CAPF (AC) 2013 (Paper-1) (Question 1-50)

Total Questions: 50

1. A circle is drawn inside a square of length 4 units as shown in the figure given above. What is the area of the shaded portion?

Correct Answer: (c) 4 - π
Solution:Side of square = 4 unit

Radius of circle = 4/2 = 2 unit

Area of the shaded portion = = (4² - π2²)/4

= (16 - 4π)/4 = (4 - π)

2. If the ratio of X to Y is 3/4 and the ratio of Y to Z is 12/13, then the ratio of X to Z is

Correct Answer: (d) 9/13
Solution:Ratio of X and Y = 3/4

Ratio of Y and Z = 12/13

∴ Ratio of X, Y and Z = (36/48) / 52 = (9/12) / 13

Hence, the ratio of X to Z = 9/13 = 9/13

3. The sum of the base and altitude of a triangle is 30 cm. What is the maximum possible area of such a triangle?

Correct Answer: (c) 112.5 cm²
Solution:Given, b + h = 30cm

So, maximum value can be = 15 × 15 = b × h = 225

∴ b = h = 15 cm.

= 1/2 × 15 × 15 = 7.5 × 15 = 112.5 cm².

4. If 9 mangoes cost as much as 5 oranges, 5 oranges as much as 3 apples, 4 apples as much as 9 pineapples and if 3 pineapples ₹ 48, what will a mango cost?

Correct Answer: (b) ₹ 12
Solution:Cost of 3 pineapples = ₹ 48

∴ Cost of 1 pineapple = 48/3 = ₹ 16

Cost of 4 apples = 9 × 16 = ₹ 144

∴ Cost of 1 apple = (9 × 16)/4 = ₹ 36

Cost of 5 oranges = 3 × 36 = ₹ 108

∴ Cost of 1 orange = (3 × 36)/5 = ₹ 21.60

Cost of 9 mangoes = 3 × 36

Hence, cost of a mango = (3 × 36)/9 = ₹ 12.

5. In the diagram (not to scale) given above, the value of x is

Correct Answer: (b) 360/7
Solution:4yº + 3yº = 180º

⇒ 7y = 180º

⇒ y = (180ϒ)/7

Now, x + 2y + 3y = 180º

⇒ x + 5y = 180º

[By putting value from equation (1)]

⇒ x + 5 × 180/7 = 180

⇒ x = 180 - (5 × 180)/7

= (7 × 180 - 5 × 180)/7 = (180(7 - 5))/7

⇒ x = (180 × 2)/7 = (360º)/7

6. A campus poll covering 300 under-graduate students was conducted in order to study the students' attitude towards a proposed change in the rules for hostel accommodation. The students were required to respond as 'support', 'neutral' or 'oppose' with regard to the issue. The poll outcome was presented as a pie chart as given below :

The numbers for 'support', 'neutral' and 'oppose' are respectively

Correct Answer: (b) 120, 100, 80
Solution:Number of support = 300 × 144/360 = 120

Number of oppose = 300 × 96/360 = 80

Number of neutral = 300 × {(360 - (144 + 96))/360} = 100 .

7. The following tables show the expenditure (in percentage) of two families A and B :

Which one among the following statements is true?

Correct Answer: (c) Families A and B spend equally on food
Solution:Expenditure Table 
EntertainmentMiscellaneousFood
Family A20000 × 30/100 = 600020000 × 20/100 = 400020000 × 50/100 = 10000
Family B100000 × 20/100 = 20000100000 × 70/100 = 70000100000 × 10/100 = 10000

8. Which one among the following diagrams illustrates relationship among animals, cows and horses?

Correct Answer: (c)
Solution:

 

9. Through how many degrees does the hour hand in a clock move as the time changes from 3 hours and 12 minutes to 6 hours?

Correct Answer: (d) 84
Solution:Angle moves by hour hand in one hour

= 360/12 = 30º

Angle moved by hour hand

= 30º × [6 - (3 + 11/60)] = (30 × 14/5)º = 84º

10. As shown in the above diagram, a person starts from the centre O of a circular path AB, walks along the line indicated by arrows and returns to the same point. If the radius OA = OB = 100 metres, what is the total distance walked to the nearest metres?

Correct Answer: (b) 723
Solution:

Here, radius AO = OB = 100m

Total distance covered = OA+ hat ACB + BO

= 100 + ((360º - 60º)/(360º)) × 2 × π × 100 + 100

= ((5π + 6)/3) × 100 = 723m .