Engineering FE Engineering Common Sem 1 Applied Mathematics I Dec 2019 R19 Question Paper - Mumbai University | munotes

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

Questions asked in this paper

Q1 Question No.1 is compulsory
Q2 Attempt any three out of remaining five questions
Q3 Figures to the right indicate full marks
- a) Ifsin(@ + ig) = tana + iseca, then show that cos 20 .cosh2y = 3 5
- b) If u + tany), then show that sin2x + sin2y =2 5
- c) Express the 1. 1 and skew symmetric matrix
- d) Expand sinx in ascending powers of x upto x* term. 5
- a) Find non-singular matrices P and Q such that PAQ is in normal form where, A=| 2. 2. Also find the rank of A 6
- c) Prove that Log + tan . Hence evaluate Log ( )
- a) If are the roots of the equation — z sin 29 +1 = 0, then prove that
- b) Solve the following equations by Gauss—Seidal Method ; 6
- c) Prove z is a homogeneous function of two variables x and y of degree n, then x? + 2xy +y? —1)z. Hence find the value of x? + +y?
- a) =cos then prove that 6
- b) Expand + x? in powers of (x — 1) and hence find the value of 6
- c) For what values of and p, the equations, 8
Q1 have a unique solution
Q2 have infinite solution Find the solution in each case for a possible value of and
- a) Find the nth derivative of 6
- b) Discuss the maxima and minima of + — + 16 6
- c) Prove that if A and B are two unitary matrices then AB is also unitary. Verify the result when
- a) If x = cosh (— log y), prove that 6
- b) Find a root of the equation xe* = cos x using the Regular Falsi Method correct to three decimal
- c) 1) Expand sin*@ of multiples of 6. 4
Q2 If one root of x* — 6x? + 18x* — 24x + 16 is (1+i); find the other roots. 4 marks

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