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int(pi//6)^(pi//3)dx/(1+sqrtcotx)...

`int_(pi//6)^(pi//3)dx/(1+sqrtcotx)`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Evaluate int0^1frac[ln(1+x)][1+x^2]dx

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  2. Find the solution of the following differential equations: xdy/dx+sqrt...

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  3. int(pi//6)^(pi//3)dx/(1+sqrtcotx)

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  4. Prove the following by vector method. The diagonals of a rhombus are a...

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  5. Show that the vector area of the triangle whosse vertices have positio...

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  6. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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

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  8. Find the image of the point (3,5,7) with respect to the plane 2x+y+z=6...

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  9. Prove that intxlog(1+1/x)dx =x^2/2log((x+1)/x)-x^2/2 logx-1/2log(x+1)+...

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  10. Prove that int(dx)/(2+sinx)=2/sqrt(3)tan^-1((2tanx//2+1)/sqrt3)+c.

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  11. Solve dy/dx-y/x=xy^2.

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  12. Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...

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  13. If "cos"^(-1)(x/y) +"cos"^-1(y/3)= theta, "prove that" 9x^2- 12xy "co...

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  14. Maximize:Z=10x1+12x2+8x3 "Subject to": x1+2x2 le 30 5x1 -7x3 ge 12 x1+...

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  15. Prove by vector method that the medians of a triangle are concurrent.

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  16. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

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  17. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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  18. If A=[{:(1,-2,2),(3,1,-1):}]andB=[{:(2,4),(1,2),(3,-1):}] , then veri...

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  19. Let A={1,2,3}, which of the following functions on A is invertible?

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  20. Let A={1,2,3}, which of the following functions on A is invertible?

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