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If p+q+r=0=a+b+c , then the value of the...

If `p+q+r=0=a+b+c ,` then the value of the determinant `|[p a, q b, r c],[ q c ,r a, p b],[ r b, p c, q a]|i s` (a)`0` (b) `p a+q b+r c` (c) `1` (d) none of these

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x, c2+x),(a3+x, b3+x, c3+x)|, s...

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  2. If alpha,beta,gamma are different from 1 and are the roots of a x^3+b ...

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  3. If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],...

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  4. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

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  5. If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...

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  6. Find the value of lambda for which |{:(2a1+b1 , 2a2+b2 , 2a3+b3),(2b1+...

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  7. 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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  8. if a determinant of order 3xx 3 is formed by using the numbers 1 ...

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  9. If z=|[-5, 3+4i,5-7i],[3-4i,6 ,8+7i],[5+7i,8-7i,9]|,t h e nz is (a) p...

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  10. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

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  11. Let omega be the complex number cos((2pi)/3)+isin((2pi)/3). Then the...

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  12. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

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  13. Consider the determinant Delta=|[a1+b1x^2,a1x^2+b1,c1],[a2+b2x^2,a2x^2...

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  14. If a x1^2+b y1^2+c z1^2=a x2 ^2+b y2 ^2+c z2 ^2=a x3 ^2+b y3 ^2+c z3 ^...

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  15. If A , B ,a n dC are the angles of triangle, show that the system of...

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  16. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

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  17. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|[a1,a2,a3],[5, 4,a6...

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  18. Column I, Column II The value of the determinant |x+2x+3x+5x+4x+6x+...

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  19. If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))​is ...

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  20. Prove that =|[a,c,c-a,a+c],[c,b,b-c,b+c],[a-b,b-c,0,a-c],[x,y,z,1+x+y]...

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