JEE Mains · Maths · STD 11 - 7. binomial theoram
If for \(3 \leq r \leq 30\), \(\binom{30}{30-r} + 3\binom{30}{31-r} + 3\binom{30}{32-r} + \binom{30}{33-r} = \binom{m}{r}\), then \(m\) equals:
- A \(31\)
- B \(32\)
- C \(33\)
- D \(34\)
Answer & Solution
Correct Answer
(C) \(33\)
Step-by-step Solution
Detailed explanation
Using the property \(^{n}C_{r} = ^{n}C_{n-r}\), the given expression can be written as: \(^{30}C_{r} + 3 \cdot ^{30}C_{r-1} + 3 \cdot ^{30}C_{r-2} + ^{30}C_{r-3}\) This expression represents the coefficient of \(x^r\) in the expansion of:…
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