Which of the following permutations in S5 is a conjugate of = (a) = (c) * = 12345 1 3 4 5 2 1 2 3 4 5 3 4 1 25 (b) = (d) π = 1 5 1 2 3 4 5 23154 2 3 4 5 1423 1 2 3 4 5 3 45 21 ?

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Q: The permutations p= p and q in Se have the two-line symbols 1 2 3 4 5 6 4 621 5 3 and q= 1 2345 1 5…

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Q: O pts Question 15 Which of the following is equivalent to the expression V125æ³ y – V5æ? O 5|æy³|/5æ…

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Q: Show that C(p,1), C(p,2),..., C(p,p-1) are all divisible by p if and only if p is a prime.

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Q: 6. What is the order of each of the following permutations? [1 2 3 4 5 6 [1 2 3 4 5 6 7 7 6 1 2 3 4…

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A: The number of permutations of n elements taken r at a time is given by nPr where nPr is given by,

Q: The permutations P = p and q in So have the two-line symbols 1 2 3 4 5 6 15 2 3 4 6 1 2 3 4 5 6 4 6…

A: We can find the given permutations in cycle form and order.

Q: n! = (1) Dn + (1) Dn-1 + (2) Dn-2 + ··· + (₂²₁) D₁ + (2) Do.

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Q: B D E None (iii), (iv) (i), (iii), (iv) (ii) (i), (iii) Find all even permutations. (i): (257) (ii):…

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Q: ) Express the pern 2546 1 product of the generators Wo=(12), `wa=(13), W1# (17) as a (125)(3 4 6 7)…

A: The generator of the permutation group S7 are given by: w2=1,2, w3=1,3, w4=1,4, w5=1,5, w6=1,6,…

Q: n-1 2)Let an = 2( 2 (²1) ¹²-¹ Write the first 5 terms of an. Σ ¹00 k=1 ak

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Q: b) 21315η - 1= Σακ(π) κ. ΚΣΟ (n)2+(ηλι+6= Σάκη

A: Given that, a) 4n4-2n2+5n-1=∑k≥0aknk b) -n2+n1+6=∑k≥0bknk. We have to find the values of ak and bk…