BSc IT Sem III ATKT 2017-18 ATKT Applied Maths Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Attempt any three of the following: Show that ! is an orthogonal matrix 15 marks
   • b. For different values of k, discuss the following equations: Find the eigen values of the matrix Prove that (1 + + iv3) Show that sec h @) = log cot (2)
2. Q2 Attempt any three of the following: 15 marks
   • a. Solve: (D* = cos 2x +x
   • d. Solve — py + x=0
   • f. du dv Solve: = sin x; x. givenat x=0,u=1 and v=0
   • Q. P. Code: 20944
3. Q3 Attempt any three of the following: 15 marks
   • a. Find the Laplace Transformation of f (t) Find L[y(t)] of the following differential equation: Find the inverse Laplace transform of : Find the Laplace transform of : f(t) = 4
   • f. Solve the following differential equation by using Laplace transform method:
4. Q4 Attempt any three of the following: Evaluate by changing polar co-ordinates r @ d@ where R is the region of curve r = 2a cos 0 15 marks
   • d. dx dy d Evaluate throughout the volume of sphere Evaluate y dx dy overthe area bounded by y= =2
   • f. Find the volume bounded by the cylinder = = y’ andthe planes z=0 and Attempt any three of the following: 15 Show that: log using DUIS
   • Q. P. Code: 20944 If y= [a(x —t)]. dt then show that, ay = af (x)
   • f. Define error function and prove that error function is an odd function

Read from the scan above, so a character or two may differ. The scan is the original.