MBA Exam

What is the remainder when 128^1000 is divided by 153What is the remainder when 128^1000 is divided by 153

1) 103
2) 145
3) 118
4) 52

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Let [x] denote the greatest integer that is less than or equal to x, e.g. [3.45] = 3, then [1/3] + [2/3] + [22/3] + [23/3] +...+ (101 terms) equals

1) 1/3( 4<sup>50</sup> - 1) - 50
2) 1/3( 4<sup>51</sup> - 1) - 51
3) 2/3(4<sup>50</sup> - 1) - 50
4) None of these
A fair coin is tossed 10 times. find the probability that two heads dont occur consecutively ?
Approach plz !

1) 1/2^4
2) 1/2^3
3) 1/2^5
4) NOT