JEE Main 2021 — Probability Question with Solution
From: JEE Main 2021 (Online) 20th July Morning Shift
Question
The probability of selecting integers a[ 5, 30] such that x2 + 2(a + 4)x 5a + 64 > 0, for all xR, is :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
D < 0
4(a + 4)2 4(5a + 64) < 0
a2 + 16 + 8a + 5a 64 < 0
a2 + 13a 48 < 0
(a + 16) (a 3) < 0
a (16, 3)
Possible a : {5, 4, ............., 3}
Required probability = =
4(a + 4)2 4(5a + 64) < 0
a2 + 16 + 8a + 5a 64 < 0
a2 + 13a 48 < 0
(a + 16) (a 3) < 0
a (16, 3)
Possible a : {5, 4, ............., 3}
Required probability = =
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This is a previous-year question from JEE Main 2021, covering the Probability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.