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Show that int0^1(Inx)/sqrt(1-x^2)dx=pi...

Show that
`int_0^1(Inx)/sqrt(1-x^2)dx=pi/2In1/2`

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USHA PUBLICATION-PREVIOUS YEAR QUESTION 2018-PREVIOUS YEAR QUESTION
  1. Show that 2sinx+3tanxgt3x for all xin(0,frac[pi][2])

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  2. Evaluate int (dx)/((x+1)sqrt(1-x^2))

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  3. Show that int0^1(Inx)/sqrt(1-x^2)dx=pi/2In1/2

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  4. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

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  5. From the differential equation whose general solution is y=asint+be^t.

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  6. Solve the following differential equations (1+y^2)dx+(x-e^(-tan^(-1)...

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  7. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

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  8. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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  9. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  10. Prove that the measure of the angle between two main diagonals of a cu...

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  11. If the position vectors of two points A and B are 3hati + hatk and 2ha...

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  12. If A and B are invertible matrices of the same order, then prove that ...

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  13. In a triangle ABC "if" m/A =90^@, "prove that "tan"^(-1) b/(a+b) +"ta...

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  14. Solve the following LPP graphically: Maximize Z=3x1+2x2, x1le2, x1+x2l...

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  15. Solve the following system of equations by the matrix inversion method...

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  16. Two cards are drawn successively with replacement from a well-shuffled...

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  17. By elementary operations, find A^(-1) for the following: A=[[1,1,0],[1...

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  18. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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  19. Find the coordinates of the point on the curve x^2y - x + y = 0 wher...

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  20. Evaluate intfrac[2cosx+7][4-sinx]dx

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