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
Answer ALL questions: (10 x 2 = 20)
- If, find.
- Integrate with respect to x.
- 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.
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.
- 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.
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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