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If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2...

If `A_r=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|,` the value of `sum_(r=1)^n A_r` is (A) `n` (B) `2n` (C) `-2n` (D) `n^2`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
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  2. If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0...

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  3. If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum(...

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  4. If the determinant |[a,b,2aalpha+3b],[b,c,2balpha+3c],[2aalpha+3b,2bal...

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  7. Let |x^2+3xx-1x+3x+1-2xx-4x-3x+4 3x|=a x^4+b x^3+c x^2+e be an identi...

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  8. If Dk=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum(k=1)^...

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  9. If Delta1=|(1, 1 ,1),(a, b, c ),(a^2,b^2,c^2)|,Delta2=|(1,b c, a),(1,c...

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  10. The value of the determinant |a^2a1cosn xcos(n+1)xcos(n+2)xsinn xsin(n...

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  11. Evaluate: (i) |(5 ,4),(-2, 3)| (ii) |(sintheta,costheta),(-costheta,si...

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  13. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by expanding it along th...

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  14. Evaluate the determinant D=|[2 ,3,-2],[ 1, 2 ,3],[-2, 1,-3]| by expa...

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  15. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]|

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  16. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by method.

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  17. For what value of x the matrix A=[[1,-2,3],[1,2,1],[x,2,-3]] is singul...

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  18. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 ...

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  19. If A=[1 3 2 1] , find the determinant of the matrix A^2-2A .

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  20. If A=[1 2 4 2] , then show that |2A|=4|A| .

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