JEE Mains 25-Jan-2023 Shift 1 Solved Paper

Section: Mathematics

Question : 74 of 90

Marks: +1, -0

Let S1 and S2 be respectively the sets of all a∈R−{0} for which the system of linear equations
‌ax+2ay−3az=1
‌(2a+1)x+(2a+3)y+(a+1)z=2
‌(3a+5)x+(a+5)y+(a+2)z=3
has unique solution and infinitely many solutions. Then

[25-Jan-2023 Shift 1]

n(S1)=2 and S2 is an infinite set
S1 is an infinite set an n(S2)=2
S1=Φ and S2=ℝ−{0}
S1=ℝ−{0} and S2=Φ

Validate

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a	2a	−3a
2a+1	2a+3	a+1
3a+5	a+5	a+2