LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – CHEMISTRY
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THIRD SEMESTER – November 2008
MT 3103/MT 3101 – MATHEMATICS FOR CHEMISTRY
Date : 11-11-08 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
Section A
Answer ALL questions: (10 x 2 = 20)
- If, find.
- Find the slope of at (2, 4).
- Integrate with respect to x.
- Solve
- Prove that
- If , show that
- Simplify.
- Expand tan 6θ in terms of tanθ.
- Find the arithmetic mean of the following frequency distribution:
x: 1 2 3 4 5 6 7
f: 6 10 11 15 11 12 10
- Define the probability mass function of binomial distribution.
Section B
Answer any FIVE questions: (5 x 8 = 40)
- Determine the maxima and minima of.
- Find the equation of the tangent and normal to the curve at.
- Evaluate (a); (b).
- Show that
- Find the sum to infinity the series.
- Expand in terms.
- Two unbiased dice are thrown. Find the probability that:
- Both the dice show the same number,
- The first die shows 6,
- The total of the numbers on the dice is 8.
- The total of the numbers on the dice is greater than 8.
- A car hire firm has two cars, which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson distribution with mean 1.5. Calculate (i) the proportion of days on which neither car is used, and (ii) the proportion of days on which some demand is refused.
Section C
Answer any TWO questions: (2 x 20 = 40)
- (a) Find the angle of intersection of the cardioids and .
(b) If, prove that. (12 + 8)
- (a) Evaluate .
(b) Integrate with respect to x using Bernoulli’s formula.
(c) Solve . (8 + 4 + 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) If in show that. (10 + 10)
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