Engineering FE Engineering Common Sem 1 Applied Mathematics I May 2023 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
1 a) the equation 7cosh x+8sinh x =1, for real values of x. 5
b) Find when is orthogonal
c) Ifu= 3(ax + by -(x? + 2) and +07 =]
d) Find derivative of 4 42
If cosa+2cos sn a+2sin B+3sin y then prove
that sin 3a@+8sin 3y =
b) If v=(x -y ) f(xy), show that + -(x#
c) If then prove that 8
b) Verify Euler’s theorem for U =
c) Examine the consistency of the system of equations 8
x+2y+z=2, and solve then
if found consistent
4 a) Find the real values of for which the system has non-zero solutions. 6
b) Find the product of all the values of E 6
c) U=SM (x Ty then show that
5 a) Using De Moivre’s theorem, express “sin in powers of SIN 6
b) If XYZ= 8 find the values of x,y,z for which U = is maximum. 6
c) Considering only principle value, if ( ) is real prove 8
value is Sec
6 a) Reduce to normal form and find its rank 2 6
b) Find the extreme value of U= xy” — 2y* P
Show that ‘an —|=—+ —log 8

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