Q. If 54th row of a 67th row matrix is linearly independent with each other then find the rank of the matrix.

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Q. Let M be an 4×4 matrix with real entries such that Mᵏ=0, for some k≥1. Find the determinant value of (I+M), where, I be the 4 x 4 identity matrix.

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Q. Suppose (2, 5, 8, 4) and (3, 6) are the two permutation groups that form cycles. What type of permutation is this?

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Q. Which of the following is not an abelian group?

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Q. If we take a collection of {∅, {2}, {3}, {5}} ordered by inclusion. Which of the following is true?

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Q. _______ characterizes the properties of distributive lattices.

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Q. Suppose that H be an X-set and suppose that a∼b and |Xₐ|=|Xᵦ|, the which of the following is true?

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Q. If the 4 sides of a square are to be colored by colors. How many different colourings with 50 colours are there if two arrangements that can be obtained from each other by rotation are identical?

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Q. Let H be a finite group. The order of Sylow p-subgroup of H for every prime factor p with multiplicity 9 is?

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Q. How many indistinguishable necklaces can be made from beads of 4 colors with exactly 9 beads of each color where each necklace is of length 16?

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Q. Invariant permutations of two functions can form __________

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Q. Suppose P(h) is a group of permutations and identity permutation(id) belongs to P(c). If ϕ(c)=c then which of the following is true?

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Q. An isomorphism of Boolean algebra is defined as _______

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