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Without expanding show that |b^2c^2 bc...

Without expanding show that `|b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+b|=0` .

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Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

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Without expanding or evaluating show that |[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0

Without expanding show that, if s= a +b +c, then 2s is a factor of |{:( s+c, a,b),(c, s+a, b),(c,a,s+b):}|

Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|=2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Without expanding show that: =|[cose c^2theta,cot^2theta,1],[cot^2th...

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  2. Find the value of the determinant =|(2, 3, 4) ,(5, 6, 8),( 6x,9x, 12...

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  3. Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+...

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  4. Without expanding evaluate the determinant |sinalphacosalphasin(alp...

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  5. Without expanding evaluate the determinant |(a^x+a^-x)^2(a^x-a^-x)^2 1...

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  6. If a ,\ b ,\ c are in A.P., find the value of |(2y+4, 5y+7, 8y+a),(3...

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  7. Without expanding evaluate the determinant =|(265, 240, 219), (240, ...

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  8. If D1=|1 1 1 x^2 y^2 z^2 x y z| and D2=|1 1 1y z z xx y x y z| , with...

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  9. Let D=|Ax x^2 1 By y^2 1 Cz z^2 1| and D1=|A B C x y z yz zx xy| ...

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  10. If A=|[a, b, c],[ x, y, z],[ p, q, r]| and B=|[q, -b, y],[ -p, a, -x...

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  11. If A is a skew-symmetric matrix of odd order n , then |A|=O .

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  12. Prove that: |[0,a,-b],[-a,0,-c],[ b, c,0]|=0 .

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  13. Without expanding or evaluating show that |(0,b-a, c-a),( a-b,0,c-b)...

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  14. Without expanding, prove that |(a+b x, c+dx, p+q x), (a x+b, c x+d, ...

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  15. Prove that: |-a^2 ab ac ba -b^2 bc ...

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  16. Prove that: |(1, 1, 1),( 1, 1+x,1) ,(1, 1, 1+y)|=x y .

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  17. Evaluate: |(1,a ,a^2), (1,b,b^2) ,(1,c,c^2)| .

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  18. Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z...

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  19. Prove that: |[alpha,beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,g...

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  20. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

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