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If `a ,b ,c ,d ,e`, and `f`are in G.P. then the value of `|((a^2),(d^2),x),((b^2),(e^2),y),((c^2),(f^2),z)|` depends on (A) x and y (B) x and z (C) y and z (D) independent of x ,y ,and z

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Show that: |a, b-c,c+b, a+c, b, c-a,a-b,b+a, c|=(a+b+c)(a^2+b^2+c^2)d...

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  2. In triangle A B C , if |1, 1, ,1,cotA/2,cotB/2,cotC/2,tanB/2+tanC/2,ta...

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  3. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

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

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  5. If xi=ai bi c+i,i=1,,23 are three-digit positive integer such that ...

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  6. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

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  7. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

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  8. If p q r!=0 and the system of equation (p+a)x+b y+c z=0, a x+(q+b)y+c...

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  9. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=...

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  10. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-...

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  11. If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c]...

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  12. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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  13. Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)...

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  14. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

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

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  16. If a1,a2,a3,.....an.... are in G.P. then the determinant 'Delta=|[loga...

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  17. Using properties of determinants, prove the following |(a^2,ab,ac),(ab...

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  18. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

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  19. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

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  20. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

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