CAPF (AC) 2016 (Paper-1) (Question 51-100)

Total Questions: 50

1. In the diagram given below, there is a circle, a square and a triangle dividing the region into five disjoint bounded areas. Each of these areas are labelled with number of players belonging to that area. The circle contains cricketers, the square contains football players and the triangle contains hockey players.

Correct Answer: (b) Every cricket players plays either football or hockey
Solution:

Every cricket player plays either football or hockey is not true, because number 8 in cricketers neither play hockey nor play football.

2. There are two concentric circles. The radii of the two circles are 100 m and 110 m respectively. A wheel of radius 30 cm rolls on the smaller circle and another wheel rolls on the larger circle. After they have completed one revolution, it is found that the two wheels rolled equal number of times on their respective axes. What is the radius of the other wheel?

Correct Answer: (c) 33 cm
Solution:Let R be the radius of the circle which is rotating on the bigger circle.

According to the question,

(2π×10000)/(2π×30) = (2π×11000)/(2πR)

(∴ No. of rolls done by the wheel = circumference of the circle)

R = (11/10) × 30 = 33cm.

∴ The radius of the wheel rotating on the bigger circle = 33 cm.

3. A triangle is formed with vertices (0,0), (0, 100) and (100, 100). What is the number of points inside the triangle with integer coordinates?

Correct Answer: (c) 4851
Solution:

Total no. of points in the square = 100 × 100 = 10000.

Points in side the triangle = (100×100)/2 = 5000

∴ Points inside the triangle with integer coordinates are 5000.

4. Which one of the following is the wrong number in the series 6, 14, 30, 64, 126 ?

Correct Answer: (b) 64
Solution:The pattern of the series is as :

6 × 2 + 2 = 14

14 × 2 + 2 = 30

30 × 2 + 2 = 62

62 × 2 + 2 = 126

So, 64 is the wrong number in the series.

5. Given below is a figure of a square transparent sheet with a pattern:

Which one of the following is the correct figure showing how the pattern would appear after folding the above mentioned transparent sheet at the dotted line?

Correct Answer: (a)

6. In a school there are three batches of players who play cricket, football and hockey. An incomplete chart of number of students playing an individual sport belonging to an individual batch is displayed in the following table:

Batch IBatch IIBatch IIITotal
Cricket players814
Football players1016
Hockey players6617
Total

Which one of the following is correct?

Correct Answer: (b) Batch I and Batch II do not have equal number of students
Solution:Table 1:
Batch IBatch IIBatch IIITotal
Cricket players6814
Football players61016
Hockey players65617
Total

Table 2:

Batch IBatch IIBatch IIITotal
Cricket players6814
Football players61016
Hockey players65617
Total

7. There are two boxes. Box I contains one white card and two black cards and Box II contains one white card and a black card. Two persons P and Q play a game. P picks a card randomly from Box I. If P finds the white card, P wins and the game stops. If P finds the black card, Q draws a card randomly from Box II. If Q finds the white card Q wins. The game stops whether Q draws the white card or the black card. Which one of the following is correct?

Correct Answer: (d) Both P and Q may lose
Solution:Here, for winning either P or Q has to pick a white card Q can get a chance to pick card if and only if P picks a black card i.e. P loses.

Hence, option (b) and (c) get eliminated. Also, P and Q both can not lose the game as card picking will be continued till any of both pick a white card to win the game and there are limited number of cards. Hence, option (d) also get eliminated.

Now, check option (a), we find it correct as P pick a black card and Q picks a white card.

8. Suppose R is the region bounded by the two curves Y = x² and Y = 2x² - 1 as shown in the following diagram :

Two distinct lines are drawn such that each of these lines partitions the regions into at least two parts. If 'n' is the total number of regions generated by these lines, then :

Correct Answer: (d) 'n' can be 6
Solution:

It is clear that maximum value of n will be 6.

Hence, possible values of n = 1, 2, 3, 4, 5 or 6

9. Consider the following sequence :

 

0, 6, 24, 60, 120, 210

Which one of the following numbers will come next in the sequence?

Correct Answer: (c) 336
Solution:The pattern of the sequence is as :

0 × 1 × 2 = 0

1 × 2 × 3 = 6

2 × 3 × 4 = 24

3 × 4 × 5 = 60

4 × 5 × 6 = 120

5 × 6 × 7 = 210

6 × 7 × 8 = 336

10. Consider the following figure :

Which one of the following is the number of triangles in the figure given above?

Correct Answer: (b) 27
Solution:Total number of triangles are 27.