Q80.Let S = {1, 2, 3, … , 2022}. Then the probability, that a randomly chosen number n from the set S such that HCF(n, 2022) = 1, is (1) 128 (2) 166 1011 1011 (3) 127 (4) 112 337 337
What This Question Tests
This problem involves calculating the probability of a number being coprime to a given number, which can be solved using number theory concepts like Euler's totient function or the Principle of Inclusion-Exclusion.
Concepts Tested
Formulas Used
P(E) = n(E)/n(S)
Inclusion-Exclusion Principle for counting coprime numbers
Euler's totient function φ(N) = N * Π(1 - 1/pᵢ)
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
11.6 — The Threshold Frequency For A Certain Metal Is 3.3 × 1014 Hz. If Light
Physics Class 12 · Chapter 11
11.6 The threshold frequency for a certain metal is 3.3 × 1014 Hz. If light of frequency 8.2 × 1014 Hz is incident on the metal, predict the cut- off voltage for the photoelectric emission.
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
- Probability
- Topic
- Probability, Number Theory
- Year
- 2022
- Shift
- 29 Jul Shift 1
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 13: Probability
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