MAY 2018 Sub. Code: 4012
M.Sc. MEDICAL PHYSICS EXAMS
FIRST YEAR
PAPER II RADIOLOGICAL MATHEMATICS
Q.P. Code 284012
Time Three hours Maximum 100 Marks
I. Elaborate on: x 20 40)
1. Derive Newton-Raphson formula to find the actual root of an equation 0.
Using Newton-Raphson iteration method show that the root of the equation
Xlog10X= 1.2 is approximately 2.5.
2. Discuss correlation and regression.
Fit a regression line of Y on X and then predict Y if X 10 from the bivariate
data
X 1 5 3 2 1 1 7 3
Y 6 1 0 0 1 2 1 5
II. Write notes on: (10 x 6 60)
1. In a computational work, the approximate value of 4 is determined as 4.00012.
Find the error, absolute error, relative error and percentage error.
2. Define decay constant and prepare a decay chart and tabulate for Co-60 isotope
for the period one half life.
3. Use Runge-Kutta method to find y for x 0.2 for the differential equation dy/dx
x y2. Given 1 and h 0.1.
4. Discuss poisson distribution.
5. Find the variance and standard deviation for the following data:
57, 64, 43, 67, 49, 59, 44, 47, 61, 59
6. Given dy/dx 1 xy, 1. Obtain Taylor series for and compute f(0.1).
Correct it to 4 decimal places.
7. Evaluate the integral of by 6 intervals using Simpson's 3/8 rule.
8. Explain data collection and its graphical representation.
9. The values of capacitances in of ten capacitors selected at random from a large
batch of similar capacitors are: 34.3, 25.0, 30.4, 34.6, 29.6, 28.7, 33.4, 32.7, 29.0
and 31.3. Determine the standard deviation from the mean for these capacitors.
10. State the properties and applications of Chi-squared distribution.