Mathematics-IV PYQ 2023-24 AKTU (BAS303) Question Paper

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Session 2023-24 · PYQ

AKTU Mathematics-IV (BAS303) previous year question paper 2023-24 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 2023-24

  1. Q1a. Determine the partial differential equation from the equation z = f(2x – y). (2 marks, 2023-24)
  2. Q1b. Classify the following partial differential equation: u_tt + t·u_xt + x·u_xx + 2u_t + u_x + 6u = 0. (2 marks, 2023-24)
  3. Q1c. Write the normal equations to fit the curve y = c₀/x + c₁√x. (2 marks, 2023-24)
  4. Q1d. Find expected mean for the following probability distribution: x: 8 12 16 20 24, p(x): 1/8 1/6 3/8 1/4 1/12. (2 marks, 2023-24)
  5. Q1e. If f(x) has probability density function as px⁴, 0 < x < 1, then calculate p. (2 marks, 2023-24)
  6. Q1f. Explain null hypothesis. (2 marks, 2023-24)
  7. Q1g. Describe control limits of R-chart. (2 marks, 2023-24)
  8. Q2a. Solve y²(x+y)p + x²(x+y)q = (x²+y²)z. (7 marks, 2023-24)
  9. Q2b. Use separation of variables method to solve ∂²u/∂x² + ∂²u/∂y² = 0 subject to boundary conditions u(0,y) = u(5,y) = u(x,0) = 0 and u(x,b) = sin(nπx/5). (7 marks, 2023-24)
  10. Q2c. The first four moments of a distribution about the value 5 of the variable are 2, 20, 40 and 50. Comment upon the skewness and kurtosis of the distribution. (7 marks, 2023-24)
  11. Q2d. If X is a Poisson variate such that P(X=2) = 9P(X=4) + 90P(X=6), find the standard deviation. (7 marks, 2023-24)
  12. Q2e. The mean life of 10 motors was found to be 1450hrs with S.D. of 423hrs. A second sample of 17 motors chosen from a different batch showed a mean life of 1280hrs with a S.D. of 398hrs. Is there a significant difference between means of the two samples? (Given t₀.₀₅ = 2.13). (7 marks, 2023-24)
  13. Q3a. Solve the partial differential equation px + qy = pq. (7 marks, 2023-24)
  14. Q3b. Solve: (D² + DD' - 6D'²)z = cos(2x + y). (7 marks, 2023-24)
  15. Q4a. A tightly stretched string with fixed end points x=0 and x=2 is initially in a position given by y = sin(3πx/2). If it is released from rest from this position, find the displacement y(x,t). (7 marks, 2023-24)
  16. Q4b. Solve the equation ∂u/∂t = ∂²u/∂x², x > 0, t > 0 under the conditions: (i) u(0,t) = 0, (ii) u(x,0) = x for 0 ≤ x ≤ 1, 0 for x ≥ 1, (iii) u(x,t) is bounded. (7 marks, 2023-24)
  17. Q5a. Using the method of least squares to fit a curve of the form y = ae^(bx) to the following data: x: 1 2 3 4 5, y: 1 1.2 1.8 2.5 3.6. (7 marks, 2023-24)
  18. Q5b. Two lines of regression are given by x + 2y - 5 = 0 and 2x + 3y - 8 = 0 and σ²_x = 12. Calculate: (a) the mean values of x and y, (b) variance of y, (c) the coefficient of correlation between x and y. (7 marks, 2023-24)
  19. Q6a. Out of 320 families with 5 children each, how many families would be expected to have (i) 2 boys and 3 girls (ii) at least one boy? Assume equal probability for boys and girls. (7 marks, 2023-24)
  20. Q6b. The daily wages of 1000 workers are distributed around a mean of Rs.140 and with a standard deviation of Rs.10. Estimate the number of workers whose daily wages will be (i) between Rs.140 and Rs.144 (ii) less than Rs.126 (iii) more than Rs.160. (7 marks, 2023-24)
  21. Q7a. The following table gives the classification of 50 workers corresponding to their gender and nature of the work. Discuss whether the nature of work is independent of the gender of the workers. Skilled/Unskilled: Male: 10/20, Female: 25/20. (7 marks, 2023-24)
  22. Q7b. In a manufacturing process, the number of defective items found in the inspection of 10 samples of size 100 each. Construct np-chart and give your comments. Sample no: 1-10, No. of defectives: 6 9 12 5 12 8 8 16 13 7. (7 marks, 2023-24)

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

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