Mathematics-IV PYQ 2023-24 AKTU (BAS403) Question Paper

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

AKTU Mathematics-IV (BAS403) 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. Solve the Partial Differential Equation (D² - 3DD')z = 0. (2 marks, 2023-24)
  2. Q1b. Tell the classification of the following partial differential equation: 4(∂²u/∂x²) - 4(∂²u/∂x∂t) + (∂²u/∂t²) = 0. (2 marks, 2023-24)
  3. Q1c. Write the formula for rank correlation in the case of tied ranks. (2 marks, 2023-24)
  4. Q1d. Calculate the value of k for which the function f(x) = 1/k for a ≤ x ≤ b, 0 otherwise, is a probability density function. (2 marks, 2023-24)
  5. Q1e. Two coins are tossed simultaneously. What is the probability (upto two decimal points accuracy) of getting at least one head? (2 marks, 2023-24)
  6. Q1f. For the Binomial distribution (1/3 + 2/3)^10, determine the mean. (2 marks, 2023-24)
  7. Q1g. Write the control limits of C charts. (2 marks, 2023-24)
  8. Q2a. Determine a real function V of x and y, reducing to zero when y=0 and satisfying ∂²V/∂x² + ∂²V/∂y² = -4π(x² + y²). (7 marks, 2023-24)
  9. Q2b. A tightly stretched string with fixed end points x=0 and x=l is initially in a position given by y = y₀ sin³(πx/l). If it is released from rest from this position, evaluate the displacement y(x,t). (7 marks, 2023-24)
  10. Q2c. From the data given, determine the lines of regression: x: 2 4 6 8 10, y: 5 7 9 8 11. (7 marks, 2023-24)
  11. Q2d. Prove that Poisson distribution is a limiting case of binomial distribution. (7 marks, 2023-24)
  12. Q2e. Distinguish between np-chart and p-chart. Following is the data of defectives of 10 samples of size 100 each. Construct np-chart and explain your findings. Sample no: 1-10, No. of defectives: 6 9 12 5 12 8 8 16 13 7. (7 marks, 2023-24)
  13. Q3a. Solve the partial differential equation x²(∂²z/∂x²) - y²(∂²z/∂y²) + x(∂z/∂x) - y(∂z/∂y) = log x. (7 marks, 2023-24)
  14. Q3b. By using Charpit's method evaluate the solution of 2zx - px² - 2qxy + pq = 0. (7 marks, 2023-24)
  15. Q4a. Determine the Fourier Transform of F(x) = 1 - x², |x| < 1; 0, |x| > 1. (7 marks, 2023-24)
  16. 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, determine the temperature at a distance x from A at time t. (7 marks, 2023-24)
  17. Q5a. Examine the least square fit of f(x) = a + bx + cx² for the following data: x: 0 1 2 3 4, f(x): 1 4 10 17 30. (7 marks, 2023-24)
  18. Q5b. Determine the skewness and kurtosis for the following data: Marks: 10-20 20-30 30-40 40-50 50-60, No. of students: 18 20 30 22 10. (7 marks, 2023-24)
  19. Q6a. Records taken of the number of male and female births in 800 families having four children: No. of male birth: 0 1 2 3 4, No. of families: 32 178 290 236 64. Test whether the data is consistent with the hypothesis that the binomial law holds and chance of male birth equals female birth (p=q=1/2). (7 marks, 2023-24)
  20. Q6b. The income of a group of 10,000 persons was found to be normally distributed with mean 750 Rs. per month and S.D. of 50 Rs. Show that about 95% had income exceeding 668 Rs and only 5% had income exceeding 832 Rs. Also determine the lowest income among the richest 100. (7 marks, 2023-24)
  21. Q7a. The height of 6 randomly chosen sailors in inches are 63, 65, 68, 69, 71 and 72. Those of 9 randomly chosen soldiers are 61, 62, 65, 66, 69, 70, 71, 72 and 73. Test whether the sailors are on the average taller than soldiers. (7 marks, 2023-24)
  22. Q7b. Discuss whether there is any association between area and pollution index of the city. Area/Pollution Index: Urban: High 150, Low 350, Total 500; Rural: High 250, Low 350, Total 600. Given χ²₀.₀₅ = 3.84. (7 marks, 2023-24)

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

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