Mathematics-IV PYQ 2025-26 AKTU (BAS403) Question Paper

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Session 2025-26 · PYQ

AKTU Mathematics-IV (BAS403) previous year question paper 2025-26 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 2025-26

  1. Q1a. Form the partial differential equation by eliminating the arbitrary function from z=x+yf(xy). (2 marks, 2025-26)
  2. Q1b. Find the complementary function of the PDE: (2D^2-5DD^{\prime}+2D^{\prime 2})z=0. (2 marks, 2025-26)
  3. Q1c. Find the Fourier transform of f(x)=\begin{cases}1,&|x|<a,\\0,&|x|>a.\end{cases} (2 marks, 2025-26)
  4. Q1d. The first two moments of a distribution about the value 2 of the variable are 1 and 16. Find the first two moments about the mean. (2 marks, 2025-26)
  5. Q1e. The standard deviation of a symmetric distribution is 5. What must be the value of the fourth moment about the mean for a mesokurtic distribution? (2 marks, 2025-26)
  6. Q1f. A continuous random variable X has p.d.f. f(x)=3x^2, 0\le x\le1. Find a such that P(X\le a)=P(X>a). (2 marks, 2025-26)
  7. Q1g. Write the degree of freedom for a p\times q contingency table. (2 marks, 2025-26)
  8. Q2a. Solve the first-order partial differential equation: (x^2-yz)p+(y^2-zx)q=z^2-xy. (7 marks, 2025-26)
  9. Q2b. A tightly stretched violin string of length l, fixed at both ends, is plucked at x=l/3 and initially assumes the shape of a triangle of height a. Find the displacement y at any distance x and any time t after the string is released from rest. (7 marks, 2025-26)
  10. Q2c. Calculate Karl Pearson’s coefficient of skewness for the following table. | Income (Rs.) | 500-600 | 600-700 | 700-800 | 800-900 | 900-1000 | 1000-1100 | | --- | --- | --- | --- | --- | --- | --- | | No. of employees | 8 | 12 | 4 | 2 | 1 | 1 | (7 marks, 2025-26)
  11. Q2d. If X and Y have joint density f(x,y)=\begin{cases}\frac18(6-x-y),&0\le x<2,\ 2\le y<4,\\0,&\text{otherwise},\end{cases} find (i) P(X<1\cap Y<3) and (ii) P(X+Y<3). (7 marks, 2025-26)
  12. Q2e. Samples of sizes 10 and 14 were taken from two normal populations with standard deviations 3.5 and 5.2. The sample means were 20.3 and 18.6. Test whether the population means are the same at the 5% level. The tabulated value of t at 5% significance for 22 degrees of freedom is 2.0739. (7 marks, 2025-26)
  13. Q3a. Solve the non-homogeneous linear PDE: (D+D^{\prime}-1)(D+2D^{\prime}-3)z=4+3x+6y. (7 marks, 2025-26)
  14. Q3b. Solve the linear PDE: (D^2+DD^{\prime}-6D^{\prime 2})z=y\cos x. (7 marks, 2025-26)
  15. Q4a. Find the inverse Fourier transform of f(p)=e^{-|p|y}. (7 marks, 2025-26)
  16. Q4b. Find the temperature in a bar of length 2 whose ends are kept at zero and whose lateral surface is insulated, if the initial temperature is \sin(\pi x/2)+3\sin(5\pi x/2). (7 marks, 2025-26)
  17. Q5a. For 10 observations on price (x) and supply (y), the following data were obtained (in appropriate units): \sum x=130,\quad\sum y=220,\quad\sum x^2=2288,\quad\sum y^2=5506,\quad\sum xy=3467. Obtain the two lines of regression and estimate the supply when the price is 16 units. (7 marks, 2025-26)
  18. Q5b. Fit a straight line y=a+bx to the following data by the least-squares method. | x | 0 | 1 | 2 | 3 | 4 | | --- | --- | --- | --- | --- | --- | | y | 1 | 1.8 | 3.3 | 4.5 | 6.3 | (7 marks, 2025-26)
  19. Q6a. A manufacturer knows that the condensers he makes contain, on average, 1% defectives. He packs them in boxes of 100. What is the probability that a box picked at random contains 4 or more faulty condensers? (7 marks, 2025-26)
  20. Q6b. The heights of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches. Find the height below which 99% of the students lie. Given: P(Z=2.327)=0.49. (7 marks, 2025-26)
  21. Q7a. From the following data, find whether hair colour and sex are associated. Given: the \chi^2 value at 5% significance for 4 degrees of freedom is 9.488. | Colour / Sex | Fair | Red | Medium | Dark | Black | Total | | --- | --- | --- | --- | --- | --- | --- | | Boys | 592 | 849 | 504 | 119 | 36 |… (7 marks, 2025-26)
  22. Q7b. The average fraction defective in a large sample of a product is 0.1537. Calculate the control limits given that the subgroup size is 2000. (7 marks, 2025-26)

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

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