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`int_0^pi(xsinxdx)/(1+cos^2x)`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. int(1+x^2)/(xsqrt(x^4+1))dx

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  2. Determine the area within the ellipse x^2/a^2+y^2/b^2=1.

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  3. int0^pi(xsinxdx)/(1+cos^2x)

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  4. Evaluate the following integrals int(3sinx+28cosx)/(5sinx+6cosx)dx

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  5. Find the equation of the plane passing through the line (x-8)/3=(y+19)...

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  6. Prove that the sum of the vectors directed from the vertices to the mi...

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  7. If A (1,0,-1), B (-2,4,-2) and C(1,5,10) be the vertices of a triangle...

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  8. Find the image of the point (3,-2,1) in the plane x-y+3z=2.

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

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  10. Prove that intdx/((x-1)^2(x+2))=1/9ln abs((x+2)/(x-1))-1/(3(x-1))+c

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  11. int0^pi((xtanx)/(secx+tanx))dx

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  12. Solve: (1+x^2)dy/dx+2xy-x^3=0

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  13. Find (dy)/(dx) if x=(3at)/(1+t^3), y=(3at^2)/(1+t^3) at t=1/2

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  14. If x cos alpha + y sin alpha = p is a tangent to the curve (x/a)^(n/...

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  15. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  16. If A=[(0,1,0),(-1,0,2),(0,0,1)], then show that A^3-A^2+I3=[(2,-1,0),(...

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

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  18. Solve the following LPP graphically: Maximize: Z=4x1+3x2 subject to x1...

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  19. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

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  20. A line makes angles alpha, beta, gamma, delta with the four main diago...

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