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If the system of linear equations  x+2ay+az=0,  x+3by+bz=0,x+4cy+cz=0 has a non-zero solution, then a,b,c 

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a
are in G.P
b
are in H.P
c
satisfy a+2b+3c=0
d
are in A.P

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detailed solution

Correct option is B

Given system of equations has a non-zero solution 1    2a    a1    3b    b1    4c    cC2−2C1⇒10a1bb12cc=0⇒2ac=ab+bc⇒b=2aca+c⇒a,b,c are in H.P


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If the system of equations, ax+by+cz=0 , bx+cy+az=0  and cx+ay+bz=0  have non trivial solution, then


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