Mathematics-IV PYQ 2021-22 AKTU (KAS402) Question Paper

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Session 2021-22 · PYQ

AKTU Mathematics-IV (KAS402) previous year question paper 2021-22 for B.Tech Semester 3/4. Covers Partial Differential Equations, Applications of PDE and…

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Mathematics-IV AKTU syllabus

  1. Unit 1: Partial Differential Equations
  2. Unit 2: Applications of PDE and Fourier Transform
  3. Unit 3: Statistical Techniques I
  4. Unit 4: Statistical Techniques II
  5. Unit 5: Statistical Techniques III

Questions in Mathematics-IV AKTU PYQ 2021-22

  1. Q1a. Solve the partial differential equation p + q = 1. (2 marks, 2021-22)
  2. Q1b. Calculate particular Integral (P.I.) of (D - 3D' + 2)z = e^(x+2y). (2 marks, 2021-22)
  3. Q1c. Tell the classification of the following partial differential equation: 5(∂²u/∂x²) - 9(∂²u/∂x∂t) + 4(∂²u/∂t²) = 0. (2 marks, 2021-22)
  4. Q1d. Write down the two-dimensional wave equation. (2 marks, 2021-22)
  5. Q1e. Calculate the moment generating function of the negative exponential function f(x) = λe^(-λx); x, λ > 0. (2 marks, 2021-22)
  6. Q1f. If Regression Coefficients are 0.8 and 0.8, what would be the value of coefficient of correlation? (2 marks, 2021-22)
  7. Q1g. A die is tossed twice. A success is getting 2 or 3 on a toss. Calculate mean. (2 marks, 2021-22)
  8. Q1h. Write Statement of Baye's theorem. (2 marks, 2021-22)
  9. Q1i. When we use F-test? (2 marks, 2021-22)
  10. Q1j. Explain one-way ANOVA classification. (2 marks, 2021-22)
  11. Q2a. Solve the following partial differential equation by Charpit Method: px + qy = pq. (10 marks, 2021-22)
  12. Q2b. Determine the solution of one dimensional heat equation ∂u/∂t = ∂²u/∂x² where the boundary conditions are u(0,t) = 0, u(l,t) = 0 (t > 0) and the initial condition u(x,0) = 3sin(πx/l), l being the length of the bar. (10 marks, 2021-22)
  13. Q2c. From the following data, determine the equations of line of regression of y on x and x on y. x: 6 2 10 4 8, y: 9 11 5 8 7. (10 marks, 2021-22)
  14. Q2d. In a test on 2000 electric bulbs, the life was normally distributed with average life of 2040 hours and S.D of 60 hours. Calculate the number of bulbs likely to burn for: (i) More than 2150 hours, (ii) less than 1950 hours, (iii) between 1920 hours and 2160 hours. (10 marks, 2021-22)
  15. Q2e. The 9 items of a sample have the following values: 45, 47, 50, 52, 48, 47, 49, 53, 51. Does the mean of these values differ significantly from the assumed mean 47.5? [t₀.₀₅ = 2.31 for 8 d.f.]. (10 marks, 2021-22)
  16. Q3a. Solve the partial differential equation x²(∂²z/∂x²) - y²(∂²z/∂y²) = xy. (10 marks, 2021-22)
  17. Q3b. Use Cauchy's method of characteristics to solve the first order PDE: u_x + u_y = 1 + cos y, u(0,y) = sin y. (10 marks, 2021-22)
  18. Q4a. Solve the following PDE by method of separation of variables: ∂u/∂t - ∂u/∂x + 2u = 0, u(x,0) = 10e^(-x) - 6e^(-4x). (10 marks, 2021-22)
  19. Q4b. Determine the solution of Laplace equation ∂²u/∂x² + ∂²u/∂y² = 0 subject to the boundary conditions u(0,y) = u(l,y) = u(x,0) = 0 and u(x,a) = f(x). (10 marks, 2021-22)
  20. Q5a. Compute skewness and kurtosis, if the first four moments of a frequency distribution about the value 4 of the variable are 1, 4, 10 and 45. (10 marks, 2021-22)
  21. Q5b. Use the method of least squares to fit the curve y = c₀x + c₁/√x for the following data: x: 0.2 0.3 0.5 1 2, y: 16 14 11 6 3. (10 marks, 2021-22)
  22. Q6a. Two urns contain 4 white, 6 blue and 4 white, 5 blue balls respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is white, what is the probability that it was drawn from the (i) first urn (ii) second urn? (10 marks, 2021-22)
  23. Q6b. The following table gives the number of days in a 50-day period during which automobile accidents occurred in a city: No. of accidents: 0 1 2 3 4, No. of days: 21 18 7 3 1. Fit a Poisson distribution to the data and calculate the theoretical frequencies. (10 marks, 2021-22)
  24. Q7a. The demand for a particular spare part in a factory was found to vary from day to day: Days: Mon Tue Wed Thu Fri Sat, No. of parts demanded: 1124 1125 1110 1120 1126 1115. Use χ²-test to test the hypothesis that the number of parts demanded does not depend on the day of the week. [χ²₀.₀₅ = 11.07… (10 marks, 2021-22)
  25. Q7b. Following is the data of defectives of 10 samples of size 100 each. Sample no: 1-10, No. of defectives: 15 11 9 6 5 4 3 2 7 1. Construct p-chart and state whether the process is in statistical control. (10 marks, 2021-22)

AKTU paper codes: BAS303, BAS303H, BAS403, BAS403H, KAS302, KAS402

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