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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)
India (2002)
Morning Paper
Total Marks 100
NB : (1)All Questions are Compulsary
(2)All Questions carry equal marks
(3)Neatness in handwriting and clarity in expression carries weightage
1. a) Solve
ax  ax

ax  ax
log c a
b) Show that logba = .
log c b
a
.
x

2a
2. a) Find the 5 term of  x 2  3
3y

th



7
 2a 3 

b) Find the middle term of 

 3 2a 
6
3. a) Find the equation of the circle which passes through the points A(–2, 3), B(5, 2) and
C(6, –1).
b) A circle touches the line 5x – y = 3 at the point (2, 7) and the center is on the line
x + 2y = 19. Find the equation of the circle.
4. a)Find the condition that the line lx + my + n = 0 may be normal to the circle
x2 + y2 + 2gx + 2fy + c = 0.
b) Find the equation to the circle whose center is at (, ) and which passes through
the origin, and prove that the equation of the tangent at origin is
x + y = 0.
5. Find the turning points and the points of inflexion, if any, of the graph
y = (x – 2)3 (x + 2).
6. A uniform sector of a circle of radius ‘a’ subtends an angle 2 at the center. Find C.G.
of the arc of the sector.
1
3 
7. Find all the values of  
i
2 2 
3/4
8. Find the whole area of the curve x = a cos3, y = a sin3.
9. Determine the equation center and radius of the circle whose center lies on the line
3x + 7y = 2 and which passes through the two points (6, 2), (8, 10).
10. A mason constructs a wall such that there are 28 bricks in the base of a wall and in
each pile thereafter 3 bricks less. If altogether there are 10 such piles, how many bricks
will there be in the last pile?
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