Binomial Expansion
The coefficient of x⁵ in the expansion of (1 + x)¹⁰ is
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Solution
252
- Expansion Rule: In the expansion of (1+x)n, the coefficient of xr is simply the binomial coefficient (rn).
- Identify Values: Here, n=10 and we need the coefficient of x5, so r=5.
- Calculate Coefficient:
- Coefficient =(510)=5!5!10!
- Coefficient =5×4×3×2×110×9×8×7×6=2×3×2×7×3=252.
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About This Question
- Subject
- mathematics
- Chapter
- binomial theorem and its simple applications
- Topic
- binomial expansion
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
252
- Expansion Rule: In the expansion of (1+x)n, the coefficient of xr is simply the binomial coefficient (rn).
- Identify Values: Here, n=10 and we need the coefficient of x5, so r=5.
- Calculate Coefficient:
- Coefficient =(510)=5!5!10!
- Coefficient =5×4×3×2×110×9×8×7×6=2×3×2×7×3=252.
This easy difficulty mathematics question is from the chapter binomial theorem and its simple applications, covering the topic of binomial expansion. It appeared in the 2025 exam.
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