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|(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab)|...

`|(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=`

A

`(a-b)(b-c)(c-a)`

B

`(a-b)(b-c)(c-a)(a+b+c)`

C

`(a-b)(b-c)(c-a)abc`

D

`(a-b)(b-c)(c-a)(ab+bc+ca)`

Text Solution

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The correct Answer is:
D
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|(1,1,1),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

Match the following from List - I to List - II {:("List-I","List-II"),((I)|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=,(a)(a-b)(b-c)(c-a)),((II)|{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3)):}|=,(b)(a-b)(b-c)(c-a)abc),((III)|{:(1,1,1),(a,b,c),(a^(3),b^(3),c^(3)):}|=,(c)(a-b)(b-c)(c-a)(a+b+c)):}

|(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|=

|(1,1,1),(a,b,c),(bc,ca,ab)|=

|(b^(2)-ab,b-c,bc-ac),(ab-a^(2),a-b,b^(2)-ab),(bc-ac,c-a,ab-a^(2))|=

If bc+ca+ab=18 , and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=lambda|(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))| the value of lambda is

|((b+c)^(2),a^(2),bc),((c+a)^(2),b^(2),ca),((a+b)^(2),c^(2),ab)|=

|(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=

DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1B MCQ (DETERMINANTS)
  1. |(1,1,1),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

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  2. |(1,1,1),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3))|=

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  3. |(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

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  4. |(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=

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  5. If a,b,c are sides of a triangle and |(a^(2),b^(2),c^(2)),((a+1)^(2),(...

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  6. If A(x)=|(1,1,1),((e^(x)+e^(-x))^(2),(pi^(x)+pi^(-x))^(2),2),((e^(x)-e...

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  7. If a,b,c are sides of a triangle and |(a^(2),b^(2),c^(2)),((a+1)^(2),(...

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  8. |(b^(2)-ab,b-c,bc-ac),(ab-a^(2),a-b,b^(2)-ab),(bc-ac,c-a,ab-a^(2))|=

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  9. |(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2))|=

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  10. |((b+c)^(2),a^(2),bc),((c+a)^(2),b^(2),ca),((a+b)^(2),c^(2),ab)|=

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  11. If A=|(b^(2)c^(2),bc,b+c),(c^(2)a^(2),ca,c+a),(a^(2)b^(2),ab,a+b)| the...

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  12. The determinant Delta=|(a,a+b,a+2b),(a+2b,a,a+b),(a+b,a+2b,a)|=

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  13. If omega is a cube root of unit, then Delta=|(x+1,omega, omega^(2)),(o...

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  14. |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|=

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  15. |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(2))|=0,x!=y!=zimpli...

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  16. If |(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))|=0 and vecto...

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  17. If a,b,c are all different and |(a,a^(3),a^(4)-1),(b,b^(3),b^(4)-1),(c...

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  18. If a,b,c are different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(...

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  19. If a,b,c are all different and |(1+a^(2),1+b^(2),1+c^(2)),(a,b,c),(a^(...

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  20. If p+q+r=0 and |(pa,qb,rc),(qc,ra,pb),(rb,pc,qa)|=k|(a,b,c),(c,a,b),(b...

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