2022 Level-1 Term-I Mathematics-I exam (MS 101) from BUTEX affiliated colleges. Questions span Wallis's formula, matrix reduction to normal form, inverse computation, Gauss elimination, and three-dimensional coordinate geometry with plane loci problems.
Level-1 Term-I, Final Exám-2022
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 Gamma function and Beta function. Prove that,
(b) Prove that,
(c) Find out the value of .
[(2+4+6)+3+3=12]
2. (a) State and prove that, Walli’s formula.
(b) If then show that . Using above equation find out the value of .
[6+(3+3)=12]
3. (a) Define matrix with example. Reduce the matrix to normal form.
(b) Find the inverse matrix of this matrix
(c) Describe the properties of consistency.
[4+4+4=12]