Mathematics-IV PYQ 2024-25 AKTU (BAS303) Question Paper

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Session 2024-25 · PYQ

AKTU Mathematics-IV (BAS303) previous year question paper 2024-25 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 2024-25

  1. Q1a. Solve the PDE yzp - xzq = xy. (2 marks, 2024-25)
  2. Q1b. How many arbitrary constants in the solution of 1-dimensional wave equation? (2 marks, 2024-25)
  3. Q1c. The first three moments of a distribution are 6, 25, -41. Find the moment coefficient of skewness. (2 marks, 2024-25)
  4. Q1d. Find p and q of Binomial distribution whose mean is 9 and variance 9/4. (2 marks, 2024-25)
  5. Q1e. Explain the probability density function. (2 marks, 2024-25)
  6. Q1f. What do you mean by statistical quality control? (2 marks, 2024-25)
  7. Q1g. Define the Null hypothesis. (2 marks, 2024-25)
  8. Q2a. Solve: r - 4s + 4t + p - 2q = e^(x+y) cos(2x + 3y). (7 marks, 2024-25)
  9. Q2b. Solve by the method of separation of variables: 4(∂u/∂t) + (∂u/∂x) = 3u, u = 3e^(-x) - e^(-5x), when t = 0. (7 marks, 2024-25)
  10. Q2c. The two regression equations are 3x + 2y = 26 and 6x + y = 31. Find (i) mean of x and y (ii) the correlation coefficient between x and y (iii) if variance of x = 9 then find variance of y. (7 marks, 2024-25)
  11. Q2d. If Z is a standard normal variable, find the following probabilities: (i) P(Z < 1.2) (ii) P(Z > -1.2) (iii) P(-1.2 < Z < 1.3). (7 marks, 2024-25)
  12. Q2e. What are statistical quality control techniques? Discuss the objectives and advantages of SQC. (7 marks, 2024-25)
  13. Q3a. Solve: (x² – y² – yz)p + (x² – y² – zx)q = z(x – y). (7 marks, 2024-25)
  14. Q3b. Solve: (D² – DD' – 2D'²)z = (y – 1)eˣ. (7 marks, 2024-25)
  15. Q4a. Solve the Laplace equation ∂²u/∂x² + ∂²u/∂y² = 0, which satisfies the conditions: u(0,y) = u(l,y) = u(x,0) = 0 and u(x,a) = sin(nπx/l). (7 marks, 2024-25)
  16. Q4b. A string is stretched and fastened to two points l apart, motion is started by displacing the string into the form y = k(lx – x²) from which it is released at time t=0. Find the displacement of any point on the string at a distance of x from one end at time t. (7 marks, 2024-25)
  17. Q5a. Fit the curve y = ae^(bx): x: 2 4 6 8 10, y: 4.077 11.084 30.128 81.897 222.62. (7 marks, 2024-25)
  18. Q5b. Calculate all four moments about mean and also skewness and kurtosis. Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70, Students: 1 6 10 15 11 7 10. (7 marks, 2024-25)
  19. Q6a. In a certain factory turning out razor blades, there is a small chance of 0.002 for any blade to be defective. The blades are supplied in packets of 10. Calculate the approx. no. of packets containing (i) no defective (ii) one defective (iii) two defective blades in a consignment of 10,000 packets. (7 marks, 2024-25)
  20. Q6b. 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. (7 marks, 2024-25)
  21. Q7a. Two independent samples of 8 and 7 items respectively had the following values of the variables: Sample I: 9 11 13 11 15 9 12 14, Sample II: 10 12 10 14 9 8 10. Is the difference between the means of the sample significant? (7 marks, 2024-25)
  22. Q7b. By using Chi-square test, find whether there is any association between income level and type of schooling: Income vs Public school / Govt. School: Low: 200, 400; High: 1000, 400. (7 marks, 2024-25)

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

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