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If Delta(r )=|(r,2r-1, 3r-2),((n)/(2), n...

If `Delta_(r )=|(r,2r-1, 3r-2),((n)/(2), n-1, a),((1)/(2)n(n-1), (n-1)^(2), (1)/(2)(n-1)(3n-4))|`, then the value of `sum_(r=1)^(n-1)Delta_(r )`

A

depends only on a

B

depends only on a

C

depends both on a and n

D

is independent of both a and n

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The correct Answer is:
D
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AAKASH SERIES-APPENDICES (REVISION EXERCISE)-DETERMINANTS
  1. If A(K)=[(K,K-1),(K-1,K)] then |A(1)|+|A(2)|+...+|A(2011)|=

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  2. If f(x)=|(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x)| then f(root(3)(2))=

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  3. If f(x)=|(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)...

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  4. |(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b)|=

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  5. |(sin theta, cos theta, sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2p...

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  6. |(3, a+b+c, a^(2)+b^(2)+c^(2)),(a+b+c, a^(2)+b^(2)+c^(2), a^(3)+b^(3)+...

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  7. |(1,a,a^(2)+bc),(1,b,b^(2)+ac),(1,c,c^(2)+ab)|=k(a-b),(b-c), (c-a) the...

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  8. If A=[(0, 1,0),(0, 0,1),(-c,-b,-a)] then A^(3)+aA^(2)+bA+cI is

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  9. If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...

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  10. If A=((1,2,1),(-1,0,3),(2,-1,1)) then characteristic equation is given...

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  11. Let A be a 2xx2 matrix with non-zero entries and let A^(2)=I, where I...

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  12. If alpha, beta ne 0 and f(n)=a^(n)+beta^(n) and |(3,1+f(1),1+f(2)),(1+...

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  13. If B is a 3xx3 matrix such that B^(2)=0, then det. [(I+B)^(50)-50B]...

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  14. If |(a^(2), b^(2), c^(2)),((a+lambda)^(2), (b+lambda)^(2), (c+lambda)^...

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  15. If f(theta)=|(1, cos theta, 1),(-sin theta, 1,-cos theta),(-1,sin thet...

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  16. If Delta(r )=|(r,2r-1, 3r-2),((n)/(2), n-1, a),((1)/(2)n(n-1), (n-1)^(...

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  17. If a, b, c are sides of a scalene triangle, then the value of |(a,b,c...

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  18. Let S={((a(11), a(12)),(a(21), a(22))):a(ij) in {0,1,2},a(11)=a(22)} ...

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  19. If A is an 3xx3 non-singular matrix such that AA' = A'A and B=A^(-1)A'...

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  20. The least value of the product xyz for which the determinant |(x,1,1)...

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