Verified Solution • 2025–26 Session moderate

QJEEM21Maa98d: JEE Main 2021 Mathematics - Class 12 JEEM21Maa98d Solution: Two fair dice are thrown. The numbers on them are taken as and…

Two fair dice are thrown. The numbers on them are taken as λ\lambda and μ\mu , and a system of linear equations

x + y + z = 5

x + 2y + 3z = μ\mu

x + 3y + λ\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 :

Multiple Choice Options

  • A p=16p = {1 \over 6} and q=136q = {1 \over 36}
  • B p=56p = {5 \over 6} and q=536q = {5 \over 36}
  • C p=56p = {5 \over 6} and q=136q = {1 \over 36}
  • D p=16p = {1 \over 6} and q=536q = {5 \over 36}

Step-by-Step Verified Solution

D≠0⇒|11112313λ|≠0⇒λ≠5

For no solution D = 0 ⇒\Rightarrow λ\lambda = 5

D1=|11512μ131|≠0⇒μ≠3

p=56p = {5 \over 6}

q=16×56=536q = {1 \over 6} \times {5 \over 6} = {5 \over {36}}

Option (b).

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