LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – CHEMISTRY
THIRD SEMESTER – APRIL 2012
MT 3103 – MATHEMATICS FOR CHEMISTRY
Date : 28-04-2012 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
Part A. Answer all the questions. Each question carries two marks. (10 x 2 = 20)
- Find for x = a(+sin ); y = a(1-cos),
- Find if
- Evaluate
- Evaluate
- Prove that
- If
- If, show that the angle is 3o approximately
- Prove that sinh 3x = 3 sinh x + 4 sinh3 x
- If the probability of defective bolt is 0.1; find the mean and standard deviation for the distribution of defective bolts in a total of 500.
- What are the significance of normal distribution.
Part B. Any 5 questions only. Each question carries 8 marks. (5 x 8=40)
- Find the equation of the tangent and normal for y2= 4ax at (at2,2at).
- Prove that the tangents to the curve y = x2 -5x + 6 at the points (2,0) and (3,0) cut at right angles.
- Solve (3D2– 4D + 5) y = 3 e2x
- Prove that
- If x is large, prove that nearly.
- Prove that
- Find the standard deviation for the following data:
| Age (x) | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 |
| No of frequencies (f) | 170 | 110 | 80 | 45 | 40 | 35 |
- Ten percent of the tools produced in a certain manufacturing process turn out to be defective. Find the probability that in a sample of 10 tools chosen at random, exactly two will be defective by using (a) Binomial distribution and (b) the Poisson approximation to the binomial distribution.
Part C. Any two questions only. Each question carries 20 marks. (2 x20 = 40)
- a) Prove that
19) b) Solve xp + yq = x
20)a) Evaluate
20)b) Evaluate
21) Find the Fourier series to the function f(x) = in the interval (0,2).
- a) Find the maximum or minimum values of xy + 1/x +1/
22) b) A family has six children. Find the probability P that there are (a) three boys and three girls and (b) fewer boys than girls.
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