Home › Worksheets › CBSE Grade 11 Math › Binomial Theorem Prepared by Mohsim Digital Education
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The expansion of (x + a)ⁿ contains n + 1 terms and its general term T(r+1) is ⁿCr xⁿ⁻ʳ aʳ, so this Class 11 theorem sheet works straight from the binomial skeleton. The key also answers 2ab for a missing middle term and 2ⁿ for the sum of coefficients.
Key Takeaways
(x + a)ⁿ expands to n + 1 terms (Q1).
The general term is ⁿCr xⁿ⁻ʳ aʳ (Q2).
The key records 2ab and the coefficient sum 2ⁿ.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
The number of terms in the expansion of (x + a)ⁿ is
(a) n (b) n + 1 (c) n - 1 (d) 2n
2.
The general term Tr+1 in the expansion of (x + a)ⁿ is
(a) ⁿCr xⁿ⁻ʳ aʳ (b) ⁿCr xʳ aⁿ⁻ʳ (c) ⁿCr xⁿ aʳ (d) ⁿCr xʳ aⁿ
3.
The middle term in the expansion of (a + b)² is
(a) a² (b) 2ab (c) b² (d) ab
4.
The coefficient of x² in the expansion of (1 + x)⁴ is
(a) 4 (b) 6 (c) 12 (d) 8
5.
The sum of all the binomial coefficients in the expansion of (1 + x)ⁿ is
(a) 2ⁿ (b) n (c) 2n (d) n + 1
6.
The term independent of x in the expansion of (x + 1/x)² is
(a) 1 (b) 2 (c) 0 (d) 3
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
Write the number of terms in the expansion of (x + a)ⁿ.
8.
Write the general term Tr+1 in the expansion of (x + a)ⁿ.
9.
Find the coefficient of x² in the expansion of (1 + x)⁵.
10.
Find the middle term in the expansion of (x + y)².
11.
Write the binomial expansion of (1 + x)ⁿ.
12.
Find the sum of all the binomial coefficients in the expansion of (1 + x)ⁿ.
13.
Find the fourth term in the expansion of (x + a)³.
14.
Write the constant term in the expansion of (x + 1/x)².
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.
Expand (1 + x)³ using the binomial theorem.
16.
Find the coefficient of x³ in the expansion of (1 + x)⁵.
17.
Expand (a + b)⁴ using the binomial theorem.
18.
Find the middle term in the expansion of (x + a)⁴.
19.
Using the binomial theorem, find the value of (101)².
20.
Find the term independent of x in the expansion of (x - 1/x)².
Answer Key
1. b) n + 1
2. a) ⁿCr xⁿ⁻ʳ aʳ
3. b) 2ab
4. b) 6
5. a) 2ⁿ
6. b) 2
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
How many terms are in (x + a)ⁿ?
n + 1, option (b) in this worksheet (Q1).
What is the general term T(r+1)?
ⁿCr xⁿ⁻ʳ aʳ, option (a) in this worksheet (Q2).
What is the sum of the coefficients in the binomial expansion?
2ⁿ, from the answer key on this page.