Engineering FE Engineering Common Sem 1 Applied Mathematics I Dec 2022 R19 Question Paper - Mumbai University | munotes

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Questions asked in this paper

(4) Figures to the right indicate full marks

(Time: 3 hours) Max.Marks:80
N.B (1) Question No.1 is compulsory
(2) Answer any three questions from Q.2 to Q.6
(3) Use of Statistical Tables permitted
(4) Figures to the right indicate full marks
b) If then prove that
c) are the roots of the quadratic equation x+4=0, 5
find the value of +
d) Test the consistency and if possible solve 5
a) Is A= | $ a unitary matrix?
b) Find the derivative of
c) then find the value of 8
3a) Prove that log (1 + cos 26 + isin 20) = log 6
c) Discuss for all values of k for which the system of equations 8
has a non-trivial solution
4 a) then show that 6
b) Find two non-singular matrices P and Q such that PAQ is in 6
the normal form where a = | 21 4 3
Prove that tan tan 2 | 8
5 a) Considering principal value, express in the form a + the 6
b) Prove that 59 =
c) Ify=e Prove that
a) If u= ty +2 then prove that
b) If find the values of such that y+ Z is
c) Prove that every Skew-Hermitian matrix can be expressedin
the form B+iC, where B is real Skew-Symmetric and C is real
Symmetric matrix and express the matrix
A= | as B+iC where B is real Skew
symmetric matrix and C is real Symmetric matrix

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