Download VTU B-Tech/B.E 2019 June-July 1st And 2nd Semester 10 Scheme 10MAT41 Engineering Mathematics IV Question Paper

Firstranker's choice

FirstRanker.com

Fourth Semester B.E. Degree Examination, June/July 2019

--- Content provided by‍ FirstRanker.com ---

Engineering Mathematics - IV

10MAT41

Time: 3 hrs.

Max. Marks:100

Note: Answer FIVE full questions, selecting atleast TWO questions from each part.

--- Content provided by​ FirstRanker.com ---

PART - A

1. 1. Find by Taylor's series method the value of y at x = 0.1 and x = 0.2 correct to four decimal places from dx = x²y -1, y(0)=1.

      (07 Marks)

   2. Using modified Euler's method find y(20.2) and y(20.4) given that dx = lo2 10 (I-.) with y(20) = 5 taking h = 0.2 (use modified formula twice).

      --- Content provided by​ FirstRanker.com ---

      (07 Marks)

   3. Given d = x²(1 + y) and y(1)=1, y(1.1)=1.233, y(1.2)=1.548, y(1.3)=1.979. Evaluate y(1.4) by Adam's Bashforth method.

      (06 Marks)

   --- Content provided by FirstRanker.com ---

2. 1. Obtain the solution using fourth order Runge-Kutta method of the system of equations d/dt = 2x + y, d/dx = x-3y; t = 0, x = 0, y = 05 Take h = 0.2.

      (07 Marks)

   2. Obtain second approximation values of vaz to x = 0.1 using Picard's method, given that y(0) = 2, z(0) = 1 and dy/dx = x + Z, dz/dx = X - y

      --- Content provided by‌ FirstRanker.com ---

      (07 Marks)

   3. Given y" + xy' + y - 0, using Milne's method by the following data :

      X	0	0.1	0.2	0.3
      y	1	0.995	0.9801	0.956
      y'	0	-0.995	-0.196	-0.2867

      (06 Marks)

   --- Content provided by⁠ FirstRanker.com ---

3. 1. Derive Cauchy-Riemann equations in polar form.

      (06 Marks)

   2. If (I) + ill' represents the complex potential of an electrostatic field where kv = x² - y², find the complex potential as a function of z and hence determine 4).

      --- Content provided by⁠ FirstRanker.com ---

      (06 Marks)

   3. If f(z) is analytic, show that (?²/?x² + ?²/?y²)\if(z)\²=4\f'(z)\²

      (07 Marks)

   --- Content provided by FirstRanker.com ---

4. 1. Find the bilinear transformation which maps the points z = 1, i, -1 into w = 0, 1, 8.

      (07 Marks)

   2. Find the image of the circles |z| = 1 and |z| = 2 under the mapping w = z + (1/z)

      --- Content provided by‌ FirstRanker.com ---

      (06 Marks)

   3. State and prove Cauchy's integral formula for the analytic function f(z) inside and on a simple closed curve.

      (07 Marks)

   --- Content provided by‌ FirstRanker.com ---

PART - B

1. 1. Find the series solution of Bessel's differential equation leading to Bessel function.

      (07 Marks)

   --- Content provided by‌ FirstRanker.com ---

   2. If a and 13 are two roots of .11(x) = 0, then show that ?xJ n (ax).1,(13x)dx = 0 if a ? 13.

      (07 Marks)

   3. Show that x⁴ -3x² + x = (4/5)P₄(x) + (4/7)P₂(x) + (1/5)P₁(x)= -5110(x)-

      (06 Marks)

      --- Content provided by​ FirstRanker.com ---

2. 1. A problem in mathematics is given to three students A, B and C whose changes of solving it are 1/2, 3/4 and 3/4 respectively. What is the probability that the problem will be solved?

      (07 Marks)

   --- Content provided by‍ FirstRanker.com ---

   2. Give P(A) = 3/5, P(B)= 1/5 and P(An B) = 1/20. Find : i) P(A/B) ii) P(A / B) iii) P(A / B) .

      (06 Marks)

   3. State and proved Baye's theorem o conditional probability.

      (07 Marks)

      --- Content provided by‍ FirstRanker.com ---

3. 1. A die is tossed thrice. A success is 'getting 1 or 6' on a toss. Find the mean and variance of the number of successes.

      (07 Marks)

   --- Content provided by​ FirstRanker.com ---

   2. A die is thrown 8 times. Find the probability that '3' falls, i) Exactly 2 times ii) Atleast once iii) At the most 7 times.

   3. Define exponential distribution and obtain the mean and standard deviation of exponential distribution.

      (07 Marks)

   --- Content provided by‍ FirstRanker.com ---

4. 1. Certain tubes manufactured by a company have mean life time of 800 hours and standard deviation of 60 hours. find the probability that a random sample of 16 tubes taken from the group will have a mean life time : i) Between 770 hours and 830 hours ii) Less than 785 hours iii) More than 820 hours (Given (I)(2) = 0.4772 ; 4)(1) = 0.3413; (1(1.33) = 0.4082).

      (07 Marks)

   2. A sample of 900 days was taken in a coastal town and it was found that on 100 days the weather was very hot. Obtain the probable limits of the percentage of very hot weather.

      --- Content provided by FirstRanker.com ---

      (06 Marks)

   3. A sample analysis of examination results of 500 students was made. It was found that 220 students had failed, 170 had secured third class, 90 had secured second class and 20 had secured first class. Do these figures support the general examination result which is in the ratio 4:3:2:1 for the respective categories (x².05 = 7.81 for 3 d.f)

      (07 Marks)

   --- Content provided by⁠ FirstRanker.com ---

FirstRanker.com