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Chapter 8: Binomial Theorem

NCERT Solutions for CBSE Class 10 Mathematics — 95 solved questions with detailed explanations.

95

Questions

0

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Solved Questions

Q1. The number of terms in (a+b)ⁿ is:

n
n+1
n-1
2n

Difficulty: Easy · Topic: Binomial Expansion

Solution

The expansion of (a+b)ⁿ has n+1 terms: from the term with aⁿ to the term with bⁿ.

Q2. 1C0 =

Difficulty: Easy · Topic: Binomial

Solution

1C0=1.

Q3. 1C1 =

Difficulty: Easy · Topic: Binomial

Solution

1C1=1.

Q4. 2C0 =

Difficulty: Easy · Topic: Binomial

Solution

2C0=1.

Q5. 2C1 =

Difficulty: Easy · Topic: Binomial

Solution

2C1=2.

Q6. 2C2 =

Difficulty: Easy · Topic: Binomial

Solution

2C2=1.

Q7. 3C0 =

Difficulty: Easy · Topic: Binomial

Solution

3C0=1.

Q8. 3C1 =

Difficulty: Easy · Topic: Binomial

Solution

3C1=3.

Q9. 3C2 =

Difficulty: Easy · Topic: Binomial

Solution

3C2=3.

Q10. 3C3 =

Difficulty: Easy · Topic: Binomial

Solution

3C3=1.

Q11. 4C0 =

Difficulty: Easy · Topic: Binomial

Solution

4C0=1.

Q12. 4C1 =

Difficulty: Easy · Topic: Binomial

Solution

4C1=4.

Q13. 4C2 =

Difficulty: Easy · Topic: Binomial

Solution

4C2=6.

Q14. 4C3 =

Difficulty: Easy · Topic: Binomial

Solution

4C3=4.

Q15. 4C4 =

Difficulty: Easy · Topic: Binomial

Solution

4C4=1.

Q16. 5C0 =

Difficulty: Easy · Topic: Binomial

Solution

5C0=1.

Q17. 5C1 =

Difficulty: Easy · Topic: Binomial

Solution

5C1=5.

Q18. 5C2 =

Difficulty: Easy · Topic: Binomial

Solution

5C2=10.

Q19. 5C4 =

Difficulty: Easy · Topic: Binomial

Solution

5C4=5.

Q20. 5C5 =

Difficulty: Easy · Topic: Binomial

Solution

5C5=1.

Q21. 6C0 =

Difficulty: Easy · Topic: Binomial

Solution

6C0=1.

Q22. 6C1 =

Difficulty: Easy · Topic: Binomial

Solution

6C1=6.

Q23. 6C2 =

Difficulty: Easy · Topic: Binomial

Solution

6C2=15.

Q24. 6C5 =

Difficulty: Easy · Topic: Binomial

Solution

6C5=6.

Q25. 6C6 =

Difficulty: Easy · Topic: Binomial

Solution

6C6=1.

Q26. 7C0 =

Difficulty: Easy · Topic: Binomial

Solution

7C0=1.

Q27. 7C1 =

Difficulty: Easy · Topic: Binomial

Solution

7C1=7.

Q28. 7C2 =

Difficulty: Easy · Topic: Binomial

Solution

7C2=21.

Q29. 7C6 =

Difficulty: Easy · Topic: Binomial

Solution

7C6=7.

Q30. 7C7 =

Difficulty: Easy · Topic: Binomial

Solution

7C7=1.

Q31. 8C0 =

Difficulty: Easy · Topic: Binomial

Solution

8C0=1.

Q32. 8C1 =

Difficulty: Easy · Topic: Binomial

Solution

8C1=8.

Q33. 8C2 =

Difficulty: Easy · Topic: Binomial

Solution

8C2=28.

Q34. 8C7 =

Difficulty: Easy · Topic: Binomial

Solution

8C7=8.

Q35. 8C8 =

Difficulty: Easy · Topic: Binomial

Solution

8C8=1.

Q36. 9C0 =

Difficulty: Easy · Topic: Binomial

Solution

9C0=1.

Q37. 9C1 =

Difficulty: Easy · Topic: Binomial

Solution

9C1=9.

Q38. 9C2 =

Difficulty: Easy · Topic: Binomial

Solution

9C2=36.

Q39. 9C8 =

Difficulty: Easy · Topic: Binomial

Solution

9C8=9.

Q40. 9C9 =

Difficulty: Easy · Topic: Binomial

Solution

9C9=1.

Q41. 10C0 =

Difficulty: Easy · Topic: Binomial

Solution

10C0=1.

Q42. 10C1 =

Difficulty: Easy · Topic: Binomial

Solution

10C1=10.

Q43. 10C2 =

Difficulty: Easy · Topic: Binomial

Solution

10C2=45.

Q44. 10C9 =

Difficulty: Easy · Topic: Binomial

Solution

10C9=10.

Q45. 10C10 =

Difficulty: Easy · Topic: Binomial

Solution

10C10=1.

Q46. 11C0 =

Difficulty: Easy · Topic: Binomial

Solution

11C0=1.

Q47. 11C1 =

Difficulty: Easy · Topic: Binomial

Solution

11C1=11.

Q48. 11C2 =

Difficulty: Easy · Topic: Binomial

Solution

11C2=55.

Q49. 11C10 =

Difficulty: Easy · Topic: Binomial

Solution

11C10=11.

Q50. 11C11 =

Difficulty: Easy · Topic: Binomial

Solution

11C11=1.

Q51. 12C0 =

Difficulty: Easy · Topic: Binomial

Solution

12C0=1.

Q52. 12C1 =

Difficulty: Easy · Topic: Binomial

Solution

12C1=12.

Q53. 12C2 =

Difficulty: Easy · Topic: Binomial

Solution

12C2=66.

Q54. 12C11 =

Difficulty: Easy · Topic: Binomial

Solution

12C11=12.

Q55. 12C12 =

Difficulty: Easy · Topic: Binomial

Solution

12C12=1.

Q56. 13C0 =

Difficulty: Easy · Topic: Binomial

Solution

13C0=1.

Q57. 13C1 =

Difficulty: Easy · Topic: Binomial

Solution

13C1=13.

Q58. 13C2 =

Difficulty: Easy · Topic: Binomial

Solution

13C2=78.

Q59. 13C12 =

Difficulty: Easy · Topic: Binomial

Solution

13C12=13.

Q60. 13C13 =

Difficulty: Easy · Topic: Binomial

Solution

13C13=1.

Q61. 14C0 =

Difficulty: Easy · Topic: Binomial

Solution

14C0=1.

Q62. 14C1 =

Difficulty: Easy · Topic: Binomial

Solution

14C1=14.

Q63. 14C2 =

Difficulty: Easy · Topic: Binomial

Solution

14C2=91.

Q64. 14C13 =

Difficulty: Easy · Topic: Binomial

Solution

14C13=14.

Q65. 14C14 =

Difficulty: Easy · Topic: Binomial

Solution

14C14=1.

Q66. The coefficient of x³ in the expansion of (1+x)¹⁰ is:

120
720
10
210

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

¹⁰C₃ = 10!/(3!×7!) = 120.

Q67. The coefficient of x^0 in (1+x)^5 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 5C0 = 1.

Q68. The coefficient of x^1 in (1+x)^5 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 5C1 = 5.

Q69. The coefficient of x^2 in (1+x)^5 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 5C2 = 10.

Q70. The coefficient of x^3 in (1+x)^5 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 5C3 = 10.

Q71. The coefficient of x^0 in (1+x)^6 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 6C0 = 1.

Q72. The coefficient of x^1 in (1+x)^6 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 6C1 = 6.

Q73. The coefficient of x^2 in (1+x)^6 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 6C2 = 15.

Q74. The coefficient of x^3 in (1+x)^6 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 6C3 = 20.

Q75. The coefficient of x^0 in (1+x)^7 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 7C0 = 1.

Q76. The coefficient of x^1 in (1+x)^7 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 7C1 = 7.

Q77. The coefficient of x^2 in (1+x)^7 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 7C2 = 21.

Q78. The coefficient of x^3 in (1+x)^7 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 7C3 = 35.

Q79. The coefficient of x^0 in (1+x)^8 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 8C0 = 1.

Q80. The coefficient of x^1 in (1+x)^8 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 8C1 = 8.

Q81. The coefficient of x^2 in (1+x)^8 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 8C2 = 28.

Q82. The coefficient of x^3 in (1+x)^8 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 8C3 = 56.

Q83. The coefficient of x^0 in (1+x)^10 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 10C0 = 1.

Q84. The coefficient of x^1 in (1+x)^10 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 10C1 = 10.

Q85. The coefficient of x^2 in (1+x)^10 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 10C2 = 45.

Q86. The coefficient of x^3 in (1+x)^10 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 10C3 = 120.

Q87. The coefficient of x^0 in (1+x)^12 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 12C0 = 1.

Q88. The coefficient of x^1 in (1+x)^12 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 12C1 = 12.

Q89. The coefficient of x^2 in (1+x)^12 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 12C2 = 66.

Q90. The coefficient of x^3 in (1+x)^12 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 12C3 = 220.

Q91. The coefficient of x^0 in (1+x)^15 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 15C0 = 1.

Q92. The coefficient of x^1 in (1+x)^15 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 15C1 = 15.

Q93. The coefficient of x^2 in (1+x)^15 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 15C2 = 105.

Q94. The coefficient of x^3 in (1+x)^15 is:

Difficulty: Easy-Medium · Topic: Binomial Coefficients

Solution

Coefficient = 15C3 = 455.

Q95. The middle term in the expansion of (x + 1/x)¹⁰ is:

¹⁰C₅ x⁵
¹⁰C₅
¹⁰C₅ x
252

Difficulty: Medium · Topic: Middle Term

Solution

n=10 (even), middle term is T₆ = ¹⁰C₅ × x⁵ × (1/x)⁵ = ¹⁰C₅ = 252.

Other Chapters in Mathematics

Ch 1: Sets Ch 2: Relations & Functions Ch 3: Trigonometric Functions Ch 4: Principle of Mathematical Induction Ch 5: Complex Numbers Ch 6: Linear Inequalities Ch 7: Permutations & Combinations Ch 9: Sequences & Series Ch 10: Straight Lines Ch 11: Conic Sections Ch 12: Intro to 3D Geometry Ch 13: Limits & Derivatives Ch 14: Mathematical Reasoning Ch 15: Statistics Ch 16: Probability

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