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Engineering FE Engineering Common Sem 1 Applied Mathematics I May 2023 R16 Question Paper - Mumbai University | munotes

Applied Mathematics I Question Paper, May 2023.pdf
HAS · 351 KB · 1 May 2025

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Older exam May 2023 - R19 Semester-end · Applied Mathematics I → Newer exam Dec 2023 Semester-end · Applied Mathematics I →

Questions asked in this paper

  1. Q1 Question 1 is compulsory
  2. Q2 Attempt any three from the remaining questions If y = Sin*x Cosx find yy. (5 Marks) 1-b) State Euler’s theorem on homogeneous function of two variables and evaluate ay where, u= (5 Marks) 1-c) Separate into real and imaginary part of (=) . (5 Marks) 1-d) Prove that the matrix | is unitary. (5 Marks) 2-a) If u= PT y2 (6 Marks) 2-b) Show that = 16Cos*@ — + 1 (6 Marks) 2-c) Test for consistency the following system & solve them if consistent. (8 Marks) 3-a) Show that minimum value of u = xy + + is 3a’. (6 Marks) 3-b) Using Newton-Raphson method find the root of equation — 3x + 4 = 0 lying between 2 and -1 correct to four places of decimals. (6 Marks) 3-c) If + = 2x prove that ( x? — + (2n + + (n? — =0 4-a) Apply Gauss elimination method to solve the equations x+3y-2z=5, 2x+y-3z=1, 3x+2y-z=6 4-b) Solve = 1 + iand find the continued product of the roots. (6 Marks) 4-c) For what value of the equations x + have a solution and solve them completely in each case. (8 Marks) 5-b) If u= , then show that x? + + 2? = 0. (6 Marks) 5-c) Prove that log = 2i tanhy) (8 Marks) 6-a) Find the derivative of (6 Marks) 6-b) Reduce the following matrix to its normal form and hence find its rank 6-c) i) Express + 3x? — 8x + 7) in terms of (x — 2) using Taylor’s theorem
    • ii) Prove that = x — + — 8

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