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Class 11 Mathematics
Chapter 7 Solutions — Binomial Theorem
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Step-by-step NCERT solutions for Binomial Theorem (Chapter 7, NCERT Class 11 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Binomial Theorem textbook chapter.
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What these solutions cover
All 20 questions in Binomial Theorem are solved in the PDF. Here's what's inside, exercise by exercise:
Exercise 7.1
- Expand the expression: (1 – 2x)^5
- Expand the expression: (2/x – x/2)^5
- Expand the expression: (2x – 3)^6
- Expand the expression: (x/3 + 1/x)^5
- Expand the expression: (x + 1/x)^6
- Using binomial theorem, evaluate: (96)^3
- Using binomial theorem, evaluate: (102)^5
- Using binomial theorem, evaluate: (101)^4
- Using binomial theorem, evaluate: (99)^5
- Using Binomial Theorem, indicate which number is larger: (1.1)^10000 or 1000.
- Find (a + b)^4 – (a – b)^4. Hence, evaluate (√3 + √2)^4 – (√3 – √2)^4.
- Find (x + 1)^6 + (x – 1)^6. Hence or otherwise evaluate (√2 + 1)^6 + (√2 – 1)^6.
- Show that 9^(n+1) – 8n – 9 is divisible by 64, whenever n is a positive integer.
- Prove that Σ (r=0 to n) 3^r · C(n,r) = 4^n.
Miscellaneous Exercise
- If a and b are distinct integers, prove that a – b is a factor of a^n – b^n, whenever n is a positive integer. [Hint: write a^n = (a – b + b)^n and expand]
- Evaluate: (√3 + √2)^6 – (√3 – √2)^6.
- Find the value of (a² + √(a²–1))^4 + (a² – √(a²–1))^4.
- Find an approximation of (0.99)^5 using the first three terms of its expansion.
- Expand using Binomial Theorem: (1 + x/2 – 2/x)^4, x ≠ 0.
- Find the expansion of (3x² – 2ax + 3a²)^3 using binomial theorem.
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