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Prove that : tan^(-1)sqrtx=1/2cos^(-1)...

Prove that :
`tan^(-1)sqrtx=1/2cos^(-1)((1-x)/(1+x)),x in[0,1]`

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KUMAR PRAKASHAN-ANNUAL EXAMINATION :SAMPLE PAPER-PART-B ( SECTION-A)
  1. Prove that : tan^(-1)sqrtx=1/2cos^(-1)((1-x)/(1+x)),x in[0,1]

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  2. Differentiate sqrt((x-3) (x^(2) + 4))/sqrt((3x^(2) + 4x + 5)) w.r.t x.

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  3. find int ((x +1) (x + log x)^2)/(x)dx

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  4. find the area of the region bounded by the two parabolas y= x...

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  5. Find the area bounded by the ellipse (x^2 )/( a^2) +(y^2)/(b^2) ...

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  6. Find the area of the region bounded by curve y= 4x^2 and lines ...

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  7. If a unit vector veca makes angles (pi)/(3) with hati,(pi)/(4) with ha...

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  8. Find the coordinates of the point where the line through the points A ...

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  9. Three cards are drawn successively, without replacement from a pack of...

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  10. Events A and B are such that P(A) =(1)/(2), P(B) =(7)/(12) and "P(not ...

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  11. Prove that : tan^(-1)sqrtx=1/2cos^(-1)((1-x)/(1+x)),x in[0,1]

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  12. Differentiate sqrt((x-3) (x^(2) + 4))/sqrt((3x^(2) + 4x + 5)) w.r.t x.

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  13. find int ((x +1) (x + log x)^2)/(x)dx

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  14. find the area of the region bounded by the two parabolas y=x^2...

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  15. Find the area bounded by the ellipse (x^2 )/( a^2) +(y^2)/(b^2) ...

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  16. Find the area of the region bounded by curve y= 4x^2 ' and st. l...

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  17. If a unit vector veca makes angles (pi)/(3) with hati,(pi)/(4) with ha...

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  18. Find the coordinates of the point where the line through the points A ...

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  19. Three cards are drawn successively, without replacement from a pack of...

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  20. Events A and B are such that P(A) =(1)/(2), P(B) =(7)/(12) and "P(not ...

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