Delhi Police Constable Previous Year Paper (Held on: 8 Dec 2020 Shift 3)

The correct answer is Krishna.

Key Points

• Musi River is a tributary of the Krishna River in the Deccan Plateau flowing through Telangana.
• Musi River is also known as Musinuru or moosa River or Muchukunda.
• Hyderabad is situated on the banks of the Musi river.
• Osman Sagar and Himayat Sagar are dams built on it that used to act as a source of water for Hyderabad.

Additional Information

• The Krishna River is the 4^th biggest river after the Ganga, Godavari, and Brahmaputra in terms of water inflows and river basin area in India.
• The Krishna river is almost 1288 kilometers long.
• The river is also known as Krishnaveni.

The correct answer is cell wall.

Key Points

• Antibiotics are not effective on a virus as it lacks a cell wall.
• How antibiotics work
• They are used to treat infections caused by bacteria.
• There are two types of antibiotics that work to stop bacterial infections.
• Some slow down the growth of bacteria and damage their ability to reproduce and spread.
• While others kill the bacteria by destroying the bacteria cell walls. The choice of antibiotic depends on the type of bacteria.

Additional Information

• Viruses are different from bacteria; they have a different structure and a different way of surviving. **Viruses don’t have cell walls that can be attacked by antibiotics.**​

Important Points

• Antibiotics were discovered by Alexander Fleming in 1928.

The correct answer is rolling friction.

Key Points

• For a moving solid body, there are 2 principal types of friction are following
• Rolling friction
• Sliding friction
• On a surface, The force resisting the motion of a rolling body is known as Rolling resistance or Rolling friction.
• The Rolling of a wheel or ball on the ground is an example of Rolling friction.
• In Sliding friction, there is a restriction on the movement of the body as only one side of the body is in contact with the surface.
• An example of Sliding friction is Pushing a box across the table.
• Rolling resistance is weaker than sliding friction.

Additional Information

• When 2 surfaces are rubbed against each other, Sliding friction takes place.
• When an object rolls on the surface, Rolling friction takes place.
• Because of rolling friction, A basketball rolled on the court will eventually come to a halt.
• A broad tire bike will burn extra fuel because of the increased Rolling friction.

The correct answer is 43^rd.

Key Points

• Since 1989, India has ranked 41^st on the IMD World Competitiveness ranking every year.
• In 2017, The rank slipped to 45^th and improved to 44^th in 2018.
• The ranking is produced by the business school based in Singapore and Switzerland.

Additional Information 

• The World Competitiveness Index is compiled by Institute for Management Development (IMD).
• Singapore is in top position in 2020 and has retained its top position on the 63-nation list.
• The top five nations in World Competitiveness Index 2020 are following
• Singapore
• Denmark
• Switzerland
• Netherlands
• Hong Kong

The correct answer is 1236.

Key Points

• In the northern part of the Indian subcontinent, Razia Sultana was the ruler of the Delhi Sultanate.
• Razia reign from 1236 to 1240.
• Razia Sultana was the only female Muslim ruler of Delhi and Razia was the first female Muslim ruler of the subcontinent.
• "Sultan Raziyyat-Ud-Dunya Wa Ud-Din" was the name of a female ruler and popularly known by Razia Sultana.

Additional Information

• In April 1240, She was deposed by a group of nobles**.**
• In October that year, She was defeated by her half-brother and successor Muizuddin Bahram and she was killed shortly after.

The correct answer is Ashoka got the inspiration for such pillars from his father Bindusar.

Key Points

• Characteristics of Ashokan pillars are
• Ashoka got the inspiration for such pillars from Persians and the Greeks.
• They were generally monolithic and were made up of sandstone.
• They were polished pillars like the Lion Capital of Ashoka from Sarnath.
• The similarity of architecture suggests that they were all sculpted by craftsmen from the same region.
• The pillars have four component parts in two pieces.
• The three sections of the capitals are made in a single piece, often of a different stone to that of the monolithic shaft to which they are attached by a large metal dowel.

Additional Information

• The Ashoka pillars are a series of columns dispersed throughout the Indian subcontinent.
• The Mauryan Empire Ashoka used the expression Dhaṃma thaṃbha "pillars of the Dharma" to describe his own pillars.
• The Ashoka's pillars are among the earliest known stone sculptural remains from India.
• All Ashoka's pillars were built at Buddhist monasteries, many important sites from the life of the Buddha and places of pilgrimage.
• Some pillars were erected to commemorate visits by Ashoka.

The correct answer is Alauddin Khilji.

Key Points

• Alauddin Khilji was an emperor of the Khalji dynasty and he ruled the Delhi Sultanate.
• Alauddin Khalji reign from 1296 to 1316.
• Khalji is noted for repulsing the Mongol invasions of India.
• During 1310-1311, the Delhi Sultanate ruler Alauddin Khalji sent an army led by Malik Kafur to the southernmost kingdoms of India.
• After subjugating the Hoysalas, Malik Kafur invaded the Pandya kingdom in present-day Tamil Nadu, taking advantage of a war of succession between the Pandya brothers Vira and Sundara.
• During March–April 1311, he raided several places in the Pandya territory, including their capital Madurai.
• He was unable to make the Pandya king a tributary to the Delhi Sultanate but obtained huge plunder, including elephants, horses, gold, and precious stones.

Additional Information

• Alauddin Khilji was a nephew and a son-in-law of his predecessor Jalaluddin.
• After killing Jalaluddin, Khilji consolidated his power in Delhi and subjugated Jalaluddin's sons in Multan.

The correct answer is Article 31.

Key Points

• Article 31 is being deleted by the Forty-Fourth Amendment Act, of 1978.
• 44^th Amendment to the Constitution of India was enacted as The Constitution (44^th Amendment) Act, 1978.
• This amendment says that the ‘Right to property under Article 31 of the Constitution is removed from the fundamental rights and is made a legal right.
• This act was passed in 1978 by the Morarji Desai government who served between 1977 and 1979 as the 4^th Prime Minister of India.

Additional Information

• 44^th Amendment made a few changes in the provisions of the constitution. They are given in points below:
• Any changes in the basic structure of the constitution can be made only if they are approved by the people of India by a majority of votes at a referendum in which at least fifty-one per cent of the electorate participated.
• Article 368 is being amended to ensure this.
• The 44^th Amendment Act of 1978 reversed the provision made by the 42^nd amendment act that allowed the government to amend the constitution on its wish by Article 368.
• 44^th Amendment Act nullified this unjustified power to the government.
• The right to Property was removed from the list of fundamental rights (Article 31) and was made a legal right under Article 300A.
• Proclamation of Emergency can be issued only when the security of India or any part of its territory is threatened by war or external aggression or by armed rebellion.
• Internal disturbance not amounting to armed rebellion would not be a ground for the issue of a Proclamation.
• An emergency can be proclaimed only on the basis of written advice tendered to the President by the Cabinet.
• The right to liberty is further strengthened by the provision that the law for preventive detention cannot authorise, in any case, detention for a longer period than three months, unless an Advisory Board has reported that there is sufficient cause for such detention.
• Right of the media to report freely and without censorship the proceedings in Parliament and the State Legislatures.

The correct answer is Public health and sanitation.

Key Points

• The Seventh Schedule to the Constitution of India defines and specifies the allocation of powers and functions between Union & States. It contains three lists; i.e. 1) Union List, 2) State List and 3) Concurrent List.
• "Public health and sanitation" is on the State list.
• Some important subjects of the state list are following
• Police
• Public health and sanitation
• Public order
• Betting and gambling
• Hospitals and dispensaries

Additional Information

• Some important subjects of the Concurrent list are following
• Forest
• Trade unions
• Adoption
• Succession
• Education
• Marriage
• Some important subjects of the Union list are following
• Army
• International Relations
• Ports
• Railways
• Defence
• Communication
• Highways

The correct answer is option 2.

Key Points

Pro tem Speaker-

• He is appointed by the President of India.
• Generally, the senior-most member of Lok Sabha is elected as Protem Speaker.
• He resides over the first meeting of Lok Sabha and administers the oath of office to the newly elected MPs.
• Once the new Speaker is elected, the office of the pro tem speaker ceases to exist.

The correct answer is Kerala.

Key Points

• The Top Rice Producing state is West Bengal.
• The Top Wheat Producing state is Uttar Pradesh.
• India is the second-largest producer of Wheat after China.
• The leading Maize producer is Karnataka.

Additional Information

• The top Millets Producing state is Rajasthan.
• The top Pulses producer is Madhya Pradesh.
• Cotton (Kharif) Producer states are Maharashtra,  Gujarat, Tamil Nadu, Andhra Pradesh, Odisha.
• Assam, Darjeeling (West Bengal) are the main producer of Tea.

The correct answer is Ajatashatru.

Key Points

• Ajatashatru sent his chief minister "Vassakara" to Buddha to ask him why the Vaishali should be so invincible.
• For that Buddha gave 7 reasons, including
• Their behavior of disciplined
• Respect for elders
• Their Respect for women
• Vajjis are always punctual to meetings
• They do not marry their daughters forcefully
• They give spiritual protection to the Arhats
• The principal reason was the Chaityas (altar), which was inside the town
• In East India, Ajatashatru was the king of the Haryanka dynasty of Magadha.
• Ajatashatru was the son of King Bimbisara and was a contemporary of both Gautama Buddha and Mahavira.

Additional Information

• Ajatashatru fought a war against Vajji (ruled by the Lichchhavis) and conquered the republic of Vesali.
• The Pataliputra city was formed by the fortification of a village by him.
• Ajatashatru is the inventor of 2 weapons used in war were following:
• The Rathamusala (scythed chariot)
• The Mahashilakantaka (engine to eject big stones)

The correct answer is historian.

Key Points

• Shams ud-Din Iltutmish was the 3^rd king of the Mamluk kings.
• In northern India, He ruled the former Ghurid territories.
• Iltutmish reign from 1211 to 1236.
• Iltutmish was the first Muslim sovereign to rule from Delhi.
• Thus, he is considered the effective founder of the Delhi Sultanate.

The correct answer is Brahmaputra.

Key Points

• The Lohit River is a river in China and India.
• The Lohit River is also known as the Zayu River.
• Lohit River is a tributary to the Brahmaputra River.
• The Dhola–Sadiya Bridge or the Bhupen Hazarika Setu, is a beam bridge in India and it spans the Lohit River.

Additional Information

• The Brahmaputra River is a transboundary river that flows through Tibet, India, and Bangladesh.
• The Brahmaputra river is the 9^th largest river by discharge and the 15^th longest in the world.
• The Brahmaputra river is also called  Dihang River in Arunachal Pradesh, Yarlung Tsangpo in Tibet and Luit Dilao in Assam.

The correct answer is Rajasthan.

Key Points

• The Pachpadra Lake is a salt lake near Pachpadra in Barmer of Rajasthan.
• The lake's sodium chloride level is marked at 98 percent.
• The famous salt lakes of India are as follows
• Pulicat Lake, Nellore
• Pangong Lake, Ladhak
• Chilika Lake, Puri
• Lonar Crater Lake, Lonar
• Sambhar Lake, Ajmer

Additional Information

• Some important lakes in Rajasthan are following
• Pachpadra Lake
• Sambhar Salt Lake
• Pichola Lake
• Dhebar Lake
• Pushkar Lake
• Ana Sagar Lake
• Kaylana Lake
• Balsamand Lake
• Man Sagar Lake
• Ramgarh Lake
• Rajsamand Lake
• Nakki Lake

The correct answer is Telangana.

Key Points

• Sammakka Sarakka Jatara is a festival to honor the Hindu Tribal goddesses and it is celebrated in Telangana.
• The word Jatara is used for witnessing one of the largest people gatherings.
• Sammakka Sarakka Jatara is also known as Sammakka Saralamma Jatara and Medaram Jatara.
• The festival is observed by Koya tribes.
• Koya is an Indian tribal community found in Andhra Pradesh, Chhattisgarh, Telangana, and Odisha.

Additional Information 

• Bathukamma, Bonalu are also the festivals of Telangana.
• Thaipusam, Natyanjali Festival, Pongal are the festivals celebrated in Tamil Nadu.
• Bhogali Bihu, Ambubachi, Baishagu, Dehing Patkai are the festivals celebrated in Assam.

The correct answer is Kashmir.

Key Points

• Queen Didda is also known as The Witch Queen and The Catherine of Kashmir.
• Didda was the ruler of Kashmir from 980 CE to 1003 CE.
• Didda first acted as regent for her son and various grandsons from 958 CE to 980 CE, and from 980 CE as sole Ruler and monarch.

Additional Information

• Most knowledge relating to Didda is obtained from the Rajatarangini.
• In the twelfth century, Rajatarangini is a work written by Kalhana.
• Ashish Kaul's novel Didda: The Warrior Queen of Kashmir is based on Didda's life.

The correct answer is Bill Gates.

Key Points

• William Henry Gates III is an American business magnate, investor, author, software developer, landowner, and philanthropist.
• Gates is a co-founder of Microsoft Corporation.
• The book "The Road Ahead" written by Gates with Microsoft executive Nathan Myhrvold and journalist Peter Rinearson and it was published in November 1995.
• The book "Business @ the Speed of Thought" was also written by bill gates.

Additional Information

• Al Gore is an American politician and environmentalist and he served as the 45^th vice president of the US and his tenure from 1993 to 2001.
• RK Pachauri was the chairman of the (IPCC) Intergovernmental Panel on Climate Change and during his tenure, the IPCC was awarded the Nobel Peace Prize.
• Greta Thunberg is a Swedish environmental activist who is known for challenging world leaders to take immediate action against climate change internationally.

The correct answer is England.

Key Points

• Stuart Broad is a right-arm seam bowler and left-handed batsman.
• In the 4^th Test of the 2015 Ashes series, Stuart Broad took career-best figures of 8-15, and in the Australian first innings as they were dismissed for just sixty.
• This performance in 2015 was named Wisden's Men's Test spell of the decade.
• NET tram 237 was named in honor of Broad on 17 September 2015.

Additional Information

• Captains of various ODI cricket teams are as follows
• Afghanistan - Asghar Afghan
• Australia - Aaron Finch
• Bangladesh - Tamim Iqbal
• England - Eoin Morgan
• India - Virat Kohli
• Ireland - Andrew Balbirnie
• New Zealand - Kane Williamson
• Pakistan - Babar Azam
• South Africa - Temba  Bavuma
• Srilanka - D Karunaratne
• West Indies- Kieron Pollard

The correct answer is Government of India Act, 1935.

Key Points

• The act originally received royal assent in August 1935.
• Because of Act's length, the Act was retroactively split by the Government of India Act, 1935 into two separate Acts are following
• The Government of India act, 1935
• Has 10 schedules and 321 sections.
• The Government of Burma act, 1935
• Has 6 schedules and 159 sections.

Additional Information

• Major Provisions of the Government of India Act, 1935
• Established Provincial autonomy
• Diarchy is abolished at provinces and introduced in Center
• Bicameral Legislature is introduced in Parliament
• Establishment of RBI.
• Federal Court in 1937.
• A Federal Railway Authority was set up to control Indian railways.
• The Act also provided for the establishment of federal, provincial, and joint Public Service Commissions.
• Government of India Act of 1919
• Bicameralism and direct elections were introduced for the first time in the country.
• Dyarchy, meaning double rule, was introduced in the provinces.
• The act provided for the establishment of a public service commission for recruiting civil servants.

The correct answer is Shah Jahan.

Key Points

• Badshah Nama is a group of works written as the official history of the reign of Shah Jahan (Mughal Emperor).
• Badshah Nama used for the illustrated manuscript versions.
• Badshah Nama is also known as "Padshahnama".
• During the period of Mughal Emperor Shah Jahan, Abdul Hamid Lahori was a historian and traveler who later became a court historian of Shah Jahan.
• In this book, Lahori has described Shah Jahan's life and activities during the first twenty years of his reign.
• Lahori wrote the book Badshah Nama, about the reign of Shah Jahan.

Additional Information 

• Mughal Emperor Shah Jahan reign from 1628 to 1658.
• Babur, Humayun, Akbar, Jahangir, Alamgir 1, Bahadur Shah are the important emperors of the Mughal dynasty.

The correct answer is red.

Key Points

• Turmeric is an acid-base indicator
• Turmeric compound remains yellow when acid or neutral solutions are added to it.
• When basic solutions such as sodium hydroxide are added to it, the solution turns pinkish-red.

Additional Information

• Turmeric is a flowering plant, Curcuma longa of the ginger family, Zingiberaceae.
• Turmeric is a rhizomatous, perennial, herbaceous plant native to the Indian subcontinent and Southeast Asia.
• It requires a considerable amount of annual rainfall to thrive and temperatures between 20 and 30 °C.
• Turmeric powder has a bitter, warm, black pepper–like flavor and earthy, mustard-like aroma.
• A bright yellow chemical produced by the turmeric plant is Curcumin.
• Curcumin is approved as a food additive by the European Parliament, WHO, and United States Food and Drug Administration.
• It is long used in Ayurvedic medicine, where it is also known as Haridra.
• Turmeric is commonly used in Indian clothing, like saris and Buddhist monks' robes.

The correct answer is Kisan Rail and Krishi Udaan.

Key Points

• Nirmala Sitharaman, the Finance Minister presented the Union Budget for 2019-20, laid out sixteen action points to revive the struggling agriculture sector.
• Finance Minister also said a provision of Rs. 2.83 lakh crore had been set aside for this, the Rural sector, and allied activities.

Additional Information 

• The Finance Minister announced plans by the Indian Railways to run a 'Kisan Rail' that will provide refrigerated coaches in trains, thereby helping farmers access faraway markets cheaply, quickly, and efficiently.
• The Finance Minister, Sitharaman also announced a 'Krishi Udaan' - a tie-up with the Civil Aviation ministry to help farmers transport grains and produce by air.
• Nirmala Sitharaman spoke about a 'blue Economy', saying the govt. had plans to improve returns from marine fishery resources and Sitharaman said that fish production would be raised to two hundred lakh tonnes by 2022/23.

The correct answer is 9^th.

Key Points

• The 2020 World Investment Report is the 30^th-anniversary edition and it was released in May 2020.
• India ranked 12^th in 2018 among the world’s largest FDI recipients.
• The FDI inflows into India jumped over 20 percent to $ 51 billion ​ in 2019.
• The World Investment Report also observed that FDI into India may decline sharply in 2020 because of the impact of the Covid-19 pandemic.

Additional Information 

• The World Investment Report 2020 is released by United Nations Conference on Trade and Development (UNCTAD).
• In 1964, United Nations Conference on Trade and Development (UNCTAD) was established.
• Singapore is the major investor in India$.

The correct answer is Tamil Nadu and Andhra Pradesh.

Key Points

• The Buckingham Canal is a freshwater navigation canal and it is 796 km long.
• The Buckingham Canal parallels the Coromandel Coast of South India from Kakinada city in the East Godavari of Andhra Pradesh to Viluppuram District in Tamil Nadu.
• The Buckingham canal connects most of the natural backwaters along the coast to Chennai port.
• During British rule, The canal was constructed.
• During the late nineteenth and early twentieth centuries, It was an important waterway.

Additional Information 

• The first segment of this canal was a saltwater navigation canal, from Madras to Ennore for a distance of 18 km constructed in 1806.
• The canal was initially called Cochrane's Canal, after its main financier Basil Cochrane.

The correct answer is Beijing 2008.

Key Points

• Abhinav Bindra is a retired sport shooter and he is also an Indian businessman.
• Bindra is India's first individual Olympic gold medalist.
• He won the gold medal in the 10-meter air rifle event at the 2008 Summer Olympics.
• Since 1980, It was also India's first Olympic gold medal.
• He won the Arjuna award in 2000.
• He was also awarded "Rajiv Gandhi Khel Ratna" in 2002 and "Padma Bhushan" in 2009.

Additional Information 

• Bindra is the first shooter to have held concurrently the world and Olympic titles for the men's 10-meter air rifle event and having earned those honors at the Summer Olympics 2008 and the ISSF World Shooting Championships 2006.
• He has also won 9 medals at the Commonwealth Games.
• Bindra also won 3 gold medals at the Asian Games.

The correct answer is Sania Mirza.

Key Points

• Sania Mirza is a professional tennis player of India.
• Mirza has won 6 Grand Slam titles in her career but she never won any Olympic medal in her career.
• Mirza was ranked by the Women's Tennis Association as India's No. 1 player from 2003 until her retirement from singles in 2013.
• She was awarded by Arjuna award in 2004.
• She was also awarded from "WTA Newcomer of the Year" in 2005 and "Padma Shri" in 2006.

Additional Information 

• She was also honored by "Rajiv Gandhi Khel Ratna" in 2015 "Padma Bhushan" 2016.
• Mirza is the highest-ranked female player ever from India.

 

Important Points 

• Gagan Narang won the Bronze Medal in the Men's 10 m Air Rifle Event at the 2012 Summer Olympics.
• Vijay Kumar Silver medal in Pistol event at the 2012 London Olympics.
• Vijender Singh had won India's first Olympic medal in boxing, a bronze, in the 2008 Beijing Games.

The correct answer is Goa.

Key Points

• The International Film Festival of India was founded in 1952.
• The International Film Festival is hosted by Goa Government and it is held annually in Goa.
• The International Film Festival aims at providing a common platform for the cinemas of the world to project the excellence of film art.
• The festival is conducted jointly by the Directorate of Film Festivals (under the Ministry of Information and Broadcasting) and the state Government of Goa.

Additional Information

• The National Film Awards was established in 1954.
• The National awards are given for Excellence in cinematic achievements for Indian cinema.
• The Dadasaheb Phalke Award is also an award in the field of cinema and it is India's highest award in cinema.

Important Points

• The 51^st International Film Festival of India was held from 16 to 24 January 2021 in Goa.
• Best Film - Into the Darkness
• Best Director - Chen Nien Ko

The correct answer is ₹1.20 lakh crore.

Key Points

• Finance Minister Nirmala Sitharaman had in her previous budget for 2020-21 set a target of raising Rs 2.1 lakh crore from privatization and sale of minority stakes in state-owned companies.
• This includes Rs 1.20 lakh crore from selling a stake in CPSEs and Rs 90,000 crore from stake sale in financial institutions.
• In 2021-22, disinvestment is estimated at Rs 1,75,000 crore which is 3.5 times higher than the actual disinvestment in 2019-20.
• The highest disinvestment achieved over the last few years was in 2017-18, of Rs 1,00,045 crore.

Additional Information

• Disinvestment in Public sector undertakings in India is a process of public asset sales of India on behalf of the Government of India done by the President.
• From the financial year 1991-92 to 2017-18, the Indian Government sold public assets totaling Rs. 3,47,439 Crore.
• PSU's like BSNL, Air India, and MTNL made huge losses, costing the taxpayer massive amounts of money.
• A state-owned enterprise is called a Public Sector Undertaking (PSU) or a Public Sector Enterprise in India.
• The total expenditure of the Indian Government increased from Rs. 1,13,422 crore in 1991-92 to Rs. 21,46,735 Crore in 2017-18.
• Between 2014 and 2018 the Central NDA government divested a total of Rs. 1,94,646 crore.

The correct answer is Protoplasm.

Key Points

• Purkinje was a Czech physiologist and anatomist.
• Purkinje coined the term 'protoplasm' for the fluid substance of a cell.
• He coined the term "protoplasm" in 1839.
• Such was Purkinje's fame that when people wrote letters from outside Europe to him, all that they needed to put as the address was 'Purkyne, Europe'.

Important Points

• The protoplasm is the living part of the cell, which comprises various cellular organelles.
• Protoplasm contains cytoplasm and the nucleus.
• The cytoplasm contains cell organelles like endoplasmic reticulum,  Golgi bodies, mitochondria, ribosomes, but no nucleus.

The correct answer is liver.

Key Points

• The variants of the endoplasmic reticulum are following
• Rough ER
• Smooth ER
• The Rough ER has ribosomes embedded within its structure, giving a 'rough' appearance.
• The smooth ER does not have these ribosomes, hence appears 'smooth.'
• The smooth endoplasmic reticulum is responsible for the synthesis of essential lipids such as cholesterol and phospholipids.
• The majority of the functions of the rough endoplasmic reticulum are associated with protein synthesis.

Additional Information

• The liver is the largest gland in the human body.
• Production of Bile, Metabolization of Fats, Absorption of Bilirubin are the main functions of the Liver.
• Cirrhosis, Fascioliasis, Hepatitis, and Alcoholic Liver Disease are some diseases related to the liver.

The correct answer is To pay taxes by due date.

Key Points

• The 11 Fundamental duties under 51-A are following
• Abide by the Indian Constitution and respect its ideals and institutions, the National Flag and the National Anthem.
• Cherish and follow the noble ideals that inspired the national struggle for freedom.
• Uphold and protect the sovereignty, unity, and integrity of India
• Defend the country and render national service when called upon to do so
• Promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic, and regional or sectional diversities and renounce practices derogatory to the dignity of women
• Value and preserve the rich heritage of the country’s composite culture
• Protect and improve the natural environment including forests, lakes, rivers, and wildlife, and have compassion for living creatures
• Develop scientific temper, humanism, and the spirit of inquiry and reform
• Safeguard public property and abjure violence
• Strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavor and achievement
• Provide opportunities for education to his child or ward between the age of six and fourteen years. This duty was added by the 86^th Constitutional Amendment Act, 2002

Additional Information

• 10 Fundamental Duties to the Indian Constitution added by 42^nd Amendment Act of 1976.
• 11^th Fundamental Duty added by 86^th Amendment Act 2002.
• In 1976, Swaran Singh Committee recommended Fundamental Duties.
• The Fundamental Duties are dealt with Article 51A under Part-IV A of the Constitution of India.

The correct answer is Herdmania.

Key Points

• Some characters of Herdmania are following
• With a length of 6-13 cms, the body has a flat purse-like structure.
• Its breadth is 4-7 cms.
• Its Colour is brownish.

Additional Information

• Scientific classification of Herdmania are following
• Kingdom - Animalia
• Phylum - Chordata
• Subphylum - Tunicata
• Class - Ascidiacea
• Order - Stolidobranchia
• Family - Pyuridae
• Genus - Herdmania

The correct answer is Thawar Chand Gehlot.

Key Points

• Thawar Chand Gehlot is the leader of the upper house since 11 June 2019.
• Currently, Thaawar Chand Gehlot serves as the Minister of Social Justice and Empowerment in the Central Government.
• Gehlot is a member of the Rajya Sabha, the upper house of the Indian Parliament, representing Madhya Pradesh.
• Gehlot formerly represented Shajapur in the Lok Sabha of Indian Parliament, from 1996 to 2009.

Important Points

• Piyush Goyal has been appointed as the Leader of the House in the Rajya Sabha in 2022.

Additional Information

• Note that, Mallikarjun Kharge is the leader of opposition in Lok Sabha.
• Prime Minister Narendra Modi is the leader of the house in Lok Sabha.
• Ludhiana MP Ravneet Singh Bittu was made Leader of Opposition in Lok Sabha.
• Om Birla is the current Speaker who presides over the 17^th Lok Sabha.
• Jagdeep Dhankar is the speaker of Rajya Sabha and he is also the Vice President.

The correct answer is 7.9%.

Key Points

• As per Economic Survey 2020, Livestock income has become an important secondary source of income for millions of rural families and has assumed an important role in achieving the goal of doubling farmers.
• Livestock sector has been growing at a Compound Annual Growth Rate (CAGR) of 7.9 per cent during last five years.
• It provides livelihood to about 16 million fishers and fish farmers in the country.
• The fisheries sector has registered annual average growth rate of more than 7 per cent in the recent years.

Additional Information

• The breeding, slaughter, and maintenance of livestock, known as animal husbandry.
• Livestock is defined as domesticated animals raised in an agricultural setting to produce labor and commodities such as eggs, milk, meat, fur, leather, and wool.
• The term "livestock" is sometimes used to refer solely to those that are bred for consumption, while other times it refers only to farmed ruminants, such as sheep, cattle, and goats.

The correct answer is Tamil Nadu.

Key Points

• Terukkuttu is a Tamil street theatre form practiced in Tamil Nadu (India) and Tamil-speaking regions of Sri Lanka.
• It is a form of entertainment, a medium of social instruction, and a ritual.
• It plays various themes.
• One theme is from the Tamil language versions of the Hindu epic "Mahabharata", focusing on the Draupadi character.

Additional Information

• M. Shanmugam Pillai (writer) has compared terukkuttu to the Tamil epic "Silappatikaram".
• Silappatikaram is called a proto-form of terukkuttu.
• The core themes of the terukuttu play are following
• Supattirai Kalyanam (The marriage of Subhadra)
• Alli Arjunan (The Marriage of Arjuna with Alli)
• Pancal Capatam (The Vow of Draupadi)
• Draupadi Kalyanam (The marriage of Draupadi)
• Karna Mokshayam (The defeat of Karna)
• Abhimanyu Cantai (The defeat of Abhimanyu)

The correct answer is Gujarati.

Key Points

• Hellaro is a 2019 Indian Gujarati period drama film.
• The film is co-written and directed by Abhishek Shah and produced by Ashish Patel, Aayush Patel,  Nirav Patel, Prateek Gupta, Mit Jani, and Abhishek Shah under the banner of Saarthi Productions and Harfanmaula films.
• Hellaro was officially selected as the opening film at Indian Panorama, at the 50^th International Film Festival of India.
• On 8 November 2019, The film was released in theatres in India to positive reviews.

Additional Information

• Some highlights of the 66^th National Film Awards are following:-
• "Son-Rise" and "The Secret Life Of Frogs" are the best Nonfeature film in 66^th National Film Awards.
• The best book is Mouna Prarthana Pole.
• The best film critics are
• Blais Johnny
• Anant Vijay

The correct answer is $164.

Key Points

• Since April 2020, the government has received over 120 foreign direct investment (FDI) proposals worth ~Rs. 12,000 crore (US$ 1.64 billion) from China.
• Between April 2000 and September 2020, India received US$ 2.43 billion FDI from China.
• According to the Department for Promotion of Industry and Internal Trade (DPIIT), FDI equity inflow in India stood at US$ 500.12 billion between April 2000 and September 2020.

Additional Information

• In 2020-21 (between April 2020 and September 2020), Gujarat received the maximum FDI of US$ 16.0 billion, followed by Maharashtra at US$ 3.61 billion, Karnataka at US$ 3.66 billion, and Delhi at US$ 2.66 billion.
• India is expected to attract foreign direct investments (FDI) of US$ 120-160 billion per year by 2025, according to CII and EY reports$.

The correct answer is Veena.

Key Points

• In the Lyrist type of coins, Depicts Samudragupta wearing waist-cloth and seated on a couch, playing the veena that lies on his knees.
• Samudragupta's empire extended from the Himalayan foothills in the north to central India in the south-west and from Ravi River in the west to the Brahmaputra River in the east.
• He performed the Ashvamedha sacrifice to prove his imperial sovereignty.
• According to his coins, he remained undefeated.
• Initially, The coinage of the Gupta Empire was derived from the coinage of the Kushan Empire.
• The Guptas adopted from the Kushans the name of Dinara for their coinage.

Additional Information 

• The following types of Samudragupta's coins, inscribed with Sanskrit language legends, have been discovered are
• Standard type
• Archer type
• Tiger-slayer type
• Battle-axe type
• Lyrist type
• Ashvamedha type

The correct answer is 34^th.

Key Points

• As per JLL, the improvement in the ranking of India in the Global Real Estate Transparency Index is because of the progress in the country’s Real Estate Investment Trust (REIT) framework.
• The 2020 Global Real Estate Transparency Index covers 99 countries and territories and 163 cities.
• The latest Index is based on 210 indicators, having been extended to include additional data on sustainability and resilience, health and wellness, protect and alternatives.

Additional Information

• India’s rank in "Ease of doing business ranking" has improved from 142 in 2014 to 63 in 2019.
• India ranked 3^rd "Global Manufacturing Risk Index (MRI) 2020".
• India ranked 9^th in the "Climate Change Performance Index 2020".
• India ranked 43^rd in the "World Competitive Index 2020".
• India ranked 116 in "Human Capital Index 2020".

The correct answer is Tiger.

Key Points

• The Tiger census conducted in 2018 by India has entered into the Guinness Book of World Records in July 2020 as the largest camera-trap wildlife survey ever conducted.
• It was the 4^th edition of this census.
• Government claimed that India fulfilled its resolve to double tiger numbers four years before the target.
• The survey covered unprecedentedly 522,996 km of trails and sampled 317,958 habitat plots for vegetation and prey dung.

Additional Information

• This census assessment was carried out over three phases with the various datasets then combined to be extrapolated via statistical computation.
• The main outcome of this census was that India's tiger population had increased by roughly one-third: from 2,226 in 2014 to 2,927 in 2018.

The correct answer is Avanti.

Key Points

• Among the Mahajanapadas, Ujjain was the capital of Avanti.
• The Mahajanapadas were 16 kingdoms that existed in Northern ancient India from the sixth to fourth centuries BCE during the early second urbanization period.

Additional Information

• List of 16 Mahajanapadas are following

The correct answer is 49.

Key Points

• 49 children received the Pradhan Mantri Rashtriya Bal Puraskar 2020.
• Bengaluru's Yash Aradhya became the first Indian motorsports star to win the renowned and auspicious Pradhan Mantri Rashtriya Bal Puraskar Award.

Additional Information

• The National Child Welfare Awards were started in the year 1979 to give recognition to those who have made outstanding contributions in the fields of Child Development, Child Protection, and Child Welfare.
• It is important to distinguish and cognize such individuals and institutions as they help complement the efforts of the Government.
• In the year 2018, the award has been renamed Bal Kalyan Puraskar.
• This Award is provided in two categories - Individual and Institution.
• Three awards are given in each of these fields of two categories along with some cash prizes.

The correct answer is a subordinate ruler.

Key Points

• During the seventh century, the term 'Samanta' meant a subordinate ruler.
• Samanta was a name given to big landlords or warrior chiefs in various regions of the Indian subcontinent by that time existed kings of the seventh century.
• They were told to bring gifts for their kings or overlords, be present in their courts and also provide them with military support.
• In North India, the betimes use of the term in a similar sense was in Bengal in the Barabar Hill Cave Inscription of the Maukhari Chief, Anantavarman in which his father is described as the Samanta-Chudamanih of the imperial Guptas.

The correct answer is Aditya Puri.

Key Points

• Aditya Puri will relinquish the post of the Managing Director of HDFC Bank in October 2020.
• The new Managing Director of HDFC Bank is Sashidhar Jagdishan.
• At HDFC Bank, Jagdishan previously held the position of Additional Director and Head of Finance, HR.
• He assumed the charge of Chief Financial Officer in 2008 and was replaced by Srinivasan Vaidyanathan in 2019.

Additional Information

• HDFC Bank Limited is an Indian Development finance institution whose headquarter is located in Mumbai, Maharashtra.
• It has a family of 104,154 permanent employees as of 30 June 2019.
• HDFC Bank is India’s largest private sector bank in terms of assets.
• It is the largest bank in India by market capital as of March 2021.

The correct answer is river.

Key Points

• The landform named ‘meander’ is created by a river.
• A meander is a winding curve or twist in a river.
• They are typically found in the middle and inferior course of a river.
• This is due to the vertical erosion is substituted by a sideways form of erosion called lateral erosion, plus deposition within the floodplain.
• A meander is one of a category of steady sinuous curves, bends, loops, turns, or windings in the channel of a river, stream, or another watercourse.
• It is generated by a stream or river swinging from side to side as it flows across its floodplain or shifts its channel within a valley.
• A meander is generated by a stream or river as it erodes the sediments including an outer, concave bank (cut bank), and deposits this and other sediments downstream on an inner, convex bank which is typically a point bar.

The correct answer is a style of temple architecture.

Key Points

• In the context of ancient Indian culture, 'panchaytana' refers to a style of temple architecture.
• Hindu temples are built in the Panchayatana layout: the main shrine is adjoined by four subsidiary shrines.
• The derivation of the name are the Sanskrit words Pancha (five).
• Generally, Hindu temples are constructed along a west-east axis.
• So the four auxiliary shrines are at the **north-east, south-east, south-west, north-west.**​

Important PointsPanchayatana style temples in India along with their respective states:

Additional Information

• A military formation used to surround enemies is known as Padmavyuha.
• A pattern of defense walls in a city is called town halls.
• A city with five residential complexes is known as Apartments.

The correct answer is Urban rejuvenation.

Key Points

• As per the Union Budget 2020, Urban rejuvenation is not a component of the theme titled ‘Aspirational India'.
• The theme of the Budget 2020 is Aspirational India; Economic Development for all & A Caring Society.
• Under the section Aspirational India, the main focused sectors were:
• Agriculture, irrigation, and rural development
• Wellness, Water, and Sanitation
• Education Sector

Additional Information

• Agriculture, irrigation, and rural development - The main focus was to double the income of farmers by 2022.
• Wellness, Water, and Sanitation - It talked about the “Fit India Movement” in the context of India’s fight against the NCDs - non-communicable diseases.
• Education Sector - The aim is to open 150 higher education institutions, apprenticeships in 2020-21.

The correct answer is West Indies.

Key Points

• Cricketer Roston Chase is a Barbadian cricketer who plays for West Indies.
• His full name is Roston Lamar Chase.
• He made his test debut on 21 July 2016 Vs India.
• He has been awarded Test Cricketer of the Year as well as Cricketer of the Year for West Indies.
• On 26 January 2019, Chase performed exceptionally well with bowling figures of 8/60 in the fourth innings of the first Test against England in Barbados adding a 54 with the bat in the first innings

The correct answer is Dholavira.

Key Points

• The evidence of a large open area with terraced stands, identified as ‘stadium’ was found at Dholavira.
• The City of Dholavira is situated in Khadir island of the Rann of Kutch belonged to matured Harappan phase.
• Today it is seen as a fortified quadrangular city set in a harsh arid land, was once a thriving metropolis for 1200 years (3000 BCE-1800 BCE), and had an access to the sea prior to a decrease in sea level.
• Dholavira was founded in 1968-68 by architect J.P. Joshi.
• It was the fifth largest site among the 8 major sites discovered during the Harappan Civilization.

Additional Information

• The excavation revealed the urban planning and architecture and unearthed large numbers of old materials such as animal bones, gold, silver, terracotta ornaments, pottery, and bronze vessels.
• Archaeologists believed that Dholavira was a vital center of trade between settlements in south Gujarat, Sindh, and Punjab, and Western Asia.

The given figure:

As it is a symmetrical figure, the missing part will complete the smaller square and the rhombus along with the diagonal and a circle as shown below.

Hence, the third figure is the answer figure.

The given figure:

The position of the 'star' and the 'circle' are in alternate order in the outer circle. Also, the square is solid and blank in the alternate order. Thus, the complete figure will look like the one below.

Hence, the first figure will complete the question figure.

The given word: DIsCOVeREY

If we place a mirror to the right of the word then all the letters of the word will be reversed on its vertical axis by 180 degrees and the order of the letters will also be reversed as shown below.

Hence, the third figure is the reflection of the given word.

The given series:

The 'T' shape is rotating by 90 degrees in the clockwise direction in every image. Also, the letter or the symbol on the top in the previous image moves to the bottom in the next image. As the 'T' shape is facing the north-west direction in the fifth figure, implies, the 'T' shape will face the north-east direction in the answer figure. Also, Z will be at the bottom in the answer figure with a new letter at the top as shown below.

Hence, the first option will complete the series.

Except for the first figure, in all other figures, two corners of the square and one corner of the rhombus is shaded. In the first figure, three corners of the rhombus are shaded.

Hence, the first figure is different from the other three.

The sound of a Bat is called screech, similarly, the sound of Kangaroos is called chortle.

Hence, 'chortle' is the correct answer.

The given figure:

Some of the positions of the dice after folding the given figure are:

Clearly, 5, 6, 3, and 4 are adjacent to 1.

Hence, '2' will be opposite '1' in the dice.

Both Carrot and Potatoes are vegetables. Thus, the 'carrot' circle and the 'potato' circle will lie inside the 'vegetable circle as shown below.

Hence, the first figure is the answer figure.

The given figure:

There are six symbols in the dice, &, % # *, ×, ÷. 

From the first three positions of the dice, it is clear that %, &, ×, and ÷ are adjacent to #.

Hence, '*' is opposite '#' in the dice.

The given series:

The shape on the top right corner moves to the bottom left corner in the next image after rotating it by 180 degrees on its horizontal axis. Also, in the answer image, the shape on the top right will be different from all the shapes in previous images.

Hence, the first figure is the answer figure.

Jupiter is a planet while the moon is a natural satellite. Thus, the 'Jupiter' circle will be inside the 'planet circle and these two circles will not intersect with the 'Moon' circle as shown below.

The third figure represents the relationship between Jupiter, Planet, and Moon.

Hence, the correct answer is "Option 3".

The given equation: 7 × 96 ÷ 8 + 39 - 25 = 70

1) × and ÷ 

On interchanging × and ÷, we get:

7 ÷ 96 × 8 + 39 - 25 

⇒ 7 ÷ 12 + 14 ≠ 70 (incorrect)

2) + and -

On interchanging + and -, we get:

7 × 96 ÷ 8 - 39 + 25 = 70

⇒ 84 - 14 = 70 (correct)

3) + and ÷ 

On interchanging + and ÷, we get:

7 × 96 + 8 ÷ 39 - 25 

⇒ 672 + 0.2 - 25 ≠ 70 (incorrect)

4) × and -

On interchanging × and -, we get:

7 - 96 ÷ 8 + 39 × 25 

⇒ 7 - 12 + 975 ≠ 70 (incorrect)

Hence, we need to interchange + and - to make the equation correct.

The given figure:

The missing part of the figure will complete the square, the rhombus and the diagonal. Thus, the complete figure will look like the one below:

Hence, the second option will complete the given figure/

The given series: 3, 15, 38, 78, 141, 235, 370, 552, ?

11, 17, 23, 31, 41, and 47 are prime numbers. Also, if we make a series of prime numbers starting from 11m we will get:

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, and 59.

Clearly, 11, 17, 23, 31, 41, and 47 are alternate numbers in the above series. Thus, the next number will be 59.

59 + 182 = 241

241 + 552 = 793

Hence, 793 will be the next term in the series.

24 is a multiple of 6, similarly, among the given options 112 is a multiple of 14.

Hence, 112 is the correct answer.

Discord, turmoil and chaos are synonyms while harmony is an antonym of the other three.

Harmony is different from the other three

Hence, the correct answer is "Harmony".

Additional Information 

The given series:

Each shape is rotated upside down in the next figure as compared to the previous figure. The two shapes at the bottom moves to the top in the same order and the two shapes at the top move to the bottom but there order is reversed such that the shape at the left moves to the right and the shape at the right moves to the left. Using this, we can determine the third figure based on the position of the shapes of the fourth figure.

Hence, the third figure is the answer figure.

In all the figures, except for the second figure, there is no line passing from the leaf that is at the top. In the second figure, there is a line passing through the leaf that is at the top.

Hence, the second figure is different from the other three.

The given figure:

In each image, except for C, there is line outside the circle on the same side where the 'rhombus' is. In image C, the line is on the side where the 'star' is.

Hence, image C is different from the other three.

The given series: 11, 17, 28, 51, 96, 187, 368, ?

11 × 2 - 5 = 17

17 × 2 - 6 = 28

28 × 2 - 5 = 51

51 × 2 - 6 = 96

96 × 2 - 5 = 187

187 × 2 - 6 = 368

368 × 2 - 5 = 731

Hence, 731 will be the next term in the series.

The pattern being followed here is:

Letters are arranged in reverse order.

And then letters are increased or decreased by +3, or -3 alternatively.

VERSION is coded as 1712121621225

• VERSION → Reverse order → NOISREV
• Letters are increased or decreased by +3, or -3 alternatively.

TEARFUL is coded as 15189154223

• TEARFUL → Reverse order → LUFRAET
• Letters are increased or decreased by +3, or -3 alternatively.

Similarly,

LOCALITY be coded ?

• LOCALITY → Reverse order → YTILACOL.
• Letters are increased or decreased by +3, or -3 alternatively.

Hence, 281712940189 is the code for LOYALTY.

The speed of Aravind = 30 kmph

The speed of Biswanath = 60 kmph

Let the time take by Biswanath = X hours

Implies, the time taken by Aravind = X hours + 20 minutes = (X + 1/3) hours

Now,

Speed × Time = Distance

30 × (X + 1/3) = 60 × X 

⇒ 30X + 10 = 60X

⇒ 30X = 10

⇒ X = 1/3 hours = 20 minutes

Distance = 1/3 × 60 = 20 km

Hence, the distance between the hostel and the ground is 20 km.

The given shape:

Clearly, the above shape is hidden in the figure below:

Hence, the given shape is embedded in the fourth figure.

The logic followed here is:

(1^st number + 2^nd number) × 2 - 1 = 3^rd number

(11, 19, 59)

(11 + 19) × 2 - 1

= 30 × 2 - 1

= 60 - 1 = 59

Option 3: (8, 13, 41)

(8 + 13) × 2 - 1

= 21 × 2 - 1 

= 42 - 1 = 41

Hence, the correct answer is "(8, 13, 41)".

Alternate Method

The logic followed here is:

(11, 19, 59)

(11 × 2 - 3 = 19, 19 × 3 + 2 = 59),

Similar,

(8 × 2 - 3 = 13, 13 × 3 + 2 = 41),

Hence, (8, 13, 41) is similar to the given set of numbers.

the given series:

In figure B, with respect to figure A, the number of triangle is increased by one and the incomplete diagonals are completed. Similarly, in figure D, with respect to figure C, the number of circles will be increased by one and both diagonals will be completed. Hence, there will be three concentric circles in the answer figure with three diameters as shown below.

Hence, the third option is the answer figure.

Given:

Radius of sphere = 8 cm

Radius of cylinder = x cm

Height of cylinder = 3 × radius of sphere    

Formula Used:

Volume of solid sphere = 4/3 πr³

Volume of solid cylinder = πr²h 

Calculation:

A solid metallic sphere is converted into a solid right circular cylinder.

According to the question,

Volume of Solid metallic sphere = Volume of Solid right circular cylinder

⇒ 4/3 πr³ = πr²h

⇒ 4/3 r³ = r²h

⇒ 4/3 × 8 × 8 × 8 = x² × 24

⇒ 4/3 × 1/24 × (8 × 8 × 8) = x²

⇒ 256/9 = x²

⇒ 16/3 = x ⇒ \(5\dfrac{1}{3}\)

∴ The value of x is  \(5\dfrac{1}{3}\)

Given:

 (a² + b²) ∶ (b² + c²) ∶ (c² + a²) = 34 ∶ 61 ∶ 45

Calculation:

 (a2 + b2) ∶ (b2 + c2) ∶ (c2 + a2) = 34 ∶ 61 ∶ 45

⇒ (a² + b²) + (b² + c²) + (c² + a²) = 34 + 61 + 45

⇒ 2(a² + b² + c²) = 140

⇒ (a² + b² + c²) = 140/2

⇒ (a² + b² + c²) = 70

⇒ So, a²  = (a² + b² + c²) - (b² + c²)

⇒ a²  = 70 – 61

⇒ a²  = 9

Similarly, b² = 70 – 45 which gives 25, and c²  = 70 – 34 which gives 36.

So, a ∶ b ∶ c = √9 ∶ √25 ∶ √36

⇒ a : b : c = 3 : 5 : 6

∴ The value of a : b : c is 3 : 5 : 6.

Shortcut Trick 

Given:

 (a2 + b2) ∶ (b2 + c2) ∶ (c2 + a2) = 34 ∶ 61 ∶ 45

Calculation:

Now we will use the option method to verify the answer.

1. a ∶ b ∶ c = 6 ∶ 3 ∶ 5

⇒ (a2 + b2) ∶ (b2 + c2) ∶ (c2 + a2) = 44 ∶ 34 ∶ 61

2. a ∶ b ∶ c = 5 ∶ 3 ∶ 6

⇒ (a2 + b2) ∶ (b2 + c2) ∶ (c2 + a2) = 34 ∶ 45 ∶ 61

3. a ∶ b ∶ c = 3 ∶ 5 ∶ 6

⇒ (a2 + b2) ∶ (b2 + c2) ∶ (c2 + a2) = 34 ∶ 61 ∶ 45

4. a ∶ b ∶ c = 3 ∶ 6 ∶ 5

⇒ (a2 + b2) ∶ (b2 + c2) ∶ (c2 + a2) = 45 ∶ 61 ∶ 34

∴ The value of a : b : c is 3 : 5 : 6.

Given:

The average score of 52 students is 45.

Formula used:

The sum of the scores of all students = The average × Total number of students

Calculation:

The sum of the scores of 52 students(A) = 52 × 45 = 2340

If the highest and the lowest scores are excluded then the average decreases by 1

The sum of the scores of remaining 50 students(B) = 50 × 44 = 2200

The sum of the highest and the lowest scores = A - B

⇒  A - B = 2340 - 2200

⇒  A - B = 140

The average of the highest and the lowest scores = 140/2 = 70

∴ The average of the highest and the lowest scores 70.

Given:

The amount for 4 years is 9900 Rs, and the amount for 7 years is 11700 Rs at simple interest

The rate for \(2\frac{1}{4}\) years is \(8\frac{2}{3}% \)

Formula:

Simple interest = P × R × T/100

Calculation:

Amount of 4 year = P (1 + 4R/100)

Amount of 7 year = P (1 + 7R/100)

P (1 + 4R/100) = 9900      ----(1)

P (1 + 7R/100) = 11700    ----(2)

Subtract equation (1) from (2)

We get,

⇒ 3PR/100 = 1800

⇒ PR/100 = 600

We put the value of PR/100 in equation (1)

⇒ P + 4 × 600 = 9900

⇒ P = 9900 – 2400 = 7500for

So, the principle we get 7500

The value of amount at simple interest if the rate is \(8\frac{2}{3}% \) for \(2\frac{1}{4}\)years

The amount = P (1 + 26 × 9/100 × 3 × 4)

⇒ 7500 (1 + 234/1200)

⇒ 7500 (1434/1200)

⇒ 8962.50

∴ The amount is Rs. 8962.50

 

4-year amount 9900

7 years amount 11700

⇒ 3 year simple interest = 1800

⇒ 1 year simple interest = 600

⇒ p = 7500

The amount = P (1 + 26 × 9/100 × 3 × 4)

⇒ 7500 (1 + 234/1200)

⇒ 7500 (1434/1200)

⇒ 8962.50

∴ The amount is Rs. 8962.50

Given:

 80% of 50% of A = 3 × (25% of B)

Calculation:

80% × 50% × A = 3 × (25% × B)

⇒ 4/5 × 1/2 A = 3 × B/4

⇒ 8A = 15B

⇒ A : B = 15 : 8

Percentage difference = (A - B)/B × 100

⇒ (15 – 8)/8 × 100

⇒ 87.5%

∴ The value of A is 87.5% more than B.

Given:

Rs.12,705 in 2½  years at 10% p.a. interest compounded annually.

Formula used:

Compound interest = P{1 + (r/100)} ^t  - P

P = Principle, r = rate, t = time

Calculation:

Let the Principle be P

Sum amounts to Rs.12,705 in 2½  years at 10% p.a. interest compounded annually.

P(100+10)^2½/100 = 12,705

⇒ P(110/100 × 110/100 × 105/100) = 12,705

⇒ 1.2705P = 12,705

⇒ P = 10000

If the interest is compounded half-yearly on Rs. 10000 in one year at 10% p.a.

⇒ Amount = 10000(105/100 × 105/100)

⇒ 11025

C.I. = Amount - Principle

⇒ 11025 – 10000

⇒ 1025

∴ The amount for compound interest is Rs. 1025

Alternate Method

Sum of C.I = 500 + 525

⇒ 1025

∴ The amount for compound interest is Rs. 1025.

Given:

A circle is inscribed in an equilateral triangle of side 30 cm.

Formula Used:

Area of a triangle = 1/2 × base × height  

Area of an equilateral triangle = √3/4 × a²

where a = side of the triangle

Calculation:

Let the triangle be Δ ABC with sides, a = 30 cm,

and draw the angle bisectors of all three angles of the triangle as shown in the above figure.

Let the centre of the circle be O. 

Here, OP = OQ = OR = r           where r = radius of the circle

We have O as the incentre and OP, OQ and OR are equal.

 Now, from the above figure,

Area of Δ ABC = Area of Δ OAB + Area of Δ OBC + Area of Δ OCA

⇒ √3/4 × a² = (1/2 × AB × OP) + (1/2 × BC × OR) + (1/2 × AC × OQ)

⇒ √3/4 × (30)² = (1/2 × a × r) + (1/2 × a × r) + (1/2 × a × r)

⇒ √3/4 × 900 = 3 × (1/2 × a × r)

⇒ √3/4 × 900 = 3 × (1/2 × 30 × r)

⇒ r = 15/√3 cm

Now, Area of the Circle = πr²

⇒ Area of the Circle = π × (15/√3)²

⇒ Area of the Circle = π × 225/3

⇒ Area of the Circle = 75π

∴ The area of the triangle is 75π cm²

Alternate Method

Here, AR is the median of the triangle.

We know that the Median of an equilateral triangle = (√3/2) × a

So, AR = (√3/2) × 30 

⇒ AR = 15√3 cm

Now, We know that the Centroid of a triangle divides its median in the ratio of 2 ∶ 1.

So, AO ∶ OR = 2 ∶ 1

⇒ OR ∶ AR = 1 ∶ 3 

So, from the above figure,  Radius of Circle, r = OR 

⇒ r = (1/3) × AR

⇒ r = (1/3) × 15√3

⇒ r = 15/√3 cm

Now, Area of the Circle = πr2

⇒ Area of the Circle = π × (15/√3)2

⇒ Area of the Circle = π × 225/3

⇒ Area of the Circle = 75π

∴ The area of the triangle is 75π cm2

Given:

The marked price is 25% above its cost price.

Selling price = Rs. 480, Discount = Rs. 60

Calculation:

C.P = cost price, S.P = selling price, M.P = marked price, d = discount

Let the C.P of the article be 100x

M.P = 100x + 25% of 100x

⇒ M.P = 125x

Also M.P = S.P + d = 480 + 60 = 540

Now it is clear that 125x = 540

⇒ x = 540/125 = 108/25

⇒ 100x = 100 × (108/25)

⇒ 100x = 4 × 108

⇒ 100x = 432

Profit = S.P - C.P

⇒ 480 - 432 ⇒ 48

Percentage profit = (48/432) × 100

⇒ (1/9) × 100 ⇒ 11.1%

∴ The profit percentage is 11.1%.

M.P = 125% of c.p

⇒ M.P/C.P = 125/100 = 5/4

M.P = 5R = 480 + 60 = 540 

⇒ R = 108 

4R = 432

⇒ C.P = 432

Profit = 480 - 432 = 48

Percentage profit = (48/432) × 100 = (1/9) × 100 = 11.1%

∴ The profit percentage is 11.1%.

Given:

\(1\dfrac{1}{6}\div \dfrac{2}{3} of \dfrac{7}{8}-\dfrac{7}{8}\div \dfrac{5}{6}\times\dfrac{5}{24}-(0.6\bar5 \div 0.\overline{59})\times 1\dfrac{1}{11} \)

Concept:

Follow The BODMAS rule which is given in the table below-

Calculation:

\(1\dfrac{1}{6}\div \dfrac{2}{3} of \dfrac{7}{8}-\dfrac{7}{8}\div \dfrac{5}{6}\times\dfrac{5}{24}-(0.6\bar5 \div 0.\overline{59})\times 1\dfrac{1}{11} \)

\(\Rightarrow\dfrac{7}{6}\div \dfrac{2}{3} of \dfrac{7}{8}-\dfrac{7}{8}\div \dfrac{5}{6}\times\dfrac{5}{24}-\left(\dfrac{59}{90} \div \dfrac{59}{99}\right)\times \dfrac{12}{11} \)

\(\Rightarrow 2 - \dfrac{7}{32}-\dfrac{11}{10} \times \dfrac{12}{11} \)

\(\Rightarrow \dfrac{57}{32}-\dfrac{6}{5} \)

\(\Rightarrow \dfrac{93}{160} \)

∴ The value of  \(1\dfrac{1}{6}\div \dfrac{2}{3} of \dfrac{7}{8}-\dfrac{7}{8}\div \dfrac{5}{6}\times\dfrac{5}{24}-(0.6\bar5 \div 0.\overline{59})\times 1\dfrac{1}{11} \) is \(\dfrac{93}{160} \)

Confusion Points

Let \(0.6\bar5\) be x 

x = \(0.6\bar5\)

10x = 6.555...      ----(1)

100x = 65.555...      ----(2)

Subtracting eq (1) from eq (2)

90x = 59

x = 59/90

Given:

The remainder is 3 when the smallest 4-digit number is divided by 4, 5, 6, 9.

Concept used:

Dividend = divisor × quotient + remainder

Calculation:

Let the smallest number be N.

Using the standard identity,

Dividend = divisor × quotient + remainder 

N = 4 × p + 3 

⇒ N - 3 = 4 × p 

N = 5 × q + 3

⇒ N - 3 = 5 × q

N = 6 × r + 3

⇒ N - 3 = 6 × r

N = 9 × s + 3

⇒ N - 3 = 9 × s

Since N - 3 is the smallest number satisfying the given condition, N - 3 will be the LCM of 4, 5, 6, 9.

N - 3 = LCM(4, 5, 6, 9) = 180

As 180 is not a 4-digit number, we have to find the smallest 4-digit number multiple of 180.

180 × 5 = 900 (not a 4-digit number), so take its next multiple.

180 × 6 = 1080

So, N - 3 = 1080

⇒ N = 1083

Sum of digits of 1083 = 1 + 0 + 8 + 3 = 12

∴ The sum of digits of N is 12.

Given:

The number of students that appeared from school A is 20% more than the number of students that appeared from school B.

The total number of students that passed from both schools is 80% more than the number of students that passed from school B.

Calculation:

Let be the number of students who appeared in the examination from school B is 100.

According to the question, the number of students who appeared in the examination from school A = 120% of 100 ⇒ 120

Number of students passed from school B  = 100 × (75/100) ⇒ 75

Total number of students passed in schools A and B = 75 × (180/100) ⇒ 135

The number of students passed in school A = 135 – 75 ⇒ 60

The number of students passed in school A percentage = (students pass in school A)/(Total students appeared in school A)

⇒ (60/120) × 100 ⇒ 50%

∴ The percentage of students that passed from school A to those who appeared from school A is 50%.

Given:

A completed 2/3^rd part of a work in 16 days

B completed 1/3^rd part of a work in 5 days

Total work completed in 21 days

Formula:

Total time = (Total work)/(One day work)

Calculation:

Let total work be x

A completed 2/3^rd part of a work in 16 days

⇒ 2x/3 = 16

⇒ x = (16 × 3)/2 = 24

⇒ Total work done by A in 24 days

B completed 1/3^rd part of a work in 5 days

⇒1x/3 = 5

⇒ x = 15

⇒ Total work done by B in 15 days

Now,

One day work of A and B = (x/24 + x/15)

⇒ (5x + 8x)/120

⇒ 13x/120

Total time taken by A and B = (Total work)/(One day work)

⇒ [x/(13x/120)]

⇒ Total time taken by A and B is 120/13

We have to find the time in which 65% of total work is done by A and B

⇒ [(120/13) × (65/100)] = 6

∴ A and B together will complete 65% of the work in 6 days

Alternate Method

2a/3 = 16

⇒ a = 24

1b/3 = 5

⇒ b = 15

LCM of 24 & 15 is 120

Total time = 120/13

⇒ Required time = (120/13) × (65/100)

∴  A and B together will complete 65% of the work in 6 days

Given:

If Sumit sold an article at fourth-fifth of the original selling price, he would have lost 10%.

Formulae Used:

Profit% = [(SP – CP)/CP] × 100

Loss% = [(CP – SP)/CP] × 100

Where, SP = Selling Price, and CP = Cost Price

Calculation:

Let the original selling price be Rs.x and the Cost Price of the article be CP

If selling at a price that is (4/5)^th of the original selling price, then we get:

New SP = (4/5)x = 0.8x

At this SP, the loss is 10%. Hence, we get:

10 = [(CP – 0.8x)/CP] × 100

⇒ 10CP = 100CP – 80x

⇒ 9CP = 8x

⇒ CP = (8/9)x      ----(i)

Now, when it is sold at an SP, which is 95% of the original SP, we get:

Final SP = (95/100)x = (19/20)x      ----(ii)

Hence, the finally obtained profit is:

Profit% = {[(19/20)x – (8/9)x]/[(8/9)x]} × 100

⇒ Profit% = (11/180) × (9/8) × 100 = (55/8)%

∴ The required profit will be \(6\frac{7}{8}\)%

Given:

After passing each other, X and Y take \(8\dfrac{2}{5}\) hours and \(4\dfrac{2}{7}\) hours

The speed of X is 50 km/h

Concept Used:

If two trains start at the same time with speeds x km/h and y km/h and after meeting they reach their destination in t₁ hours and t₂ hours then the relation between speed and time is \({x \over y} = \sqrt {t_2 \over t_1}\)

Calculation:

Here x = 50 km/h

t₁ = \(8{2 \over 5}\) hours = 42/5 hours

t₂ = \(4{2 \over 7}\) hours = 30/7 hours

Let, the speed of the train Y be a km/h

Accordingly,

\({50 \over a} = {\sqrt{{30 \over 7} \over {42 \over 5}}}\)

⇒ \({{50} \over a} = {\sqrt{{30 \times 5} \over {7 \times 42}}}\)

⇒ \({50 \over a} = \sqrt {5 \times 5 \over 7 \times 7}\)

⇒ 50/a = 5/7

⇒ a = 70

∴ The speed of the train Y is 70 km/hr.

Given:

The unit digit of a 2-digit number exceeds the tens digit by 3

The product of the given number and the sum of its digits = 324

Concept Used:

Principle of Place Values (Unit digit and Ten's Digit) of a number 

Calculation:

Let the 2 digit number be (10x + y)

From the given conditions, we get the following equations:

y – x = 3      ----(i)

(10x + y) × (x + y) = 324      ----(ii)

From the equation (i), we get:

y = x + 3      ----(iii)

On substituting the value of equation (iii) into equation (ii), we get:

(10x + x + 3) × (x + x + 3) = 324      

⇒ (11x + 3) × (2x + 3) = 324      

⇒ 22x² + 33x + 6x + 9 = 324

⇒ 22x2 + 39x – 315 = 0

⇒ [x + (105/22)](x – 3) = 0

As we cannot have a negative value of x,

⇒ x = 3      ----(iv)

Also, from equation (iii), we get:

y = 3 + 3 = 6      ----(v)

On combining equations (iv) and (v), we obtain the 2-digit number as:

(10 × 3) + 6 = 36

∴ The given two-digit number lies between 35 and 40