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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

`x=1/3(a+b+c)`

B

`x=2/3(a+b+c)`

C

`x=a+b+c`

D

none of these

Text Solution

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The correct Answer is:
A
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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. If Delta=|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=k(a-b)(b-c)(c-a) then k...

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  2. If abc!=0 and if |(a,b,c),(b,c,a),(c,a,b)|=0 then (a^(3)+b^(3)+c^(3))/...

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

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  4. Let A=[(5,5 alpha, alpha),(0, alpha, 5 alpha),(0,0,5)] If |A|^(2)=25 t...

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  5. If k gt1, and the determinant of the matrix A^(2), where A=[(k,kalpha,...

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  6. If a!=6,b,c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 then abc

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  7. If a!=6,b,c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 then abc

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  8. If f(x)=|(a,-1,0),(ax,a,-1),(ax^(2),ax,a)| then f(3x)-f(2x)=

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  9. If Delta=|(a,1,1),(1,b,1),(1,1,c)|gt0, then

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  10. If A is a 3xx3 matrix and det(3A)=k(detA) then k=

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  11. If the matrix [(x,4),(2,8)] is singular, then x=

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  12. If the matrix [(x,b,b),(1,1,1),(0,x,a)] is singular, then x=

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  13. If the matrix A=[(8,-6,2),(-6,7,-4),(2,-4,lamda)] is singular one, the...

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  14. If ((1,2,x),(4,-1,7),(2,4,-6)) is a singular matrix, then x=

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  15. If the matrix [(cos theta, sin theta, 0),(sin theta, cos theta, 0),(0,...

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  16. If Delta=|(1, sin theta, 1 ),(-sin theta, 1, sin theta),(-1 , -sin the...

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  17. If |(3x-8,3,3),(3,3x-8,3),(3,3,3x-8)|=0 then x=0

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  18. If |(x,2,7),(5,0 ,2),(3,-4,6)|=-180 then x=

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  19. If one of the roots of |(3,5,x),(7,x,7),(x,5,3)|=0 is -10, then the ot...

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  20. If x!=0 and |(1,x,2x),(1,3x,5x),(1,3,4)|=0 then x=

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