Q65.If (30C1)2 + 2(30C2)2 + 3(30C3)2. . . . . . . . . . 30(30C30)2 = (30!)2α60! , then (1) 30 (2) 60 (3) 15 (4) 10
What This Question Tests
This question tests advanced summation identities involving squares of binomial coefficients, requiring a non-trivial manipulation to arrive at the solution.
Concepts Tested
Formulas Used
k * (nCk)² = n * (n-1)Ck-1 * nCk
Σ (nCk)² = 2nCn
(nCk) = n! / (k! * (n-k)!)
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📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- Properties of binomial coefficients
- Year
- 2023
- Shift
- 24 Jan Shift 2
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
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