EN09 101 ENGINEERING MATHEMATICS I

Model Question PaperTime: 3 hours Total Marks: 70

Part A (Answer all questions: 5 x 2 marks = 10 marks)

1. Evaluate .

2. Define absolute and conditional convergence of a series

3. Obtain the quadratic form associated with the matrix

4. Define a system of homogeneous linear equations; Discuss the solutions of a

system of homogeneous linear equations.

5. Find , if in , with

period 2π.

Part B(Answer any four questions: 4 x 5 marks = 20 marks)

6. Evaluate

7. Find the radius of curvature at the point on the curve .

8. Discuss the convergence of

9. Expand in ascending powers of , as far as the term containing

.

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10. Find the Eigen value and the Eigen vector corresponding to the largest Eigen

value of the matrix

11. Find the Fourier series expansion for in and deduce that,

Part C(Answer section (a) or section (b) of each question: 4 x 10 marks = 40 marks)

12. (a) State Euler’s theorem for homogeneous functions and

use it to show that , where .

Or

(b) Define Evolute and prove that the evolute of the ellipse is given

by .

13. (a) Define interval of convergence and find the interval of convergence of

the series

Or

(b) State and prove Leibnitz’s theorem for alternating series and

test the convergence of the series

14. (a) Solve completely the system of equations by stating the conditions for

non-trivial solutions :

Or

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(b) By orthogonal transformation, reduce

to canonical form and state the nature.

15. (a) Find the last three harmonics of the Fourier series of , given

Or

(b) Obtain (i) the Fourier Sine series and

(ii) the Fourier Cosine series

for the function, , .

* * * * * *

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