Mathematics-I paper (MS 101) from BUTEX affiliated colleges' 2021 Level-1 Term-I finals. Includes domain and range determination, continuity and differentiability testing, Gauss elimination solutions, homogeneous functions, and matrix rank and inverse problems.
Level-1 Term-I, Final Exám-2021
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) Define Domain and Range. Find the domain and range of
(b) Define continuity. Test the continuity and differentiability of f(x) at x=1 where
(c) Define limit. Evaluate:
[4+4+4=12]
2. (a) Find the upper triangular, lower triangular and diagonal form of a matrix:
(b) Solve 3x3 system of equation using Gauss Elimination method:
2x+4y+6z=4
1x+5y+9z=2
2x+1y+3z=7
(c) Check the consistency of the following system and if possible to find the solution:
x+y+z=6
x+2y+3z=14
x+4y+4z=36
[4+4+4=12]
3. (a) If touches the curve then show that .
(b) Define homogeneous function. If then show that
(c) Integrate: (i) (ii)
[4+4+4=12]
4. (a) Discuss the continuity and differentiability of the function f(x), when
If f(x) =