Q1 The integers from 1 to n are written in increasing order from left to right on a blackboard. David and Goliath play the following game: starting with David, the two players alternate erasing any two consecutive numbers and replacing them with their sum or product. Play continues until only one number on the board remains. If it is odd, David wins, but if it is even, Goliath wins. Find the probability that Goliath wins if n=2011?
a) 0 b) 1 c) 1/2 d) None of these
Q2 A classroom has 30 students and 30 desks arranged in 5 rows of 6.The class has 15 boys and 15 girls.If the students be placed in the chairs such that no boy is sitting in front of, behind, or next to another boy, and no girl is sitting in front of, behind, or next to another girl in x(y!)(z!), where x, y and z are positive integers. Find x+y+z?
a) 32 b) 30 c) 27 d) 29
Q3. Find the sum of all integers x such that 2x^2 + x- 6 is a positive integral power of a prime positive integer?
a) 7 b) 5 c) 4 d) 12
a) 0 b) 1 c) 1/2 d) None of these
Q2 A classroom has 30 students and 30 desks arranged in 5 rows of 6.The class has 15 boys and 15 girls.If the students be placed in the chairs such that no boy is sitting in front of, behind, or next to another boy, and no girl is sitting in front of, behind, or next to another girl in x(y!)(z!), where x, y and z are positive integers. Find x+y+z?
a) 32 b) 30 c) 27 d) 29
Q3. Find the sum of all integers x such that 2x^2 + x- 6 is a positive integral power of a prime positive integer?
a) 7 b) 5 c) 4 d) 12
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