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Engineering FE Engineering Common Sem 1 Applied Mathematics I Dec 2018 CBSGS Question Paper - Mumbai University | munotes

Applied Mathematics I Question Paper, Dec 2018.pdf
HAS · 439 KB · 1 May 2025

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Older exam Dec 2018 - R16 Semester-end · Applied Mathematics I → Newer exam May 2019 - R16 Semester-end · Applied Mathematics I →

Questions asked in this paper

  1. Q1 a) = y then prove that sinh ny = x — | 3 marks
    • c) z= uvw-find Show that A = is unitary ) Find derivative of [4] 3
  2. Q2 a) and find the continued product of the roots. Reduce the matrix 4 2 | to the normal form and find its Rank 6 marks
    • c) State and Prove Euler’s theorem for two variables hence find value of +y ay where u = 8
  3. Q3 a) Test the consistency of And Solve if consistent Examine the function for its extreme values [6] 6 marks
    • c) Ifsin(@ + ig) = then Prove cos* = = sinh*@ prove that y = x tan(tanq 8
    • c) by Gauss Elimination method 8
    • a) Prove @ + = cos 46 + 5] 6
    • b) Evaluate lim 6
    • c) then 8
  4. Q6 a) Checkif the following vectors X, = [-6,0,—3,—4] are linear dependent hence find the relation between them if any 6 marks
    • b) If f(xy?,z— 2x) = 0 then prove that 2x Va = 4x 6
    • c) Fit degree parabola y = ax* + bx +c to the following data 8

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