DSSSB TGT Social Studies Female 16 Oct 2018 Official Paper (Shift 2) (Previous Year Paper)

The correct answer is Option 4: Hand over the chain to the nearby police station.

 

• Qualities Projected in this situation:  (Sense of responsibility and determination).

Key Points

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Concepts of BODMAS rule:

• BODMAS has to be used when there is more than one operation in a mathematical expression. There is a sequence of certain rules that need to be followed when using the BODMAS method.

Conditions to follow:

• If there is any bracket, open the bracket, then add or subtract the terms. a + (b + c) = a + b + c,  a + (b - c) = a + b - c
• If there is a negative sign just open the bracket, multiply the negative sign with each term inside the bracket. a – (b + c) ⇒ a – b – c
• If there is any term just outside the bracket, multiply that outside term with each term inside the bracket. a(b + c) ⇒ ab + ac

Remember BODMAS Rule:

One easy way to remember the BODMAS rule is to perform these steps:

The logic follows here is :

 

Given expression is : 26 $ 4 @ 3 # 56 * 7 ?

Replacing the signs as per the given directions and using the BODMAS rule:

26 + 4 × 3 - 56 ÷ 7 = ?

26 + 4 × 3 - 8 = ?

26 + 12 - 8 = ?

38 - 8 = ?

30

Hence, the correct answer is "30".

Given:

‘Vyshnavi has done graduation in Engineering with 61% marks.

Her date of birth is 4, 3. 1991.

She has qualified in the selection process and has secured 69% marks in it.

She also has three years of post-qualification work experience.

All conditions are as follows;

 

Vyshnavi doesn't fulfill the criteria of a commerce graduate or post-graduation degree in finance with a minimum of 60% marks neither she has scored 75% marks in the selection process.

So, She is not eligible for any position. 

Hence, the correct answer is "The candidate is not to be selected".

From the given diagram:

The people who speak Gujarat and Hindi but not Marathi are 26. 

Now,

The people who speak only Hindi are 52. 

Thus the ratio of people who speak Gujarati and Hindi but not Marathi to the people who speak only Hindi,

= 26 : 52

= 1 : 2 

Hence, the correct answer is "1 ∶ 2".

Total Sale of Company XYZ in 2016 = Q1 + Q2 + Q3 + Q4

= 15 + 20 + 10 + 10

= 55

Total Sale of Company XYZ in 2017 = Q1 + Q2 + Q3 + Q4

= 25 + 25 + 15 + 10

= 75

Ratio of total sales of the company ‘XYZ’ for the year 2016 to the total sales for the year 2017 = Total Sale of Company XYZ in 2016/Total Sale of Company XYZ in 2017

= 55/75

= 11/15

= 11 : 15

Hence, "11 :15" is the correct answer.

The logic followed is:

The second number = (first number × 4) + 1 

Option 1 → 9 ∶ 37 

37 = 9 × 4 + 1

37 = 36 + 1

37 = 37

Option 2 → 6 ∶ 25

25 = 6 × 4 + 1

25 = 24 + 1

25 = 25

Option 3 → 4 ∶ 13

13 = 4 × 4 + 1

13 = 16 + 1

13 ≠ 17 

Option 4 → 7 ∶ 29

29 = 7 × 4 + 1

29 = 28 + 1

29 = 29

Hence, the correct answer is "4 ∶ 13".

Given:

Suma cuts a cake into two halves and further cuts one half into smaller pieces of equal size.

If she has nine pieces of the cake in all with her means one half and 8 pieces from the other half.

And each of the smaller pieces is 30 gram and this will be equal to 8 × 30 = 240 gram 

And since 240 grams is the weight of half.

Then for full weight will be

240 × 2 = 480 

Hence, the correct answer is "480 grams".

As we can see the given figure is embedded in Option 4. 

Hence, the correct answer is "Option 4".

The logic followed is:

A bicycle also called a bike or cycle, is a human-powered or motor-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A bicycle rider is called a cyclist, or bicyclist.

As per the basic definition of the cycle, some compulsory things must be present in the cycle:

i) Wheels

ii) Brakes

iii) Cycle handle

iv) Seat e.t.c 

Option 1 - Wheels

It is the most important part of the cycle. Without it, we cannot move the cycle forward. 

Option 2 - Battery

There are non-battery-operated cycles also. It is not compulsory part to be present in a normal cycle. 

Option 3 - Rainproof Roof

This is not relevant to a cycle.

Option 4 - Vegetable Basket

It is optional not always present in the cycle.

Hence, the correct answer is "Wheels".

The logic followed is:

Similar pattern:

1. The number of single-sided arrow = total number of the side of the given figure

2. The single-sided arrow is in the middle of the side

Option 1 → 

The number of single-sided arrows ≠ number of the sides i.e 2 ≠ 4 

Option 2 → 

1. The number of single-sided arrow = total number of the side of the given figure i.e 3 = 3
2. The single-sided arrow is in the middle of the side 

Option 3 → 

The single-sided arrow is not in the middle of the side of the figure

The number of single-sided arrows ≠ number of the sides i.e 4 ≠ 5 

Option 4 → 

The single-sided arrow is not in the middle of the side of the figure

Thus only option (2) is satisfying the similar common pattern.

Hence, the correct answer is "Option 2".

Zoroaster: An ancient Persian prophet and founder of Zoroastrianism. Zoroaster is from Parsis religion.

Similarly;

Jesus: Christianity originated with the ministry of Jesus, a Jewish teacher and healer who proclaimed the imminent kingdom of God and was crucified c. AD 30–33 in Jerusalem in the Roman province of Judea. Jesus is from the Christian religion.

Hence, "Jesus" is the correct answer.

The given figure when unfolded is as follows:

Hence, option (3) is correct.

The logic followed is:

All except option (4), Second denotes the purpose for which the first is used.

Option 1 → Sword : Slaughter

Sword is used for the purpose of slaughtering animals usually for food.

Mistake Points

1. Here sword doesn't mean the weapon which was used in ancient times for war.

Sword synonyms → Blade, Edge, Knife, Shank e.t.c

Option 2 → Gun : Shoot

Gun is basically used for the purpose to shoot.

Option 3 → Spanner : Grip

Spanner is basically used for the purpose to grip nut bolts.

Option 4 → Spoon : Cut

Spoon is not used for the purpose to cut things. It is used to eat.

Thus this is odd from the rest of the option.

Hence, the correct answer is "Spoon : Cut".

The faces opposite to each other is shown below:

The opposite sides are:

1) 

 → This cube can be formed as no two opposite faces appear together on the same dice. 

2) 

 → This cube cannot be formed as

 and

 faces is opposite faces and no two opposite faces can appear together on the same dice.

3) 

 → This cube cannot be formed as

 and

 face are opposite faces and no two opposite faces can appear together on the same dice. In the unfolded figure there are three 

 faces and two are opposite. So, Not three 

 faces are together.

4) 

 → This cube cannot be formed as 

 and 

 faces is opposite faces and no two opposite faces can appear together on the same dice.

Hence, ‘option 2’ is the correct answer.

According to the English alphabet series and its positional value:

The logic follows here is:

Hence, "D" is the correct answer.

Let, age of Son = p

Age of Father = 2p

Ten years back:

Age of father = (2p - 10)

Age of son = (p - 10)

So;

Age of father = 3 × Age of son

(2p - 10) = 3 × (p - 10)

2p - 10 = 3p - 30

3p - 2p = 30 - 10

p = 20

So, age of son = 20 years.

Hence, "20" is the correct answer.

The logic followed is:

Multiplication between digits of the number gives the next number 

4 × 7 = 28

2 × 8 = 16

Similarly,

1 × 6 = ?

? = 6 

Hence, the correct answer is "6".

The given figure when unfolded is as follows:

Hence, option (3) is correct.

In Figure A, B, and C the inner half circle is dark and outer half circle is blank.

But;

In Figure D inner half circle is blank and outer half circle is shaded with lines.

So, Figure D is odd among all the figures.

Hence, option (4) is the correct answer.

Preparing the family tree using the following symbol:

According to the given information,

Hence, Vanaja's daughter is the niece of Vardhaman.

The correct answer is Raghunath Seth.

Key Points

• Raghunath Seth was born in Gwalior in 1931.
• He was an eminent flute player.
• He had received Sangeet Natak Akademi Award in 1994, this award is given by Sangeet Natak Akademi.
• Some Indian Fluet Players:
• ​Hariprasad Chaurasia.
• S. Akash.
• Mayavaram Saraswathi Ammal.
• K. Bhaskaran.
• Sikkil Mala Chandrasekar.

Additional Information

The correct answer is 69.

Key Points

• India’s Medals in Asian Games 2018
• Gold: 15
• Silver: 24
• Bronze: 30
• Total: 69

 

• Upcoming Asian Games 
• 2022: Hangzhou, Zhejiang, China.
• 2026: Nagoya, Japan.

Additional Information

• About Asian Games 2018
• India competed at the 2018 Asian Games in Jakarta and Palembang, Indonesia, from 18^th August to 2^nd September.
• Neeraj Chopra was the flag bearer for the opening ceremony while Rani Rampal was named as the flag bearer for the closing ceremony.
• India ranked 8^th in the 2018 Asian Games Medal Table with 69 medals in total.
• China topped the medal tally with 132 Golds and a total of 289 Medals.
• Japanese swimmer Ikee Rikako has been named as the Most Valuable Player (MVP) of the recently-concluded 18^th edition of the Asian Games.

The correct answer is Pali.

Key Points

• The sacred book of Buddhism is called the Tripitaka it is written in the Pali language.
• It is also called the Pali Canon, after the language in which it was first written.

Important Points

• Buddhism:
• ​The founder of Buddhism, Siddhartha Gautama, lived from 563 - c. 483 BCE
• Gautama was known as the Buddha, meaning the "Enlightened One."
• The Buddha spent the remainder of his life journeying about India, teaching others what he had come to understand.
• The main symbol of Buddhism is the dharma chakra, the dharma wheel is one of the oldest and most iconic symbols of the Buddhist faith.
• According to Buddhism, the cause of all sorrow is Tanha or Trishna(Desire).
• According to the Buddha, sorrow, and suffering are caused by attachment, specifically to a particular outcome or possession.
• By freeing themselves of all attachments and cravings, individuals can also free themselves from suffering and sorrow

The correct answer is Eighth.

Key Points

• India ranked 8^th position in terms of medal tally arranged as per the number of gold medals in the 2018 Asian Games.
• India’s Medals in Asian Games 2018:

• China topped the medal table with 129 gold, 78 silver and 67 bronze.
• A total of 1,223 medals were awarded.

Important Points

• Upcoming Asian Games
• 2022 Asian Games: Zhejiang, China.
• 2026 Asian Games: Japan.
• All About Asian Games 2018:
• India competed at the 2018 Asian Games in Jakarta and Palembang, Indonesia, from 18^th August to 2^nd September.
• Neeraj Chopra was the flag bearer for the opening ceremony while Rani Rampal was named as the flag bearer for the closing ceremony.
• India ranked 8^th in the 2018 Asian Games Medal Table with 69 medals in total.
• China topped the medal tally with 132 Golds and a total of 289 Medals.
• Japanese swimmer Ikee Rikako has been named as the Most Valuable Player (MVP) of the recently-concluded 18^th edition of the Asian Games.
• The 18-year-old, who bagged six gold and two silver medals in the tournament, became the first female athlete to win the MVP title.

The correct answer is Rajasthan.

Key Points

• Khyal folk music is related to Rajasthan.
• Khyal or Khayal is the modern genre of classical singing in the Indian subcontinent.
• Its name Khyal bases itself on a repertoire of short songs (two to eight lines).
• Khyal song is called a bandish.
• The cultural celebrations consist of Rajasthani folk dances and the traditional musical style of Dausa and Swai Madhopur known as Hela Khayal.
• Gwalior Gharana is considered the oldest Khyal Gharana in Indian classical music.
• Some folk songs of Rajasthan:
• ​Ghoomar.
• Bhavai Dance.
• Kalbelia.
• Chari or Pot Dance.
• Dandiya.
• Kachhi Ghodi.
• Terah Taal.
• Gair.

Additional Information

• About Rajasthan (as of June 2021)
• CM: Ashok Gehlot
• Governor: Kalraj Mishra
• State flower: Rohira (Tecomella undulata)
• State Animal: Chinkara
• National Parks and Wildlife Sanctuaries: Ranthambore National Park, Sariska Tiger Reserve (Native wildlife & tiger sanctuary), Desert National Park, Mount Abu WS.
• Highest Peak: Guru Sikhar (1732 mt)
• Important river: Chambal and Luni (Inland river)
• UNESCO site: Chittorgarh Fort, Kumbhalgarh, Ranthambore Fort, Amber Fort.

The correct answer is Neptune.

Key Points

• The first four planets are called  Terrestrial, meaning earth-like planets like Mercury, Venus, Earth, and Mars.
• They are also called inner planets.
• They lie between the sun and the belt of asteroids.
• They are made up of rock and metals and have relatively high densities.
• The terrestrial planets were formed in the close vicinity of the parent star where it was too warm for gases to condense to solid particles.
• The terrestrial planets are smaller and their lower gravity could not hold the escaping gases.
• Other than them the planets are called jovian or giant planets like Jupiter, Saturn, Uranus, and Neptune.
• They are also called the outer planets.
• Most of them are much larger than the terrestrial planets and have a thick atmosphere, mostly of helium and hydrogen.
• The solar winds were not all that intense to cause the removal of gases from the Jovian planets.

​

Additional Information

• Inner or Terrestrial planets: 

1. Mercury
2. Venus
3. Earth
4. Mars

• Outer Planets or Jovian planets:

1. Jupiter
2. Saturn
3. Uranus
4. Neptune

• My Very Excited Mother Just Served Us Nachos
• M →  Mercury, V → Venus, E → Earth, M → Mars, J → Jupiter, S → Saturn, U → Uranus, N → Neptune

The correct answer is Nandas.

Key Points

• The Nandas ruled the Magadha empire between 344 BC and 321 BCE.
• Nandas are known as the first “empire builders” of India.
• The first Nanda ruler was Mahapadma.
• The Shisunada dynasty was overthrown by Mahapadma and established the Nanda Kingdom.
• Mahapadma is called the “first historical emperor of India.”
• Mahapadma expanded his empire to include a larger part of northern India.
• The Nandas were the first Non-Kshatriya rulers in India.
• The Nandas made the methodical collection of taxes by regularly appointed officials a part of their administrative system.
• Mahapadma was succeeded by his eight sons, Dhana Nanda was the last one.
• Dhana Nanda is referred to as Agrammes or Xandrames in Greek texts.
• Alexander invaded northwest India during the reign of Dhana  Nanda.
• Dhana Nanda was overthrown by Chandra Gupta Maurya.

Additional Information

• The Gupta dynasty ruled the northern and parts of central and western India from the early 4^th to the late 6^th century CE.
• The period is referred to as the "classical age" or "golden age" of ancient India.
• It was founded by king Sri Gupta.
• Mauryan empire was lasted from about 321 to 185 BCE. 
• It was the first empire to encompass most of the Indian subcontinent.
• It was founded by Chandragupta Maurya in 322 BCE.
• Sungas was the first Brahmin dynasty in India.
• ​The founder was Pushyamitra Sunga.

The correct answer is Madhya Pradesh.

Key Points

• The Indian Government has signed a $375 million loan agreement with Asian Development Bank for improving irrigation efficiency in Madhya Pradesh.
• It contributes to double farming incomes in Madhya Pradesh by expanding irrigation networks and system efficiency.
• The ADB funds will be used to develop a large-scale pressurized and automated irrigation system for boosting irrigation efficiency.

Additional Information

• Asian Development Bank: ADB is committed to achieving a prosperous, inclusive, resilient, and sustainable Asia and the Pacific while sustaining its efforts to eradicate extreme poverty.
• Established in 1966.
• It is owned by 68 members.
• Headquarter: Philippines.
• Current President: Masatsugu Asakawa (as of June 2021)$

The correct answer is 15^th Constitutional Amendment Act, 1963.

Key Points

• 15^th Constitutional amendment act 1963:
• ​Enabling high court to issue writs to any person or authority even outside its territorial jurisdiction if the cause of action arises within the territorial limit.
• Increasing the retirement age of HC judges from 60 to 62.
• Provided for the appointment of retired judges of the high court and acting judges of the same court.
• Provided for compensatory allowance to judge after transfer from one court to another.
• Enabled the retired HC judges to act as ad-hoc judges for SC.
• Procedure for determining the age of HC and SC judges

 

Additional Information

The correct answer is 29.

Key Points

• 25^th GST Council has reduced the tax rate on 29 goods and 53 categories of services by bringing them in lower category.
• The GST rate on transportation of petroleum crude and petroleum products including ATF has bee cut down from 18% to 5% without input tax credit & 12% with it.
• The GST rate on tailoring service has been reduced from 18 to 5%
• The new rates will be effective from 25^th Jan 2018.

Additional Information

• GST (Goods and Service Tax) is an indirect tax levied on the sale of goods and services.
• This will lead to the same type of indirect tax across India, and various indirect taxes such as central excise, service tax, VAT, entertainment, lottery tax etc. will be absorbed in GST.
• The GST was launched at midnight on 1 July 2017 by the President of India.
• The GST is divided into five different tax slabs: 0%, 5%, 12%, 18% and 28%.
• The GST is a unified tax that will levy both goods and services.
• This is the 122^nd amendment to the Constitution.
• GST is divided into four parts-
• IGST - Integrated Goods and Services Tax.
• CGST - Central Goods and Services Tax.
• SGST - State Goods and Services Tax.
• UTGST - Union Goods and Services Tax.

The correct answer is Kyrgyzstan.

Key Points

• Kyrgyzstan:
• ​Capital - Bishkek
• Currency - Kyrgyzstani som
• President - Sadyr Japarov
• Prime Minister - Ulukbek Maripov
• Kyrgyzstan is a landlocked country in Central Asia
• ​​Kyrgyzstan is also referred to as "the Switzerland of Central Asia".

​

Additional Information

The correct answer is Article 49.

Key Points

• The provision of Article 49 of the Constitution of India Protection of monuments and places and objects of natural importance.
• It shall be the obligation of the State to protect every monument or place or object of artistic or historic interest, to be of national importance, from spoliation, disfigurement, destruction, removal, disposal or export, as the case may be.

Additional Information

The correct answer is Ahmedabad.

Key Points

• Founded in 1947 by Dr. Vikram A. Sarabhai, the Physical Research Laboratory (PRL) had a modest beginning at his residence, the RETREAT, with research on Cosmic Rays.
• The Laboratory was formally established on November 11, 1947, in the M. G. Science College, Ahmedabad, with support from the Karmkshetra Educational Foundation and the Ahmedabad Education Society.
• The initial focus was research on Cosmic Rays and the properties of the Upper Atmosphere. Research in Theoretical Physics and Radio Physics were added later with grants from the Atomic Energy Commission.
• The main campus of the Physical Research Laboratory (PRL) is located in Navrangpura, Ahmedabad.
• The Thaltej campus at Ahmedabad houses the infrared, optical and radio astronomy laboratories and the Planetary Science and Exploration Programme.
• Present Director - Dr. Anil Bhardwaj.

Important Points

 

Additional Information

The correct answer is 27^th

Key Points

• The State Uttarakhand came into existence on 09^th November 2000 under the Reorganization of Uttar Pradesh Act 2000.
• It became the 27^th state of India.

 

Important Points

• The State of Uttarakhand was earlier a part of the United Province of Agra and Awadh, which came into existence in 1902.
• In 1935, the name of the State was shortened to the United Province.
• In January 1950, the United Province was renamed Uttar Pradesh.
• Uttaranchal remained a part of Uttar Pradesh before it was carved out of Uttar Pradesh on 09 November 2000.
• It is often called the Land of the Gods (Dev Bhoomi) because of its various holy places.

 

Additional Information

Uttarakhand - 

• Chief Minister - Pushkar Singh Dhami
• Governor - Gurmit Singh
• State animal - musk deer
• Lok Sabha seats - 5
• Rajya Sabha seats - 3

The correct answer is ​Kalbelia.

Key Points

• Kalbelia dance is a folk dance of the Rajasthan state of India. It is well known by other names like 'Sapera Dance' or 'Snake Charmer Dance'.
• Kalbelia dance is particularly performed by a Rajasthani tribe called 'Kalbelia'.
• The popularity of this dance is so much worldwide that Rajasthan's Kalbelia dance and songs are now in UNESCO's representative list of the Intangible Cultural Heritage of Humanity from the year 2010.
• Gulabo bai is a famous dancer of the Kalbeliya caste.
• Gulabo bai is also called as ' Gulabo Sapera'.

Important Points

• Dance of Kalbelia
• Panihari Dance - Dance performed by both men and women
• Indauli Dance - Dance performed by both men and women in doubles
• Sankariya Dance - love affair The couple is based on dance.
• Bagdiya Dance - This dance performed by women only while begging.

Additional Information

The correct answer is Singapore.

Key Points

• The then Union Minister for Commerce & Industry and Civil Aviation, Suresh Prabhu, led the delegation for the meeting for trade Ministers of RCEP member countries which took place in Singapore on November 12-13, 2018.
• The Regional Comprehensive Economic Partnership (RCEP) is a pact that aims to cover goods, services, investments, economic and technical cooperation, competition and intellectual property rights.
• India already has a free trade agreement with the Association of Southeast Asian Nations (ASEAN), Japan and South Korea and it is negotiating similar pacts with Australia and New Zealand.
• The RCEP members include 10 ASEAN members – Brunei Cambodia, Indonesia, Malaysia, Myanmar, Singapore, Thailand, the Philippines, Laos and Vietnam and their 6 free trade agreement partners – India, China, Japan, South Korea, Australia and New Zealand.

Additional Information

The correct answer is Bank of Rajasthan.

Key Points

• Together we Prosper is a tagline of Bank of Rajasthan.
• In 1943, Bank of Rajasthan was set up, with Udaipur as its registered office.
• It was the brainchild of late Rai Bahadur PC Chatterjee, the then finance minister of what used to be Mewar.
• It was formed as a public company, with shares owned by investors, including founder-chairman Seth Govind Ram Seksaria, an eminent industrialist of his time.

 

Important Points

• Bank of Rajasthan was merged with ICICI Bank which is the country's highest private lender bank.
• The Reserve Bank of India (RBI) approved the merger of the Bank of Rajasthan with ICICI Bank Ltd.
• All branches of BoR will function as branches of ICICI Bank.
• The boards of both the banks on May 23, 2010, approved the merger for a share exchange ratio of 25 shares of ICICI Bank for 118 shares of BoR.
• Subsequent to the merger of BoR and ICICI Bank, ICICI bank ensured that erstwhile BoR customers avail the benefits as available to all ICICI Bank customers.
• Some of the benefits are:
• 24X7 banking through the Internet and Mobile Banking.
• A Suite of products and services to meet all the Banking requirements.

Additional Information

The correct answer is H2CO3.

Key Points

• Carbonic acid is a chemical compound with the chemical formula H2CO3 (equivalently OC(OH)2).
• It is also a name sometimes given to solutions of carbon dioxide in water (carbonated water) because such solutions contain small amounts of H2CO3.
• In physiology, carbonic acid is described as volatile acid or respiratory acid, because it is the only acid excreted as a gas by the lungs.
• It plays an important role in the bicarbonate buffer system to maintain acid-base homeostasis.
• Carbonic acid, which is a weak acid, forms two kinds of salts, the carbonates and the bicarbonates.
• In geology, carbonic acid causes limestone to dissolve producing calcium bicarbonate which leads to many limestone features such as stalactites and stalagmites.

The correct answer is K Vijay Raghavan.

Key Points

• The government constituted a 21-member panel to advise PM Narendra Modi on science, technology and innovations.
• Headed by the principal scientific adviser to the government K Vijay Raghavan.
• The panel is called Prime Minister’s Science, Technology & Innovation Advisory Council (PMSTIAC).
• It will also assist the government in using science, technology and innovation for “solving socio-economic problems” in the country.
• Advising the government on developing ‘Clusters of Excellence’ in science including city-based R&D clusters will also be one of the 17 tasks of the panel.
• It will work to bring together all science & technology partners from academia\ institutes to industries near such centres or cities.
• Besides the chairperson, the panel has eight members and 12 special invitees. The members include noted mathematician and Princeton University professor Manjul Bharghava; former Isro chairman A S Kiran Kumar and industrialist and MD of Bharat Forge Baba Kalyani.

Additional Information

The correct answer is Sravasti.

Key Points

Kosala Kingdom

• The Mahajanapada of Kosala was bounded on the west by the river Gomati.
• To its east flowed the river Sadanira which separated it from the Videha Janapada. Towards the north it skirted the Nepal hills while the river Syandika defined its southem boundary.
• Literary references indicate how Kosala emerged out of an assimilation of many smaller principalities and lineages.
• For example, we know that the Sakyas of Kapilavastu were under the control of Kosala.
• The Buddha calls himself a Kosalan in the Majjhima Nikaya. But at the same time the Kosalan King Vidudhaba is said to have destroyed the Sakyas.
• It would only indicate that the Sakya lineage was under the nominal control of the Kosalas. The newly emergent monarchy established a centralized control and thus destroyed the autonomy of the Sakyas.
• Names of Kings like Hiranyanabha, Mahakasala Prasenajita and Suddhodana are mentioned as rulers of Kosala in the 6^th century B.C.
• These rulers are said to have ruled from Ayodhya, Saketa, Kapilavastu or Sravisti.
• Towards the end of the 6^th century B.C. kings like Prasenajita and Vidudhabha managed to bring all other chiefships under their control. They ruled from Sravasti.
• Thus, Kosala became a prosperous Kingdom having three big cities under its control i.e. Ayodhya, Saketa and Sravasti.
• Kosala also annexed the Kingdom of Kashi in its territory. The Kings of Kosala favoured both Brahmanism and Buddhism.
• King Prasenajita was a contemporary and friend of the Buddha.
• In the succeeding phases Kosala proved to be one of the most formidable adversaries of the emergent Magadhan empire.

Formula used:

(a + b)² = a² + b² + 2ab

(a - b)2 = a2 + b2 - 2ab

√a × √a = a

Calculation:

$\dfrac{\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}}{(4\sqrt{3}-5\sqrt{2})\times(3\sqrt{2}+4\sqrt{3})}=a\sqrt{2}+b\sqrt{3}$

⇒ $\dfrac{\sqrt{(\sqrt 3)^2+ (\sqrt 5)^2 + 2 \times \sqrt{3} \times \sqrt{2}}-\sqrt{(\sqrt 3)^2+(\sqrt 2)^2 -2\times \sqrt{3}\times \sqrt {2}}}{(12\sqrt{6} + 48 -20\sqrt{6} - 30)}=a\sqrt{2}+b\sqrt{3}$

⇒ $\dfrac{\sqrt{(\sqrt 3+ \sqrt 2)^2 }-\sqrt{(\sqrt 3-\sqrt 2)^2 {}}}{(18 -8\sqrt{6} )}=a\sqrt{2}+b\sqrt{3}$

⇒ $\dfrac{{(\sqrt 3+ \sqrt 2) }-{(\sqrt 3-\sqrt 2) {}}}{(18 -8\sqrt{6} )}=a\sqrt{2}+b\sqrt{3}$

⇒  $\dfrac{{(2 \sqrt 2) {}}}{\sqrt 2(9\sqrt 2 -8\sqrt{3} )}=a\sqrt{2}+b\sqrt{3}$

Now, Rationalising it,

⇒ $\dfrac{{2 {}\times(9\sqrt 2 + 8\sqrt{3})} }{(9\sqrt 2 -8\sqrt{3} )\times(9\sqrt 2 +8\sqrt{3})}=a\sqrt{2}+b\sqrt{3}$

⇒  $\dfrac{{(18\sqrt 2 + 16\sqrt{3})} }{(162 -{192} ){}}=a\sqrt{2}+b\sqrt{3}$

⇒  $\dfrac{{-(18\sqrt 2 + 16\sqrt{3})} }{{30} {}}=a\sqrt{2}+b\sqrt{3}$

⇒  $\dfrac{{-2(9\sqrt 2 + 8\sqrt{3})} }{{30} {}}=a\sqrt{2}+b\sqrt{3}$

⇒  ${{-\dfrac{9}{15}\sqrt 2 - \dfrac{8}{15}\sqrt{3}} }{{} {}}=a\sqrt{2}+b\sqrt{3}$

On comparing,

a = -9/15 and b = -8/15

Now, (a - b) = $\dfrac{-9}{15} -\dfrac{-8}{15}$

⇒ (-9 + 8)/15 = $\dfrac{-1}{15}$

∴ The value of (a - b) is $\dfrac{-1}{15}$.

Given:

Length of train = 100 m

Speed of person = 5 km/h

Time = 7.2 seconds

Formula used:

Speed = Distance/Time

Time = Distance/Speed

Concept used:

Two trains or two objects bodies are moving in opposite direction at u km/hr and v km/hr, then

Relative speed = (u + v) km/hr

I hour = 60 minutes

To convert a speed from m/s to km/h, we multiply it by 18/5

Calculation:

Let the speed of the train be u km/h

Relative speed = (u + 5) × 5/18

According to the question:

$\dfrac{100}{(u + 5)× \dfrac{5}{18}} = 7.2$

⇒ 18 × 100 = 7.2(5u + 25)

⇒ 1800 = 36u + 180

⇒ 36u = 1620

⇒ u = 1620/36 = 45 km/h

∴ The speed of the train is 45 km/h.

Concept Used:

Using BODMAS rule:

 

Calculation:

$\dfrac{(0.2\times0.3\times 0.173)\div(0.2\div0.2\ \rm of\ 0.1-0.03\div0.6\ \rm of\ 0.01)}{0.12\ \rm of \ (0.0123-0.004)+0.36\times0.003}$

⇒ $\dfrac{0.01038\div(0.2\div0.02-0.03\div0.006)}{0.12\ \rm of \ 0.0083+0.36\times0.003}$

⇒ $\dfrac{0.01038\div(10-5)}{0.000996+0.36\times0.003}$

⇒ $\dfrac{0.01038\div5}{0.000996+0.36\times0.003}$

 $\dfrac{0.002076}{0.000996+0.36\times0.003}$

 $\dfrac{0.002076}{0.000996+ 0.00108}$

 $\dfrac{0.002076}{0.002076}$

⇒ 1

∴ The value of $\dfrac{(0.2\times0.3\times 0.173)\div(0.2\div0.2\ \rm of\ 0.1-0.03\div0.6\ \rm of\ 0.01)}{0.12\ \rm of \ (0.0123-0.004)+0.36\times0.003}$ is 1.

Given:

The numbers = 21, 33, 35 and 55

Calculation:

LCM of 21, 33, 35 and 55 = 1155

Hence, the number can be written in the form (1155k + 3) which is divisible by 67

(1155k + 3)/67,

Where, Quotient = 17k and Remainder = 16k + 3

Now, (16k + 3) divisible by 67

Put k = 1, 2, 3, 4...

If k = 1, number = (1155 × 1) + 3 = 1158 which is not divisible by 67

If k = 2, number = (1155 × 2) + 3 = 2313 which is not divisible by 67

If k = 3, number = (1155 × 3) + 3 = 3468 which is not divisible by 67

If k = 4, number = (1155 × 4) + 3 = 4623 which is divisible by 67

Sum of digits of numbers = 4 + 6 + 2 + 3 = 15

∴ The sum of the digits of x is 15.

Hint

To find the least number we have to calculate the the LCM of the given numbers first then we will set the number as 1155k + 3 as in the question given that remainder is 3. Then check for what value of k the number is divisible by 67. At last put the value of k and and the required least number.

Given: 

Price of oil is increased by 20%

Expenditure of oil is increased by 10%

Calculation:

Let initially oil is consumed 100lt at 100Rs/lt.

Initial expenditure = 100 × 100 = 10000

Now, new price = 120% of 100 = 120rs

And, New expenditure = 110% of 10000 = 11000

Hence, new consumption = 11000/120 = 275/3 lit.

Required percentage = [{(275/3) - 100}/100] × 100 = -25/3% = - $8\dfrac{1}{3}\%$ (negative sign shows decrement)

∴ The percentage decrease in consumption by $8\dfrac{1}{3}\%$.

Alternate Method

Given: 

Price of oil is increased by 20%

Expenditure of oil is increased by 10%

Concept used:

Expenditure = Price × Consumption

Calculation:

Price increased by 20 %

⇒ 20% = 1/5

Expenditure increased by 10%

⇒ 10% = 1/10

According to the concept,

C₁ = 10/5 = 2

C₂ = 11/6

Change in consumption:

⇒ 2 - 11/6 = 1/6 (dercreased)

Change in percentage,

⇒ $\dfrac{1}{6 \times 2}\ \times 100$ = 25/3 = $8\dfrac{1}{3}\%$ dercreased

∴ The percentage decrease in consumption by $8\dfrac{1}{3}\%$.

Additional Information

 $16\dfrac{2}{3}\%= \dfrac{1}{6}$

$14\dfrac{2}{7}\%= \dfrac{1}{7}$

$11\dfrac{1}{9}\%= \dfrac{1}{9}$

$12\dfrac{1}{2}\%= \dfrac{1}{8}$

$9\dfrac{1}{11}\%= \dfrac{1}{11}$

Given:

Firstly sold at loss of 5%

Secondly sold at profit of 10%

Formula used:

S.P = $\frac{{(100 + P\%)}}{100}× C.P$

 

S.P = $\frac{{(100 - L\%)}}{100}× C.P$

Where, S.P = Selling Price, C.P = Cost Price, P = Profit, L = Loss

Calculation:

Firstly sold at loss of 5%

Then, S.P₁ = $\frac{{(100 - L\%)}}{100}× C.P$

⇒ S.P₁ = $\frac{{(100 - 5\%)}}{100}× C.P$

⇒ S.P₁ = 95/100 × C.P

Secondly sold at profit of 10%

Then, S.P₂ = $\frac{{(100 + P\%)}}{100}× C.P$

⇒ S.P₂ = $\frac{{(100 + 10\%)}}{100}× C.P$

⇒ S.P2 = 110/100 × C.P

According to the question:

S.P₂ - S.P₁ = (110/100 × C.P) - (95/100 × C.P)

⇒ S.P1 - S.P2 = 110% C.P - 95% C.P

⇒ 225 = 15% × C.P

⇒ C.P = [(225/15) × 100] = Rs. 1500

Now, S.P at 8% profit

S.P = $\frac{{(100 + P\%)}}{100}× C.P$

⇒ S.P = $\frac{{(100 + 8\%)}}{100}× 1500$

⇒ S.P = [(108/100) × 1500] = Rs. 1620

∴ The selling price is Rs. 1620, if she sells it a gain of 8%.

Shortcut Trick

 110%  - 95% = 225

⇒ 15% = 225

⇒ 1% = 225/15%

⇒ 100% = [(225/15) × 108] = Rs. 1620

Given:

Income of A = x% of income of B

Expenditure of A = 80% of B's expenditure

A's income = 90% of B’s expenditure

The ratio of the savings of A to that of B is 1 ∶ 2

Concept used:

Income = Expenditure + Saving

Calculation:

According to the question, we get,

Income of A = x% of income of B

⇒ Income of A : Income of B = x : 100

Expenditure of A = 80% of B's expenditure

⇒ Expenditure of A : Expenditure of B = 80 : 100 = 8 : 10 

Income of A = 90% of B’s expenditure

⇒ Income of A : Expenditure of B = 90 : 100 = 9 : 10

Let Income of A be Rs. x

And Income of B be Rs. 100     

Let Expenditure of A be Rs. 8 units

And expenditure of B be  Rs. 10 units

Let, the savings of A be Rs. 1 units

And the savings of B be Rs. 2 units

According to the concept,

In case of B,

(10 + 2) units = 100

⇒ 12 units = 100

In case of A,

(8 + 1) units = 9 units (Income of A)

Now, 

12 units = 100x

⇒ 1 units = (100/12)

⇒ 9 units = (100/12) × 9 = Rs. 75

Income of A = Rs. 75

According to the question:

Income of A = x% of income of B

⇒ 75 = x/100 × 100

⇒ x = 75

∴ The value of x is Rs. 75.

Given: 

Time = 3 years

Rate = 5%

The interest for the third year is Rs. 21 more than that for the second year.

Formula used:

A = P(1 + r/100)ⁿ

Where, A = Amount, r = Rate of interest, n = Time in year

Ammount = Principal + Interest

Calculation:

Let the principal be Rs. P.

Amount after first year,

A = P(1 + r/100)n

⇒ A = P(1 + 5/100)¹

⇒ A = P × 105/100 =  21P/20

This 21P/20 will be principal for next year (principal for 3^rd year)

Amount for second year = 21P/20 × 105/100 = 441P/400

Interst earned in second year = 441P/400 - 21P/20

⇒ (441P - 420P)/400 = 21P/400

Amount for third year = 441P/400 × 21/20 = 9261P/8000

Interst eaerned in third year = 9261P/8000 - 441P/400

⇒ (9261P - 8820P)/8000 = 441P/8000

Difference between of third year and second year = 21

441P/8000 - 21P/400 = 21

⇒ (441P - 420P)/8000 = 21

⇒ 21P/800 = 21

P = Rs. 8000

At double rate i.e 10%

Amount after 2 years = 8000(1 + 10/100)²

⇒ 8000 × 121/100 = Rs. 9680

Interest gained in 2/5 years = 2/5 × 10 = 4%

Amount after 2/5 years more = 9680 × 104/100 = 387.2 × 26 = Rs. 10067.2 = Rs. 10067(approx)

∴ Required amount will be Rs. 10067.

Calculation:

Let three numbers are lowest (l), second lowest (sl), and g (greatest)

According to the question:

$\frac{1}{3} \times\frac{l + sl + g}{3}$ = g - 8      ----(1)

$\frac{l + sl}{2}$ = 8

⇒ l + sl = 16      ----(2)

Putting the value of equation (2) in equation (1);

$\frac{16 + g}{9}$ = g - 8

⇒ 16 + g = 9g - 72

⇒ 8g = 88

⇒ g = 88/8 = 11

∴ The greatest number is 11.

Given:

ABCD is a quadrilateral

AB = 9 cm

BC = 40 cm

AD = 15 cm

AC = 41 cm

Formula used:

Area of triangle = 1/2 × base × height

Herons formula,

S = (a + b + c)/2

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

Where, S = semi perimeter,

And a, b and c are sides of traingle

Concept used:

40, 9, 41 is a pythagorean triplet, 

so, angle B is 90° 

Calculation:

According to the question:

  

Area of triangle = 1/2 × base × height

⇒ 1/2 × AB × BC = 1/2 × 9 × 40= 180 cm²

S = (a + b + c)/2

⇒ S = (15 + 28 + 41)/2 = 84/2 = 42

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

⇒ Area = $\sqrt{42(42-28)(42-41)(42-15)}$

⇒ Area = $\sqrt{(42 × 14 × 1 × 27)}$ = 14 × 9 = 126 cm³

Area of quadrilateral ABCD = 180 + 126 = 306 cm²

 

Pythagorean triples: Pythagorean triples are a² + b² = c² where a, b and c are the three positive integers.

These triples are represented as (a, b, c).

Where, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.

Pythagorean triples

Given:

A and B together can complete a work in 5 days

Calculation:

According to the question:

(A + B) × 5 = 2A × 4

⇒ 5A + 5B = 8A

⇒ 5B = 3A

⇒ A/B = 5/3 

Ratio of efficiency of A : B = 5 : 3

Total work = (5 + 3) × 5 = 40 units

First 5 days working alone done by A,

Work done = 5 × 5 = 25 unit

Left work = 40 - 25 = 15 unit

Remaining work done by B = 15/3 = 5 days

∴ The remaining work will be completed by B in 5 days.

Given:

One year ago, the ratio of salaries of A and B = 4 ∶ 5

The ratio of their individual salaries of last year and present year are 3 ∶ 4 and 2 ∶ 5 respectively,

Their total salary for the present year = Rs. 256800

Calculation:

According to the question:

One year ago, Ratio of salary A and B

A : B = 4 : 5      ----(1)

Salary of A,

Last year : present = 3 : 4

Salary of B,

Last year : present = 2 : 5

In case of A, last year salary should be same as equation (1), became to in order to make that 3 as 4 multiply whole ratio by 4/3 

Then,

Salary of A = Last year : present = 3 : 4

⇒ 3 × 4/3 : 4 × 4/3

⇒ 4 : 16/3

In case of B, 

Last salary should be same as equation (1), became to in order to make 2 as 5 multiply whole ratio by 5/2

Then,

Salary of B = Last year : present = 2 : 5

⇒ 2 × 5/2 : 5 × 5/2

⇒ 5 : 25/2

Let the present salary of A be Rs. 16x/3

And the present salary of B be Rs. 25x/2

Now,

16x/3 + 25x/2 = 256800

⇒ 107x/6 = 256800

⇒ x = Rs. 14400

The present salary of B = Rs. 25x/2 = (25/2) × 14400 = Rs. 180000

∴ The present salary of B is Rs. 180000.

Given:

Two numbers are such that their mean proportional = 6

Third proportional =  $20\dfrac{1}{4}$

Calculation:

Let, the two numbers be x and y respectively,

Mean proportional between x and y = 6

⇒ x : 6 = 6 : y

⇒ xy = 36

⇒ x = 36/y      ----(1)

Third proportional to x and y =  $20\dfrac{1}{4}$ = 81/4

⇒ x : y = y : 81/4

From equation(1), 

⇒ y² = (81/4) × (36/y)

⇒ y³ = 81 × 9 

⇒ y3 = 9 × 9 × 9 = (9)³

⇒ y = 9

Again, From equation(1), we get,

x = 36/y = 36/9 = 4

The difference between the numbers = 9 - 4 = 5

∴ The difference between the numbers are 5.

Given:

5 articles are purchased at 10% discount

8 articles are purchased at $12\dfrac{1}{2}\%$ discount

Formula used:

Mark up = M.P - C.P

Mark up % = $\dfrac{Mark up}{C.P}× 100$

Where, M.P = Marked price

C.P = Cost price

Profit = Selling price - Cost price

Calculation:

Let Marked price of 1 article be Rs. x

Then, M.P of 5 articles = Rs. 5x

M.P of 8 articles = Rs. 8x

According to the question:

5 articles are purchased at 10% discount,

⇒ S.P = 5x × 90/100 = 9x/2

8 articles are purchased at $12\dfrac{1}{2}\%$ discount,

⇒ S.P = 8x × 87.5/100 = Rs. 7x

As profit is same,

5S.P - 5C.P = 8S.P - 8C.P

⇒ 9x/2 - 5C.P =  7x - 8C.P

⇒ - 5C.P + 8C.P = 7x - 9x/2

⇒ 3C.P = 5x/2

⇒ C.P = 5x/6

Mark up = M.P - C.P = x - 5x/6 = x/6

Mark up % = $\dfrac{Mark up}{C.P}× 100$

⇒ $\dfrac{\dfrac{x}{6}\ \rm\rm}{\dfrac{5x}{6}} \times 100$

⇒ ${{\dfrac{x}{6} \times\dfrac{6}{5x}}}\times 100$

⇒ 20%

∴ The required mark up % is 20%.

Given:

Ravi rowed a certain distance downstream in  $7\dfrac{1}{2}$ hours

And he too row the same distance upstream in  $12\dfrac{1}{2}$hours

Concept Used:

If 'b' is the speed of a boat and 's' is the speed of a stream then,

Upstream speed of boat = b - s

Downstream speed of boat = b + s

If distance is constant, then ratio of speed is inversely proportional to ratio of time.

Formula used:

Distance = Speed × Time

Speed of boat in still water = (Downstream speed of boat + Upstream speed of boat)/2

Calculation:

Downstream speed of boat = b + s = 12.5 km/hr

Upstream speed of boat = b - s = 7.5 km/hr

Speed of boat in still water = (Downstream speed of boat + Upstream speed of boat)/2

⇒ (12.5 + 7.5)/2 = 20/2 = 10 km/hr

According to the concept:

D_S : U_S = 12.5 : 7.5

D_T : U_T = 7.5 : 12.5

According to the question:

Twice the distance to be covered by still boat, then

Time = [(2 × 12.5 × 7.5)/10] = 37.5/2 = $18\dfrac{3}{4}$ hours

∴ Required time taken by Ravi in stiil water $18\dfrac{3}{4}$hours.

Hint

DS = Speed of downstream

US = Speed of upstream

DT = Distance of of downstream

UT = Distance of upstream

Additional Information

1. Still water: The water of a river or any other water body which is not flowing is known as still water.

2. Stream: It is the flowing water of a river which is moving at a certain speed.

3. Upstream: The boat or a swimmer moving against the stream is known as moving upstream (against the flow of water).

4. Downstream: The boat or a swimmer moving along the stream is known as moving downstream (along the flow of water).

5. If the speed of the boat or swimmer is X km/hr and the speed of the stream is Y km/hr,

a) The speed of the boat or swimmer in the direction of the stream is known as speed downstream. It is given by;

Speed downstream= (X + Y) km/hr

b) And, the speed of the boat or swimmer against the stream is known as speed upstream. It is given by;

Speed upstream= (X - Y) km/hr

Given:

The ratio of radius ∶ height = 4 ∶ 3

The area of the base = 154 cm2

Formula used:

Curved surface area of cone = πrl

l² = r² + h²  

Where,

r = Radius of cone

l = Slant height of cone 

h = Height of cone

Area of the base(circle) = πr²

Calculations: 

Let the radius and height of the cone be 4x and 3x respectively,

Area of base = πr²

⇒ 154 = 22/7 × (4x)²

⇒ x2 = (154 × 7)/22 

⇒ x2 = 49/16

⇒ x² = (7/4)²

⇒ x = 7/4

Now, Radius = 4x = 4 × 7/4 = 7 cm

Height = 3x = 3 × 7/4 = 21/4 cm

l2 = r2 + h2  

⇒ l = √[7² + (21/4)²]

⇒ l = √[49 + (5.25)²] = √(49 + 27.5625) = √(76.5625) = 8.75 cm 

Curved surface area of cone = πrl

⇒ [(22/7) × 7 × 8.75] = 192.5 cm²

∴ Curved surface area (in cm2) will be 192.5.

Concept Used:

Using BODMAS rule:

 

Calculation:

\dfrac{\left(7\dfrac{3}{4}\ \rm of\ \dfrac{5}{31}\right)\div\left(15\dfrac{1}{3}\ \rm of\ \dfrac{2}{23}\right)\times1\dfrac{1}{3}}{1\dfrac{2}{3}+\left[16\dfrac{1}{2}-\left{1\dfrac{1}{10}\times\left(3\dfrac{1}{3}+5\right)\right}\right]}

⇒ \dfrac{\left(\dfrac{31}{4}\ \rm of\ \dfrac{5}{31}\right)\div\left(\dfrac{46}{3}\ \rm of\ \dfrac{2}{23}\right)\times\dfrac{4}{3}}{\dfrac{5}{3}+\left[\dfrac{33}{2}-\left{\dfrac{11}{10}\times\left(\dfrac{10}{3}+5\right)\right}\right]}

⇒ $\dfrac{\dfrac{5}{4}\ \rm\div \dfrac{4}{3}\ \rm\times\dfrac{4}{3}}{\dfrac{5}{3}+\left[\dfrac{33}{2}-\dfrac{55}{6}\right]}$

 

⇒ $\dfrac{\dfrac{5}{4}\ \rm\times\dfrac{3}{4}\ \rm\times\dfrac{4}{3}}{\dfrac{5}{3}+\left[\dfrac{33}{2}-\dfrac{55}{6}\right]}$

⇒ $\dfrac{\dfrac{5}{4}\ \rm\rm}{\dfrac{5}{3}+\left[\dfrac{99 -55}{6}\right]}$

⇒ $\dfrac{\dfrac{5}{4}\ \rm\rm}{\dfrac{5}{3}+\dfrac{44}{6}}$

⇒ $\dfrac{\dfrac{5}{4}\ \rm\rm}{\dfrac{10 + 44}{6}}$

⇒ $\dfrac{\dfrac{5}{4}\ \rm\rm}{\dfrac{54}{6}}$

⇒ ${\dfrac{5}{4}\ }\times{\dfrac{6}{54}}$

⇒ $\dfrac{5}{36}$

∴ The value of \dfrac{\left(7\dfrac{3}{4}\ \rm of\ \dfrac{5}{31}\right)\div\left(15\dfrac{1}{3}\ \rm of\ \dfrac{2}{23}\right)\times1\dfrac{1}{3}}{1\dfrac{2}{3}+\left[16\dfrac{1}{2}-\left{1\dfrac{1}{10}\times\left(3\dfrac{1}{3}+5\right)\right}\right]} is $\dfrac{5}{36}$.

Given: 

3 men and 8 women can do a piece of work in 16 days

6 men and 7 women can do the same work in $12\dfrac{1}{2}$days

Formula:

Total work = Efficiency × Time Taken

Calculation:

Let efficiency of 1 man and 1 woman be x and y respectively

According to the question

(3x + 8y) × 16 = (6x + 7y) × 25/2

⇒ 96x + 256y = 150x + 175y

⇒ 96x – 150x = 175y – 256y

⇒ 54x = 81y

⇒ x/y = 81/54

⇒ x : y = 3 : 2

Suppose, x = 3 and y = 2

Total work = (3 × 3 + 8 × 2) × 16 = (9 + 16) × 16 = 400 units      ----(1)

Work done by 14 men and 'w' women in 8 days be = (14 × 3 + x × 2) × 8 = (42 + x)8      ----(2)

From equation (1) and equation (2):

(42 + 2x) × 8 = 400

⇒ 42 + 2x = 400/8

⇒ 42 + 2x = 50

⇒ 2x = 8

⇒ x = 4

∴ 4 women should assist 14 men to complete the same work in 8 days.

Given:

 

Calculation:

Total number of trees planted by X in cities A and D = 75 + 150 = 225

Total number of trees planted by Y in cities A and F = 150 + 300 = 450

Total number of trees planted by Z in cities B and D = 225 + 300 = 525

Required ratio = 225 : 450 : 525 = 3 : 6 : 7.

∴ The ratio between the total number of trees planted by X in cities A and D, the total number of trees planted by Y in cities A and F, and the total number of trees planted by Z in cities B and D is 3 : 6 : 7.

Given:

 

Calculation:

The difference between total number of trees planted by ‘X’ and ‘Y” in all the six cities = (150 + 175 + 200 + 200 + 300 + 300) - (75 + 125 + 250 + 150 + 200 + 225)= 1325 - 1025 = 300

Total number of trees planted by ‘Z’ in cities B, E and D = 225 + 175 + 300 = 700

Required% = (300/700) × 100 = 42.85% = 43%(approx)

∴ The Required% is 43%.

The correct answer is 'the'.

Key Points

• Articles are used before the noun to make them specific or unspecific.
• The indefinite article: There are two indefinite article- 'a' and 'an'. They are both used before nouns which are unspecific i.e. they give a general idea or thought and don't point towards anything that will be particular.
• Example: This is a lake.
• The definite article: The definite article 'the' is used before a noun which is specific i.e. unlike indefinite article they give a particular idea or thought.
• Example: This is the lake that was mentioned in yesterday's newspaper.
• Here, in the given sentence the noun i.e. 'qualification' is a specific noun as it is pointing towards the skills that will be specific to the job mentioned.
• Thus, article 'the' will be used in the blank.

Therefore, the correct sentence is: Vysakh was found to possess the required qualification for the job.

The correct answer is 'hadn't made'.

Key Points

• The given sentence is an example of the third conditional sentence.
• The third conditional sentence: The third conditional sentence is used to describe a situation that doesn't happen and it is used to imagine the result of this situation. It is known to describe a result of a hypothetical situation.
• Structure:
• If+ past perfect, would+have+past participle.
• Example:
• If she had studied, she would have passed the exam.
• She wouldn't have been tired if she had gone to bed earlier
• Thus, from the above-given explanation, it is clear that 'hadn't made' will be used in the blank.

Therefore, the correct answer is: If my husband hadn't made us a big dinner tonight, I would have suggested that we go to that nice Italian restaurant.

Additional Information

• ​Conditional Sentence: As the name suggests they are used to express conditions. This type of sentence contains two clauses-one is conditional clause which  is used to tell condition and another is main clause which is used to express the result of the conditional clause.
• These are of four types-
• Zero conditional sentence: These are used to tell facts that are generally true and do not change. 
• Structure: If+present simple, Present simple.
• Example: If you touch a fire, you get burned.
• First Conditional Sentence: These sentences are used to talk about things that might happen in the future.
• Structure: If+ present simple, simple future.
• Example: If I study today, I'll go to the party tonight.
• Second Conditional Sentence: These sentences are used to talk about things in the future that are probably not going to happen.
• Structure: If +past simple, would + the first form of verb.
• Example: If I won the lottery, I would buy a car.
• Third Conditional Sentence: The third conditional sentence is used to describe a situation that doesn't happen and it is used to imagine the result of this situation. It is known to describe a result of a hypothetical situation.
• Structure:
• If+ past perfect, would+have+past participle.
• Example:
• If she had studied, she would have passed the exam.