Mathematics-I exam (MS 101) from BUTEX affiliated colleges' 2024 Level-1 Term-I finals. Questions cover Euler's and Maclaurin's theorems, Gamma and Beta functions, matrix consistency with orthogonal checks, Cramer's rule, and solid geometry.
Level-1 Term-I, Final Exám-2024
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) State and proof Euler’s theorem.
(b) If prove that .
(c) If the straight line touches the curves then show that .
[4+4+4=12]
2. (a) Define Gamma and Beta function. Show that
(b) State and proof Walli’s formula.
(c) Prove that
[6+4+2=12]
3. (a) Describe the properties of consistency.
(b) Find a, b, c if is orthogonal.
(c) Test the consistency and if possible to find the solution.
x+y+z=6, x+2y+3z=14, x+4y+4z=36