Rajasthan Technical University 2009-4th Sem B.E Electrical Engineering : (- ) Advanced Mathmetics - Question Paper
Rajasthan tech. University(RTU)
B.Tech IV sem. back exam
January 2009
Advanced Mathmetics
7. (a) A and B throw alternately with a pair of dice. The one who throws 9 first wins. Show that the
chances of their winning are 9 : 8.
8
(b) There are 3 boxes containing respectively 1 white,
2 red and 3 black balls ; 2 white, 3 red and 1 black ball; 3 white, 1 red and 2 black balls. A box is chosen at random and from it two balls are drawn at random. The two balls are one red and one white. Find the probability that these came from
(i) the first box, (ii) the second box, (iii) the third box. 8
8. (a) Define Binomial distribution. Find mean and
variance of Binomial distribution.
8
(b) A coin is tossed 4 times. What is the probability of getting (i) two heads, (ii) at least two heads? 8
9. (a) If the probability of a bad reaction from a certain injection is 0-001, determine the chance that out of 2000 individuals more than two will get a bad reaction. 8
(b) If the heights of 300 students are normally distributed with mean 64-5 inches and standard deviation 3-3 inches, how many students have heights
(i) less than 5 feet, i.e., 60 inches
(ii) between 5 feet and 5 feet 9 inches?
[Use P(Q<t<\ *36)=0'4131.J
8
4181 Paper VI ii
II B.E. (IV SEMESTER) (BACK) EXAMINATION, 2009
(New Four Year Semester Scheme)
[Branch : Electrical Engineering]
Paper VI (i) ADVANCED MATHEMATICS
Time Allowed : Three Hours Maximum Marks 80
(1) No supplementary answer-book will be given to any candidate. Hence the candidates should vjrite the answer precisely in the Main answer-book only.
(2) All the parts of one question should be answered at one place in the answer-book. One complete question should not be answered at different places in the answer-book.
Turn over
Attempt any five questions. All questions carry equal marks.
1. (a) From the following table of values of x and f(x), determine:
x : 0-20 0-22 0-24. 0-26 0-28 0-30
f(x) : 1-6596 1-6698 1-6804 1-6912 1-7024 1-7139
8
(b) Consider the following data: x: 1 3 4
y: 4 12 19 Use Lagranges formula for inverse interpolation to obtain the value of x for which y7. 8
(a-) Solve jc15jc+3=0 by Newton-Raphson method.
8
(b) Solve the following equations:
10x+2y+z=9 2x+20y2z=44 2x+3y+ 10z=22 by using Gauss-Seidel method: 8
je : 123456789 _y: 2. 6 7 8 10 11 11 10 9
using Simpsons i rule
r
(ib) Evaluate
1+x2
4. (a) Using Picards method, obtain the solution of:-
=x+x y,
dx
given that when x=0, y=3. Findy(Ol) and y(0- 2)- 8
(b) Use Runge-Kutta fourth order method to solve:
= 2xy , y (0) = 1 with /z=0 2
dx
for x= '02 and xQ-4.
5. (a) Find:
(b) Find:
/ \ z
Z~x
6. (a) Solve:
yn+2-3yn+i-4yn=3n.
(b) State and prove the Bayes theorem.
4181 Turn over
(a) Fit a second degree parabola to the following data taking x as the independent variable:
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