Reg ण. । (೧೮೮07೧೬. _ Name: (VER0OMCA

Max. Marks: 60

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APJ ABDUL KALE MG NOL OE AL UNIVERSITY

First Semester MCA (2 Year) Degree Examination December 2020

Course Code: 2011൧101
Course Name: MATHEMATICAL FOUNDATIONS FOR COMPUTING

PART A
Answer all questions, each carries 3 marks.

Let A= {1.2.3.4} and B= {p, ‏بن‎ ಓ ऽ} and if र = {(1,p)(1.q)
.(1൧.(2.9),(2..(2.5)) 15 a relation from A to 8. Write the matrix representation
of R.
Show that (A ‏نا‎ B)’ = 4' 5"
Use Euclidean algorithm to obtain x and y satisfying
200 (752,1000) = 752x+1000y.
Solve the recurrence relation 66, — 7൭ = 0;n > 1, 63 = 343.
Define planar and non-planar graphs.
A connected planar graph has 5 vertices having degrees 4,3,3,2,2. Find the
number of edges and faces.
Find the Eigen values of the matrix
2 1 1
A= | 2 1
0 0 1
Show that the vectors (1, -1,0), (1,3, -1), (5,3, -2) are linearly dependent.
Define scatter diagram. Describe the various types of correlation using scatter
diagram.
State the principle of least squares.

PART B

Answer any one question from each module. Each question carries 6 marks.
Module I

Define Equivalence relation. Prove that for x, y ‏ع‎ 7 the relation defined by

R= {(x, y);5 divides x-y} is an equivalence relation.
OR

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Duration: 3 Hours

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