Q83.For k ∈N, let α(α+1)(α+2)…….(α+20) 2 1 = ∑20K=0 α+kAk , where α > 0. Then the value of 100( A14+A15A13 ) is equal to ____________.
What This Question Tests
This problem involves algebraic manipulation using partial fractions to decompose a product into a sum, followed by comparing coefficients to find Ak terms and then evaluating a complex expression. It's a non-trivial application of partial fractions combined with algebraic insight.
Concepts Tested
Formulas Used
Partial fraction decomposition
Binomial theorem for negative integers
📚 NCERT Sections This Tests
3.26 — The Decomposition Of Hydrocarbon Follows The Equation
Chemistry Class 11 · Chapter 3
3.26 The decomposition of hydrocarbon follows the equation k = (4.5 × 1011s–1) e-28000K/T Calculate Ea. 87 Chemical Kinetics Reprint 2025-26
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
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- Partial fractions and Binomial expansion
- Year
- 2021
- Shift
- 20 Jul Shift 2
- Q Number
- Q83
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
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