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MathsHardAssertion Reasoning2010 · Unknown

Q89.Four numbers are chosen at random (without replacement) from the set {1, 2, 3, … . , 20} . Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is 1 . Statement-2: If the 85 four chosen numbers from an AP, then the set of all possible values of common difference is {±1, ±2, ±3, ±4, ±5}. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is false Statement-2 is not the correct explanation for Statement-1 (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

What This Question Tests

This question is challenging as it requires calculating the number of ways to choose four numbers from a set that form an arithmetic progression, which involves systematic enumeration of all possible APs, and comparing it to the total number of ways to choose four numbers.

Concepts Tested

CombinationsArithmetic Progression (AP)Calculating probability

Formulas Used

C(n, k) = n! / (k!(n-k)!)

Probability = (Favorable outcomes) / (Total outcomes)

📚 NCERT Sections This Tests

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