BSc IT Sem III 2022 2023 Oct 2023 APPLIED MATHS II Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q4 Attempt any three of the following 15 marks
   • a) Evaluate f f ydxdy ;R:x
   • b) Evaluate f, ydxdy
   • c) Evaluate — dx dy dz over the volume of an ellipsoid + +
   • d) Evaluate fff(x +z) dxdydz over the tetrahedron formed by x=0, y=0, z=0
   • e) Prove that J, xdydxdz
   • f) Evaluate fff over the annulus between the sphere
2. Q5 Attempt any three of the following 15 marks
   • a) Prove that erf (00) =1
   • b) Prove that . — dx = log(a + 1)
   • c) Evaluate dx
   • d) Prove that Reduction formula of Gamma function
   • e) Show that
   • f) Evaluate dx SEM APPLIED 75MARKS 2 Indicate the full marks
3. Q1 Attempt any three of the following 15 marks
   • a) Find the Rank of the given 4 3 2] by Echelon form method
   • b) Prove that following matrix is orthogonal and hence find if A z
   • f) By considering principle value express (1 + in the form of
4. Q2 Attempt any three of the following 15 marks
   • a) Solve Non -exact differential equation if + 2xydy =0
   • b) Solve , =
   • c) Solve differential equation if =-xy +
   • d) Find the general solution of the equation — D* — + 2D? + D — 1)y = e
   • e) Solve p? + =0
   • f) Solve + (2x
5. Q3 Attempt any three of the following 15 marks
   • a) Prove that L [sinat ] =
   • c)Find the inverse Laplace Transformation by using Convolution Theorem if
   • d) Express in Heaviside unit step function and find the Laplace transformation

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