Math Problem Statement
(a) Find the Coefficient of x5y2 in the Expansion of (2x3y)7 (b) Find the Coefficient of x9y3 in the Expansion Of (x+2y)12 Determine the Coefficient of xyz2 in the Expansion of (2xyz)4 . a2b3c2d5 in the Expansion of (a2b3c=2d=5)16. (a) Explain about The Principle of InclusionExclusion. (b) Consider a set of integers from 0 to 499 (i) Find the number of integers are divisible by 3 or 5 or 11. (ii)Find the number of integers are divisible by 3 0r 5 Not 11. (iii)Find the number of integers are divisible by 3 0r 11 Not 5. (iv)Find the number of integers cannot be divisible by 3 or 5 or 11. (a) Explain about Euler Graph. (b) Let “G” be a connected Planar Simple Graph with “e” edges “v” vertices, Let “r” be No .of Regions in Planar representation “G” Then Prove r=ev=2. Explain about Working Rules of Isomorphism with Example. What is Minimum Spanning Tree? Explain about Kruskal’s Algorithm with Example
Solution
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Math Problem Analysis
Mathematical Concepts
Binomial theorem
Coefficient extraction
Formulas
Binomial theorem: (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{nk} b^k
Theorems

Suitable Grade Level
Advanced High School