LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – CHEMISTRY

THIRD SEMESTER – April 2009
MT 3103 / 3101 – MATHEMATICS FOR CHEMISTRY
Date & Time: 17/04/2009 / 1:00 – 4:00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL questions: (10 x 2 = 20)
 If, find.
 Solve.
 Integrate with respect to x.
 Solve
 Show that .
 Define characteristic roots.
 Expand tan 7θ in terms of tanθ.
 Find the real and imaginary parts of.
 Find the arithmetic mean of the following frequency distribution:
x: 1 2 3 4 5 6 7
f: 5 9 12 17 14 10 6
 Write the moment generating function of Poisson distribution.
SECTION B
Answer any FIVE questions: (5 x 8 = 40)
 Find the maxima and minima of the function.
 Find the equation of the tangent to the ellipse at.
 Evaluate.
 If a,b,c denote three consecutive integers show that
 Sum to infinity the series.
 Show that
 Prove that.
 A coffee connoisseur claims that he can distinguish between a cup of instant coffee and a cup of percolator coffee 75% of the time. It is agreed that his claim will be accepted if he correctly identifies at least 5 of the 6 cups. Find his chances of having the claim (i) accepted, (ii) rejected, when he does have the ability he claims.
SECTION C
Answer any TWO questions: (2 x 20 = 40)
 (a) For the curves and, find the angle of intersection.
(b) Differentiate. (12 + 8)
 (a) Evaluate .
(b) Integrate with respect to x.
(c) Solve . (7 + 5 + 8)
 (a) Sum to infinity the series .
(b) Find the characteristic roots and the characteristic vectors of the matrix
. (8 + 12)
 (a) Prove that.
(b) Obtain a Fourier expansion for the function. (10 + 10)
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