2017 Level-1 Term-I Mathematics-I exam (MS 101) from BUTEX affiliated colleges. Questions address function domains, Lagrange's mean value theorem, Rolle's theorem verification, Beta-Gamma functions with reduction formulas, Wallis's formula, and Cramer's rule solutions.
Level-1 Term-I, Final Exám-2017
Subject: Mathematics-I, Subject 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 function. Find the domain and range of the following function .
(b) Define continuity. Prove that Every finitely differentiable function is continuous.
(c) Prove that the segment (between the co-ordinates axis) of a tangent of astroid is of constant length.
[4+4+4=12]
2. (a) State and proof lagranges mean value theorem.
(b) If , then show that
(c) Verify the Rolle’s theorem of the function over (-6, 1).
[4+4+4=12]
3. (a) Integrate: (i) (ii) (iii)
(b) What is Beta and Gamma function? Prove that .
(c) Find reduction formula for .
[4.5+4.5+3=12]