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Prove that the determinant Delta =|{...

Prove that the determinant
`Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,,1),(cos 0,,1,,x):}|`
is independent of 0 .

A

x only

B

`theta` only

C

x and `theta` both

D

None ot these

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The correct Answer is:
B
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DISHA PUBLICATION-DETERMINANTS-EXERCISE -1 CONCEPT BUILDER
  1. If |{:(a,b,0),(0,a,b),(b,0,a):}| = 0, (a ne 0 ) then

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  2. If A [{:(1,2),(3,5):}] , then the value of the determinant | A^(2009) ...

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  3. Prove that the determinant Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,...

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  4. If Delta = |{:(1,2,3),(2,3,5),(3,6,12):}|and Delta' = |{:(4,8,15),(3,6...

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  5. If C(ij) is the cofactor of the element a(ij) of the determinant |{:(2...

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  6. The parameter on which the value of the determinant |1a a^2"cos"(p-d)x...

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  7. If a != b != c, are value of x which satisfies the equation |(0,x -a...

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  8. If |{:(x^(2) +x , 3x - 1 , -x + 3),(2x +1 , 2 + x^(2) , x^(3) - 3),(x ...

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  9. Matrix M(r) is defined as M(r) = ({:(r,r-1),(r-1,r):}), r in N. The v...

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  10. If a, b, c are complex numbers, then the determinant Delta = |(0,-b,...

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  11. If in a triangle ABC, |{:(1, sin A ,sin^(2)A),(1,sin B , sin^(2)B),(1,...

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  12. The value of |(.^(10)C(4).^(10)C(5).^(11)C(m)),(.^(11)C(6).^(11)C(7).^...

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  13. If f(x) = |{:(cos^(2)x, cosx.sinx, -sin x),(cos x sinx ,sin^(2)x ,cos ...

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  14. If plambda^(4) + q lambda^(3) + r lambda^(2) + s lambda + t = |{:(b^(...

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  15. If a,b,c are in A.P then the value of |[x+1, x+2, x+a] , [x+2, x+3, x+...

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  16. |[sin^2(13^@),sin^2(77^@),tan135^@],[sin^2(77^@),tan135^@,sin^2(13^@)]...

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  17. The roots of the equations |{:(1+x,3,5),(2,2+x,5),(2,3,x+4):}| = 0 are

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  18. The value of the determinant |((a^x+a^-x)^2, (a^x-a^-x)^2, 1),(b^x+b^-...

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  19. If a, b, c, are in A.P, find value of |a y+4 5y+7 8y+a3y+5 6y+8 9y+b4...

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  20. suppose D= |{:(a(1),,b(1),,c(1)),(a(2),,b(2),,c(2)),(a(3),,b(3),,c(3...

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