Binomial Theorem — Class 11 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Binomial Theorem" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Binomial Theorem" — 8 important questions with detailed answers for CBSE board exa…
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Key Questions Covered:
- Find the binomial expansion of (2x + 3)⁴.
- Find the 5th term in the expansion of (x - 2y)⁸.
- Find the middle term(s) in the expansion of (p + q)¹⁰.
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the binomial expansion of (2x + 3)⁴. | ✓ Solved |
| Find the 5th term in the expansion of (x - 2y)⁸. | ✓ Solved |
| Find the middle term(s) in the expansion of (p + q)¹⁰. | ✓ Solved |
Showing 3 of 8 questions
Q1: Find the binomial expansion of (2x + 3)⁴.
Step 1: Identify the binomial theorem formula.
(a + b)ⁿ = Σ(k=0 to n) [nCk × aⁿ⁻ᵏ × bᵏ]
= nC0 a^n + nC1 a^(n-1) b + nC2 a^(n-2) b² + ... + nCn b^n
Step 2: Identify parameters.
a = 2x, b = 3, n = 4
Step 3: Calculate binomial coefficients.
4C0 = 1
4C1 = 4
4C2 = 6
4C3 = 4
4C4 = 1
Step 4: Expand term...
Q2: Find the 5th term in the expansion of (x - 2y)⁸.
Step 1: Recall the general term formula in binomial expansion.
Tr+1 = nCr × a^(n-r) × b^r
where the (r+1)th term is given, with r starting from 0.
Step 2: Identify parameters for the 5th term.
We need T5, which means r + 1 = 5, so r = 4.
a = x, b = -2y, n = 8
Step 3: Calculate the binomial coeffic...
Q3: Find the middle term(s) in the expansion of (p + q)¹⁰.
Step 1: Determine the total number of terms.
For (a + b)ⁿ, the total number of terms = n + 1
For (p + q)¹⁰, total terms = 10 + 1 = 11 terms
Step 2: Find the middle term(s).
Since there are 11 terms (odd), there is exactly one middle term.
The middle term is the (11 + 1)/2 = 6th term.
Step 3: Ident...
Showing 3 of 8 questions. Visit the full page for complete solutions.