The logic followed here is :-

‘DESERT’ is coded as ‘415163’.

And

‘ARMY’ is coded as 2687’.

Similarly,

‘SMART’ will be coded as :

Hence, the correct answer is "58263".

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

2. Favourable
3. Favourably
4. Favoured
5. Favourite
6. Favouritism

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

The logic followed here is :-

Hence, the correct answer is "912".

Given :- kg_pg_kgt_gnk_tpg_kg_p_n

By checking options and substituting accordingly.

1) t, n, p, g, n, t, g → k g t p g n - k g t p g n - k g t p g n - k g t p g n

• Here, "kgtpgn" is repeated.

2) t, n, p, g, g, n, t → k g t p g n - k g t p g n - k g t p g g - k g n p t n

3) t, p, n, n, g, g, t → k g t p g p - k g t n g n - k n t p g g - k g g p t n

4) t, p, n, g, n, g, t → k g t p g p - k g t n g n - k g t p g n - k g g p t n

• Option (1) gives the pattern of :- k g t p g n - k g t p g n - k g t p g n - k g t p g n

Hence, the correct answer is "t, n, p, g, n, t, g".

The logic followed here is :-

'FOAMING' is written as 'AOFMGNI'.

Similarly,

'BELIEVE' will be written as :

Hence, the correct answer is "LEBIEVE".

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

Hence, the correct answer is "Option 1".

The logic followed here is :-

Hence, the correct answer is "42".

The logic followed here is :-

Hydrophobia means extreme or irrational fear of water.

Similarly,

Acrophobia means extreme or irrational fear of heights.

Hence, the correct answer is "Height".

Preparing the family tree using the following symbols:

According to the given information,

The given expression is :

'K $ H % Y # M # R' → K is wife of H, H is father of Y, Y is brother of M, M is brother of R.

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∴ Here, 'K' is mother of 'R'.

Hence, the correct answer is "Mother".

The logic followed here is:

The opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surfaces are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

In the given figure, Opposite faces are :

∴ Here, the opposite face to the face showing '&' is '$'.

Hence, the correct answer is "$".

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

• The square box moves one step clockwise with half part darken and alternatively from figure to figure.
• The circle below half part darken in 1st figure and un darken part is darken in next figure and repeated.

Hence, the correct answer is "Option 3".

The logic followed here is :-

YKMP : QNLZ

Similarly,

SURC : ?

Hence, the correct answer is "DSVT".

Six friends, namely Avik, Rishi, Piyush, Sonal, Aashu, and Rohit, are standing in a row facing north.

1) Rishi is standing to the left of Avik and to the right of Piyush.

2) Sonal is standing to the right of Avik and to the left of Aashu and Aashu is standing to the left of Rohit.

∴ Here, In the row Avika and Sonal are sitting in centre.

Hence, the correct answer is "Avik and Sonal".

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

Conclusions:

I. Some chocolates are not coconuts → False (As All chocolates are fruits and All fruits are coconuts so, Some chocolates are not coconuts is false)

II. All chocolates are coconuts → True (As All chocolates are fruits and All fruits are coconuts so, All chocolates are coconuts is true)

III. Some coconuts are fruits → True (As All fruits are coconuts so, Some coconuts are fruits is true)

∴ Here, Conclusions II and III are true.

Hence, the correct answer is "Only conclusions II and III follow".

The logic followed here is :-

(Third number - First number)³ = + Second number

(5, 27, 8) → (8 - 5)³ = 3³ = 27

1) (8, 60, 6) → (6 - 8)³ = - 2³ = - 8

2) (4, 54, 6) → (6 - 4)³ = 2³ = 8

3) (16, 24, 12) → (12 - 16)³ = - 4³ = - 64

4) (11, 64, 15) → (15 - 11)³ = 4³ = 64

Hence, the correct answer is "(11, 64, 15)".

The image not embedded in given figure is as shown below :

Hence, the correct answer is "Option 1".

The logic followed here is :-

<br> <br>

1) QNLH

2) QNKH

3) MJGE

4) URPL

Hence, the correct answer is "QNKH".

Six friends, K, L, M, N, O and P, are sitting around a hexagonal shaped table at equal distances between them.

1) K is facing P and M is to the immediate left of P.

2) N is sitting between K and L and O is second to the right of N.

∴ Here, 'M' is sitting to immediate right of 'O'.

Hence, the correct answer is "M".

Given,

Mr. Gupta is 26 years older than his son Shashank.

Let us consider Shashank age = X

⇒ Age of Mr. Gupta = X + 26 .......... (1)

Shashank's sister Gargi is 4 years younger than Shashank.

⇒ Age of Gargi = X - 4 ........... (2)

The age of Mr. Gupta is four times the age of Gargi.

⇒ Age of Mr. Gupta = 4 × Age of Gargi ........... (3)

Substitute equation 1 and 2 in equation 3.

∴ X + 26 = 4(X - 4)

⇒ X + 26 = 4X - 16

⇒ 3X = 42

⇒ X = 14

Age of Shashank is X = 14 years.

Hence, the correct answer is "14 years".

The logic followed here is :-

By using BODMAS RULE 

Option 1) : 7 and 24

Given equation : 15 × 7 + 40 – 24 ÷ 8 = 124

After interchanging the number in given equation the equation is as follows : 15 × 24 + 40 – 7 ÷ 8 = 124

⇒ 15 × 24 + 40 – 7 ÷ 8 = 124

⇒ 15 × 24 + 40 – 0.875 = 124

⇒ 360 + 40 – 0.875 = 124

⇒ 400 – 0.875 = 124

⇒ 399.125 ≠ 124

LHS ≠ RHS

Option 2) : 7 and 15

Given equation : 15 × 7 + 40 – 24 ÷ 8 = 124

After interchanging the number in given equation the equation is as follows : 7 × 15 + 40 – 24 ÷ 8 = 124

⇒ 7 × 15 + 40 – 24 ÷ 8 = 124

⇒ 7 × 15 + 40 – 3 = 124

⇒ 105 + 40 – 3 = 124

⇒ 145 – 3 = 124

⇒ 142 ≠ 124

LHS ≠ RHS

Option 3) : 24 and 8

Given equation : 15 × 7 + 40 – 24 ÷ 8 = 124

After interchanging the number in given equation the equation is as follows : 15 × 7 + 40 – 8 ÷ 24 = 124

⇒ 15 × 7 + 40 – 8 ÷ 24 = 124

​⇒ 15 × 7 + 40 – 0.33 = 124

​⇒ 105 + 40 – 0.33 = 124

​⇒ 145 – 0.33 = 124

​⇒ 144.67 ≠ 124

LHS ≠ RHS

Option 4) : 24 and 40

Given equation : 15 × 7 + 40 – 24 ÷ 8 = 124

After interchanging the number in given equation the equation is as follows : 15 × 7 + 24 – 40 ÷ 8 = 124

⇒ 15 × 7 + 24 – 40 ÷ 8 = 124

⇒ 15 × 7 + 24 – 5 = 124

⇒ 105 + 24 – 5 = 124

⇒ 129 – 5 = 124

⇒ 124 = 124

LHS = RHS

Hence, the correct answer is "24 and 40".

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

Hence, the correct answer is "Option 1".

The logic followed here is :-

'FREE' is written as 'AQRR'.

And

'ASTER' is written as DNXRQ'.

Similarly,

'STARS' will be written as :

Hence, the correct answer is "NXDQN".

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

• All Colony are part of a District.
• All Districts are part of State.

Hence, the correct answer is "Option 1".

The logic followed here is :-

1) NGI

2) PLK

3) KDF

4) QJL

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

Hence, the correct answer is "PLK".

The logic followed here is :-

Second number³ + 1 = First number.

• 126 : 5 → 5³ + 1 = 125 + 1 = 126
• ? : 4 → 4³ + 1 = 64 + 1 = 65
• 28 : 3 → 3³ + 1 = 27 + 1 = 28

Hence, the correct answer is "65".

The correct answer is Boxing.

Key Points

• Sportsperson Duryodhan Singh Negi is renowned for Boxing.
• He played the first time in World Boxing Championship.
• Negi lost to Jordan's Zeyad Eashash in the second round.
• He already had won the silver medal (69Kg) in the commonwealth games.

Additional Information

• Boxing is a combat sport in which two people wearing protective gloves and other protective equipment such as hand wraps and mouthguards, throw punches at each other for a predetermined amount of time in a boxing ring.
• Depiction of boxing comes from a Sumerian relief in Iraq from the 3rd millennium BC.
• Boxers are prohibited from hitting below the belt, holding, tripping, pushing, biting, or spitting.

The correct answer is Paulo Coelho.

Key Points

• The Alchemist is a novel by Brazilian author Paulo Coelho that was first published in 1988.
• Originally written in Portuguese, it became a widely translated international bestseller.
• The Alchemist follows a young Andalusian shepherd in his journey to the pyramids of Egypt, after having a recurring dream of finding a treasure there.
• Paulo Coelho de Souza is a Brazilian lyricist and novelist and a member of the Brazilian Academy of Letters since 2002.
• His novel The Alchemist became an international best-seller and he has published 28 more books since then.

Additional Information

• Anthony Doerr is an American author of novels and short stories.
• He gained widespread recognition for his 2014 novel All the Light We Cannot See, which won the Pulitzer Prize for Fiction.
• Catherine Burns was an American actress on stage, film, radio and television.
• She was nominated for an Academy Award for Best Supporting Actress for her performance in Last Summer.
• Ruskin Bond is an Anglo-Indian author.
• His first novel, The Room on the Roof, was published in 1956, and it received the John Llewellyn Rhys Prize in 1957.

The correct answer is Depreciation.

Key Points

• Depreciation is an annual allowance for wear and tear of a capital good.
• In simple terms means the decrease in the monetary value of an asset because of its wear and tear over the years.
• It may also become obsolete because of technological advancements over the years.
• It refers to determining the monetary value of the asset spread over its useful life years.
• It is the reduction in the value of an asset with the passage of time.
• This decline in value is due to wear and tear deterioration, or obsolescence.

Additional Information

• Different methods to calculate depreciation are as follows :
• Straight-line method → Used for buildings, etc
• Constant percentage method → Used for electronics equipment etc.
• Sinking fund method
• Double decline method
• Sum of year digit method
• ​Straight-line method:
• It is used when the assets lose their value by a fixed amount every year.
• At the end of the utility period book value becomes equal to salvage value.
• It is used for all the assets which do not get obsolete during their utility period.
• ​Constant percentage method:
• It is used for the assets which lose their value at a constant percentage of their book value.
• It is most useful for assets that have the probability of obsolescence before their utility period.
• It can not be used when the salvage value of the asset is zero.
• ​Double decline method:
• It is used when assets are assumed to lose their value by a fixed factor of the book value i.e. double the straight-line method.
• It is used for all the assets which may get obsolete before estimated life.
• ​Sinking fund method:
• In this method of depreciation calculation, the amount is the sum of the amount deposited into the sinking fund every year and the amount of interest earned on the accumulated value of the sinking fund at the beginning of the particular year.
• ​Sum of year digit method:
• It is used when the asset value is reduced to zero at the end of the utility period.

The correct answer is the Raja Todar Mal.

 Key Points

• ​Raja Todar Mal was the finance minister of the Mughal emperor Akbar.
• He introduced the Dahsala system of taxation in 1580 AD.
• This system was based on the average production of different crops over the past 10 years.
• The state's share was one-third of the average produce.
• The Dahsala system was adopted in most of the provinces of the Mughal Empire, except for the ones that were predominantly Muslim.
• The Dahsala system was a more efficient and equitable system of taxation than the previous systems.
• It helped to ensure that the state received a fair share of the revenue, while also protecting the interests of the farmers.
• The Dahsala system was also one of the factors that contributed to the economic prosperity of the Mughal empire during Akbar's reign.

Additional Information

• Raja Todar Mal divided all cultivable land into four categories:
• Polaj: It was the best land cultivated every year.
• Parauti: It was the land of the second category which was left uncultivated for one year or two so that it could recover its fertility.
• Chachar: It was left uncultivated for three to four years in order to make it cultivable.
• Banjar: Land that was not fit for agriculture and was mostly left uncultivated for a long time.

The correct answer is Dividend distribution tax.

Key Points

• Tax on cooperative societies was to be reduced to 22% plus surcharge and cess as against 30% at present.
• Dividend Distribution Tax (DDT) was abolished under the Budget of 2020-2021.

Additional Information

• Changes in Taxation
• Dividend Distribution Tax (DDT) was removed.
• Instead of companies paying DDT on the dividend they give out, the dividend income will now be added to the taxable income of the recipient and taxed at the applicable rate.
• Income Tax
• New tax slabs and lower income tax rates.
• Around 70 of the existing exemptions and deductions to be removed in the new simplified regime.
• New tax regime to be optional - an individual may continue to pay tax as per the old regime and avail deductions and exemptions.
• Corporate Tax: Concessional corporate tax rate of 15% to new domestic companies in the manufacturing and power sector.
• 5% health cess to be imposed on imports of medical equipment given these are made significantly in India.
• Issuance of Unique Registration Numbers to all charity institutions for easy tax compliance.
• ‘Vivad Se Vishwas’ scheme, with a deadline of 30th June 2020, to reduce litigations indirect taxes.
• 100% tax exemption to the interest, dividend and capital gains income on the investment made in infrastructure and priority sectors before 31st March 2024 with a minimum lock-in period of 3 years by the Sovereign Wealth Fund of foreign governments.

The correct answer is Johan Cruyff.

Key Points

• Johan Cruyff was a Dutch professional football player and coach.
• He was named European Footballer of the Year in 1971, 1973 and 1974.
• He was a key player in the great Netherlands team that reached the 1974 World Cup final.
• He was considered an exceptional manager winning four Spanish titles and the European Cup when he was in charge of Barcelona.

Additional Information

• Jacques Henry Kallis is a South African cricket coach and former cricketer.
• Sir Donald George Bradman, nicknamed "The Don", was an Australian international cricketer.
• Edson Arantes do Nascimento, known as Pelé, is a Brazilian former professional footballer who played as a forward.

The correct answer is Tomb of Jahangir.

Key Points

• The Tomb of Jahangir is a 17th-century mausoleum built for the Mughal Emperor Jahangir.
• The mausoleum dates from 1637 and is located in Shahdara Bagh near the city of Lahore, Pakistan, along the banks of the Ravi River.
• Hence it is not in Uttar Pradesh.

Important Points

• Akbar's tomb is the tomb of the Mughal emperor Akbar.
• It was built in 1605–1613 by his son Jahangir and is situated on 119 acres of grounds in Sikandra, a sub of Agra, Uttar Pradesh, India.
• The Tomb of Salim Chishti is famed as one of the finest examples of Mughal architecture in India, built during the years 1580 and 1581, along with the imperial complex at Fatehpur Sikri, Agra UP.
• Tomb of I'timād-ud-Daulah is a Mughal mausoleum in the city of Agra in the Indian state of Uttar Pradesh.

Additional Information

• Uttar Pradesh has the maximum number of monuments in India that count a total number of 3,685 monuments.
• The place is known as the ‘heartland of India’ due to its cultural heritage and historical relevance.
• Most of the monuments in India are well-maintained by the Archaeological department of India. However, these popular spots foresay the ruthlessness of previous rulers and their impact on them.
• Maharashtra has the maximum number of UNESCO World Heritage Sites.
• There are now 42 World Heritage sites in India, out of which 34 are cultural sites, 7 natural sites, and 1 mixed site.

The correct answer is Chutkay.

Key Points

• Chutkay is the traditional dance form of the state of Sikkim.
• Through this romantic group dance, performed by a group of male and female dancers, joys of life and feeling of happiness is shared during the harvesting season and on some other happy occasions.

Additional Information

The correct answer is capillaries.

Key Points

• The arteries divide into smaller vessels. On reaching the tissues, they divide further into extremely thin tubes called capillaries.
• Capillaries are delicate blood vessels that exist throughout your body.
• They transport blood, nutrients and oxygen to cells in your organs and body systems.
• Capillaries are the smallest blood vessels in your vascular system.

Additional Information

• An arteriole is a very small blood vessel that branches off from your artery and carries blood away from your heart to your tissues and organs.
• Arterioles are small arteries that link up to capillaries, which are smaller yet.
• Venules are the smallest veins and receive blood from capillaries.
• They also play a role in the exchange of oxygen and nutrients for water products.
• Veins are blood vessels located throughout your body that collect oxygen-poor blood and return it to your heart.
• Veins are part of your circulatory system.

The correct answer is Ancy Sojan.

Key Points

• Ancy Sojan became the fastest athlete at the Khelo India Youth Games 2020.
• Ancy Sojan claimed the under-20 men and women's 200m crowns respectively on the final day of the 36th National Junior Athletics Championships on 10 Feb 2021.

Additional Information

• Khelo India Youth Games 2020 was held in Guwahati.
• Winner - Maharashtra
• The champions trophy was handed over to Maharashtra, the first runner-up trophy to Haryana, and the second runner-up trophy to Delhi.
• Khelo India Youth Games is an annual event.
• The first edition was held in 2018 in Delhi.
• The second edition was held in Pune, Maharashtra.

The correct answer is Amish Tripathi.

Key Points

• Amish Tripathi is the author of the Indian English Novel ‘Sita: Warrior of Mithila’ published in 2017.
• The book is based on the epic Ramayana and the story of the Hindu goddess Sita.
• The author has transformed Indian Fiction with a unique combination of mystery, mythology, religious symbolism and philosophy.
• It is the second book of the Ram Chandra Series of Amish Tripathi published in the English language.

Additional Information

• Some important novels of Amish Tripathi-

1. The Immortals of Meluha.
2. Sita: Warrior of Mithila.
3. The Secret of the Nagas.
4. The Oath of the Vayuputras.

The correct answer is Rajasthan.

Key Points

• National Research Centre on Rapeseed-Mustard is located in Rajasthan, India.
• National Research Centre on Rapeseed-Mustard (NRCRM)
• Founded- October 20, 1993
• Established By- ICAR
• Center Location- Sewar, Bharatpur

Additional Information 

• Indian Council of Agricultural Research (ICAR)
• Founded-  16 July 1929
• Headquater- New Delhi
• Organization Body-  Autonomous
• Ministery- The Department of Agricultural Research and Education (DARE), Ministry of Agriculture and Farmers Welfare.

The correct answer is SR Rao.

Key Points 

• SR Rao discovered the remains of the Harappan Civilization at the Lothal site. 
• ​It is a Harappan site located between the Bhogavo and Sabarmati rivers in present-day Gujarat.
• This city was mathematically planned with streets crossing at right angles and drainage systems.
• Divided into two parts i.e. the upper town and the lower town.
• This site is famous for the rectangular basin that was said to be the dockyard.

Important Points

• Indus Valley Civilization :
• It is ​also known as the Harappan Civilization after the first city to be excavated, Harappa.
• It dates back to around 2,500 BC in the western part of South Asia.
• In the 1920s, the Archaeological Department of India unearthed two old cities namely Mohenjodaro and Harappa.
• Geographically, this civilization covered Punjab, Rajasthan, Sindh, Gujarat, Baluchistan, and Western Uttar Pradesh.

Additional Information

• Kalibang​a​n:
• ​This Harappan site is located in Rajasthan on the bank of the Ghaggar river.
• This site was excavated by Ghose in 1953.
• Important findings from this site are fire alter, camel bones, and a wooden plough.
• ​Banawali:
• Located in the Fatehabad district of Haryana.
• This site was excavated by R.S Bisht in 1974.
• This site is famous for beads, barley and shows evidence of both pre-Harappan and Harappan culture.

The correct option is 2008.

Key Points

• In 2008, the monarchy was abolished and Nepal became a federal democratic republic.
• In 2015, it adopted a new constitution. The struggle of the Nepali people is a source of inspiration to democrats all over the world.
• On 24 April 2006, the last day of the ultimatum, the king was forced to concede all three demands.
• The SPA chose Girija Prasad Koirala as the new Prime Minister of the interim government.
• The restored parliament met and passed laws taking away most of the powers of the king. The SPA and the Maoists came to an understanding about how the new Constituent Assembly was going to be elected.

Additional Information 

• All the major political parties in the parliament formed a Seven Party Alliance (SPA) and called for a four-day strike in Kathmandu, the country’s capital.
• This protest soon turned into an indefinite strike in which MAOIST insurgents and various other organizations joined hands.
• People defied curfew and took to the streets.
• The security forces found themselves unable to take on more than a lakh people who gathered almost every day to demand the restoration of democracy.
• The number of protesters reached between three and five lakhs on 21 April and they served an ultimatum to the king.
• The leaders of the movement rejected the half-hearted concessions made by the king.
• They stuck to their demands for the restoration of parliament, power to an all-party government, and a new constituent assembly.

The correct answer is Six.

Key Points

• Swajal Yojana
• Launched in the year February 2018 under the National Rural Drinking Water Program.
• AIM – To ensure sustainable, adequate piped drinking water supply through replenishment of ground water and augmentation of water resources by means of solar energy.
• Decentralized planning and implementation of the scheme where state governments facilitate and promote rural communities, CSOs, NGOs, SHG groups to take up the implementation of the scheme.
• Initially, launched as a pilot program in six states with critical ground water-depleted states – Bihar, Madhya Pradesh, Maharashtra, Rajasthan, Uttar Pradesh and Uttarakhand.
• The scheme is also implemented in 117 aspirational districts as these districts only 25% of piped water supply.

Additional Information

• Atal Bhujal yojana
• It is a Central Sector Scheme.
• AIM – Sustainable management of groundwater resources through people’s participation.
• This is a World Bank (50%) funded project.
• To be implemented in over-exploited and water-stressed regions in the states of Gujarat, Haryana, Karnataka, Madhya Pradesh, Maharashtra, Rajasthan and Uttar Pradesh.

The correct answer is Xuanzang.

Key Points

• Xuanzang wrote the book 'The Great Tang Dynasty Record on the Western Regions'.
• Xuan Zang was a famous scholar from China, who stayed in Vijaywada to study the Buddhist Scriptures.
• He described the interaction between Indian Buddhism and Chinese Buddhism.
• He came to India during the early Tang Dynasty.

Additional Information

• Fa-Hien Visited India during the reign of Chandragupta-II.
• He was the first Chinese Buddhist monk to travel to India in search of Buddhist Scriptures.
• He mentioned about  Untouchability that prevailed in India during that time
• He gave a detailed account of Buddhist monasteries, life, and teachings of Buddhists at that time.
• Fa-Hien described his journey in his travelogue, A Record of Buddhist Kingdoms.
• Nicolo de Conti, an Italian, was at Vijayanagara in about 1420, just after the accession of Devaraya I. 
• ​The first known foreign traveller, he mentions the fortifications of the city and the thousands of men employed in the army of the rulers.
• Al-Beruni was a Persian scholar.
• He accompanied Mahmud of Ghazni and wrote a book titled ‘Tahqiq-i-hind’.
• He is considered the father of Indology.
• In the 11th century, Abu al-Rayhan Muhammad was designated a royal astrologer.

The correct answer is Kerala.

Key Points

• Kerala Tourism’s internationally acclaimed ‘Human by Nature’ campaign bagged the prestigious PATA Grand Award 2020 for Marketing.
• Kerala Tourism has bagged one of the three PATA Grand Awards, which were announced live during a virtual presentation ceremony in Beijing.
• The distant event was attended virtually by Tourism Minister Kadakampally Surendran, Tourism Secretary Rani Georg, and Tourism Director P. Bala Kiran.

Additional Information

• ‘Human by Nature’ was a marketing strategy to revive tourism that was hit by the 2018 floods and the Nipah outbreak.
• The campaign had helped Kerala Tourism achieve a record growth of 17.2% in tourism arrivals in 2019, the highest in 24 years.
• This year’s awards recognised the achievements of three Grand title winners and 21 gold awards.
• This year’s Pacific Asia Travel Association (PATA) award was supported and sponsored by the Macao Government Tourism Office (MGTO).

The correct answer is Kevadia.

Key Points

• The Statue of Unity is located in Kevadia, Gujarat.
• The Statue of Unity is the world's tallest statue, with a height of 182 meters (597 feet) which is almost double the height (including the pedestal) of the Statue of Liberty, USA.
• It is located on the Narmada river-facing Sardar Sarovar Dam in Kevadiya colony, Narmada District in the Indian State of Gujarat.

Additional Information

• Famous sculptor Ram V. Sutar, a Padma Bhushan Awardee is the sculptor of the Statue of Unity.
• India’s largest engineering and construction company Larsen & Toubro (L&T) was assigned the responsibility for designing, engineering, procurement, construction, operation and maintenance of the project.
• The statue was inaugurated by Prime Minister Narendra Modi on 31 October 2018, the 143rd birth anniversary of Patel.
• The Statue was built in just 46 months.
• The previous tallest statue in India was the 41 m (135 ft) statue of Veera Abhaya Anjaneya Hanuman Swami at the Paritala Anjaneya Temple near Vijayawada in the state of Andhra Pradesh.

The correct answer is Godavari.

Key Points

• The Godavari is a major river in South India.
• Major left-bank tributaries: 
• Purna, Pranhita, Indravati, and Sabari river.
• Major right bank tributaries: 
• Pravara, Manjira, and Manair river.​

​

 

Additional Information

• Godavari river is the largest peninsular river.
• It is also called Dakshin Ganga.
• It originates from the Nashik district in Maharashtra.
• Its length is usually 1465 kilometres.
• The main tributaries of Godavari are Pranahita, Indravati and Manjira.
• It flows through Maharashtra, Telangana and Andhra Pradesh and joins the Bay of Bengal near the city of Rajahmundry.

The correct answer is 24th December.

Key Points 

• Every Year 24th December is observed as National Consumer Day with a specific theme in India.
• On this day, the Consumer Protection Act, 1986 had received the assent of the president.
• The enactment of this Act is considered a historic milestone in the consumer movement in the country.

Additional Information 

• The main objective of the Consumer Protection Act is to provide consumers with effective safeguards against various types of exploitation, including defective goods, unsatisfactory services as well as unfair trade practices.
• The Department of Consumer Affairs has also launched the Jago Grahak Jago programme to make consumers aware of information and rights.
• The theme for National Consumer Day 2020 is New features of the Consumer Protection Act, 2019.

The correct answer is 200 seconds.

Key Points

• Google researchers claimed they had passed a milestone known as quantum supremacy when their quantum computer Sycamore performed in 200 seconds an abstruse calculation they said would tie up a supercomputer for 10,000 years.
• Quantum computing is a new generation of technology that involves a type of computer 158 million times faster than the most sophisticated supercomputer we have in the world today.
• It is a device so powerful that it could do in four minutes what it would take a traditional supercomputer 10,000 years to accomplish.

Additional Information

• What is Quantum Supremacy?
• It is a term proposed in 2012 by John Preskill, professor of theoretical physics at the California Institute of Technology.
• It describes the point where quantum computers can do things that classical computers cannot.
• Superposition and entanglement are what give quantum computers the ability to process so much more information so much faster.

The correct answer is Anil Soni.

Key Points 

• US-based Indian-origin health expert, Anil Soni has been appointed as the first Chief Executive Officer (CEO) of the newly-created “World Health Organization (WHO) Foundation”.
• Before this, he was working with Viatris, a global healthcare company in the US, where he served as Head of Global Infectious Diseases.
• He will assume his role as CEO with effect from 1st January 2021.

Additional Information 

• Tedros Adhanom Ghebreyesus is an Ethiopian public health researcher and official who has been Director-General of the World Health Organization since 2017.
• Randeep Guleria is an Indian pulmonologist and the current director of the All India Institute of Medical Sciences, New Delhi.
• Melinda French Gates is an American philanthropist and former computer scientist and general manager at Microsoft.

The correct answer is 26th.

Key Points

• 26th Constitutional Amendment Act of 1971 abolished the privy purses and privileges of the former rulers of princely states.
• The 24^th Constitutional Amendment Act made it compulsory for the President to give his assent to a constitutional amendment bill.
• Part XX of the Indian Constitution deals with the procedure for its amendment.

Additional Information

• 24^th Amendment:
• The 24th amendment was enacted as a reaction to the Golak Nath case, in 1967.
• The Golak Nath ruling led to increased parliamentary authority to amend the Constitution.
• Through the Amendment, Parliament restored to itself undisputed authority to amend the Constitution, including its repeal.
• The 24th Amendment was the first of a series of several constitutional amendments designed to weaken the judiciary and enhance the authority of Parliament and the Prime Minister’s office.
• 25^th Amendment Act, 1971 Restrict property rights and compensation in case the state takes over private property.
• However, the Supreme Court quashed a part of Article 31C, to the extent it took away the power of judicial review.
• This was done in the landmark case of Kesavananda Bharati v. the State of Kerala.
• The 27^th amendment act was enacted in the year 1971.
• In order to reorganize the northeastern areas of India.
• The Union Territory of Mizoram was proposed under the scheme to have a legislature and council of ministers.

The correct answer is Polio.

Key Points

• In the year 2014, India was officially declared free of Polio.
• India was declared Polio free on 27th March 2014 by the WHO
• India started a program named ''pulse polio'' to completely eradicate polio from the country.
• It involved vaccinating all children under the age of five years against the poliovirus.
• Tamil Nadu became the first polio-free state in India.

Additional Information

• Poliomyelitis is the scientific term or synonym of the disease Polio.
• It is a viral disease that destroys the nerve cells present in the spinal cord, causing paralysis or muscle weakness to some parts of the body.
• The virus is transmitted person-to-person in the following ways – Through the faecal-oral route and By contaminated water or food.

The correct answer is Gujarat.

Key Points

• The ancient Harappan settlements of Dholavira and Lothal are located in the present day Indian state of Gujarat.

Additional Information

• Dholavira: 
• It was located on Khadir Beyt in the Rann of Kutch, and it had fertile land and a good supply of freshwater.
• It was divided into three parts, and each part was surrounded by massive stone walls and had large open areas for public ceremonies.
• Large letters of Harappan scripts written using white stone were found in Harappan wood carvings, seals, etc.
• Lothal:
• It was located on the bank of a tributary of the Sabarmati river in Gujarat.
• It was an important center where many different things were made out of stone, shells, and metals (easily available local raw materials).
• Buildings such as a storehouse containing many seals and their impressions, and also a bead-making workshop were found in Lothal.

Given:

A student travelled a distance of 30 km in 3 hours, partly on foot at a speed of 4km/h and the remaining on a bicycle at a speed of 12km/h. 

Concept used:

Time × Speed = Distance

Calculation:

Let's suppose, he walked for T hours.

According to the question,

4 × T + 12 × (3 - T) = 30

⇒ 4T + 36 - 12T = 30

⇒ T = 6/8 = 0.75

Now, the ratio of the distance travelled on foot and that travelled on the bicycle

⇒ 4 × 0.75 : 12 × (3 - 0.75)

⇒ 3 : 12 × 2.25

⇒ 3 : 27 =  1 : 9

∴ The ratio of the distance travelled on foot and that travelled on the bicycle is 1 : 9.

Concept used:

Loss% = ${(Cost\ Price\ -\ Selling\ Price) \over Cost\ Price} \times 100\%$

Calculation:

In the case of option 3, 

Loss% = 

⇒ 13.133% ≠ 13%

∴ 3 is incorrect.

Shortcut Trick

Solve 'of' first: 5/7 × 2/5 = 2/7.

Solve division and multiplication: (1/14 × 2 ÷ 1) = 2/14 = 1/7.

Combine results: 2/7 + 3/7 − 1/7 = 4/7.

∴ The correct answer is 4/7.

Alternate Method

Given expression: 5/7 of 2/5 + 3/7 − 1/14 × 2 ÷ 1

According to the BODMAS rule, the order of operations is Bracket, Of, Division, Multiplication, Addition, and Subtraction.

⇒ Step 1 (Of): (5/7 × 2/5) + 3/7 − 1/14 × 2 ÷ 1

⇒ 2/7 + 3/7 − 1/14 × 2 ÷ 1

⇒ Step 2 (Division): 2/7 + 3/7 − 1/14 × 2

⇒ Step 3 (Multiplication): 2/7 + 3/7 − 1/7

⇒ Step 4 (Addition/Subtraction): (2 + 3 − 1)/7

⇒ 4/7

∴ The correct answer is 4/7.

Additional Information

BODMAS Rule

BODMAS stands for Brackets, Of, Division, Multiplication, Addition, and Subtraction. This rule defines the precedence of operators in an arithmetic expression.

The 'Of' Operator

In mathematical simplification, 'of' represents multiplication but it must be performed before division and after brackets.

Same Denominator Rule

For adding or subtracting fractions like a/c + b/c − d/c, the result is simply (a + b − d)/c.

Shortcut Trick

For any proportion, Product of means = Product of extremes.

(1/a) × (1/a) = (1/7) × (1/3.43)

1/a² = 1/24.01

a² = 24.01 ⇒ a = 4.9

∴ The correct answer is 4.9.

Alternate Method

Given:

1/a : 1/7 = 1/3.43 : 1/a

Formula Used:

In a proportion A : B = C : D, the equation can be written as A/B = C/D.

Calculations:

⇒ (1/a) / (1/7) = (1/3.43) / (1/a)

⇒ 7/a = a/3.43

Cross-multiplying both sides:

⇒ a × a = 7 × 3.43

⇒ a² = 24.01

⇒ a = √24.01

⇒ a = 4.9

∴ The correct answer is 4.9.

Additional Information

Proportion Rule

When two ratios are equal, they form a proportion (A : B = C : D). The fundamental rule states that the product of the means equals the product of the extremes: B × C = A × D.

Mean Proportional

If three numbers x, y, and z are in a continued proportion (x : y = y : z), then y is called the mean proportional between x and z. The formula is y² = x × z.

Decimal Multiplication Trick

To multiply decimals quickly, multiply them as whole numbers (7 × 343 = 2401) and then place the decimal point by counting the total decimal places from both numbers (2 places in this case → 24.01).

Given:

Series of successive discounts, 20%, 10% and 15%.

Concept used:

Final discount percentage after two successive discounts of A% and B% = $(A + B - {AB \over 100})\%$

Calculation:

Resultant discount after 20% and 10%

⇒ 20 + 10 - (20 × 10/100) = 28%

Final discount = 28 + 15 - (28 × 15/100) = 38.8%

∴ A single discount equivalent to a series of successive discounts, 20%, 10% and 15%, is 38.8%.

Shortcut Trick

Initial CP : MP ratio = (100 − Discount%) : (100 + Profit%) = 87 : 120.

Let CP = 87 and MP = 120. New CP = 87 × 1.1 = 95.7.

To maintain 20% profit, New SP = 95.7 × 1.2 = 114.84.

New Discount = 120 − 114.84 = 5.16.

New Discount% = (5.16 ÷ 120) × 100 = 4.3%.

∴ The correct answer is 4.3%.

Alternate Method

Given: Discount₁ = 13%, Profit = 20%, CP increase = 10%.

Formulas: MP = CP × (100 + P%) ÷ (100 − D%) | SP = CP × (100 + P%) ÷ 100 | D% = (MP − SP) ÷ MP × 100

⇒ Let CP = 100. Then SP = 100 × 1.20 = 120.

⇒ MP = 120 ÷ (1 − 0.13) = 120 ÷ 0.87 = 4000 ÷ 29.

⇒ New CP = 100 × 1.10 = 110.

⇒ New SP (to earn 20% profit) = 110 × 1.20 = 132.

⇒ New Discount = MP − New SP = (4000 ÷ 29) − 132 = (4000 − 3828) ÷ 29 = 172 ÷ 29.

⇒ New Discount% = [(172 ÷ 29) ÷ (4000 ÷ 29)] × 100 = (172 ÷ 4000) × 100 = 172 ÷ 40 = 4.3%.

∴ The correct answer is 4.3%.

Additional Information

CP, SP, and MP Relation

The ratio of Cost Price to Marked Price is always (100 − Discount%) : (100 + Profit%).

Profit on Increased Cost

When CP increases, to keep the Profit% constant, the SP must increase proportionally by the same percentage.

Given:

Sumer bought 6 chairs at the rate of Rs. 800 per chair and a table for Rs. 1,200.

He sold all the chairs and the table for Rs. 7,200.

Concept used:

Profit% = ${(Selling\ Price\ -\ Cost\ Price) \over Cost\ Price} \times 100\%$

Calculation:

Total cost price = 800 × 6 + 1200

⇒ 4800 + 1200 = Rs. 6000

Now, his gain% = ${{7200 - 6000} \over 6000} \times 100\%$ = 25%

⇒ 20%

∴ His gain percentage is 20%.

Given:

Two pipes can fill a cistern in 12 and 15 hours, respectively, while a third pipe can empty it in 24 hours.

Concept used:

Total work = Efficiency (Work done per hour) × Total time taken

Calculation:

LCM (12, 15, 24) = 120

Let the capacity of the cistern be 120 units.

Efficiency of the first pipe = 120/12 = 10 units an hour

Efficiency of the second pipe = 120/15 = 8 units an hour

Efficiency of the third pipe = 120/24 = 5 units an hour

Now, when all pipes are open simultaneously, the cistern will be filled in

⇒ 120 ÷ (10 + 8 - 5) (Since the third pipe empties the cistern, its efficiency is taken in negative)

⇒ 120/13

⇒ $9{3 \over 13}\ hours$

⇒ 9 hours 3/13 × 60 minutes

⇒ 9 hours 13.846 minutes ≈ 9 hours 14 minutes

∴ When all pipes are open simultaneously, the cistern will be filled in 9 hours 14 minutes.

Given:

A rectangular park 14 m long, 8 m wide is surrounded by a path 1 m wide. 

Concept used:

Area of a rectangle = Length × Breadth

Calculation:

Including the path, the length of the park = 14 + 1 × 2 = 16 m

Including the path, the bredth of the park = 8 + 1 × 2 = 10 m

Without the path, area of the park = 14 × 8 = 112 m²

Including the path, the area of the park = 16 × 10 = 160 m²

Now, the area of the path = 160 - 112 = 48 m²

∴ The area of the path is 48 m².

Given:

Sazia's income is 20% less than that of Rehana. 

Calculation:

Let's suppose, Rehana's income is Rs. 100.

Sazia's income

⇒ 100 - 100 × 20% =  Rs. 80

Now, % more =স = 25%

⇒ ∴ Rehana's income is more than that of Sazia by 25%.

Concept used:

LCM is the smallest common multiple of two or more numbers.

Calculation:

LCM (8, 9, 10) = 360

So, 360 is the smallest number exactly divisible by 8, 9 and 10.

Now, the smallest number which when divided by 8, 9 and 10 leaves remainder 1 in each case = 360 + 1 = 361

∴ 361 is the smallest number which when divided by 8, 9, and 10 leaves remainder 1 in each case.

Given:

Four friends A, B, C and D made investments in a business in the ratio 3 ∶ 7 ∶ 9 ∶ 13, respectively. 

The share of the profit of C is Rs. 8,910.

Concept used:

Profit is shared in the ratio of the investment of partners.

Calculation:

Let the total profit be P.

According to the question,

P × 9/(3 + 7 + 9 + 13) = 8910

⇒ P = (8910 × 32)/9 = 31,680

Now, the total share of the profits of A and B

⇒ 31680 × ${3 + 7}\over {3 + 7 + 9 +13}$

⇒ 31680 × ${10 \over 32}$ =  Rs. 9,900

∴ The total share of the profits of A and B is Rs. 9,900.

Shortcut Trick

LCM of 10, 20, and 25 is 100, so the total sweets must be a multiple of 100.

We check multiples of 100 for the condition: (Number ÷ 27) leaving a remainder of 3.

100 ÷ 27 → Remainder is 19.

200 ÷ 27 → Remainder is 11.

300 ÷ 27 → Remainder is 3 (since 300 = 27 × 11 + 3).

∴ The correct answer is 300 sweets.

Alternate Method

Given:

The number of sweets is completely divisible by 10, 20, and 25.

When divided among 27 children, 3 sweets are left.

Concept Used:

Number = LCM(a, b, c) × k

Dividend = Divisor × Quotient + Remainder

Calculations:

⇒ LCM of 10, 20, and 25 = 100

⇒ Let the required minimum number of sweets be 100k, where k is a positive integer (1, 2, 3...).

⇒ According to the second condition, 100k ÷ 27 leaves a remainder of 3.

⇒ This can be expressed as: 100k = 27q + 3

⇒ Since 100 = 27 × 3 + 19, we can simplify the expression by checking only the remainder part: 19k ÷ 27.

⇒ For k = 1: 19(1) ÷ 27 → Remainder is 19

⇒ For k = 2: 19(2) = 38 → 38 ÷ 27 → Remainder is 11

⇒ For k = 3: 19(3) = 57 → 57 ÷ 27 → Remainder is 3 (since 57 = 27 × 2 + 3)

⇒ Thus, the smallest integer value for k is 3.

⇒ Minimum number of sweets = 100 × 3 = 300

∴ The correct answer is 300 sweets.

Additional Information

LCM and HCF Relationship

For any two numbers A and B, the product of the numbers is equal to the product of their LCM and HCF: A × B = LCM × HCF.

Remainder Theorem

Dividend = (Divisor × Quotient) + Remainder. This is the core equation used for solving divisibility and remainder problems.

Common Remainder Rule

The smallest number which when divided by x, y, and z leaves a common remainder r in each case is represented as: LCM(x, y, z) + r.

Given:

The average marks obtained by 30 students in a Mathematics test, out of 100, is 76.

Inadvertently, the marks of one student were written as 56 instead 65 and the marks of another student were written as 84 instead of 48. 

Concept used:

Total = Average × Number of entities

Calculation:

Total marks scored by 30 students (considering the mistaken inputs)

⇒ 30 × 76 = 2280

 Actual total marks

⇒  2280 + 65 + 48 - 56 - 84 = 2253

Now, the correct average

⇒ 2253/30 = 75.1 

∴ The correct average is 75.1%.

Given:

Amit sells an almirah to Bimal and makes a profit of 10%. Bimal sells the same almirah to Chetan and makes a profit of 10%.

Chetan bought the almirah for Rs. 14,520.

Concept used:

Selling Price = Cost Price + Cost Price × Gain%

Calculation:

Let the cost price of the almirah occurred to Amit be Q.

Cost price occurred to Bimal = Q + Q × 10% = 1.1Q

Cost price occurred to Chetan = 1.1Q + 1.1Q × 10% = 1.21Q

According to the question,

1.21Q = 14520

Q = 12000

∴ The price of the almirah for Amit is Rs. 12000.

Concept used:

Total = Average × Number of entities

Calculation:

Prime numbers between 25 and 45 = 29, 31, 37, 41, 43

Sum (29, 31, 37, 41, 43) = 181

Now, the average = 181/5

⇒ $36\frac{1}{5}$

∴ $36\frac{1}{5}$ is the average of the prime numbers lying between 25 and 45.

Given:

Three years ago, the value of a flat was Rs. 65,00,000. Its value depreciated at the rate of 5%, 4% and 3% at the end of the first, the second and the third year, respectively. 

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

where

P = Principal amount & R = Rate of interest per year

T = Time in years

One year of Simple interest = One year of Compound Interest

Calculation:

Depreciated by for the first year = (6500000 × 5 × 1)/100

⇒ Rs. 325000

New value becomes = 6500000 - 325000 = Rs. 6175000

Depreciated by for the second year = (6175000 × 4 × 1)/100

⇒ Rs. 247000

New value becomes = 6175000 - 247000 = Rs. 5928000

Depreciated by for the third year = (5928000 × 3 × 1)/100

⇒ Rs. 177840

Present value of the flat = 5928000 - 177840 = Rs. 57,50,160

∴ The present value of the flat is Rs. 57,50,160.

Shortcut Trick According to the question, 

⇒ 65,00,000 × 95/100 × 96/100 × 97/100

⇒ 57,50,160

∴ The present value of the flat is Rs. 57,50,160.

Given:

$\left( {2\frac{6}{7}of4\frac{1}{5} \div \frac{2}{3}} \right) \times 5\frac{1}{9} \div \left( {\frac{3}{4} \times 2\frac{2}{3}of\frac{1}{2} \div \frac{1}{4}} \right)$

Concept used:

Calculation:

$\left( {2\frac{6}{7}of4\frac{1}{5} \div \frac{2}{3}} \right) \times 5\frac{1}{9} \div \left( {\frac{3}{4} \times 2\frac{2}{3}of\frac{1}{2} \div \frac{1}{4}} \right)$

⇒ $({{20 \over 7} of {21 \over 5} \div {2 \over 3}}) \times {46 \over 9} \div ({{3 \over 4} \times {8 \over 3} of {1 \over 2} \div {1 \over 4}})$

⇒ $({12 \div {2 \over 3}}) \times {46 \over 9} \div ({{3 \over 4} \times {4 \over 3} \div {1 \over 4}})$

⇒ $({12 \times {3 \over 2}}) \times {46 \over 9} \div ({{3 \over 4} \times {4 \over 3} \times {4 \over 1}})$

⇒ $18 \times {46 \over 9} \div 4$

⇒ $18 \times {46 \over 9} \times {1 \over 4}$

⇒ 23

∴ The simplified answer is 23.

Shortcut Trick

Circumference of circle = 2 × (22/7) × 21 = 132 m

Perimeter of square = 4 × Side = 132 m

Side of square = 132 ÷ 4 = 33 m

∴ The correct answer is 33 m.

Alternate Method

Given:

Radius of circular park (r) = 21 m

Formula Used:

Circumference of circle = 2πr

Perimeter of square = 4a (where a is the side)

Calculations:

⇒ Distance around circular park = 2 × (22/7) × 21

⇒ Distance = 2 × 22 × 3 = 132 m

⇒ According to question, Perimeter of square = 132 m

⇒ 4 × Side = 132

⇒ Side = 132 ÷ 4

⇒ Side = 33 m

∴ The correct answer is 33 m.

Additional Information

Area of Circle

The space occupied by a circle is given by the formula Area = πr².

Area of Square

The space occupied by a square is given by Area = Side².

Relation between Perimeter and Area

For a given perimeter, a circle encloses the maximum area compared to any polygon.

Given:

Walking at $\frac{3}{4}$ of this usual speed, a man covers a certain distance in 1 hour and 40 minutes more than the time he takes to cover the distance at his usual speed. 

Concept used:

Distance = Speed × Time

Calculation:

1 hour 40 minutes = (1 + 40/60) hours

⇒ (1 + 2/3) = 5/3 hours

Let the usual speed and distance be Q km/h and D km respectively.

Time taken to cover the distance in usual speed = D/Q hours

According to the question,

D/(3Q/4) - D/Q = 5/3

⇒ 4D/3Q - D/Q = 5/3

⇒ D/Q × 1/3 = 5/3

⇒ D/Q = 5

∴ The time taken by him to cover the same distance at his usual speed is 5 hours.

Given:

A and B working together can complete a work in 30 days.

A alone can complete the same work in 50 days. 

Concept used:

Total work = Efficiency (Work done per day) × Total time taken

Calculation:

LCM (30, 50) = 150

Let the total work be 150 units.

Efficiency of A = 150/50 = 3 units

Efficiency of A and B together = 150/30 = 5 units

So, efficiency of B = 5 - 3 = 2 units 

Now, B will alone do the work in = 150/2

⇒ 75 days

∴ B alone do the same work in 75 days.

Given:

Saurabh spends 20% of his monthly income on the education of his children. He spends 30% of the remaining on conveyance and clothes.

Further, he spends 50% of the amount still with him on rent and maintenance of the house.

After all the expenditures, he sends 50% of the amount still with him to his parents. 

Concept used:

Income = Expenditure + Savings

Calculation:

Considering the entire salary be 100%.

Education expenditure = 20%

Conveyance and clothes expenditure = (100 - 20) × 30%

⇒ 24%

Rent and maintenance of the house = (100 - 20 - 24) × 50%

⇒ 28%

Remaining = 100 - 20 - 24 - 28 = 28%

Percentage sent to his parents = 28 × 50% = 14%

Remaining with him = 28 - 14 = 14%

According to the question,

14% of his income = 11200

So, His total income = 11200/14%

⇒ Rs. 80,000

∴ His monthly income is Rs. 80,000.

Given:

Principal = Rs. 6000

Rate of interest = 5% & Time = 2 years

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

where,

P = Principal amount & R = Rate of interest per year

T = Time in years

In case of the compound interest,

Amount = P(1 + R/100)^N

CI = P(1 + R/100)^N - P

Calculation:

Simple interest incurred = (6000 × 2 × 5)/100

⇒ Rs. 600

Compound interest incurred = 6000(1 + 5/100)² - 6000

⇒ RS. 615

Now, the difference = 615 - 600 = Rs. 15

∴ The difference in the simple interest and compound interest compounded annually on a sum of Rs. 6,000 in 2 years at the interest rate of 5% per annum will be Rs. 15.

Given:

The compound interest on a sum of Rs. 10,000 for 3 years at the rate of 8% for the 1st year, 10% for the 2nd year, and 12% for the 3rd year.

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

where

P = Principal amount & R = Rate of interest per year

T = Time in years

One year of Simple interest = One year of Compound Interest

Calculation:

Interest incurred for the first year

⇒ (10000 × 8 × 1)/100 = Rs. 800

Principal becomes = 10000 + 800 = Rs. 10800

Interest incurred for the second year

⇒ (10800 × 10 × 1)/100 = Rs.1080

Principal becomes = 10800 + 1080 = Rs. 11880

Interest incurred for the third year 

⇒ (11880 × 12 × 1)/100 = Rs.1425.6

Now, total interest = 800 + 1080 + 1425.6 =  Rs.3305.6

∴ The compound interest on a sum of Rs. 10,000 for 3 years at the rate of 8% for the 1st year, 10% for the 2nd year, and 12% for the 3rd year will be Rs. 3305.6.

Shortcut Trick

Value ratio = (1 × 8)  ∶  (2 × 5)  ∶  (5 × 3) = 8  ∶  10  ∶  15

Total value in ratio units = 8 + 10 + 15 = 33 units

33 units = ₹132 ⇒ 1 unit = ₹4

Number of ₹5 coins = 3 ratio units × 4 = 12 coins

∴ The correct answer is 12 coins.

Alternate Method

Given:

Denominations = ₹1, ₹2, ₹5

Ratio of number of coins = 8  ∶  5  ∶  3

Total amount in purse = ₹132

Formula Used:

Total Value = Number of Coins × Denomination Value

Calculation:

Let the number of ₹1, ₹2, and ₹5 coins be 8x, 5x, and 3x respectively.

⇒ Total value of ₹1 coins = 1 × 8x = 8x

⇒ Total value of ₹2 coins = 2 × 5x = 10x

⇒ Total value of ₹5 coins = 5 × 3x = 15x

⇒ Total value of all coins = 8x + 10x + 15x = 33x

⇒ 33x = 132

⇒ x = 132 ÷ 33

⇒ x = 4

⇒ Number of ₹5 coins = 3x

⇒ Number of ₹5 coins = 3 × 4 = 12

∴ The correct answer is 12 coins.

Additional Information

Ratio of Values vs Ratio of Coins

When the ratio of coins is given, multiply it by the respective denominations to get the ratio of their values. If the ratio of values is given, divide by the denomination to get the coin count ratio.

Proportions in Coin Problems

The total sum of money must always be equated to the sum of the monetary value of individual denominations to find the base multiplier constant (x).

The correct answer is option 1) i.e. 'Carcass.'

Key Points  

  

• Let's look at the meaning of the marked option:

• Example:
• The vultures fly in a circling motion which alerts other vultures that a carcass has been spotted.
• ​Let's look at the meanings of the other given options:

• Hence, from the given meanings, we find that 'Carcass' is the correct one-word substitute.
• So, the correct answer is option 1.

 

Correct one-word substitute: Carcass*.*

The correct answer is option 2) i.e. 'even when our minds.'

Key Points  

• The error lies in Part (if our minds) of the sentence.
• As per instructions, the remaining portion of the sentence is correct.
• The conjunction 'if' is used to say a particular thing that can or will happen only after something else happens or becomes true.
• The conjunction 'even when' is used when we want to add emphasis to show that something is surprising or extreme.
• Therefore, in the erroneous part the use of 'if' in the sentence should be replaced with 'even when' to make it grammatically correct.
• Therefore, the correct answer is Option 2.

 

Correct sentence: Poetry can be the voice of our feelings even when our minds are speechless with grief or joy.

The correct answer is option 1) i.e. "Healthy and doing well."

Key Points  

• Let’s look at the meaning of the given idiom/ phrase:
• The phrase 'Alive and kicking' means 'to continue to live or exist and be full of energy.'
• Example:
• Sneha said she'd seen John last week and he was alive and kicking.
• Hence, the only possible answer is option 1 'Healthy and doing well,' which exactly resembles the meaning of the given idiom/ phrase.

 

Correct meaning: Healthy and doing well.

The erroneous part is option 1) i.e. 'that if she could.'

 

Key Points 

• The error lies in the part 'that if she could.'
• According to the rules of Indirect Speech in interrogative sentence, the conjunction 'if' is used and comma and inverted commas will be removed.
• Therefore the use of 'that' is redundant here and should be omitted.
• Therefore in the given sentence we need to use only 'if' in place of 'that if' to make the sentence grammatically correct.
• Hence, the correct answer is option 1.

 

Correct sentence: She asked her teacher if she could explain that problem again.

The correct answer is option 3) i.e. 'adjacent.'

Key Points 

• Let's look at the meaning of the words given in the options:

 

• The context of the sentence is that the doctor's clinic is next to my house.
• The preposition 'to' is used with 'adjacent.'
• According to the above-mentioned points, the most appropriate word to fill the blank is "adjacent."
• Therefore, the correct answer is Option 3.
• Another example:
• The land for the shop is conveniently located adjacent to the main market.

 

Complete Sentence: The doctor’s clinic is adjacent to my house.

The correct answer is option 2) i.e. 'Astronomy.'

Key Points  

  

• Let's look at the meaning of the marked option:

• Example:
• Mohit's taste for mathematics led him to study astronomy.
• ​Let's look at the meanings of the other given options:

• Hence, from the given meanings, we find that 'Astronomy' is the correct one-word substitute.
• So, the correct answer is option 2.

 

Correct one-word substitute: Astronomy.

The correct answer is option 3) i.e. 'Persuade.'

Key Points 

• Let's look at the meanings of the given word and marked option:

 

• ​Let's look at the meanings of the other given options:

 

• Hence from the given meanings, we find that 'Dissuade' and 'Persuade' are antonyms.
• So, the correct answer is option 3.​

The correct answer is option 2) i.e. 'sound.'

Key Points 

• Let's look at the meaning of the words given in the options:

 

• The context of the sentence is that the most crucial component of a healthy relationship is trust.
• Here "sound" is used as an adjective to modify the noun 'relationship.'
• According to the above-mentioned points, the most appropriate word to fill the blank is "sound."
• Therefore, the correct answer is Option 2.
• Another example:
• Tarun is a person of sound mind​.

 

Complete Sentence: Trust is the most important element of a sound relationship.

The correct answer is option 1) i.e. "From all directions."

Key Points  

• Let’s look at the meaning of the given idiom/ phrase:
• The phrase 'From far and wide' means 'in every direction; everywhere.' (हर दिशा में; हर जगह)
• Example:
• ​Many people had come from far and wide to watch the magic show.
• Hence, the only possible answer is option 1 'From all directions,' which exactly resembles the meaning of the given idiom/ phrase.

 

Correct meaning: From all directions.

The erroneous part is option 1) i.e. 'to be she.'

Key Points  

• The error lies in the part 'to be she.'
• The given sentence is in simple past tense because it starts with 'I thought,' here the verb 'thought' is in past form.
• According to the rules of grammar, the verb 'to be' in the erroneous part need to be ins the past form which is 'was.'
• Therefore in the given sentence we need to use 'was' in place of 'to be' to make the sentence grammatically correct.
• Hence, the correct answer is option 1.

 

Correct sentence: I thought the actress was she, but I was not sure.

The correct answer is option 2) i.e. 'Definitely.'

 

Key Points   

• Let's look at the meaning of the given word:

• Let's look at the meaning of the words given in the options:

 

• Clearly, the word 'Definitely' is closest in meaning to the given word 'Absolutely.'
• Therefore, the correct synonym of the given word is option 2.

The correct answer is option 4) i.e., 'Utopia.'

Key Points    

• Let's look at the meaning of the marked option:

• Example:
• I am not saying ancient people lived in a utopia.
• ​Let's look at the meanings of the other given options:

• Hence, from the given meanings, we find that 'Utopia' is the correct one-word substitute.
• So, the correct answer is option 4.

 

Correct one-word substitute: Utopia.