Mathematics-IV PYQ 2025-26 AKTU (BAS303) Question Paper

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Session 2025-26 · PYQ

AKTU Mathematics-IV (BAS303) previous year question paper 2025-26 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 2025-26

  1. Q1a. What is a linear partial differential equation of first order? Write its general form. (2 marks, 2025-26)
  2. Q1b. Write the one-dimensional heat equation and mention the physical meaning of each term. (2 marks, 2025-26)
  3. Q1c. Define the coefficient of skewness based on moments. (2 marks, 2025-26)
  4. Q1d. State Charpit's method and mention when it is used. (2 marks, 2025-26)
  5. Q1e. What is a control chart? Name any two types of control charts. (2 marks, 2025-26)
  6. Q1f. Define a probability density function (p.d.f.) and state its two properties. (2 marks, 2025-26)
  7. Q1g. What is meant by regression line of Y on X? (2 marks, 2025-26)
  8. Q2a. Solve the linear partial differential equation (y + z) ∂z/∂x + (x + z) ∂z/∂y = x + y using Lagrange's method. (7 marks, 2025-26)
  9. Q2b. Solve the one-dimensional heat equation ∂u/∂t = c² (∂²u/∂x²), 0 < x < L, t > 0 subject to the boundary conditions u(0,t) = 0, u(L,t) = 0 and the initial condition u(x, 0) = x(L - x) using the method of separation of variables. (7 marks, 2025-26)
  10. Q2c. The following data relate to variables X and Y: X: 2 4 6 8 10, Y: 5 9 13 17 21. Find the correlation coefficient and obtain the regression lines of Y on X and X on Y. (7 marks, 2025-26)
  11. Q2d. The lifetime of an electric bulb is normally distributed with mean 1200 hours and standard deviation 100 hours. 1. Find the probability that a bulb lasts (a) more than 1300 hours, (b) between 1100 and 1250 hours. 2. Out of 2000 bulbs, how many are expected to last more than 1400 hours? (7 marks, 2025-26)
  12. Q2e. Two independent random samples from two normal populations gave the following results: Sample I: size 10, mean 52, SD 6; Sample II: size 12, mean 47, SD 5. Test whether the difference between the sample means is significant at 5% level of significance. Assume population variances are equal. (7 marks, 2025-26)
  13. Q3a. Solve the non-linear partial differential equation p² + q² = z where p = ∂z/∂x, q = ∂z/∂y using Charpit's method. (7 marks, 2025-26)
  14. Q3b. Solve the partial differential equation (D² - 4DD' + 4D'²)z = e^(2x+y). (7 marks, 2025-26)
  15. Q4a. Solve the wave equation ∂²u/∂t² = c² ∂²u/∂x², 0 < x < L subject to u(0,t) = 0, u(L,t) = 0, u(x, 0) = sin(πx/L), ∂u/∂t(x, 0) = 0. (7 marks, 2025-26)
  16. Q4b. Using the Fourier transform method, solve the partial differential equation ∂u/∂t = k ∂²u/∂x², -∞ < x < ∞, t > 0 subject to the initial condition u(x, 0) = e^(-a|x|). (7 marks, 2025-26)
  17. Q5a. The following data give the frequency distribution of a variable X: X: 10 20 30 40 50, f: 3 7 12 8 4. Find the first four moments about the mean and hence determine the coefficients of skewness and kurtosis. (7 marks, 2025-26)
  18. Q5b. Fit a parabola of the form y = a + bx + cx² to the data: x: 0 1 2 3 4, y: 1 2 5 10 17. (7 marks, 2025-26)
  19. Q6a. The number of typing errors per page in a book follows a Poisson distribution with mean 2. 1. Find the probability that a randomly chosen page has (a) no error (b) at most two errors. 2. If a book has 500 pages, estimate the expected number of pages with exactly three errors. (7 marks, 2025-26)
  20. Q6b. A discrete random variable X has the following probability distribution: x: 0 1 2 3 4, P(X=x): k 2k 3k 2k k. Find the value of k and determine the mean and variance of X. (7 marks, 2025-26)
  21. Q7a. The following table shows the distribution of students according to gender and preference of subject: Male: Science 50, Arts 30, Commerce 20, Total 100; Female: Science 40, Arts 50, Commerce 30, Total 120; Total: 90, 80, 50, 220. Test at 5% level of significance whether gender and subject… (7 marks, 2025-26)
  22. Q7b. Five samples, each of size 4, were taken from a production process. The sample means and ranges are given below: Sample 1: mean 20, R 4; Sample 2: mean 22, R 5; Sample 3: mean 19, R 3; Sample 4: mean 21, R 4; Sample 5: mean 23, R 6. Construct x̄-chart and R-chart and comment on whether the process… (7 marks, 2025-26)

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

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