JEE Main 2021 — Probability Question with Solution
From: JEE Main 2021 (Online) 25th February Morning Shift
Question
The coefficients a, b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
ax2 + bx + c = 0
a, b, c {1,2,3,4,5,6}
n(s) = 6 × 6 × 6 = 216
For equal roots, D = 0 b2 = 4ac
ac =
Favourable case :
If b = 2, ac = 1 a = 1, c = 1
If b = 4, ac = 4 :
a = 1, c = 4
a = 4, c = 1
a = 2, c = 2
If b = 6, ac = 9 a = 3, c = 3
Favorable cases = 5
Required probability =
a, b, c {1,2,3,4,5,6}
n(s) = 6 × 6 × 6 = 216
For equal roots, D = 0 b2 = 4ac
ac =
Favourable case :
If b = 2, ac = 1 a = 1, c = 1
If b = 4, ac = 4 :
a = 1, c = 4
a = 4, c = 1
a = 2, c = 2
If b = 6, ac = 9 a = 3, c = 3
Favorable cases = 5
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.