Live Leak - RRB ALP 2018 Model Answer Key

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1 | Page Live Leak - RRB ALP 2018 Model Answer Key (Get this Answer Key in Hindi too) 1. a 2. a 3. 3 4. a 5. a 6. b 7. a 8. 2 9. b 10. b 11. a 12. c 13. 2 14. c 15. a 16. b 17. b 18. 3 19. d 20. d 21. d 22. d 23. b 24. c 25. c 26. c 27. b 28. d 29. c 30. a 31. d 32. d 33. d 34. d 35. c 36. b 37. c 38. c 39. d 40. c 41. a 42. b 43. a 44. a 45. a 46. d 47. c 48. a 49. a 50. d 51. b 52. a 53. c 54. b 55. d 56. b 57. a 58. b 59. a 60. c 61. c 62. b 63. d 64. c 65. c 66. d 67. c 68. b 69. c 70. a 71. b 72. d 73. c 74. b 75. d Solution: 1. Soft Iron has very high relative permeability i.e. it can magnetise itself very quickly when current is pass around the core and demagnetised when current is stopped. Electromagnet is basically used for different electrical or mechanical devices like picking iron or calling bell where this quick transformation property is very important. So, soft iron is the ideal material for this operation. 2. Work done= Force × Displacement W = 50 cos θ × 4 = 50 cos 60° × 4

Transcript of Live Leak - RRB ALP 2018 Model Answer Key

1 | P a g e

Live Leak - RRB ALP 2018

Model Answer Key (Get this Answer Key in Hindi too)

1. a 2. a 3. 3 4. a 5. a

6. b 7. a 8. 2 9. b 10. b

11. a 12. c 13. 2 14. c 15. a

16. b 17. b 18. 3 19. d 20. d

21. d 22. d 23. b 24. c 25. c

26. c 27. b 28. d 29. c 30. a

31. d 32. d 33. d 34. d 35. c

36. b 37. c 38. c 39. d 40. c

41. a 42. b 43. a 44. a 45. a

46. d 47. c 48. a 49. a 50. d

51. b 52. a 53. c 54. b 55. d

56. b 57. a 58. b 59. a 60. c

61. c 62. b 63. d 64. c 65. c

66. d 67. c 68. b 69. c 70. a

71. b 72. d 73. c 74. b 75. d

Solution:

1. Soft Iron has very high relative

permeability i.e. it can magnetise itself

very quickly when current is pass

around the core and demagnetised when

current is stopped.

Electromagnet is basically used for

different electrical or mechanical devices

like picking iron or calling bell where

this quick transformation property is

very important.

So, soft iron is the ideal material for this

operation.

2. Work done= Force × Displacement

W = 50 cos θ × 4

= 50 cos 60° × 4

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= 50 × 1/2 × 4 = 100 J [where cos 60° =

1/2]

3. The World Wide Fund for

Nature (WWF) is an international NGO

founded in 1961.

It is working in the field of the

wilderness preservation, and the

reduction of human impact on the

environment.

4. Femto is a unit prefix in the metric

system. The other SI prefixes are shown

in the table.

SI Prefix Factor

Milli (m) 10-3

Micro (μ) 10-6

Nano (n) 10-9

Pico (p) 10-12

Femto (f) 10-15

5. The famous Kashmir red deer, also

known as hangul and Kashmir stag, is a

subspecies of elk native to India.

6. Mass of body (m) = 40 kg

Acceleration (a) = 5 m/sec2

Time (t) = 20 seconds

According to kinematics equation,

assuming acceleration is constant,

𝑆 = 𝑢𝑡 +1

2𝑎𝑡2

Where

S = Distance travelled by the body (m)

u = Initial velocity (m/s)

a = Acceleration (m/s2)

t = Time taken

As body starts from rest u = 0 i.e. Initial

velocity.

𝑆 = 0 +1

2× 5 × 202 = 1000 𝑚

S = 1000 metres

Distance is 1000 metres.

7. A barometer is a scientific instrument

used in meteorology to

measure atmospheric pressure.

Evangelista Torricelli invented it in

1643.

8. Calcination is a process in which

the ore is heated below its melting point

in the absence or in a limited supply of

air. Its aim is to drive off moisture,

hydrates of water and organic matter

from the ore.

Other processes are defined as:-

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Refining is a process of

removing impurities or unwanted

elements from a substance, typically as

part of an industrial process.

Roasting is a process of heating of

sulphide ore to a high temperature in

presence of air. It is a step in the

processing of certain ores.

Smelting is a process of extracting

metal from its ore by a process involving

heating and melting.

9. In HCO – COOH molecule, the

oxygen with HCO has three lone pairs.

And two oxygen together in COOH has

five lone pairs. Hence total lone pairs

are 8.

10. Baking powder has the chemical

formula NaHCO3 and IUPAC name is

Sodium bicarbonate.

Vinegar has the chemical formula

CH3COOH and IUPAC name is Acetic

acid.

Bleaching powder has the chemical

formula Ca(ClO)2 and IUPAC name is

Calcium hypochlorite.

Chalk has the chemical formula

CaCO3 and IUPAC name is Calcium

carbonate.

11. Lichens are generally useful bio

indicators for air pollution, especially

sulphur dioxide because they derive

their essential needs and water mostly

from the atmosphere rather than

deriving it from the soil.

12. Red Blood Cells or Erythrocytes of

adult mammals are formed in the bone

marrow of the body.

The general lifespan of the RBC is about

120 days after which new cells replace

the old ones.

13. Isotones are atoms with same

neutrons. The no. of neutrons can be

found by subtracting atomic number

from atomic mass.

No. of Neutrons of 32Ge76 = Atomic

mass (in this case 76) - Atomic no. (in

this case 32) = 44

No. of Neutrons of 34 Se78 = Atomic

mass (in this case 78) - Atomic no. (in

this case 34) = 44

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Therefore, in both the cases, the number

of neutrons is the same.

Hence 32Ge76 and 34 Se78 are isotonic.

14. REDD stands

for Reducing Emissions from

Deforestation and Forest

Degradation.

So in REDD, E stands for emissions.

Its objective is to mitigate climate

change by reducing the emission of

greenhouse gases and enhancing forest

management in developing countries.

15. Bonn convention, also known as The

Convention on the Conservation of

Migratory Species of Wild Animals aims

to conserve terrestrial, marine and avian

migratory species throughout their

range.

It is an intergovernmental treaty,

concluded under the aegis of the United

Nations Environment Programme,

associated with the conservation of

wildlife and habitats on a global scale.

Head Quarter: Bonn, Germany

16. Paleontology is the study of Fossils

Geology is the study of Earth and rocks

Myrmecology is the study of Ants

Anthropology is the study of origin,

development, and relationship between

the culture of past and present human

17.

Functional Group Suffix Nomenclature

Aldehyde -al Propanal

Halogen -pane Bromopropane

Ketone -one Propanone

Alcohol -ol Propanol

18.

Element Symbol Atomi

c No.

Meltin

g Point

(°C)

State in

room

temperatur

e (15 - 25°c)

Bromine Br 35 -7.2 Liquid

Hafniu

m Hf 72 2231 Solid

Iodine I 53 113.7 Solid

Mercury Hg 80 -38.83 Liquid

19. Conductivity is depends upon

number of electrons present in outer

shell of atom i.e. Valence electron.

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It is inversely proportional to outer shell

electron number i.e. If number of

electron is high then conductivity is low

and vice versa.

Number of electrons in outer shell of

silver, aluminium, silicon, and glass are

1, 3, 4, 8, so that conductivity is

decreasing from silver to glass.

Silver > Aluminium > Silicon > Glass.

20. According to Archimedes principle,

volume or weight of water displaced is

equal to volume or weight of body

immersed partially or fully in water.

So that the weight of water displaced is

equal to weight of boat floats i.e. 200 kg.

21. The Indian Navy hosted the multi-

national MILAN exercise at Port Blair in

Andaman and Nicobar islands from

March 6 to March 13, 2018. MILAN is a

congregation of littoral navies conducted

biennially by the Indian Navy under the

aegis of the Andaman and Nicobar

Command. It began in 1995. This year's

theme was ‘Friendship Across the Seas’.

It witnessed professional exercises and

seminars.

22. Stephen Hawking, the British

Physicist and the black hole theorist

have died on 14th March. Hawkings

redefined cosmology by proposing that

black holes emit radiation and later

evaporate. He is also the author of the

best-selling book, "A Brief History of

Time".

23.

Country Capital

Philippines Manila

Maldives Male

Lebanon Beirut

Oman Muscat

24. The largest ever Winter Paralympics

were officially inaugurated in freezing

conditions at the Olympic Stadium in

Pyeongchang, South Korea. A record 567

athletes from 48 different nations

paraded into the Pyeongchang Olympic

Stadium to officially commence the 10-

day festival that runs till March 18. A

neutral Paralympic athletes team

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consisting of Russian competitors is also

participating.

25. The Bay of Bengal Initiative for

Multi-Sectoral Technical and Economic

Cooperation (BIMSTEC) celebrates its

20th anniversary on June 06, 2017.

BIMSTEC or Bay of Bengal Initiative for

Multi-Sectoral Technical and Economic

Cooperation has formed nearly two

decades ago, on June 06, 1997.

26. The South Central Railway (SCR)

has become the first railway zone in the

country to complete 100% LED lighting

at all the stations under its jurisdiction.

The SCR has been on the forefront of

adopting energy conservation measures.

It has attained the status of becoming

the first zone in the Indian Railways to

complete 100% LED lighting in all the

733 stations under its jurisdiction.

27. India defeated Pakistan in the

inaugural IBSF Snooker Team World

Cup in Doha. The Indian combine of

Pankaj Advani and Manan Chandra

came back from 0-2 down in the best-of-

five final to clinch it with a margin of 3-

2. The Indian team was awarded

$15,000 (nearly ₹ 10 lakh) for winning

the tournament.

28. Prime Minister flagged off the

country’s first high-powered electric

locomotive assembled in Madhepura in

Bihar. This first locomotive is part of a

joint venture of the railways with

Alstom, signed in 2015 and the first

major FDI project in the rail sector.

India will join countries like Russia,

China, Germany and Sweden that have

12,000 horsepower & above capacity

electric locomotives.

29. Aadhaar and Umang app won the

awards at 6th World Government

Summit 2018 in Dubai.

Umang App was named the winner of

the Best M - Government Service award

while Aadhar won the best emerging

technology award.

Aadhaar was also recognised as the

world’s largest biometric enabled

identification programme.

30. Kolattam is a folk dance of Andhra

Pradesh.

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There are “eight” types of recognized

classical dance.

DANCE STATE DANCE STATE

Bharatanatyam Tamil

Nadu Manipuri Manipur

Kathak Uttar

Pradesh Odissi Orissa

Kathakali Kerala Sattriya Assam

Kuchipudi Andhra

Pradesh Mohiniyattam Kerala

31. All except Read are synonyms.

Hence, Read is different from the rest.

32. All except Leander Paes are

badminton players of India. While

Leander Paes is a tennis player.

Hence, Leander Paes is odd one from

rest.

33. All other places are hill areas while

Diu is situated near sea.

34. As given in the question,

GREAT → number of letters = 5,

So, 5 × 3 - 3 = 12

Similarly,

TESTBOOK → number of letters 8.

So, 8 × 3 - 3 = 21.

Hence, the correct answer is 21.

35. Here from the question it is clear

that the relation is between cities and

the bank on which they are situated.

Agra is on the bank of Yamuna and

Guwahati is on the bank of

Brahmaputra.

36. In the code, the first three letters are

kept as it is. The fourth letter is made

fifth, fifth is made sixth and sixth is

made fourth, then the last two letters are

interchanged.

Similarly,

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Hence, the answer is 2.

37.

In the first and second statements, the

common code word is ‘wek’ and the

common word is ‘she’.

So, ‘wek’ stands for ‘she’.

In the first and third statements, the

common code word is ‘koed’ and

common word is ‘grapes’.

So, ‘koed’ stands for ‘grapes’.

Thus, ‘wek’ and ‘koed’ stands for ‘she’

and ‘grapes’.

38. The given logic is as follows:

(Column 1 × Column 2) – Column 3 =

Column 4,

5 × 15 = 75 – 10 = 65

12 × 13 = 156 – 69 = 87

17 × 8 = 136 – 47 = 89

Hence, the missing number is 89.

39. Given expression: 56 + 14 / 3 – 6 ×

15

After changing: 56 / 14 – 3 × 6 + 15

= 4 – 18 + 15 = 1

40. All except Appendix are bones.

Hence, Appendix is odd one from the

rest.

41. CE = C + 2 = E; E + 1 = F

FI = F + 3 = I; I + 1 = J

JL = J + 2 = L; L + 1 = M

MP = M + 3 = P; P + 1 = Q

QS = Q + 2 = S; S + 1 = T

TW = T + 3 = W

Hence, “TW” will complete the series.

42. We can observe that the logic is –

First digit of given number × Second

digit of given number × Third digit of

given number = Required number.

For 891, 8 × 9 × 1 = 72

For 257, 2 × 5 × 7 = 70

Similarly for 529, 5 × 2 × 9 = 90

Hence, the answer is 90.

43.

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44.

Above diagram shows mirror image of

the question figure.

Hence, image present in option 1) is the

correct answer.

45. Let us check each option

1) 87, 67, 24, 32 → BORD

2) 87, 76, 24, 32 → BKRD

3) 87, 67, 12, 23 → BORN

4) 87, 67, 42, 01 → BOND

Hence, the set which represents BORD

is 87, 67, 24, 32.

46. I. P goes to study in Ramjas college

on Tuesday and R goes to his college on

Saturday.

S. N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

II. Q goes to Hindu college a day after P.

S. N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

3 Q Hindu Wednesday A day after P

III. S goes to Indraprastha college a day

after Q.

S. N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

3 Q Hindu Wednesday A day after P

4 S Indraprastha Thursday A day after Q.

IV. Someone goes to Miranda college

two days before Hindu.

S. N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

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3 Q Hindu Wednesda

y -

4 S Indrapra

stha Thursday

A day

after Q.

5 - Miranda Monday

Two days

before

Hindu.

V. U goes to Gargi college.

S. N.

Name College Day Condition

1 P Ramjas Tuesday -

2 R Hansraj Saturday -

3 Q Hindu Wednesday A day after

P

4 S Indraprastha Thursday A day after

Q.

5 T Miranda Monday Two days

before Hindu.

6 U Gargi Friday -

Hence, T goes to study in Miranda

college.

47. I. P goes to study in Ramjas college

on Tuesday and R goes to his college on

Saturday.

S. N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

II. Q goes to Hindu college a day after P.

S. N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

3 Q Hindu Wednesday A day after P

III. S goes to Indraprastha college a day

after Q.

S. N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

3 Q Hindu Wednesday A day after P

4 S Indraprastha Thursday A day after Q.

IV. Someone goes to Miranda college

two days before Hindu.

S.

N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

3 Q Hindu Wednesday -

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4 S Indraprastha Thursday A day

after Q.

5 - Miranda Monday

Two days

before

Hindu.

V. U goes to Gargi college.

S.

N. Name College Day Condition

1 P Ramjas Tuesday -

2 R Hansraj Saturday -

3 Q Hindu Wednesday A day after P

4 S Indraprastha Thursday A day after Q.

5 T Miranda Monday Two days before

Hindu.

6 U Gargi Friday -

Hence, R goes to study in Hansraj

college.

48. I. P goes to study in Ramjas college

on Tuesday and R goes to his college on

Saturday.

S. N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

II. Q goes to Hindu college a day after P.

S. N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

3 Q Hindu Wednesday A day after P

III. S goes to Indraprastha college a day

after Q.

S.

N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

3 Q Hindu Wednesday A day

after P

4 S Indraprastha Thursday A day

after Q.

IV. Someone goes to Miranda college

two days before Hindu.

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S.

N. Name College Day Condition

1 P Ramjas Tuesday -

2 R - Saturday -

3 Q Hindu Wednesday -

4 S Indraprastha Thursday A day after Q.

5 - Miranda Monday Two days

before Hindu.

V. U goes to Gargi college.

S.

N. Name College Day Condition

1 P Ramjas Tuesday -

2 R Hansraj Saturday -

3 Q Hindu Wednesday A day after

P

4 S Indraprastha Thursday A day after

Q.

5 T Miranda Monday

Two days

before

Hindu.

6 U Gargi Friday -

Hence, Q goes to Hindu college on

Wednesday.

49. Figure (1) has all the four images

embedded in it.

Hence, figure in option 1 is the correct

answer.

50. From figure 1, 5 is adjacent to 3 and

2. From figure 2, 5 is adjacent to 4 and

6. Obviously, 5 is opposite to 1, 3 is

opposite to 4 and 2 is opposite to 6.

Hence, 6 is opposite to 2.

51. Here, $ means÷, ? means ×

57 ÷ 3 × 7 = 133

87 ÷ 3 × 2 =58

Similarly,

82 ÷ 2 × 4 = 164

Hence, 164 is the answer.

52. A salesman visits 274 houses in a

town to find out the views about three

products X, Y and Z.

People who use product X = 157,

People who use only product X = 98

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People who use all three product X, Y

and Z = 22

People who use X and Z product but not

Y = 14

People who use Y and Z product = 39

People who use only product Y = 48

Therefore,

People who use only Y and Z = people

who use Y & Z – people who use all = 39

– 22 = 17

People who use only Z = all people –

people who use X – people who use only

Y – people who use only Y and Z = 274 –

157 – 48 – 17 = 52

People who use only X and Y

People who use only X and Y product =

people who use X – people who use only

X and Z – people who use only X –

people who use all three = 157 – 14 – 98

– 22 = 23.

Hence, X is most popular product.

53. A salesman visits 274 houses in a

town to find out the views about three

products X, Y and Z.

People who use product X = 157,

People who use only product X = 98

People who use all three product X, Y

and Z = 22

People who use X and Z product but not

Y = 14

People who use Y and Z product = 39

People who use only product Y = 48

Therefore,

People who use only Y and Z = people

who use Y & Z – people who use all = 39

– 22 = 17

People who use only Z = all people –

people who use X – people who use only

Y – people who use only Y and Z = 274 –

157 – 48 – 17 = 52

People who use only X and Y

People who use only X and Y product =

people who use X – people who use only

X and Z – people who use only X –

people who use all three = 157 – 14 – 98

– 22 = 23.

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Therefore, 52 people used product Z

only.

54. A salesman visits 274 houses in a

town to find out the views about three

products X, Y and Z.

People who use product X = 157,

People who use only product X = 98

People who use all three product X, Y

and Z = 22

People who use X and Z product but not

Y = 14

People who use Y and Z product = 39

People who use only product Y = 48

Therefore,

People who use only Y and Z = people

who use Y & Z – people who use all = 39

– 22 = 17

People who use only Z = all people –

people who use X – people who use only

Y – people who use only Y and Z = 274 –

157 – 48 – 17 = 52

People who use only X and Y

People who use only X and Y product =

people who use X – people who use only

X and Z – people who use only X –

people who use all three = 157 – 14 – 98

– 22 = 23.

Therefore, people who used at least two

products = people who used two

products + people who used all products

= people who used X & Y only + people

who used X & Z only + people who used

Y & Z only + people who used all =

people who used X & Y only + people

who used X & Z only + people who used

Y & Z = 23 + 14 + 39 = 76.

Therefore, 76/274 fraction of total

people used at least two products.

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55. Since the statement says nothing

about cowards or about the necessity of

risks. They are unrelated to the

statement.

Hence, neither conclusion I nor II

follows.

56. ⇒ 14.14 + 0.2 × 31.34 – 2.6 × 2.43

⇒ 14.14 + 6.268 – 6.318

⇒ 14.14 + 6.27 – 6.32

⇒ 20.41 – 6.32

⇒ 14.09

∴ 14.14 + 0.2 × 31.34 – 2.6 × 2.43 =

14.09

57. ⇒ 3x + 3 + 3x - 2 = 244

⇒ 3x.33 + 3x/32 = 244

⇒ 3x (27 + 1/9) = 244

⇒ 3x × (244/9) = 244

⇒ 3x = 32

∴ x = 2

58. Let x be the number and y be the

quotient. Then,

x = 893 × y + 193

⇒ x = (47 × 19 × y) + (47 × 4) + 5

⇒ x = 47 × (19y + 4) + 5

∴ Required remainder = 5

59. 15% of 34 = 0.15 × 34 = 5.1

60. Speed of car during first part of

journey = 35/(40/60) = 52.5 km/hr.

Speed of car during next part of journey

= 52.5 + 7.5 = 60 km/hr.

Time taken in next part of journey =

45/60 = 0.75 hr. = 45 min.

∴ Time taken to reach the office = 40 +

45 = 85 min. = 1 hr. 25 min.

61. Let the number of students in the

class be ‘x’

No. of boys = (100 - 40)% of x = 60% of

x = 0.6x

No. of boys which either passed with a

low percentage or failed = (100 - 70)% of

0.6x = 0.3 × 0.6x = 0.18x

No. of boys that failed = (100 – 80)% of

0.18x = 20% of 0.18x

But, 9 boys failed in the examination,

hence,

⇒ 0.2 × 0.18x = 9

⇒ 0.036x = 9

⇒ x = 9/0.036 = 250

∴ There are 250 students in the class

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62. Let their current age be ‘4x’ years

and ‘3x’ years

Six years ago, their age ratio = (4x – 6) ∶

(3x – 6) = 10 ∶ 7

⇒ 7(4x – 6) = 10(3x – 6)

⇒ 28x – 42 = 30x – 60

⇒ 30x – 28x = 60 – 42

⇒ 2x = 18

⇒ x = 18/2 = 9

∴ Their age ratio after 9 years = (4 × 9 +

9) ∶ (3 × 9 + 9) = 45 ∶ 36 = 5 ∶ 4

63. Let Vinod and Vicky do the work

alone in ‘x’ and ‘y’ days respectively

Vinod’s 1 day work = 1/x

Vicky’s 1 day work = 1/y

Together their 1 day work = 1/x + 1/y =

1/6 ---- (1)

Also,

Ratio of their work efficiencies = Ratio

of their wages

⇒ (1/x) ∶ (1/y) = 2 ∶ 3

⇒ y/x = 2/3

⇒ y = (2/3)x

Substituting in (1),

⇒ 1/x + 3/2x = 1/6

⇒ 5/2x = 1/6

⇒ x = (6 × 5)/2 = 15 days

∴ Vinod can do the work alone in 15

days.

64. Let the initial number of friends be

‘x’

Their total weight = 54x

When one friend weighing 40 kg left the

group, total weight of friends = 55(x – 1)

Hence,

⇒ 54x = 40 + 55(x – 1)

⇒ 55x – 54x = 55 – 40

⇒ x = 15

∴ There were 15 friends in the group.

65. The given series follows the below

pattern.

45

45 + 42 + 8 = 69

69 + 52 + 7 = 101

101 + 62 + 6 = 143

143 + 72 + 5 = 197

∴ ? = 197

66. Let the length of a diagonal be T cm

and another diagonal be (T - 49) cm.

The area of the rhombus is 1911 square

cm.

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⇒ (1/2) × T × (T – 49) = 1911

⇒ T2 – 49T – 3822 = 0

⇒ (T + 42) (T - 91) = 0

Since diagonal length cannot be

negative, T = 91

∴ Diagonals have lengths 91 cm and 42

cm

67. Given series follow pattern shown

below,

⇒ 4,

⇒ (4 × 3) + 1 = 13

⇒ (13 × 3) + 1 = 40

⇒ (40 × 3) + 1 = 121

⇒ (121 × 3) + 1 = 364

Hence, “364” is correct option.

68. As we know, (x + y)2 = x2 + y2 +

2xy

We can write,

(a + b + c)2 = [(a + b) + c]2 = (a + b)2 +

c2 + 2c(a + b)

⇒ (a + b + c)2 = (a + b)2 + c2 + 2bc +

2ac ----(1)

Also, (b + c)2 = b2 + c2 + 2bc

⇒ c2 + 2bc = (b + c)2 – b2 ----(2)

Substituting (2) in (1), we get,

⇒ (a + b + c)2 = (a + b)2 + (b + c)2 – b2

+ 2ac

⇒ b2 – 2ac = (a + b)2 + (b + c)2 – (a + b

+ c)2

Substituting values,

⇒ b2 – 2ac = 9 + 1 – 4

∴ (b2 – 2ac) = 6

69. According to the given information,

x = tan2A + cot2A + 2

= (tan2A + 1) + (cot2A + 1)

= sec2A + cosec2A

= 1/cos2A + 1/sin2A

= (sin2A + cos2A)/cos2Asin2A

= 1/cos2Asin2A

= sec2Acosec2A

70. Given: secθ = 13/12

⇒ secθ = 1/cosθ

⇒ cosθ = 12/13

We know that: sin2θ + cos2θ = 1

⇒ sin2θ + (12/13)2 = 1

⇒sin2θ = 1 - 144/169

⇒ sin2θ = (169 - 144)/169

⇒ sinθ = √(25/169)

∴ sinθ = 5/13

18 | P a g e

71. ∠CDB + ∠BDA = ∠ADC

⇒ (8y + 8°) + 5y – 3° = 70°

⇒ 13y + 5° = 70°

⇒ y = 65°/13 = 5°

∴ ∠CDB = 8y + 8 = 48° and ∠BDA = 5y

– 3 = 22°

72. Let P1 be (a, b)

P1 is reflected in x - axis to get P2 which

is (a, -b)

When (-1, 4) is reflected in x - axis we

get (-1, -4)

73. Let the cost price be Rs. ‘x’

Profit earned = 8% of x = 0.08x

Selling price = Cost price + Profit = x +

0.08x = 1.08x

Now,

Selling Price = Marked price – Discount

⇒ 1.08x = MP – 10% of MP

⇒ 1.08x = 0.9 × MP

⇒ MP = 1.08x/0.9 = 1.2x

⇒ MP = x + 20% of x

∴ the marked price should be 20% above

the cost price.

74. Time taken upstream = 2 hrs. 40

min. = 2 + 40/60 = 2.667 hrs.

Upstream speed = 20/2.667 = 7.5

km/hr.

As we know, speed of boat in still water

= 1/2 × (Downstream speed + Upstream

speed)

⇒ 12 × 2 = Downstream speed + 7.5

⇒ Downstream speed = 24 – 7.5 = 16.5

km/hr.

∴ The boat will return at a speed of 16.5

km/hr.

75. Sum of ratios = 3 + 1 = 4

Amount of honey in initial mixture =

(3/4) × 15 = 45/4 litres

Amount of water in initial mixture =

(1/4) × 15 = 15/4 litres

Let amount of water to be added be ‘x’

litres

Amount of water in new mixture = x +

15/4

Now, ratio of new mixture = 2 ∶ 1

⇒ (45/4) ∶ (x + 15/4) = 2 ∶ 1

⇒ 45/4 = 2x + 30/4

⇒ 2x = 45/4 – 30/4 = 15/4

⇒ x = 15/8 = 1.875 litres

∴ Amount of water to be added = 1.875

litres.