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If A=[{:(3,1),(-1,2):}] then prove that ...

If `A=[{:(3,1),(-1,2):}]` then prove that `A^(2)-5A+7I=O`

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SHARAM PUBLICATION-MODEL QUESTION PAPER -1-EXERCISE
  1. Solve cos(tan^-1x) = sin(cot^-1 (3/4))

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  2. Write the solution of the following LPP Maximise Z=x+y Subject to ...

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  3. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  4. If A=[{:(-1,3,5),(1,-3,-5),(-1,3,5):}], then find A^(3)-A^(2).

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

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  6. Find the inverse of the matrix [{:(2,5),(1,3):}]

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  7. Find the value of [[1,a,b+a],[1,b,c+a],[1,c,a+b]].

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  8. Find (dy)/(dx), when y^(x)=x^(siny)

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  9. Show that f(x)=|x| is continuous at x=0 but not deferentiable at x=0.

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  10. If sin y=(2t)/(1 + t^2),cos x= 1/(sqrt(1+t^2)) then show that (dy)/(dx...

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  11. Find the interval where the function f(x) = sin x + cos x, x in [0, 2p...

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  12. Show that no two normals to a parabola are parallel.

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  13. int(cos2x-cos2alpha)/(cosx-cosalpha)dx

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  14. Integrate: int0^(3/2)[x^2]dx

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  15. Solve : (x+y)dy +(x-y)dx = 0.

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  16. Solve: (x^2-1)dy/dx+2xy=1

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  17. If the sum of two unit vectors is a unit vectors find the magnitude of...

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  18. If veca, vecb and vecc are mutually perpendicular, show that [veca.(ve...

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  19. Find the direction cosines of the line (x + 2)/2 = (2y-7)/6 = (5 -z)/...

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  20. Find the equation of a plane biscting the line segment joining (-1,4,3...

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