Mathematics Iii (BAS402) - AKTU Question Paper 2025-26
B.Tech · Semester 4 · Free PDF Download
This is the official AKTU Mathematics Iii Previous Year Question Paper for B.Tech Semester 4, academic session 2025-26. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.
Course:B.Tech
Semester:Semester 4
Session:2025-26
University:AKTU / UPTU
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Questions Asked in 2025-26
Mathematics Iii (BAS402) — complete question paper · 70 marks · 3 Hours
Section AAttempt all questions in brief. ( Ůʲ Ő ŐI) 02 x 7 = 14
- aForm the partial differential equation by eliminating the arbitrary function from 𝑧=𝑓(𝑥ଶ+𝑦ଶ)
- bWrite the general solution of the one-dimensional heat equation using separation of variables
- cWhat is the null hypothesis? Give one example
- eWhat is interpolation? Distinguish between interpolation and extrapolation
- fDefine Gauss-Seidel method. How does it differ from Jacobi method?
- gDefine Fourier sine transform and write its formula
Section BAttempt any three of the following (ɻİ Ő Ů
- aSolve (𝐷ଶ−3𝐷𝐷ᇱ +2𝐷ᇱଶ)𝑧=𝑒௫ାଶ௬
- bA rectangular plate of dimensions 𝑎×𝑏 has three sides maintained at zero 2 K2 (SEM. IV) THEORY EXAMINATION 2025-26 MATHEMATICS –III temperature. The fourth side 𝑦=𝑏 is maintained at temperature 𝑓(𝑥). Find the steady-state temperature distribution inside the plate
- cThe following data shows time (x) and output (y): Fit a straight line 𝑦= 𝑎+𝑏𝑥 using least squares method and estimate value at 𝑥=6
- dFind the root of 𝑥ଷ−2𝑥−5=0 using Newton-Raphson method starting from 𝑥 =2
- eAn electrical network leads to the following system of equations: Use the Gauss–Seidel method to find the approximate solution after two iterations
Section CAttempt any one part of the following: (ɻİ Ő Ů
- bSolve (SEM. IV) THEORY EXAMINATION 2025-26 MATHEMATICS –III
- aSolve using Fourier Transform
- bA string of length 𝑙is fixed at both ends. Initially, the string is at rest in equilibrium position, but it is given an initial velocity ப௨ ப௧(𝑥,0)=sin ቀଶగ௫ Find the displacement 𝑢(𝑥,𝑡) at any time. ப௧(𝑥, 0) = sin ቀଶగ௫
- aThe following data gives marks in Mathematics (X) and Physics (Y): Find correlation coefficient and regression line of Y on X
- bA researcher collected the following data representing marks of students: Using step-deviation method, calculate: (i) Mean (ii) Variance Class Interval Frequency 5 9 15 20 11
- aThe population of a town (in thousands) is given below: Estimate the population in the year 2008 using Lagrange’s interpolation formula. Year 2000 2005 2010 2015 Population 20 27 39 52
- bDetermine the root of the equation 𝑥ଷ−𝑥−2=0 in the interval [1,2] using the bisection method , correct up to three decimal places
- aEvaluateන ଵ ௗ𝑑𝑥 using (i)Trapezoidal rule (ii) Simpson’s 1/3rule with step size ℎ = 1
- bSolve the differential equation ௗ௬ using Picard’s method up to second approximation
Question text is extracted from the official AKTU question paper PDF above. Hindi translations are omitted — every question is printed in English in the original paper. Last verified: 2026-08-23.
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