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Engineering FE Engineering Common Sem 1 Applied Mathematics I Dec 2022 R16 Question Paper - Mumbai University | munotes

Applied Mathematics I Question Paper, Dec 2022.pdf
HAS · 123 KB · 1 May 2025

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Older exam Dec 2022 - R19 Semester-end · Applied Mathematics I → Newer exam May 2023 - R19 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 1-a) Prove that the matrix 1 1+ is unitary. (S Marks) 1-b) State Euler’s theorem on homogeneous function of two variables and evaluate x Yay where, u = Marks) 1-c) Separate into real and imaginary part of (=) . (5 Marks) 1-d) If y = 2* Sin?x Cosx find y,. (5 Marks) 2-a) Show = — 12Cos*6 + 1 (6 Marks) 2-b) If u ) P.T x +y cosu (6 Marks) 2-c) Test fer consistency the foliowing system & soive them if consistent. (8 Marks) 3-a) Show that minimum value of u = xy + + is (6 Marks) 3-b) Using Newton-Raphson method find the root of equation 2x? 3x +4=0 lying between 2 and -1 correct to four places of decimals. (6 Marks) 3-c) + = 2x prove that ( x? + (2n + + (n? — y, =0. (8 Marks) 4-a) Solve = 1 + i and find the continued product of the roots. (6 Marks) 4-b) Apply Gauss elimination method to solve the equations x+3y-2z=5, 2x+y-3z=1, 3x+2y-z=6 4-c) For what value of A the equations x+ have a solution and solve them completely in each case. (8 Marks) 5-b) If u = ) , then show that x Y ay + 0. (6 Marks) 5-c) Prove that log = 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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