# For how many primes p is p2 + 3p − 1 also prime

1.  0

2.  1

3.  2

4.  3

5.  none of these

5

1

Explanation :
No Explanation available for this question

# Find the number of pairs of positive integers (x, y) such that x6 =y2 + 127

1.  0

2.  1

3.  2

4.  3

5.  none of these

5

1

Explanation :
No Explanation available for this question

# Let m > 1 be a positive integer then find the number of pairs (x, y) of positive integers such that x2 − y2 = m3

1.  0

2.  4

3.  8

4.  12

5.  none of these

5

none of these

Explanation :
No Explanation available for this question

# Let N be a positive integer. Then which of the following is(are) true

1.  If N is divisible by 4, then N can be expressed as the sum of two or more consecutive odd integers.

2.  If N is a prime number, then N cannot be expressed as the sum of two or more consecutive odd integers.

3.  If N is twice some odd integer, then N cannot be expressed as the sum of two or more consecutive odd integers

4.  At least two of the foregoing

5.  All of the foregoing

5

All of the foregoing

Explanation :
No Explanation available for this question

# Let n and m be positive integers. An n * m rectangle is tiled with unit squares. Let r(n,m) denote the number of rectangles formed by the edge of these unit squares. Thus, for example, r(2, 1) = 3. Find r(11, 12)

1.  132

2.  5148

3.  20592

4.  10296

5.  none of these

5

5148

Explanation :
No Explanation available for this question

# How many ways to fill the 4X4 board by nonnegative integers, such that sum of the numbers of each row and each column is 3

1.  2006

2.  2007

3.  2008

4.  2009

5.  2010

5

2008

Explanation :
No Explanation available for this question

# Let H be a set of 2000 nonzero real numbers. How many negative elements should H have in order to maximize the number of four-elemen subsets of H with a negative product of elements

1.  1039

2.  961

3.  either a or b

4.  neither a nor b

5.  none of these

5

either a or b

Explanation :
No Explanation available for this question

# Find the sum of all positive integers m such that m2 + 25m + 19 is a perfect square

1.  125

2.  130

3.  159

4.  164

5.  198

5

164

Explanation :
No Explanation available for this question

# Given that m, a, and b are positive integers such that m + 5a + 7b = 84 and m + 7a + 10b = 114 then find 9m + 23a + 30b =

1.  210

2.  426

3.  145

4.  325

5.  none of these

5

426

Explanation :
No Explanation available for this question

1.  3

2.  4

3.  5

4.  6

5.  7

5