Download - Live Leak - RRB ALP 2018 Model Answer Key
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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
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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.
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