Q52.Let f : R →R be such that for all x ∈R(21+x + 21−x), f(x) and (3x + 3−x) are in A.P., then the minimum value of f(x) is (1) 2 (2) 3 (3) 0 (4) 4
What This Question Tests
This question involves using the definition of an arithmetic progression to express f(x) in terms of other functions, then applying the AM-GM inequality to find its minimum value.
Concepts Tested
Formulas Used
If a,b,c are in AP, then 2b = a+c
AM ≥ GM for positive numbers
📚 NCERT Sections This Tests
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.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
3.18 — For A First Order Reaction, Show That Time Required For 99% Completion
Chemistry Class 11 · Chapter 3
3.18 For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Arithmetic Progression and AM-GM inequality
- Year
- 2020
- Shift
- 08 Jan Shift 1
- Q Number
- Q52
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
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