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

`|(1,1,1),(a,b,c),(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)`

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The correct Answer is:
A
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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)|=

If Delta_(1)=|(1,a,bc),(1,b,ca),(1,c,ab)|,Delta_(2)=|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))| then

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

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

Evaluate Delta = {:[ (1,a,bc),( 1,b,ca),(1,c,ab)]:}

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

Without expanding the determinant , prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

If a,b,c are the p^(th),q^(th),r^(th) terms in H.P. then |{:(bc,p,1),(ca,q,1),(ab,r,1):}|=

Without expanding the determinant, prove that (i) |{:(a,a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=|{:(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3)):}| (ii) |{:(ax,by,cz),(x^(2),y^(2),z^(2)),(1,1,1):}|=|{:(a,b,c),(x,y,z),(yz,zx,xy):}| (iii) |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|

DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1B MCQ (DETERMINANTS)
  1. Prove that |{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a...

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

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  3. |(1,1,1),(a,b,c),(bc,ca,ab)|=

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  4. |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=

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  5. |(1,1,1),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

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  6. |(1,1,1),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3))|=

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

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

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

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

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

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

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

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

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

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  18. |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|=

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  19. |(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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  20. 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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