LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – CHEMISTRY
FIRST SEMESTER – NOVEMBER 2012
MT 1102 – MATHEMATICS FOR CHEMISTRY
Date : 03/11/2012 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
Part A
Answer ALL questions: (10 x 2 =20)
- Differentiate with respect to .
- Find the slope of the tangent at to the curve
- Change the limits of as lower limit to and upper limit to .
- Solve .
- State Binomial theorem.
- Solve the partial differential equation .
- State DeMoivre’s theorem.
- Show that
- From a well-shuffled pack of 52 cards, one card is drawn at random. What is the probability that it will be (i) a jack (ii) a spade?
- Define Normal distribution.
Part B
Answer any 5 questions: (5 x8 = 40)
- Find the angle of intersection of the cardioids and
.
- If , then show that .
- Evaluate: (i), using Bernoulli’s formula.
(ii) Evaluate: . (4+4)
- Solve the differential equation .
- Find the sum of the series
- If , then show that
- Obtain the expansion of .
- Find the maxima and minima of the function .
Part C
Answer any TWO questions: (2 x 20 = 40)
- (i) Evaluate:
(ii) Prove that . (10+10)
- (i)Obtain the characteristic roots and the associated characteristic vectors of the
matrix .
(ii) Solve the partial differential equation with usual notations. (15+5)
- Given that in the interval 0 to . Find the Fourier coefficients and .Hence deduce that .
- (i)Expand in series of cosines of multiples of .
(ii)The mean mark of students were found to be 40. Later it was observed that a score of 53 was misread as 83. Find the correct mean using the correct score.
(14+6)
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