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If A=[[costheta,sintheta],[-sintheta,cos...

If `A=[[costheta,sintheta],[-sintheta,costheta]]` , then for any natural number, find the value of `D e t\ (A^n)` .

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Write the value of the determinant |[p ,p+1],[p-1,p]| .

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  2. Write the value of |(x+y,y+z,z+x),(z,x,y),(-3,-3,-3)|

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  3. If A=[[costheta,sintheta],[-sintheta,costheta]] , then for any natural...

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  4. The maximum value of |(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)| is

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  5. If x in N and |[x+3,-2],[-3x,2x]|=8, then find the value of xdot

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  6. If |[x,sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]|=8 , write t...

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  7. If A and B are square matrices of order 2, then det(A+B)=0 is possib...

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  8. Which of the following is not correct? (a)|A|=|A^T| , where A=[a(i j...

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  9. If Delta=|[a(11),a(12),a(13)],[a(21),a(22),a(23)],[a(31),a(32),a(33)]|...

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  10. Which of the following is not correct in a given determinant of A , wh...

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  11. Let |[x,2,x],[x^2,x,6],[x,x,6]|=a x^4+b x^3+c x^2+dx+edot Then, the va...

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

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  13. If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,...

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

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  15. Let |[x^2+3x,x-1,x+3],[x+1,-2x,x-4],[x-3,x+4, 3x]|=a x^4+b x^3+c x^2+e...

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  16. Using the factor theorem it is found that a+b , b+c and c+a are three ...

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  17. If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b], [x^2+a,...

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  18. If the determinant |(a ,b,2aalpha+3b),(b, c,2balpha+3c),(2aalpha+3b,2b...

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  19. If 1.omega, omega^2 are the roots of unity, then Delta=|(1,omega^n,ome...

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  20. If Ar=|(1,r,2^r),(2,n,n^2),(n,(n(n+1))/2 ,2^(n+1))| , then the value o...

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