JEE Main 2023MathematicsDeterminantsEasyMCQ

JEE Main 2023 — Determinants Question with Solution

JEE Main 2023 (24 Jan Shift 1)

Question

Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations

x+y+z=12x+Ny+2z=23x+3y+Nz=3

has unique solution is k6, then the sum of value of k and all possible values of N is

Choose an option

Show full solutionCorrect option: C
Correct answer
C20

Step-by-step explanation

Given equations are

x+y+z=12x+Ny+2z=23x+3y+Nz=3

So,

∆=1112N233N

Applying C2↔C2-C1 and C3↔C3-C1

⇒∆=1002N-2030N-3

⇒∆=N-2N-3

For unique solution ∆≠0, so

N≠2,3

Also, N∈1,2,3,4,5,6 and for unique solution N can take values 1,4,5,6.

⇒P(system has unique solution ) =46=k6

So, k=4

Therefore, required sum is

=4+1+4+5+6=20

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About this question

This is a previous-year question from JEE Main 2023, covering the Determinants 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.