SSB Constable (Non GD) 13 July 2023 (Shift 2) Official Paper (Previous Year Paper)

The correct answer is Pawan Goenka.

Key Points

• Pawan Goenka is the current chairman of the Indian National Space Promotion and Authorization Center (IN-SPACe).
• He was appointed to the position in June 2020.
• Goenka is a former Managing Director of Mahindra & Mahindra.
• He is a graduate of the Indian Institute of Technology, Bombay and holds a Master's degree in Business Administration from Harvard Business School.

Important Points

• S Somnath is the 10^th Chairman of the Indian Space Research Organisation.
• He was appointed to the chairman post in January 2022.

The correct answer is Losar - Monpa.

Key Points

• Losar is the Tibetan New Year festival, which is celebrated in the state of Arunachal Pradesh, Sikkim and Ladakh.
• The Monpa people are of Tibetan descent and follow Tibetan Buddhism, and Losar is one of the most important festivals in their tradition.
• It is a festival that marks the beginning of the new year and is celebrated with various rituals, dances, and feasts.

Additional Information

Hornbill - Bodo: Incorrect.

• The Hornbill Festival is celebrated by the Naga tribes in Nagaland, India.
• It is named after the Hornbill bird, which is prominently featured in the folklore of most of the state's tribes.
• The festival showcases the rich tradition and cultural heritage of the Naga people.

Garia - Cole: Incorrect.

• The Garia festival is an important festival for the Tripuri people, an ethnic group in Tripura, India.
• It is a traditional festival celebrated to worship the deity 'Garia,' who is considered the god of livestock and wealth.

Chad Laho - Carby: Incorrect.

• Chad Laho is a festival celebrated by the Lepcha community in the Indian state of Sikkim.
• The festival is observed to celebrate the ripening of paddy crops.

The correct answer is lymphatic filariasis.

Key Points

• The Ministry of Health and Family Welfare launched a nationwide Mass Drug Administration (MDA) campaign in February 2023 to eradicate lymphatic filariasis.
• Lymphatic filariasis is a mosquito-borne disease that causes swelling of the limbs, known as elephantiasis.
• The MDA campaign aims to distribute free tablets of diethylcarbamazine citrate (DEC) and albendazole to all people living in filaria-affected areas.
• These tablets kill the filarial worms and prevent them from transmitting the disease.

The correct answer is Only II.

Key Points

Let's analyze both statements:

I. The industrial working class participated in large numbers across the country:  Incorrect.

• While there were pockets of participation from the industrial working class, the Civil Disobedience Movement did not see widespread support from this segment across the country.
• The movement was primarily led by the middle classes, peasants, and urban inhabitants.

II. Indian merchants and industrialists supported the movement when it was first started: Correct.

• Many Indian merchants and industrialists supported the Civil Disobedience Movement, especially at its inception.
• Leaders like Gandhi advocated for the boycott of British goods and the promotion of Indian-made products, aligning with the interests of Indian business owners.
• The financial contributions and support from this segment played a crucial role in the initial success of the movement.

Therefore, the correct option is 4) Only II, as it accurately represents the participation and support dynamics of the Civil Disobedience Movement against the British Empire in India.

The correct answer is 62%

Important Points

• A person aged seven and above, who can both read and write with understanding in any language, is treated as literate.
• Children below five years of age were necessarily treated as illiterates until the 1991 census.
• The 15^th official census in India was calculated in the year 2011.

Key Points 

• According to the 2011 census:
• The national literacy rate in the country is 74.04%.
• The literacy rate among males is 82.14%.
• The literacy rate among females is 65.46%.
• Kerala retained the top with a 93.91% literacy rate.
• Bihar ranks the last in the overall ranking with a 61.8% literacy rate.
• Serchip in Mizoram is the most literate district in India.
• Alirajpur in Madhya Pradesh is the least literate district in India.
• Lakshadweep is the most literate union territory in India with a 91.85% literacy rate.
• Dadra Nagar Haveli is the least literate union territory in India with a 76.24% literacy rate.

The correct answer is Lithium.

Key Points

• In February 2023, the Geological Survey of India discovered estimated resources of 5.9 million tonnes of lithium in the Salal-Haimana area of Reasi district in Jammu and Kashmir.
• Lithium is a soft, silvery-white metal that is highly reactive.
• It is used in a variety of applications, including batteries, ceramics, and lubricants.

Additional Information

• Thorium is a radioactive metal that is used in nuclear power plants.
• Platinum is a precious metal that is used in jewelry and electronics.
• Uranium is a radioactive metal that is used in nuclear weapons and nuclear power plants.

The correct answer is  Badminton.

Key Points

• Lakshya Sen
• He hails from Almora in Uttarakhand.
• He is an Indian badminton player.
• He won gold medals at the 2018 Asian Junior Championships in the boys' singles and at the Summer Youth Olympics in the mixed team event.
• He won the bronze medal at the 2021 World Championships.
• He also won the gold medal at the 2022 Commonwealth Games.
• He was bestowed with Arjuna Award for badminton in November 2022.

The correct answer is Duns.

Key Points

• The valleys lying between the lesser Himalayas and Shivaliks are called Duns.
• Longitudinal valleys which are formed as a result of folding when Eurasian plate and Indian plate collide.
• These valleys are deposited with coarse alluvium which is brought down by the Himalayan rivers.

Shivaliks

• These are mountain range of the outer Himalayas that stretches from the Indus River about 2,400 km eastwards close to the Brahmaputra River, spanning across the northern parts of the Indian subcontinent.
• It is 10–50 km wide with an average elevation of 1,500–2,000 m.

Additional Information Duars

• The alluvial floodplains in eastern-northeastern India that lie south of the outer foothills of the Himalayas and north of the Brahmaputra River basin.
• This region is about 30 km wide and stretches over about 350 km from the Teesta River in West Bengal to the Dhansiri River in Assam.

Terai

• Lowland region in northern India and southern Nepal that lies south of the outer foothills of the Himalayas, the Sivalik Hills, and north of the Indo-Gangetic Plain.
• This lowland belt is characterised by tall grasslands, scrub savannah, sal forests and clay rich swamps.

The correct option is 2

Concept:

The Indo-Aryan language family is a significant branch of the Indo-European language family, spoken largely in the Indian subcontinent.

1. Kurmali - Indo-Aryan
2. Bodo - Tibeto-Burman
3. Oriya (Odia) - Indo-Aryan
4. Angika - Indo-Aryan

Among the options, Bodo does not belong to the Indo-Aryan language family. Instead, it is part of the Tibeto-Burman language family, which includes languages spoken in the northeastern part of India, Tibet, Nepal, Bhutan, and Burma. The other three languages are part of the Indo-Aryan language family.

The correct answer is 543.

Key Points

The Lok Sabha is called the lower house of the Parliament of India or the house of the people.

• For the purpose of constituting the Lok Sabha, the whole country has been divided into 543 Parliamentary Constituencies, each one of which elects one member.
• The members of the Lok Sabha are elected directly by the eligible voters.
• The President of India can nominate a maximum of two members as representatives of the Anglo- Indian community.
• (In January 2020, the Anglo-Indian reserved seats in the Parliament and State Legislatures of India were abolished by the 104^th Constitutional Amendment Act, 2019)
• Some seats are reserved in Lok Sabha for the members of the Scheduled Castes and Scheduled Tribes.
• As per the order issued by the Delimitation Commission in 2008, 412 are general, 84 seats are reserved for Scheduled Castes and 47 seats for the Scheduled Tribes.
• Earlier it was 79 and 41 for Scheduled Castes and Scheduled Tribes respectively.

Thus, it is clear that a total of 543 Lok Sabha Constituencies is there in India.

The correct answer is Tropical Deciduous Forests.

Key Points

• Tropical Deciduous Forests
• These are the most widespread forests in India.
• They are also called the monsoon forests because the trees in these forests shed their leaves during the dry season and re-grow during the monsoon.
• They spread over regions that receive rainfall between 70-200 cm.
• The average temperature of Tropical Deciduous forests is 30oC.
• The humidity in these forests lies in the range of 80-90 per cent.
• The prime feature of these forests as trees shed their leaves in the dry season and grow back leaf in rainy seasons.
• Major states where tropical deciduous forests are found:
• Madhya Pradesh
• Uttar Pradesh
• Chhattisgarh
• Jharkhand
• Odisha
• Maharashtra
• Some parts of Tamil Nadu and Andhra Pradesh
• On the basis of the availability of water, these forests are further divided into
• Moist Deciduous
• Dry Deciduous
• Moist Deciduous forests
• They spread over regions that receive rainfall between 100-200 cm.
• These forests are found in the northeastern states along the foothills of the Himalayas, eastern slopes of the Western Ghats, and Odisha.
• Teak, Sal, Shisham, Hurra, Mahua, Amla, Semul, Kusum, and Sandalwood, etc. are the main species of these forests. Hence, Statement 3 is correct.​
• Dry Deciduous forests
• They spread over regions that receive rainfall between 70-100 cm.
• These forests are found in the rainy areas of Peninsular India, Plains of Uttar Pradesh, and Bihar.
• In the higher rainfall regions of the Peninsular plateau and the northern Indian plain, these forests have a parkland landscape with open stretches in which teak and other trees interspersed with patches of grass are common.
• As the dry season begins, the trees shed their leaves completely and the forest appears like a vast grassland with naked trees all around.
• Tendu, Palas, Amaltas, Bel, Khair, Axlewood, etc. are the common trees of these forests.

Key Points

• Al-Biruni wrote Kitab-Ul-Hind and it was written in Arabic.
• Al-Biruni spent years in the company of Brahmana priests and scholars, learning Sanskrit, and studying religious and philosophical texts.
• He translated several Sanskrit works, including Patanjali’s work on grammar, into Arabic.
• Al-Biruni’s Kitab-ul-Hind, written in Arabic, is simple and lucid.
• It is a voluminous text, divided into 80 chapters on subjects such as religion and philosophy, festivals, astronomy, alchemy, manners and customs, social life, weights and measures, iconography, laws and metrology.

The correct answer is Article 61.

Key Points

• President of India:
• The Indian President is the head of the state and he is also called the first citizen of India.
• He is a part of the Union Executive, provisions of which are dealt with Article 52-78 including articles related to President (Article 52-62).
• He is the first citizen of India and is a symbol of solidarity, unity, and integrity of the nation.
• He is a part of the Union Executive along with the Vice-President, Prime Minister, Council of Ministers, and Attorney-General of India.
• Qualifications of the President:
• He should be an Indian Citizen.
• His age should be a minimum of 35 years.
• He should qualify the conditions to be elected as a member of the Lok Sabha.
• He should not hold any office of profit under the central government, state government, or any public authority.

America joined the First World War in 1917.

Important Points

• On 6 April 1917, the United States of America declared war on Germany.
• USA had become the main source of arms and other essential supplies for the Entente countries.
• In 1915, the German U-Boats had sunk a British ship Lusitania.
• Among the 1153 passengers killed,128 were Americans.
• The Americans were generally sympathetic to Britain, and this incident further roused anti-German feelings in USA.
• Economic considerations had turned them even more in favour of the Entente countries.
• These countries had raised vast amounts of loans in USA to pay for the arms and other goods bought by them.
• Many Americans had subscribed to these loans which could be paid back only, if these countries won the war.
• There was also a fear that if Germany won the war, she would become a serious rival to USA.
• The sinking of ships, including American ships carrying American citizens, by the German U-boats finally led USA to join the war in 1917.

Hence, we can conclude that America joined the First World War in 1917.

The correct answer is Indonesia.

Key Points

• India beat 14-time winners Indonesia in the final of the Thomas Cup in Bangkok on May 15, 2022, and won the title by defeating the defending champions 3-0.
• Lakshya Sen defeated Anthony Jinting 8-21, 21-17, 21-16 in a thrilling match.
• India's doubles pair of Satwik and Chirag defeated Ahsan-Sukamuljo 18-21, 23-21, 21-19 to give India a 2-0 lead in what was the most sensational win of their career.
• In the third game, Kidambi Srikanth defeated Jonathan Christie 21-15, 23-21 to make it 3-0. He has done this feat without losing any match in the final.

Additional Information

• The Thomas Cup is a biennial international badminton championship.
• This is the first time the tournament took place in Europe after England hosted it in 1982.

The correct answer is III-I-II.

Key Points

• Jharkhand (III): The sex ratio in Jharkhand was 948 females per 1000 males.
• Nagaland (I): Nagaland's sex ratio was 931 females per 1000 males.
• Rajasthan (II): The sex ratio in Rajasthan was 928 females per 1000 males.

Additional Information

• Regarding the 2011 census, it was the 15^th nationwide census conducted by the Census Organization of India.
• The census was carried out in two phases: the house listing and housing census phase, followed by the population enumeration phase.
• The data collected provided comprehensive statistics on the population, including aspects like age, sex ratio, literacy, urban-rural divide, economic status, and more.
• The sex ratio is an essential demographic indicator, reflecting the number of females per 1000 males.
• It provides valuable insights into gender disparities within a society and can be an essential factor in understanding social dynamics and policy planning.
• In the 2011 census, Kerala had the highest sex ratio among Indian states, while Haryana had the lowest.

The answer is Total product.

Key Points

• Total product is the total output produced by all units of a variable input, such as labor or capital.
• It is calculated by multiplying the number of units of the variable input by the marginal product of each unit.
• Marginal product is the change in total product resulting from a unit change in a variable input.
• It is calculated by dividing the change in total product by the change in the variable input.
• Average product is the total product divided by the number of units of the variable input.
• It is calculated by dividing total product by the variable input.
• Diminishing marginal product is the phenomenon that the marginal product of a variable input eventually declines as more units of the input are added.

Explanation:

The pair that is not correctly matched is: Complete Swaraj – 1926

• "Complete Swaraj" was not an event that took place in 1926.
• "Complete Swaraj" was a resolution adopted by the Indian National Congress at its Lahore session in 1929.
• It called for the attainment of complete self-governance or independence for India.
• This resolution led to the Civil Disobedience Movement and various protests against British rule in India.

The correct event-year matches are as follows:

1) Complete Swaraj – 1929

2. Gandhi-Irwin Pact – 1931

3. Simon Commission – 1928

4. Chauri Chaura – 1922

The correct answer is Damodar Mauzo.

In News

• Goan writer Damodar Mauzo gets 57^th Jnanpith Award in May 2023.

Key Points

• Goan writer Damodar Mauzo Goa has received the prestigious Jnanpith Award, the country's highest literary honour.
• Mauzo's 25 books have been published in Konkani and one in English.
• Many of his books have also been translated in different languages.
• Mauzo's famous novel 'Karmelin' received the Sahitya Akademi Award in 1983.
• The novel, published in 1981, has been translated in Hindi, Marathi, English, Punjabi, Sindhi, Tamil, Odia and Maithili languages.
• Mauzo is the second Goan to receive the Jnanpith Award.
• Earlier, Ravindra Kelekar from the coastal state got the award in 2008.

Additional Information 

The correct option is  Article 21.

• There are six Fundamental Rights in the Indian Constitution and they are as follows:
• Right to equality
• Right to freedom
• Right against exploitation
• Right to freedom of religion
• Cultural and educational right
• Right to constitutional remedies
• Article 21A is added in the Indian Constitution in the 86^th Constitutional Amendment Act 2002.
• Article 19 to 22 comes under the Right to freedom of the Fundamental Right of the Indian Constitution.

The correct answer is Prokaryotes .

Key Points

• Prokaryotes are creatures without a nucleus or other organelles in their cells.
• Prokaryotes differ from eukaryotes by not having internal membranes.
• Bacteria and archaea, which are considered to have separate evolutionary lineages, are the two main categories of prokaryotes.
• Prokaryotic cells include organisms like cyanobacteria, E. coli, mycoplasma, etc.

Additional Information

• Eukaryotes:
• Any cell or creature with a distinct nucleus is said to be eukaryote.
• The nucleus, which houses the clearly delineated chromosomes, is encased in a nuclear membrane in eukaryotic cells.

The correct answer is Only I.

Key Points I. The Election Commission of India can be single-member or multi-member:

Correct

• The Election Commission of India (ECI) can function either as a single-member body or a multi-member body.
• Initially, it was a single-member commission but later expanded to a three-member body.

II. Till 1993, the Election Commission was single member: Incorrect.

• The Election Commission was a single-member body until 16 October 1989, when it was expanded to a three-member body.
• The change was reversed to a single-member body in January 1990 and then reverted to a three-member body again on 1 October 1993.

Additional Information

• The Election Commission of India (ECI) is an autonomous constitutional body that supervises the election process in India.
• It administers the election process from the election of the President of India to the State Legislative Assembly.
• As per Article 324 of the Indian Constitution, ECI has the supervisory and directional control of the complete process election to Parliament and Legislature of every State and to the office of the President and the Vice-President of India.

Functions:

• It ensures that political parties and candidates adhere to the Model Code of Conduct.
• Allotting territorial areas for electoral constituencies in the country.
• Organise and amend electoral rolls and register eligible voters.
• Sets up polling booths.
• Inform dates and schedules of elections and scrutinize nomination papers.
• Give recognition to political parties and assign election symbols to them.
• Proposes the limit of campaign expenditure per candidate to all parties.

The correct option is 3

Concept:

• When the supply curve shifts to the right, it indicates an increase in the supply of a good at a given price. Conversely, when the demand curve shifts to the left, it means a decrease in the quantity demanded at a given price.
• In this context, the effect on the quantity in the market depends on the relative magnitude of these shifts. If the shift in supply is more significant than the shift in demand, the quantity will increase. Conversely, if the shift in demand is more pronounced than the shift in supply, the quantity will decrease.

The Correct Answer is Kambala.

Key Points

• Kambala is a buffalo race held annually in Karnataka.
• This event is sponsored by the local Tuluva landlords in the Dakshina Kannada and Udupi districts.
• Kambala samithis organize these events. Annually, more than 45 races are held in the coastal region of coastal Karnataka.
• Format of this race: The race track where this event takes place in a paddy field that is slushy.
• Some of the organizing committees award a gold coin which is of eight-grams to the winner whereas in some places cash prizes are given.
• Buffalo decorations: The buffaloes taking part in this event are decorated with head-pieces made of silver and brass, bridles made of ropes, and colored jhūls.
• Paavade is the name of the towel that is used to cover the neck of the buffalo.

Additional Information

• Jallikattu:
• Jallikattu is a traditional event in which a bull is released into a crowd of people, and multiple people attempt to grab the bull's hump with both arms to bring it to a stop.
• It is more about "taming" the bull than a race.
• This event is traditionally held in the Tamil Nadu region of India during the Pongal celebrations in January.
• Bonalu:
• Bonalu is a Hindu festival where Goddess Mahakali is worshipped.
• It is an annual event celebrated in the Telangana region of India, primarily in the twin cities of Hyderabad and Secunderabad.
• The festival involves an elaborate procession and offerings of food and other items to the goddess, but it is not associated with buffalo or other animal races.
• Ugadi:
• ​Ugadi, also known as Yugadi, is the New Year's Day for the people of Andhra Pradesh, Telangana, and Karnataka in India.
• The day is observed by drawing colorful patterns on the floor called kolamulus, mango leaf decorations on doorways, buying and giving gifts, preparing and sharing special foods, and visiting Hindu temples.
• But this festival is not associated with buffalo or other animal races.

The correct answer is Delhi.

Key Points

• The 'Make India No. 1' mission was launched by the Chief Minister of Delhi, Arvind Kejriwal, on August 17, 2022.
• The mission aims to make India the number one country in the world in terms of health, education, agriculture, employment, and women's empowerment.

The mission has five key pillars:

• Health: Providing quality healthcare to all citizens, regardless of their income or background.
• Education: Providing quality education to all children, from early childhood to higher education.
• Agriculture: Making India self-sufficient in food production and improving the incomes of farmers.
• Employment: Creating jobs for all youth and providing them with the skills they need to succeed.
• Women's empowerment: Empowering women and girls and ensuring that they have equal opportunities in all spheres of life.

The mission is apolitical and open to all citizens and political parties. Kejriwal has called on all Indians to join the mission and make India the number one country in the world.

Calculation:

Deepak's rate of work: 1/50

Deepak and Rahul's combined rate of work: 1/40

Rahul's rate of work: 1/40 - 1/50 = 5/200 - 4/200 = 1/200

Rahul and Varun's combined rate of work: 1/25

Varun's rate of work: 1/25 - 1/200 = 8/200 - 1/200 = 7/200

Varun's time to complete the work: 200/7 hours

Therefore, Varun alone can complete the same work in 200/7 hours.

Given:

Two boys are standing at opposite ends of a bridge 350 m long.

If they walk towards each other at the speed of 3 m/min and 4 m/min 

Formula Used:

Time = Distance / Speed

Calculation:

As both are moving in the opposite direction. So 

Relative Speed = Sum of their speed

Relative Speedc  = 3 + 4 = 7 m/min

Time = Distance / Speed

∴ Time = 350 / 7 = 50 min.

Calculation:

Let the original number be N.

N × (85/100) x (75/100) x (82/100) = 6273

N = 6273 / [(85/100) x (75/100) x (82/100)]

N = 6273 / (0.85 x 0.75 x 0.82)

N = 6273 / 0.52275

N = 12000

Therefore, the original number is 12000.

Given Data:

The radius of the cone (r) = 12 cm

Height of the cone (h) = 16 cm

Formula Used:

The total surface area of a cone = πr² + πrl

Where, 

l = √(r² + h²)

Calculation:

Using the above concept

l = √(12² + 16²) = √(144 + 256) = √400 = 20

Required Area = π(12²) + π × 12 × 20

Required Area = 144π + 240π

Required Area = 384 π = 384 × (22/7) = 1206.85 cm²

Given:

A room is in the shape of a cube and the length of the longest rod placed in it is 40√3 cm

Calculation:

The length of the longest rod placed in the cubical room is equal to the length of the diagonal of the cubical room.

We know,

Length of the diagonal of a cube =  a√3

Where a is the Length of each side of a cube.

⇒ ​a√3 = ​40√3 cm

⇒ a = 40 cm

Therefore, The Length of each side of a cube is 40 cm.

Now, The area of the floor = a3

⇒ The area of the floor = 403

⇒ The volume of the floor = 64000 cm³

Formula Used:

S.I = PRT/100

Calculation:

Here, 

P = 1000, T = 6 yr, 

S.I = (1000 × 6 × R)//100

(60/100) × 1000 = 60R

600 = 60R

∴ R = 10 %.

Given Data:

Pipes A and C together fill the tank in 30 hours.

Pipes C and D together fill the tank in 15 hours.

Pipes A and D together fill the tank in 20 hours.

Calculation:

    Eff.                                      LCM (total work)

    2            A + C       30

    4            C + D      15                  60

    3            A + D       20 

Total efficiency

(A + C) + (C + D) + (A + D) = 2 + 4 + 3  

2(A + C + D) = 9 unit/hour

(A + C + D) = 9/2 unit/hour

(A + C + D) - (A + D) = (9/2 - 3) = 3/2 unit/hour

C = (9/2 - 3) = 3/2 unit/hour

Therefore, 

3/2 unit work completed by C in 1 hour

60  unit work completed by C in 60 × (2/3) = 40 hour

Given Data:

Amount after 2 years: Rs.11520

Amount after 3 years: Rs.13824

Compound interest is compounded annually

Formula Used:

Use the formula for compound interest,

A = P (1 + r/100)ⁿ,

Where A is the amount, P is the principal,

r is the rate of interest, n = time 

Calculation:

Using the given data for 2 years, we have:

A₁ = 11520 = P (1 + r/100)²          -----(1)

Using the given data for 3 years, we have:

A₂ = 13824 = P (1 + r/100)³         ----(2)

Dividing the second equation by the first equation, we get:

(1 + r/100) = 13824 / 11520 = 1.2

Substituting this back into the equation for 2 years: 

P (1.2)² = 11520

P (1.44) = 11520

P = 11520 / 1.44 = 8000

Shortcut Trick

For any Arithmetic Progression, the average increases by (d ÷ 2) for every next term added, where d is the common difference.

For consecutive odd numbers, the common difference d = 2.

Increase in average = 2 ÷ 2 = 1.

New average = Old average + 1 = 7 + 1 = 8.

∴ The correct answer is 8.

Alternate Method

Given: Average of 5 consecutive odd numbers = 7.

Formula Used: Average = (Sum of all observations) ÷ (Total number of observations)

⇒ For 5 consecutive terms in AP, the middle term (3^rd term) is the average.

⇒ 3^rd term = 7

⇒ The 5 consecutive odd numbers are: 3, 5, 7, 9, 11

⇒ Sum of 5 numbers = 3 + 5 + 7 + 9 + 11 = 35

⇒ Adding the next odd number: 13

⇒ New Sum = 35 + 13 = 48

⇒ New Count = 6

⇒ New Average = 48 ÷ 6 = 8

∴ The correct answer is 8.

Additional Information

Average of Arithmetic Progression (AP)

For any sequence in AP, Average = (First term + Last term) ÷ 2. Also, for an odd number of terms, the middle term is the average.

Sum of First n Odd Numbers

The sum of the first n consecutive odd numbers starting from 1 is given by the formula: Sum = n².

Consecutive Numbers Increment Rule

If the next k terms are added to a sequence with common difference d, the average increases by (k × d) ÷ 2.

Calculation:

Let the smaller number be x and the larger number be y.

56.2% of x = 11.24% of y   

0.562 x = 0.1124 y              ---(1)

x + y = 1200                        ---(2)

⇒ x = (0.1124 times y) / 0.562

Substitute the expression for x into Equation 2:

⇒ (0.1124 y) / 0.562 + y = 1200

⇒ 0.2 y + y = 1200

⇒ 1.2 y = 1200

∴ y = 1000

Given:

The income ratio of A and B is 5:7

Expenditure ratio is 1:1

A saves Rs. 2000

B saves Rs. 4000

Calculation:

Let's assume the common factor of their incomes is x:

A's income = 5x

B's income = 7x

Since the expenditure ratio is 1:1, and

A and B save Rs. 2000 and Rs. 4000 respectively:

A's expenditure = 5x - 2000

B's expenditure = 7x - 4000

Since the expenditures are equal:

5x - 2000 = 7x - 4000

Now, we'll solve for x:

7x - 5x = 4000 - 2000

2x = 2000

x = 2000 / 2 = 1000

Now, A's income:

A's income = 5 multiplied by 1000 = 5000

So, the income of A is Rs. 5000.

Given data:

Difference between length and breadth: 18 meters

The perimeter of the rectangle: 144 meters

Concept Used:

Use the perimeter formula for a rectangle P = 2 x (l + b), where

l is the length and b is the breadth,

Calculation:

Let length = x & breadth = x - 18

Substitute the values of length and breadth into the perimeter formula:

⇒ 144 = 2(x + (x - 18))

⇒ 144 = 2(2x - 18)

⇒ x = 45

Substitute back to find the length and breadth:

⇒ Length = 45 m

⇒ Breadth = 45 - 18 = 27 m

Area = l x b

Area = 45 m x 27 m = 1215 square meters

So, the area of the rectangle is 1215 square meters.

Shortcut Trick

Assume total distance = 100 units.

First part = 50 units at 20 km/h. Remaining = 50 units.

Second part = 60% of 50 = 30 units at 15 km/h. Third part = 20 units at 10 km/h.

Total Time = (50/20) + (30/15) + (20/10) = 2.5 + 2 + 2 = 6.5 hours.

Average Speed = 100 ÷ 6.5 = 1000/65 = 200/13 km/h.

∴ The correct answer is 200/13 km/h.

Alternate Method

Given:

Speed₁ = 20 km/h, Speed₂ = 15 km/h, Speed₃ = 10 km/h.

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

Let total distance be D.

⇒ Time taken for first half = (D/2) ÷ 20 = D/40

⇒ Remaining distance = D − D/2 = D/2

⇒ Distance for second part = 60% of D/2 = 0.6 × 0.5D = 0.3D

⇒ Time taken for second part = 0.3D ÷ 15 = 3D/150 = D/50

⇒ Distance for third part = D/2 − 0.3D = 0.2D

⇒ Time taken for third part = 0.2D ÷ 10 = 2D/100 = D/50

⇒ Total Time = D/40 + D/50 + D/50 = D/40 + 2D/50 = D/40 + D/25

⇒ Total Time = (5D + 8D) / 200 = 13D/200

⇒ Average Speed = D ÷ (13D/200) = 200/13 km/h

∴ The correct answer is 200/13 km/h.

Additional Information

Average Speed (Equal Distances)

If two equal distances are covered at speeds u and v, Average Speed = 2uv / (u + v).

Relative Speed

In the same direction, relative speed is the difference (u − v). In opposite directions, it is the sum (u + v).

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Given Data:

Speed of the first man: 45 km/hr

Speed of the second man: 60 km/hr

Start time of the first man: 9:00 am

Start time of the second man: 9:00 am + 2 hours = 11:00 am

The distance that the second man needs to be ahead: 60 km

Formula Used:

The relative speed between two objects moving in the same direction is the difference between their speeds. The time taken to cover a distance at a given speed is given by the formula: time = distance ÷ speed.

Calculation:

Distance covered by the first man in 2 hours (before the second man starts running) = 45 km/hr × 2 hours = 90 km

Relative speed of the second man with respect to the first = 60 km/hr - 45 km/hr = 15 km/hr

The distance that the second man needs to cover to be 60 km ahead of the first man = 90 km + 60 km = 150 km

Time taken by the second man to be 60 km ahead = 150 km ÷ 15 km/hr = 10 hours

Time when the second man will be 60 km ahead = 11:00 am + 10 hours = 9:00 pm

Given Data:

X, Y, and Z together can complete the work in 25 days.

X and Y together can complete the same work in 50 days.

Calculation:

⇒ X + Y + Z's rate = 1/25 (work done per day)

⇒ X + Y's rate = 1/50

⇒ Z's rate = (X + Y + Z's rate) - (X + Y's rate)

Substituting Known Values:

⇒ Z's rate = (1/25) - (1/50)

⇒ Z's rate = 2/50 - 1/50

⇒ Z's rate = 1/50

Z alone can complete the work in 50 days.

Formula Used:

a² - b² = (a + b)(a - b)

Calculation:

(171 + 129)2 – (171 – 129)2

By using the above identity

[(171 + 129) + (171 - 129)][(171 + 129) - (171 - 129)]

[171 + 129 + 171 - 129][171 + 129 - 171 + 129]

(2 × 171) × (2 × 129) = 342 × 258.

Formula Used:

The average speed is the total distance traveled divided by the total time

taken.

Calculation:

Total time = d/80 + d/40 + d/20 + d/10

Total time = d/80 + 2d/80 + 4d/80 + 8d/80

Total time = (1 + 2 + 4 + 8)d/80 = 15d/80 hours

Total distance = 4 times multiplication sign d = 4d

Average speed = Total distance / Total time

Average speed = 4d / (15d/80)  =  64/3 km/hr

Formula Used:

Total Surface Area of Sphere = 4πr²

Calculation:

Given that, r = 35 cm

TSA of Sphere = 4πr²

⇒ TSA of Sphere = 4 × (22/7) × 35 × 35

⇒ TSA of Sphere = 15400 cm²

∴ The total surface area of the sphere is 15400 cm2.

Given Data:

Selling Price (Loss) = Rs.1350

Loss Percentage = 25%

Required Profit Percentage = 28%

Formula Used:

Cost Price = Selling Price / (1 - Loss/Profit Percentage)

Calculation:

Cost Price = Rs.1350 / (1 - 25/100) = Rs.1350 / 0.75 = Rs.1800

New Selling Price for 28% Profit = Cost Price + (Cost Price × 28/100)

New Selling Price = Rs.1800 + (Rs.1800 × 28/100)

New Selling Price = Rs.1800 + Rs.504 = Rs.2304

Given Data:

Selling Price (SP) = Rs.1722

First Discount = 30%

Second Discount = 18%

Formula Used:

MP = SP / ((1 - Discount1) x (1 - Discount2))

Calculation:

Effective Price1 = 1 - (First Discount) = 1 - 0.30 = 0.70

Effective Price2 = 1 - (Second Discount) = 1 - 0.18 = 0.82

Total Effective Price = Effective Price1 x Effective Price2

Total Effective Price = 0.70 x 0.82 = 0.574

 MP = SP / Total Effective Price = Rs.1722 / 0.574 = Rs.3000

The marked price of the article is Rs.3000.

Calculation:

We have

3M = 8N = 24P

M /(1/3) = N/(1/8) = P/(1/24) = k (let)

M = k/3, N = k/8, P = k/24

M : N : P = k/3 : k/8 : k/24

Multiply by 24

M : N : P = 24k/3 : 24k/8 : 24k/24

M : N : P = 8 : 3 : 1

Formula Used:

Curved Surface Area of Cylinder = 2πrh

Calculation:

We have, r = 42 cm, h = 84 cm

A = 2πrh

A = 2 × (22/7) × 42 × 84 

∴ A = 22176 cm²

Shortcut Trick

The Greatest Common Factor (GCF) or HCF of any set of numbers must always be a factor of their Least Common Multiple (LCM).

Given LCM = 180.

Check which option does not divide 180 perfectly: 180 ÷ 5 = 36 | 180 ÷ 6 = 30 | 180 ÷ 10 = 18.

180 ÷ 25 = 7.2 (Not a whole number).

Since 25 is not a factor of 180, it cannot be the GCF.

∴ The correct answer is 25.

Alternate Method

Given:

LCM of three different numbers = 180.

Method:

A fundamental property of numbers states that the HCF (GCF) always divides the LCM without leaving any remainder.

Calculations:

⇒ Let us find the factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.

⇒ Comparing factors with the given options:

⇒ 5 is a factor (180 ÷ 5 = 36).

⇒ 6 is a factor (180 ÷ 6 = 30).

⇒ 10 is a factor (180 ÷ 10 = 18).

⇒ 25 is not a factor because 180 is not exactly divisible by 25 (Remainder = 5).

∴ The correct answer is 25.

Additional Information

HCF and LCM Relationship

For any set of numbers, the Highest Common Factor (HCF) is always a divisor of the Least Common Multiple (LCM).

Product of Two Numbers

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

Co-prime Numbers

For co-prime numbers (numbers with no common factor other than 1), the HCF is always 1 and the LCM is the product of the numbers themselves.

Shortcut Trick

Cost Price (CP) of the mixture = 143 × 100 / 130 = Rs. 110.

By using the rule of alligation:

Ratio = (Dearer Price − Mean Price) : (Mean Price − Cheaper Price)

Ratio = (150 − 110) : (110 − 90) = 40 : 20 = 2 : 1.

∴ The correct answer is 2 ∶ 1.

Alternate Method

Given:

CP of first tea (CP₁) = Rs. 90/kg

CP of second tea (CP₂) = Rs. 150/kg

Selling Price (SP) of mixture = Rs. 143/kg

Profit percentage = 30%

Formula used:

CP = [SP × 100] / [100 + Profit%]

CP1 (90)

CP2 (150)

110

150−110 = 40 110−90 = 20

Ratio = 40 : 20 = 2 : 1

Calculations:

⇒ Mean CP of mixture = (143 × 100) / (100 + 30)

⇒ Mean CP = (143 × 100) / 130

⇒ Mean CP = 11 × 10 = Rs. 110

⇒ According to Alligation Rule:

⇒ (Quantity of tea 1) / (Quantity of tea 2) = (CP₂ − Mean CP) / (Mean CP − CP₁)

⇒ Ratio = (150 − 110) / (110 − 90)

⇒ Ratio = 40 / 20

⇒ Ratio = 2 / 1

∴ The correct answer is 2 ∶ 1.

Additional Information

Rule of Alligation

It is used to find the ratio in which two or more ingredients at given prices must be mixed to produce a mixture of a specified price.

Profit and CP Relation

When profit is made, CP = SP / (1 + Profit/100). Always ensure all prices used in the alligation cross (CP1, CP2, and Mean Price) are in the same unit (all must be Cost Prices).

Weighted Average

Mean Price = (n₁ × c₁ + n₂ × c₂) / (n₁ + n₂), where n is quantity and c is price per unit.

Shortcut Trick

Lateral Surface Area (LSA) of a cube = 4 × (side)²

Given side = 24 cm

LSA = 4 × 24² = 4 × 576 = 2304 cm²

∴ The correct answer is 2304 cm².

Alternate Method

Given:

Side of the cube (a) = 24 cm

Formula Used:

Lateral Surface Area of a cube = 4a²

Calculations:

⇒ LSA = 4 × (24)²

⇒ LSA = 4 × (24 × 24)

⇒ LSA = 4 × 576

⇒ LSA = 2304 cm²

∴ The correct answer is 2304 cm².

Additional Information

Total Surface Area of Cube

The total surface area (TSA) includes all 6 faces and is calculated as 6a².

Volume of Cube

The space occupied by the cube is given by the formula V = a³.

Diagonal of Cube

The longest rod that can be placed inside a cube is the body diagonal = a√3.

Let's analyze the relationships:

1. Axe - Woodcutter:

A tool used by the woodcutter.

2. Sculptor - Chisel:

A tool used by the sculptor.

3. Writer - Pen:

A tool used by the writer.

4. Doctor – Stethoscope:

A tool used by the doctor.

All of the pairs show a relationship between a professional and a tool they use.

In All the option except Option (1) Professional : Tool.

But;

In Option (1) Tool : Profession.

So, option (1) is odd one out.

Hence, the correct answer is "Axe - Woodcutter"

The pattern followed here is:

similarly,

Hence, the correct answer is "Option (2)".

The series followed the pattern as shown:

Hence, the correct answer will be "Option (4)".

Word Given: MORTEIN

Now;

The letters of the given word are arranged according to the English alphabetical order from left to right:

New Word: EIMNORT

 There is no letter is at same place.

Hence, the correct answer is "Neither".

The number of triangles are shown below:

Hence, the correct answer is "Option (1)".

The logic followed by the images is:

1. The number of dotted containing lines outside the figure is equal to the number of sides of the figure.

The pentagon and hexagon both have 5 and 6 dot containing lines respectively.

similarly, "Option (3) has a square with 4 dot containing lines.

Hence, the correct answer is "Option (3)".

The logic followed is:

I. 62 × 2 + 31 – 12 ÷ 6 = –2

After replacing the signs from left to right and using the BODMAS rule,

Signs: + and ÷

62 × 2 ÷ 31 – 12 + 6 = –2

= 62 × 2/31 - 12 + 6

= 4 - 12 + 6

= 10 - 12 = -2

Equation 1 is true.

II. 84 ÷ 39 + 3 × 4 – 16 = 118

After replacing the signs from left to right and using the BODMAS rule,

Signs: + and ÷

84 + 39 ÷ 3 × 4 – 16 = 118

= 84 + 13 × 4 – 16 = 118

= 84 + 52 – 16 = 118

= 136 - 16 = 120 ≠ 118

Equation 2 is false.

Thus, equation 1 is correct.

Hence, option (4) is the correct answer.

The logic followed here is:

1. The elements inside the square are 2 together and 1 with some gap between them.

But in Option (1), the elements are all settled together, with no spacing.

Hence, the correct answer is "Option (1)".

The pattern followed here is:

1. The pattern followed by letters is from backward to forward, and forward to backward both ways)
2. There is an unfixed gap between three letters, but the whole bracket follows the same rule)

(STQ, NQP, MNK)

(ABC, ZYX, UVW)

Now, in options:

(GMT, QJD, AGM)

(WRC, ZNT, QKW)

(KSB, YPH, FMV) (irregular pattern)

but,

(LQE, BNI, FKY)

Hence, the correct answer is "Option (1)".

The pattern followed by the series is as follows:

1. Every element, being unchanged in shape, is moving one step anticlockwise.

The Next part of the series is shown below:

Hence, the correct answer is "Option (1)".

The number of rectangles is shown below:

 

 → 15

Hence, the correct answer is "Option (2)".

The given figure when unfolded is as follows:

Hence, answer will be "Option (1)".

The pattern followed here is:

and

similarly,

Hence, the correct answer is "Option (4)".

By using BODMAS rule, we get

Given Equation:

 \(\sqrt{325.08}× 9.906+14.27%\) of 343 + 13.86 × 11.23

Taking Approximate values:

 \(\sqrt{326}× 10+14%\) of 343 + 14 × 11

= 18.05 × 10 + 14% of 343 + 14 × 11

= 18.05 × 10 + 48.02 + 14 × 11

= 180.5 + 48.02 + 154

= 382.52

= Approximately 383

Hence, the correct answer is "383".

The pattern followed here is:

1. Every Odd placed figure has a diamond shaped outer figure. 2. Every Even placed figure has a pentagon shaped outer figure
2. The number of dark dots keep incrementing in every next figure.

So, the next figure of the series will be:

Hence, the correct answer is "Option (3)".

Word Given: CJLCULSTOR

Now;

The letters are interchanged with the previous letter according to the English alphabetical order.

New Word: BIKBTKRSNQ 

The second letter from the left = I

BIKBTKRSNQ 

Seventh letter to the right of the second letter from the left = N

BIKBTKRSNQ 

Hence, the correct answer is "N".

Left K W L U J F I S F G U D H T O I J C E U B D I X M N G U Right

Vowels are preceded by a consonant:

Consonants - Vowels

K W (L U) J (F I) S F (G U) D H (T O) I J (C E) U B (D I) X M N (G U)

So, there are Seven consonants which is immediately preceded by a consonant and immediately followed by a number.

Hence, "Seven" is the correct answer.

The pattern followed here is:

(AL, ET, IB)

(BH, FP, JX)

similarly,

(HM, LU, PC)

Hence, the correct answer is "Option (4)".

The embedded part of image is:

Hence, the correct answer is "Option (4)".

The pattern followed here is:

Option (2): BHS – XMG

Option (3): ANJ – OSF

Option (4): HRV – AWM

But,

Option (1): ORB – GWS

Hence, the correct answer is "Option (1)".

Completing the incomplete pattern;

Hence, the correct answer is "Option (2)".

Preparing a family tree using the following set of symbols:

Now, S + M × T ÷ F – K ⇒ S is the Father of M, M is the brother of T, T is the son of F, and F is the mother of K.

Therefore, S will be the Father of K.

Hence, the correct answer is "Option (4)".

After the dice will be folded into a box, the pair of opposite faces will be:

5 ⇔ H

4 ⇔ 7

3 ⇔ 2

Therefore, the figure of "Option (2) won't be possible as 3 and 2 are opposite faces, they cannot be adjacent to each other.

Hence, the correct answer is "Option (3)".

Preparing a family tree using the following set of symbols:

Given: A # J @ K + R + G ⇒ J is the Husband of A, K is the son of J, R is the sister of K, G is the sister of R.

Therefore, G will be the Daughter of J.

Hence, the correct answer is "Option (1)".

The series follows a following pattern:

Hence, the correct answer is "Option (3)".

The correct answer is 'more'.

Key Points

• The sentence is comparing the number of vaccine doses that have been secured with the number that the populations need.
• The word 'more' is used to indicate a greater quantity or degree.
• In the context of the sentence, 'more' is the only option that can be used to compare the quantities of two things. The sentence is expressing that the number of vaccine doses is greater than what is necessary.
• The use of 'more' provides a clear and concise comparison without ambiguity.
• In English grammar, 'more' is the comparative form of 'many' and 'much,' and it is used to compare two quantities.

Therefore, the correct answer is Option 3.

Additional Information

• Option 1, 'most,' would imply the majority, not a comparison, and doesn't fit the context.
• Option 2, 'many,' doesn't indicate a comparison between the amounts but simply states a large number.
• Option 4, 'much,' could be used to describe a large amount, but in this context, it does not fit grammatically since we are comparing two quantities.

The correct answer is 'Deliberate' .

Key Points

• "Accidental" means occurring by chance or unexpectedly.
• "Deliberate" means done consciously and intentionally.
• The two words are antonyms as they represent opposite ends of the spectrum concerning intention.
• While an accidental event happens without planning, a deliberate action is carefully thought out and planned.

Therefore, the correct answer is Option 2.

Additional Information

• "Random" and "Arbitrary" are more synonymous with "Accidental," not opposite.
• "Desultory" means lacking a plan, purpose, or enthusiasm, and is not a direct opposite of "Accidental."

The correct answer is 'Impressoin'.

Key Points

• "Impressoin" is not a recognized word in the English language.
• The correct spelling for this word is "Impression," which means an effect or influence.
• Spelling is essential for clear communication, and incorrect spelling can lead to misunderstandings.
• It's vital to be aware of common misspellings to ensure clear and effective written communication.

Therefore, the correct answer is Option 3.

Additional Information

• "Motif," "Gaudy," and "Happiness" are all spelled correctly and are standard English words.

The correct answer is 'a'

 Key Points

• The phrase "a soft spot" refers to a particular liking or fondness for something or someone.
• "A" is used when referring to something for the first time, or something that is a common noun.
• Example Sentence: Many people have a soft spot for their first pet.

Therefore, the correct answer is Option 3.

 Additional Information

• "No article" would not be correct here, as it would create an awkward and incorrect sentence structure.
• "The" would also be incorrect, as it specifies a particular noun, which is not the case here.
• "An" would be incorrect, as "soft" does not begin with a vowel sound.

The correct answer is 'Stay away from someone or something'

 Key Points

• "Give a wide berth" is an idiom that means to stay away from someone or something, either to avoid danger or to avoid interacting with them.
• Example Sentence: After the scandal, everyone gave him a wide berth at social gatherings.

Therefore, the correct answer is Option 3.

The correct answer is 'To be sure or certain'

 Key Points

• "Bet one's boots" is an idiom that means to be absolutely certain or sure about something.
• Example Sentence: I would bet my boots that he will win the election this year.

Therefore, the correct answer is Option 4

The correct answer is 'the'

 Key Points

• When referring to countries with plural names or those that include words like "kingdom" or "states," "the" is used.
• "The UK" refers specifically to the United Kingdom, and the definite article "the" is required in this context.
• Example Sentence: Many people travel to the UK for business and leisure.

Therefore, the correct answer is Option 4.

Additional Information

• "An" and "a" would not be appropriate here, as they are indefinite articles and do not suit the context.

The correct answer is 'accompanying'

 Key Points

• The correct spelling of the word is "accompanying," meaning to go somewhere with someone as a companion or escort.
• Example Sentence: The manager was accompanying the new employee to the meeting room.

Therefore, the correct answer is Option 2.

The correct answer is 'Throng'

Key Points

• "Throng" is a word that specifically means a large, densely packed crowd of people or animals.
• Example Sentence: A throng of supporters gathered outside the stadium to cheer for their team. -

Therefore, the correct answer is Option 4.

 Additional Information

• "Flock" generally refers to a group of birds or sometimes, metaphorically, to a group of people, but it doesn't capture the large crowd context.
• "Swarm" typically refers to a large or dense group of flying insects.
• "Pack" usually refers to a group of wild animals like wolves or a small, close-knit group of people, but it doesn't imply the large crowd context that "throng" does.

The correct answer is 'Honorary'

 Key Points

• "Honorary" refers to a title or position given without payment or the usual requirements or functions.
• Example Sentence: He holds an honorary position on the board of directors.

Therefore, the correct answer is Option 1.

Additional Information

• "Lecher" means a lecherous person, one who shows excessive or offensive sexual desire.
• "Pedestrian" can mean ordinary or dull, or it refers to a person walking rather than traveling in a vehicle.
• "Itinerant" refers to traveling from place to place, especially to perform work or duties.

The correct answer is 'Limited'

 Key Points

• Assuming "Absolut" is a typo for "Absolute," it means complete or whole, without limitation or condition.
• "Limited" is the opposite, as it refers to restricted in size, amount, or extent.
• Example Sentence: The absolute power of the ruler was challenged by limited resources.

Therefore, the correct answer is Option 3.

 Additional Information

• "Imperious" means assuming power or authority without justification.
• "Pure" refers to being uncontaminated or wholesome.
• "Classic" refers to being judged over time to be of the highest quality and outstanding of its kind.

The correct answer is 'Paul have brought forth crumbled'

 Key Points

• The error is in the use of "have" with the singular subject "Paul."
• The correct tense should be "had" to match the past perfect tense of the rest of the sentence.
• Correct Sentence: They had laughed when Paul had brought forth crumbled sugar cubes from his coat pocket

Therefore, the correct answer is 'Option 3'.

The correct answer is 'The nurse did gave her'

 Key Points

• The error in the sentence is in the use of the verb "did gave."
• With "did," the verb should be in its base form(V₁).
• "Did" is used for emphasis or to make a negative statement in the past simple tense.
• Correct Sentence: The nurse did give(V1) her an update each day, and it was always the same.

Therefore, the correct answer is 'Option 2'.

The correct answer is 'in'

 Key Points

• The phrase "come in" is used to describe something entering or arriving in a place or situation, such as goods coming into a port.
• Example Sentence: The shipments come in through the port every week, and we have to sort them quickly.
• In this context, "in" refers to goods arriving or being received at the port of Lagos.

Therefore, the correct answer is Option 4.

 Additional Information

• "on" would imply continuing or proceeding, but it doesn't fit the context here.
• "of" is generally used to indicate a point of reckoning or origin, and it doesn't make sense in this sentence.
• "off" typically means departing or being removed, and it also doesn't fit this context.

The correct answer is 'Doppelganger'

 Key Points

• Facsimile refers to an exact copy or reproduction of something. (किसी चीज़ की ठीक प्रतिलिपि या प्रतिरूप।)
• Example Sentence: The museum displayed a facsimile of the original manuscript to prevent wear and tear on the authentic artifact.
• Doppelganger also means a duplicate or a look-alike of someone or something.

Therefore, the correct answer is Option 4.

 Additional Information

• Archetype: An original model or type after which other similar things are patterned. (अन्य समान चीजों के बाद एक मूल मॉडल या प्रकार।)
• Veneer: A thin decorative covering of fine wood applied to coarser wood or other material. (कठिन लकड़ी या अन्य सामग्री के लिए लगाई गई बारीक लकड़ी की सजावटी परत।)
• Façade: The front of a building, or a deceptive appearance. (एक इमारत का सामना, या एक धोखाधड़ी रूप।)

The correct answer is 'Facticity'

 Key Points

• Verity refers to the quality or state of being true or real. (सच या असली होने की गुणवत्ता या स्थिति।)
• Example Sentence: In an era of fake news, verifying the verity of information has become increasingly critical.
• Facticity refers to the quality of being factual or having existence in reality. (वास्तविकता में अस्तित्व रखने या तथ्यात्मक होने की गुणवत्ता।)

Therefore, the correct answer is Option 3.

 Additional Information

• Flimsy: Lacking solidity, strength, or logical basis. (दृढ़ता, शक्ति, या तार्किक आधार की कमी।)
• Fallacy: A mistaken belief, especially one based on unsound arguments. (विशेषकर अतर्कित तर्कों पर आधारित एक गलत विश्वास।)
• Erroneousness: The state of being wrong or incorrect. (गलत या अशुद्ध होने की स्थिति।)

The correct answer is 'To hold the horses'.

Key Points

• The sentence implies that everyone was asked to wait patiently.
• The phrase "To hold the horses" means to be patient or to hold back.
• The situation described in the question involves waiting patiently, so this phrase is the most suitable.
• The police inspection of the crash site is a delicate and time-consuming process, so everyone must wait.

Therefore, the correct answer is Option 1.

 Additional Information

• "To spill the beans" means to reveal secret information.
• "To see eye to eye" means to agree completely.
• "To hit the books" means to study hard.

The correct answer is 'over and run her'.

 Key Points

• The verb "run" should be in the past tense, "ran," to match the tense of the sentence.
• The error occurs in the part "over and run her," where "run" should be replaced with "ran."
• The correct sentence would be: "She turned the box over and ran her hand around the edges."
• This error relates to the tense consistency in the sentence.

Therefore, the correct answer is Option 4.

The correct answer is 'Recharge one's batteries' (Option 3).

 Key Points

• The phrase "Recharge one's batteries" means to rest and regain energy.
• The sentence describes the need to relax and regain energy to continue working.
• This idiomatic expression perfectly encapsulates the sentiment expressed in the sentence.
• The idea of needing to recharge implies that energy has been depleted and needs to be restored.

Therefore, the correct answer is Option 3.

 Additional Information

• "Keep one's chin up" means to stay positive.
• "Get off someone’s back" means to stop criticizing or nagging someone.
• "Drive a hard bargain" means to negotiate shrewdly or forcefully.

The correct answer is 'longer, the' (Option 4).

 Key Points

• The sentence structure used here is a comparative form, often following the pattern: "The [comparative adjective], the [comparative adjective]."
• In this case, the more one works in the company (longer), the harder it becomes to leave.
• Option 4, "longer, the," fits this structure perfectly and makes the sentence grammatically correct.
• The use of "longer" implies a comparison between different durations of time, and "the" emphasizes that an increase in one aspect results in an increase in the other.

Therefore, the correct answer is Option 4.

 Additional Information

• Option 1, "long, the," lacks the comparative form needed in the sentence.
• Option 2, "long, a," has incorrect use of the article "a" and also lacks the comparative form.
• Option 3, "longest, a," misuses the superlative form "longest" and the incorrect article "a."

The correct answer is 'Two' (Option 2).

Key Points

• The passage states that the period of excavation can be divided into two broad phases.
• The first phase is associated with the Hinayana phase of Buddhism, roughly from the 2^nd century BCE to 1^st century CE.
• The later phase occurred between the 5^th and 6^th centuries CE.

Therefore, the correct answer is Option 2.

The correct answer is 'Frail'.

Key Points

• "Potent" means having great power, influence, or effect. It signifies something strong or forceful.
• "Frail" refers to something weak, delicate, or easily broken. It is the opposite of being strong or effective.
• The two words are antonyms, as "potent" describes something with a great ability to produce effects, while "frail" indicates a lack of strength or resilience.
• Understanding the contrast between these words helps in appreciating nuances in language and can enhance communication skills.

Therefore, the correct answer is Option 4.

Additional Information

• "Mighty" is synonymous with "potent" as both words mean having great power or strength.
• "Concentrated" and "Undiluted" might be related to "potent" in certain contexts, such as describing a substance's strength, but they are not opposite in meaning.

The correct answer is 'The earliest caves, belonged to the Vajrayana phase of Buddhism.'.

Key Points

• The passage specifies that the earliest caves belonged to the Hinayana phase of Buddhism, not the Vajrayana phase.
• All other statements are consistent with the information provided in the passage.

Therefore, the correct answer is Option 4.