Download PTU B-Tech AE 2020 Dec 2nd Sem 54092 Engineering Mathematics Ii Question Paper

Total No. of Pages : 02
Total No. of Questions : 08

B.Tech. (Aeronautical Engg./Aerospace Engg./ Automation & Robotics/Automobile Engg./BT/CE/CSE/Electrical & Electronics Engg./EE/ECE/Electronics & Electrical Engg./IT/ICE/Marine Engg./Mechanical Engg./Petroleum Refinary Engg./Textile Engg.) (2012 to 2017) (Sem.-2)

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INSTRUCTIONS TO CANDIDATES :

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1. Sum the series e cos ? — e²/2 cos 2? + e³/3 cos 3?— ...
2. Verify Cayley’s Hamilton theorem for the matrix A = 4 & 2 & 3 \\ 1 & 2 & 1 \\ 1 & 1 & 2 and hence obtain the inverse of the given matrix.
3. Test the convergence of the following series
   x + x²/2! + x³/3! + x⁴/4! + ...

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4. a) Prove Log(d^m/dx^m) (xⁿ) = (n!/(n-m)!)x^n-m where m, n are integers.
   b) Discuss the convergence of S n²e^-n
5. Solve 2xydx + (3x² + 2y³) dy =0
6. a) Solve:(1+y²) dx=(tan^-1 y—x)dy
   b) Solve y" —6y" +9y = e^3x by variation of parameter method

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7. Solve x²d²y/dx² - 3xd/dx + y = log x
8. A constant electromotive force E volts is applied to a circuit containing a constant resistance R ohms in series and a constant inductance L henries. If the initial current is zero, show that the current builds up to half its theoretical maximum in (Llog2)/R seconds.

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