Examination of Marine Engineer Officer s6

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 (2004) Morning Paper 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) Find the sum to ‘n’ terms of the sequence {an} when an = 5 – 6n, n Î N.

b) Insert three A.Ms between 3 and 19.

2. a) Resolve into partial fractions

b) Resolve into partial fractions

3. a) If A + B + C = p, show that

cos 2A + cos 2B + cos 2C = –1 – 4 cosA cosB cosC.

b) Evaluate tan 105°.

4. a) Find the equation to the straight line, which passes through the point (4, –5) and which is parallel to the line 3x + 4y + 5.

b) Find the equation to the straight line which passes through (4, –5) and is parallel to the line 3x + 4y + 5 = 0.

5. a) Find the equation to the circle which touches the axis of ‘y’ at a distance +4 from the origin and cuts off on intercept 6 from the axis of x.

b) Find the equation of the chord joining the two points (3, 4), (4, 3) on the circle x2 + y2 = 25.

6. Draw the graphs of y = 3 – x and y = ex–1 between x = 1 and x = 2 and find approximately the value of ‘x’ which satisfies the equation 3 – x = ex–1.

7. A loop of the curve y2 = x2(1 – x2) is rotated about ‘x’ axis. Find the volume generated limits = 3

x = -1, x = +1

8. Integrate using substitution:

a) ex cos ex b) sin2x cos x c)

9. Find the ortho center of the Triangle whose vertices are (1, 1), (2, –2) and (–1, 0).

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