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If siny=xcos(a+y),show that dy/dx=cos^2(...

If` siny=xcos(a+y)`,show that `dy/dx=cos^2(a+y)/cosa`and find the value of `dy/dx at x=0`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  2. Find the interval where f(x)=sinx,x in[0,2pi] increasing.

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  3. If siny=xcos(a+y),show that dy/dx=cos^2(a+y)/cosaand find the value of...

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  4. Determine the area of the region bounded by y^2=x^3 and the double ord...

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  5. int(xe^x)/(1+x^2)dx

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  6. Evaluate int0^1frac[ln(1+x)][1+x^2]dx

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

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

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

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

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

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

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

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

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

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

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

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

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

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