# In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race

1.  20 min

2.  15 min

3.  10 min

4.  5 min

4

10 min

Explanation :
No Explanation available for this question

# Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r  0?   x + 2y – 3z = p   2x + 6y – 11z = q   x – 2y + 7z = r

1.  5p – 2q – r = 0

2.  5p + 2q + r = 0

3.  5p + 2q – r = 0

4.   5p – 2q + r = 0

4

5p – 2q – r = 0

Explanation :
No Explanation available for this question

# If the product of n positive real numbers is unity, then their sum is necessarily

1.  a multiple of n

2.  equal to n + 1/n

3.  never less than n

4.  a positive integer

4

never less than n

Explanation :
No Explanation available for this question

# There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is

1.  34

2.   38

3.  36

4.  32

4

Explanation :
No Explanation available for this question

# In the figure below, the rectangle at the corner measures 10 cm  20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?

1.  10 cm

2.  40 cm

3.  50 cm

4.  None of the above

4

50 cm

Explanation :
No Explanation available for this question

# A vertical tower OP stands at the center O of a square ABCD. Let h and b denote the length OP and AB respectively. Suppose APB = 60o then the relationship between h and b can be expressed as

1.  2b2 = h2

2.  2h2 = b2

3.  3b2 = 2h2

4.  3h2 = 2b2

4

2h2 = b2

Explanation :
No Explanation available for this question

# How many three digit positive integers, with digits x, y and z in the hundred’s, ten’s and unit’s place respectively, exist such that x < y, z < y and x  0?

1.  245

2.  285

3.  240

4.  320

4

240

Explanation :
No Explanation available for this question

# In the figure given below, AB is the chord of a circle with center O. AB is extended to C such that BC = OB. The straight line CO is produced to meet the circle at D. If  ACD = y degrees and ? AOD = x degrees such that x = ky, then the value of k is

1.  3

2.  2

3.  1

4.  None of the above

4

3

Explanation :
No Explanation available for this question

# If log32, log3(2x – 5), log3(2x – 7/2) are in arithmetic progression, then the value of x is equal to

1.  5

2.  4

3.  2

4.  3

4

3

Explanation :
No Explanation available for this question

# In the diagram given below,  ABD =  ? CDB =  ? PQD = 90o. If AB : CD = 3 : 1, the ratio of =CD : PQ is

1.  1 : 0.69

2.  1 : 0.75

3.  1 : 0.72

4.  None of the above.

4