of terms in (x + y)¹⁵:

A) 14
B) 15
C) 16
D) 30

Answer: C
Explanation: n+1 = 16.

12. Coefficient of x² in (1 + x)⁶:

A) 6
B) 10
C) 15
D) 20

Answer: C
Explanation: ⁶C₂ = 15.

13. Middle term of (a + b)⁷:

A) 3rd
B) 4th
C) 5th
D) Two middle terms

Answer: D
Explanation: Odd power → two middle terms.

14. Sum of coefficients of (1 − x)⁵:

A) 0
B) 1
C) 32
D) −1

Answer: B
Explanation: Put x=1 → (1−1)⁵ = 0? Wait sum uses absolute → actually sum = (1−1)⁵ = 0. Correction → Answer A.

15. ⁸C₀ equals:

A) 0
B) 1
C) 8
D) 64

Answer: B
Explanation: nC0 = 1.

16. Coefficient of x³ in (1 + x)⁶:

A) 10
B) 20
C) 15
D) 6

Answer: B
Explanation: ⁶C₃ = 20.

17. Greatest coefficient in (1 + x)¹⁰ is:

A) 45
B) 120
C) 252
D) 210

Answer: C
Explanation: Largest = ¹⁰C₅ = 252.

18. Value of ⁶C₁ + ⁶C₂:

A) 21
B) 30
C) 36
D) 15

Answer: A
Explanation: 6 + 15 = 21.

19. Coefficient of x⁰ in (2 + x)⁵:

A) 32
B) 1
C) 2⁵
D) 10

Answer: A
Explanation: Constant = 2⁵ = 32.

20. Expansion valid for |x| < 1 is:

A) (1+x)ⁿ
B) (1−x)⁻¹
C) (a+b)²
D) None

Answer: B
Explanation: Infinite binomial expansion valid for |x| < 1.

Binomial Theorem MCQs with Explanations for Class 11

Binomial Theorem MCQs with Explanations for Class 11

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