JEE Main 2021 — Probability Question with Solution
From: JEE Main 2021 (Online) 26th August Evening Shift
Question
Two fair dice are thrown. The numbers on them are taken as and , and a system of linear equations
x + y + z = 5
x + 2y + 3z =
x + 3y + z = 1
is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :
x + y + z = 5
x + 2y + 3z =
x + 3y + z = 1
is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :
Choose an option
Show full solutionCorrect option: B
Correct answer
B and
Step-by-step explanation
D \ne 0 \Rightarrow \left| {\matrix{
1 & 1 & 1 \cr
1 & 2 & 3 \cr
1 & 3 & \lambda \cr
} } \right| \ne 0 \Rightarrow \lambda \ne 5
For no solution D = 0 = 5
{D_1} = \left| {\matrix{ 1 & 1 & 5 \cr 1 & 2 & \mu \cr 1 & 3 & 1 \cr } } \right| \ne 0 \Rightarrow \mu \ne 3
Option (b).
For no solution D = 0 = 5
{D_1} = \left| {\matrix{ 1 & 1 & 5 \cr 1 & 2 & \mu \cr 1 & 3 & 1 \cr } } \right| \ne 0 \Rightarrow \mu \ne 3
Option (b).
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Probability chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
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.