Mathematics-I exam (MS 101/AS 101) from the 2020 Level-1 Term-I finals at BUTEX affiliated colleges. Questions cover Laplace method proofs, matrix solutions, Euler's theorem, Taylor expansions, and direction cosine relations between lines.
Level-1 Term-I, Final Exám-2020
Subject: Mathematics-I (Code: MS 101 / AS 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 Laplace method.
(b) Solve the following system of linear equation with the help of matrix:
(c) If A and B are non-singular matrix of same order, then AB is also a non-singular matrix and .
[4+4+4=12]
2. (a) State and proof Euler’s theorem.
(b) If , then show that
(c) Expand (Log sinx) in power (x-2), by Taylor's theorem.
[4+4+4=12]
3. (a) State and prove relations between Gamma and Beta function.