Q83.Let n ∈N and [x] denote the greatest integer less than or equal to x. If the sum of (n + 1) terms of nC0, 3 ⋅nC1, 5 ⋅nC2, 7 ⋅nC3, … is equal to 2100 ⋅101, then 2[ n−12 ] is equal to n is equal to :
What This Question Tests
This question involves evaluating a complex summation of binomial coefficients multiplied by an arithmetic progression, which can be solved using properties of binomial expansions and their derivatives.
Concepts Tested
Formulas Used
Σ nCk * k = n * 2^(n-1)
Σ nCk * (2k+1) = Σ nCk * (2k) + Σ nCk * (1)
Σ nCk = 2^n
📚 NCERT Sections This Tests
8.17 — Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 · Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- Binomial series summation
- Year
- 2021
- Shift
- 25 Jul Shift 2
- Q Number
- Q83
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
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