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)
- Evaluate .
- Show that.
- Find .
- If are the roots of the equation , then show that are the roots of the equation .
- Find the equation whose roots are the roots of with signs changed.
- Define Null hypothesis.
- Write the normal equations for the curve .
- Solve the system of equations 5x–y+6=0 & x-2y+3=0.
- Write down Newton backward formula.
Part B (Answer any FIVE questions) (5×8=40)
- Evaluate and .
- By changing the order of integration, evaluate .
- Find the Laplace transform of
- Solve the equation of which one root is .
- If, show that.
- Fit a straight line for the following data.
- Solve the following equations by Gauss-Seidel method:,, .
- Find a root of the equation correct to three decimal places by using bisection method.
Part C (Answer any TWO questions) (2×20=40)
- (a) Evaluate over the region in the first quadrant bounded by the hyperbolas and and the circles and .
(b) Prove that . (10+10)
- (a) Find and .
(b) Using Laplace transform solve given that .
- (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)
- (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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