Mathematics-IV PYQ 2024-25 AKTU (BAS403) Question Paper

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

AKTU Mathematics-IV (BAS403) 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. Form the partial differential equation by eliminating arbitrary function from the following: z = f(x + it) + g(x - it). (2 marks, 2024-25)
  2. Q1b. Use the method of characteristics to solve the first order PDE u_x - yu = 0; u(0, y) = 1. (2 marks, 2024-25)
  3. Q1c. Classify the following operator: t(∂²u/∂t²) + 2(∂²u/∂x∂t) + x(∂²u/∂x²) - (∂u/∂x). (2 marks, 2024-25)
  4. Q1d. The first three moments of a distribution, about the value '2' of the variable are 1, 16 and -40. Find the mean and variance of the distribution. (2 marks, 2024-25)
  5. Q1e. Find the regression coefficient of y on x for the following: n = 10, x̄ = 13, ȳ = 22. (2 marks, 2024-25)
  6. Q1f. If X and Y are two random variables having joint density function: f(x,y) = (1/8)(6-x-y); 0 ≤ x < 2, 2 ≤ y < 4; 0 otherwise. Find P(X < 1 ∩ Y < 3). (2 marks, 2024-25)
  7. Q1g. Write the formula of Chi-square χ² test. (2 marks, 2024-25)
  8. Q2a. Solve the following differential equation using Lagrange's equation: (x² - yz)p + (y² - zx)q = z² - xy. (7 marks, 2024-25)
  9. Q2b. A tightly stretched flexible string has its ends fixed at x = 0 and x = l. At time t = 0, the string is given a shape defined by F(x) = μx(l − x), μ is a constant and then released. Find the displacement y(x,t) of any point x of the string at any time t > 0. (7 marks, 2024-25)
  10. Q2c. The first four moments about the working mean 28.5 of a distribution are 0.294, 7.144, 42.409 and 454.98. Calculate the moments about the mean. Also evaluate β1, β2 and comment upon the skewness and kurtosis of the distribution. (7 marks, 2024-25)
  11. Q2d. If the heights of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches, find the height below which 99% of the students lie (P(z=2.327)=0.49). (7 marks, 2024-25)
  12. Q2e. The following table shows the distribution of digits in numbers chosen at random from a telephone directory: Digits 0-9, Frequency: 1026 1107 997 966 1075 933 1107 972 964 853. Test whether the digits may be taken to occur equally frequently in the directory. (χ² at 5% level of significance for 9… (7 marks, 2024-25)
  13. Q3a. Solve the partial differential equation: ∂²z/∂x² - ∂²z/∂y² = tan³x·tany − tanx·tan³y. (7 marks, 2024-25)
  14. Q3b. Solve: (D − D' − 1)(D − D' − 2)z = sin(2x + 3y). (7 marks, 2024-25)
  15. Q4a. A bar with insulated sides is initially at a temperature 0°C throughout. The end x = 0 is kept at 0°C, and heat is suddenly applied at the end x = l so that ∂u/∂x = A for x = l, where A is a constant. Find the temperature function u(x,t). (7 marks, 2024-25)
  16. Q4b. Find the Fourier Cosine transform of f(x) = 1/(1 + x²). (7 marks, 2024-25)
  17. Q5a. Obtain a relation of the form y = ab^x for the following data by the method of least squares: x: 2 3 4 5 6, y: 8.3 15.4 33.1 65.2 127.4. (7 marks, 2024-25)
  18. Q5b. For 10 observations on price (x) and supply (y), the following data were obtained: Σx = 130, Σy = 220, Σx² = 2288, Σy² = 5506 and Σxy = 3467. Obtain the two lines of regression and estimate the supply when the price is 16 units. (7 marks, 2024-25)
  19. Q6a. A manufacturer knows that the condensers he makes contain on an average 1% of defectives. He packs them in boxes of 100. What is the probability that a box picked at random will contain 4 or more faulty condensers? (7 marks, 2024-25)
  20. Q6b. In a sample of 1000 cases, the mean of a certain test is 14 and S.D. is 2.5. Assuming the distribution to be normal, find (i) How many students score between 12 and 15? (ii) How many score above 18? (iii) How many score below 8? (iv) How many score 16? Given P(Z=0.8)=0.2881, P(Z=0.4)=0.1554,… (7 marks, 2024-25)
  21. Q7a. 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 γ = 8). (7 marks, 2024-25)
  22. Q7b. In a blade manufacturing factory, 1000 blades are examined daily. Draw the np chart for the following table and examine whether the process is under control? Date 1-15, No. of Defective blades: 9 10 12 8 7 15 10 12 10 8 7 13 14 15 16. (7 marks, 2024-25)

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

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