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Let M be any 3 x 3 matrix with entries from the set 0 1 2 Th: null (Mathematics) | DivineJEE

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Mathematics

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Mathematics

Let M be any 3

\times

3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of M^TM is seven, is ________.

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Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a relation defined on A X B such that R = {( ( a_{1},b_{1} ), ( a_{2},b_{2} )):a_{1} ? b_{2} and b_{1} ? a_{2}}. Then the number of elements in the set R is

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Let Z be the set of integers. If A = { x in Z:2^{(x + 2) ( x^{2} - 5x + 6 )} = 1 } and = { x in Z : - 3 < 2x - 1 < 9}, then the . number of subsets of the set A X B is

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