SSC GD Constable Previous Year Paper (Held on: 6th December 2021 Shift 2)

The logic followed here is :-

Hence, the correct answer is "691".

The logic followed here is :-

∴ Here, 'ROSE' is written as 'sic'.

Hence, the correct answer is "sic".

The figure that can replace the question mark (?) in the following series is as shown below :

• The symbol moves two steps anti-clockwise and becomes water image from figure 1 to figure 2.
• The symbol moves three steps anti-clockwise and becomes mirror image from figure 2 to figure 3.
• This process repeats.

 

Hence, the correct answer is "Option 4".

The logic followed here is :-

ATRG : BWSJ

Similarly,

MQSJ : ?

Hence, the correct answer is "NTTM".

Given,

The age of Anuj's grandfather is 4 times the age of Anuj.

Let us consider age of Anuj = X

Age of Anuj's grandfather is 4 times the age of Anuj.

Age of Anuj's grand father = 4X

Anuj's grandmother is 5 years younger than his grandfather.

Age of Anju's grand mother = 4X - 5

The total of age of Anuj's grandmother and grandfather is 107 years.

⇒ (4X - 5) + 4X = 107

⇒ 8X - 5 = 107

⇒ 8X = 112

⇒ X = 14

∴ Here, the age of Anuj is X = 14 years.

Hence, the correct answer is "14 years".

After unfolding the given paper the figure formed is as shown below :

Hence, the correct answer is "Option 2".

The logic followed here is :-

By using BODMAS RULE :

Option 1) : + and ÷

Given equation : 63 ÷ 21 – 7 + 28 × 3 = 144 

After interchanging the symbols in given equation the equation formed is as follows : 63 + 21 - 7 ÷ 28 × 3 = 144

⇒ 63 + 21 - 7 ÷ 28 × 3 = 144

⇒ 63 + 21 - 0.25 × 3 = 144

⇒ 63 + 21 - 0.75 = 144

⇒ 84 - 0.75 = 144

⇒ 83.25 ≠ 144

LHS ≠ RHS

Option 2) : × and +

Given equation : 63 ÷ 21 – 7 + 28 × 3 = 144 

After interchanging the symbols in given equation the equation formed is as follows : 63 ÷ 21 - 7 × 28 + 3 = 144

⇒ 63 ÷ 21 - 7 × 28 + 3 = 144

⇒ 3 - 7 × 28 + 3 = 144

⇒ 3 - 196 + 3 = 144

⇒ 6 - 196 = 144

⇒ - 190 ≠ 144

LHS ≠ RHS

Option 3) : ÷ and –

Given equation : 63 ÷ 21 – 7 + 28 × 3 = 144 

After interchanging the symbols in given equation the equation formed is as follows : 63 - 21 ÷ 7 + 28 × 3 = 144

⇒ 63 - 21 ÷ 7 + 28 × 3 = 144

⇒ 63 - 3 + 28 × 3 = 144

⇒ 63 - 3 + 84 = 144

⇒ 147 - 3 = 144

⇒ 144 = 144

LHS = RHS

Option 4) : + and –

Given equation : 63 ÷ 21 – 7 + 28 × 3 = 144 

After interchanging the symbols in given equation the equation formed is as follows : 63 ÷ 21 + 7 - 28 × 3 = 144

⇒ 63 ÷ 21 + 7 - 28 × 3 = 144

⇒ 3 + 7 - 28 × 3 = 144

⇒ 3 + 7 - 84 = 144

⇒ 10 - 84 = 144

⇒ - 74 ≠ 144

LHS ≠ RHS

Hence, the correct answer is "÷ and –".

The arrangement of the given words in the order in which they appear in an English dictionary is as shown below :

5. Marvellous
6. Midstream
7. Migraine
8. Modernize
9. Modification

Hence, the correct answer is "5, 3, 2, 4, 1".

The least possible Venn diagram for the given diagram is as shown below :

∴ Here, the number of rural government teachers who are NOT graduate is '2'.

Hence, the correct answer is "2".

Family chart :-

Family Tree :

There are seven members, S, T, U, V, W, X and Y, in a family. Five members are in different professions, namely Teacher, Doctor, Nurse, Engineer and Scientist. There are two married couples in the family.

1) S is a Doctor who is married to Y who is a Teacher and S is the brother of T.

2) W is a Scientist, who is the father-in-law of Y and X is the mother of T.

3) V and U are the children of S and studying in class 6th and 8th, respectively.

∴ Here, the wife of W is 'X'.

Hence, the correct answer is "X".

The logic followed here is :-

The alphabet positional value of given letter in a word is added +1 and subtracted -1.

FAX is written as EGZBWY.

Similarly,

SKIN will be written as :

Hence, the correct answer is "RTJLHJMO".

Six friends, Ajay, Neetu, Seema, Kavita, Manoj and Vijay, are sitting around a circular table, with their backs towards the centre of the table.

1) Ajay is sitting to the immediate left of Seema and Manoj is sitting between Seema and Neetu.

2) Kavita is not the neighbour of Neetu.

∴ Here, 'Vijay' is sitting third to right of Seema.

Hence, the correct answer is "Vijay".

The correct mirror image of the given combination when the mirror is placed at AB is as shown below :-

Hence, the correct answer is "Option 2".

The logic followed here is :-

The alphabet positional value of letters of given word × 2.

‘BATTLE’ is coded as ‘4240402410’.

Similarly,

‘KINGDOM’ will be coded as :

Hence, the correct answer is "2218281483026".

The logic followed here is :-

Hence, the correct answer is "OSV".

The logic followed here is :-

Hence, the correct answer is "225".

The least possible Venn diagram for the given statements is as shown below :

Conclusions: 

I. No employer is an expert → True (As All experts are creative and No creative is an employer so, No employer is an expert is true)

II. No worker is an employer → True (As All workers are experts and All experts are creative and No creative is an employer so, No worker is an employer is true)

∴ Here, Both the conclusions I and II are true.

Hence, the correct answer is "Both conclusions I and II follow".

The logic followed here is :-

Kabul is capital of Afghanistan

Similarly,

Canberra is capital of Australia.

Additional Information

Hence, the correct answer is "Australia".

From the given dice 1 and dice 2.

Dice 1 is rotated 90⁰ clockwise so the opposite side are obtained :

∴ Here, the opposite side of '3' is '5'.

Hence, the correct answer is "5".

The logic followed here is :-

44, 70, 57

 

Similarly,

34, 68, 51

Hence, the correct answer is "34, 68, 51".

The figure embedded in the given options is as shown below :

Hence, the correct answer is "Option 3".

Seven friends are sitting around a circular table facing the centre.

1) Raj is second to the left of Sachin and Dinu is second to the right of Sachin.

2) Raj is fourth to the right of Veer and Dinu is between Krip and Veer.

3) Rocky is second to the right of Sam.

∴ Here, 'Rocky' is second to the left of Veer.

Hence, the correct answer is "Rocky".

The logic followed here is :-

1) LQS

2) RWY

3) RXZ

4) FKM

∴ Here, 'RXZ' is different from other three alternatives.

Hence, the correct answer is "RXZ".

The logic followed here is :-

First digit × Second digit of the First number = Second number

• 48 : 32 → 4 × 8 = 32
• 73 : ? → 7 × 3 = 21
• 25 : 10 → 2 × 5 = 10

Hence, the correct answer is "21".

Given :- K_TQ_KPT_R_PTQ_KP_QR

By checking options and substituting accordingly.

1) P, K, Q, R, T, R → K P T Q K - K P T Q R - R P T Q T - K P R Q R

2) P, R, T, P, K, Q → K P T Q R - K P T T R - P P T Q K - K P Q Q R

3) P, K, R, Q, R, T → K P T Q K - K P T R R - Q P T Q R - K P T Q R

4) P, R, Q, K, R, T → K P T Q R - K P T Q R - K P T Q R - K P T Q R

• Here, "KPTQR" is repeated.
• Option (4) gives the pattern of :- K P T Q R - K P T Q R - K P T Q R - K P T Q R

Hence, the correct answer is "P, R, Q, K, R, T".

The correct answer is Muslim League.

Key Points

• The Muslim League Council was declared 16th August 1946 as the ‘Direct Action Day’ in order to kept their demand for the separate Muslim country after the Britishers left the Indian subcontinent. Their main objective was to claim a different country with a Muslim majority population.
• This day also known as the Great Calcutta Killings, was a day of Widespread Communal Riots between the Hindus and the Muslims in the city of Calcutta in the Bengal province of British India.
• This Action Day was initiated by Mohammad Ali Jinnah. The purpose of Direct Action Day was when the Cabinet Mission plan of 1946 Failed a way between the Indian National Congress and the Muslim League for a united India as the League wanted a separate land for the Muslims population.

Additional Information

• Swaraj Party was formed on  1 January 1923.
• Chittaranjan Das, Narasimha Chintaman Kelkar and Motilal Nehru formed the Congress-Khilafat Swarajaya Party with Das as the president and Nehru as one of the secretaries.
• The Oudh Kisan Sabha was founded in 1920 by Baba Ram Chandra.
• He was a trade unionist who gathered Oudh's farmers and led the first anti-landlord demonstration.
• Jawaharlal Nehru, Baba Ramchandra and others founded the Oudh Kisan Sabha, commonly known as the Oudh Kisan Sabha.
• The Indian National Congress (INC), a political party in India, was founded in 1885. INC conducted its first session in Bombay from 28 to 31 December 1885.
• Dadabhai Naoroji is also known as the "Grand Old Man of India" and "official Ambassador of India".
• He was a Liberal Party Member of Parliament (MP) in the United Kingdom House of Commons between 1892 and 1895.

The correct answer is Indra Navy.

Important Points

• The Indian Navy and Russian Navy commenced the 11th edition of bilateral maritime exercise called India Navy 2020.
• The 11th edition of exercise INDRA NAVY, a biennial bilateral maritime exercise between the Indian Navy and Russian Navy is scheduled in the Bay of Bengal from 04 to 05 September 2020.
• Initiated in 2003, EX INDRA NAVY epitomises the long-term strategic relationship between the Navies of India and Russia.
• The primary aim of exercise INDRA NAVY-20 is to further consolidate inter-operability built up by the two Navies over the years and also to enhance understanding and procedures for multi-faceted maritime operations.
• The Indian Navy will be represented by guided-missile destroyer Ranvijay, indigenous frigate Sahyadri and fleet tanker Shakti, along with their integral helicopters.
• The last edition of the exercise was conducted off Visakhapatnam in December 2018.

The correct answer is A Night of Knowing Nothing.

Key Points

• A Night of Knowing Nothing won the Oeil d'or (The Golden Eye) award for best documentary at the 74th Cannes Film Festival.
• The Mumbai-based filmmaker and director Payal Kapadia's "A Night of Knowing Nothing" won the Oeil d'Or (GoldenEye) award for best documentary at the 74th Cannes Film Festival on 17 July 2021.
• Kapadia, an alumna of the Film and Television Institute of India (FTII), also has films such as the documentary "And What is the Summer Saying" (2018) and "Last Mango Before the Monsoon", to her credit.
• In 2016, the Indian film "The Cinema Travellers", directed by Shirley Abraham and Amit Madheshiya, earned an Oeil d'or Special Mention.

Additional Information

• Casablanca Beats is a 2021 Moroccan drama film directed by Nabil Ayouch.
• In June 2021, the film was selected to compete for the Palme d'Or at the 2021 Cannes Film Festival.
• The Velvet Underground was an American rock band formed in New York City in 1964.
• Titane is a 2021 body horror drama film written and directed by Julia Ducournau.

The correct answer is Gujarat.

Key Points

• Champaner-Pavagadh Archaeological Park is located in the Panchmahal District of Gujarat State in north-western India, features a concentration of archaeological, historical, and living cultural heritage properties cradled in an  impressive landscape.
• It includes prehistoric (chalcolithic) sites, a hill fortress of an early Hindu capital, and remains of the 16th-century capital of the state of Gujarat.
• The site also includes, among other vestiges, fortifications, palaces, religious buildings, residential precincts, agricultural structures and water installations, from the 8th to 14th centuries.
• The Kalikamata Temple on top of Pavagadh Hill is considered to be an important shrine, attracting large numbers of pilgrims throughout the year.
• The site is the only complete and unchanged Islamic pre-Mughal city.

Additional Information

• Gujarat:
• Chief Minister - Bhupendrabhai Patel
• Governor - Acharya Devvrat.
• Number of Districts - 33.

The correct Answer is 1986.

Key Points

• The Central Rural Sanitation Programme, which was started in 1986.
• It was one of India’s first efforts to provide safe sanitation in rural areas.
• This programme focussed mainly on providing subsidies to people to construct sanitation facilities.
• A study done by the government in 1996-97 showed that it was more important to raise awareness about sanitation as a whole rather than to just provide subsidies for construction.
• This understanding marked the first shift in the programme.
• In 1999, a restructured Total Sanitation Campaign (TSC) was initiated to create supply-led sanitation by promoting local sanitary marts and a range of technological options.

Additional Information​ 

• The rural sanitation campaign has the following as its objectives:
• Accelerate sanitation coverage in rural areas.
• Generate a push from the people to get facilities rather than expect the Government to do it (demand-led promotion).
• Focus on intensive education and awareness campaigns to ensure that people understand the need for safe sanitation.
• Take the scheme beyond rural households to rural schools and nursery schools. Here again, the emphasis was placed on promoting good hygiene practices.
• Promote cost-effective and appropriate technologies.
• Through all the above, improve the health and quality of life in rural areas.

The correct answer is code of conduct.

Important Points

• A compilation of norms and guidelines to be followed by political parties and contesting candidates at the time of election is called code of conduct.
• Code of Conduct is a set of norms and guidelines to be followed by the political parties and contesting candidates during election time.
• The Election Commission of India issues a set of guidelines for candidates and political parties to follow during elections.
• Speeches, polling booths, polling day conduct, election manifestos, processions, and general conduct are all covered under the criteria.
• It comes into effect as soon as the election schedule is announced by the Election Commission of India.
• Respective parties are required to notify the local police department in advance of scheduled meetings, providing accurate information on the location and time, in order to maintain law and order and control traffic in the area.
• During the election process, government bodies are barred from participating in any recruitment procedure.
• Kerala was the first state in India to use the model code of conduct in its elections in 1960.

The correct answer is Gahadavala.

Key Points

• In the battle of Chandawar (1194 CE) King Jaichand was defeated by Muhammad Gori.
• The present geographical location of Chandawar is Etawah district in U.P. at the bank of river Yamuna.
• King Jai Chand was defeated by Muhammad Ghori in the Battle of Chandawar.
• The Battle of Chandwar took place between 1193 and 1194 CE.

Additional Information

• The Gahadavala dynasty also Gahadavalas of Khanauj, were among the rulers of the Indian subcontinent, that ruled parts of the present-day Indian states of Uttar Pradesh and Bihar, during 11th and 12th centuries.
• Their capital was located at Varanasi in the Gangetic plains, and for a brief period, they also controlled Kanyakubja (modern Kannauj).

The correct answer is 9.

Key Points

• In 9 countries was the international version of the UMANG mobile app launched by Ravi Shankar Prasad in coordination with Ministry of External Affairs in November 2020.
• The international version of the UMANG App is for select countries including US, UK, Canada, Australia, UAE, Netherlands, Singapore, Australia and New Zealand.
• On the completion of three years of the UMANG (Unified Mobile Application for New-age Governance) app, the international version of the app has been launched.

Additional Information

• Ministry of Electronics and Information Technology developed the UMANG mobile application in 2017.
• UMANG (Unified Mobile Application for New-age Governance) is a Government of India all-in-one single, unified, secure, multi-channel, multi-platform, multi-lingual, multi-service mobile application.
• UMANG is developed by the Ministry of Electronics and Information Technology (MeitY) and National e-Governance Division (NeGD) to drive Mobile Governance in India.
• UMANG provides a single platform for all Indian Citizens to access pan India e-Gov services ranging from Central to Local Government bodies and other citizen-centric services.
• UMAG is supported by a robust back-end platform providing access to high impact services of the various organisation including both Central And State Government.

The correct answer is 1911.

Key Points

• The first Indian commercial bank which was wholly owned and managed by Indians was established in 1911.
• First Indian commercial bank which was wholly owned and managed by Indians was Central Bank of India which was established in 1911.

Additional Information

• Oudh Commercial Bank was established in the year 1881 and ceased operation in 1958.
• It was a privately-owned bank, and its headquarters was in Faizabad.
• Oudh Commercial Bank only served locals and had no branches.
• Allahabad Bank was established in 1865.
• Punjab National was established in 1894.
• Bank Bank of India was established in 1906.

The correct answer is Manmohan Singh.

Key Points

• The author of the book “Changing India” is the former Prime Minister Dr. Manmohan Singh.
• It is a five-volume book and published by Oxford University Press.
• The book covers the social, political and economic issues that Singh faced in his 10 years tenure as a PM.

Additional Information

• Some facts about Manmohan Sing:
• He is an Indian economist and politician who served as the Prime Minister of India from 2004 to 2014.
• He became the first PM after Jawahar Lal Nehru to be re-elected after completing his five years tenure. Now our present PM Narendra Modi become the third PM of India who was re-elected after completing his tenure.
• He was the 15th Governor of the Reserve Bank of India.

The correct answer is Sudeep Tyagi.

Key Points

• Sudeep Tyagi announced his retirement from all formats of the game in November 2020.
• Former India pacer Sudeep Tyagi announced retirement from all formats of the game.
• The 33-year-old played four ODIs -- from which he took three wickets -- and one T20 International.
• He featured in 14 Indian Premier League matches for Chennai Super Kings and Sunrisers Hyderabad.
• Tyagi played 41 first-class matches from which he picked 109 wickets and also featured in 23 List A matches.

Additional Information

• Indian cricketers who retired from international cricket in 2020 are as follows.
• MS Dhoni
• Suresh Raina
• Parthiv Patel
• Rajat Bhatia
• Irfan Pathan
• Wasim Jaffer
• Pragyan Ojha
• Sudeep Tyagi

The correct answer is Kerala.

Key Points

Hence Kerala has population density more than 800.

Additional Information

• As per the 2011 Census, the density of population in Delhi worked out at 11320 persons per square kilometer.
• The availability of jobs and economic activities within the region lead to an increase in population density.
• The population density of India in 2011 was 382 per sq km.
• Population density is the measure of the number of people per unit area.
• Population density data can be used to quantify demographic information and assess relationships with ecosystems, human health, and infrastructure.

The correct answer is Human beings.

Key Points

• Human beings are the producers and consumers of the earth’s resources.
• Human beings are the producers and consumers because they only produce food in the earth.
• And they also depend on plants and animals to eat.so humans are called the producers and consumers.

Additional Information

• Every organism depends on other organisms for food material and all organisms are (producers to consumers) arranged in series in which food energy is transferred through repeated eating and being eaten.
• The green plant in the ecosystem is called producers.
• Producers prepare food from solar energy(sun).
• All the heterotrophs of the ecosystem are known as consumers.
• Consumer, directly and indirectly, depends on the producers for food.

The correct answer is Muhammad Bin Qasim.

Key Points

• In 712 AD, Muhammad Bin Qasim conquered the Sind province.
• It was the first Arab victory in India and it led to the foundation for Arab invasion in India.
• Qasim succeeded in conquering Sind in his third attempt in which he defeated Dahir, the King of Sind.

Additional Information 

• Muhammad bin Qasim was born on 31st December, 695 AD and he is also known as Laquab of Imad-ad-Din.
• During the invasion of Mohammad Bin Qasim, many Hindus in Sindh were forcibly converted to Islam and they were reconverted to Hinduism by the authority of Devala Smriti.
• Mohammad Bin Qasim was the first Muslim to invade India in 712 AD and was the commander of the Umayyad Caliphate.
• He was sent as a prisoner to Mesopotamia.
• In 711 AD he defeated Raja Dahir.

The correct answer is Lakshmi Vilas Bank Ltd.

Key Points

• Lakshmi Vilas Bank Ltd was placed under moratorium for a period of one month by the Reserve Bank of India in November 2020.
• The RBI appointed the Committee of Directors (CoD) composed of three independent directors Meeta Makhan, Shakti Sinha, and Satish Kumar Kalra.
• The committee will be headed by Meeta Makhan.
• After shareholders ousted seven directors of the board, the Reserve Bank of India has approved the appointment of a three-member Committee of Directors (CoD) to run the daily affairs of debt-ridden Lakshmi Vilas Bank (LVB).
• This CoD will exercise the discretionary powers of MD & CEO in the ad-interim.

Additional InformationImportant information related to Banks:(Sept 2022)

The correct answer is Trail.

Key Points

• The full form of VVPAT is Voter Verifiable Paper Audit Trail.
• T stands for Trail.
• In the context of Elections in India, the term VVPAT stands for Voter Verifiable Paper Audit Trail.
• VVPAT is the system that allows voters to verify their votes.
• The VVPAT machine prints a slip along with the name of the candidate and the corresponding election symbol and automatically drops it in a sealed box.
• It was first introduced in India in 2013.
• VVPAT was first used in Noksen (assembly constituency) in Nagaland.
• It can be accessed by polling officers only.
• During the 2019 general election, VVPAT was introduced in all 543 Lok Sabha constituencies.

Additional Information

• Some important Abbreviations

The correct answer is Sanskrit.

Key Points

• ​Prayag is an ancient name of Allahabad as it is the meeting place or ‘Sangam’ of rivers Ganga, Yamuna, and Sarasvati.
• Prashasti means “in praise of someone”.
• Prayag Prashasti is the name given to the Allahabad Pillar.
• It is an Ashokan Stambh and has 4 different inscriptions.

Additional Information

• Harisena, also Harishena or Hirisena, was a 4th-century Sanskrit poet, panegyrist, and government minister.
• He was an important figure in the court of the Gupta emperor, Samudragupta.
• His most famous poem, written c. 345 CE, describes the bravery of Samudragupta and is inscribed on the Prayag-Prasasti inscription (Allahabad Pillar Inscription).
• ​Thus, we can say that Harisena wrote Prayag Prashasti.

The correct answer is  Rajasthan.

Key Points

• The mountain peaks Delwara and Jarga located at Rajasthan.
• Delwara is located in Sirohi district.
• Its height is 1442 metres.
• The highest peak of Udaipur-Rajsamand Aravali hills is Jarga.
• The Aravalli Range is also known as Jarga near Udaipur.
• Jarga hill is confined to Udaipur and Rajsamand districts in southern Aravallis.
• Its height is 1431 metres.

Additional Information

• Achalgarh is located in Sirohi district.
• Its height is 1380 metres.
• Guru Shikhar is the highest peak in Rajasthan.
• Its height is 1722 metres.
• Ser Peak is located in Sirohi​
• Its height is 1597 metres.

The correct answer is Rs. 250.

Key Points

• Rs. 250 is the present minimum yearly deposit required under the popular girl child savings scheme ‘Sukanya Samriddhi Yojana’.
• Sukanya Samriddhi Yojana is a savings scheme launched by the government of India.
• The scheme targeted the parents of girl children in India.
• The scheme was launched in 2015.
• It was launched by prime minister Narendra Modi.
• It was launched as a part of the Beti Bachao, Beti Padhao campaign.

Additional Information

• The Sukanya Samriddhi Account can be opened any time after the birth of a girl child till she turns 10, with a minimum deposit of Rs. 1,000 and a maximum of Rs. 1.5 lakh can be deposited during the ongoing financial year.
• The account will remain operative for 21 years from the date of its opening or till the marriage of the girl after she turns 18.
• The account allows 50% withdrawal at the age of 18 for higher education purposes.
• The interest rate is fixed by the government and revised quarterly.
• From April 2020, this scheme offers an interest rate of 7.6% compounded annually.
• Parents can now open up to two Sukanya Samriddhi Account for girls and a third account can be opened in case of birth of twins/triplets.
• The minimum annual contribution to the Sukanya Samriddhi Account is Rs.250 and the maximum of Rs.1.50 lakh in a financial year.
• Subscribers have to invest at least the minimum amount every year for up to 15 years from the date of account opening. Thereafter the account will continue to earn interest till maturity.

The correct answer is Vagir.

Key Points

• In November 2020, Indian Navy's fifth Scorpene class submarine Vagir was launched at Mumbai's Mazagon Dock.
• INS Vagir (S25) is the fifth submarine of the first batch of six Kalvari-class submarines for the Indian Navy.
• The submarine was launched in Nov 2020 from the Kanhoji Angre Wet Basin of Mazagon Dock Shipbuilders Limited (MDL).
• The submarine would be named Vagir, after commissioning.
• It is scheduled for delivery to the Indian Navy in the year 2022 after the completion of other trials.

Additional Information

• ​ In 1997, the Indian Ministry of Defence approved a plan to acquire 24 submarines under Project 75.
• After the Kargil War in 1999, Cabinet Committee on Security approved a 30-year submarine building plan that called for two parallel production lines, each constructing six submarines.
• The first submarine, INS Kalvari (Malayalam: tiger shark), was launched on 28 October 2015 and commenced sea trials on 1 May 2016.

The correct answer is calcium oxide.

Key Points

• In a chemical reaction, calcium oxide reacts vigorously with water to produce calcium hydroxide releasing a large amount of heat.
• Calcium oxide reacts vigorously with water to produce slaked lime (calcium hydroxide) releasing a large amount of heat.

CaO (s) + H2O (l) → Ca(OH)2 (aq) + Heat

Additional Information

• In the above reaction, calcium oxide and water combine to form a single product, calcium hydroxide.
• Such a reaction in which a single product is formed from two or more reactants is known as a combination reaction.
• The reaction produces a slaked lime solution, which is used to whitewash walls. Calcium hydroxide slowly reacts with carbon dioxide in the air, forming a thin layer of calcium carbonate on the walls. After two to three days of whitewashing, calcium carbonate forms and gives the walls a shiny finish.

Ca(OH)2 (aq) + CO2 (g) → CaCO3 (s) + H2O (l)

The correct answer is 7 September.

Key Points

• The International Day of Clean Air for blue skies is observed globally on September 07 to promote and facilitate actions to improve air quality.
• The very first International Day of Clean Air for blue skies was held on September 7th, 2020.
• The Day aims to raise public awareness at all levels that clean air is important for health, productivity, the economy and the environment.
• The UN General Assembly adopted the resolution to hold an International Day of Clean Air for blue skies on December 19, 2019, during its 74th session.

Additional Information

The correct answer is Bhavai.

Key Points

• Goddess Amba is the presiding deity of Bhavai dance/drama performances.
• Bhavai Dance is a very difficult form of dance performed by skilled experts.
• In this dance, women dancers balance 8 to 9 pitchers on their heads and dance simultaneously.
• And sway with the soles of their feet perched on the top of a glass and also sometimes on the edge of a naked sword.
• This dance is believed to be originated in Gujarat.

Additional Information

The correct answer is Football.

Key Points

• Football is related to the ‘CONCACAF Gold Cup’.
• The Confederation of North, Central America, and Caribbean Association Football is abbreviated as CONCACAF.
• It is one of FIFA's six continental governing bodies for association football.
• It is the third-most successful FIFA confederation.
• Its 41 member associations represent countries and territories.

Additional Information

The correct answer is Swimming.

Key Points

• Michael Phelps
• He is ​an American former competitive swimmer.
• He is the most successful and most decorated Olympian of all time with a total of 28 medals.
• Phelps also holds the record for Olympic gold medals with a total of 23 medals.
• Phelps is the long course world record holder in the men's 400-meter individual medley as well as the former long course world record holder in the 200-meter freestyle, 100-meter butterfly, 200-meter butterfly, and 200-meter individual medley.​

Additional Information 

• Olympics 
• Olympic Games originated in ancient Greece.
• The Summer Olympics have been held every four years since 1896"
• The honour of holding the Olympic Games is entrusted to a city, not to a country.
• The architect of the modern Olympics Games was Pierre, baron de Coubertin.

Given: 

A takes 10 days more than B to finish a task.

They both do the work together for 5 days and finish part of the work.

Concept used:

The time is taken by A to complete the work = a

The time is taken by B to complete the work = b

The amount of work done = L.C.M of (a and b) = c

Efficiency of A = $\frac{c}{a}$

Efficiency of B = $\frac{c}{b}$

Calculation:

According to the question,

Let the time taken by B to complete the work = x days

The time taken by A to complete the work = x + 10 days

The amount of work done = (x)(x + 10)

Efficiency of A = $\frac{(x)(x+10)}{x+10}$ = x units a day

Efficiency of B = $\frac{(x)(x+10)}{x}$ = (x + 10) units a day

Now, 

The amount of work done by A in 5 days = 5x

The amount of work done by B in 5 days = 5(x + 10) = 5x + 50

The total amount of work done in 5 days = 5x + 5x + 50 = 10x + 50

Again according to the question,

⇒ 10x + 50 = $\frac{8}{{15}}$ of (x)(x + 10)

Now by using the value of option.

Option A: x = 15

⇒ 10(15) + 50 = $\frac{8}{{15}}$ of (15)(15 + 10)

⇒ 150 + 50 = 8 × 25

⇒ 200 = 200

Therefore, the time is taken by B to complete the work = 15 days

Therefore, '15 days' is the required answer.

<br>

Shortcut Trick

A takes 10 days more than B to finish a task.

They both do the work together for 5 days and finish $\frac{8}{{15}}$  part of the work. 

<br>

⇒ $8\over15$(Total work) = 5 Days  

<br>

⇒ Total work = $15\times5\over 8$  Days

⇒ Total work = 75/8 Days    ..... (1)

<br>

Now we will help from the option,

<br>

Option (1) - B = 15 Days

⇒ A = 15 + 10 = 25 Days  

<br>

⇒ They both do the work together,

⇒ ${Total work\over Efficiency} = {75\over8}$ Days, which is equal to the value given in eq (1)

<br>

Hence, the correct answer is 15 days.

Concept used:

Calculation:

According to the question,

⇒ ? = 4 × 6 ÷ 4 of 6 - 6 ÷ 2 × (4 - 6) + 4 + 2 × 3 ÷ 6 of $\frac{1}{{3}}$

⇒ ? = 4 × 6 ÷ 24 - 6 ÷ 2 × (-2) + 4 + 2 × 3 ÷ 2

⇒ ? = 4 × 0.25 - 3 × (-2) + 4 + 2 × 1.5

⇒ ? = 1 + 6 + 4 + 3

⇒ ? = 14

Therefore, '14' is the required answer.

Shortcut Trick

Amount of 4 years = 894

Amount of 3 years = 820

Amount in 1 year = 894 - 820

⇒ 74, which is also the simple interest earned in one year on the principal amount.

Interest accumulated in 9 years, 

⇒ 9 × 74 = Rs. 666

Hence, the correct is Rs. 666

Alternate Method

Given:

Amount at simple interest in 3 years = Rs. 820

Amount at simple interest in 4 years = Rs. 894

Time = 9 years

Concept used:

S.I = $\frac{PRT}{100}$

A = P + S.I

Where, A = Final amount, P = principal, R = rate of interest, and T = time of investment

Calculation:

According to the question,

P + $\frac{PR(3)}{100}$ = 820

⇒ P(1 + $\frac{3R}{100}$) = 820    ----(1)

Similarly, P(1 + $\frac{4R}{100}$) = 894    ----(2)

On dividing the equation (2) by (1), we get,

⇒ $(1 + 4R/100)\over(1+3R/100)$ = $894\over820$

⇒ $100+4R \over100 +3R$ = $447\over410$

⇒ 41000 + 1640R = 44700 + 1341R

⇒ 3700 = 299R

⇒ R = $\frac{3700}{299}$%

Now, on substituting the value of R in equation (1) or (2), we get,

⇒ P = $\frac{820 × 299}{410}$

Again according to the question,

Time = 9 years, Simple Interest will be

⇒ S.I = $\frac{820 × 299}{410} × \frac{3700}{299} × 9 × \frac{1}{100}$

⇒ S.I = 666

Hence, Rs. 666 is the required answer.

Shortcut Trick

Let the Selling Price (SP) of 1 article be ₹1.

Total SP of 30 articles → ₹30.

Profit → SP of 8 articles = ₹8.

Cost Price (CP) = SP − Profit = 30 − 8 = ₹22.

Profit % = (Profit ÷ CP) × 100 = (8 ÷ 22) × 100 = 400/11% = 36⁴/₁₁%.

∴ The correct answer is 36⁴/₁₁%.

Alternate Method

Given: Number of articles sold = 30. Profit = SP of 8 articles.

Formula Used: Profit = SP − CP; Profit % = (Profit/CP) × 100.

⇒ Let SP of 1 article = x.

⇒ Total SP (30 articles) = 30x.

⇒ Profit = 8x.

⇒ Total CP = 30x − 8x = 22x.

⇒ Profit % = (8x ÷ 22x) × 100

⇒ Profit % = (4 ÷ 11) × 100 = 400/11

⇒ Profit % = 36⁴/₁₁%.

∴ The correct answer is 36⁴/₁₁%.

Additional Information

Profit/Loss based on Quantity

If profit is expressed in terms of Selling Price, then CP = Total SP − Profit SP. If expressed in terms of Cost Price, then Profit % = (Profit Quantity / Total Quantity) × 100.

Successive Discounts

Two successive discounts of a% and b% are equivalent to a single discount of [a + b − (ab/100)]%.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount. The ratio CP/MP = (100 − D%)/(100 + P%).

Given:

A train covers a distance of 14 km in 10 min.

Its speed is decreased by 4 km/h in the second case.

Concept used:

Speed = $\frac{distance}{time}$

Calculation:

The time taken by the train to cover 14 km = 10 min = $\frac{10}{60}$ hour

The speed of train = $\frac{14}{\frac{10}{60}}$ = 84 kmph

The decreased speed = 84 - 4 = 80 kmph

The time taken by the train to cover the same distance = $\frac{14}{80}$ × 60 = 10$\frac{1}{2}$ min

∴ 10$\frac{1}{2}$ min is the required answer.

Given:

The ratio of acid and water in solution A is 1 ∶ 5 and that in solution B is 2 ∶ 7.

Equal quantities of both solutions are mixed

Calculation:

In solution A:

The amount of acid = 1 unit

The amount of water = 5 units

The total unit of acid and water in solution A = 6 units

In solution B:

The amount of acid = 2 unit

The amount of water = 7 units

The total unit of acid and water in solution A = 9 units

∵ The quantity of both solutions are mixed in equal quantity 

∴ Multiply the ratio of acid and water in solution A by 9 and multiply the ratio of acid and water in solution B by 6.

The ratio of acid and water in solution A = 9 ∶ 45 

The ratio of acid and water in solution B = 12 ∶ 42

The total quantity of acid in the final solution,

⇒ 9 + 12 = 21 units

The total quantity of water in the final solution,

⇒ 45 + 42 = 87 units

The required ratio of acid and water = 21 : 87 = 7 : 29

Hence, '7 : 29' is the required answer.

Given:

The profit is 120% of the cost.

If the cost increases by 20% but the selling price remains the same.

Concept used:

Profit = Selling price - Cost price

Calculation:

Let the cost price of the article = Rs. 100

According to the question,

The profit earned = 120% of 100 = Rs. 120

∴ The selling price of the article = Rs. 100 + Rs. 120 = Rs. 220

If the cost price increases by 20%,

The cost price of the article = (100% + 20%) × 100 = 120

The profit earned = Rs. 220 - Rs. 120 = Rs. 100

The required percentage = $\frac{100}{220}$ × 100 = 45.45%

∴ '45.45%' is the required answer.

Given:

Ravina saves $16\frac{2}{3}$% of her monthly income.

When her monthly expenses increase by 10% (income remains the same), she is able to save Rs. 1,275 a month.

Calculation:

Let x be the monthly income of Ravina.

The amount Ravina saves = 16$\frac{2}{3}$% of x = $\frac{x}{6}$

The monthly expenses of Ravina = x - $\frac{x}{6}$ = $\frac{5x}{6}$

According to the question,

The increased monthly expenses = (100% + 10%) of $\frac{5x}{6}$ = $\frac{5.5x}{6}$

The amount Ravina saves = x - $\frac{5.5x}{6}$ = $\frac{0.5x}{6}$

Now,

⇒ $\frac{0.5x}{6}$ = 1275

⇒ x = Rs. 15300

∴ 'Rs. 15300' is the required answer.

Alternate Method

Ravina saves 1/6th of the monthly income,

Thus, if Income = 6a then, savings = a 

Then expenditure = 6a - a = 5a

When expenditure increases by 10%, 

New expenditure = 5a × 110/100

⇒ 5.5a

Now, new savings = 6a - 5.5a 

0.5a, which is equal to Rs. 1275.

⇒ a = 2550

Monthly income = 6a

⇒ 6 × 2550 = 15300.

Hence, the correct answer is Rs. 15300

Given:

The HCF of 767, 1003 and 2773 is x.

Calculation:

First, take the largest value 2773 as the dividend and the smallest value 767 as the divisor.

Now take the remaining value of 1003 as a dividend and the common factor as 59.

The HCF of 767, 1003 and 2773 is 59.

Therefore, '55 and 60' is the required answer

Shortcut Trick

HCF is the highest common divisor: All numbers 15, 20, 25, 30 are divisible by 5.

LCM is the lowest common multiple: LCM(15, 20, 25, 30) = 300.

Required Sum = LCM + HCF = 300 + 5 = 305.

∴ The correct answer is 305.

Alternate Method

Given: The numbers are 15, 20, 25, and 30.

Formula Used: Sum = LCM + HCF; Prime Factorization method for LCM and HCF.

Step-by-step Calculations:

⇒ Prime factorization of 15 = 3 × 5

⇒ Prime factorization of 20 = 2² × 5

⇒ Prime factorization of 25 = 5²

⇒ Prime factorization of 30 = 2 × 3 × 5

⇒ HCF (highest common factor) = 5¹ = 5

⇒ LCM (lowest common multiple) = 2² × 3¹ × 5²

⇒ LCM = 4 × 3 × 25 = 300

⇒ Required Sum = LCM + HCF = 300 + 5

⇒ Required Sum = 305

∴ The correct answer is 305.

Additional Information

Product of Two Numbers

For any two numbers 'a' and 'b', the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

HCF and LCM of Fractions

HCF of fractions = (HCF of Numerators) ÷ (LCM of Denominators). LCM of fractions = (LCM of Numerators) ÷ (HCF of Denominators).

Co-prime Numbers

Two numbers are called co-prime if their HCF is 1. In such cases, their LCM is simply the product of the two numbers.

Given:

If x2 ∶ y2 = 4 ∶ 9 and 2 ∶ x = 1 ∶ 2

Calculation:

According to the question,

2 ∶ x = 1 ∶ 2

⇒ $\frac{2}{x}$ = $\frac{1}{2}$

⇒ x = 4    ----(1)

Again according to the question,

⇒ $\frac{x^2}{y^2}$ = $\frac{4}{9}$

From equation (1), we get,

⇒ $\frac{4^2}{y^2}$ = $\frac{4}{9}$

⇒ y² = 36

⇒ y = 6

Therefore, '6' is the required answer.

Shortcut Trick

Apply Componendo and Dividendo on (2x + 3y) / (3y − 2x) = 3 / 1.

⇒ 3y / 2x = (3 + 1) / (3 − 1) = 4 / 2 = 2

⇒ y / x = 4 / 3 → Substitute x = 3 and y = 4.

⇒ Required Ratio = (3 × 3 + 4 × 4) : (3 × 3 − 4) = 25 : 5 = 5 : 1.

∴ The correct answer is 5 : 1.

Alternate Method

Given: (2x + 3y) : (3y − 2x) = 3 : 1

Formula: If a : b = c : d, then a/b = c/d. Use substitution for the target ratio.

⇒ (2x + 3y) / (3y − 2x) = 3 / 1

⇒ 1 × (2x + 3y) = 3 × (3y − 2x)

⇒ 2x + 3y = 9y − 6x

⇒ 2x + 6x = 9y − 3y

⇒ 8x = 6y → x/y = 6/8 = 3/4

⇒ Substitute x = 3k and y = 4k into (3x + 4y) / (3x − y)

⇒ [3(3k) + 4(4k)] / [3(3k) − 4k] = (9k + 16k) / (9k − 4k)

⇒ 25k / 5k = 5 / 1

∴ The correct answer is 5 : 1.

Additional Information

Componendo and Dividendo Rule

If a/b = c/d, then (a + b) / (a − b) = (c + d) / (c − d). This simplifies equations involving ratios of sums and differences.

Duplicate and Triplicate Ratios

The duplicate ratio of a : b is a² : b², and the triplicate ratio is a³ : b³.

Compounded Ratio

The compounded ratio of (a : b) and (c : d) is (a × c) : (b × d).

Given:

First Discount = 30%

Second Discount = 10%

Marked price = Rs. 500

Concept used:

Overall discount,

D_o = D₁ + D₂ - $\frac{D_1 × D_2}{100}$

Where, D₁ = First discount, D₂ = Second discount,

D_o = Overall discount

Selling price = (100% - Discoun%) × Marked Price

Calculation used:

According to the question,

⇒ Do = 30 + 10 - $\frac{30 × 10}{100}$

⇒ Do = 40 - 3 = 37%

The selling price of the pen = (100% - 37%) of 500 = Rs. 315

Therefore, 'Rs. 315' is the required answer.

Alternate MethodGiven:

First Discount = 30%

Second Discount = 10%

Marked price = Rs. 500

Concept used:

Selling price = (100% - Discoun%) × Marked Price

Calculation used:

According to the question,

The selling price of the pen after first discount = (100% - 30%) of 500 = Rs. 350

The selling price of the pen after second discount = (100% - 10%) of 350 = Rs. 315

Therefore, 'Rs. 315' is the required answer.

Given:

A train covers a distance of 56 km in 40 minutes.

In the second case: its speed is decreased by 9 km/h,

Concept used:

(1.) Speed = $\frac{\text {Distance}}{\text {Time}}$

(2.) Distance = Speed × Time

Calculation:

According to the question,

Initially, The speed of the train $\frac{56}{\frac{40}{60}}$ = 84 kmph

The decreased speed = 84 - 9 = 75 kmph

Again according to the question,

The time is taken by the train to cover 225 km with decreased speed = $\frac{225}{75}$ = 3 hours

Therefore, '3 hours' is the required answer.

Given:

The cost price of one toy is Rs. 375.

In the first case:

A shopkeeper sells 12 toys at a profit of 20% and 8 toys at a loss of 10%.

In the second case:

Had he sold all the 20 toys at 9% profit, 

Concept used:

Selling price = (100% + Profit%) of Cost price

Selling price = (100% - Loss%) of Cost price

Calculation:

According to the question,

In the first case:

The selling price of the toy for selling it at 20% profit = (100% + 20%) of 375 = Rs. 450

The total price of selling 12 toys = 450 × 12 = Rs. 5400

The selling price of the toy for selling it at 10% loss = (100% - 10%) of 375 = Rs. 337.5

The total selling price of 8 toys = 337.5 × 8 = Rs. 2700

Therefore, the total selling price of 20 toys = Rs. 5400 + Rs. 2700 = Rs. 8100

The cost price of 20 toys = Rs. 375 × 20 = Rs. 7500

The net profit = Rs. 8100 - Rs. 7500 = Rs. 600

In the second case:

The selling price of one toy at 9% profit = (100% + 9%) of Rs. 375 = Rs. 408.75

The selling price of all 20 toys = Rs. 408.75 × 20 = Rs. 8175

The net profit = Rs. 8175 - Rs. 7500 = Rs. 675

The net increase in profit = Rs. 675 - Rs. 600 = Rs. 75

Therefore, 'increased by Rs. 75' is the required answer.

Given:

Principal = Rs. 64000

Rate = 5% p.a.

Time = 1 year 6 months = 1$\frac{1}{2}$ year

Concept used:

Amount in case of principal is compounded for $1\frac{1}{2}$ years:

Amount = P × (1 + $\frac{R}{100}$)¹ × (1 + $\frac{R}{2 × 100}$)

Calculation:

According to the question,

Amount = 64000 × (1 + $\frac{5}{100}$) × (1 + $\frac{5}{200}$)

Amount = 64000 × $\frac{105}{100}$ × $\frac{205}{200}$

Amount = 68880

Now, 

C.I = 68880 - 64000

C.I = 4880

Therefore, 'Rs. 4880' is the required answer.

Given:

Principal amount = Rs. 1,25,000

Rate = 15% per annum

Time = 2 years

Compounding is done 8-monthly, n = 8

Concept used:

Effective rate, R = r% × $\frac{n}{12}$ per annum

Effective time, T = t × $\frac{12}{n}$ years

Now, 

Amount = P × (1 + $\frac{R}{100}$)T 

C.I = Amount - P

Calculation:

According to the question, 

Effective rate = 15% × $\frac{8}{12}$ = 10% per annum

Effective time = 2 × $\frac{12}{8}$ = 3 years

Now, 

Amount = 125000 × (1 + $\frac{10}{100}$)³ 

⇒ 125000 × (1 + $\frac{1}{10}$)³

⇒ 125000 × ($\frac{11}{10}$)³

⇒ 125000 × $\frac{1331}{1000}$

⇒ 125 × 1331 = Rs. 166375

⇒ C.I = Rs. 166375 - Rs. 125000 = Rs. 41375

Therefore, 'Rs. 41375' is the required answer.

Shortcut Trick

∵ The effective rate is 10%, And the effective time is 3 years

10% = 1/10

so the successive increase of 10% for 3 years is

For first year         10  →  11

For second year   10  →  11           

For third year        10  →  11

Overall change     1000 → 1331

Thus, the principal is 1000 units and the amount is 1331 units 

So, the compound interest is 1331 - 1000 = 331

∵1000 units = 125000  

⇒ 1 unit = 125

So, the compound interest at Rs. 125000 is,

⇒ 331 × 125 = Rs. 41375

Hence, the correct answer is Rs. 41375.

Given:

A can complete 60% of a work in 6 days and B can complete the same work in 15 days.

They work together for 3 days.

The remaining work is completed by C alone in 12 days.

Concept used:

The time is taken by A to complete the work = a

The time is taken by B to complete the work = b

The amount of work done = L.C.M of (a and b) = c

Efficiency of A = $\frac{c}{a}$

Efficiency of B = $\frac{c}{b}$

Calculation:

According to the question,

The time is taken by A to complete 60% of the work = 6 days

The time is taken by A to complete 100% of the work = $\frac{6}{60}$ × 100 = 10 days

The time is taken by B to complete the work = 15 days

The total unit of work = L.C.M of (10 and 15) = 30 units

Efficiency of A = $\frac{30}{10}$ = 3 units a day

Efficiency of B = $\frac{30}{15}$ = 2 units a day

Now,

The amount of work done by A in 3 days = 3 × 3 = 9 units

The amount of work done by B in 3 days = 2 × 3 = 6 units

The total amount of work by A and B in 3 days = 9 + 6 = 15 units

The remaining amount of work = 30 - 15 = 15 units

The time is taken by C to complete the remaining work = 12 days

Efficiency of C = $\frac{15}{12}$ = 1.25 units a day

Again according to the question,

The time is taken by C to complete the $\frac{1}{8}$ of work = $\frac{\frac{30}{8}}{1.25}$ = 3 days

Therefore, '3 days' is the required answer.

Shortcut Trick

Let the average of the two consecutive odd numbers be A.

The numbers can be written as (A − 1) and (A + 1).

Average of their squares = [(A − 1)² + (A + 1)²] ÷ 2 = (2A² + 2) ÷ 2 = A² + 1

Given, A² + 1 = 145 ⇒ A² = 144 ⇒ A = 12

∴ The correct answer is 12.

Alternate Method

Given:

The average of the squares of two consecutive odd natural numbers is 145.

Calculations:

Let the two consecutive odd natural numbers be n and n + 2.

⇒ Average of their squares = [n² + (n + 2)²] ÷ 2 = 145

⇒ n² + n² + 4n + 4 = 145 × 2

⇒ 2n² + 4n + 4 = 290

⇒ 2n² + 4n − 286 = 0

Dividing the equation by 2:

⇒ n² + 2n − 143 = 0

⇒ n² + 13n − 11n − 143 = 0

⇒ n(n + 13) − 11(n + 13) = 0

⇒ (n − 11)(n + 13) = 0

Since n is a natural number, n cannot be negative. Hence, n = 11.

The two numbers are 11 and (11 + 2) = 13.

Average of the numbers = (11 + 13) ÷ 2 = 12.

∴ The correct answer is 12.

Additional Information

Properties of Consecutive Odd Numbers

Consecutive odd numbers always have a difference of 2. They can be generally represented as 2k − 1 and 2k + 1, where k is a natural number.

Algebraic Identity for Squares

The sum of squares of (A − B) and (A + B) simplifies calculations directly: (A − B)² + (A + B)² = 2(A² + B²).

Average of Consecutive Numbers

The arithmetic mean or average of any two consecutive odd numbers is strictly the even number present exactly between them.

Shortcut Trick

Check for right-angled triangle triplet: 60, 297, 303 → Divide by 3: 20, 99, 101.

Since 20² + 99² = 400 + 9801 = 10201 = 101², it is a right-angled triangle.

Area of triangle = 1/2 × 60 × 297 = 30 × 297 = 8910 m².

Area of square = 8910 ⇒ side = √(81 × 110) = 9√110 m.

Perimeter of square = 4 × 9√110 = 36√110 m.

∴ The correct answer is 36√110 m.

Alternate Method

Given: Sides of triangular park = 60 m, 297 m, and 303 m.

Formula Used: Area of right triangle = 1/2 × base × height; Area of square = side²; Perimeter = 4 × side.

⇒ First, verify the nature of the triangle: 60² + 297² = 3600 + 88209 = 91809.

⇒ Square of hypotenuse = 303² = 91809.

⇒ Area of triangular park = 1/2 × 60 × 297 = 30 × 297 = 8910 m².

⇒ Let the side of the square be s. Area of square = s² = 8910.

⇒ s = √8910 = √(81 × 110) = 9√110 m.

⇒ Perimeter of the square garden = 4 × s = 4 × 9√110 = 36√110 m.

∴ The correct answer is 36√110 m.

Additional Information

Heron's Formula

For any triangle with sides a, b, and c, Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2.

Pythagorean Triplet Identification

If the sum of squares of two smaller sides equals the square of the largest side (a² + b² = c²), the triangle is right-angled.

Square Properties

Area of a square with side 's' is s² and its perimeter is 4s. Diagonal length = s√2.

Given:

An article is marked at Rs. 750,

If it is sold at a discount of 16%, then the selling price becomes $\frac{3}{2}$ times its cost price.

Concept used:

Selling price = (100% - Discount%) of Marked price

Calculation:

According to the question,

The selling price of the article = (100% - 16%) of 750 = Rs. 630

Again according to the question,

The cost price of the article = $\frac{2}{3}$ × 630 = Rs. 420

Therefore, 'Rs. 420' is the required answer.

Shortcut Trick ${CP \over MP} = {100-D\% \over 100+P\%}$

${CP \over MP} = {100-16 \over 100+50}$ 

${CP \over MP} = {84 \over 150}$

CP = ${84 \over 150} ×750$

CP = 84 × 5 

CP = Rs. 420

Hence, the correct answer is Rs. 420.

Given:

? = 5 × 3 ÷ 3 of 6 - 8 ÷ 2 × (3 - 5) + 3 - 2 × 4 ÷ 6 of $\frac{1}{2}$

Concept used:

Calculation:

According to the question,

⇒ ? = 5 × 3 ÷ 3 of 6 - 8 ÷ 2 × (3 - 5) + 3 - 2 × 4 ÷ 6 of $\frac{1}{2}$

⇒ ? = 5 × 3 ÷ 18 - 8 ÷ 2 × (-2) + 3 - 2 × 4 ÷ 3

⇒ ? = 5 × $\frac{1}{6}$ - 4 × (-2) + 3 - 2 × $\frac{4}{3}$

⇒ ? = $\frac{5}{6}$ + 8 + 3 - $\frac{8}{3}$

⇒ ? = $\frac{5 + 48 + 18 - 16}{6}$

Therefore, '$\frac{55}{6}$' is the required answer.

Given:

The difference between the two positive numbers x and y where x > y, is 25% of x.

Value of y is 15

Calculation:

According to the question,

⇒ x - y = 25% of x

⇒ x - y = 0.25x

⇒ x - 0.25x = y

⇒ 0.75x = y

Now,

⇒ 0.75x = 15

⇒ x = 20

Therefore, '20' is the required answer.

Shortcut Trick

Area of Parallelogram = Base₁ × Height₁ = Base₂ × Height₂

Here, Shorter side (Base₁) = 10 cm and its Distance (Height₁) = 6 cm.

Longer side (Base₂) = 15 cm and its Distance (Height₂) = h.

⇒ 10 × 6 = 15 × h

⇒ 60 = 15 × h ⇒ h = 4 cm.

∴ The correct answer is 4 cm.

Alternate Method

Given:

Adjacent sides of parallelogram = 10 cm and 15 cm.

Distance between shorter sides (h₁) = 6 cm.

Formula Used:

Area of a parallelogram = Base × Perpendicular Distance (Height)

Calculations:

⇒ Area using shorter side as base = 10 cm × 6 cm = 60 cm²

⇒ Let the distance between longer sides be h cm.

⇒ Area using longer side as base = 15 cm × h

⇒ Since the area remains the same:

⇒ 15 × h = 60

⇒ h = 60 ÷ 15

⇒ h = 4 cm

∴ The correct answer is 4 cm.

Additional Information

Properties of Parallelogram

Opposite sides are equal and parallel. Opposite angles are equal. Diagonals bisect each other.

Area and Perimeter

Area = Base × Height. Perimeter = 2 × (Sum of adjacent sides).

Relation between Sides and Heights

a × h_a = b × h_b, where a and b are adjacent sides and h_a, h_b are corresponding altitudes.