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95M-4
Sr. No. 3
EXAMINATION OF MARINE ENGINEER OFFICER
Function: Marine Engineering at Operational Level
MATHEMATICS
M.E.O. Class IV
(Time allowed - 3hours)
Morning Paper
India (2003)
Total Marks 100
NB : (1)All Questions are Compulsory
(2)All Questions carry equal marks
(3)Neatness in handwriting and clarity in expression carries weightage
(4) Illustration of an Answer with clear sketches / diagrams carries weightage.
1.
a) If the roots of the equation
p(q – r)x2 + q(r – p)x + r(p – q) = 0 be equal, show that
1 1 2
 
p r q
b) Express 9 as a power of e.
2.
a) Solve 2cos2t + 3sint = 0.
b) Solve sin + sin 3 + sin 5 = 0.
3.
a) Find the distance from 5x – 12y + 35 = 0 to the point (3, 2).
b) Find the distance between parallel lines 15x – 8y – 34 = 0 and 15x – 8y + 51 = 0.
4.
a)Find the condition that the line y = mx + c becomes a tangent to the circle
x2 + y2 = a2.
b) The equation of a chord of the circle x2 + y2 + 4x – 6y = 0 is given by
x + 2y = 0. Find the equation of the circle describe on this chord as diameter.
5. At the end of t seconds, the distances of a moving point from two rectangular axes are given by x = a +
c cos t, y = b + c sin t. Show that the resultant velocity and acceleration are constant in magnitude. Show
also the equation to the locus of the moving point.
6. Water escapes at the rate of 8 c.c. per minute from an inverted conical container whose depth is 12 m
and whose base is a circle of radius 4 m. At what rate is the water sinking when there are 6 m water in the
container?
7. The center of a regular hexagon is at the origin and one vertex is given by
diagram. Determine the other vertices.
3 + i on the Argond
Y B
C
A
X
o
D
F
E
8. Find the root mean square value of the expression a sin pt + b cos qt over the interval (0, 2).
9.
Differentiate
a) y = e cos
10.
1
1 x 2
b) y = x e
sin x
c) y= 94x
1
log10 7 x
.
Insert four G.Ms between 2 and 64.
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