Class 11 Mathematics

1. The total number of terms in the expansion of (x + a)ⁿ is:

• A. n + 1
• B. n
• C. n - 1
• D. 2ⁿ

2. The general term (r + 1)th term Tᵣ₊₁ in the expansion of (a + b)ⁿ is:

• A. ⁿCᵣ aⁿ⁻ʳ bʳ
• B. ⁿCᵣ aʳ bⁿ⁻ʳ
• C. ⁿCᵣ⁻₁ aⁿ⁻ʳ bʳ
• D. ⁿCᵣ₊₁ aⁿ⁻ʳ bʳ

3. The sum of all binomial coefficients in the expansion of (1 + x)ⁿ is:

• A. 2ⁿ
• B. 2ⁿ⁻¹
• C. 2ⁿ⁺¹
• D. n²

4. The sum of coefficients of even terms ⁿC₀ + ⁿC₂ + ⁿC₄ + ... is equal to:

• A. 2ⁿ⁻¹
• B. 2ⁿ
• C. 2ⁿ⁺¹
• D. 2ⁿ - 1

5. Number of terms in the expansion of (x + 2y)⁹ is:

• A. 10
• B. 9
• C. 8
• D. 18

6. If n is even, the middle term in the expansion of (a + b)ⁿ is:

• A. (n/2 + 1)th term
• B. (n/2)th term
• C. ((n+1)/2)th term
• D. (n/2 + 2)th term

7. If n is odd, the middle terms in the expansion of (a + b)ⁿ are:

• A. ((n+1)/2)th and ((n+3)/2)th terms
• B. (n/2)th and (n/2 + 1)th terms
• C. (n+1)th and (n+2)th terms
• D. ((n-1)/2)th and ((n+1)/2)th terms

8. The 4th term in the expansion of (x - 2y)¹² is:

• A. -1760 x⁹ y³
• B. 1760 x⁹ y³
• C. -220 x⁹ y³
• D. -1760 x⁸ y⁴

9. The coefficient of x⁵ in the expansion of (x + 3)⁸ is:

• A. 1512
• B. 56
• C. 27
• D. 1120

10. Find the middle term in the expansion of (x + 1/x)¹⁰:

• A. 252
• B. 210
• C. 120
• D. 252 x

11. The term independent of x in the expansion of (x + 1/x)²ⁿ is:

• A. ²ⁿCₙ
• B. ²ⁿCₙ₊₁
• C. ²ⁿCₙ⁻¹
• D. ⁿCₙ

12. What is the value of ⁿC₀ - ⁿC₁ + ⁿC₂ - ⁿC₃ + ... + (-1)ⁿ ⁿCₙ?

• A. 0
• B. 1
• C. 2ⁿ
• D. -1

13. In the expansion of (a - b)ⁿ, the signs of the terms are:

• A. Alternately positive and negative
• B. All positive
• C. All negative
• D. Dependent on n only

14. Number of terms in the expansion of (x + a)ⁿ + (x - a)ⁿ when n is even is:

• A. n/2 + 1
• B. n/2
• C. (n + 1)/2
• D. n + 1

15. Number of terms in the expansion of (x + a)ⁿ - (x - a)ⁿ when n is even is:

• A. n/2
• B. n/2 + 1
• C. (n + 1)/2
• D. n

16. The coefficient of a²b³ in the expansion of (a + b)⁵ is:

• A. 10
• B. 5
• C. 20
• D. 1

17. Find the coefficient of x⁶ y³ in the expansion of (x + 2y)⁹:

• A. 672
• B. 84
• C. 504
• D. 252

18. The number of terms in the expansion of (a + b + c)ⁿ is:

• A. (n + 1)(n + 2) / 2
• B. n + 1
• C. n + 2
• D. (n + 1)²

19. The number of terms in (x + y + z)¹⁰ is:

• A. 66
• B. 55
• C. 11
• D. 121

20. The 13th term in the expansion of (9x - 1/(3√x))¹⁸ is:

• A. 18564
• B. 18564 x
• C. 18564 / x
• D. 18564 x²

21. Expanding (101)⁴ using Binomial Theorem gives:

• A. 104060401
• B. 104060400
• C. 104040601
• D. 104060101

22. Which is larger: (1.1)¹⁰⁰⁰⁰ or 1000?

• A. (1.1)¹⁰⁰⁰⁰
• B. 1000
• C. Both are equal
• D. Cannot be determined

23. In Pascal's Triangle, each row starts and ends with:

• A. 1
• B. 0
• C. n
• D. 2

24. The middle term in the expansion of (x/3 + 9y)¹⁰ is:

• A. 61236 x⁵ y⁵
• B. 252 x⁵ y⁵
• C. 61236 x⁶ y⁴
• D. 61236 x⁴ y⁶

25. In the binomial expansion of (a + b)ⁿ, the degree of each term is always:

• A. n
• B. n - 1
• C. n + 1
• D. Variable

26. If the coefficient of x⁷ and x⁸ are equal in (2 + x/3)ⁿ, then n is:

• A. 55
• B. 50
• C. 45
• D. 60

27. The first term in the binomial expansion of (x + a)ⁿ is:

• A. xⁿ
• B. aⁿ
• C. n xⁿ⁻¹
• D. ⁿC₁ xⁿ

28. The last term in the binomial expansion of (x + a)ⁿ is:

• A. aⁿ
• B. xⁿ
• C. n aⁿ⁻¹
• D. ⁿC₁ aⁿ

29. The coefficient of xⁿ⁻¹ in the expansion of (x - 1)(x - 2)(x - 3)...(x - n) is:

• A. -n(n + 1) / 2
• B. n(n + 1) / 2
• C. -n
• D. (-1)ⁿ n!

30. Find the coefficient of x⁴ in the expansion of (1 + x)⁸:

• A. 70
• B. 56
• C. 28
• D. 35