CAPF (AC) 2018 (Paper-1) (Question 1-50)

Total Questions: 50

41. Which one of the following ocean currents is not a warm current?

(a) North Pacific
(b) Falkland
(c) North Equatorial
(d) Canary
(*)

Correct Answer: (*)

Solution:

List-I (Current)	List-II (Type)
North Pacific	Warm
Falkland	Cold
North Equatorial	Warm
Canary	Cold

42. What is the largest value for n (natural number) such that 6" divides the product of the first 100 natural numbers?

(a) 18
(b) 33
(c) 44
(d) 48

Correct Answer: (d) 48

Solution:We know that multiple of 2 come more time than multiple of 3 in the first two natural numbers.

Multiple of 3 = 3, 6, 9, ..., 99

Number of power 99/3 = 33 ....... (1)

But some numbers have more than one multiple,

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

Number of powers (3)

1 + 1 + 2 + 1 + 1 + 2 + 1 + 1 + 3 + 1 + 1 = 15 ....... (2)

Total power of 3 = 33 + 15 = 48

So, maximum pair would be 48.

∴ Largest value of n will be 48.

43. The angle between the hour hand and the minute hand of a clock at 10 minutes past 3 is

(a) 30°
(b) 35°
(c) 37.5°
(d) 40°

Correct Answer: (b) 35°

Solution:The angle between hour hand and minute hand = = (30 × h - 11/2 × M)

∴ Angle at 3:10 minute = (30 × 3 - 11/2 × 10)

44. An international conference is attended by 65 people. They all speak at least one of English, French and German language. Suppose 15 speak English and French, 13 speak English and German, 12 speak French and German and 5 speak all the three languages. A total of 30 people can speak German and 30 can speak French. What is the number of people who can speak only English?

(a) 17
(b) 20
(c) 22
(d) 40

Correct Answer: (a) 17

Solution:

Hence, only speak English = 65 - (All speak German + Only speak French + only speak French and English)

= 65 - (30 + 10 + 8) = 65 - 48 = 17

Hence, 17 persons speak only English.

45. Suppose 72 = m × n where m and n are positive integers such that 1 < m < n How many possible values of m are there?

(a) 5
(b) 6
(c) 10
(d) 12

Correct Answer: (a) 5

Solution:72 = 2 × 2 × 2 × 3 × 3

m × n = 2 × 36

3 × 24

4 × 18

8 × 9

6 × 12

There are only 5 possible values of m.

46. Suppose x, y, z are three positive integers such that x ≤ y ≤ z and xyz = 72. Which one of the following values of S yields more than one solution to the equation x + y + z = S

(a) 13
(b) 14
(c) 15
(d) 16

Correct Answer: (b) 14

Solution:For S = 14 we have x = 2 y = 6 and z = 6

or x = 3 y = 3 and z = 8 .

Hence, S = 14 yields more than one solution to the question,

x + y + z = S

47. Which one of the following is the remainder when 10²⁰ is divided by 7?

(a) 1
(b) 2
(c) 4
(d) 6

Correct Answer: (b) 2

Solution:(10²⁰)/7 = (3²⁰)/7

[∴ 10/7 = 3 (remainder)]

= (3¹⁸ × 3²)/7 = (27⁶ × 9)/7

= (-1)⁶ × 2

[∴ 27/7 = -1 (remainder)]

= 1 × 2 = 2

So, remainder is '2'.

48. Which one of the following is anisotropic in nature?

(a) Glass
(b) Rubber
(c) Plastic
(d) Quartz

Correct Answer: (d) Quartz

Solution:The materials whose properties are dependent upon the directions along which they are measuredare called anisotropic materials. While measuring objects along various axes, it is a difference in the physical or mechanical properties of an object, such as absorbance, refractive index, conductivity, tensile strength, etc. For example, wood and quartz. On the other hand, the materials that show the same properties in all directions are called isotropic materials. For example, rubber and plastic. Therefore, the correct option is (d).

49. Which one of the following is not a condensation polymer?

(a) Nylon
(b) DNA
(c) Polythene
(d) Bakelite

Correct Answer: (c) Polythene

Solution:A substance or material that consists of molecules having a big size or macromolecules with many repeating subunits is called a polymer. Condensation polymers are formed due to the joining of molecules, i.e., condensation reaction. Some of the natural condensation polymers are cellulose, starch, and polypeptide chains of proteins. Some of the synthetic condensation polymers are nylon, kevlar, polyester, Bakelite, Melamine, polycarbonates, polyurethanes, epoxies. Polyethene is a vinyl polymer that consists of monomer ethylene. Therefore, the correct option is (c).

50. The tides whose height is 20 percent more than normal tide are called

(a) spring tides
(b) neap tides
(c) apogean and perigean tides
(d) daily and semi-diurnal tides

Correct Answer: (a) spring tides

Solution:The gravitational forces exerted by the moon and the sun and the rotation of the earth cause the rise and fall of sea levels known as tides.

Spring tides, also known as hugs tides, occur during the full moon and new moon phases. They occur due to the alignment of the moon and the sun and their combined effects. They occur twice each lunar month all year long irrespective of any specific season. They are about 20% higher than the normal tides. Therefore, the correct option is (c).

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