Q. For the group Sn of all permutations of n distinct symbols, what is the number of elements in Sn?

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Q. For the group Sn of all permutations of n distinct symbols, Sn is an abelian group for all values of n.

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Q. Is S a ring from the following multiplication and addition tables?

+ a b x a b
a a b a a a
b b a b a b

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Q. Does the set of residue classes (mod 3) form a group with respect to modular addition?

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Q. A very common field in this category is GF(2) with the set {1, 2} and two operations, addition and multiplication.”

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Q. Multiplication / Division follow which operation?

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Q. 0 1 2 3 4
0 4 3 2 1

0 1 2 3 4
– 1 3 2 4

What do the above numbers correspond to?

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Q. How many numbers cannot be used in GF(p) in 2n where n=4?

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Q. If f(x)=x^3+x^2+2 and g(x)=x^2-x+1, find: f(x) + g(x)

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Q. Find the 8-bit word related to the polynomial x^5 + x^2 + x

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Q. Find the 8-bit word related to the polynomial x^6 + x^5 + x^2 + x +1

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Q. Primitive Polynomial is also called a ____

i) Perfect Polynomial
ii) Prime Polynomial
iii) Irreducible Polynomial
iv) Imperfect Polynomial

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Q. Which of the following are irreducible polynomials?

i) X^4+X^3
ii) 1
iii) X^2+1
iv) X^4+X+1

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Q. The polynomial f(x)=x^3+x+1 is a reducible.

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Q. 5/3 mod 7 =

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Q. -5 mod -3 =

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Q. Multiply 00100110 by 10011110 in GF(2^8) with modulus 100011011.The result is

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Q. Find the inverse of (x^7+x+1) modulo (x^8 + x^4 + x^3+ x + 1).

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Q. 7x = 6 mod 5. Then the value of x is

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Q. State whether the following statement is true or false over a field.

The product of monic polynomials is monic.

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