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 \frac{1}{85}. Statement - 2: If the four chosen numbers form an AP, then the set of all possible values of common difference is (\pm 1, \pm 2, \pm 3, \pm 4, \pm 5). [AIEEE 2010]

Correct Answer is : Statement −1 is true, Statement −2 is false.

Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.

Statement -1 is true, Statement -2 is false.

Statement -1 is false, Statement -2 is true.

Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement - 1.

AIEEE 2010 Solved Paper

Section: Mathematics

Question : 81 of 89

Marks: +1, -0

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 ‌

.
Statement - 2: If the four chosen numbers form an AP, then the set of all possible values of common difference is (±1,±2,±3,±4,±5).

[AIEEE 2010]

Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
Statement −1 is true, Statement −2 is false.
Statement −1 is false, Statement −2 is true.
Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement - 1.

Validate

Common Difference (d)	Possible Sets	No of AP
d=1	(1,2,3,4)(2,3,4,5)(3,4,5,6)(17,18,19,20)	17
d=2	(1,3,5,7)(2,4,6,8)(3,5,7,9)	14
d=3	(1,4,7,10)(2,5,8,11)(3,6,9,12)	11
d=4	(1,5,9,13)(2,6,10,14)(3,7,11,15)	8
d=5	(1,6,11,16)(2,7,12,17)(3,8,13,18)(4,9,14,19)(5,10,15,20)	5
d=6	(1,7,13,19)(2,8,14,20)	2

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