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UPSC NDA I 2023 Mathematics Solved Paper

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Consider the following for the next two (02) items that follow :
Let ∆(a,b,c,α)=|

a	b	aα+b
b	c	bα+c
aα+b	bα+c	0

|

[NDA I 2023]

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Question : 51

Total: 120

If ∆(a,b,c,α)=0 for every α>0, then which one of the following is correct ?

a,b,c are in AP
a,b,c are in GP
a,2b,c are in AP
a,2b,c are in GP

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