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int(pi/5)^(3pi/10) (sinxdx)/(sinx+cosx)...

`int_(pi/5)^(3pi/10) (sinxdx)/(sinx+cosx)`

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USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. Show that 2sinx+3tanxgt3x for all xin(0,frac[pi][2])

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  2. Evaluate inte^(tan-1)x((1+x+x^2)/(1+x^2))dx.

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  3. int(pi/5)^(3pi/10) (sinxdx)/(sinx+cosx)

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  4. Find the area of the region bounded by y=6x-x^2x-axis and between ordi...

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  5. Solve : (dy)/(dx)= sin(x+y)+cos(x+y)

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  6. From a differential equation from the equation y=ae^(2x)+be^(-x) by el...

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  7. Prove the following by vector method. An angle inscribed in a semi-cir...

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

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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 two lines whose direction cosines are connected by the ...

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  11. passing through the point (-1,3,2) perpendicular to the planes x+2y+...

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  12. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

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  13. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

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  14. Solve the following LPP graphically Maximize z=20x1+10x2 Subject to x1...

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

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  16. Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...

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

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

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  19. Find the altitude of a right circular cylinder of maximum volume inscr...

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  20. Evaluate intfrac[dx][cosx(1+2sinx)]

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