Find the number of pairs of positive integers (x, y) such that xy = y50

1.  6

2.  7

3.  8

4.  5

5.  10

5

7

Explanation :
No Explanation available for this question

Let n be a positive integer such that when we add 1 to the product of any n consecutive positive integers, the result is a perfect square, then n equals

1.  2

2.  3

3.  4

4.  5

5.  none of these

5

4

Explanation :
No Explanation available for this question

Let x = 3a + 3b, where a and b are chosen independently from the integers1 through 100 inclusive (with each integer having an equal likelihood of being chosen). Compute the probability that x is an integral multiple of 5.

1.  1/2

2.  1/3

3.  5/6

4.  1/4

5.  none of these

5

1/4

Explanation :
No Explanation available for this question

Express the base 7 repeating decimal 0.023023023023... as a base 10 fraction in lowest terms.

1.  119/2400

2.  23/999

3.  17/342

4.  23/666

5.  none of these

5

17/342

Explanation :
No Explanation available for this question

How many of the first 1000 positive integers can be expressed in theform [2x] + [4x] + [6x] + [8x], where x is a real number, and [z] denotes thegreatest integer less than or equal to z

1.  50

2.  125

3.  250

4.  500

5.  600

5

600

Explanation :
No Explanation available for this question

A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next one minute, πr/4 during next 2 minutes, πr/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round

1.  4

2.  8

3.  16

4.  32

4

16

Explanation :
No Explanation available for this question

Consider the sequence of numbers a1, a2, a3, ..... to infinity where a1 = 81.33 and a2 = –19 and aj = aj–1 –aj–2 for j ≥ 3. What is the sum of the first 6002 terms of this sequence

1.  –100.33

2.  –30.00

3.  62.33

4.  119.33

4

62.33

Explanation :
No Explanation available for this question

The remainder, when (1523 + 2323) is divided by 19, is

1.  4

2.  15

3.  0

4.  18

4

0

Explanation :
No Explanation available for this question

Let C be a circle with centre P0 and AB be a diameter of C. Suppose P1 is the mid point of the line segment P0B, P2 is the mid point of the line segment P1B and so on. Let C1, C2, C3, ...... be circles with diameters P0P1, P1P2, P2P3  ... respectively. Suppose the circles C1 C2, C3, ....  are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is

1.  8 : 9

2.  9 : 10

3.  10 : 11

4.  11 : 12

4

11 : 12

Explanation :
No Explanation available for this question

Let u = (log2x)2 – 6 log2x + 12 where x is a real number. Then the equation xu = 256, has

1.  no solution for x

2.  exactly one solution for x

3.  exactly two distinct solutions for x

4.  exactly three distinct solutions for x

4