Mathematics-IV PYQ 2021-22 AKTU (KAS302) Question Paper

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Session 2021-22 · PYQ

AKTU Mathematics-IV (KAS302) previous year question paper 2021-22 for B.Tech Semester 3/4. Covers Partial Differential Equations, Applications of PDE and…

Open the interactive reader to study this resource on AcademicArk.

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 2021-22

  1. Q1a. Solve the following partial differential equation (D² + DD')z = 0. (2 marks, 2021-22)
  2. Q1b. Derive a partial differential equation by eliminating the constants a and b from z = ax + a²y² + b. (2 marks, 2021-22)
  3. Q1c. Write radio wave equations. (2 marks, 2021-22)
  4. Q1d. Classify the partial differential equation u_xx + 3u_xy + u_yy = 0. (2 marks, 2021-22)
  5. Q1e. In an asymmetrical distribution mean is 16 and median is 20. Calculate the mode of the distribution. (2 marks, 2021-22)
  6. Q1f. The lines of regression of y on x and x on y are respectively y = x + 5 and 16x - 9y = 94. Find the correlation coefficient. (2 marks, 2021-22)
  7. Q1g. Four persons are chosen at random from a group containing 3 men, 2 women and 4 children. Prove that the chance that exactly two of them will be children is 10/21. (2 marks, 2021-22)
  8. Q1h. If the probability density function f(x) = kx³, 0 ≤ x ≤ 3; 0 elsewhere, find the value of k. Also find the probability between x = 1/2 and x = 3/2. (2 marks, 2021-22)
  9. Q1i. Explain t-test for small samples. (2 marks, 2021-22)
  10. Q1j. What do you mean by statistical quality control (SQC)? (2 marks, 2021-22)
  11. Q2a. Solve the partial differential equation (D - D' - 1)(D - D' - 2)z = sin(2x + 3y). (10 marks, 2021-22)
  12. Q2b. A laterally insulated bar of length l has its ends A and B maintained at 0°C and 100°C respectively until steady state conditions prevail. If the temperature at B is suddenly reduced to 0°C and kept so while that of A is maintained at 0°C. Find the temperature at a distance x from A at any time t. (10 marks, 2021-22)
  13. Q2c. Calculate the first four central moments about the mean of the following data: x: 0 1 2 3 4 5 6 7 8, f: 1 8 28 56 70 56 28 8 1. (10 marks, 2021-22)
  14. Q2d. 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? Given f(0.8)=0.2881, f(0.4)=0.1554, f(1.6)=0.4452, f(2.4)=0.4918. (10 marks, 2021-22)
  15. Q2e. In an experiment on immunization of cattle from tuberculosis the following results were obtained: Inoculated: Affected 12, Unaffected 28; Not Inoculated: Affected 13, Unaffected 7. Examine the effect of vaccine in controlling the incidence of the disease. [χ²₀.₀₅,₁ = 3.84]. (10 marks, 2021-22)
  16. Q3a. Solve (y + zx)p - (x + yz)q = x² - y². (10 marks, 2021-22)
  17. Q3b. Solve (x²D² - 4xyDD' + 4y²D'²)z = x³y⁴. (10 marks, 2021-22)
  18. Q4a. Solve the following PDE by method of separation of variables: ∂z/∂x + ∂²z/∂y² = 0; z(x,0) = 0, z(x,π) = 0, z(0,y) = 4sin3y. (10 marks, 2021-22)
  19. Q4b. A string is stretched and fastened to two points l m 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) cos(πct/l). (10 marks, 2021-22)
  20. Q5a. Fit a parabolic curve of regression of y on x to the following data: x: 1.0 1.5 2.0 2.5 3.0 3.5 4.0, y: 1.1 1.3 1.6 2.0 2.7 3.4 4.1. (10 marks, 2021-22)
  21. Q5b. Let the random variable X assume the value r with the probability law P(X=r) = q^(r-1)·p; r = 1,2,3... Find the m.g.f of X and hence its mean and variance. (10 marks, 2021-22)
  22. Q6a. Fit a binomial distribution for the following data and compare the theoretical frequencies with the actual ones. x: 0 1 2 3 4 5, f: 2 14 20 34 22 8. (10 marks, 2021-22)
  23. Q6b. The number of accidents in a year involving taxi drivers in a city follows a Poisson distribution with mean equal to 3. Out of 1000 taxi drivers, find approximately the number of drivers with: (i) No accident in a year (ii) More than three accidents in a year. (given e⁻³ = 0.04979). (10 marks, 2021-22)
  24. Q7a. In two independent samples of size 8 and 10, the sum of squares of deviations of the sample values from the respective means were 84.4 and 102.6. Test whether the difference of variances of populations is significant or not. Use 5% level of significance. [F₀.₀₅,(7,9) = 3.29]. (10 marks, 2021-22)
  25. Q7b. An inspection of 10 samples of size 400 each from 10 lots revealed the following number of defective units: 17, 15, 14, 26, 9, 4, 19, 12, 9, 15. Draw the np-chart and state whether the process is under control or not. (10 marks, 2021-22)

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

Mathematics-IV previous year papers

More Mathematics-IV resources

Browse all notes · Semester 3 notes