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Evaluate : int0^(pi//2)(cosxdx)/((2-sinx...

Evaluate : `int_0^(pi//2)(cosxdx)/((2-sinx)(3+sinx))`

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USHA PUBLICATION-PREVIOUS YEAR QUESTION 2019-PREVIOUS YEAR QUESTION
  1. Find the intervals in which the function y=(lnx)/(x) is increasing and...

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  2. If y=e^(x^(e^(x^(e^x)))), then find dy/dx.

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  3. Evaluate : int0^(pi//2)(cosxdx)/((2-sinx)(3+sinx))

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

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  5. Find differential equation of the curve y=ae^(3x)+be^(5x).

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  6. Obtain the general solution of the following differential equations. (...

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  7. Integrate the following int[(2x+1)/sqrt(x^2+10x+29)]dx

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  8. Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2.

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  9. Find the equation of a plane which is at a distance 3 units from the o...

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

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  11. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

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  12. Find the unit vector in the direction of the vector vecr1-vecr2, where...

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  13. Find the inverse of the following matrices using elementary transforma...

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  14. Out of the adult population in a village 50% are farmers, 30% do busin...

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  15. Examining consistency and solvability, solve the following equation by...

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  16. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

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  17. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

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  18. Evaluate the following integrals int(dx)/(2cos^2x+3cosx)

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  19. Solve y^(2)+x^(2)dy/dx=xydy/dx.

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  20. Determine the area common to the parabola y^2=x and the circle x^2+y^2...

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