Q. Let G be a finite group with two sub groups M & N such that |M|=56 and |N|=123. Determine the value of |M⋂N|.

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Q. A group G, ({0}, +) under addition operation satisfies which of the following properties?

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Q. If (M, *) is a cyclic group of order 73, then number of generator of G is equal to ______

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Q. The set of even natural numbers, {6, 8, 10, 12,..,} is closed under addition operation. Which of the following properties will it satisfy?

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Q. In a group there must be only __________ element.

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Q. _____ is the multiplicative identity of natural numbers.

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Q. An identity element of a group has ______ element.

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Q. __________ matrices do not have multiplicative inverses.

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Q. If X is an idempotent nonsingular matrix, then X must be ___________

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Q. If A, B, and C are invertible matrices, the expression (AB⁻¹)⁻¹(CA⁻¹)⁻¹C2 evaluates to ____________

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Q. If the sum of elements in each row of an n×n matrix Z is zero, then the matrix is ______________

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Q. ___________ are the symmetry groups used in the Standard model.

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Q. A semigroup S under binary operation * that has an identity is called __________

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Q. An element a in a monoid is called an idempotent if ______________

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Q. A trivial subgroup consists of ___________

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Q. Minimum subgroup of a group is called _____________

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Q. Let K be a group with 8 elements. Let H be a subgroup of K and H<K. It is known that the size of H is at least 3. The size of H is __________

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Q. __________ is not necessarily a property of a Group.

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Q. A group of rational numbers is an example of __________

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Q. Intersection of subgroups is a ___________

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