Mathematics-I question paper (MS 101) from BUTEX affiliated colleges' 2018 Level-1 Term-I finals. Covers inverse and rank of matrices, Cauchy's inequalities, hyperbolic functions, Gregory's series, Rolle's and Lagrange's theorems, and cube diagonal angles.
Level-1 Term-I, Final Exám-2018
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 inverse matrix and find the inverse of this matrix .
(b) Define rank of matrix and find the rank of matrix .
(c) If A and B are non-singular matrices of same order, then AB is also a non-singular matrix and .
[4+4+4=12]
2. (a) If , prove that .
(b) If n is a positive integer, then prove that .
(c) Prove that are the roots of the equation’s and show that .
[4+4+4=12]
3. (a) State and proof Cauchy’s Inequalities.
(b) Prove that if x < 1 and to deduce that .
(c) Test the convergence .
[4+4+4=12]