SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 1) (Previous Year Paper)

The logic followed here is:

Hence, the correct answer is "XRS".

According to the sequence in the dictionary:

3. Nation
4. National
5. Nationalism
6. Nationality
7. Native

According to the arrangement, "Nationalism" is the third in the sequence.

Hence, the correct answer is "Option 1".

The logic followed here is:

COMPLEX is coded as OCXELPM

BALANCE is coded as ABECNAL

Similarly, AIRLINE is coded as,

So, 'AIRLINE' will be coded as 'IAENILR'.

Hence, the correct answer is IAENILR.

Statements:

All bikes are cars.

Some cars are trucks.

All trucks are cycles

Venn Diagram:

Conclusions:

I. Some cars are cycles → Follow → Because, 'some cars are trucks' and 'all trucks are cycles' which means there are some cars that are cycles.

II. Some cycles are trucks → Follow → Because, 'all trucks are cycles' which means some cycles are definitely trucks.

III. Some bikes are trucks → Does not follow → There is no definite relation given between bikes and trucks so, it can be possible only.

So, only conclusions I and II follows.

Hence, the correct answer is Option 3.

The correct mirror image of the given combination is shown below:

Hence, the correct answer is option 2.

In the given series the pattern followed is:

Each step repeats alternatively.

Here the figure in first and third steps is same.

Next step:

The figure in the fourth step will be same as second step.

Now we consider the given options:

Option 1) 

The circle is shaded.

Option 2) 

The circle is shaded & positions of circle and cross is incorrect.

Option 3) 

The figure is correct.

Option 4) 

The positions of circle and cross is incorrect.

Hence, the correct answer is Option 3.

The logic followed here is:

Hence, the correct answer is "DWEV".

The pattern followed here is:

Logic: (First term × 2) + Second term = Third term

Now we apply the pattern in the given sets:

(17, 24, 58)

17 × 2 + 24 = 58

34 + 24 = 58

58 = 58

(26, 37, 89)

26 × 2 + 37 = 89 

52 + 37 = 89

89 = 89

Now we apply the pattern on the given options:

Option 1) (15, 17, 47)

15 × 2 + 17 = 47

30 + 17 = 47

47 = 47

Option 2) (41, 39, 125)

41 × 2 + 39 = 125 

82 + 39 = 125

121 ≠ 125

Option 3) (10, 20, 44)

10 × 2 + 20 = 44

20 + 20 = 44

40 ≠ 44

Option 4) (21, 38, 96)

21 × 2 + 38 = 96 

42 + 38 = 96

80 ≠ 96

Hence, the correct answer is "Option 1".

Rule :

If any two numbers are the same in two dice irrespective of their position on the dice then the remaining third number in both the dice is opposite to each other.

In the given dice figure,

From figure 1 & figure 2, Face with number 1 & 4 are the same irrespective of their position, so the third number with face 3 is opposite to face 5.

Hence, the correct answer is 3.

The logic followed here is:

Hence, the correct answer is 15.

The logic here follows is :

(2^nd Number ÷ 1^st Number) x 2 = 3^rd Number

For, (13, 39, 6) 

⇒ (39 ÷ 13) x 2 = 6

⇒ 3 x 2 = 6.

For, (9, 18, 4)

⇒ (18 ÷ 9) x 2 = 4

⇒ 2 x 2 = 4.

By checking the options,

1. (12, 48, 8)

⇒ (48 ÷ 12) x 2 = 8

⇒ 4 x 2 = 8

2. (12, 50, 13)

⇒ (50 ÷ 12) x 2 = 13

⇒ 4.1 x 2 = 13

⇒ 8.2 ≠ 13

3. (15, 45, 3)

⇒ (45 ÷ 15) x 2 = 3

⇒ 3 x 2 = 3

⇒ 6 ≠ 3

4. (20, 28, 8)

⇒ (28 ÷ 20) x 2 = 8

⇒ 1.4 x 2 = 8

⇒ 2.8 ≠ 8

Hence, the correct answer is "Option 1".

We apply the options on the given equation & solve it using BODMAS rule:

Given Equation: 7 × 4 ÷ 14 + 12 + 30 = 50

Now, Checking the options:

Option 1) 12, 14

7 × 4 ÷ 12 + 14 + 30 = 50

7 x 0.33 + 14 + 30 = 50

2.33 + 14 + 30 = 50

46.33 ≠ 50

Option 2) 7, 14

14 × 4 ÷ 7 + 12 + 30 = 50

14 x 0.57 + 12 + 30 = 50

8 + 12 + 30 = 50

50 = 50

Option 3) 4, 7

4 × 7 ÷ 14 + 12 + 30 = 50

4 × 0.5 + 12 + 30 = 50

2 + 12 + 30 = 50

44 ≠ 50

Option 4) 30, 50

7 × 4 ÷ 14 + 12 + 50 = 30

7 × 0.28 + 12 + 50 = 30

2 + 12 + 50 = 30

64 ≠ 30

Hence, the correct answer is Option 2.

The pattern followed in the given series is:

The star moves between two places in every step.

The letter at the far corners in every two step is deleted and a new alphabet is introduced which is placed at the middle left.

Next step:

The star will be placed at the center.

There will be a new alphabet will be added which will be placed at middle left.

Now we consider the given options:

Option 1) 

Star is not positioned correctly and no new alphabet is introduced.

Option 2) 

No new alphabet is introduced.

Option 3) 

The positioning of 'S' and star is incorrect, also 'P' must be replaced by 'X'.

Option 4) 

The pattern is correct.

Hence, the correct answer is "Option 4".

According to the English alphabets & their positional values:

The pattern followed here is:

The alphabets are increased by 2.

The fourth & sixth alphabets are interchanged.

Now,

'CABLES' is written as 'ECDUGN'.

‘PHONES’ is written as ‘RJQUGP’.

So, MOBILE can be written as,

So, 'MOBILE’ is written as ‘OQDGNK’.

Hence, the correct answer is Option 4.

Statements:

I. Some table are chair.

II. No chair is stool.

Venn Diagram:

Conclusions:

I: All chair are table → Does not follow → Since 'some table are chair', so all chair are table can be possible not definite.

II: Some chair are stool → Does not follow → 'No chair is stool'.

III: All table are stool → Does not follow → 'No chair is stool'.

So, Neither conclusion follows.

Hence, the correct answer is Option 4.

The mirror image of the given  combination is:

Now we consider the given options:

Option 1) '

4' and 't' are inverted.

Option 2) '

4' and 'd' are inverted.

Option 3)'

The combination is correct.

Option 4) '

d' is not mirrored.

Hence, the correct answer is Option 3.

We interchange the signs in the given equations & solve them using BODMAS rule:

After interchanging '+ and ×':

Option 1) 7 + 5 × 2 – 8 ÷ 4 = 36

7 × 5 + 2 - 8 ÷ 4 = 36

7 × 5 + 2 - 2 = 36

35 + 2 - 2 = 36

37 - 2 = 36

35 ≠ 36

Option 2) 95 ÷ 19 + 5 × 3 – 6 = 22

95 ÷ 19 × 5 + 3 - 6 = 22

5 × 5 + 3 - 6 = 22

25 + 3 - 6 = 22

28 - 6 = 22

22 = 22

Option 3) 13 + 4 × 5 – 6 ÷ 2 = 51

13 × 4 + 5 - 6 ÷ 2 = 51 

13 × 4 + 5 - 3 = 51 

52 + 5 - 3 = 51 

57 - 3 = 51 

54 ≠ 51

Option 4) 4 × 3 + 6 – 7 ÷ 1 = 18 

4 + 3 × 6 - 7 ÷ 1 = 18

4 + 3 × 6 - 7 = 18

4 + 18 - 7 = 18

22 - 7 = 18

15 ≠ 18

Hence, the correct answer is "Option 2".

The pattern followed here is:

'GHOST’ is written as 'VVSMM' 

And, 'EATER' is written as 'THXFK'

Similarly, for 'HANDS'

'HANDS' is written as 'UGRFN'.

Hence, the correct answer is "Option 1".

Given: 

Drawing a family tree by given symbols we get,

1) P + Q × R

Here, P is the father of R.

2) P ÷ Q × R

Here, P is the sister of R.

3) P × Q ÷ R

Here, P is the Brother of R.

4) P ÷ Q + R

Here, P is the Paternal Aunt of R.

So**, Option 2** gives 'P is the sister of R'.

Hence, the correct answer is "Option 2".

The logic followed here is:

First number × 2 - 2 = Second number.

Option 1) 16 - 30 → 16 × 2 ⇒ 32 - 2 = 30 

Option 2) 44 - 84 → 44 × 2 ⇒ 88 - 4 = 84

Option 3) 14 - 26  → 14 × 2 ⇒ 28 - 2 = 26

Option 4) 18 - 34 → 18 × 2 ⇒ 36 - 2 = 34

So, Option 2 doesn't follow the pattern.

Hence, the correct answer is "Option 2".

The logic followed here is: 

Logic: (First number - Second number) × 4 = Third number.

For, (45, 15, 120) 

→ (45 - 15) × 4

⇒ 30 × 4 = 120.

For, (27, 8, 76) 

→ (27 - 8) × 4 

⇒ 19 × 4 = 76.

Similarly, for (56, 48, 32) 

→ (56 - 48) × 4

⇒ 8 × 4 = 32

Hence, the correct answer is "Option 4".

According to the BODMAS rule,

Given Equations :

• 6 - 5 × 9 + 8 ÷ 2
• 6 - 4 + 9 × 5 ÷ 3

​Now,

I. 6 - 5 × 9 + 8 ÷ 2

After interchanging + and -, 6 and 9 respectively

⇒ 9 + 5 × 6 - 8 ÷ 2

⇒ 9 + 5 × 6 - 4

⇒ 9 + 30 - 4

⇒ 39 - 4 = 35.

II. 6 - 4 + 9 × 5 ÷ 3

After interchanging + and -, 6 and 9 respectively

⇒ 9 + 4 - 6 × 5 ÷ 3

⇒ 9 + 4 - 10

⇒ 13 - 10 = 3

Hence, the correct answer is "Option 3".

The logic followed here is :

Dog : Kennel → A kennel is a shelter for a dog.

Similarly,

Bee : Hive → A Hive is a structure made by Bee for their shelter.

Hence, the correct answer is "Option 1".

Given expression : X @ Y $ J * M

By using symbols Drawing a family tree by given conditions.

Here, X is the sister of M.

Hence, the correct answer is "Option 3".

According to the English alphabets & their positional values:

The pattern followed in the given options is: 

Option 1) FKA : 

Option 2) CJZ : 

Option 3) PUK : 

Option 4). CHX : 

So, CJZ is the odd one.

Hence, the correct answer is "Option 2".

The correct answer is Gopinath.

Key Points

• Guru Gopinath broadened the boundaries of tradition while maintaining the traditional discipline that kept him in check.
• He played a significant role in bringing Kerala's renowned dance theatre, Kathakali, out of obscurity and into the public eye.
• Like Uday Shankar, he is regarded as one of the legendary figures of Indian dance in the 20^th century.
• He developed a modern dance form that was classical in form but had a broad appeal, by which Kathakali's renown quickly expanded throughout the world from the start of the 1930s.

Additional Information

• Kathakali
• The entire male troop performs in kathakali.
• Keralan temple dancing is known as Kathakali.
• Ramnattam and Krishnattam are the two dancing styles used in Kathakali.
• Episodes from the Ramayana and the Mahabharata are told in kathakali.

The correct answer is Vinai Kumar Saxena.

Key Points

• The Delhi National Capital Territory's constitutional governor is the lieutenant governor.
• On May 26, 2022, Shri Vinai Kumar Saxena became the 22^nd Lieutenant Governor of Delhi.
• Shri Saxena, 63, is the first corporate man to be chosen for such a gubernatorial position.
• He has more than three decades of extensive expertise in the corporate and social sectors.

Additional Information

• Lieutenant Governor
• ​In the Republic of India, a lieutenant governor is the constitutional head of five out of the eight union territories.
• The lieutenant governor is appointed by the President of India for a term of five years and holds office at the President's pleasure.
• Since the union territories of Delhi, Jammu, and Kashmir, and Puducherry have a measure of self-government with an elected legislature and council of ministers, the role of the lieutenant governor there is mostly a ceremonial one, akin to that of a state's governor.
• In Andaman and Nicobar Islands and Ladakh however, the lieutenant governor holds more power, being both the head of state and head of government.

The correct is Radioactive energy.

Key Points

• The heat from radioactive material decay and leftover heat from Earth's formation fuel the planet's internal heat engine.
• Atoms that are radioactive have energy inside them that spontaneously escapes as electromagnetic waves or high-energy subatomic particles.
• Radiation is the term for emissions.
• The Earth naturally contains radioactive material, which contributes to the planet's warmth.
• Cosmic rays also continuously generate radioactive material in the atmosphere.

Additional Information

• Solar Energy
• Solar power is generated by the sun.
• The sun's radiant radiation may be transformed into electrical or thermal energy, making it the most abundant energy source on Earth.
• Solar energy is used for a variety of things, including lighting and heating our homes, places of business, and other facilities.
• Solar energy is a renewable resource and, as such, is essential to the development of clean energy.
• Volcanoes
• An opening in the crust of a planet or moon known as a volcano allows molten rock, heated gases, and other things to erupt.
• As layers of rock and ash accumulate from numerous eruptions, volcanoes frequently take the form of a hill or mountain.
• There are three types of volcanoes: active, dormant, and extinct.
• Active volcanoes have recently erupted; they are likely to do so once more.
• Volcanoes that are dormant have not erupted in a very long time yet could do so in the future.
• It seems unlikely that extinct volcanoes will erupt in the near future.
• Tides
• Tides are the rise and decrease in sea levels brought on by the combined effects of the Moon's (and the Sun's, to a much lesser extent) gravitational pulls, as well as by the Earth and Moon orbiting one another.
• To determine the anticipated times and amplitude for any location, tide tables can be employed (or "tidal range").

The correct answer is Acceleration.

Key Points

• Acceleration
• The rate at which an object's velocity with respect to time changes is referred to as acceleration.
• A vector quantity is an acceleration (has magnitude and direction both).
• LT-2 or meter per second square(m/s2) is the unit of acceleration.

Additional Information

• Speed 
• A scalar quantity, speed is defined as the magnitude of the rate at which an object's position changes over time.
• The meter per second (m/s) or LT-1 unit of speed.
• Velocity
• The pace at which an object's position changes in relation to a frame of reference is known as its velocity, which is a time-dependent quantity.
• A description of an object's speed and direction of motion is what is meant by its velocity.
• The quantity is a vector.
• The meter per second (m/s) or LT-1 unit of velocity.
• Distance
• The International System of Units defines a meter as the distance unit. It's interesting to note that many other derived units or quantities, such as volume, area, acceleration, and speed, may be constructed using this as the basic unit and a few formulae.
• The meter(m) is the SI unit of length.

The correct answer is Guru Deba Prasad.

Key Points

• Indian Kathak dancer Shovana Narayan is also a career officer for the Indian Audit and Accounts Service.
• She has received Padma Shri and performs both in India and abroad.
• Her mentor was Birju Maharaj.
• In 2013, Guru Deba Prasad honors were given to Shovana Narayan.
• Her efforts to combine Kathak with other important dance genres including Tap dancing, Spanish Flamenco, and Western Classical Ballet are extraordinary.
• Shovana is a well-known author and social critic.

Additional Information

• Guru Deba Prasad Award
• ​Guru Debaprasad Das' contribution to the resurgence of Odissi dance will live on in memory forever.
• This award festival's goals are to honour illustrious Gurus and performers in the fields of classical dance and music, as well as to display and promote Odissi dance, a hybrid gharana of Guru Debaprasad that captures the essence of tribal and traditional traditions.
• Since the three streams of folk, tribal, and traditional Odissi dances are combined in Guruji's Gharana and frequently seen in Guru Gajendra Panda's choreography, mirroring both the sensual lasya aspect and the dynamic tandava part, the name TRIDHARA for the institute is highly appropriate.

The correct answer is Kerala.

Key Points

• Beginning on July 1^st, 2022, the Kerala Government will implement the MEDISEP scheme, a medical insurance programme for State Government employees, pensioners, and their qualified family members.
• The programme would offer comprehensive coverage of up to 3 lakhs in annual cashless medical assistance.
• The annual premium during the 2022–24 policy period would be Rs 4,800 + 18% GST.
• A monthly premium of Rs. 500 will be withheld from June's pay and July's pension.
• The state finance office has issued a directive in this regard.
• The public sector insurer Oriental Insurance Company is implementing MEDISEP.

Additional Information

• MEDISEP Scheme
• The Keralan government introduced the Medical Insurance Scheme for State Workers and Pensioners (abbreviated as MEDISEP) insurance programme to offer complete health insurance coverage to all currently employed State Government employees and retirees.
• All newly hired employees and their families, part-time workers, all staff members of supported schools and colleges and their families, pensioners and their wives, and family pensioners are among the beneficiaries.
• The kerala Chief minister publicly launched the programme on July 1^st, 2022.
• The programme drew almost 2.9 million beneficiaries and dependents within six months of its introduction, as well as 480 hospitals, the majority of which are in Kerala.

The correct answer is Light year.

Key Points:

• The unit of length used to express astronomical distances is the light year, which is roughly comparable to 5.88 trillion miles or 9.46 trillion kilometres.
• According to the International Astronomical Union (IAU), a light-year is the distance that light travels in a vacuum in one Julian year (365.25 days).
• Since "light-year" incorporates the term "year," which designates a unit of measurement for time, it is occasionally misinterpreted as a unit of time.
• The light-year is most typically used to depict distances to stars and other distances on a galactic scale, especially in non-specialist contexts and popular science publications.
• The measuring unit most frequently used in professional astronomy is the parsec, which is derived from astrometry and equals 3.26 light-years.

Additional Information:

• Newton: 
• A newton is a unit of force in the International System of Units (symbol: N).
• 1 kgm/s² is the force that accelerates a mass of one kilogramme by one metre per second square.
• It is named after Isaac Newton.
• Watt:
• ​The electrical power determined in Watts is the equivalent of one ampere under one volt of pressure.
• Joule:
• ​The work performed by a force of one newton acting through one metre is equivalent to one joule, a unit of work or energy in the International System of Units (SI).

The correct answer is Chola.

Key Points:

• Rajaraja I, a Chola emperor, ruled between 985 and 1014 CE.
• He is known for restoring the Chola hegemony and securing its dominance throughout the Indian Ocean during his time as the most powerful Tamil king in South India.
• He ruled over a sizable portion of northern Sri Lanka, the Chera country, and the Pandya country.
• Also, he bought Lakshadweep, the Thiladhunmadulu atoll, and a portion of the Maldives' northernmost islands in the Indian Ocean.

Additional Information:

• Pallava:
• ​Around the fourth century AD, the South saw the rise of the Pallavas, who reached the pinnacle of their supremacy in the seventh century AD.
• For over 500 years, they were able to maintain their hegemony.
• Pandya:
• ​The Pandyan dynasty, commonly known as the Pandyas of Madurai, was one of the three major kingdoms of Tamilakam, or South India, together with the Chera and Chola dynasties.
• Chalukya:
• ​During the sixth through the twelfth centuries, the Chalukya dynasty, a Classical Indian monarchy, ruled over a sizable portion of southern and central India.
• They held power as three interconnected but separate dynasties during this time.

The correct answer is Chennai Petroleum Corporation Limited.

Key Points:

• Madras Refineries Limited  (MRL) was renamed Chennai Petroleum Corporation Limited (CPCL), is a division of Indian Oil Corporation Limited, which is owned by the Ministry of Petroleum and Natural Gas of the Government of India.
• Its main office is in Chennai, India.
• It was established as a joint venture in 1965 with participation from the Government of India (GOI), AMOCO, and National Iranian Oil Corporation (NIOC), in the proportions of 74%: 13%: 13%.
• With no time or cost overruns, the CPCL Refinery was built from the ground up with an installed capacity of 2.5 million tonnes per year in a record-breaking 27 months for a cost of 430 million (US$5.4 million).

Additional Information:

• In Manali, CPCL serves as a mother industry by providing feedstocks to other companies.
• Through IOCL, CPCL's products are promoted.
• With the exception of naphtha, fuel oil, and lubricants, which are partially exported, CPCL's products are primarily used domestically.
• By constructing a wind farm, sewage reclamation facilities, and sea water desalination plants, CPCL has also made ground-breaking contributions to the fields of energy and water conservation.
• CPCL's consolidated net profit for the entire fiscal year 2021–2022 (FY22) was Rs 1,352 crore.
• For FY 2021–2022, total revenue was Rs 60,074 crore.$

The correct answer is Avogadro’s law.

Key Points:

• Avogadro proposed in 1811 that equal volumes of gases at the same temperature and pressure contain the same number of molecules.
• According to this hypothesis, the relative molecular weights of any two gases are the same as the ratio of their densities under the same temperature and pressure conditions.
• Avogadro also correctly deduced that simple gases were not made up of solitary atoms, but rather of compound molecules made up of two or more atoms.
• (Avogadro did not use the term "atom"; at the time, the terms "atom" and "molecule" were almost interchangeable. He mentioned three types of "molecules," one of which was a "elementary molecule"—what we would call an atom.)
• As a result, Avogadro was able to overcome the difficulty that Dalton and others had encountered when Gay-Lussac reported that the volume of water vapour above 100°C was twice the volume of oxygen used to form it.
• According to Avogadro, the oxygen molecule split into two atoms during the formation of water vapour.

Additional Information:

• Dalton’s law
• ​The overall pressure exerted in a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases, according to Dalton's law, often known as Dalton's law of partial pressures. John Dalton discovered this empirical law in 1801 and made it public in 1802. The ideal gas laws are connected to Dalton's law.
• Gay-Lussac’s law
• ​A gas law known as Gay-Lussac's law asserts that a gas's pressure (when kept at a constant volume and mass) varies directly with its absolute temperature. In other words, while the mass is fixed and the volume is constant, the pressure a gas exerts is proportional to the temperature of the gas.
• Charles' law
• ​The experimental gas law known as Charles' law, commonly referred to as the law of volumes, illustrates how gases tend to expand when heated. Charles's law can now be stated as follows: When the pressure on a sample of a dry gas is held constant, the volume and Kelvin temperature will be in direct proportion.

The correct answer is Kadamba.

Key Points:

• The Tripartite Struggle, also known as Kannauj Triangle Wars, took place in the ninth century between the Pratihara Empire, the Pala Empire, and the Rashtrakuta Empire for control of northern India.
• However, epigraphist Dineschandra Sircar brought a new perspective to this conflict.
• According to Sircar, the conflict between the Pratihara Empire and the Rashtrakuta Empire predated the conflict over Kannauj State.
• In Gujarat and Malwa regions, these two powers shared a common border.
• The shifting far from the permanent border caused animosity between the two powers.
• Dantidurga, the founder of the Rashtrakuta Empire, had already defeated Nagabhata I of the Gurjara Pratihara dynasty, as evidenced by the Dashavatara Temple inscription of Dantidurga at Ellora and the Sghavarsha I, both belonging to Rashtrakuta dynasty.

Additional Information:

• Rashtrakuta
• ​Between the sixth through the tenth centuries, the regal Indian dynasty known as Rashtrakuta ruled over a sizable portion of the Indian subcontinent. A copper plate grant from the seventh century is the first Rashtrakuta inscription, which describes their sovereignty over the city of Manapur in Central or West India.
• Pala
• Gopala was the first ruler of the Pala Dynasty.
• Pala Dynasty was originated in the region of Bengal during the Late Classical Period of the Indian historical era.
• Palas followed the Mahayana and Tantric schools of Buddhism.
• It was founded by Gopala in 750CE.
• He was succeeded by Dharmapala.
• Gurjara-Pratihara
• ​A large portion of Northern India was governed by the Gurjara-Pratihara dynasty from the middle of the eighth to the eleventh century.
• First ruling in Ujjain and then in Kannauj. Arab troops that were approaching from the east of the Indus River were successfully halted by the Gurjara-Pratiharas.

The correct answer is Bituminous.

Key Points:

• Bituminous coal is a commercially used type of coal.
• Bituminous coal, also known as black coal, is a relatively soft coal that contains bitumen, a tar-like substance.
• This coal is classified according to its plasticity, moisture content, volatility, and ash content.
• Plasticity is required for the production of coke, which is used in the production of fuel gases such as producer gas.
• Volatility is critical for steel production and power generation.

Additional Information:

• Anthracite:
• ​Anthracite, also known as a hard coal, and a black coal, is hard, compact variety of coal that has a submetallic lustre.
• It has the highest carbon content, the fewest impurities, and the highest energy density of any type of coal and is ranked first.
• Peat:
• Peat, also known as turf, is a type of organic matter that has partially decayed.
• Turf differs from peat in that it also refers to soil with grass.
• It can only be found in peatlands, bogs, mires, moors, or muskegs.
• Lignite:
• ​Lignite, also known as brown coal, is a soft, brown, combustible sedimentary rock composed of naturally compressed peat.

The correct answer is South Africa.

Key Points:

• The first edition of the ICC Women's Under-19 Cricket World Cup, hosted by South Africa in 2023, was the 2023 ICC Under-19 Women's T20 World Cup.
• Because of the COVID-19 pandemic, the tournament was rescheduled from the end of 2021 to January 2023.
• The tournament featured sixteen teams that were initially divided into four groups.
• India, England, Australia, and New Zealand advanced to the competition's semi-finals.
• India defeated New Zealand by 8 wickets in the semi-finals, while England defeated Australia by 3 runs.
• The final took place on 29^th January 2023 at Senwes Park, Potchefstroom.
• India beat England in the first-ever ICC U-19 Women’s T20 World Cup .
• India bowled out England for a paltry 68 and won by 7 wkts.

Additional Information:

• The tournament was originally scheduled to take place in January 2021, but it was pushed back to December 2021 due to the COVID-19 pandemic.
• The ICC considered deferring the tournament from its scheduled January 2021 date to later in the year in November 2020.
• The Bangladesh Cricket Board (BCB) confirmed in January 2021 that they would host the tournament in December 2021, but the tournament was postponed for the second time, and was moved to January 2023.
• The ICC's CEO, Geoff Allardice, stated in January 2022 that the tournament was "very much on the cards," and that the ICC was beginning the search for hosts.

The correct answer is Pacific ocean.

Key Points:

• The Mariana Trench is the deepest oceanic trench on Earth, located in the western Pacific Ocean about 200 kilometres (124 miles) east of the Mariana Islands.
• It is crescent-shaped and approximately 2,550 km (1,580 mi) long and 69 km (43 mi) wide.
• The maximum known depth is 10,984 ± 25 metres​ at the southern end of the Challenger Deep, a small slot-shaped valley in its floor.
• If Mount Everest were placed in the trench at this point, its peak would still be more than 2 kilometres underwater (1.2 mi).

Additional Information:

• Arctic ocean:
• ​The Arctic Ocean is the world's smallest and shallowest ocean, ranking fifth among the world's five major oceans.
• It is the coldest of all the oceans and covers an area of approximately 14,060,000 km² (5,430,000 sq mi).
• Although the International Hydrographic Organization (IHO) classifies it as an ocean, some oceanographers refer to it as the Arctic Mediterranean Sea.
• Atlantic ocean:
• With an area of approximately 106,460,000 km², Atlantic Ocean is the second-largest of the world's five oceans (41,100,000 sq mi).
• It covers about 20% of Earth's surface and 29% of its water surface area.​
• Southern ocean: 
• ​The Southern Ocean, also known as the Antarctic Ocean, is the world's southernmost ocean, generally defined as being south of 60° S latitude and encircling Antarctica.

The correct answer is One-tenth of the total number of Members of the House.

Key Points:

• Representatives of the Lok Sabha are elected directly by the citizens of India.
• Members of parliament are what they are called.
• Members of the Rajya Sabha are elected by representatives from state legislative assemblies.
• The quorum for Lok Sabha and Rajya Sabha is the one-tenth of each house's total membership.
• If a quorum is not present, the house cannot conduct its business, pass bills, or pass resolutions.

Additional Information:

• The minimal number of participants necessary for a meeting to start is known as a quorum.
• If a quorum is not present, it is the Speaker's responsibility to adjourn the House or suspend the meeting until a quorum is present.
• The Constitution establishes a quorum.
• Individual members have a Five-year term.
• Casual vacancies, when they occur, are filled through bye-elections for the remainder of the term.

The correct answer is M2.

Key Points:

• The total stock of money of all types (currency and demand deposits) held by the people of a country at a given point in time is referred to as the money supply.
• Money supply can be measured in a variety of ways, including M1, M2, M3, and M4 measurements.
• Every measurement has its own definition, with various components ranging from the most liquid to the most rigid.
• Savings deposits at post office savings banks are included in the M2 measurement of money supply in India, making it a little more rigid than the M1 measurement.

Additional Information:

• Money supply is defined as the total amount of currency that can be included in a country's economy.
• The total money supply includes both cash and deposits that can be easily converted into cash.
• Money supply economics is associated with direct government power because it is the government that issues currency, either in paper form or as a coin, as a combination of treasury bills and bank demand draughts.
• Similarly, banks have influence over the money supply, which they exercise through reserves and credit controls.
• Money supply has a significant impact on a country's economy.

The correct answer is 1960.

Key Points:

• In Men's Olympic Field Hockey, the Indian team has won the most gold medals, 10 in total.
• The Indian men's hockey team has won eight Olympic gold medals in total, six in a row (from 1928 to 1956, including 1936 Berlin), and two more in Tokyo in 1964 and Moscow in 1980.
• India won the silver medal in the 1960 Rome Olympics after losing to Pakistan (gold medal), ending India's run of six consecutive gold medals.
• When Abhinav Bindra won gold in the 10-metre Air rifle event at the 2008 Olympics in Beijing, he became the first Indian to win an individual Olympic gold medal.
• Neeraj Chopra is second individual Olympic champion after Abhinav Bindra.

Additional Information:

• Here's when and how India won gold at the Olympics:
• Indian men’s hockey team - Amsterdam 1928.
• Indian men’s hockey team - Los Angeles 1932.
• Indian men’s hockey team - Berlin 1936.
• Indian men’s hockey team - London 1948.
• Indian men’s hockey team - Helsinki 1952.
• Indian men’s hockey team - Melbourne 1956.
• Indian men’s hockey team - Tokyo 1964.
• Indian men’s hockey team - Moscow 1980.
• Abhinav Bindra in men’s 10m air rifle shooting - Beijing 2008.
• Neeraj Chopra in the men's javelin throw - Tokyo 2020.

The correct answer is 1989.

Key Points

• On December 6, 1988, the Lok Sabha (the lower house of Parliament) approved the bill.
• On December 7, 1988, the Rajya Sabha (the upper house of Parliament) approved the bill.
• On December 20, 1988, the bill received the President's assent and became the 61^st Constitutional Amendment Act.
• The amendment to Article 326 of the Indian Constitution, which pertains to the right to vote, was made effective on March 28, 1989.

Additional Information

• Article 326 - The Constitution provides that the elections to the House of the People and to the Legislative Assembly of every State shall be on the basis of adult suffrage.
• Article 324 of the Indian Constitution deals it the power and authority to conduct, control, and supervise the entire election process in the country including elections to the Parliament, the Legislatures of every state, and to the offices of the President and Vice-President.

The correct answer is Industry.

Key Points

• The Industry sector was given the main emphasis in the second Five-Year Plan.
• A part of the economy known as the industrial sector is made up of companies that help other companies with the production, transportation, or manufacture of their goods.
• Because the industrial sector sells its goods and services to other companies rather than to customers directly, it is referred to as a secondary sector.
• Due to its dependence on purchasing from companies in other sectors, the industrial sector is frequently driven by changes in supply and demand in other sectors.

Additional Information

• Second Five-Year Plan
• ​April 1956 through March 1961 are included in the Second Five-Year Plan.
• The second strategy involved setting India up for industrialization.
• The architect of the second five-year plan was P.C. Mahalanobis.
• He gave the industrial foundation of the economy the most attention.
• In light of this, the 1948 Industrial Policy Resolution was revised, and a new resolution was adopted in 1956.

The correct answer is Ustad Zakir Hussain.

Key Points

• Ustad Zakir Hussain
• ​The Indian tabla virtuoso and musician who won the 'Best Contemporary World Music Album' Grammy award for 'Global Drum Project' was Ustad Zakir Hussain.
• Ustad Zakir Hussain, an Indian tabla musician, composer, percussionist, music producer, and film actor, was born on March 9, 1951.
• The Indian government honoured him with the Padma Shri in 1988, the Padma Bhushan in 2002, and the Padma Vibhushan in 2023.
• Also, he received the Ratna Sadsya in 2018, the Fellowship of the Sangeet Natak Akademi, and the Sangeet Natak Akademi Prize from the Government of India in 1990.

Additional Information

• Global Drum Project
• Mickey Hart, Zakir Hussain, Sikiru Adepoju, and Giovanni Hidalgo collaborated on the album titled World Drum Project.
• The album includes music made with a variety of drums and other instruments, vocals from people chanting and singing, and electronic samples.
• It combines traditional music with contemporary electronic music, which was informed by Mickey Hart's musicological research on drumming from throughout the world.
• The 2009 Grammy Award for Best Contemporary World Music Album went to Global Drum Project.

The correct answer is R. Venkataramani.

Key Points

• R. Venkataramani
• ​R. Venkataramani has been appointed as the new Attorney General of India by President Droupadi Murmu for a period of three years.
• R. Venkataramani is a Senior Advocate in the Indian Supreme Court and an Indian constitutional lawyer.
• He was born on April 13, 1950. He is currently acting as India's attorney general.
• In 2010, the Law Commission of India selected him as a member.
• For the past 12 years, he has served as Special Senior Counsel for the State of Tamil Nadu as well as Special Senior Counsel for the State of Andhra Pradesh.

Additional Information

• President Droupadi Murmu
• ​Droupadi Murmu, also known as Puti Biranchi Tudu, was born on June 20, 1958 and has been India's 15^th president since July 25, 2022.
• She is the second woman to hold the position after Pratibha Patil and the first member of a tribal community to do so.
• She is the first President born in Independent India and the youngest person to hold the position.
• In addition, she held the positions of minister of state for the government of Odisha, member of the Legislative Assembly from Odisha, and governor of Jharkhand from 2015 to 2021.

The correct answer is Stomata.

Key Points

• Stomata
• In leaves transpiration takes place through stomata.
• The little apertures known as stomata are found on the epidermis of leaves.
• Stomata are visible under a light microscope.
• Stomata can be found on the stems and other portions of various plants.
• In gaseous exchange and photosynthesis, stomata are crucial. Via opening and closing, they regulate the rate of transpiration.

Additional Information

• Transpiration
• Water is lost from the aerial regions of plants in the form of water vapour through a biological process called transpiration.
• Like all other living things, plants need an excretory system to remove extra water from their bodies.
• Transpiration is the term for this process of removing extra water from the body of the plant. Typically, it is the evaporation of water from the leaf surface.
• The plants only use a small portion of the water they absorb for growth and development.

The correct answer is Yamini Krishnamurthy.

Key Points

• Yamini Krishnamurthy
• ​Yamini Krishnamurthy was recognised as ‘Asthana Nartaki’ (resident dancer) of the Tirumala Tirupati Devasthanam for her contribution in the development and promotion of the Indian classical dance forms.
• Mungara Yamini Krishnamurthy, an Indian dancer who specialises in Kuchipudi and Bharatanatyam, was born on December 20, 1940.
• In Madras, Yamini Krishnamurthy made his debut in 1957.
• She holds the honour of being the Tirumala Tirupati Devasthanam's Asthana Nartaki (resident dancer).
• The Padma Shree (1968), Padma Bhushan (2001), and Padma Vibhushan (2016), three of the highest civilian honours bestowed by the Republic of India, were among the many honours she received for her dancing career.

Additional Information

• At Chennai's Kalakshetra Academy of Dance, Yamini Krishnamurthy studied Bharatnatyam under Rukmini Devi Arundale.
• Afterwards, she received training from illustrious teachers like Thanjavur Kittappa Pillai and Kanchipuram Ellappa Pillai.
• Under the instruction of Vedantam Lakshmi Narayana Shastri, Chinta Krishnamurthy, and Pasumarthy Venugopal Krishna Sharma, she learned Kuchipudi.
• Yamini studied Odissi under Guru Pankaj Charan Das and Kelucharan Mahapatra in addition to Bharatnatyam and Kuchipudi.

The correct answer is Kovalan and Madhavi’s Daughter.

Key Points

• Kovalan and Madhavi’s Daughter
• ​Manimekalai describes the story of Kovalan and Madhavi’s Daughter.
• The daughter of Kovalan and Madhavi, who takes after her mother's career as a dancer and Buddhist nun, is also known by the name Manimekalai.
• Kulavanikan Seethalai Sataar penned the Tamil-Buddhist epic Manimekalai in the sixth century.
• It is an "anti-love narrative" that includes some of the heroes and their offspring from the "love romance" in the first Tamil epic Silappadikaram.
• The epic contains 30 cantos and 4,861 lines in the akaval metre.

Additional Information

• One of the only three of Tamil literature's Five Great Epics to have endured to the present day is the Manimekalai.
• The Manimekalai and its twin-epic Silappadikaram are both recognised as important works of literature that shed light on Tamil regions' (India and Sri Lanka's) way of life, culture, and civilization in the first centuries of the Common Era.

The correct answer is James Mill.

Key Points

• James Mill
• ​**“A History of British India” is a work Published by James Mill.**
• James Mill was a Scottish historian, economist, political theorist, and philosopher who lived from 6 April 1773 to 23 June 1836.
• He is one of the founding members of the Ricardian school of economics.
• He was one of the famous historians who adopted a colonial viewpoint, and he also produced The History of British India (1817).
• He was the first author to divide Indian history into three distinct periods: Hindu, Muslim, and British.
• This division has proven to be extremely influential in the field of Indian historical research.

Additional Information

• A History of British India
• ​James Mill, a Scottish historian, economist, political theorist, and philosopher, chronicled the history of Company rule in India in his three-volume masterpiece The History of British India.
• When it was initially published in 1817, the book was an immediate hit and brought Mill "a measure of affluence."
• In accordance with the prominent political forces and their religious ties, Mill divided Indian history into the Hindu, Muslim, and British periods.

Given:

In Δ XYZ, ∠X = 90°, YZ = 15 cm, and XZ = 12 cm.

Formula used:

(Hypotenuse)² = (Perpendicular)² + (Height)²

Calculation:

According to the formula, 

⇒ 15² = 12² + (XY)² 

⇒ (XY)² = 225 - 144 = 81

⇒ XY = 9 cm

⇒ CosY = XY/YZ = 9/15 = 3/5

⇒ Hence, CosY is equal to 3/5

Given Equation:

(8x3 + 80x2 + 200x) and (4x4 + 16x3 - 20x2)

Concept Used:

LCM is taking the least common multiples 

Calculations:

First we will take the common from the equations

⇒ 8x3 + 80x2 + 200x

⇒ 8x(x² + 10x + 25) 

⇒ 8x(x2 + 5x + 5x + 25)

⇒ 8x{x(x+ 5) + 5(x + 5)}

⇒ 8x(x + 5)(x + 5)

Now we take common from the second equation

⇒ 4x4 + 16x3 - 20x2

⇒ 4x² (x² + 4x - 5)

⇒ 4x2 (x2 - x + 5x - 5)

⇒ 4x2 {x(x - 1) + 5(x - 1)}

⇒ 4x2 (x - 1)(x+ 5)

Now we have to take common from the two equations

⇒ 1^st equation = 8x(x + 5)(x + 5)

⇒ 2^nd equation = 4x2 (x - 1)(x+ 5)

⇒ LCM = 8x2(x + 5)2(x - 1)

⇒ Hence, Option 1 is correct

Given:

25 men and 45 women complete work in 15 days

15 men and 60 woman complete the work in 20 days

Formula Used:

M₁D₁ = M₂D₂

Calculations:

As in both case they complete the same work 

so,

⇒ M1D1 = M2D2

⇒ $(25M + 45W) \times 15 = (15M+60W)\times 20$

⇒ $(25M + 45W) \times 3 = (15M+60W)\times 4$

⇒ 75M + 135W = 60M + 240W

⇒ 75M - 60M = 240W -135W

⇒ 15M = 105W

⇒ $\frac{M}{W}=\frac{105}{15}$

⇒ $\frac{M}{W}=\frac{7}{1}$

⇒ Efficiency of Men = 7

⇒ Efficiency of Woman = 1

⇒ Total efficiency of men and woman = 25M + 45W = 25 × 7 + 45 × 1  = 175 + 45 = 220

⇒ Total work = Efficiency × Time = 220 × 15 = 3300

Now, the Efficiency of 69 men and 67 women

⇒ Efficiency = 69 × 7 + 67 × 1 = 483 + 67 = 550

Time is taken by 69 men and 67 women to complete the work

⇒ Time = Total work / Efficiency = 3300 / 550 = 6 days

⇒ Hence, The time taken by 69 men and 67 women is 6 days

Given:

Distance = 1500 m

Vehicle P gives vehicle Q a start of 200 m, and P wins the race by 8 sec

If vehicle P gives vehicle Q a start of 400 m, the race ends in a dead heat

Formula used:

Speed = Distance / Time

Calculations:

For case 1:

Vehicle P gives vehicle Q a start of 200 m, and P wins the race by 8 sec

⇒ Distance travel by P = 1500 m

⇒ Distance travel by Q = 1500 - 200 = 1300 m

⇒ Speed of vehicle P = $\frac{1500}{t}$

⇒ Speed of vehicle Q = $\frac{1300}{t+8}$

Now for case 2:

If vehicle P gives vehicle Q a start of 400 m, the race ends in a dead heat

⇒ Distance travel by P = 1500 m

⇒ Distance travel by Q = 1500 - 400 = 1100 m

As the race is end at dead heat, they finish the race at tie or equal time

⇒ Time taken by vehicle P = Time taken by vehicle Q

⇒ $\frac{1500}{\frac{1500}{t}}=\frac{1100}{\frac{1300}{t+8}}$

⇒ $t=\frac{11(t+8)}{13}$

⇒ 13t = 11t + 88

⇒ 13t - 11t = 88

⇒ 2t = 88

⇒ t = 44 sec

⇒ Hence, The time taken by vehicle P is 44 sec

Given:

tan A - tan B - tan C = tan A tan B tan C

Formula Used:

tan (A - B) = $\frac{tanA - tanB}{1+ tanAtanB}$

Calculations:

⇒ tan A - tan B - tan C = tan A tan B tan C

⇒ tan A - tan B  = tan A tan B tan C + tan C

⇒ ​tan A - tan B  = tan C(tan A tan B + 1)

⇒ tan C = $\frac{tanA-tanB}{1+tanAtanB}$

⇒ tanC = tan(A - B)

⇒ C = A - B

⇒ A = B + C

⇒ Hence, The option 1 is correct

Given:

Budget allocation of state K = 175

Budget allocation of state L = 350

Formula used:

Percentage = $\frac{state A} {state B} \times100$

Calculation:

According to the formula 

⇒ Percentage = $\frac{175} {350} \times100$ = 50 %

⇒ Hence, The percentage is 50%

Given:

The diameter of a hemisphere = 35 cm

Calculations:

Radius = Diameter/2 = 35/2

Volume of hemisphere

= 2πr³/3

= (2/3)×(22/7)(35/2)³

= 11229.17 cm³

Hence, The Required value is 11229.17

Given:

Two variety of rice worth Rs. 80 per kg and Rs. 50 per kg respectively are mixed with another variety in the ratio 1 ∶ 2 ∶ 3.

If the mixture is worth Rs. 75 per kg. 

Calculations:

Let the price of third variety is Rs. x per kg

Ratio of first, second and third variety of rice in the mixture is 1 ∶ 2 ∶ 3

Let amount of first, second and third variety of rice in the mixture are 1 kg, 2 kg and 3 kg respectively

⇒ Total quantity of the mixture = (1 + 2 + 3) kg = 6 kg

⇒ Total amount of the mixture in Rs. = 1 × 80 + 2 × 50 + 3x  = 180 + 3x

∵ Price of the mixture per kg in Rs. 75

⇒ (180 + 3x) /6 = 75

⇒ 180 + 3x = 450

⇒ 3x = 270

⇒ x = Rs. 90/kg

Hence, The Required value is Rs.90/Kg.

Shortcut Trick

Mean Proportional of a and b is √(a × b).

Mean proportional = √(6 × 54) = √324 = 18.

Difference from 15 = 18 − 15 = 3.

∴ The correct answer is 3.

Alternate Method

Given:

First number (a) = 6

Second number (b) = 54

Reference value = 15

Formula Used:

Mean proportional (x) = √(a × b)

Calculations:

⇒ x = √(6 × 54)

⇒ x = √(6 × 6 × 9)

⇒ x = 6 × 3 = 18

⇒ Required value = Mean proportional − 15

⇒ Required value = 18 − 15 = 3

∴ The correct answer is 3.

Additional Information

Third Proportional

For two numbers a and b, the third proportional c is calculated as c = b² ÷ a.

Fourth Proportional

For three numbers a, b, and c, the fourth proportional d is calculated as d = (b × c) ÷ a.

Continued Proportion

Three numbers a, b, c are in continued proportion if a:b = b:c, which implies b² = ac.

Given:

The initial profit percentage on the sale of an item was 55%.

Concept used:

SP = CP + CP × profit%

Here,

SP = Selling price

CP = Cost price

Calculation:

Let the CP of an article be 100a

So, profit = 100a × 55%

⇒ 55a

So, SP = 100a + 55a

⇒ SP = 155a

New CP = 100a + 100a × 24%

⇒ 100a + 24a = 124a

So, new profit = 155a - 124a

⇒ 31a

Profit% = (31a/124a) × 100

⇒ 25%

∴ The new profit percentage would be 25%.

 Shortcut Trick

Profit increases by 55% then CP1 : SP = 20 : 31

Cost price went up by 24% then CP1 : CP2 = 25 : 31

Then, CP1 : CP2 : SP = 100 : 124 : 155   [ by making CP1 equal in both the ratio]

So, the new profit% = (155 - 124)/124 × 100 = 31/124 × 100 = 25%

Study the table and answer the question that follows.

Calculations:

Wheat is highest in year 2018-2020 with 54.

Total consumption in year 2018-2020

= 288

Percentage

= 54 × 100/288

= 18.75%

Hence The Required value is 18.75.

Given::

Inner radius = 6 cm

Thickness = 0.37 cm

Formula used:

Outer radius = Inner radius + Thickness

Curved surface area of the hemisphere = $2\pi r^2$

Calculations:

According to the formula,

⇒ Outer radius = 6  + 0.37 = 6.37 cm

⇒ Curved surface area = $2 \times \frac{22}{7} \times 6.37 \times 6.37$ = 255.0548 cm²

⇒ Hence, Curved surface area of the hemisphere is 255.0548 cm²

Given:

tan² $α$ = 3 + Q²

Formula used:

Sec² $α$ - tan² $α$ = 1

Calculations:

⇒ tan² $α$ = 3 + Q²

⇒ Sec² $α$ - 1  = 3 + Q²

⇒ Sec² $α$ = 4 + Q²

⇒ Sec $α$ = $√{4+Q^2}$

The given equation is 

⇒ Sec $α$  + tan³ $α$ cosec $α$

$\frac{1}{cos α} + \frac{ sin^3 α}{cos^3 α}×\frac{1}{sin α}$

$\frac{1}{cos α} + \frac{ sin^2 α}{cos^3 α}$

$\frac{cos^2α +sin^2 α}{cos^3 α}$

$\frac{1}{cos^3 α}$

⇒ Sec³ $α$

(Sec $α$)³

$(√{4+Q^2})^3$

$(4+Q^2 )^{\frac{3}{2}}$

⇒ Hence, Option 4 is correct

Given:

Height of the equilateral triangle = 9√3

Formula used:

Height = a√3 / 2

Area = a²√3 / 4

Calculations:

According to the formula,

⇒ Height = a√3 / 2

⇒ 9√3 = a√3 / 2

⇒ a = 18 cm

Now area of the triangle

⇒ Area = a²√3 / 4

⇒ Area = $\frac{18 \times 18 \times \sqrt3}{4}$

⇒ Area = 81√3 cm²

⇒ Hence, The area of the equilateral triangle is 81√3 cm²

Given:

Ratio of the angles = 1 : 2 : 3

Concept used:

The sum of all angles of the triangle is 180°

Calculations:

Let 1^st angle be x

⇒ 2^nd angle = 2x

⇒ 3^rd angle = 3x

Now,

⇒Sum of angles = 180

⇒ x + 2x + 3x = 180

⇒ 6x = 180

⇒ x = 30°

Angles will be

⇒ 1^st angle = x = 30°

⇒ 2^nd angle = 2x = 2 $\times$ 30 = 60°

⇒ 3^rd angle = 3x = 3 $\times$ 30 = 90°

Here, One angle is 90, so the triangle is right angled triangle

⇒ Hence, The triangle is right angle triangle

Formula used:

Average = $\text{Sum of observation}\over{\text{Total observation}}$

Calculations:

⇒ Total production of the country P = 30 + 50 + 20 + 40 + 10 = 150 

⇒ Average of country P = 150 / 5 = 30

⇒ Total production of the country Q = 20 + 40 + 30 + 50 + 30 = 170

⇒ Average of the Country Q = 170 / 5 = 34

⇒ Total production of the country R = 40 + 30 + 50 + 20 + 50 = 190

⇒ Average of the country R = 190 / 5 = 38

⇒ Hence, The maximum average production is by country R

Given:

Rate = 7%

Time = 11 years

Formula used:

SI = PRT/100

Calculations:

Let the amount lent be P

Interest earned = P - 920

According to the formula,

⇒ SI = PRT/100

⇒ P - 920 = $\frac{P\times 7\times 11}{100}$

⇒ 100P - 92000 = 77P

⇒ 100P - 77P = 92000

⇒ 23P = 92000

⇒ P = 4000

⇒ Hence, The amount lent is Rs. 4000

Given Equation:

$7x+4 \lbrace { x^2 \div (5x \div 10)}\rbrace - 3\lbrace {5\frac{1}{3}-x^3 \div (3x^2 \div x)} \rbrace=0$

Concept Used:

The concept of BODMAS is used

B = Bracket

O = Of

D = Division

M = Multiplication

A =Addition

S = Subtraction

Calculations:

First we have to solve brackets

⇒ $7x+4 \lbrace { x^2 \div (5x \div 10)}\rbrace - 3\lbrace {5\frac{1}{3}-x^3 \div (3x^2 \div x)} \rbrace=0$

⇒ $7x+4 \lbrace { x^2 \div (x \div 2)}\rbrace - 3\lbrace {5\frac{1}{3}-x^3 \div 3x} \rbrace=0$

⇒ $7x+4 \lbrace {2x}\rbrace - 3\lbrace {\frac{16}{3}-\frac{x^2}{3}} \rbrace=0$

⇒ $7x+8x -16 + x^2$

⇒ $x^2+15x -16 =0$

⇒ $x^2-x +16x -16 =0$

⇒ x(x - 1) + 16(x - 1) = 0

⇒ (x - 1)( x + 16) = 0

The value of x is 

⇒ x = +1 or -16

Now, The difference between the two values of x is 

⇒ Difference = 1 - (-16) = 1 + 16 = 17

⇒ Hence, The difference between the two values of x is 17

Given:

K = 42 × 25 × 54 × 135 is divisible by 3^a

Concept used:

Simple division is used here

Calculations:

⇒ K = 42 × 25 × 54 × 135 = 7654500

Here we go by options

For option (i),

⇒ a = 6

⇒ So, 3⁶ = 729

On dividing 7654500 by 729, we get 10500

Which is completely divisible

For option (ii)

⇒ a = 7 

⇒ 3⁷ = 2187

On dividing 7654500 by 2187, we get 3500

Which is also completely divisible

Value of a which is 7 is greater than other numbers 

⇒ Hence, Option (ii) is correct

Given:

x2 + y2 + 2y + 4x + 5 = 0

Concept Used:

The concept of quadratic equation is used

Calculations:

The given equation is 

x2 + y2 + 2y + 4x + 5 = 0

To make the equation quadratic for x and y we have to add some values according to the coefficient of x  =and y respectively

⇒ The coefficient of x is 4x = 2 × 2 × x 

so for x, we have to add square of 2 and subtract square of 2

⇒ The coefficient of y is 2x = 2 × 1 × y 

so for x, we have to add square of 1 and subtract square of 1

So, The equation will become

⇒ x2 + y2 + 2y + 4x + 5 + 4 - 4 + 1 - 1 = 0

⇒ x2 + 4x + 4 + y2 + 2y + 1 + 5 - 4 - 1= 0

⇒ (x + 2)² + (y + 1)² = 0

On putting the value of x = -2 and y = -1, we get the value 0

⇒ So , x = - 2 and y = -1

The value of $\frac{x+y}{x-y}=$

⇒ $\frac{x+y}{x-y}=\frac{-2-1}{-2 - (-1)}=\frac{-3}{-1}$ = 3

⇒ Hence, The value of the given equation is 3

Alternate Method

x2 + y2 + 2y + 4x + 5 = 0

⇒ x2 + y2 + 2y + 4x + 4 + 1 = 0 

⇒ x2 +  4x + 4 + y2 + 2y + 1 = 0 

⇒ (x + 2)2 + (y + 1)2 = 0

So, x = -2 and y = -1

Then, $\frac{x+y}{x-y}=$ -3/-1 = 3

Given:

30% increased in 2019

15% increased i. 2020

40% decreased in 2021

Mask manufactured in 2021 = 179400

Formula used:

Increased % = 100 + increased

Decreased %  = 100 - decreased

Calculations:

⇒ Mask manufactured in 2019 = X × (100 + 30) = X × 130%

⇒ Mask manufactured in 2020 = (130%X) × (100 + 15) = 115% (130% of X)

⇒ Mask manufactured in 2021 = 115% (130% of X) × (100 - 40) = 60% ( 115%( 130% of X))

But according to the question,

⇒ Manufactured in 2021 = 179400

So,

⇒ 60%{115%(130% of X)} = 179400

⇒ $\frac{X × 60×115×130}{100×100×100}= 179400$

⇒ X =  $\frac{179400 × 100×100×100}{60×130×115}$ 

⇒ X = 200000

⇒ Hence, The manufacture  of mask in 2018 is 200000

Shortcut Trick

So, 897 unit → 179400

then, 1000 unit → 179400/897 × 1000 = 200000

Calculations:

According to the question,

(x - y) + (y - z) + (z - x) = 0

So, (x - y)³ + (y - z)³ + (z - x)³ = 3(x - y)(y - z)(z - x)

Now, $\frac{(x-y)^3+(y-z)^3+(z-x)^3}{6(x-y)(y-z)(z-x)}$

⇒ 3(x - y)(y - z)(z - x)/6(x - y)(y - z)(z - x)

⇒ 3/6

⇒ 1/2

Hence, The Required value is 1/2.