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.Solve𝑥 ≡ 7(𝑚𝑜𝑑 11) 𝑥 ≡ 6(𝑚𝑜𝑑 8) 𝑥 ≡ 10(𝑚𝑜𝑑 15) Also find the
smallest non-negative solutions
Solve the following congruences x≡1 mod3, x≡2mod4
x≡3mod5
Prove that n=2 mod4,and when n=p ,where p is a prime and p≡3 mod4
Prove that the set of arithmetic functions form an abelian group under the
mapping Dirichlet multiplication with f1≠0
If m,n=1,show that m,φn=1
Find all integers such that n=12
Suppose p=0.9 and n=4 ,C={0000,1010,1100}.Compute pC,v where
v=1100
Define K-edge colouring and K-vertex colouring of a graph. Find the edge chromatic numbers to colour the edges of the complete graph with four and five vertices
Define K-edge colouring and K-vertex colouring of a graph. Find the edge chromatic numbers to colour the edges of the complete graph with four and five vertices
Identify whether each of the followings is permutation or combination and find the
answers.
(i) lsha wants to invest 12 million in three projects. She decided to invest 4 million in
each project and if seven shortlisted projects are available, in how many possible
ways she can invest her money?
(ii) Instead of equal allocation, she decided to invest 3million, 4 million and 5 million for
each project. How many possible arrangements are available for her investment
decision?
