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Show that int0^pixInsinx=pi^2/2In1/2...

Show that
`int_0^pixInsinx=pi^2/2In1/2`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove that the line (x+5)/3=(y+4)/1=(z-7)/-2 and x/1=(y+7)/5=(z-16)/-1...

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  2. Evaluate the following integrals int(3)/(x^3-1)dx

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  3. Show that int0^pixInsinx=pi^2/2In1/2

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  4. Solve dy/dx+y/x=sinx/x,y(0)=0

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

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  6. A figure consists of a semi-circle with a rectangle on its diameter. G...

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  7. Find the points on the curve y = x^2+1 which are nearest to the point ...

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  8. Prove that a-=bmod 3 is an equivalence relation on the set of integers...

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  9. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  10. A factory uses three different respurce for the manufacture of two dif...

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  11. If the edges of a rectangular parallelopiped are of lengths a, b, c, t...

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  12. Find the distance of the point (3,-4,5)from the plane 2x+5y-6z-19=0 me...

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  13. A variable plane is at a constant distance p from the origin and meets...

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  14. Without expanding show that the following determinant is equal to Ax+B...

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  15. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

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  16. Find the probability distribution of number of doublets in four throws...

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  17. What is the value of int0^picos^(101)xdx?

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  18. If f(x)={(3x+2,xle0),(2-3x,xgt0):}

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  19. What is the equation of the plane |r to y-axis and passing through(2,-...

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  20. Find least non negative integer r such that 7xx13xx23xx413 -= r "(mod ...

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