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

`|(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=`

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

Verified by Experts

The correct Answer is:
B
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If a , b, c are real numbers such that a-b=1, b-c=3 , then the number of matrices of the form A[(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))] such that |A|=-12 , is

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

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)):}

If Delta_(1)=|{:(a_(1)^(2)+b_(1)+c_(1),a_(1)a_(2)|b_(2)|c_(2),a_(1)a_(3)+b_(3)+c_(3)),(b_(1)b_(2)+c_(1),b_(2)^(2)+c_(2),b_(2)b_(3)+c_(3)),(c_(1)c_(3),c_(2)c_(3),c_(3)^(2)):}|" and " Delta_(2)=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| , then find the value of (Delta_(1))/(Delta_(2)) .

IF Delta_1=|{:(a_1^2+b_1+c_1,a_1a_2+b_2+c_2,a_1a_3+b_3+c_3),(b_1b_2+c_1,b_2^2+c_2,b_2b_3+c_1),(c_3c_1,c_3c_2,c_3^2):}|,Delta_2|{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}| then find the value of (Delta_1)/(Delta_2)

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

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

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

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  4. |(1,1,1),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

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  5. |(1,1,1),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3))|=

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

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

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

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

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

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

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

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

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

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  17. |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|=

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  18. |(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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  19. 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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  20. 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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