# Download JNTUA B.Tech 1-1 R13 2014 June Regular 13A54101 Mathematics I Question Paper

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Code: 13A54101
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)

******
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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