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Prove that:|[1, a ,a^2],[a^2, 1 ,a],[a, ...

Prove that:`|[1, a ,a^2],[a^2, 1 ,a],[a, a^2, 1]|` is a perfect square.

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SHARAM PUBLICATION-MODEL QUESTION PAPER 14-EXERCISE
  1. Find x, so that [{:(1,x,1):}][{:(1,3,2),(0,5,1),(0,3,2):}][{:(1),(1),(...

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  2. If A =[[1,2,2],[2,1,2],[2,2,1]] then prove that A^2-4A-5I=0.

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  3. Prove that:|[1, a ,a^2],[a^2, 1 ,a],[a, a^2, 1]| is a perfect square.

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  4. Solve for x, |{:(15-2x,11,10),(11-3x,17,16),(7-x,14,13):}|=0

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  5. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  6. If x=a(cost+tsint) and y=a(sint-tcost), then find (d^(2)y)/(dx^(2)) at...

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  7. Find the equation of tangent to the curve x^2 + 3y = 3 which is parall...

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  8. Find the extreme values of the function y = X + 1/x.

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  9. int0^1(x^5(4-x^2))/sqrt(1-x^2)dx

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  10. Integrate the following intsec^2sqrtx/sqrtxdx

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  11. intx^2tan^-1xdx

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  12. Solve (dy)/(dx)+y=e^(-x)

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  13. Using vector method find the area of the triangle with vertices (1, 0,...

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  14. Find [veca vecb vecc] when veca= hati -2hatj + 3hatk, vecb=2hati+ hatj...

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  15. Find the image of the point (2,-1,3) in the plane 3x-2y+z-9=0

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  16. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

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  17. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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  18. Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a...

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  19. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

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  20. Solve the following LPP graphically Maximize z=5x1+3x2 Subject to 3x1...

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