Engineering FE Engineering Common Sem 1 Applied Mathematics I Dec 2019 R16 Question Paper - Mumbai University | munotes

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Older exam Dec 2019 - R19 Semester-end · Applied Mathematics I → Newer exam Dec 2019 - CBSGS Semester-end · Applied Mathematics I →

Questions asked in this paper

Q1 a) Prove = 3 marks
- b) If A= 1 is orthogonal find a,b,c. 3
- c) =6 find and where z is an implicit function of x and y. (3)
- e) Find the derivative of y = 4
- f) Find a,b if lim =2 by Rule. 4
Q2 a) Find the roots common to x* + 1=0 and = 0 6 marks
- b) If y = Prove That
- c) Discuss the maxima and minima of Hence find maximum and minimum value of f(x,y)
Q3 a) Find the values of k for which the equations solve them for these values of k where @ is the function of x,y,z 6 marks
- c) If tan(a+ Prove that + log(x? + y? — — Find the value of (6) 8
- b) Using encoding matrix encode and decode the message 6
- C) Solve the following equations by Gauss Jacobi’s Iteration method 8
Q5 a) Prove that the general value of (1 + itana)~ is 6 marks
- b) State and Prove Eulers Theorem for function of Three Variables. 6
- c) Expand — x* + x3 in powers of and 8
Q6 a) Prove that:
- b) Find nonsingular matrices P and Q such that PAQ is in Normal form also find Rank of A , where A= . (6)
- c) Using Newton Raphson Method find an iterative formula for VN where N is positive number, Hence find V35. (8)

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