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If a="cos"(4pi)/3+I"sin"(4pi)/3,then |(1...

If `a="cos"(4pi)/3+I"sin"(4pi)/3`,then `|(1,1,1),(1,a,a^(2)),(1,a^(2),a)|` is

A

purely real

B

purely imaginary

C

a complex number

D

none

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1B MCQ (DETERMINANTS)
  1. Which of the following is not tre? A is a square matrix. Then

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  2. A and B are square matrices of order 3xx3, A is on orthogonal matrix a...

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  3. If a="cos"(4pi)/3+I"sin"(4pi)/3,then |(1,1,1),(1,a,a^(2)),(1,a^(2),a)|...

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  4. If x,y,z are all positive and are the pth, qth and rth terms of a geom...

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  5. If a(1),a(2)…… form G.P and a(i)gt0,AAige1, then |(loga(m),loga(m+1),l...

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  6. If a(1),a(2),…………..,a(n), ……… are in G.P and a(i)gt0 for each i then t...

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  7. If a,b,c are pth, qth rth terms respectivelyy of a G.P then |(loga, p,...

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  8. If a,b, c are pth, qt, rth terms of a H.P then |(bc,ca,ab),(p,q,r),(1,...

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  9. If =sin px and y(n) is the nth derivative of y then |(y,y(1),y(2)),(y(...

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  10. If F(alpha)=|(cos alpha, -sin alpha, 0),(sin alpha, cos alpha, 0),(0,0...

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  11. 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))|i...

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  12. Let a,b, c be such that b(a+c)!=0. If |(a,a+1,a-1),(-b,b+1,b-1),(c,c-1...

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  13. 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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  14. |(2bc-a^(2),c^(2),b^(2)),(c^(2),2ca-b^(2),a^(2)),(b^(2),a^(2),2abc-c^(...

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  15. |(0,c,b),(-c,0,a),(b,a,0)|-|(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(a...

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  16. Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(...

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  17. Prove that |{:((1+ax)^(2),(1+ay)^(2),(a+az)^(2)),((1+bx)^(2),(1+by)^(2...

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  18. A factor o |((a-x)^(2),(b-x)^(2),(c-x)^(2)),((a-y)^(2),(b-y)^(2),(c-y)...

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  19. |(cos (alpha+beta),-sin (alpha+beta),cos 2 beta),(sin alpha, cos alpha...

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  20. |(sin alpha, cos alpha, sin (alpha+delta)),(sin beta, cos beta, sin(be...

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