JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 August 2021, Shift 2, Maths Q63

Question 63 of 90 in this shift, Maths question 3 of 30, Section A.

Two fair dice are thrown. The numbers on them are taken as

\lambda

and

\mu

, and a system of linear equations

x+y+z=5

x+2y+3z=\mu

x+3y+\lambda 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 :

(1) $\mathrm{p}=\frac{1}{6}$ and $\mathrm{q}=\frac{1}{36}$
(2) $\mathrm{p}=\frac{5}{6}$ and $\mathrm{q}=\frac{1}{36}$
(3) $\mathrm{p}=\frac{1}{6}$ and $\mathrm{q}=\frac{5}{36}$
(4) $\mathrm{p}=\frac{5}{6}$ and $\mathrm{q}=\frac{5}{36}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Probability in Linear Systems

Same topic in other shifts

All Cramer's Rule questions

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.