Delhi Police Head Constable (Ministerial) 10 Oct 2022 Shift 2 Official Paper (Previous Year Paper)

The correct answer is Fertiliser.

• Fertiliser industries are included in the Schedule B of the Industrial Policy Resolution 1956.

Key Points

• The Industrial policy statement of 1956 was regarded as the “Economic Constitution of India” or “The Bible of State Capitalism”.
• The 1956 Policy empha­sised on:
• Need to expand the public sector
• To build up a large and growing coop­erative sector and
• to encourage the separation of ownership and management in private in­dustries
• Prevent the rise of pri­vate monopolies.
• It provided the basic framework for the government’s policy in regard to in­dustries till June 1991.
• Classification of industries into three categories:
• Schedule A:
• It consisted of 17 industries and was the exclusive responsibility of the State.
• Out of these, four industries, namely arms and ammunition, atomic en­ergy, railways, and air transport, Ship Building had Central Government monopolies.
• New units in the remaining industries were developed by the State Governments.
• Schedule B:
• It consisted of 12 industries that were open to both the private and public sectors, however, such industries were progressively State-owned.
• Industries included under this schedule are: All minerals (except minor minerals); Aluminum and other non-ferrous metals (not included in Schedule ‘A’);  Machine tools;  Ferro alloys and tool steels;  Basic and intermediate products required by chemical industries (like drugs, dye, and plastics); Antibiotics and other essential drugs; Fertilizers;  Synthetic rubber; Carbonization of coal; Chemical pulp; Road transport; Sea transport.
• Schedule C:
• All the other industries not included in these two Schedules constituted the third category which was left open to the pri­vate sector.
• However, the State reserved the right to undertake any type of indus­trial production.
• The IPR 1956, stressed the importance of cottage and small-scale industries for expand­ing employment opportunities and wider decentralization of economic power and activity
• The Resolution also called for efforts to maintain industrial peace; a fair share of the proceeds of production was to be given to the toiling masses in keeping with the avowed objectives of democratic socialism.

The correct answer is Personal Disposable Income (PDI) ≡ Personal Income – Personal tax payments – Non-tax payments.

Key Points

• The part of National Income (NI) that is received by households is referred to as Personal Income (PI).
• First, let us note that out of NI, which is earned by the firms and government enterprises, a part of the profit is not distributed among the factors of production.
• This is called Undistributed Profits (UP).
• We have to deduct UP from NI to arrive at PI since UP does not accrue to households.
• Similarly, Corporate Tax, which is imposed on the earnings made by the firms, will also have to be deducted from the NI, since it does not accrue to the households.
• On the other hand, the households do receive interest payments from private firms or the government on past loans advanced by them.
• And households may have to pay interest to the firms and the government as well, in case they had borrowed money from either.
• So we have to deduct the net interests paid by the households to the firms and government.
• The households receive transfer payments from the government and firms (pensions, scholarships, prizes, for example) which have to be added to calculate the Personal Income of the households.
• Thus, Personal Income (PI) = NI – Undistributed profits – Net interest payments made by households – Corporate tax + Transfer payments to the households from the government and firms.
• However, even PI is not the income over which the households have complete say. They have to pay taxes from PI. If we deduct the Personal Tax Payments (income tax, for example) and Non-tax Payments (such as fines) from PI, we obtain what is known as Personal Disposable Income.
• Thus Personal Disposable Income (PDI ) = PI – Personal tax payments – Non-tax payments.
• Personal Disposable Income is part of the aggregate income which belongs to the households. They may decide to consume a part of it and save the rest.

The correct answer is 1296-1316.

Key Points

• The Khalji dynasty was the dynasty which ruled the Delhi sultanate, covering large parts of the Indian subcontinent between 1290 and 1320.
• It was founded by Jalal ud din Firuz Khalji as the second dynasty to rule the Delhi Sultanate of India.
• Alauddin Khilji who ruled from 1296-1316 was the second sultan of the Khalji dynasty of Delhi in India.
• He reigned for about 20 years.
• During his rule, he introduced a number of significant administrative changes, related to revenues, price controls, and society.
• Alauddin Khilji introduced the scientific method of measurement of land for the assessment of land revenue.
• He imposed heavy taxes on the Sardars, Jagidars, and Ulemas. Jazia was imposed on non-Muslims. They had to pay it along with other taxes like pilgrim tax, octroi, etc.
• He introduced market regulations to help soldiers and to make ends meet. Prices of all articles of common use were fixed. Separate departments and special officers were appointed to regulate the market. The price fixed in the capital was applicable to all towns.
• He died in January 1316, and the Khalji dynasty came to an end only 4 years later.

The correct answer is Rajasthan.

Key Points

• Gangaur festival
• The festival of Gangaur is celebrated in the month of Chaitra.
• The festival is celebrated in the honor of the goddess Parvati.
• It is one of the most famous festivals in Rajasthan.
• The festival is celebrated in the month of March and April.
• The festival lasts for 18 days during which the women observe fasting with only one meal a day.
• The festival is celebrated with colorful processions, folk dances, and women singing songs.

Additional Information

The correct answer is Start Up India Scheme.

Key Points

• Start-up India, Stand up India campaign is launched to promote bank financing for starting businesses by the youths.
• This initiative is planned by the government to encourage Dalits, Adivasi, and women towards entrepreneurship.
• Stand Up India Scheme facilitates bank loans between 10 lakhs and 1 crore to at least one scheduled caste (SC) or Scheduled Tribe, borrower, and at least one woman per bank branch for setting up a greenfield enterprise.
• This enterprise may be in manufacturing, services, or the trading sector.
• The scheme was announced by PM Modi in his speech on Independence Day 2015.
• Start-Up India, Stand Up India is a scheme launched by the Modi Government on 16th January 2016.
• It is organized by the Department of Industrial Policy and Programmes (DIPP).

Additional Information

• Stand Up India Scheme facilitates bank loans to finance SC/ST and/or Women Entrepreneurs.
• SC/ST and/or women entrepreneurs; above 18 years of age are eligible for the loan.
• Loans under the scheme are available for the only greenfield project.
• Pradhan Mantri Kaushal Vikas Yojana (PMKVY) is the flagship scheme of the Ministry of Skill Development & Entrepreneurship (MSDE) implemented by the National Skill Development Corporation.
• The objective of this Skill Certification Scheme is to enable a large number of Indian youth to take up industry-relevant skill training that will help them in securing a better livelihood.
• ​Individuals with prior learning experience or skills will also be assessed and certified under Recognition of Prior Learning (RPL).
• Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) is one of the largest work guarantee programs in the world.
• Objective: The primary objective of the scheme is to guarantee 100 days of employment in every financial year to adult members of any rural household willing to do public work-related unskilled manual work.
• The Mahatma Gandhi National Rural Employment Guarantee Act, earlier known as the National Rural Employment Guarantee Act was passed in 2005 to augment employment generation and social security in India.
• The Mahatma Gandhi National Rural Employment Guarantee Act, 2005 (MGNREGA) was notified on September 7, 2005.
• It covers all districts of India except the ones with a 100% urban population.

The correct answer is Sunni.

Key Points

• According to Article 2 of the Constitution, Islam is recognized as Pakistan's official religion.
• Approximately 96.47% of the people in the nation practice it.
• Less than 4% of people practice various religions, including Sikhism, Ahmadiyya, Hinduism, and Christianity.
• There are several different Muslim sects
• ​the majority practice Sunni Islam (85–90%),
• while the minority follow Shia Islam (10–15%).
• The Barelvi and Deobandi traditions, representative of the Hanafi school of law, are commonly practiced among Pakistan's Sunni Muslims.
• The Twelver Islamic law school is followed by the vast majority of Shia Muslims in Pakistan.

Additional Information

• Catholic:
• The Vatican's pope serves as the spiritual head of the Catholic Church worldwide, which includes the Catholic Church in Pakistan.
• In Pakistan in 2018, there were 1,333,450 Catholics or less than 1% of the population.​

The correct answer is The Reserve Bank of India.

Key Points 

• RBI Governor Shaktikanta Das on 8 March 2022 launched UPI for feature phones called UPI123Pay.
• He also launched a 24x7 helpline for digital payments – DigiSaathi.
• UPI on feature phones will help people in rural areas who cannot afford a smartphone.
• UPI123Pay is a three-step method to initiate and execute services for users which will work on simple phones.

Important Points 

• UPI 123Pay will allow customers to use feature phones for almost all transactions except scan and pay.
• It doesn't need an internet connection for transactions.
• Customers have to link their bank accounts with feature phones to use this facility.
• Customers will also be able to link bank accounts, and set or change UPI PINs.
• The helpline christened 'Digisaathi' will assist the callers/users with all their queries on digital payments via the website and chatbot.
• Users can visit www.digisaathi.info or call on 14431 and 1800 891 3333 from their phones for their queries on digital payments and grievances.

The correct answer is 1945.

Key Points 

• The Constitutional Proposals of the Sapru Committee commonly referred to as the Sapru committee report was published in 1945.
• It was prepared by a committee appointed by the Non-Party Conference in November 1944.
• Sir Tej Bahadur Sapru was the head of the committee.
• The Sapru Committee Report contained 21 recommendations concerning constitutional questions concerning India's governance and politics.
• It also distinguished for making a distinction between justiciable and non-justiciable rights.

Additional Information 

Sir Tej Bahadur Sapru -

• Sapru was at first a member of the Indian National Congress (December 28, 1885). He advocated Swaraj.
• He was a member of the Legislative Council of the United Provinces between 1913 and 1916 and also in the Imperial Legislative Council from 1916 to 1920.
• He believed that dialogue with the British authorities was the only manner in which political rights and freedom could be achieved for the country.
• He was also a law member of the Viceroy’s Council from 1920 to 1923.
• He mediated between Mahatma Gandhi and Lord Irwin and facilitated the Gandhi-Irwin Pact.
• He represented the Liberal Party in the Round Table Conferences in London.

The correct answer is 2010.

Key Points

• Private microfinance institutions in Andhra Pradesh were forced to cease operations in 2010 as a result of state regulation.
• This had a negative impact on their ability to recoup and maintain liquidity.
• According to claims made by the authorities, the organizations used to charge their customers exorbitant interest rates.
• They shut down the organization because they utilized aggressive methods to recoup the money.
• They had a history of stealing clients from the government-run Self-Help Group program.
• 57 microcredit debtors killed themselves in the fall of 2010 in the Andhra Pradesh region in south-eastern India.
• The over-indebtedness of the clients, the MFIs' own lack of control over the loan process, and the protectionist structure of India's financial industry were all contributing factors to the microfinance crisis and its effects.

Additional Information

• A company called microfinance institutions (MFIs) provides low-income people with financial services.
• Microloans, micro savings, and microinsurance are some of these services.
• Any loans in India that are less than Rs. 1 lakh can be categorized as microloans.
• Throughout the past few decades, the microfinance industry has expanded quickly.
• At this time, it is serving 102 million accounts of India's underprivileged people.

The correct answer is Gujarat.

Key Points

• The badminton player Tasnim Mir is from India.
• When the BWF junior rankings for under-19 girls singles were released in January 2022, she became the first Indian to hold the top rank.
• She was awarded **Sportstar Emerging Hero Award 2022.**​

Additional Information

• The official language of Gujarat is Gujarati.
• Capital: Gandhinagar.
• State animal: Asiatic lion.
• State bird: Greater Flamingo.
• State tree: Mango.
• State flower : Marigold.

The correct answer is Karnataka.

Key Points

• Basavaraj Bommai took oath as the 23rd Chief Minister of Karnataka.
• Governor Thaawarchand Gehlot administered the oath of office and secrecy to him.
• The Bharatiya Janata Party's (BJP) legislature elected him as the successor of BS Yediyurappa who resigned from the top post on 26 July 2021.
• Basavaraj Bommai was the home minister in the BS Yediyurappa government.

Additional Information

• Karnataka:
• Chief Minister: Basavaraj Bommai.
• Governor: Thaawarchand Gehlot.
• Number of Districts: 31.
• Lok Sabha seats: 28.
• Rajya Sabha seats: 12.

The correct answer is Urvashi Butalia.

Key Points

• The Other Side of Silence: Voices from the Partition of India is a book by Urvashi Butalia.
• Urvashi Butalia is an Indian feminist writer, publisher and activist.
• She is known for her work in the women's movement of India, as well as for authoring books such as:
• The Other Side of Silence: Voices from and the Partition of India
• Speaking Peace: Women's Voices from Kashmir

Additional Information 

The correct answer is net sown area.

 Key Points

• The area seeded with crops but only tallied once is known as the net sown area.
• This means that the areas where crops are grown more than once within a specific agriculture year can be determined by subtracting the net seeded area from the gross cropped area.
• This region is the actual plot of land where crops are cultivated and harvested.
• The entire area seeded once or more during a given year is known as the gross cropped area (GCA).
• The same area is considered twice in GCA when a crop is planted twice on it.

Additional Information

• land under permanent crops:
• Land under permanent crops is cultivated with crops that occupy the land for long periods and need not be replanted after each harvest.
• cultivated area:
• After harvest, destroyed regions are not included in the term "area under cultivation," which refers to the area that corresponds to the entire area sowed.
• arable land:
• Land used for temporary crops like cereals, grazing, or market or kitchen gardens, as well as land that is momentarily fallow, all fall under the category of arable land.

The correct answer is New Delhi.

Key Points

• PM Modi inaugurated India's biggest Drone Festival - Bharat Drone Mahotsav-2022 in New Delhi, on 27 May 2022.
• The event will also witness a virtual award of drone pilot certificates, panel discussions, product launches, display of a ‘Made in India’ Drone Taxi prototype, and flying demonstrations, among others.
• It is a 2-day event being held from 27 to 28 May 2022.​

Additional Information

• During the Mahotsav, Prime Minister interacted with five Kisan Drone Operators.
• He also witnessed open-air drone demonstrations and interacted with start-ups at the drone exhibition.
• Several Union Ministers including Health and Family Welfare Minister Mansukh Mandaviya, Railways Minister Ashwini Vaishnaw, Agriculture Minister Narendra Singh Tomar and other dignitaries were present during the Mahotsav.
• At the Mahotsav, over 1,600 delegates are participating and more than 70 exhibitors displaying drones.
• Drones offer tremendous benefits to almost all sectors of the economy.
• These include - agriculture, mining, infrastructure, surveillance, emergency response, transportation, geo-mapping, defense, and law enforcement.

The correct answer is Mauryan.

Key Points

• Sanchi Stupa
• The Construction of the "Sanchi Stupa" was commissioned by Ashoka.
• It is situated at Sanchi Town in Raisen District of Madhya Pradesh.
• It is also a UNESCO World heritage site.
• Its official name is Buddhist Monument at Sanchi.
• Sanchi Stupa number 1 has a large number of Brahmi Inscription*.*
• Bindusara was the son of the dynasty's founder Chandragupta.
• Kautilya or Chanakya (c. 350 - 283 B.C.E.) was an adviser and a Prime Minister to the first Maurya Emperor Chandragupta.

Additional Information

• Gupta Dynasty:
• The founder of the Gupta dynasty was Sri Gupta.
• He was succeeded by Ghatotkacha. These two were called Maharajas.
• The next ruler was Chandragupta I and he was the first to be called Maharajadhiraja.
• Chandragupta, I was succeeded by Samudragupta in about 330 A.D., who reigned for about fifty years.
• He was a great military genius and is said to have commanded a military campaign across the Deccan, and also subdued the forest tribes of the Vindhya region.
• Samudragupta's successor Chandragupta II, also known as Vikramaditya, conquered the extensive territories of Malwa, Gujarat and Kathiawar.
• Shishunaga
• People elected Shishunaga who was a minister at King Nagdasaka court, as their ruler.
• Thus Shishunaga dynasty was founded in 412 BC and it extended up to 345 BC.
• ​Nanda Dynasty
• The Nanda Dynasty was ruled by Magadhas in northern India from 345-321 BCE.
• It was founded by Mahapadma Nanda, also known as Ugrasena i.e owner of a huge army, who defeated many kingdoms such as Kurus, Kalingas, and Kasis.
• He has also been described as the “The destroyer of all the Kshatriyas” in the Puranas.
• The Puranas call Mahapadma Ekrat i.e the sole Monarch. He seems to have overthrown all the dynasties which ruled at the time of Shisunagas. He is often described as the 'First Empire Builder of Indian History".
• Mahapadma Nanda was succeeded by his eight sons. Dhananada was the last one.

The correct answer is Karnataka.

Key Points

• The Karnataka Assembly enacted measures to alter the Karnataka Police Act, 1963, on September 21, 2021.
• The new law made gambling an offense that is both cognizable and punishable by a fine.
• This includes playing online poker.
• The law defined gambling as any activity that involves placing a bet, including those involving
• tokens that are worth money paid before or after they are issued,
• electronic means,
• virtual currencies, and
• electronic transfers of money in connection with games of chance.
• The law also makes it illegal to own gaming establishments or platforms, punishable by up to a year in prison and a fine of Rs 1,000 to Rs 1 lakh.
• Numerous gaming apps, including Mobile Premier League and Paytm First Games, have restricted user access in the state.

Additional Information

The correct answer is 8.

Key Points

• Sangeet Natak Akademi ​
• Sangeet Natak Akademi (The National Academy of Music, Dance, and Drama in English) is the national level academy for performing arts set up by the Government of India.
• It was set up by the Indian education ministry on 31 May 1952 and became functional the following year, with the appointment of its first chairman, Dr. P. V. Rajamannar.
• Dr. Rajendra Prasad, the first President of India, inaugurated it on 28 January 1953 in a special function held in the Parliament House. The academy's Fellowship and Award are considered very prestigious.
• In India, it functions as the headquarters of performing arts.
• It presents the Sangeet Natak Akademi Awards which is the highest Indian recognition given to performing/practicing artists.
• The Awards in Hindustani and Carnatic music were instituted as early as 1951, even before the Akademi was set up and these were known as Presidential Awards.
• With the formation of the Akademi, the Awards came to be known as Sangeet Natak Akademi Awards and the investiture became the responsibility of the Akademi. The Presidential Awards for 1952 and 1953 were subsequently incorporated into the list of Sangeet Natak Akademi Awards.​

Confusion Points

• The Sangeet Natak Akademi became functional in 1953 but the awards were started given under its name from 1952 onwards.

The correct answer is Subhash Chandra Bose.

Key Points

• Forward BlocK:
• All India Forward Bloc (AIFB) is a Left Wing Nationalist political party founded by Subhas Chandra Bose in West Bengal in 1939.
• Forward Bloc of the Indian National Congress (INC) was formed on May 3, 1939, by Subhas Chandra Bose.
• On the formation of this party Netaji said that all were joining the Forward Bloc, they had to never turn their back on the Britisher's camp and must fill out the oath form by cutting their Finger and signing it with their blood the form.
• All India Conference of Forward Bloc held in Nagpur 1940.
• The conference passed a resolution titled "All Power to the Indian People", urging militant action for the struggle against the East India Company.

Additional Information

• Subhas Chandra Bose:
• He was born on 23rd January 1897 in Cuttack, Odisha.
• Subhas Chandra Bose was an active leader of the Indian National Congress.
• After splitting from Congress, he made an Azad Hind Fauj in Singapore in 1942 to fight against the East India Company.
• In the year 1923, Subhas Chandra Bose was elected the President of the All India Youth Congress and also the Secretary of the Bengal State Congress.
• He also worked as the Editor of the Newspaper 'Forward', founded by Chittaranjan Das (Deshbandhu).

Image of the Forward Bloc:

Notes:

• Subhas Chandra Bose earned the title of "Netaji" in Germany by the Indian soldiers of the Azad Hind Fauj.

The correct answer is Iodine.

Key Points

• Goitre is caused, due to the deficiency of iodine.
• It can also happen due to the production of too much hormone by the thyroid gland.
• The enlargement of the throat below the voice box is Goitre.
• Radioactive Iodine treatment is used for the curing of this disease.

Additional Information

The correct answer is Dras.

Key Points

• The coldest region in India is Dras.
• It has a Continental Mediterranean climate impacted by altitude (Köppen climatic classification: Dsb).
• The winter season lasts from mid-October to mid-May.
• It is extremely cold, with average lows around 20 °C and lows as low as 23 °C at the height of the season.
• It is also referred to as ‘The Gateway to Ladakh'.
• In this frozen land, Dardic and Balti populations have made their homes and have endured the bitter cold.
• There are 1,201 people living in this tiny hamlet, the bulk of whom are Muslims.

Additional Information

• Thar desert:
• It is the ninth-largest hot subtropical desert in the world and the twentieth-largest desert overall.
• The mean average temperature ranges from 4 degrees C to 10 degrees C in the winter to a low of 24 degrees C to 26 degrees C in the summer.
• Chennai:
• The majority of the year is hot and muggy.
• Late May and early June, sometimes referred to as Agni Nakshatram or Kathiri Veyyil, are the hottest months of the year, with average highs of 38–42 °C.
• Thiruvananthapuram:
• The location experiences the most lovely weather of the entire year during the winter.
• The summers can be a little uncomfortable because they are so hot and muggy.
• On the other side, the monsoons are generally cooler.

Given:

X, Y, and Z can do a piece of work in 10 days, 20 days, and 30 days

X is assisted by Y and Z together, on every alternate day

Concept Used:

⇒ Total units of work is equal to the LCM of the total number of days required to complete the work.

⇒ Efficiency = Total units of work/Total number of days required to complete the work.

Solution:

LCM of 10, 20, and 30 is 60 

⇒ Total units of work is 60 units

X completes the work in 10 days

⇒ A _efficiency = 60/10 = 6 units/day

Y completes the work in 20 days

⇒ A efficiency = 60/20 = 3 units/day

Z completes the work in 30 days

⇒ A efficiency = 60/30 = 2 units/day

According to the question, 

X work on the first day, 

Total units of work done on day 1 = 6 units.

On the next day, Y & Z will work with X, 

Total units of work done on day 2 = 6 + 3 + 2 = 11 units

⇒ Total units of work done in 2 days = 6 + 11 = 17 units

⇒ 2 Days = 17 units of work

Multiplying by 3, we get, 

⇒ 6 days = 51 units of work 

Now on 7th day X alone will work, 

⇒ 51 + 6(A efficiency ) = 57 units in 7 days,

Total units remaining to complete the work = 60 - 57 = 3 units

Now on 8th day Y & Z will help X, 

⇒ Time required to complete 3 units of work = 3/11 day

Hence, total number of days to complete 60 units of work, = 7days + 3/11 day

⇒ 7 + 3/11 = 7$3\over 11$days.

∴ The number of days required to complete the work is  7$3\over 11$days.

Given:

x = 1.2̅3̅4

y = 4.3̅2̅1

Calculation:

⇒ For x = $1.\overline{234}$

⇒ As there are three terms repeating, so we'll multiply both the sides by 1000.

⇒ 1000x = 1234.234234

⇒ Subtracting the original term of x from the same, we get

⇒ 1000x – x = 1234.234234 – 1.234234

⇒ 999x = 1233

⇒ x = $\frac{1233}{999}$

⇒ For y = $4.\overline{321}$

⇒ As there are again three terms repeating, so we'll multiply both the sides by 1000.

⇒ 1000y = 4321.321321

⇒ Subtracting the original term of y from the same, we get

⇒ 1000y – y = 4321.321321 – 4.321321

⇒ 999y = 4317

⇒ y = $\frac{4317}{999}$

⇒ x + y = $\frac{1233}{999}$ + $\frac{4317}{999}$ = $\frac{5550}{999}$

Therefore, the required value of x + y is $\frac{5550}{999}$.

Given:

HCF of 11, 44, 121, 88 and 1331

Calculation:

⇒ Prime factors of 11 = 1 × 11

⇒ Prime factors of 44 = 2 × 2 × 11

⇒ Prime factors of 88 = 2 × 2 × 2 × 11

⇒ Prime factors of 121 = 11 × 11

⇒ Prime factors of 1331 = 11 × 11 × 11

⇒ Common factors of 11, 44, 121, 88 and 1331 = 11

Therefore, the HCF of 11, 44, 121, 88 and 131 is 11.

Given:

Concept Used:

Average = Sum of all observations ÷ Total number of observations

Calculation:

⇒ Total production of all the fruits in 2019 (in million kg) = 1680 + 990 + 850 + 1460 + 760 + 1150

⇒ Total production of all the fruits in 2019 (in million kg) = 6890

⇒ Average production of fruits in 2019 = 6890 ÷ 6 = 1148.33 million kg

⇒ Total production of all the fruits in 2020 (in million kg) = 1970 + 1230 + 1080 + 1280 + 560 + 980

⇒ Total production of all the fruits in 2020 (in million kg) = 7100

⇒ Average production of fruits in 2020 = 7100 ÷ 6 = 1183.33 million kg

⇒ Difference in average production of fruits in 2019 and 2020 = 1183.33 – 1148.33 = 35 million kg

Therefore, the difference between average fruit production (in million kg) in 2019 and that of in 2020 is 35.

Given:

Time taken by 6 men or 8 women to do a work = 86 days

Calculation:

⇒ We can say that, 6 men = 8 women

⇒ 1.5 men = 2 women

⇒ Based on that,

⇒ 10 women = 1.5 × 5 = 7.5 men

⇒ Total number of men for the work = 14 + 7.5 = 21.5

⇒ Work done by 6 men in = 86 days

⇒ Work done by 21.5 men = $\frac{86\times 6}{21.5}$ = 24 days

Therefore, 14 men and 10 women will complete the same work in 24 days.

Given:

Cost of 3 shirts and 2 pants = Rs 950

Cost of 2 shirts and 3 pants = Rs 1,050

Calculation:

⇒ Let the cost of one shirt be Rs x and cost of one pant be Rs y.

⇒ For 3 shirts and 2 pants,

⇒ 3x + 2y = 950               → (1)

⇒ For 2 shirt and 3 pants,

⇒ 2x + 3y = 1050             → (2)

⇒ Multiplying (1) by 2 and (2) by 3, we get

⇒ 6x + 4y = 1900             → (3)

⇒ 6x + 9y = 3150             → (4)

⇒ Subtracting (3) from (4), we get

⇒ 9y – 4y = 3150 – 1900

⇒ 5y = 1250

⇒ y = $\frac{1250}{5}$ = 250

⇒ Putting the value in (1), we get

⇒ 3x + 2 × 250 = 950

⇒ 3x = 950 – 500 = 450

⇒ x = $\frac{450}{3}$ = 150

⇒ Cost of 4 pants and 5 shirts = 4y + 5x

⇒ Cost of 4 pants and 5 shirts = 4 × 250 + 5 × 150 = 1000 + 750 = Rs 1750

Therefore, the cost of 4 pants and 5 shirts is Rs 1,750.

Given:

(x3 + y3) ∶ (x2 − xy + y2) = 3 ∶ 1

(x2 − y2) ∶ (x + y) = 5 ∶ 6

Concept Used:

x³ + y³ = (x + y)(x² + y² – xy)

x² – y² = (x + y)(x – y)

Calculation:

⇒ According to the question,

⇒ $\frac{x^3+y^3}{x^2+y^2-xy}=\frac{3}{1}$

⇒ Putting the formula expansion, we get

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

⇒ x + y = 3               → (1)

⇒ x = 3 – y               → (2)

⇒ $\frac{x^2-y^2}{x+y}=\frac{5}{6}$

⇒ $\frac{(x+y)(x-y)}{x+y}=\frac{5}{6}$

⇒ $x-y=\frac{5}{6}$              → (3)

⇒ Putting the value of equation (2) in (3), we get

⇒ ${3-y-y}=\frac{5}{6}$

⇒ $3-\frac{5}{6}=2y$

⇒ $\frac{18-5}{6}=2y$

⇒ $y=\frac{13}{12}$

⇒ x = $\frac{13}{12}+\frac{5}{6}$ = $\frac{13+10}{12}=\frac{23}{12}$

⇒ 2x : 3y = $\frac{2\times \frac{23}{12}}{3\times \frac{13}{12}}=\frac{\frac{23}{6}}{\frac{13}{4}}$

⇒ 2x : 3y = $\frac{23\times 4}{6\times 13}=\frac{46}{39}$ = 46 : 39

Therefore, the value of 2x : 3y is 46 : 39.

Given:

Price of a digital note-pad = Rs 25,000

Down payment = Rs 2500

Monthly installments = 4

Rate of interest = 24% p.a.​

Calculation:

Rate per annum = 24%

Rate per month = 24/12 = 2 %  = 0.02

Amount financed (after down payment) = 25,000 - 2,500 = Rs. 22,500

Therefore,

x/(1 + 0.02) + x/(1 + 0.02)² + 1/(1 + 0.02)³ + 1/(1 + 0.02)⁴ = 22500 

x[1/(1.02) +1/(1.02)2 + 1/(1.02)3 + 1/(1.02)⁴] = 22500 

Doing approximate calculation

x[1/(1.02) + 1/(1.04) + 1/(1.06) + 1/(1.08)] = 22500 

x[1/(1.02) + 1/(1.04) + 1/(1.06) + 1/(1.08)] = 22500 

x(0.98 + 0.96 + 0.94 + 0.92) = 22500

3.8x = 22500

x = 5921 ≈ 5900

∴ The monthly installment is Rs. 5900.

Given:

1st term = 15

2nd term = 25

4th term = 75

Concept Used:

a × d = b × c

Calculation:

⇒ Let the third term be x.

⇒ 15 × 75 = 25 × x

⇒ x = $\frac{15\times 75}{25}$ = 45

Therefore, the third term is 45.

Given:

Five positive multiples of 5

Concept Used:

Average = Sum of all observations / Total number of observations

Calculation:

⇒ First five positive multiples of 5 = 5, 10, 15, 20, and 25

⇒ Sum of first five multiples of 5 = 5 + 10 + 15 + 20 + 25 = 75

⇒ Average of first five positive multiples of 5 = 75 ÷ 5 = 15

Therefore, the average of the first five positive multiples of 5 is 15.

Given:

Time taken at speed of 40 km/h = 5 hours

New total time = 2.5 hours

Concept Used:

Speed = Distance ÷ Time

Calculation:

⇒ For the speed of 40km/h,

⇒ Distance = Speed × Time = 40 × 5 = 200 km

⇒ Now, the total time to cover the same distance = 2.5 hours

⇒ Speed of car = 200 ÷ 2.5 = 80 km/h

Therefore, the speed of a car to cover the same distance in 2.5 hours is 80 km/h.

Given:

Dimensions of wall = 12 m × 9 m × 90 cm

Number of bricks in one pack = 450

Dimensions of one brick = 10 cm x 7.5 cm x 7 cm

Volume occupied by cement and sand mixture = One-eighteenth volume of wall

Concept Used:

Volume of cuboid = Length × Breadth × Height

Calculation:

⇒ Length of wall = 12 m = 1200 cm

⇒ Height of wall = 9 m = 900 cm

⇒ Volume of wall = 1200 × 900 × 90 = 97200000 cm3

⇒ Volume of cement and sand mixture = $\frac{1}{18}$ × 97200000 = 5400000 cm3

⇒ Volume of wall left = 97200000 – 5400000 = 91800000 cm3

⇒ Volume of one brick = 10 × 7.5 × 7 = 525 cm3

⇒ Total number of bricks required = Total volume of wall left ÷ Volume of one brick

⇒ Total number of bricks required = 91800000 ÷ 525 = 174857

⇒ Number of pack of bricks required = $\frac{174857}{450}$ $\approx$ 389

Therefore, the number of packs of bricks required to construct the wall is 389.

Given:

AB = 8 cm

BC = 10 cm

AC = 12 cm

PQ = 8 cm

QR = 10 cm

PR = 12 cm

Calculation:

⇒ Based on the sides of the triangle,

⇒ AB = PQ = 8 cm

⇒ BC = QR = 10 cm

⇒ AC = PR = 12 cm

⇒ So, ABC will be congruent to the triangle PQR.

Therefore, among the following ΔABC ≅ ΔPQR is true.

Shortcut Trick

Multiply the numerator and denominator by 2 to apply transformation formulas.

Num: (cos θ + cos 5θ) − (cos 5θ + cos 9θ) + (cos 9θ + cos 11θ) = cos θ + cos 11θ

Den: (cos θ − cos 7θ) − (cos 3θ − cos 7θ) + (cos 3θ − cos 11θ) = cos θ − cos 11θ

Expression = (cos θ + cos 11θ) ÷ (cos θ − cos 11θ)

Apply sum-to-product rules: (2 × cos 6θ × cos 5θ) ÷ (2 × sin 6θ × sin 5θ) = cot 6θ × cot 5θ

∴ The correct answer is cot 6θ × cot 5θ.

Alternate Method

Given:

Expression = (cos 2θ × cos 3θ − cos 2θ × cos 7θ + cos θ × cos 10θ) ÷ (sin 4θ × sin 3θ − sin 2θ × sin 5θ + sin 4θ × sin 7θ)

Formulas Used:

2 × cos A × cos B = cos(A − B) + cos(A + B)

2 × sin A × sin B = cos(A − B) − cos(A + B)

cos C + cos D = 2 × cos((C + D) ÷ 2) × cos((C − D) ÷ 2)

cos C − cos D = 2 × sin((C + D) ÷ 2) × sin((D − C) ÷ 2)

Calculations:

⇒ Multiply numerator and denominator by 2.

⇒ Numerator = (2 × cos 2θ × cos 3θ) − (2 × cos 2θ × cos 7θ) + (2 × cos θ × cos 10θ)

⇒ Numerator = (cos θ + cos 5θ) − (cos 5θ + cos 9θ) + (cos 9θ + cos 11θ)

⇒ Numerator = cos θ + cos 5θ − cos 5θ − cos 9θ + cos 9θ + cos 11θ

⇒ Numerator = cos θ + cos 11θ

⇒ Denominator = (2 × sin 4θ × sin 3θ) − (2 × sin 2θ × sin 5θ) + (2 × sin 4θ × sin 7θ)

⇒ Denominator = (cos θ − cos 7θ) − (cos 3θ − cos 7θ) + (cos 3θ − cos 11θ)

⇒ Denominator = cos θ − cos 7θ − cos 3θ + cos 7θ + cos 3θ − cos 11θ

⇒ Denominator = cos θ − cos 11θ

⇒ Expression = (cos θ + cos 11θ) ÷ (cos θ − cos 11θ)

⇒ Applying Sum to Product formulas on the resulting terms:

⇒ cos θ + cos 11θ = 2 × cos 6θ × cos 5θ

⇒ cos θ − cos 11θ = 2 × sin 6θ × sin 5θ

⇒ Ratio = (2 × cos 6θ × cos 5θ) ÷ (2 × sin 6θ × sin 5θ)

⇒ Ratio = cot 6θ × cot 5θ

∴ The correct answer is cot 6θ × cot 5θ.

Additional Information

Product to Sum Formulas

Used to convert trigonometric products into sums or differences: 2 × sin A × sin B = cos(A − B) − cos(A + B), and 2 × cos A × cos B = cos(A − B) + cos(A + B).

Sum to Product Formulas

Used to convert trigonometric sums into products to simplify terms: cos C + cos D = 2 × cos((C + D) ÷ 2) × cos((C − D) ÷ 2) and cos C − cos D = 2 × sin((C + D) ÷ 2) × sin((D − C) ÷ 2).

Quotient Identities

Basic relationships expressing tan and cot in terms of sin and cos: tan θ = sin θ ÷ cos θ and cot θ = cos θ ÷ sin θ.

Given:

Selling price of a table fan = Rs 840

Gain % on a table fan = 20%

Selling price of a wall clock = Rs 1,008

Gain % on a wall clock = 12%

New selling price of a table fan = Rs 980

Concept Used:

Cost Price = \(\frac{SP}{100+Profit%}\times 100\)

Calculation:

⇒ CP of a table fan = $\frac{840}{100+20}\times 100$

⇒ CP of a table fan = 7 × 100 = Rs 700

⇒ CP of a wall clock = $\frac{1008}{100+12}\times 100$

⇒ CP of a wall clock = 9 × 100 = Rs 900

⇒ Total CPs of both the items = 700 + 900 = Rs 1,600

⇒ New selling price of table fan = Rs 980

⇒ Selling price of a wall clock to have no loss = 1600 – 980 = Rs 620

Therefore, the least price for which a wall clock must be sold to avoid any loss on two together is Rs 620.

Shortcut Trick

We can use the constant product ratio method.

Percentage increase in price = 25% = 1/4

If price increases by a ratio of 1/x, consumption must decrease by 1/(x + 1) to keep expenditure constant.

Required decrease in consumption = 1 ÷ (4 + 1) = 1/5

Percentage decrease = (1/5) × 100% = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Price increase = 25%

Expenditure remains the same.

Formula Used:

Expenditure = Price × Consumption

Percentage decrease = [ (Original Value − New Value) ÷ Original Value ] × 100%

Calculation:

⇒ Let the initial price of fruits be ₹100 per unit.

⇒ Let the initial consumption be 100 units.

⇒ Initial Expenditure = 100 × 100 = ₹10000

⇒ The new price after a 25% increase = 100 + 25 = ₹125 per unit.

⇒ To keep the expenditure at ₹10000, let the new consumption be C units.

⇒ 125 × C = 10000

⇒ C = 10000 ÷ 125 = 80 units

⇒ Decrease in consumption = 100 − 80 = 20 units

⇒ Percentage decrease in consumption = (20 ÷ 100) × 100% = 20%

∴ The correct answer is 20%.

Additional Information

Constant Product Rule

If the product of two variables A and B is constant, an increase of 1/x in A requires a corresponding decrease of 1/(x+1) in B to maintain the same total.

Percentage Increase to Decrease Conversion

If a value is increased by R%, to restore it back to the original value, it must be decreased by [R ÷ (100 + R)] × 100%.

Successive Percentage Change

If a value changes by a% and then consecutively by b%, the net percentage change is given by the formula (a + b + ab ÷ 100)%.

Given:

105 ÷ 5 × 5 + (32 × 4 ÷ 2 + 6) − 10

Concept Used:

Calculation:

⇒ 105 ÷ 5 × 5 + (32 × 4 ÷ 2 + 6) − 10

⇒ 105 ÷ 5 × 5 + (32 × 2 + 6) − 10

⇒ 105 ÷ 5 × 5 + 70 − 10

⇒ 21 × 5 + 70 – 10

⇒ 105 + 70 – 10

⇒ 165

Therefore, the simplified value of an expression is 165.

Given:

Price of an item = Rs 1,000

Discount = 40%

Additional discount = 10%

Concept Used:

⇒ Price after discount = 1000 – 40% of 1000

⇒ Price after discount = 1000 – $\frac{40}{100}$ × 1000 = 1000 – 400

⇒ Price after discount = Rs 600

⇒ Now, after additional discount of 10%,

⇒ Final price to pay = 600 – 10% of 600

⇒ Final price to pay = 600 – $\frac{10}{100}$ × 600 = 600 – 60 = Rs 540

Therefore, customer has to pay Rs 540 for an item of Rs. 1000.

Given:

Principal amount = Rs 8,000

Time = 1 year

Rate = 10% p.a. compounded semi-annually

Concept Used:

Compound Interest = P$[\left(1+\frac{r}{n}\right)^{nt}-1]$

Calculation:

⇒ For compounded semi-annually, n = 2.

= 10/100 = 0.1% p.a.

⇒ Compound Interest = 8000 × $[\left(1+\frac{0.1}{2}\right)^2-1]$

⇒ Compound Interest = 8000 × [(2.1 ÷ 2)² – 1]

⇒ Compound Interest = 8000 × [1.1025 – 1]

⇒ Compound Interest = 8000 × 0.1025 = Rs 820

Therefore, the compound interest for the period of one year is Rs 820.

Given:

Area of base of cylinder = 40 cm²

Height of cylinder = 9 cm

Concept Used:

Volume of cylinder = Area of base × Height

Calculation:

⇒ Base area of cylinder = 40 cm²

⇒ Putting the value in the volume formula,

⇒ Volume of cylinder = 40 × 9 = 360 cm³

Therefore, the volume of a cylinder is 360 cm³.

As per the venn diagram,

From the above-shaded region, we can say that the number of Government toy factories outside town P = 50

Hence, the correct answer is '50'.

The option that represents the correct order of the given words as they would appear in the English dictionary is shown below:

3. Redundant
4. Relax
5. Relegate
6. Replenish
7. Rescue
8. Resonate

Hence, "3,4,1,5,6,2" is the correct answer.

The position of the letters according to the English alphabet series:

The logic followed here is:

The sum of the alphabet follows the reverse analogy of the English alphabet series and then adds 10 to the result.

The code for EYES is written as '64'

EYES → E = 22, Y = 2, E = 22, S = 8

EYES = (22 + 2 + 22 + 8) + 10 = 64

In the same way, NOSE is written as '65'

NOSE → N = 13, O = 12, S = 8, E = 22

NOSE = (13 + 12 + 8 + 22) + 10 = 65

Similarly, 'LIPS' will be written as,

LIPS → L = 15, I = 18, P = 11, S = 8

LIPS = (15 + 18 + 11 + 8) + 10 = 62

Hence, the correct answer is 'option 3)'.

The position of the letters according to the English alphabet series:

The logic followed here is:

The difference between the positional values of alternate alphabets are 4 and 2 respectively as shown below:

Let's check each option: 

​option 1) FUJW

option 2) EVIX

option 3) HTMV

option 4) CXGZ

Thus, the HTMV letter cluster does not belong to that group as it is not following the above logic.

Hence, the correct answer is option 3).

Logic: The difference of difference between the terms is 7.

The logic that follows in the given number series is shown below:

Hence, the correct answer is option 3).

The correct mirror image for the given figure is shown below,

Hence, the correct answer is option 1).

Given,

Six letters S, T, U, V, W and X are written on different faces of a dice.

Here it is observed that the 'X' is common in both dice.

If one of the numbers is common in both the dice, then the remaining surfaces of both dice are opposite to each other.

Now after rotating around the 'X' face in a clockwise direction.

The faces will be 

Here the opposite side of 'S' is 'V' and the opposite side of 'W' is 'U'

So, the letters S, U, and W can not be opposite to the letter X

Thus, T is the only possible letter that could be opposite to X.

Hence, the correct answer is ' T '.

Given,

A, B, C, D, E, F, G and H are sitting around a square table facing the centre of the table.

• A sits at the centre of one of the sides.
• B sits third to the left of A

• Only three people sit between B and C.
• F is neither an immediate neighbour of C nor B.
• E sits third to the left of F
• D sits to the immediate right of H.

Hence, the correct answer is 'A'.

The position of the letters according to the English alphabet series:

The pattern followed  here is shown below:

The word FAIRY is written as QXHEZ

In the same way, the word BANDS is written as CRMAZ

Similarly, the word QUEEN is written as

Hence, the correct answer is 'DMDPT'.

Given,

Six friends - P, Q, R, S, T, and U - are seated in a row, facing north.

    

• Exactly three people are sitting to the right of R
• T is second to the left of R

• P is third to the right of T
• Q is not an immediate neighbor of P, nor does he sit at the either of the extreme ends

As given in the question, if Q is fourth to the left of S, where is U seated

According to the arrangement U seats second to the right of R.

Hence, the correct answer is 'Second to the right of R'

Given: 13 * 6 * 12 * 20 * 5 * 70

We substitute the values in the given equation and solve it using the BODMAS rule:

By, checking all the options:

option 1) +, –, ×, ÷, = 

13 + 6 – 12 × 20 ÷ 5 = 70

13 + 6 – 12 × 4 = 70 

13 + 6 – 48 = 70

19 – 48 = 70

- 29 ≠ 70

option 2) +, ×, –, ÷, =

13 + 6 x 12 - 20 ÷ 5 = 70

13 + 6 x 12 - 4 = 70

13 + 72 - 4 = 70

85 - 4 = 70

81 ≠  70

option 3) ÷, –, +, ×, =

13 ÷ 6 – 12 + 20 x 5 = 70

2.16 - 12 + 20 x 5 = 70

2.16 + 100 - 12  = 70

102.16 - 12 = 70

90.16  ≠  70

option 4) ×, –, +, ÷, =

13 × 6 - 12 + 20 ÷ 5 = 70

13 x 6 - 12 + 4 = 70

78 + 4 - 12 = 70

82 - 12 = 70

70 = 70

Hence, the correct answer is 'option 4'

Given,

Six letters S, T, U, V, W and X are written on different faces of a dice.

Here it is observed that the 'X' is common in both dice.

If one of the numbers is common in both the dice, then the remaining surfaces of both dice are opposite to each other.

Now after rotating around the 'X' face in a clockwise direction.

The faces will be 

Here the opposite side of 'V' is 'S' and the opposite side of 'U' is 'W'

Hence, the correct answer is option 3).

The position of the letters according to the English alphabet series:

The logic followed here is:

Each letter represents the reverse order of the analogy of the English alphabet series and then the addition of all the numbers.

In the word, JACOB the reverse analogy for each letter is,

J ⇒ 17, A ⇒ 26, C ⇒ 24, O ⇒ 12, B ⇒ 25

JACOB ⇒  17 + 26 + 24 + 12 + 25 = 104

In the same way, HENRY

H ⇒ 19, E ⇒ 22, N ⇒ 13, R ⇒ 9, Y ⇒ 2

HENRY⇒ 19 + 22 + 13 + 9 + 2 = 65

Similarly, JAMES is coded as:

J ⇒ 17, A ⇒ 26, M ⇒ 14, E ⇒ 22, S ⇒ 8

JAMES ⇒ 17 + 26 + 14 + 22 + 8 = 87

Hence, the correct answer is option 2).

The given equation is:

96 + 32 – 60 ÷ 20 × 5 = 79

We substitute the values in the given equation and solve it using the BODMAS rule:

By checking all the options,

option 1) ÷ and ×

⇒ 96 + 32 – 60 × 20 ÷ 5 = 79

⇒ 96 + 32 – 60 × 4 = 79

⇒ 96 + 32 – 240 = 79

⇒ 128 – 240 = 79

⇒ 112 ≠ 79

option 2) × and –

⇒ 96 + 32 × 60 ÷ 20 – 5 = 79

⇒ 96 + 32 × 3 – 5 = 79

⇒ 96 + 96 – 5 = 79

⇒ 192 – 5 = 79

⇒ 187 ≠ 79

option 3) – and ÷

⇒ 96 + 32 ÷ 60 – 20 × 5 = 79

⇒ 96 + 0.53 – 20 × 5 = 79

⇒ 96 + 0.53 – 100 = 79

⇒ 96.53 – 100 = 79

⇒ – 3.47 ≠ 79

option 4) + and –

⇒ 96 – 32 + 60 ÷ 20 × 5 = 79

⇒ 96 – 32 + 3 × 5 = 79

⇒ 96 + 15 – 32 = 79

⇒ 111 – 32 = 79

⇒ 79 = 79

Hence, the correct answer is 'option 4'.

Given:

A _ R _ O _ G R T _ A G _ _ O A G R _ _

Checking all the options and substituting accordingly, we get:

option 1) GTARRTOO

A G R T O A G R T R A G R T O A G R O O ⇒ This doesn't follow the pattern.

option 2) GATORTTO

A G R A O T G R T O A G R T O A G R T O ⇒ This doesn't follow the pattern.

option 3) GTAORTTO

A G R T O A G R T O A G R T O A G R T O ⇒ It follows the pattern

option 4) GATROTTO

A G R A O T G R T R A G O T O A G R T O ⇒ This doesn't follow the pattern.

Thus, by putting 'GTAORTTO' in the series 'A G R T O' is repeating itself.

Hence, the correct answer is 'option 3)'.

The logic followed here is, 

• The triangle gets increased by one in consecutive steps and the triangles shift towards the right.
• The upcoming triangle gets reversed as pair of triangles found in the same orientation.

The figure shows the pattern as followed, therefore the next pattern will be,

Hence, the correct answer is 'option 2'

The pattern followed here in the number series is:

Hence the correct answer is option 1).

Preparing the family tree using the following symbols

As given,

• P and Q are sisters.
• Q is married to R
• S is R’s father.
• T is the wife of S
• U is S’s daughter.

Family Tree:

According to the family tree U, is the sister-in-law/husband's sister of Q.

Hence, the correct answer is 'option 2)'.

The logic that follows here is that,

Witch is the feminine gender of Wizard.

Similarly,

Nun is the feminine gender of Monk.

Hence, the correct answer is 'Nun'

In the given question,

The logic followed here is, 

• Alternate figures have a circle outside, so the upcoming image should have a circle on the outermost part.
• The decreasing order of sides of the polygon on the second shape in the first figure and outermost shape are changing their position alternatively, so the upcoming figure should have second figure with a polygon having three sides.

So, the correct answer that follows the pattern is 

Hence, the correct answer is option 1).

The logic followed here is,

The multiplication of the 2nd number of the set with 2, and then adding the result with the 3rd number, we get the 1st number of the set.

(34, 12, 10) → (12 x 2) + 10 = 24 + 10 = 34

(56, 17, 22) → (17 x 2) + 22 = 34 + 22 = 56

Checking all the options:

1. (48, 19, 8) 

⇒ (19 x 2) + 8 = 48

⇒ 38 + 8 = 48

⇒ 46 ≠ 48 (The result is not equal to the 1st number of the set)

2. (46, 19, 8)

⇒ (19 x 2) + 8 = 46

⇒ 38 + 8 = 46

⇒ 46 = 46 (The result matches the 1st number of the set)

3. (46, 29, 8)

⇒ (29 x 2) + 8 = 46

⇒ 58 + 8 = 46

⇒ 66 ≠ 46 (The result is not equal to the 1st number of the set)

4. (45, 19, 8)

⇒ (19 x 2) + 8 = 45

⇒ 38 + 8 = 45

⇒ 46 ≠ 45 (The result is not equal to the 1st number of the set)

Hence, the correct answer is option 2).

Preparing the family tree using the following symbols

David described the girl as the daughter of his brother's only brother means David's brother has only one brother and i.e. David.

Family Tree:

According to the family tree, the girl in the picture is David's daughter.

Hence, the correct answer is option 4).

The pattern followed here is as follows:

Hence, the correct answer is 'ICWB'.

Given:

Statements:

All computers are laptops. 

Some laptops are costly.

All costly things are imported.

The possible Venn Diagram is:

Conclusions:

1. All laptops are imported ⇒ FALSE (As we have no direct and definite relation between laptops and imported.) 2. Some computers are costly. ⇒ FALSE(This can be true but not definite because there is no direct relation between computers and costly.)

Thus, '"Neither conclusion 1 nor Conclusion 2 follow".

Hence, the correct answer is option 1).

The logic followed here is:

(First Number)² ÷ Second Number = Third Number

(76, 8, 722) 

⇒ (76)² ÷ 8 = 722 

⇒ 5776 ÷ 8 = 722

⇒ 722 = 722

(14, 4, 49)

⇒ (14)² ÷ 4 = 49

⇒ 196 ÷ 4 = 49

⇒ 49 = 49

Now, checking the options

option 1) (42, 8, 202) 

⇒ (42)² ÷ 8 = 202

⇒ 1764 ÷ 8 = 202

⇒ 220.5 ≠ 202

option 2) (24, 8, 72)

⇒ (24)² ÷ 8 = 72

⇒ 576 ÷ 8 = 72

⇒ 72 = 72

option 3) (23, 6, 68)

⇒ (23)² ÷ 6 = 68

⇒ 529 ÷ 6 = 68   

⇒ 88.16 ≠ 68

option 4) (35, 7, 162)

⇒ (35)² ÷ 7 = 162

⇒ 1225 ÷ 7 = 162

⇒ 175 ≠ 162

Hence, the correct answer is option 2).

The correct answer is "stop discussing an issue".

Key Points

• The idiom "Let sleeping dogs lie" means to stop discussing an issue.
• Stop discussing an issue- Avoid interfering in a situation that is currently causing no problems but may well do so as a result of such interference.
• Example: We know that we would never reach an agreement over this matter, so it is better to let sleeping dogs lie and not discuss it anymore.

Additional Information

<br>

Let us learn some other idioms have the word 'sleep' in them.

The correct answer is "BDAC".

Key Points 

• Sentence B should come in first at the opening of the paragraph.
• Sentence D is the second sentence as it states about The fact is that kids pay a hundred percent attention when they are playing or doing something creative. So, naturally, they do not heed and thus cannot answer their parents’ or elders’ calls.
• Sentence A is the third sentence as it states that Parents need to understand this simple fact so that they can treat children fairly and understandingly when they fail to have the attention of the kids.
• Sentence C comes at the end that is Paying full attention to a specific thing is also difficult for elderly people, but unlike children, it is because many more things keep racing in their minds.

Additional Information

• The correct sequence is :
• Parents always blame their kids or feel bad when their kids do not pay any attention to their words. The fact is that kids pay a hundred percent attention when they are playing or doing something creative. So, naturally, they do not heed and thus cannot answer their parents’ or elders’ calls. Parents need to understand this simple fact so that they can treat children fairly and understandingly when they fail to have the attention of the kids. Paying full attention to a specific thing is also difficult for elderly people, but unlike children, it is because many more things keep racing in their minds.

The correct answer is "Time; tide".

Key Points

• The correct answer is "Time and tide wait for a none".
• This is an idiom that means to emphasize that people cannot stop the passing of time, and therefore should not delay doing things.
• Example: I always remind myself that time and tide wait for none.

Additional Information

• All other options don't fit here as this is an idiom.

The correct answer is "E, C, D, B".

Key Points

• Sentence A comes at the opening of the paragraph.
• Sentence E is the second sentence as it states that by chance, one fine Sunday morning I woke up at 5.
• Sentence C is the third sentence and states that it was pleasant to see the sun rising in the sky, and birds chirping on the branches of trees.
• Sentence D is the fourth sentence which states that the experience was so awesome that I decided to wake up early every morning.
• Sentence B is the fifth sentence which states - But all my excitement was gone the next morning as it was 8 in the morning when I woke up.
• Sentence F comes in last.

Additional Information

• This is the correct sequence:
• I am not an early riser. By chance, one fine Sunday morning I woke up at 5. It was pleasant to see the sun rising in the sky, and birds chirping on the branches of trees. The experience was so awesome that I decided to wake up early every morning. But all my excitement was gone the next morning as it was 8 in the morning when I woke up. I still enjoy sleeping till late and could never turn myself into an early riser.

The correct answer is "right".

Key Points

• The correct sentence: He is always right in his choices.
• Right - correct or true, exactly.
• Example - I am always right.
• The best-suited option in this question is 'right'.

Additional Information

• Rite - A ceremony performed by a particular group of people, often for religious purposes.
• Example: He performed his father's last rites yesterday.
• Write - To make words, or letters on paper using a pen or pencil.
• Example: I am writing a letter to my friend.
• Writ - A legal order to do or not to do something.
• Example: They filed a writ against their families.

The correct answer is "liberty".

Key Points

• Antonym means a word that means opposite to another word.
• Liberty means freedom to do anything.
• ​Example: The laws restrict our liberty.
• Yoke - something that limits your freedom and makes life difficult.
• ​Example: He didn't know how to shake off that yoke or his anger.
• So, the above statement means that black people used to suffer as they did not have any freedom.

Additional Information

• Fraternity - Feeling of support or friendship.
• ​Example: The racing world is a pretty close-knit fraternity.
• Mediocrity - Moderate, not very good.
• ​Example - He thinks that he is mediocre.
• Alacrity - Great willingness or enthusiasm.
• Example - She accepted her work with alacrity.

The correct answer is "philanthropist".

Key Points

• A philanthropist means a person who helps others by donating, money or time or anything.
• Synonyms- Benefactor, humanitarian.
• Example - He is one of the famous philanthropists.

Additional Information

• Misanthropist- A person who hates or avoids other people.
• Example: The corruption he saw around made him misanthropic.
• Plagiarist - A person who uses another person's work or idea and pretends that it's his own.
• Example: The news reporter was a plagiarist.
• Misogynist - A person who discriminates against women.
• Example: He is a misogynist and hates the idea of women's empowerment.

The correct answer is "no error".

Key Points

• The correct sentence is:
• These pens were found in the upper drawer of your table.
• The given sentence is grammatically correct and also does not have any spelling mistakes.​

Additional Information

• These - is the plural form of this.
• Example: These dogs bark a lot.

The correct answer is "aquit".

Key Points

• The correct spelling is 'acquit'.
• The word 'acquit' means to state that person is not guilty of a crime.
• Example: The jury acquitted his murder.
• Another meaning of 'acquit' is to behave in the way that is mentioned.
• Example: He acquitted himself well in front of her parents.

Additional Information

• Forfeit - To lose something or have something taken away from you because you have done something wrong.
• ​Example: He forfeited his right to meet his children as he use to beat them.
• Aesthetic - concerned with beauty or art.
• Example: The sunset seems so aesthetic.
• Hideous - ugly or unpleasant.
• Example: She saw a hideous face on the lawn.​

The correct answer is "stop working on something".

Key Points

• The idiom ' call it a day ' means to stop doing something.
• It is used by someone who wants to take a break from the work.
• Example: I'm getting a bit tired so let's call it a day.
• So, the most appropriate answer is to stop working on something.

 Additional Information

• ​Calling out - to shout something, especially when you are trying to get someone's attention.
• ​Example: I tried to call out to him through the windows.
• Stop depending means to stop seeking help from others.
• Example: After some years, children should stop depending on their parents.
• Some idioms have 'call' in them:
• | Idiom | Meaning | Example | | --- | --- | --- | | Call a spade a spade | Speak directly. | Only the courageous can call a spade a spade. | | Call names | To speak or talk about a person in an offensive way. | Don't call him names. He will kill you. |

The correct answer is**"as many of their members were absent".**

Key Points

• The correct sentence is: "The committee decided to adjourn the meeting as many of its members were absent".
• In the question, we are talking about committee members so for committee 'it' is used instead of theirs.
• It's - of or belonging to a thing.
• Their - of or belonging to them, it is used instead of his/her.
• Example: This necklace is theirs.

Additional Information

• Adjourn means to stop for short time and start again.
• Example - The trial was adjourned until the next week.

The correct answer is "friendly".

Key Points

• The word cordial means in a friendly and polite way.
• Synonyms are word that has the same meaning as another word.
• So the question states that the student maintains a friendly relationship with the teacher.
• Example: You are cordially invited to our wedding.
• Example: Muskan had been friendly to me.

Additional Information

• Unpleasant - causing discomfort, or a bad feeling.
• Example: The weather is unpleasant today.
• Unfriendly - Not polite to someone.
• Example: Saumya has a very unfriendly nature.
• Beneficial - Having a good or helpful effect.
• Example: Sunlight is beneficial to us.

The correct answer is "DABC".

Key Points

• Sentence S1 comes first as it is the opening of the paragraph.
• Sentence D is the second sentence which connects the first sentence to the second.
• Sentence A comes third continuing the story.
• Sentence B comes forth which states that 'the last lights we see are those of the train of carts.
• Sentence C comes fifth which states that "the last voice we hear is that of the cart-man".
• Sentence S6 comes in last giving a perfect ending.

Additional Information 

• **The correct sequence is:**​ Cart after cart groans through the roads of Kanthapura and on many a night before the eyes are shut the last lights we see are those of the train of carts, and the last voice we hear is that of the cart-man who sings through the hollows of the night.

The correct answer is: Option(2) i.e. Woe.

Key Points

• The word "WOE" means great sorrow or distress. (बड़ा दुख या परेशानी)
• Example: She stood gazing at the funeral with a heart full of woe.
• Hence, "WOE" is the one-word substitute for the given group of words "Great sorrow or distress".

Therefore, the correct answer is: Option(2) i.e. Woe.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Rigour (कठिनाई): The quality of being extremely thorough and careful; strictness or severity.
• Example: The rigour of military training is meant to prepare soldiers for the toughest conditions.
• Asperity (कटुता): Harshness of tone or manner.
• Example: He spoke with asperity when he found out his orders were not followed.
• Cross (नाराज): Annoyed or angry.
• Example: She was cross with her friend for cancelling their plans at the last minute.

The correct answer is "stalk".

Key Points

• A homonym is a word that is spelled and pronounced like another word but has a different meaning.
• Stalk as a noun means one of the long thin parts of a plant on which the flowers and fruits are grown but in this question, the stalk is used as a verb that means to follow a person over a period of time in a frightening or annoying way.
• Example: The stranger had been stalking her for two years.
• So, the correct homonym to fill in the blank is 'stalk'.

Additional Information

• Laugh at - to say unkind things about someone.
• Example: The kids laughed at his clothes.
• Adore - to be very fond of, to worship, or honor as a deity.
• Example: He adores Muskan like there is no tomorrow.
• Like - to find something/someone pleasant or to want.
• Example: I like chocolates.

The correct answer is "certainty".

Key Points

• Certainty means the state of being completely sure about something.
• Example: Death has to come to everyone and this is certain.
• Casuistry - use of clever arguments to trick people.
• Antonym means words having different meaning from other words.
• So, in this question, 'certainty' is opposite to 'casuistry' that's why an answer is 'certainty'.

Additional Information

• Sophistry - the use of clever but false arguments, especially with the intention of deceiving.
• Example: She knows that it is pure sophistry on his part.
• Insinuation - the action of suggesting, without being direct, that something unpleasant is true.
• Example: I reject the insinuation behind your question.
• Cacophony - a mixture of loud, unpleasant sounds or noise.
• Example: I could not think of the cacophony of traffic.

The correct answer is "loquacious".

Key Points

• The person who loves to talk is generally referred to as talkative, chatty, or 'loquacious'.
• Example: Mina is a loquacious personality.
• So, the most suitable one-word substitute for "one who loves to speak" is 'loquacious.

Additional Information

• Misanthropist - a person who avoids other people.
• ​Example: My friend is a misanthropist so he doesn't go to parties.
• Misogamist - a marriage hater.
• ​Example: Your friend might just like the independence or he might be a misogamist.
• Extrovert - a person who enjoys being with other people.
• ​Example: Marketing and sales persons are extroverts.

The correct answer is "unsuitable".

Key Points

• An antonym is a word that means the opposite of another word.
• The word 'proper' means right, suitable, or correct.
• Example: You should wear proper clothes to the office.
• So, the correct option from the above options is 'unsuitable'.

Additional Information

• The sentence means that 'there is an unsuitable drainage system in the locality'.
• Bizzare - very strange or unusual.
• Example: The story had a most bizarre ending.
• Incongruous - strange and out of place.
• Example: The dinner table looks incongruous in the small room.

The correct answer is "srinkage".

Key Points

• The correct spelling is "shrinkage".
• Shrinkage means the amount by which anything decreases in size, value, etc.
• So, the correct option is 'shrinkage'.

Additional Information

• Parentage - the origin of a person's parents.
• Example: He is a young American of Australian parentage.
• Storage - the keeping of things until they are needed.
• Example: This room is being used for storage.
• Percentage - The number, amount, etc of something, expressed as if it is part of a total which is a hundred.
• Example: What percentage did you get in your exams?

The correct answer is "has quit".

Key Points

• The correct answer is "Ritu has quit the soccer team".
• The tense used in this sentence is Present perfect tense.
• The rule for present perfect tense: Subject+has/have+verb(3rd form)+object.
• So, the third form of 'quit' is 'quit' only.

 Additional Information

• The present perfect tense describes an action that happened in the past but still happening in present.
• Rita has quit the soccer team and at present, she is still not part of it.

The correct answer is "involving".

Key Points

• Involve means to make something necessary, to include something.
• Example: The job involves a lot of effort.
• So the correct option to fill in the blank is "involving".The statement becomes: It experiments with teaching-learning strategies involving new methods and technologies.

Additional Information

• Precluding - to prevent something from happening or to make something impossible.
• ​Example: She suffered a head injury that precluded the possibility of her career.
• Inclusive - containing everything, including the thing mentioned.
• ​Example: The salt is inclusive of taxes.
• Excluding - leaving out, without.
• ​Example: The cost of lunch is excluding taxes.

The correct option is "related to".

Key Points

• Related to means in connection with like if people are related, they belong to a family.
• Example: Chapter 9 of history relates to chapter 5 of geography.
• So the correct option is "related to" which will be filled in the following sentence: It also extends its cooperation and expertise to other departments and divisions of NIE as well as other constituents of the NCERT in various activities related to the development of curricular, co-curricular and other support materials for students as well as teachers.

Additional Information

• Unrealted to - not related to something or not having any connection.
• ​Example: My syllabus is unrelated to biology.
• Unconnected to - not associated or not joined together.
• Example: This web series is unconnected to ramayana.
• Separated to: not together.
• Example: They separated last year.

The correct answer is "dissemination".

Key Points

• Dissemination means to spread or give out something, especially news, information etc.
• Example: The dissemination of COVID 19 guidelines was done during lockdown.
• The correct option to be filled in the following sentence is 'dissemination'. So the statement is given as: Major activities of the DESM include curriculum development, conducting teacher orientation or training programmes, dissemination of information in Science, Mathematics and Environmental Education, development of innovative laboratory practices and publication of the Journal School Science.
• The given statement means that DESM includes curriculum development, conducting teacher orientation or training programs and spreading information about science.

Additional Information

• Congregating - to come together in a crowd or group.
• ​Example: Many animals are social, congregating in colonies.
• Concealing - to hide something/somebody.
• ​Example: She tried to conceal her anger from her friend.
• ​Hiding - to put anything in place where you cannot be seen or found.
• ​Example: She always hide whenever I visit her.

The correct answer is "to replicate".

Key Points

• To replicate means to copy something.
• Example: Scientists replicates the original experiment.
• Synonym of replicate - copy, duplicate.
• The correct option to be filled in the blank is "to replicate". So the statement becomes: The department has also developed a Science Park, a herbal garden which provides valuable information and idea for schools to replicate the same for benefit of children.

Additional Information

• To originate - to appear for the first time in a particular place or situation.
• Example: The game is originated from our ancestors.
• To exclude - to leave out.
• Example: Women are excluded from some temples.
• To comprehensive - including everything that is connected with a particular subject.
• Example: The guide gives comprehensive information about monuments.

The correct answer is "marks".

Key Points

• Marks - something that shows who or what somebody/something is, especially by making it different from others.
• Example: My horse has white mark on it.
• So, the statement becomes: It also organises the Jawaharlal Nehru National Science, Mathematics and Environment Exhibition (JNNSMEE) for children, which is an annual event that marks the culmination of a series of science exhibitions, organised at district, zonal and state levels. DESM also provides academic guidance and financial support for the State Level Science Exhibitions.

Additional Information

• Gives - to let somebody have something which he/she wants.
• ​They're giving us chocolates.
• Takes - to carry or move something along.
• ​Example: You can take my shoes.
• Noted - well known, famous.
• ​Example: TRhis hotel is noted for its food.

The correct answer is Uploading.

Key Points

• The server can be a computer system that accepts web requests from the users and also revert back with the response.
• When a user requests for a webpage, the server then authenticates the request and responds back with the webpage and displays it on the client's browser.
• The servers that are hosted remotely are called data centres.
• Copying a page or transferring something onto the server from a local storage is called uploading. Hence option 4 is correct.
• The files from the computer are uploaded on to the server using a File Transfer Protocol or FTP.

Additional Information

• When you request something from the server and store it on your local computer, it is called downloading.
• Saving refers to copying the data from the web server temporarily.

The correct answer is CTRL + F1.

Key Points

• A ribbon is a set of tools that are found on the top of the window in the MS Office suite.
• This provides the tools for changing the format of the document.
• This gives the extra space to view the document.
• To expand or collapse the ribbon, double-click on any of the tab names on the top.
• You can also use the shortcut CTRL + F1 to do it. Hence option 1 is correct.

Additional Information

• CTRL + F2 shortcut displays the print preview. To access it without a shortcut:
• Go to the File tab, and click the print option, there you can find the print preview box.
• ALT + F1 shortcut creates an embedded chart of the data in the current range.
• ALT + F2 shortcut opens the "Save As" dialog box to save the workbook in a specific location.

The correct answer is Ctrl + Delete.

Key Points

• Both the Delete and Backspace keys are used to delete one character at a time in the text.
• To delete the word, press and hold the Delete key.
• MS Word provides Ctrl + Delete shortcut to delete one word at a time to the right side. Hence option 3 is correct.
• To delete the whole word at a time to the left side, use Ctrl + Backspace shortcut key.

Additional Information

• Alt + Backspace or Ctrl + Z shortcut is used for the Undo command to go to the previous position.
• Ctrl + Y or Ctrl + Shift + Z shortcut is for the Redo command.

The correct answer is Blog.

Key Points

• A blog is a type of website or webpage, that is updated regularly by the author.
• They are interactive pages that the author uploads in the form of articles and the readers have the option to interact using the comment box.
• A blog can be a travel blog, food blog, personal blog etc
• Traditional blogs and microblogging are the two types of blogs.
• Traditional blogs include more text like old style whereas microblogs include images and other interactive elements to enhance the appearance.
• Blogs usually contain the experiences, observations, thoughts and opinions of the author. Hence option 2 is correct.
• A website may contain more than one webpage depending on the type of the website.
• There are different types of websites like eCommerce, Business, Personal websites etc.

Additional Information

• An instant message is a text-based real-time communication that happens over the internet. This can also include images, videos and files.
• The applications that provide the instant messaging service are WhatsApp, Signal, Telegram etc.
• A Virus is malware or a malicious program that when activated, replicates itself and spreads onto the system.
• Email is a messaging service used for the exchange of messages between users over the internet.
• ​The email services examples are Gmail from Google, Yahoo, Outlook from Microsoft etc.

The correct answer is In MS Excel 2010, we can save the file by using F3.

Key Points

• A dialog box is a form that lets you add information and make decisions about various aspects of the current worksheet and the data it has.
• The F3 shortcut displays the paste name dialog box. This is available only if the names have been defined in the workbook. Hence option 3 is correct.
• You can also do that without a shortcut. Paste the list of names to a location in the current worksheet.
• Select the cell to paste, go to Formulas, followed by Defined names.
• Then click Use in Formula and finally Paste Names.

 Additional Information

• Shortcut Shift + F3 displays the Insert function dialog box.
• Ctrl + F shortcut is used to search the text in the worksheet. Click that shortcut and enter the word you want to search for.
• To start a new line or to add a space between the lines or a paragraph in a worksheet, press Alt + Enter shortcut.
• The ribbon is a set of toolbars that contains frequently used commands.

The correct answer is Right.

Key Points

• Alignment changes the way how the values or data in the cells appear.
• You can also set the rotation clockwise or anti-clockwise, or change the angle and orientation of the text.
• MS Excel provides four types of alignment. They are Right, Left, Center and Justified.
• Right alignment is the default alignment. Hence option 4 is correct.
• You can also use an Alt + H and A + R shortcut for the right alignment. Here, first press Alt + H followed by A + R.
• To change the alignment, select the cells, in the Home tab, go to the alignment group and pick the alignment you want.

Additional Information

• To change the alignment to left, click Alt + H and then the A + L shortcut.
• For center alignment, click Alt + H followed by A + C.

The correct answer is NOW.

Key Points

• MS Excel provides an option to insert the current date and time in the cell.
• To insert the current date in the cell, select the cell and use Ctrl + ; (semi-colon).
• To insert the current time, select the cell and click Ctrl + Shift + ; (semi-colon) shortcut.
• You can also insert both the system date and time using the =NOW() function in the formula bar. Hence option 4 is correct.

Additional Information

• The function =TODAY() inserts the current system date in the cell. Insert this function in the formula bar.
• YEAR function returns the year corresponding to the given date. For example, =YEAR(A2) returns the year of the date in cell A2.
• You can also give a specific date and get the year of it. =YEAR("19-Jan-2023") returns the year.

The correct answer is CTRL + R.

Key Points

• MS Excel allows you to create tables to insert the data. Every time you create a table, it is created with a default name like Table1, Table2 etc.
• To rename it:
• select the table, you will find an extra tab Table Design after the Help tab.
• In Table Design, on top left corner, you will find the option to change the table name.

   

• You can also rename the table using CTRL + R shortcut. Hence option 3 is correct.

Additional Information

• CTRL + R shortcut is used to fill the selected cell with an active cell to the right.
• ALT + R shortcut opens the Review tab in the ribbon.

The correct answer is SUM.

Key Points

• Excel provides a few arithmetic in-built functions for faster calculations like SUM, COUNT, AVERAGE, COUNTIF etc.
• To calculate the aggregate of the values in the cell, use the SUM function. Hence option 1 is correct.
• Write the sum function in the formula bar as =SUM(value1, value2). Here values indicate the reference of the cell.
• If you want to add two numbers in the cells A2 and A15, then write the formula as =SUM(A2:A15).
• To calculate the sum of values present in cells from A2, A15 and B2, B15, use =SUM(A2:A15, B2:B15).

Additional Information

• The COUNT function provides the number of entries in the range of the given cells. Its syntax is COUNT(value1, value2...).
• If you have an array from A1 and A10, use the formula =COUNT(A1:A10), this gives you the output as 10.
• IF function in Excel lets you make logical comparisons between different values. It gives the results as True/False.
• The AVERAGE() function returns the average of the arguments. Its syntax is AVERAGE(number 1, [number 2],......). For example, AVERAGE(B1:25) returns the average of the numbers in between the cells B1 and B25.

The correct answer is ALL I, II and III.

Key Points

• Email is a messaging service used for the exchange of messages between users over the internet.
• It came into existence in the 1970s to exchange messages over the ARPANET (Advanced Research Projects Agency Network).
• The email services examples are Gmail from Google, Yahoo, Outlook from Microsoft etc. 
• The valid domain names are gmail.com, yahoo.com, yahoo.com etc. Hence option 4 is correct.
• The format of a valid email address looks like [email protected], where '@' is used as a separator for the username and domain name.

Additional Information

• Email offers users to send messages to all users in the organization or users can send messages privately to a few users using Cc and Bcc respectively.
• Cc means Carbon Copy.
• It allows the user to send an email to other users apart from the recipient, and add other user emails in the Cc block.
• It helps other users to have a copy of the email.
• Bcc stands for Blind Carbon Copy.
• Adding someone's email in Bcc makes it hidden.
• It helps you share the email copy securely with someone without other recipients knowing it.