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Consider the system of linear equations -x+y+2z=0 3x-ay+5z=1 2x-2y-az=7 Let S_1 be the set of all a∈ R for which the system is inconsistent and S_2…

JEE Main 2021 — Mathematics Algebra

2021mcqmedium

Consider the system of linear equations

−x+y+2z=0-x+y+2z=0−x+y+2z=0

3x−ay+5z=13x-ay+5z=13x−ay+5z=1

2x−2y−az=72x-2y-az=72x−2y−az=7

Let S1{S}_{1}S1​ be the set of all a∈Ra\in Ra∈R for which the system is inconsistent and S2{S}_{2}S2​ be the set of all a∈Ra\in Ra∈R for which the system has infinitely many solutions. If n(S1)n({S}_{1})n(S1​) and n(S2)n({S}_{2})n(S2​) denote the number of elements in S1{S}_{1}S1​ and S2{S}_{2}S2​ respectively, then

Official previous-year question

Held on 1 Sept 2021 · Verified 6 Jul 2026.

Options

  1. A

    n(S1)=2,n(S2)=0n({S}_{1})=2,n({S}_{2})=0n(S1​)=2,n(S2​)=0

  2. B

    n(S1)=2,n(S2)=2n({S}_{1})=2,n({S}_{2})=2n(S1​)=2,n(S2​)=2

  3. C

    n(S1)=0,n(S2)=2n({S}_{1})=0,n({S}_{2})=2n(S1​)=0,n(S2​)=2

  4. D

    n(S1)=1,n(S2)=0n({S}_{1})=1,n({S}_{2})=0n(S1​)=1,n(S2​)=0

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