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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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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]

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  2. Let f be a real function. Prove that f(x)-f(-x) is an odd function and...

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

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  4. Express as a sum of a symmetric and a skew symmetric matrix: [[4,-3],[...

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  5. If ABC is a triangle, then prove that abs[[tanA,1,1],[1,tanB,1],[1,1,...

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  6. Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,...

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  7. Find the inverse of the matrix [[1,2],[3,4]]

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  8. Find the number of critical points of f(x)=frac[abs(x-1)][x^2]

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  9. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  10. Find the equation of the tangent to the curve x = y^2-1 at the point w...

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  11. If y=sin^(-1)(x^3), then find that dy/dx

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  12. If y=e^(x^(e^(x^(e^x)))), then find dy/dx.

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  13. Evaluate int0^2abs(x^2+2x-3)dx

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  14. Find the area of the region bounded by the curve y=sin^(3)x and the st...

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  15. intdx/(1+tanx)

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  16. Evaluate inte^(tan-1)x((1+x+x^2)/(1+x^2))dx.

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  17. Find the solution of the following differential equations: (4x+6y+5)dx...

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  18. Let veca,vecb,vecc be three vectors such that veca+vecb+vecc=vec0 and ...

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

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  20. Find the co-ordinates of the foot of the perpendicular from the point ...

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