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Mathematics-IV (BAS303) AKTU previous year questions 2021–2026

Every Mathematics-IV question from 10 AKTU papers, tagged by unit, topic and marks. A few recent questions from each unit are listed below; open the page to filter by unit, topic or mark type.

Unit 1: Partial Differential Equations – AKTU PYQs

  • What is a linear partial differential equation of first order? Write its general form. (2 marks, 2026, Origin of PDE)
  • State Charpit's method and mention when it is used. (2 marks, 2026, Charpit's Non-Linear PDE Method)
  • Solve the linear partial differential equation (y + z) ∂z/∂x + (x + z) ∂z/∂y = x + y using Lagrange's method. (7 marks, 2026, Lagrange's Linear PDE Method)
  • Solve the non-linear partial differential equation p² + q² = z where p = ∂z/∂x, q = ∂z/∂y using Charpit's method. (7 marks, 2026, Charpit's Non-Linear PDE Method)
  • Solve the partial differential equation (D² - 4DD' + 4D'²)z = e^(2x+y). (7 marks, 2026, Higher Order Linear PDE)

Unit 2: Applications of PDE and Fourier Transform – AKTU PYQs

  • Write the one-dimensional heat equation and mention the physical meaning of each term. (2 marks, 2026, Heat and Wave Equations)
  • 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, 2026, Heat and Wave Equations)
  • 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, 2026, Heat and Wave Equations)
  • 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, 2026, Fourier Transform and Inverse)
  • How many arbitrary constants in the solution of 1-dimensional wave equation? (2 marks, 2025, Heat and Wave Equations)

Unit 3: Statistical Techniques I – AKTU PYQs

  • Define the coefficient of skewness based on moments. (2 marks, 2026, Measures of Central Tendency)
  • What is meant by regression line of Y on X? (2 marks, 2026, Regression Analysis)
  • 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, 2026, Regression Analysis)
  • 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, 2026, Measures of Central Tendency)
  • 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, 2026, Curve Fitting Least Squares)

Unit 4: Statistical Techniques II – AKTU PYQs

  • Define a probability density function (p.d.f.) and state its two properties. (2 marks, 2026, Probability and Random Variables)
  • 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, 2026, Normal Distribution)
  • 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, 2026, Poisson Distribution)
  • 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, 2026, Probability and Random Variables)
  • Find p and q of Binomial distribution whose mean is 9 and variance 9/4. (2 marks, 2025, Binomial Distribution)

Unit 5: Statistical Techniques III – AKTU PYQs

  • What is a control chart? Name any two types of control charts. (2 marks, 2026, Statistical Quality Control)
  • 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, 2026, Statistical Tests of Significance)
  • 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 preference are independent. (7 marks, 2026, Statistical Tests of Significance)
  • 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 is under control. Given A2 = 0.729, D3 = 0, D4 = 2.282. (7 marks, 2026, Statistical Quality Control)
  • What do you mean by statistical quality control? (2 marks, 2025, Statistical Quality Control)