Triangle ABC has base AB of length k and C is such that < CAB =2 < CBA < 1200 Then the locus of C is :

1.  Straight line 

2.  circle

3.  ellipse

4.  Parabola

5.  none of these

View Answer  
5
Correct Answer :

Parabola


Explanation :
No Explanation available for this question

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

1.  0

2.  1

3.  2

4.  3

5.  none of these

View Answer  
5
Correct Answer :

1


Explanation :
No Explanation available for this question

There are two ants on opposite corners of a cube. On each move,they can travel along an edge to an adjacent vertex. If the probability that they both return to their starting position after 4 moves is m/n,where m andn are relatively prime integers, find m+n. (NOTE:They do not stop if they collide.)

1.  17

2.  65

3.  73

4.  85

5.  none of these

View Answer  
5
Correct Answer :

85


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

View Answer  
5
Correct Answer :

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

View Answer  
5
Correct Answer :

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

View Answer  
5
Correct Answer :

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

View Answer  
5
Correct Answer :

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

View Answer  
5
Correct Answer :

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

View Answer  
5
Correct Answer :

either a or b


Explanation :
No Explanation available for this question

Two different teams with four students each were training for an international math contest. The students were given an assessment exam and their scores were ranked. What is the probability that the four best scores come from only one of the teams assuming that no two students got the same score

1.  1/2 

2.  1/16

3.  1/35

4.  1/288

5.  1/576

View Answer  
5
Correct Answer :

1/16


Explanation :
No Explanation available for this question
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