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If |[p, b, c],[ a, q, c],[ a, b, r]|=0, ...

If `|[p, b, c],[ a, q, c],[ a, b, r]|=0,` find the value of `p/(p-a)+q/(q-b)+r/(r-c),p!=a ,q!=b ,r!=c dot`

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To solve the problem, we start with the given determinant condition: \[ |[p, b, c], [a, q, c], [a, b, r]| = 0 \] This means that the rows of the determinant are linearly dependent. We will manipulate the determinant to find the required expression: ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
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  2. Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=...

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  3. If |[p, b, c],[ a, q, c],[ a, b, r]|=0, find the value of p/(p-a)+q/(...

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  4. Find the equation of the line joining A(1,3)a n dB(0,0) using determin...

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  6. If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f...

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  7. Prove the identities: |[a^2,a^2-(b-c)^2,b c], [b^2,b^2-(c-a)^2,c a],[...

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  8. Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x,...

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  9. Without expanding, show that the value of each of the determinants is ...

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  10. Without expanding, show that the value of the determinant is zero: ...

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  11. Without expanding, show that the value of each of the determinants is ...

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  12. Without expanding, show that the value of each of the determinants is ...

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  13. Using the properties of determinants, prove that following |(a-b,-c^2,...

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  14. Prove the identities: |[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+...

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  15. For any triangleABC, the value of determinant |[sin^2A,cotA,1],[sin^2B...

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  16. Without expanding, show that the value of each of the determinants is ...

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  17. If x , y in R , then the determinant =|(cosx,-sinx,1),(sinx,cosx,1),(...

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  18. The maximum value of Delta=|(1,1,1),(1,1+sintheta,1),(1+costheta,1,1)...

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  19. Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c...

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  20. Without expanding, show that the value of each of the determinants is ...

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