COMEDK · Maths · 7. Binomial Theorem
Number of terms in the binomial expansion of \((x+a)^{53}+(x-a)^{53}\) is
- A 25
- B 26
- C 27
- D \(26.5\)
Answer & Solution
Correct Answer
(C) 27
Step-by-step Solution
Detailed explanation
The expansion of \((x+a)^{n} + (x-a)^{n}\) is given by \(2[^{n}C_{0}x^{n} + ^{n}C_{2}x^{n-2}a^{2} + ^{n}C_{4}x^{n-4}a^{4} + \dots]\). For \(n = 53\), the expansion is \((x+a)^{53} + (x-a)^{53} = 2[^{53}C_{0}x^{53} + ^{53}C_{2}x^{51}a^{2} + \dots + ^{53}C_{52}x^{1}a^{52}]\). The…
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