Name of the University : Visvesvaraya Technological University
Name of the Exam : B.E. Degree(CBCS)Examination
Degree : B.E. / B.Tech.
Paper : Engineering Mathematics
Year : 2016-17
Document Type : Model Question Paper
Website : https://vtu.ac.in/
Download Question Paper :
Engg Maths Paper I 2016 : https://www.pdfquestion.in/uploads/14117-engmath1.pdf
Engg Maths Paper II 2016 : https://www.pdfquestion.in/uploads/14117-engmath2.pdf
Engg Maths Paper – III 2016 : https://www.pdfquestion.in/uploads/14117-engmat3.pdf
B.E./B.Tech. Engineering Mathematics Model Question Paper :
Engineering Mathematics Paper – I :
Time: 3 Hrs
Max.Marks: 80
Related : Visvesvaraya Technological University Basic Electrical Engineering Model Question Paper 2016 : www.pdfquestion.in/8712.html
Note :
** Answer any FIVE full questions, choosing at least ONE question from each module.
** Statistical tables may be provided.
Module-I :
1. (a) Using Taylor’s series method, solve the initial value problem 1,dx /dy=xy2-1y(0)=1 and hence find the the value of y at the point x =0.1. (05 Marks)
(b) Derive Cauchy-Riemann equation in cartesian form.(05 Marks)
(c)Discuss the transformation . 2 w = z (05 Marks)
Module – II :
(a) Find the analytic function whose real part is cos2 = 2 r (05 Marks)
(b) State and prove Cauchy’s theorem. (05 Marks)
(c) Find the bilinear transformation which maps the points z = i,0 into the points w – 1,i,1. (05 Marks)
Module-III :
(a) Derive mean and variance of the Poisson distribution. (05 Marks)
(b) A random variable X has the following probability function for various values of x
(c) Let X be the random variable with the following distribution and Y is defined by X2 Determine (i) the distribution of g of Y (ii) joint distribution of X and Y (iii) E(X), E(Y) , E(XY).
Module-IV :
(a) When a coin is tossed 4 times find, using binomial distribution, the probability of getting (i) exactly one head (ii) at most 3 heads (iii) at least 3 heads. (05 Marks)
(b) In a normal distribution, 31% of the items are under 45 and 8% of the items are over 64%. Find the mean and standard deviation of the distribution. (05 Marks)
(c) A fair coin is tossed thrice. The random variables X and Y are defined as follows X=0 or 1 according as head or tail occurs on the first; Y= Number of heads. Determine (i) the distribution of X and Y (ii) joint distribution of X and Y. (06 Marks)
Engineering Mathematics-IV :
Note :
** Answer any FIVE full questions, choosing at least ONE question from each module.
** Use of statistical tables allowed.
Module-I :
(a) Derive Cauchy-Riemann equation in cartesian form.
(b) Derive Cauchy-Riemann equation in polar form
(C) Find the analytic function whose real part is cos 2 . 2 r (05 Marks)
Module – II :
(a) State and prove Cauchy’s theorem. (05 Marks)
(b) Find the bi linear transformation which maps the points z , i,0 into the points w = -1,-i,1. (06 Marks)
Module – III :
(a) Derive mean and variance of the Poisson distribution. (05 Marks)
(b) A random variable X has the following probability function for various values of x Find (i) the value of k (ii) P(x 6)(iii) P(x > 6)
(c) Determine (i) the distribution of g of Y (ii) joint distribution of X and Y (iii) E(X), E(Y) , E(XY).
Module-IV :
(a) When a coin is tossed 4 times find, using binomial distribution, the probability of getting (i) exactly one head (ii) at most 3 heads (iii) at least 3 heads. (05 Marks)
(b) In a normal distribution, 31% of the items are under 45 and 8% of the items are over 64%. Find the mean and standard deviation of the distribution. (05 Marks)
(c) A fair coin is tossed thrice. The random variables X and Y are defined as follows X=0 or 1 according as head or tail occurs on the first; Y= Number of heads.
Determine (i) the distribution of X and Y (ii) joint distribution of X and Y.
Module-V :
9. (a) Define the terms:(i)Null hypothesis (ii)Confidence intervals (iii)Type-I and Type-II errors (05marks)
(b) Ten individuals are chosen at random from a population and their heights in inches are found to be 63,63,66,67,68,69,70,70,71,71.Test the hypothesis that the mean height of the universe is 66 nches. (t0.05 = 2.262 for 9 d.f.).
OR
(a) A manufacture claimed that at least 95%of the equipment which he supplied to a factory conformed to specifications. An examination of a sample of 200 pieces of equipment revealed that 18 of them were faulty. Test his claim at a significance level of 1% and 5%. (05 marks)
(b) Explain (i) transient state (ii) absorbing state (iii) recurrent state of a Markov chain. (05marks)
(c) Three boys A, B and C are throwing a ball to each other. A always throws the ball to B and B always throws the ball to C. But C is just as likely to throw the ball to B as to A. If C was the first person to throw the ball , find the probabilities that after three throws (i) A has the ball (ii) B has the ball and
(iii) C has the ball. (06marks)