“Loyola College B.Sc. Chemistry Nov 2008 Mathematics For Chemistry Question Paper PDF Download”

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – CHEMISTRY

 

AB 04

 

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)

  1. If, find.
  2. Find the slope of at (2, 4).
  3. Integrate with respect to x.
  4. Solve
  5. Prove that
  6. If  , show that
  7. Simplify.
  8. Expand tan 6θ in terms of tanθ.
  9. 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

  1. Define the probability mass function of binomial distribution.

 

Section B

Answer any FIVE questions:                                                                    (5 x 8 = 40)

  1. Determine the maxima and minima of.
  2. Find the equation of the tangent and normal to the curve at.
  3. Evaluate (a); (b).
  4. Show that

 

  1. Find the sum to infinity the series.
  2. Expand in terms.
  3. 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.
  1. 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)

 

  1. (a) Find the angle of intersection of the cardioids  and                                         .

(b) If, prove that.                  (12 + 8)

  1. (a) Evaluate .

(b) Integrate  with respect to x using Bernoulli’s formula.

(c) Solve .                                                                     (8 + 4 + 8)

  1. (a) Sum to infinity the series .

(b) Find the characteristic roots and the characteristic vectors of the matrix

 (8 + 12)

  1. (a) Prove that.

(b) If  in  show that.                   (10 + 10)

 

 

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