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

`|(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=`

A

`abc (a^(2)+b^(2)+c^(2))`

B

`abc(a+b+c)`

C

`(a+b+c)(a^(2)+b^(2)+c^(2))`

D

`abc (1+(1)/(a)+(1)/(b)+(1)/(c ))`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-APPENDICES (REVISION EXERCISE)-DETERMINANTS
  1. If Delta( r)= |(2r-1, ""^(m)C(r ), 1),(m^(2)-1, 2^(m), m+1), ("sin"^(2...

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  2. If |(1+x,1-x,1-x),(1-x,1+x,1-x),(1-x,1-x,1+x)|=0 then x=

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

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  4. If |(x(1),y(1),1),(x(2),y(2),1),(x(3),y(3),1)|=|(a(1),b(1),1),(a(2),b(...

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  5. If |(a+x, a-x, a-x),(a-x,a+x,a-x),(a-x,a-x,a+x)|=0 then

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  6. Let D(r )=|(a, 2^(r ), 2^(16)-1),(b, 3(4^(r )), 2(4^(16)-1)), (x, 7(8^...

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  7. If f(x)=|(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)x,1+cos^(2)x,4sin2x),(si...

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  8. If A(K)=[(K,K-1),(K-1,K)] then |A(1)|+|A(2)|+...+|A(2011)|=

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  9. If f(x)=|(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x)| then f(root(3)(2))=

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  10. If f(x)=|(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)...

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  11. |(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b)|=

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  12. |(sin theta, cos theta, sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2p...

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  13. |(3, a+b+c, a^(2)+b^(2)+c^(2)),(a+b+c, a^(2)+b^(2)+c^(2), a^(3)+b^(3)+...

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  14. |(1,a,a^(2)+bc),(1,b,b^(2)+ac),(1,c,c^(2)+ab)|=k(a-b),(b-c), (c-a) the...

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  15. If A=[(0, 1,0),(0, 0,1),(-c,-b,-a)] then A^(3)+aA^(2)+bA+cI is

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  16. If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...

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  17. If A=((1,2,1),(-1,0,3),(2,-1,1)) then characteristic equation is given...

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  18. Let A be a 2xx2 matrix with non-zero entries and let A^(2)=I, where I...

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  19. If alpha, beta ne 0 and f(n)=a^(n)+beta^(n) and |(3,1+f(1),1+f(2)),(1+...

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  20. If B is a 3xx3 matrix such that B^(2)=0, then det. [(I+B)^(50)-50B]...

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