LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – CHEMISTRY

FOURTH SEMESTER – APRIL 2012

# MT 4204 / 4201 – ADVANCED MATHS FOR CHEMISTRY

Date : 19-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

Part A (Answer ALL the questions)                                                                       (10×2=20)

1. Evaluate .
2. Show that.
3. Find .
4. Find.
5. If are the roots of the equation , then show that are the roots of the equation .
6. Find the equation whose roots are the roots of with signs changed.
7. Define Null hypothesis.
8. Write the normal equations for the curve .
9. Solve the system of equations 5xy+6=0 & x-2y+3=0.
10. Write down Newton backward formula.

# Part B (Answer any FIVE questions)                                                                     (5×8=40)

1. Evaluate and .
2. By changing the order of integration, evaluate .
3. Find the Laplace transform of
4. Solve the equation  of which one root is .
5. If, show that.
6. Fit a straight line for the following data.
 X 1 2 3 4 5 6 7 8 9 10 Y 52.5 58.7 65 70.2 75.4 81.1 87.2 95.5 102.5 108.4
1. Solve the following equations by Gauss-Seidel method:,, .
2. Find a root of the equation correct to three decimal places by using bisection method.

# Part C (Answer any TWO questions)                                                                     (2×20=40)

1. (a) Evaluate  over the region in the first quadrant bounded by the hyperbolas  and  and the circles  and  .

(b) Prove that .                                                                                   (10+10)

1. (a) Find and .

(b) Using Laplace transform solve  given that .

(10+10)

1. (a) Solve the equation.

(b) Find the condition that the roots of the equation   may be in geometric progression. Hence solve the equation                                                                                                                                                          (10+10)

1. (a) Obtain the equations of two lines of regressions for the following data.

X  :           65        66        67        67        68        69        70        72

Y  :           67        68        65        68        72        72        69        71

(b) Solve the following system of equations , ,  using Cramer’s rule.                                                                   (10+10)

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