Mathematics

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SECTION-A (2Marks each)

Q1. Find the symmetry of the curve x^3y^2=x^2-a^2x

Q2. if x =rcos@ ,y=rsin@ find del(x,y)/del(r,@)

Q3. Find the stationary points of the function x^3y^2(6-x-y)

Q4. Is the following matrix orthogonal ?

Q5. Evaluate β(2,3/2)

Q6. Find the outward normal vector of 2x^3+2xy+y^2=3 at point (1,2,3)

Q7. Find the acceleration of the particle moving along curve x=Sint,y=cos2t,z=e^t at (t=2)

Q8. Y=xlog(x-1/x+1) show that, Y =(-1) (n-2)! [(x-n/(x-1)^n)-(x+n/(x+1)^n)]

Q9. Show that rectangular solid of maximum volume that can be inscribed in a given sphere is a cube

Q10. Prove that Γ(m)Γ(m)+1/2=√π/2^(2m-1)Γ(2m)

Q11. Find the Eigen Values and Eigen Vectors of A =

Q12. Verify Green theorem in a plane for

Integration (3x^2-8y^2)dx + (4y-6xy)dy where c is the boundry of the region defined x=0,y=0,x+y=1

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