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If Dr= |[2^r-1,2 . 3^(r-1), 4 . 5^(r-1)]...

If `D_r= |[2^r-1,2 . 3^(r-1), 4 . 5^(r-1)],[alpha ,beta, gamma],[2^(n-1),3^(n-1),5^(n-1)]|` then `sum_(r=1)^n D_r=`

A

0

B

`alpha beta gamma`

C

`alpha+beta+gamma`

D

`alpha . 2^n+beta . 3^n+gamma . 4^n`

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The correct Answer is:
A
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HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
  1. The number of 3xx3 non - singular matrices , with four entries as 1 ...

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  2. If x, y, z being positive |[1, log x y,log x z],[log y x,1,log y z],[l...

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  3. If Dr= |[2^r-1,2 . 3^(r-1), 4 . 5^(r-1)],[alpha ,beta, gamma],[2^(n-1)...

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  4. If a, b, c are in G.P then the value of the determinant Delta= [[a, b,...

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  5. The determinant: |(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0 if :

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  6. The parameter on which the value of the determinant |[1, a, a^2],[...

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  7. Let omega=-(1)/(2)+i (sqrt(3))/(2), then the value of [[1,1,1],[1,-...

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  8. l,m,n are the pth , qth rth terms of a G.P. (all positive) , then |(lo...

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  9. If a gt 0 and discriminant of ax^2+2bx+c is negative, then : Delta=|(...

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  10. If 1, omega, omega^(2) are the cube roots of unity, then [[1, omega^...

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  11. The determinant : |(cos(alpha+beta),-sin(alpha+beta),cos2beta),(sinalp...

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  12. If a(1), a(2), a(3)"….." are in G.P. , then the value of Delta= |{:(lo...

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  13. If D= |[1,1,1],[1,1+x, 1],[1,1,1+y]| for x ne 0, y ne 0 then D is

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  14. If alpha=omega,b=omega^2,c=i, then the value of : |(a,a+2b,a+2b+3c)...

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  15. The value of Delta=|(1^2,2^2,3^2),(2^2,3^2,4^2),(3^2,4^2,5^2)| is :

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  16. If a=1+2+4+ . . . . upto n terms b=1+3+9+. . . . upto n terms c=1+5...

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  17. If |[x-2,2x-3,3x-4],[x-4,2x-9,3 x-16],[x-8,2x-27,3 x-64]|=0 then x=

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  18. If a, b, c, d, e and f are in G.P, then the value of |[a^2,d^2,x],[b^...

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  19. The value of the determinant : Delta=|(a^2,a,1),(cosnx,cos(n+1)x,co...

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  20. If a, b, c are all different from zero and Delta= |[1+a,1,1],[1,1+b,1]...

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