Mathematics-I question paper (MS 101) from BUTEX affiliated colleges' 2023 Level-1 Term-I finals. Covers Taylor and Maclaurin expansions, Euler's theorem, Gamma-Beta relations, Gauss elimination, Cramer's rule, and consistency testing by rank method.
Level-1 Term-I, Final Exám-2023
Subject: Mathematics-I (Code: MS 101)
Time: 3.0 Hrs. Full Marks: 72
(Use separate answer script for Part: A and Part: B)
(All parts of a question must be answered consecutively)
Part: A
(Answer any three questions)
1. (a) Prove that using Laplus method.
(b) If A is a orthogonal matrix, then and are all orthogonal.
(c) Find the inverse of the matrix:
[4+4+4=12]
2. (a) State and proof Maclourins theorem.
(b) If , then prove that
(c) Expand log (sinx) in power of (x-2) by Taylor’s theorem.
[4+4+4=12]
3. (a) State and prove Euler’s theorem on homogeneous function.
(b) If then show that
(c) What is Indeterminate form? Find out the value