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

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Q1 Choose the correct option for following questions. All the Questions are (20 Marks) | compulsory and carry equal marks If y = sin2x cos3x then, Find the solution of following system of equations given by No Solution Exist Find the rank of matrix
Q4 The system of equations 2x-2y+z=tx, 2x-3y+2z=ty, -x+2y=tz, will possess a solution for which values of constant t If tanh x =1/2, then find the value of x and sinh2x For the unitary matrix A = ak | , find A Ifu(x,y)= , then find the value of I = x “ Find the maxima of f = x” + subjected to the condition x + y=2 Find the value of log(V3 - i) Solve any Four out of Six (5 marks each) A Ifu = log + ), Prove that i) Coshu = secé, ii)Sinhu = Show that SinxSinhx = x? — Prove that log(1 +e ) = log (2 cos Find the Rank of the following matrix by reducing to Normal
Q3 Solve any Four out of Six (5 marks each) Test for consistency the following system & solve them if Examine the function u = — 3x — 4y) For extreme If + = x prove that Using Newton-Raphson method find the root of equation E 2x? — 3x +4 = 0 lying between -2 and -1 correct to four places lfu=f ( ) , then show that
Q4 Solve any Four out of Six (5 marks each) Show that minimum value of u= xy + a3 + is 3a’ Find the derivative of Solve = 1 find the continued product of the roots Apply Gauss elimination method to solve the equations For what value of 2 the equations x +2y+z=3,x+yt Z=A,3x+y+4+3z= J? and solve them completely in each case

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