If `a ,b ,c`are in G.P. with common ratio `r_1a n dalpha,beta,gamma`are in G.P. with common ratio `r_2`and equations `a x+alphay+z=0,b x+betay+z=0,c x+gammay+z=0`have only zero solution, then which of the following is not true?`a+b+c`b. `a b c`c.`1`d. none of theseA. `r_(1) ne 1`B. `r_(2) ne 1`C. `r_(1) ne r_(2)`D. none of these

If `a ,b ,c`are in G.P. with common ratio `r_1a n dalpha,beta,gamma`ar

1.	If `a ,b ,c`are in G.P. with common ratio `r_1a n dalpha,beta,gamma`are in G.P. with common ratio `r_2`and equations `a x+alphay+z=0,b x+betay+z=0,c x+gammay+z=0`have only zero solution, then which of the following is not true?`a+b+c`b. `a b c`c.`1`d. none of theseA. `r_(1) ne 1`B. `r_(2) ne 1`C. `r_(1) ne r_(2)`D. none of these
Answer» Correct Answer - D As a,b,c are in G.P. with common ration `r_(1) ` and `alpha , beta , gamma` are in G.P having common ratio `r_(2) , a ne 0 , alpha ne 0,b =ar_(1) c=ar_(1)^(2)` `Beta =ar_(2) ,gamma =ar_(2)^(2)` Also the system of equations has only zero (trivial) solution `Delta \|{:(a,,alpha,,1),(b,,beta,,1),(c,,gamma,,1):}\|ne 0` `rArr aalpha \|{:(1,,1,,1),(r_(1),,r_(2),,1),(r_(1)^(2),,r_(2)^ (2),,1):}\| ne 0` `rArr aalpha (r_(1)-1) (r_(2) -1) (r_(1) -r_(2)) ne 0` `rArr r_(1) ne 1 , r_(2) ne 1 " and " r_(1) ne r_(2)`