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Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][...

Solve `sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]`

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MODERN PUBLICATION-TEST PAPER 5-PROBLEM
  1. A binary operation * is defined on the set X=R-{-1} by x**y=x+y +xy,...

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  2. Let f, g: R rarr R defined by f(x) = |x| + x, g(x) = |x|-x for all x i...

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  3. Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]

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  4. An animal feed company must produce 200kg of a mixture consisting of i...

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  5. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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  6. Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...

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  7. Find the inverse of the following matrices using elementary transforma...

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  8. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

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  9. Express as a sum of a symmetric and a skew symmetric matrix: [[2,-1,3]...

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  10. If y=In(x^2 +y^2),then find dy/dx.

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  11. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

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  12. Find the equation of the normal to the curve y=(logx)^2 at x=frac[1][e...

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  13. Determine the interval in which the function f(x) = x^3-5x^2+3x+97 is ...

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  14. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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

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  16. solve:ydx-xdy=xydx

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  17. int(xe^x)/(1+x^2)dx

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  18. int0^pi(xdx)/(1+sinx)

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  19. Solve : (x + 2y^3)dy/dx = y.

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  20. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

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