Q64.Let Sn = 1 + q + q2 + … . +qn and Tn = 1 + ( q+12 ) ( q+12 ) ( q+12 ) and q ≠1. If 101C1 + 101C2 ⋅S1 + … . +101C101 ⋅S100 = αT100, then α is equal to : (1) 299 (2) 202 (3) 200 (4) 2100
What This Question Tests
This question requires recognizing the sum of a geometric progression, manipulating binomial series, and performing careful algebraic simplification to find the value of alpha.
Concepts Tested
Formulas Used
Sn = (qn+1 - 1)/(q-1)
Σ nCk = 2^n
Σ nCk x^k = (1+x)^n
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- Sums involving binomial coefficients
- Year
- 2019
- Shift
- 11 Jan Shift 2
- Q Number
- Q64
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem; Class 11 Mathematics Ch 9: Sequences and Series
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