Engineering FE Engineering Common Sem 1 Applied Mathematics I Dec 2018 R16 Question Paper - Mumbai University | munotes

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Questions asked in this paper

Q1 Question no.1 is compulsory
Q2 Answer any three from remaining
Q1 a. Show that 0) = log cot ( ) 3 marks
- b. Show that the matrix A=>| 0 J is unitary 3
- d. Find the nth derivative of y= cos? x sin x 3
- f. Using coding matrix A encode the message THE CROW FLIES AT MIDNIGHT 2.a.Find all values of and show that their continued (6) 4
- b. Find the non singular matrices P & Q such that PAQ is in normal 6
- c. Find max. and minimum values of x? + 3x — and 2xyzZu and hence show that correct to three decimal places
- c. If y =sin [log(x? + 2x +1)] then prove that 4.a. State and prove Eulers Theorem for three variables. (6) 8
- b. By using De Moivres Theorem obtain tan 5@ in terms of tan and show that 1 — 10 tan? (=) + 5tan* (=) = 0 6
- c. Investigate for what values of A and the equations 8
- (i) No solution
- (iii) An infinite number of solution nth derivative of (6)
- b. If z= f(x,y) =e" y= then 6
- c. Solve by using Gauss Jacobi Iteration method If y = log [tan + Prove that (6) 8
- (i) tanh tan 5
- c.(i) Expand 2x3 + x —6in powers of (x—2) by using Taylors theorem 4
- (ii) Expand sec x by Maclaurins theorem considering upto x* term 4

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