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B.Tech I Year (R13) Regular Examinations June/July 2014

MATHEMATICS - I

(Common to all branches)

Time: 3 hours Max. Marks: 70

Part ? A

(Compulsory Question)

*****

Part ? B

Answer all five units (5 X 10 = 50 M)

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1 Answer the following: (10 X 02 = 20 M)

(a) Solve

(b) Solve

(c) Find Taylor?s series expansion for about .

(d) Find the radius of the curvature at the origin for the curve

(e) Find the asymptote of

(f) Evaluate

(g) Find

(h) Find

(i) Show that

(j) State Stokes theorem.

2 A mass m suspended from one end of a spring is subjected to a periodic force in the

direction of its length. The force f is measured positive vertically downwards and at time t = 0, m is at

rest. If the spring constant is K, prove that the displacement of m at time t is given by

where Neglect the damping effects.

OR

3 Solve

4 Discuss the maxima and minima of

OR

5 Prove that the evolute of the cycloid is another cycloid.

6 Find the length of the arc of the parabola cut off by the straight line y = x.

OR

7

Evaluate

8 Using convolution theorem solve the IVP:

OR

9

Find

10 For a solenoidal vector prove that x x x x ))) = .

OR

11

Evaluate where C is the arc of the parabola

from (0, 0) to

R13

UNIT - I

UNIT - II

UNIT - III

UNIT - IV

UNIT - V

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