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

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Correct Answer :

2h2 = b2

Explanation :
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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

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Correct Answer :

240

Explanation :
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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

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Correct Answer :

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

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Correct Answer :

Explanation :
No Explanation available for this question

In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to

1. 1 : 1

2. 3 : 2

3. 4 : 1

4. 3 : 8

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Correct Answer :

3 : 8

Explanation :
No Explanation available for this question

Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90o or concave if the internal angle is 270o. If the number of convex corners in such a polygon is 25, the number of concave corners must be

1. 20

2. 0

3. 21

4. 22

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Correct Answer :

Explanation :
No Explanation available for this question

The 288th term of the series a, b, b, c, c, c, d, d, d, d, e, e, e, e, e, f, f, f, f, f, f…. is

1. u

2. v

3. w

4. x

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Correct Answer :

Explanation :
No Explanation available for this question

Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true

1. The minimum possible value of a2 + b2 + c2 + d2 is 4m2– 2m + 1

2. The minimum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1

3. The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1

4. The maximum possible value of a2 + b 2 + c2 + d2 is 4m2 + 2m + 1

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Correct Answer :

The minimum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1

Explanation :
No Explanation available for this question

The number of non-negative real roots of 2x – x – 1 = 0 equals

1. 0

2. 1

3. 2

4. 3

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Correct Answer :

Explanation :
No Explanation available for this question

Three horses are grazing within a semi-circular field. In the diagram given below, AB is thediameter of the semi -circular field with centre at O. Horses are tied up at P, R and S such that PO and RO are the radii of semi -circles with centers at P and R respectively, and S is the centre of the circle touching the two semi -circles with diameters AO and OB. The horses tied at P and R can graze within the respective semi -circles and the horse tied at S can graze within the circle centred at S. The percentage of the area of the semi-circle with diameter AB that cannot be grazed by the horses is nearest to

1. 20

2. 28

3. 36

4. 40

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Correct Answer :

Explanation :
No Explanation available for this question

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