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If a,b,and c are the side of a triangle ...

If a,b,and c are the side of a triangle and A,B and C are the angles opposite to a,b,and c respectively, then
`Delta=|{:(a^(2),bsinA,CsinA),(bsinA,1,cosA),(CsinA,cos A,1):}|` is independent of

A

`sin A sin B sin C`

B

abc

C

1

D

0

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. if Delta= |{:(3,,4,,5,,x),(4,,5,,6,,y),(5,,6,,7,,z),(x,,y,,z,,0):}|=0 ...

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  2. If A, B and C are the angles of a triangle and |(1,1,1),(1 + sin A,1...

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  3. If a,b,and c are the side of a triangle and A,B and C are the angles o...

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  4. If [ ] denotes the greatest integer less than or equal to the real num...

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  5. The coefficicent of x in f(x) =|{:(x,1+sinx,cosx),(1, log(1+x),2),(x^2...

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  6. The determinant |(cos C,tan A,0),(sin B,0,-tan A),(0,sin B,cos C)| h...

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  7. Using the factor theorem it is found that a+b , b+ca n dc+a are three ...

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  8. The value of |(a,a^(2) - bc,1),(b,b^(2) - ca,1),(c,c^(2) - ab,1)|, is

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  9. Find the number of real root of the equation |0x-a x-b x+a0x-c x+b x+c...

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  10. The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,...

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  11. The value of the determinant Delta = |((1 - a(1)^(3) b(1)^(3))/(1 - ...

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  12. The determinant Delta = |(b,c,b alpha +c),(c,d,c alpha + d),(b alpha...

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

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  14. If |(1 +ax,1 +bx,1 + bx),(1 +a(1) x,1 +b(1) x,1 + c(1) x),(1 + a(2) x,...

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  15. If abc!=0 then |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| is

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  16. If 1 + (1)/(a) + (1)/(b) + (1)/(c) = 0, then Delta = |(1 +a,1,1),(1,...

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  17. If a, b and c are all different from zero and Delta = |(1 +a,1,1),(1...

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  18. In a Delta ABC, a, b, c are sides and A, B, C are angles opposite to t...

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  19. If |(-12,0,lamda),(0,2,-1),(2,1,15)| = -360, then the value of lamda i...

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  20. If a(i), i=1,2,…..,9 are perfect odd squares, then |{:(a(1),a(2),a(3))...

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