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

Applied Mathematics I Question Paper, May 2019.pdf
HAS · 294 KB · 1 May 2025

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Older exam Dec 2018 - CBSGS Semester-end · Applied Mathematics I → Newer exam May 2019 - CBSGS Semester-end · Applied Mathematics I →

Questions asked in this paper

  1. Q2 Attempt any three questions from the remaining five questions
  2. Q3 Figures to the right indicate full marks If u + log find
    • b) the value of tanh(log x) if x = V3 03 Express the matrix —2i 0 1+ 2i | asthe sum of a Hermitian and a Skew-Hermitian matrix Expand in powers of (x =) 04
  3. Q2 a) Expand sin’@ of sines of multiples of 6 marks
    • b) If find 06
    • c) the stationary values of x2 + y? —3axy, 08
    • a) the real root of x — 1.2 correct to three places 06 of decimals using Newton-Raphson method
    • b) Show that the system of equations 06 can posses a non-trivial solution only if A = = —3. Obtain the general solution in each case If tan(a + isin prove that 08 Q a) Using the encoding matrix as encode and decode the message
    • b) If u=f(e* then prove that 06
  4. Q5 a) Tf 1, are the roots of — 1 = 0, find them and show Find n which will make (r 6 marks
    • C) Find the root (correct to three places of decimals) of x? — 4x —9 = 0 08 lying between 2 and 3 by using Regula-Falsi method
  5. Q6 Find non-singular matrices P and Q such that A= (2 3.5 i) is reduced to normal form. Also find its rank 6 marks
    • b) the principle value of (1 + 06
    • c) Solve the following equations by Gauss-Seidel method 08

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