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

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Q1 compulsory and carry equal marks The value of G + =) + (= =) is equal to What is the value of log(i) If u=log(tanx + tany) then the value of sin2x + sin2y is All the stationary points of the function x? + 3xy? — — 15y? 4+ 72x are If —1 rank of A is The modulus and principal value of th top e modulus and principal value of the argument o 1S The real part of cos (=) is Stationary point is a point where f(x, y) has
- 10. For non-singular matrices P and Q, PAQ is in the normal form of a matrix A, then be found by QU. Solve any Four out of Six. 5 marks each Considering only principal values separate into real and imaginary parts Ifz= (2) , find the value of + Find the extreme value of the function xy(3 Express the matrix 1 + as of Hermitian and If y = acos(logx) + b sin (logx) , then show that
Q11 Solve any Four out of Six. 5 marks each Find all the values of (1 + i)3 and show that their continued product is (1 + i) Separate into real and imaginary parts + if) Ifu = sin Prove that Divide 24 into 3 parts such that the continued product of the first, square of second and cube of the third is maximum using Lagrange’s method Find a, b,c if A is orthogonal matrix where A —2 1 Hence find inverse of A Investigate for what values of A and the system of equations
- (i) no solution unique solution an infinite no. of solutions
Q1 V. Solve any Four out of Six. 5 marks each Prove that (1 + iV3)” + (1 — = 2"*1 cos = Prove that (tan 6) = log [tan + Ifu= ) , then show that Find derivatives of Find non-singular matrices P and Q such that A = 3.5 is reduced to normal form. Also find its rank Using De Moivre’s theorem prove that

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