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Prove that tan^(-1)x+tan^(-1)((2x)/(1-x^...

Prove that `tan^(-1)x+tan^(-1)((2x)/(1-x^(2)))=tan^(-1)((3x-x^(3))/(1-3x^(2)))|x|lt1/(sqrt(3))`

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SUNSTAR PUBLICATION-SUPPLEMENTARY EXAM QUESTION PAPER JULY -2014-PART-C
  1. Solve that the relation R in the set z of intergers given by R={(x,y):...

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  2. Prove that tan^(-1)x+tan^(-1)((2x)/(1-x^(2)))=tan^(-1)((3x-x^(3))/(1-3...

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  3. For any square matrix A with real numbers. Prove that A+A^(1) is a s...

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  4. If x=a(theta-sintheta) and y= a (1+costheta) then prove that (dy)/(dx)...

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  5. Verify Mean value theorem, if f(x)= x^(2)-4x-3 in the interval [a,b] w...

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  6. Find two positive numbers x and y such that x + y = 60 and xy^(3) is m...

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  7. Evaluate : intsin3x cos 4xdx

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  8. Evaluate intx^(2)e^(x)dx

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  9. Determine the area of the region bounded by y^(2)=x and the line x=1, ...

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  10. Form the differential equation of the family of circles having centre...

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  11. If two vectors veca and vecb such that |veca|=2|vecb|=3 and veca.vecb=...

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  12. Find a unit vector perpendicular to each of the vectors ( veca +...

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  13. Find the shortest distance betweeen the line l(1) and l(2) whose vecto...

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  14. A Bag I contain 3 red and 4 black balls. White bag II contains 5 red 6...

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  15. If A=[(1,2,3),(3,-2,1),(4,2,1)] then show that A^3-23A -40 I=0.

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  16. If y=3 cos(log x)+4sin(logx) show that x^(2)y(2)+xy(1)+y=0

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  17. The length x of a rectangle is decreasing at the rate of 5 cm//minute ...

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  18. Find the integral of (1)/(sqrt(x^(2)+a^(2))) with respect to x and hen...

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  19. Find the area of the region enclosed between the circles x^(2)+y^(2)=4...

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  20. Let y(x) be the solution of the differential equaiton : (x log x ) (...

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