Mathematics-IV PYQ 2022-23 AKTU (KAS302) Question Paper

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Session 2022-23 · PYQ

AKTU Mathematics-IV (KAS302) previous year question paper 2022-23 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 2022-23

  1. Q1a. Find partial differential equation (PDE) by eliminating a and b from z = ax + by + a² + b². (2 marks, 2022-23)
  2. Q1b. Solve the PDE: ∂²z/∂x² - ∂²z/∂y² = 0. (2 marks, 2022-23)
  3. Q1c. Classify the PDE: u_xx + u_yy - u_xy = 0. (2 marks, 2022-23)
  4. Q1d. Write the wave equation in two dimensions. (2 marks, 2022-23)
  5. Q1e. Find the arithmetic mean of the following frequency distribution: x: 1 2 3 4 5 6 7, f: 5 9 12 17 14 10 6. (2 marks, 2022-23)
  6. Q1f. Write the formula of Karl Pearson correlation coefficient and write the range of correlation coefficient. (2 marks, 2022-23)
  7. Q1g. If P(A) = 1/4, P(B) = 1/2, P(A∪B) = 5/8, then find the value of P(A∩B). (2 marks, 2022-23)
  8. Q1h. Write probability mass function of binomial distribution with mean and variance of the distribution. (2 marks, 2022-23)
  9. Q1i. Define Null Hypothesis. (2 marks, 2022-23)
  10. Q1j. Discuss (in brief) Control Charts. (2 marks, 2022-23)
  11. Q2a. Solve (x²D² - y²D'²)z = xy, where D² = ∂²/∂x², D'² = ∂²/∂y². (10 marks, 2022-23)
  12. Q2b. A string is stretched and fastened to two points l meter apart. Motion is started by displacing the string in the form u(x,0) = A sin(πx/l) from which it is released at time t=0. Show that the displacement of any point at a distance x from one end at time t is given by u(x,t) = A sin(πx/l)… (10 marks, 2022-23)
  13. Q2c. Fit a parabolic curve of second degree to the following data: X: 0 1 2 3 4, Y: 1 1.8 1.3 2.5 6.3. (10 marks, 2022-23)
  14. Q2d. A bag contains 10 white and 15 black balls. If two balls are drawn in succession without replacement, find the probability that the first ball is white and the second ball is black. (10 marks, 2022-23)
  15. Q2e. The score of 10 candidates obtained in tests before and after attending coaching classes: Before: 54 76 92 65 75 78 66 82 80 78, After: 60 80 86 72 80 72 66 88 82 73. Is the coaching for the test effective? Test at 5% level of significance. (10 marks, 2022-23)
  16. Q3a. Solve: (mz - ny)p + (nx - lz)q = ly - mx. (10 marks, 2022-23)
  17. Q3b. By Charpit's method, find the complete solution of PDE: px + qy - pq = 0. (10 marks, 2022-23)
  18. Q4a. Solve by the method of separation of variables, the heat equation u_t = u_xx, 0 < x < 1, t > 0 subject to conditions u(x,0) = x - x², u(0,t) = u(1,t) = 0. (10 marks, 2022-23)
  19. Q4b. Solve the Laplace equation u_xx + u_yy = 0, x∈(0,1), y∈(0,1) with conditions u(x,0) = u(x,1) = 0, u(0,y) = 0, u(1,y) = f(y) by method of separation of variables. (10 marks, 2022-23)
  20. Q5a. Calculate the correlation coefficient for the following heights (in inches) of fathers (X) and their sons (Y): X: 65 66 67 67 68 69 70 72, Y: 67 68 65 68 72 72 69 71. (10 marks, 2022-23)
  21. Q5b. The first four moments of a distribution about the value 4 of the variables are -1.5, 17, -30 and 80. Find moments μ₁, μ₂, μ₃, μ₄ about mean. Also find β₁ and β₂. (10 marks, 2022-23)
  22. Q6a. A random variable X has the following probability distribution: X: 0 1 2 3 4 5 6 7, P(X): 0 k 2k 2k 3k k² 2k² 7k²+k. Evaluate P(X ≥ 6). (10 marks, 2022-23)
  23. Q6b. For continuous random variable X if f(x) = (3/4)(x² + 1), 0 ≤ x ≤ 1: (i) Verify that f(x) is a probability density function. (ii) Find λ such that P(X ≤ λ) = P(X > λ). (10 marks, 2022-23)
  24. Q7a. The values in two random samples are given below: Sample 1: 15 25 16 20 22 24 21 17 19 23, Sample 2: 35 31 25 38 26 29 32 34 33 27 29 31. Can we conclude that the two samples are drawn from the same population? Test at 5% level of significance. (10 marks, 2022-23)
  25. Q7b. Discuss one way analysis of variance (ANOVA) with mathematical model and assumptions in the model. (10 marks, 2022-23)

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

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