BSc IT Sem III 2023 2024 2024 APPLIED MATHEMATICS Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Attempt Any Three of the following 15 marks
   • a) Find the Rank of the following Matrix by normal form 4
   • b) Test the consistency of the given system of equation
   • c) Simplify
   • d) Verify the given Characteristic equation A? 3 0
   • e) Examine whether the following vectors are linearly dependent or linearly independent
   • f) — then prove that (x? + =1
   • ii) Write the following complex number in polar and exponential form if z = V3 +i
2. Q2 Attempt Any Three of the following 15 marks
   • a) Solve
   • c) Solve (x + y) + (x = 0 by substitution method
   • d) Evaluate general solution of linear differential equation + ycotx = sin2x
   • e) Evaluate complete solution of given differential equation if -5 + 6y =
   • f) Solve the exact differential equation (x? — + sec*y)dy = (tany — 2xy — y)dx
3. Q3 Attempt Any Three of the following 15 marks
   • a) Find the value of given laplace cos 5t dt
   • b) Find by Convolution theorem
   • c) Find the Laplace transform of L [t?e~**cosh2t]
   • d) Using Laplace Transformation for the equation SYIT APPLIED MATHS II 2%HRS 75 MARKS
   • e) Find the inverse Laplace transformation of
   • f) Find the laplace transform for following periodic function for period 2a
4. Q4 Attempt Any Three of the following 15 marks
   • a) Solve x*y? dxdy
   • b) Solve
   • c) Change the order of integration and evaluate
   • d)Evaluate xydxdy over the area bounded by parobolas
   • e) Solve Se
   • f) Evaluate fff x*yzdxdydz throughout the volume bounded by plane
5. Q5 Attempt Any Three of following 15 marks
   • a) Solve f,
   • b) Solve dx
   • c) Solve
   • e) Prove that = dx = log (1+a)
   • f) Evaluate

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