Mathematics-IV PYQ 2022-23 AKTU (KAS402) Question Paper

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

AKTU Mathematics-IV (KAS402) 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. Obtain a partial differential equation that governs the family of surfaces z = (x - α)² + (y - β)². (2 marks, 2022-23)
  2. Q1b. Find the complete integral of the partial differential equation z = px + qy + p/(p + q), where p = ∂z/∂x and q = ∂z/∂y. (2 marks, 2022-23)
  3. Q1c. Classify the partial differential equation r + 2s + (sin²x)t + q = 0. (2 marks, 2022-23)
  4. Q1d. Write down the two dimensional heat equation. (2 marks, 2022-23)
  5. Q1e. What is the relation between the regression coefficients and the coefficient of correlation? (2 marks, 2022-23)
  6. Q1f. The fourth central moment is 48. What must be its standard deviation in order that the distribution be mesokurtic? (2 marks, 2022-23)
  7. Q1g. A and B are any two independent events such that P(A) = 0.4, P(A∪Bᶜ) = 0.7. Find P(B), where Bᶜ is the complementary event of B. (2 marks, 2022-23)
  8. Q1h. The random variable X follows the Normal distribution with mean 9 and standard deviation 3. Find x* such that P(X > x*) = 0.16. (2 marks, 2022-23)
  9. Q1i. Write down the definition of the null hypothesis. (2 marks, 2022-23)
  10. Q1j. What is Statistical Quality Control (SQC)? Define in brief. (2 marks, 2022-23)
  11. Q2a. Find the general solution of the partial differential equation (y + z)p + (z + x)q = (x + y). (10 marks, 2022-23)
  12. Q2b. Solve the partial differential equation by the method of separation of variables: 4(∂u/∂x) + (∂u/∂y) = 3u, given that u = 5e⁻ʸ - e⁻⁵ʸ when x = 0. (10 marks, 2022-23)
  13. Q2c. Use the method of least squares to fit the curve y = abˣ for the following data: x: 2 3 4 5 6, y: 144 172.8 207.4 248.8 298.5. (10 marks, 2022-23)
  14. Q2d. In a normal distribution, 12% of the items are under 30 and 85% items are under 60. Find the mean and standard deviation. (10 marks, 2022-23)
  15. Q2e. The annual rainfall in Lucknow city is normally distributed with mean 45 cm. The rainfall during the last five years are 48, 42, 40, 44 and 43 cm respectively. Can we conclude that the average rainfall during the last five years is less than the normal rainfall? Test at 5% level of significance.… (10 marks, 2022-23)
  16. Q3a. Find the solution of the partial differential equation [2D² + 5DD' + 3(D')²]z = eˣ. (10 marks, 2022-23)
  17. Q3b. Find the complete integral of the partial differential equation (p² + q²)x = pz. (10 marks, 2022-23)
  18. Q4a. A tightly stretched string with fixed end points x=0 and x=l is initially in a position given by y = a sin³(πx/l). If it is released from rest from this position, find the displacement. (10 marks, 2022-23)
  19. Q4b. An insulated rod of length l has its ends A and B maintained at 0°C and 100°C respectively until steady state conditions prevail. If B is suddenly reduced to 0°C and maintained at 0°C, find the temperature at a distance x from A at time t. (10 marks, 2022-23)
  20. Q5a. If 4x - 5y + 33 = 0 and 20x - 9y = 107 are two lines of regression, find the mean values of x and y, the coefficient of correlation and the standard deviation of y if the variance of x is 9. (10 marks, 2022-23)
  21. Q5b. First four moments about 2 are 1, 2.5, 5.5 and 16 respectively. Find the first four central moments, moments about origin and coefficient of skewness. (10 marks, 2022-23)
  22. Q6a. A bag A contains 8 white and 4 black balls. A second bag B contains 5 white and 6 black balls. One ball is drawn at random from bag A and placed in bag B. A ball is then drawn from bag B and found to be white. Find the probability that a black ball was transferred from bag A. (10 marks, 2022-23)
  23. Q6b. If X follows Poisson distribution such that P(X=2) = 9P(X=4) + 90P(X=6), find mean, variance and distribution. (10 marks, 2022-23)
  24. Q7a. In an experiment on pea breeding the following frequency of seeds were obtained: Red & Yellow: 315, Wrinkled & Yellow: 101, Round & Green: 108, Wrinkled & Green: 32, Total: 556. Theory predicts frequencies in proportions 9:3:3:1. Examine the correspondence between theory and experiment at 5% level… (10 marks, 2022-23)
  25. Q7b. The given table shows the value of sample mean X̄ and the range R for 10 samples of size 5 each. Draw mean and range chart and comment on the state of control. (Given A₂ = 0.58, D₃ = 0, D₄ = 2.115). X̄: 45 46 48 52 53 37 51 46 47 38, R: 4 5 6 7 4 5 7 6 6 4. (10 marks, 2022-23)

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

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