SSC GD Constable 2026 Official Paper (Held On 20 May, 2026 Shift 1) (Previous Year Paper)

The logic followed for the given series is based on the positional values of the letters in the English alphabet.

Hence, the correct answer is "Option 3".

Logic followed here is:

Hence, the correct answer is "Option 1".

Logic followed here is:

Hence, the correct answer is "Option 2".

The logic followed in this pattern is a series of alphabetical shifts where the first letters of the clusters decrease by 5 and the second letters decrease by 6.

For the set (IS, DM, YG):

For the set (PD, KX, FR):

Applying the same logic to (WM, RG, MA):

Thus, the set (WM, RG, MA) follows the same logic as the given sets.

Hence, the correct answer is 'Option 3'.

Concept:

A month has 5 Fridays if it has enough days such that one of the Fridays falls within the first three days of a 31-day month, the first two days of a 30-day month, or on the first day of a 29-day month. Specifically, in a month with 31 days, if it starts on a Friday, Thursday, or Wednesday, it will contain 5 Fridays.

Calculation:

First, we determine if 1926 is a leap year. Since 1926 is not divisible by 4, it is an ordinary year with 365 days.

Now, let us find the day of the week on January 1, 1926 by calculating the number of odd days:

Odd days until the year 1600 = 0

Odd days from 1601 to 1900 = 1

Odd days from 1901 to 1925 (25 years):

Number of leap years in 25 years = 25 ÷ 4 = 6 leap years

Total odd days in 25 years = 25 (one for each year) + 6 (extra for leap years) = 31 days

31 days ≡ 3 odd days (since 31 ÷ 7 leaves a remainder of 3)

Total odd days until December 31, 1925 = 1 + 3 = 4 odd days.

The 4th odd day corresponds to Thursday. Therefore, January 1, 1926 was a Friday.

January has 31 days. Since it started on a Friday, the Fridays in January 1926 were:

January 1, 8, 15, 22, and 29.

This gives a total of 5 Fridays.

Checking the other options for confirmation:

• February 1926: As an ordinary year, February had 28 days. 28 ÷ 7 = 4 weeks exactly, so it had only 4 Fridays.
• March 1926: Starts on Monday (as February 28 was Sunday). A 31-day month starting on Monday has 4 Fridays (5th, 12th, 19th, 26th).
• May 1926: January (3 odd days), February (0), March (3), April (2). Total odd days from Jan 1 = 8 ≡ 1. Since Jan 1 was Friday, May 1 was Saturday. A 31-day month starting on Saturday has 4 Fridays (7th, 14th, 21st, 28th).

Hence, January is the month that had 5 Fridays.

Alternate Method

Using the day determination formula for January 1, 1926:

Day = (Date + Month Code + Century Code + Year + Leap Year Code) mod 7

• Date = 1
• Month Code (January, ordinary year) = 0
• Century Code (1900s) = 0
• Year = 26
• Leap Year Code (26 ÷ 4) = 6

Total = (1 + 0 + 0 + 26 + 6) = 33

33 ÷ 7 = 4 weeks and a remainder of 5.

In the day code system (0=Sun, 1=Mon, 2=Tue, 3=Wed, 4=Thu, 5=Fri, 6=Sat), the remainder 5 represents Friday.

Since January 1 is a Friday and the month has 31 days, it contains 5 Fridays.

Hence, the correct answer is January.

Logic followed here is.

Logic: The relationship between the figures is based on the interchange of positions between the outer shape and the inner shape while their relative properties remain constant.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: The relationship between the figures is based on a 90° clockwise rotation of the entire figure.

For the first pair:

The first figure is rotated 90° clockwise to obtain the second figure. During this rotation, all the internal elements and the main structure shift their positions by one quadrant in the clockwise direction.

For the second pair:

To find the missing figure, we must apply the same logic of 90° clockwise rotation to the third figure.

Hence, the correct answer is "Option 1".

Given:

MO44 : PR91 →

UZ28 : XC75 →

Similarly, for ? : FI68:

The cluster is CF21.

Hence, the correct answer is 'Option 2'.

To understand the pattern among related groups, we will analyze each letter-number cluster.

Analyzing pattern:

1. First Cluster (TUE150 : LZW370):

2. Third Cluster (RAC340 : JFU560):

3. Second Cluster (KJR230 : ?):

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: First Number = Second Number − 53

For the first pair 1382 : 1435

⇒ 1435 − 53 = 1382

Applying the same logic to the third pair 1354 : 1407

⇒ 1407 − 53 = 1354

Applying the same logic to the second pair ? : 4398

⇒ 4398 − 53 = 4345

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Logic: Second Number = (First Number × 4) + 9

For the first pair 658 : 2641

⇒ (658 × 4) + 9

⇒ 2632 + 9 = 2641.

For the third pair 859 : 3445

⇒ (859 × 4) + 9

⇒ 3436 + 9 = 3445.

Applying the same logic to the second pair

644 : ?

⇒ (644 × 4) + 9

⇒ 2576 + 9 = 2585.

Hence, the correct answer is 'Option 3'.

The logic followed here is the elimination method, where we compare the given sentences to find common words and their corresponding codes.

For the given codes:

'please be careful' is coded as 'ta ra sa'

'careful are you on time' is coded as 'pa ma ba sa na'

'may be next time' is coded as 'ma la ta ka'

Hence, the correct answer is "Option 4".

The logic followed in this series involves analyzing the first letters, second letters, and numbers of each term separately.

In the given series, the fourth term is PW420. However, according to the logic, the number should be 416.

Therefore, the wrong term in the series is PW420.

Hence, the correct answer is "Option 2".

Logic followed here is:

The series consists of two patterns: one for letters and one for numbers.

Hence, the correct answer is "Option 1".

Concept:

Hour hand covers 3600 in 12 hours

Angular distance covered in 1 hour = 360/12 = 300

Angular distance covered in 60 minutes = 300

Angular distance covered in 1 minute = 1/20

Calculation:

Minute hand covers 360 in 60 minutes

1 minute = 360/60 ⇒ 1 minute = 60

The time is between 5 AM and 6 AM. Let the required time be 5 hours and M minutes.

Angle covered by the minute hand in M minutes = M × 60 = 6M0

Angle covered by the hour hand in 5 hours and M minutes = 5 × 30 + M × ½ = 150 + M/2

According to the question, the angle between the hands is 135 degrees.

|(150 + M/2) − 6M| = 135

|150 − 5.5M| = 135

Case 1:

150 − 5.5M = 135

5.5M = 15

M = 15/5.5 = 150/55 = 30/11 ≈ 2.727 minutes

Rounding to the nearest minute, M ≈ 3.

Case 2:

150 − 5.5M = −135

5.5M = 150 + 135 = 285

M = 285/5.5 = 2850/55 = 570/11 ≈ 51.818 minutes

Rounding to the nearest minute, M ≈ 52.

Comparing with the given options, the approximate time is 5:03.

Hence, the angle between the hour and minute hands is 135 degrees at 5:03.

Alternate Method

The angle between the hour hand and minute hand = $|60H - 11M| \over 2$

Here, H = 5 and Angle = 135.

135 = $|60 \times 5 - 11 \times M| \over 2$

270 = |300 − 11M|

300 − 11M = 270   OR   300 − 11M = −270

11M = 30   OR   11M = 570

M = 30/11 ≈ 2.72   OR   M = 570/11 ≈ 51.81

The approximate value from the options is M = 3.

Therefore, the time is 5:03.

Hence, the correct answer is 5:03.

Concept:

The hour hand covers 360° in 12 hours.

Angular distance covered by the hour hand in 1 hour = 360/12 = 30°

Angular distance covered by the hour hand in 1 minute = 30/60 = 1/2° per minute.

The minute hand covers 360° in 60 minutes.

Angular distance covered by the minute hand in 1 minute = 360/60 = 6° per minute.

When the hour and minute hands overlap, the angle between them is 0°.

Calculation:

The time is between 8 AM and 9 AM, so H = 8.

Let the hands overlap at M minutes past 8.

Angle covered by the hour hand from 12 o'clock = 8 × 30 + M × 1/2 = 240 + M/2

Angle covered by the minute hand from 12 o'clock = M × 6 = 6M

Since the hands overlap, these angles must be equal:

6M = 240 + M/2

6M − M/2 = 240

11M/2 = 240

11M = 480

M = 480/11 = 43.6363...

Rounding to the nearest whole number, M ≈ 44 minutes.

Therefore, the hands will overlap at approximately 8:44 AM.

Alternate Method

The formula for the angle between the hands is: Angle = |30H − (11/2)M|

For the hands to overlap, Angle = 0.

0 = |30 × 8 − (11/2)M|

0 = 240 − 5.5M

5.5M = 240

M = 240/5.5 = 480/11

M = 43.6363... minutes ≈ 44 minutes.

Hence, the correct answer is 8:44.

**The logic followed here is:**The objects inside the box flip one by one in the next box, moving anti‑clockwise from the upper‑left corner

Hence, Option 4 is the correct answer.

The logic followed here is given below in the image:

Hence, "Option 3" is the correct answer.

The logic followed in this series: Shape is changing and the direction of the circle is shifting in clockwise direction and the number of circles are also increasing by +1.

Hence, the correct answer is "Option 4".

Given:

Present age ratio = 10 : 13

Difference in ages = 9 years

Calculation:

Difference in ratio = 13 − 10 = 3 parts

3 parts = 9 years

1 part = 9 ÷ 3 = 3 years

Present ages:

10 × 3 = 30 years

13 × 3 = 39 years

6 years ago:

30 − 6 = 24 years

39 − 6 = 33 years

Required ratio = 24 : 33 = 8 : 11

Hence, the correct answer is "Option 3".

The correct answer is Zoji La.

Key Points

• Zoji La is a high-altitude mountain pass located in the Himalayan Range within the Union Territory of Ladakh, India.
• It serves as the vital geographical link between the Kashmir Valley (specifically near Sonamarg) and the Ladakh region, providing access to Drass, Kargil, and Leh.
• The pass is situated at an approximate elevation of 3,528 meters (11,575 feet) above sea level, making it one of the most dangerous and strategically important passes in the world.
• It is a critical component of National Highway 1 (NH 1), which facilitates the movement of supplies and military personnel between Srinagar and Leh.
• Due to extreme weather conditions and heavy snowfall, the pass remains closed for nearly six months every year, leading to the development of the Zojila Tunnel to provide year-round connectivity.

 Additional Information

• Nathu La:
• Located in the East Sikkim district of the Indian state of Sikkim.
• It connects India with the Tibet Autonomous Region of China and was a major artery of the ancient Silk Road.
• Rohtang Pass:
• Situated in the Pir Panjal Range of the Himalayas in Himachal Pradesh.
• It connects the Kullu Valley with the high-altitude Lahaul and Spiti Valleys.
• Shipki La:
• Located in the Kinnaur district of Himachal Pradesh on the Indo-China border.
• It is the point where the Sutlej River enters India from Tibet.

The correct answer is Minimize the cascading effect of indirect taxation.

Key Points

• The primary objective of introducing Value Added Tax (VAT) was to eliminate the cascading effect of taxes, which refers to the taxation of a product at every stage of the supply chain without credits for taxes paid at previous stages, leading to tax on tax.
• VAT is a multi-point destination-based tax system where tax is levied only on the value addition made at each stage of production and distribution, ensuring that the tax burden is not cumulative.
• The mechanism of Input Tax Credit (ITC) was the backbone of VAT, allowing manufacturers and retailers to set off the tax they paid on purchases against the tax they collected on sales.
• By streamlining the indirect tax structure, VAT aimed to increase tax transparency, improve compliance, and reduce the final price of goods for consumers by removing hidden tax components.
• The transition to VAT was a significant fiscal reform recommended by the Empowered Committee of State Finance Ministers to replace the fragmented and inefficient state-level Sales Tax regimes.

 Additional Information

• Historical Context:
• Haryana was the first Indian state to implement VAT in 2003, while the majority of other states and union territories adopted it on April 1, 2005.
• The design of the VAT system in India was heavily influenced by the reports of the Asim Dasgupta Committee.
• Clarification of Terms:
• Direct Taxes: VAT is an indirect tax; it did not replace direct taxes like Income Tax or Corporate Tax, which are governed by separate central legislations.
• Fiscal Deficit: Governments utilize VAT to broaden the tax base and improve revenue collection efficiency to reduce fiscal deficits, not increase them.
• Tariffs: These are customs duties applied to international trade at borders, whereas VAT specifically targeted the internal consumption of goods within state boundaries.
• Evolution: The success and limitations of the VAT regime eventually paved the way for the Goods and Services Tax (GST), which was implemented on July 1, 2017, to further integrate the national market.

The correct answer is Harshavardhana's court.

Key Points

• Xuanzang, a prominent Chinese Buddhist monk and traveler, visited India during the 7th Century CE (specifically between 629–645 CE) during the reign of King Harshavardhana.
• His famous travelogue, Si-Yu-Ki (Record of the Western World), provides a comprehensive eye-witness account of the political, social, and economic conditions of the Vardhana Empire.
• He spent several years at Harshavardhana's court and at Nalanda University, where he studied under the guidance of the monk Shilabhadra, documenting the high standards of education and religious debates of that era.
• The monk vividly describes the Kannauj Assembly and the Prayag Assembly, highlighting Harsha's religious tolerance and his massive patronage of Mahayana Buddhism and public welfare.
• Xuanzang’s records are essential for understanding the transition from the ancient to the early medieval period in India, particularly regarding the administration and the city of Kannauj, which served as the imperial capital.

 Additional Information

• Comparison with other historical periods mentioned in the options:
• Harappan towns: This Indus Valley Civilization flourished during the Bronze Age (c. 3300–1300 BCE); knowledge of this period is based entirely on archaeological excavations at sites like Mohenjo-daro and Harappa.
• Mauryan polity: This era (c. 322–185 BCE) is primarily studied through Kautilya’s Arthashastra, the Indica by the Greek ambassador Megasthenes, and the Edicts of Ashoka.
• Chola naval expeditions: These were prominent during the 10th and 11th Centuries CE under rulers like Rajaraja I and Rajendra Chola I; they are documented in Tamil inscriptions and copper plates, long after Xuanzang's return to China.

The correct answer is Poverty alleviation ('Garibi Hatao').

Key Points

• The Fifth Five-Year Plan was implemented during the period 1974-1978. Although it was originally planned until 1979, it was terminated a year early by the Janata Party government led by Morarji Desai.
• The twin objectives of the plan were the removal of poverty (Garibi Hatao) and the attainment of self-reliance.
• The slogan Garibi Hatao was popularized by Indira Gandhi during the 1971 General Election campaign and became the ideological foundation for the Fifth Plan.
• A landmark initiative of this plan was the Minimum Needs Programme (MNP), launched in 1974, which focused on basic essentials such as rural health, water supply, nutrition, and elementary education.
• The plan targeted an annual growth rate of 4.4% and successfully achieved an actual growth rate of 4.8%, despite the global economic stress caused by the 1973 oil crisis.
• The plan also emphasized the Twenty Point Programme launched in 1975, which aimed at improving the living standards of the poor and marginalized sections of society.

Additional Information

• Heavy Industry:
• Prioritized during the Second Five-Year Plan (1956-1961), which was based on the Mahalanobis Model and led to the establishment of major steel plants in Bhilai, Durgapur, and Rourkela.
• Banking Reforms:
• Significant shifts like the nationalization of 14 major commercial banks took place in 1969 under the Fourth Five-Year Plan to ensure credit flow to the priority sector like agriculture.
• Export-led growth:
• This strategy became a central focus of the Indian economy after the 1991 New Economic Policy, specifically during the Eighth Five-Year Plan, emphasizing globalization and liberalization.

The correct answer is Agricultural sector.

Key Points

• Disguised unemployment is a scenario where more people are working in a specific task than what is technically required, a situation most prevalent in the Agricultural sector of developing countries like India.
• The defining economic indicator of this condition is that the marginal physical productivity of labor is zero or near-zero, meaning that the total agricultural output remains unchanged even if the surplus labor is withdrawn.
• In rural economies, this occurs largely due to the fragmentation of landholdings and a lack of alternative non-farm employment opportunities, forcing family members to work on the same small plot of land.
• Statistical data from India indicates that while agriculture employs nearly 44-45 percent of the workforce, its contribution to the Gross Domestic Product (GDP) remains around 16-19 percent, signifying high levels of hidden underemployment.
• Economists such as Arthur Lewis and Ragnar Nurkse highlighted that this surplus labor could be shifted to the Industrial sector to foster economic development and capital formation.

 Additional Information

• IT and Service Sectors:
• These sectors are characterized by performance-based metrics and high capital costs per employee, which generally prevents disguised unemployment.
• They are more likely to experience Structural Unemployment, where a gap exists between the technical skills of candidates and the specific industry requirements.
• Industrial Sector:
• Employment in factories and manufacturing units is usually governed by fixed capital-to-labor ratios, making it difficult to sustain surplus labor without incurring direct financial losses.
• This sector often faces Cyclical Unemployment, which fluctuates based on the economic business cycles and demand for manufactured goods.
• Seasonal Unemployment:
• Closely related to agriculture, this occurs when laborers find work only during peak seasons such as sowing or harvesting, remaining idle during the off-season.

The correct answer is Trade with India, except tea and China trade.

Key Points

• The Charter Act of 1813, also known as the East India Company Act 1813, was enacted by the British Parliament to renew the East India Company's (EIC) charter for another 20 years.
• A landmark provision of this Act was the abolition of the trade monopoly of the Company in India, effectively opening Indian trade to all British merchants and private traders.
• Despite the liberalization of general trade, the East India Company retained its exclusive monopoly over the tea trade and all commercial trade with China.
• The shift toward Free Trade was largely influenced by the Napoleonic Wars and the Continental System, which restricted British access to European markets and forced the search for new economic avenues in Asia.
• The Act was significant for formally asserting the sovereignty of the British Crown over the territories held by the Company in India.

 Additional Information

• Educational and Religious Impact:
• The Act authorized Christian Missionaries to travel to India for the purpose of religious proselytization and moral improvement of the native population.
• It mandated the Company to set aside a sum of 1 lakh rupees annually for the promotion of education, literature, and the knowledge of sciences among the inhabitants of British India.
• Transition to 1833:
• The Charter Act of 1833 later removed the remaining monopolies on tea and trade with China, transforming the East India Company into a purely administrative and political body.
• It also led to the centralization of administration, making the Governor-General of Bengal the Governor-General of India.
• Commercial Accountability:
• The 1813 Act required the Company to maintain separate accounts for its commercial transactions and its territorial revenues to ensure better financial transparency for the British Parliament.

The correct answer is Tripura.

Key Points

• The Mukhyamantri Balika Samridhi Yojana is a significant welfare initiative launched by the Government of Tripura in 2025 aimed at the socio-economic empowerment of the girl child.
• The scheme is designed to provide financial security to girls belonging to households classified under the Below Poverty Line (BPL) category, ensuring they have access to better healthcare and education.
• A primary goal of the scheme is the eradication of child marriage; therefore, the disbursement of the financial corpus is strictly contingent upon the girl remaining unmarried until she reaches the age of 18 years.
• It focuses on improving the Gross Enrolment Ratio (GER) for girls by providing staggered financial incentives at various educational milestones, thereby reducing the dropout rate in secondary education.
• By incentivizing the birth of a girl child, the Tripura government aims to positively influence the Child Sex Ratio and address gender-based discrimination in the state.

 Additional Information

• Departmental Role and Implementation:
• The Department of Social Welfare and Social Education serves as the nodal agency for the execution and regular monitoring of the Mukhyamantri Balika Samridhi Yojana.
• Transparency in the scheme is maintained through the Direct Benefit Transfer (DBT) mechanism, where funds are credited directly to the bank accounts of the eligible beneficiaries.
• Strategic Alignment:
• The initiative aligns with the national Beti Bachao Beti Padhao campaign, reinforcing the pillars of survival, protection, and education for girls across North-East India.
• It contributes significantly toward achieving Sustainable Development Goal 5 (SDG 5), which focuses on gender equality, and SDG 4, which emphasizes quality education for all.
• The scheme complements other financial instruments like the Sukanya Samriddhi Yojana, providing a robust safety net for young women in Tripura.

The correct answer is Only I.

Key Points

• The Promotion and Regulation of Online Gaming Bill, discussed in the Lok Sabha, seeks to establish a formal framework to categorize and govern the rapidly expanding digital gaming sector in India. It prioritizes the growth of the Animation, Visual Effects, Gaming, and Comics (AVGC) sector as a key driver of the digital economy.
• Statement I is accurate as the bill specifically emphasizes the promotion of e-sports and online social games. By recognizing e-sports as a professional competitive field, the bill facilitates infrastructure development, international participation, and talent scouting within a structured environment. Hence, statement I is correct.
• Online social games, which do not involve any real-money wagering, are encouraged to promote indigenous culture and educational content through gaming, aligning with the Digital India mission. Hence, statement I is correct.
• Statement II is inaccurate because the bill is designed to regulate and restrict, rather than encourage, online money gaming. The legislation introduces a strict distinction between games of skill and games of chance, imposing rigorous KYC (Know Your Customer) requirements and financial audits to prevent money laundering and illegal betting.
• The regulatory framework for money gaming focuses on consumer protection and mitigating gaming addiction. It mandates the appointment of a Grievance Redressal Officer and a Chief Compliance Officer for platforms offering monetary stakes, ensuring they operate under tight surveillance rather than broad encouragement. Hence, statement II is incorrect.

 Additional Information

• E-sports vs. Online Money Gaming:
• E-sports: These are skill-based, organized competitions often played at professional levels. The bill aims to provide these athletes with the same status as traditional sports players to enhance India's presence in global gaming tournaments like the Asian Games.
• Online Money Gaming: This involves staking money on an outcome. The bill subjects these services to high taxation slabs (e.g., 28 percent GST on the entry fee) and Self-Regulatory Bodies (SRBs) to ensure they do not facilitate unorganized gambling.
• Nodal Ministry: The Ministry of Electronics and Information Technology (MeitY) is the designated authority responsible for drafting the rules and overseeing the compliance of Intermediary Guidelines for all online gaming platforms.

The correct answer is Madhya Pradesh.

Key Points

• The Matki dance is a traditional folk dance primarily performed in the Malwa region of Madhya Pradesh.
• This dance form is performed by women on various special occasions such as weddings, festivals, and to celebrate the birth of a child.
• The name of the dance is derived from the matki (earthen pot), which the dancers balance on their heads while performing intricate footwork and circular movements.
• It usually begins with a solo performance by a woman known as the Jhela, who is then joined by other dancers following her rhythm and lead.
• The performance is characterized by the use of the Dhol, a double-headed drum that provides the primary rhythmic beat for the dancers to maintain their balance and pace.
• The dancers wear traditional attire like the lehenga or sari, often embellished with ornaments that shimmer during the performance.

 Additional Information

• Andhra Pradesh:
• Home to the classical dance Kuchipudi and folk forms such as Lambadi, Dhimsa, and Veeranatyam.
• Lakshadweep:
• Known for the Lava dance, a popular folk form performed by the people of Minicoy Island, and other dances like Kolkali and Parichakali.
• West Bengal:
• Famous for the Chhau dance (specifically the Purulia style), Gambhira, and the Brita dance, which is a traditional devotional form.

The correct answer is Masali.

Key Points

• Masali village, situated in the Jaisalmer district of Rajasthan, achieved the historic milestone of being declared India's first Border Solar Village in December 2024.
• The village is located in close proximity to the India-Pakistan international border, making its transition to renewable energy a significant achievement for national security and rural development.
• This initiative involved the installation of comprehensive Solar Photovoltaic (PV) systems, including solar rooftops for every household and solar-powered street lighting, ensuring 24/7 electricity supply in a historically power-deficit region.
• The project aims to reduce the carbon footprint of border settlements and align with the Government of India's vision of Atmanirbhar Bharat (Self-reliant India) by making remote areas energy independent.
• By providing reliable power, the government seeks to improve telecommunication, education, and healthcare services, thereby preventing migration from strategic border areas.

 Additional Information

• Mana:
• Located in the Chamoli district of Uttarakhand, it was formerly known as the last village of India but is now officially recognized as the First Indian Village at the India-China border.
• Mawlynnong:
• Situated in the East Khasi Hills of Meghalaya, this village is world-renowned for being Asia's cleanest village and is a model for sustainable community tourism.
• Khonoma:
• Located in Nagaland, it is distinguished as India's first green village, famous for its Angami tribe's efforts in forest conservation and the ban on hunting and logging since the late 1990s.
• Vibrant Villages Programme:
• A centrally sponsored scheme launched to develop infrastructure and provide livelihood opportunities in villages along India's Northern Border, promoting border security through socio-economic development.

The correct answer is 4 days.

Key Points

• Pongal is a significant harvest festival celebrated by the Tamil community, primarily in the Indian state of Tamil Nadu and the Union Territory of Puducherry.
• The festival is observed to thank the Sun God (Surya) and nature for a bountiful harvest, marking the end of the winter solstice and the start of the sun's six-month-long journey northwards (Uttarayanam).
• It traditionally takes place over four consecutive days during the start of the Tamil month of Thai, which usually falls between January 14 and January 17 every year.
• The four days of the festival are sequentially known as Bhogi Pongal, Surya Pongal, Mattu Pongal, and Kaanum Pongal, each involving distinct cultural and religious rituals.
• The term Pongal in Tamil translates to boiling over or spilling over, signifying the overflowing of prosperity and abundance.

 Additional Information

• The four-day celebration details:
• Day 1: Bhogi Pongal − People clean their homes and discard old belongings into a bonfire, symbolizing the removal of old habits and the embrace of new beginnings. It is dedicated to Lord Indra, the god of rain.
• Day 2: Surya Pongal − This is the main festival day where freshly harvested rice is boiled with milk and jaggery in a clay pot. When the mixture boils over, people shout Pongalo Pongal.
• Day 3: Mattu Pongal − Dedicated to cattle, especially bulls and cows that help farmers in the fields. Cattle are bathed, their horns are painted, and they are adorned with garlands. The traditional sport of Jallikattu often takes place on this day.
• Day 4: Kaanum Pongal − A day for socializing and family reunions. People visit relatives, parks, and beaches. The Kaka Pidi Kanu Pidi ritual is performed by women for the well-being of their brothers.

The correct answer is Bihar.

Key Points

• According to the Census of India 2011, Bihar emerged as the most densely populated state in the country, recording a density of 1,102 persons per square km (officially finalized as 1,106 in detailed reports).
• This figure represents a significant rise from the 2001 Census, where the density was 881 persons per square km, reflecting a decadal growth rate of approximately 25.4%.
• Population density is a critical demographic indicator calculated as the number of persons residing per unit of land area, typically per square kilometer.
• The high density in Bihar is attributed to its fertile Gangetic plains, which support intensive agriculture and a large rural population, alongside limited geographic area compared to its total population of over 104 million.
• By surpassing West Bengal (which was the most dense state in 2001), Bihar set a new record for state-level population concentration in the 2011 survey.

 Additional Information

• Kerala:
• Recorded a population density of 860 persons per square km in the 2011 Census.
• It holds the highest literacy rate (94%) and the highest sex ratio (1084 females per 1000 males) among all Indian states.
• Haryana:
• The population density was 573 persons per square km as per the 2011 data.
• Despite its economic development, it was noted for having one of the lowest child sex ratios (834) during the same census period.
• Nagaland:
• Exhibited a relatively low population density of 119 persons per square km.
• It was the only state in India to record a negative decadal growth rate of −0.58% between 2001 and 2011.
• India (National Average):
• The overall population density of India increased from 324 in 2001 to 382 persons per square km in 2011.

The correct answer is 273.15.

Key Points

• The melting point is the temperature at which a substance changes its state from solid to liquid at standard atmospheric pressure.
• On the Celsius scale, the melting point of pure ice is defined as 0°C under a standard pressure of 1 atmosphere (1 atm).
• The Kelvin scale is the SI unit of temperature, and the conversion between Celsius and Kelvin is given by the formula: T(K) = t(°C) + 273.15.
• By applying this relationship, the melting point of ice in Kelvin is calculated as 0 + 273.15 = 273.15 K.
• Unlike the Celsius or Fahrenheit scales, the Kelvin scale is an absolute scale and does not use the degree symbol.

 Additional Information

• 373.15:
• This value represents the boiling point of water on the Kelvin scale.
• It corresponds to 100°C on the Celsius scale (100 + 273.15 = 373.15 K).
• 0:
• On the Kelvin scale, 0 K is known as Absolute Zero, the temperature at which all thermal motion of particles ceases.
• In Celsius, Absolute Zero is equivalent to −273.15°C.
• 100:
• This is the numerical value for the boiling point of water in degrees Celsius.
• It marks the transition from the liquid phase to the gaseous phase at sea level.
• Triple Point of Water:
• Water can coexist in all three states (solid, liquid, and gas) at a specific temperature of 273.16 K (0.01°C) and a partial vapor pressure of 611.657 Pascals.

The correct answer is Both I and II.

Key Points

• Goa is one of the leading producers of Iron ore in India, with massive deposits found primarily in the Bicholim, Sanguem, Satari, Ponda, and Quepem talukas. The ores are mostly of the Hematite variety, characterized by high-grade quality suitable for export. Hence, statement II is correct.
• The state is also significantly rich in Manganese ores, which are typically found in close geographical association with iron ore deposits, especially in the Southern parts of Goa like Sanguem and Quepem. These ores occur as Pyrolusite and Psilomelane. Hence, statement I is correct.
• The mining sector in Goa is a backbone of the state economy, largely driven by the extraction of these two minerals from the Dharwar Supergroup of rocks, which date back to the Archaean and Proterozoic eras.
• The presence of the Mormugao Port, a natural harbor, has historically facilitated the large-scale export of these minerals to international markets, including Japan, China, and several European nations.

 Additional Information

• Mineral Wealth of Goa:
• Bauxite: Besides iron and manganese, Goa possesses substantial reserves of Bauxite, particularly in the Canacona and Quepem regions, which is a primary raw material for Aluminum production.
• Silica Sand: High-quality Silica Sand is found in the coastal tracts of South Goa, used extensively in the Glass and Foundry industries.
• Mining Regulation: Mineral extraction in the state is governed under the Mines and Minerals (Development and Regulation) Act, 1957, and is subject to strict environmental regulations due to the state's proximity to the Western Ghats.
• Limestone and Clay: Minor minerals such as Limestone, Basalt, and Clay are also extracted for local construction and industrial purposes.

The correct answer is 2014.

Key Points

• The Pro Kabaddi League (PKL) was launched in 2014, marking a significant milestone in the professionalization of the traditional Indian sport of Kabaddi.
• The league was established by Mashal Sports, a company co-founded by Charu Sharma and Anand Mahindra, and is currently managed by Star India.
• The first season commenced on July 26, 2014, featuring eight teams representing different Indian cities: Bengaluru, Delhi, Jaipur, Kolkata, Mumbai, Patna, Pune, and Vizag.
• The concept was influenced by the successful execution of the Indian Premier League (IPL) and the high viewership of Kabaddi during the 2006 Asian Games.
• The league implemented a caravan format, which ensured that the matches were hosted in each of the home cities of the participating franchises.

 Additional Information

• Inaugural Season Results:
• The Jaipur Pink Panthers, owned by Abhishek Bachchan, became the first-ever champions of the league by defeating U Mumba in the final.
• The tournament gained massive popularity, becoming the second most-watched sports league in India after cricket.
• Growth and Expansion:
• While the league started with 8 teams, it expanded to 12 teams in 2017 with the addition of franchises from Gujarat, Haryana, Tamil Nadu, and Uttar Pradesh.
• Key innovations introduced in the league include the Do-or-Die Raid (a mandatory point-scoring raid after two empty raids) and the Super Tackle (earning two points if three or fewer defenders tackle a raider).
• Prominent players such as Pardeep Narwal, known as the Record Breaker, and Anup Kumar became household names due to the league's success.

The correct answer is 2010.

Key Points

• The 11th edition of the South Asian Games, which was historically known as the South Asian Federation Games, was hosted in Dhaka, Bangladesh, in 2010.
• The multi-sport event took place from January 29 to February 8, 2010, marking the third time Dhaka served as the host city (previously in 1985 and 1993).
• The official name of the competition was changed from the South Asian Federation Games to the South Asian Games in 2004, though the older terminology is still frequently used in various contexts.
• A total of eight nations participated in the 2010 games, including Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, and Sri Lanka.
• The Bangabandhu National Stadium in Dhaka was the primary venue for the opening and closing ceremonies, hosting thousands of athletes competing across 23 different sports.

 Additional Information

• Overview of the South Asian Games (SAG):
• The games are a biennial multi-sport event held among the athletes from South Asia, governed by the South Asian Olympic Council (SAOC).
• The first edition of the games was held in Kathmandu, Nepal, in 1984.
• The objective of these games is to promote regional harmony and sporting excellence among the member nations of the South Asian Association for Regional Cooperation (SAARC) region.
• Highlights of the 2010 Dhaka Games:
• India maintained its dominance by topping the medal table with 90 gold, 55 silver, and 30 bronze medals.
• The host nation, Bangladesh, achieved its most successful performance in the history of the games at that time, securing the third position with 18 gold medals.
• The official mascot of the 2010 South Asian Games was Kutumb, a representation of the Magpie Robin (Doyel), which is the national bird of Bangladesh.

The correct answer is Dead ball.

Key Points

• The signal for a Dead ball in cricket is performed by the on-field umpire by crossing and uncrossing their hands or wrists in front of their body, typically at the waist or thigh level.
• According to Law 20 of the official Laws of Cricket maintained by the Marylebone Cricket Club (MCC), a ball is naturally dead when it is finally settled in the hands of the wicket-keeper or the bowler.
• The umpire intervenes to call and signal a Dead ball in specific scenarios, such as when a batsman or bowler is distracted, or if a serious injury occurs to a player or an official on the field.
• It is also signaled if the striker is not ready for the delivery and does not attempt to play, or if the ball becomes trapped in the batsman’s clothing or protective equipment after hitting them.
• Once the Dead ball signal is made, the ball ceases to be in play, meaning no further runs can be scored and no wickets can be taken until the next delivery becomes live.

 Additional Information

• Leg bye:
• The umpire signals this by touching a raised knee with their hand. It indicates that runs were completed after the ball struck the striker’s person without touching the bat or the hand holding it.
• Short run:
• This is signaled by the umpire bending one arm upwards and touching the shoulder with the fingertips. It occurs when a batsman fails to ground their bat behind the popping crease while running.
• Four:
• A Boundary Four is signaled by waving the arm from side to side in a horizontal motion across the chest. This confirms that the ball reached the boundary after touching the ground at least once.

Therefore, the Dead ball is the correct answer.

The correct answer is UNCLOS.

Key Points

• The Biodiversity Beyond National Jurisdiction (BBNJ) agreement, commonly referred to as the High Seas Treaty, is an international legally binding instrument established under the framework of the United Nations Convention on the Law of the Sea (UNCLOS).
• Its primary objective is the conservation and sustainable use of marine biological diversity in areas that lie beyond the Exclusive Economic Zones (EEZ) and continental shelves of coastal states, which encompass approximately 64 percent of the ocean surface.
• The treaty was officially adopted on June 19, 2023, after nearly 20 years of discussions and negotiations to address legal gaps in global ocean governance.
• It operates on four key pillars: the sharing of benefits from Marine Genetic Resources (MGRs); the use of Area-Based Management Tools (ABMTs), including Marine Protected Areas (MPAs); the conduct of Environmental Impact Assessments (EIAs) for deep-sea activities; and Capacity Building and the Transfer of Marine Technology (CBTMT) to assist developing nations.
• The BBNJ is considered the third implementing agreement under UNCLOS, following the 1994 Part XI Agreement and the 1995 Fish Stocks Agreement.

 Additional Information

• UNCLOS (United Nations Convention on the Law of the Sea):
• Adopted in 1982 and effective from 1994, it is often called the Constitution of the Oceans.
• It defines the legal status of various maritime zones, including Territorial Seas (up to 12 nautical miles) and EEZs (up to 200 nautical miles).
• UNESCO (United Nations Educational, Scientific and Cultural Organization):
• While it hosts the Intergovernmental Oceanographic Commission (IOC), which provides scientific data for the BBNJ, it is not the governing body for this specific treaty.
• WTO (World Trade Organization):
• An organization focused on global trade rules and dispute resolution; it does not possess jurisdiction over maritime biological conservation.

The correct answer is 13.

Key Points

• The International IP Index 2025 represents the 13th edition of the annual report produced by the U.S. Chamber of Commerce Global Innovation Policy Center (GIPC).
• The index serves as a comprehensive roadmap for nations seeking to improve their intellectual property (IP) frameworks to drive economic growth, innovation, and technological advancement.
• It evaluates the IP climate of the world leading economies using a set of 50 unique indicators that span across several critical categories of protection.
• Since its inception in 2012, the index has become a primary benchmark for investors and policymakers to assess the legal certainty and market environment for creative and innovative industries.

 Additional Information

• Evaluation Framework:
• The index benchmarks economies across nine distinct categories, including Patents, Copyrights, Trademarks, Design Rights, and Trade Secrets.
• It also scrutinizes the Commercialization of IP Assets, Enforcement mechanisms, Systemic Efficiency, and the ratification of International Treaties.
• Global Coverage:
• The previous 12th edition (released in 2024) analyzed 55 global economies, which collectively account for over 90% of the world Gross Domestic Product (GDP).
• The report highlights how robust IP standards correlate with higher levels of Foreign Direct Investment (FDI) and increased Research and Development (R&D) activities.
• In the Indian context, the Department for Promotion of Industry and Internal Trade (DPIIT) under the Ministry of Commerce and Industry monitors such indices to align domestic policies with global best practices.

The correct answer is 22nd.

Key Points

• In the World Bank Logistics Performance Index (LPI) 2023, India achieved a significant milestone by jumping to the 22nd rank in the International Shipments category.
• This specific rank marks a massive improvement of 22 spots compared to the 2018 LPI report, where India was positioned at 44th in the same category.
• The International Shipments indicator measures the ease of arranging competitively priced shipments, a factor crucial for export-led growth and global trade integration.
• This progress is largely attributed to the government's focus on logistics efficiency through the PM Gati Shakti National Master Plan and the National Logistics Policy (2022).
• India's rank in Logistics Competence and Quality also saw an upward trajectory, reaching the 38th position in 2023 compared to 42nd in 2018.

 Additional Information

• Logistics Performance Index (LPI) 2023:
• The 2023 report, titled Connecting to Compete, is the 7th edition and assesses 139 countries.
• India's overall rank in the LPI 2023 is 38th, an improvement from 44th in 2018 and 54th in 2014.
• The LPI is based on six core components: Customs, Infrastructure, International Shipments, Logistics Competence, Tracking and Tracing, and Timeliness.
• In Infrastructure, India climbed from 52nd in 2018 to 47th in 2023 due to investments in port modernization and dedicated freight corridors.
• India ranked 35th for Timeliness and 38th for Tracking and Tracing, reflecting advancements in digitalization and supply chain visibility.
• The report noted that technology-driven initiatives like the Unified Logistics Interface Platform (ULIP) have been instrumental in reducing delays.

Shortcut Trick

Apply Unit Digit method for faster calculation.

Unit digit expression: 9 + 5 − 1 + (6 + 8) × 2 − 7

⇒ 9 + 5 − 1 + (4 × 2) − 7 = 9 + 5 − 1 + 8 − 7 = 14

The unit digit of the result must be 4. Only 114 fits this criteria.

∴ The correct answer is 114.

Alternate Method

Given: 79 + 65 − 41 + (36 + 18) × 2 − 97

Method Used: BODMAS Rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction)

⇒ 79 + 65 − 41 + 54 × 2 − 97

⇒ 79 + 65 − 41 + 108 − 97

⇒ (79 + 65 + 108) − (41 + 97)

⇒ 252 − 138

⇒ 114

∴ The correct answer is 114.

Additional Information

BODMAS Rule

It dictates the sequence: Brackets, Orders (indices/roots), Division, Multiplication, Addition, and Subtraction.

Associativity Rule

For operations of equal priority (like addition and subtraction), calculations are performed from left to right.

Sign Convention

Remember that (+) × (+) = (+), (−) × (−) = (+), and (+) × (−) = (−).

Shortcut Trick

Follow the BODMAS rule: 88 + 33 − 26 + 14 of 2 + (42 ÷ 6) − 19

Solve Bracket and Of: 88 + 33 − 26 + 28 + 7 − 19

Combine positive terms: 88 + 33 + 28 + 7 = 156

Combine negative terms: −26 − 19 = −45

Result: 156 − 45 = 111

∴ The correct answer is 111.

Alternate Method

Given: 88 + 33 − 26 + 14 of 2 + (42 ÷ 6) − 19

Method: Apply the BODMAS priority (Bracket, Of, Division, Multiplication, Addition, Subtraction).

⇒ 88 + 33 − 26 + 14 of 2 + 7 − 19 (Solving Bracket: 42 ÷ 6 = 7)

⇒ 88 + 33 − 26 + 28 + 7 − 19 (Solving Of: 14 × 2 = 28)

⇒ 121 − 26 + 28 + 7 − 19 (Adding 88 + 33)

⇒ 95 + 28 + 7 − 19 (Subtracting 26 from 121)

⇒ 130 − 19 (Adding 95 + 28 + 7)

⇒ 111 (Final subtraction)

∴ The correct answer is 111.

Additional Information

BODMAS Rule

The rule defines the order of operations: Brackets, Of (multiplication), Division, Multiplication, Addition, and Subtraction.

Of Operator Priority

The word 'Of' signifies multiplication but is always solved before Division and standard Multiplication in an expression.

Hierarchy of Brackets

If multiple brackets are present, solve them in the order: Parentheses (), then Braces {}, and finally Square Brackets [].

Shortcut Trick

Convert the decimal 1.5 to the fraction 3/2 to simplify calculations.

Numerator: 8 × (3/2)³ + 1 = 8 × (27/8) + 1 = 27 + 1 = 28.

Denominator: 3² − 2 = 9 − 2 = 7.

Expression value: 28 ÷ 7 = 4.

∴ The correct answer is 4.

Alternate Method

Given:

Expression: (8(1.5)³ + 1) ÷ (3² − 2)

Formula Used:

Follow the BODMAS rule to solve the arithmetic expression (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

Calculations:

⇒ Step 1: Solve the power in the numerator: 1.5³ = 1.5 × 1.5 × 1.5 = 3.375

⇒ Step 2: Multiply the result by 8: 8 × 3.375 = 27

⇒ Step 3: Add 1 to complete the numerator: 27 + 1 = 28

⇒ Step 4: Solve the denominator: 3² − 2 = 9 − 2 = 7

⇒ Step 5: Divide the numerator by the denominator: 28 ÷ 7 = 4

∴ The correct answer is 4.

Additional Information

BODMAS Rule

The rule defines the order of operations: Brackets first, then Orders (powers/roots), then Division and Multiplication (left to right), and finally Addition and Subtraction.

Fractional Conversions

Terminating decimals like 1.5 can be written as 15/10 = 3/2. Using fractions often cancels out denominators, making complex powers easier to solve.

Power Rules

For any fraction (a/b)ⁿ, the power applies to both: aⁿ ÷ bⁿ. For example, (3/2)³ = 27/8.

Shortcut Trick

Apply the product property of square roots: √a × √b = √(a × b).

⇒ √45 × √5 = √(45 × 5)

⇒ √225 = 15

∴ The correct answer is 15.

Alternate Method

Given: √45 × √5

Formula Used: √(x² × y) = x√y and √y × √y = y

⇒ Simplify √45 by factoring out the perfect square:

⇒ √45 = √(9 × 5) = 3√5

⇒ Now multiply the expression: 3√5 × √5

⇒ 3 × (√5 × √5)

⇒ 3 × 5 = 15

∴ The correct answer is 15.

Additional Information

Product Rule of Radicals

For any non-negative real numbers a and b, √a × √b = √(a × b).

Quotient Rule of Radicals

For any non-negative real number a and positive real number b, √a ÷ √b = √(a ÷ b).

Simplifying Surds

A surd is in its simplest form when the number under the radical has no perfect square factors other than 1.

Shortcut Trick

Rationalize the fraction 1/(√10 − √3) by multiplying the numerator and denominator by the conjugate (√10 + √3).

Rationalized value = (√10 + √3) / (10 − 3) = (√10 + √3) / 7.

Now, the expression becomes: 1 × (√10 + √3) + (1/7) × (√10 + √3).

Combining the terms: (1 + 1/7) × (√10 + √3) = (8/7)(√10 + √3).

∴ The correct answer is (8/7)(√10 + √3).

Alternate Method

Given: (√10 + √3) + 1 / (√10 − √3)

Formula Used: Rationalization using (a − b)(a + b) = a² − b²

⇒ Step 1: Simplify the second term by multiplying numerator and denominator by (√10 + √3).

⇒ Second Term = [1 × (√10 + √3)] / [(√10 − √3) × (√10 + √3)]

⇒ Second Term = (√10 + √3) / [(√10)² − (√3)²]

⇒ Second Term = (√10 + √3) / (10 − 3) = (√10 + √3) / 7

⇒ Step 2: Add the first term and the simplified second term.

⇒ Total = (√10 + √3) + [(√10 + √3) / 7]

⇒ Total = (√10 + √3) × (1 + 1/7)

⇒ Total = (√10 + √3) × (8/7)

∴ The correct answer is (8/7)(√10 + √3).

Additional Information

Rationalization of Surds

To rationalize a denominator like (√a − √b), multiply both the numerator and denominator by its conjugate (√a + √b) to remove the radical sign.

Conjugate Pairs

Two binomial surds whose product is a rational number are called conjugate surds. For example, (x + √y) and (x − √y) are conjugates.

Difference of Squares

The identity (a − b)(a + b) = a² − b² is the fundamental tool used to simplify expressions involving products of surds.

Shortcut Trick

The perimeter of a square is calculated as 4 × side.

Given side = 6.5 cm.

Perimeter = 4 × 6.5 = 26 cm.

∴ The correct answer is 26 cm.

Alternate Method

Given:

The side of the square (a) = 6.5 cm.

Formula Used:

Perimeter of a square = 4 × a

Calculations:

⇒ Perimeter = 4 × 6.5

⇒ Perimeter = 26 cm

∴ The correct answer is 26 cm.

Additional Information

Area of a Square

The total space occupied by the square is given by the formula: Area = side² (a²).

Diagonal of a Square

The length of the diagonal connecting opposite corners is: Diagonal = a√2.

Properties of a Square

A square has four equal sides, and each internal angle is exactly 90°.

Shortcut Trick

The Area of a square is the square of its side length.

Area = (Side)²

Area = 12² = 144

∴ The correct answer is 144 cm².

Alternate Method

Given:

The side of the square (a) = 12 cm

Formula Used:

Area of a Square = Side × Side = a²

Calculations:

⇒ Area = 12 cm × 12 cm

⇒ Area = 144 cm²

∴ The correct answer is 144 cm².

Additional Information

Perimeter of a Square

The total boundary length of a square is given by 4 × Side.

Diagonal of a Square

The distance between opposite corners is Side × √2.

Area using Diagonal

Area can also be calculated as (Diagonal)² ÷ 2.

Shortcut Trick

Check Divisibility Rule of 3 (sum of digits must be a multiple of 3).

Check Divisibility Rule of 4 (last two digits must be divisible by 4).

9041: Sum = 14 (not divisible by 3) and Last two digits = 41 (not divisible by 4).

All other options (90120, 10020, 10068) are divisible by both 3 and 4.

∴ The correct answer is 9041.

Alternate Method

Given numbers: 9041, 90120, 10020, 10068

Analyze each number for divisibility by 3 and 4:

⇒ 90120: Sum = 9+0+1+2+0 = 12 (Divisible by 3). Last two digits = 20 (Divisible by 4).

⇒ 10020: Sum = 1+0+0+2+0 = 3 (Divisible by 3). Last two digits = 20 (Divisible by 4).

⇒ 10068: Sum = 1+0+0+6+8 = 15 (Divisible by 3). Last two digits = 68 (Divisible by 4, as 4 × 17 = 68).

⇒ 9041: Sum = 9+0+4+1 = 14. 14 ÷ 3 leaves remainder 2. Last two digits = 41. 41 ÷ 4 leaves remainder 1.

Since 9041 is not divisible by 3 and not divisible by 4, it satisfies the condition.

∴ The correct answer is 9041.

Additional Information

Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 (even last digit) and 3 (sum of digits divisible by 3).

Divisibility by 9

A number is divisible by 9 if the sum of all its digits is divisible by 9.

Divisibility by 8

A number is divisible by 8 if the last three digits are divisible by 8 or are all zeros.

Divisibility by 5

A number is divisible by 5 if its last digit is either 0 or 5.

Shortcut Trick

Apply the algebraic identity: 2(a² + b²) − (a − b)² = (a + b)².

Here, let a = 345 and b = 155.

Substitute the values into the formula: (345 + 155)² = 500².

Calculation: 500 × 500 = 250000.

∴ The correct answer is 250000.

Alternate Method

Given:

Expression: 2[(345)² + (155)²] − (345 − 155)²

Formula Used:

(a − b)² = a² + b² − 2ab

Calculations:

⇒ 2(345² + 155²) − (345² + 155² − 2 × 345 × 155)

⇒ 2(345²) + 2(155²) − 345² − 155² + 2 × 345 × 155

⇒ 345² + 155² + 2 × 345 × 155

⇒ (345 + 155)²

⇒ (500)²

⇒ 250000

∴ The correct answer is 250000.

Additional Information

Algebraic Identity for Sum of Squares

(a + b)² + (a − b)² = 2(a² + b²). This is used to simplify sums of squares of two terms.

Algebraic Identity for Difference

(a + b)² − (a − b)² = 4ab. This is useful for finding the product when the sum and difference are known.

Square of Numbers Ending in 5

For any number x5, its square is calculated by multiplying x by (x + 1) and appending 25 at the end. Example: 35² = (3 × 4)25 = 1225.

Shortcut Trick

Identify the net deviation from the initial average: 55.1 − 70.5 = −15.4.

The total decrease for 110 numbers is 110 × (−15.4) = −1694.

Sum of 40 new numbers = (New count × New average) − (Old count × Old average).

Sum = (40 × 55.1) + (Net decrease from old group) = 2204 − 1694 = 510.

∴ The correct answer is 510.

Alternate Method

Given:

Initial count of numbers (n₁) = 110

Initial average (A₁) = 70.5

Number of added numbers (n₂) = 40

Total numbers (N) = 110 + 40 = 150

Final average (A_total) = 55.1

Formula Used:

Sum = Average × Total Numbers

Calculations:

⇒ Total sum of 110 numbers = 110 × 70.5 = 7755

⇒ Total sum of 150 numbers = 150 × 55.1 = 8265

⇒ Sum of 40 newly added numbers = Total sum (150) − Initial sum (110)

⇒ Sum = 8265 − 7755

⇒ Sum = 510

∴ The correct answer is 510.

Additional Information

Combined Average Formula

If two groups have sizes n₁, n₂ and averages a₁, a₂, the combined average is (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Effect of Linear Change

If every number in a set is increased or decreased by a constant k, the Average also increases or decreases by k.

Deviation Method

The sum of deviations of all observations from their arithmetic mean is always zero (Σ(x_i − A) = 0).

Shortcut Trick

Find the LCM of 14 and 20, which is 140.

Smallest 3-digit multiple A = 140 × 1 = 140.

Largest 3-digit multiple B = 140 × 7 = 980.

Difference B − A = 980 − 140 = 840.

∴ The correct answer is 840.

Alternate Method

Given: Numbers are 14 and 20. A is the smallest 3-digit common multiple. B is the largest 3-digit common multiple.

Formula Used: LCM(x, y) gives the smallest common multiple. All other common multiples are multiples of the LCM.

⇒ Prime factorization: 14 = 2 × 7 and 20 = 2² × 5.

⇒ LCM(14, 20) = 2² × 5 × 7 = 4 × 5 × 7 = 140.

⇒ Smallest 3-digit multiple (A) = 140 × 1 = 140.

⇒ To find B, divide 999 by 140: 999 ÷ 140 ≈ 7.13.

⇒ Largest 3-digit multiple (B) = 140 × 7 = 980.

⇒ Value of B − A = 980 − 140 = 840.

∴ The correct answer is 840.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is perfectly divisible by two or more numbers. Common multiples of numbers are always multiples of their LCM.

HCF and LCM Relation

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

Finding Multiples in a Range

To find the number of multiples of k between m and n, calculate the difference between ⌊n/k⌋ and ⌊(m−1)/k⌋.

Shortcut Trick

To find the largest number that leaves the same remainder, calculate the differences between consecutive numbers.

Differences: (146 − 122) = 24, (170 − 146) = 24, and (194 − 170) = 24.

The Highest Common Factor (HCF) of 24, 24, and 24 is 24.

∴ The correct answer is 24.

Alternate Method

Given: The numbers are 122, 146, 170, and 194.

Formula Used: Required Number = HCF(|a − b|, |b − c|, |c − d|)

⇒ First difference = 146 − 122 = 24

⇒ Second difference = 170 − 146 = 24

⇒ Third difference = 194 − 170 = 24

⇒ Required largest number = HCF of (24, 24, 24)

⇒ HCF = 24

∴ The correct answer is 24.

Additional Information

HCF for Same Remainder

When the remainder is not given, the largest divisor is the HCF of the absolute differences between the numbers: HCF(|a−b|, |b−c|, |c−a|).

HCF for Given Remainder

To find the largest number which divides a, b, and c leaving remainders x, y, and z respectively, find HCF(a−x, b−y, c−z).

LCM for Same Remainder

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

Shortcut Trick

Convert percentage to fraction: 25% = 1/4.

If B is 4 units, then A is (4 − 1) = 3 units.

Given 3 units = 270 ⇒ 1 unit = 270 ÷ 3 = 90.

Value of B = 4 units = 4 × 90 = 360.

∴ The correct answer is 360.

Alternate Method

Given: A = 270, and A is 25 percent less than B.

Formula Used: A = B × (100 − Decrease %)/100

⇒ A = B × (100 − 25)/100

⇒ 270 = B × (75/100)

⇒ 270 = B × (3/4)

⇒ B = (270 × 4) ÷ 3

⇒ B = 90 × 4

⇒ B = 360.

∴ The correct answer is 360.

Additional Information

Percentage Change Rule

To find a value after an x% decrease, multiply the original value by (100 − x)/100.

Base Change Property

If A is x% less than B, then B is [x ÷ (100 − x)] × 100% more than A. Here, B is 33.33% more than A.

Fraction Equivalents

Using standard fractions like 20% = 1/5, 25% = 1/4, and 50% = 1/2 helps in solving Ratio and Proportion problems faster.

Shortcut Trick

The Loss of 30% means 30% of Cost Price (CP) = Rs. 69.

Dividing by 3: 10% of CP = Rs. 23.

Selling Price (SP) at 30% loss = 100% − 30% = 70% of CP.

⇒ SP = 7 × (10% of CP) = 7 × 23 = Rs. 161.

∴ The correct answer is Rs. 161.

Alternate Method

Given: Loss Amount = Rs. 69, Loss Percentage = 30%.

Formula used: Cost Price (CP) = (Loss × 100) ÷ Loss%

⇒ CP = (69 × 100) ÷ 30

⇒ CP = 690 ÷ 3 = Rs. 230

Formula used: Selling Price (SP) = CP − Loss

⇒ SP = 230 − 69

⇒ SP = Rs. 161

∴ The correct answer is Rs. 161.

Additional Information

Profit Percentage Formula

Profit% = (Profit ÷ CP) × 100, where Profit = SP − CP.

Direct Selling Price Formula

SP = CP × (100 − Loss%) ÷ 100 or SP = CP × (100 + Profit%) ÷ 100.

Cost Price with Profit/Loss

CP = (SP × 100) ÷ (100 ± Profit/Loss%), use (+) for profit and (−) for loss.

Shortcut Trick

Total maximum marks = 600 + 200 = 800

Overall marks needed (60%) = 0.60 × 800 = 480

Marks scored in first exam = 380

Marks required in sec examination = 480 − 380 = 100

Required percentage = (100 ÷ 200) × 100 = 50%

∴ The correct answer is 50%.

Alternate Method

Given:

Max marks of Exam 1 = 600 | Marks scored = 380

Max marks of Exam 2 = 200 | Marks scored = ?

Overall percentage = 60%

Formula Used:

Overall Percentage = [(Marks₁ + Marks₂) ÷ (Total₁ + Total₂)] × 100

Calculations:

⇒ Total Maximum Marks = 600 + 200 = 800

⇒ Overall Total Marks Obtained = (60 ÷ 100) × 800

⇒ Total Obtained = 480

⇒ Marks in sec examination = Total Obtained − Marks in 1st exam

⇒ Marks in 2nd exam = 480 − 380 = 100

⇒ Required Percentage in 2nd exam = (100 ÷ 200) × 100

⇒ Required Percentage = 50%

∴ The correct answer is 50%.

Additional Information

Weighted Average Formula

When two components have different weights (maximum marks), the overall percentage is P = (w₁p₁ + w₂p₂) ÷ (w₁ + w₂).

Percentage Calculation

To find the value when percentage is given: Value = (Percentage ÷ 100) × Total. Conversely, Percentage = (Value ÷ Total) × 100.

Aggregate Marks

Aggregate percentage is always calculated based on the sum of marks obtained across all subjects divided by the sum of maximum marks of all subjects.

Shortcut Trick

Given Cost Price (CP) : Selling Price (SP) = 9 : 11.

Let CP = 9 units and SP = 11 units.

Profit = SP − CP = 11 − 9 = 2 units.

Required Ratio (Profit : CP) = 2 : 9.

∴ The correct answer is 2 : 9.

Alternate Method

Given: Ratio of Cost Price to Selling Price = 9 : 11

Formula Used: Profit = Selling Price − Cost Price

⇒ Let the Cost Price (CP) of the article be 9x.

⇒ Then, the Selling Price (SP) of the article is 11x.

⇒ Profit = Selling Price − Cost Price

⇒ Profit = 11x − 9x = 2x

⇒ Ratio of Value of Profit to Cost Price = 2x : 9x

⇒ Ratio = 2 : 9

∴ The correct answer is 2 : 9.

Additional Information

Profit Percentage

It is the profit expressed as a percentage of the Cost Price. Formula: Profit% = (Profit ÷ CP) × 100.

Loss and Ratio

If Cost Price is greater than Selling Price, a loss occurs. Loss = CP − SP. The loss ratio is calculated similarly as Loss ÷ CP.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount.

Shortcut Trick

Efficiency ratio of A to B = 3 : 4

Time ratio of A to B = 4 : 3 (since Time ∝ 1/Efficiency)

Difference in time ratio units = 4 − 3 = 1 unit

Actual difference given = 12 days

∴ 1 unit = 12 days

Value of x (Time for A) = 4 units = 4 × 12 = 48 days

∴ The correct answer is 48 days.

Alternate Method

Given: A is 3/4 as efficient as B; Time taken by A = x days; Time taken by B = (x − 12) days.

Formula Used: Total Work = Efficiency × Time

Calculations:

⇒ Let efficiency of B = 4 units/day

⇒ Efficiency of A = 3/4 × 4 = 3 units/day

⇒ Work done by A = Work done by B

⇒ 3 × x = 4 × (x − 12)

⇒ 3x = 4x − 48

⇒ 4x − 3x = 48

⇒ x = 48 days

∴ The correct answer is 48 days.

Additional Information

Efficiency and Time Relation

The time taken to complete a certain work is inversely proportional to the efficiency of the person. If the efficiency ratio is a:b, the time ratio will be b:a.

Constant Work Equation

For the same amount of work, the product of efficiency and time remains constant: E₁ × T₁ = E₂ × T₂.

Work and Days

Total work can be assumed as the LCM of the number of days taken by different individuals to simplify calculations.

Shortcut Trick

Efficiency ratio of Man (M) : Woman (W) = 1 : 2.

Total Efficiency = (5 × 1) + (10 × 2) = 25 units.

Total Work = Total Efficiency × Time = 25 × 15.

Since the time remains 15 days, the required efficiency is 25 units.

Number of Men required = 25 ÷ 1 = 25.

∴ The correct answer is 25 men.

Alternate Method

Given: 5 Men and 10 Women can do the work in 15 days. 1 Woman = 2 Men efficiency.

Formula Used: M₁D₁ = M₂D₂ (where M is total efficiency).

⇒ Efficiency of 1 Man = 1 unit/day.

⇒ Efficiency of 1 Woman = 2 × 1 = 2 units/day.

⇒ Combined Efficiency (M₁) = (5 × 1) + (10 × 2) = 25 units/day.

⇒ Total Work = M₁ × D₁ = 25 × 15 = 375 units.

⇒ For the same work in 15 days by x Men: x × 1 × 15 = 375.

⇒ 15x = 375.

⇒ x = 375 ÷ 15 = 25.

∴ The correct answer is 25 men.

Additional Information

Work-Efficiency Relationship

Total Work = Efficiency × Time. Efficiency is the rate of doing work and is inversely proportional to the time taken to complete a task.

Man-Day Formula

The general formula is (M₁×D₁×H₁)/W₁ = (M₂×D₂×H₂)/W₂, where M is number of workers, D is days, H is hours, and W is units of work.

Efficiency Substitution

When different types of workers (men, women, children) are involved, convert them to a single unit using the given efficiency ratio to simplify calculations.

Shortcut Trick

Speed of B = 48 ÷ 6 = 8 km/h

Speed of C = 100 ÷ 10 = 10 km/h

Required Ratio = 8 : 10

Simplified Ratio = 4 : 5

∴ The correct answer is 4 : 5.

Alternate Method

Given:

Distance covered by B = 48 km | Time taken = 6 hr

Distance covered by C = 100 km | Time taken = 10 hr

Formula Used:

Speed = Distance ÷ Time

Calculations:

⇒ Speed of B = 48 ÷ 6 = 8 km/h

⇒ Speed of C = 100 ÷ 10 = 10 km/h

⇒ Required Ratio = Speed of B : Speed of C

⇒ Ratio = 8 : 10

⇒ Ratio = (8 ÷ 2) : (10 ÷ 2) = 4 : 5

∴ The correct answer is 4 : 5.

Additional Information

Definition of Speed

Speed is defined as the rate at which an object covers distance. It is a scalar quantity measured in units like km/h or m/s.

Unit Conversion Trick

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

Average Speed Formula

Average Speed = (Total Distance) ÷ (Total Time). It represents the constant speed that would cover the same total distance in the same total time.

Proportionality Rule

When time is constant, speed is directly proportional to distance (S₁/S₂ = D₁/D₂).

Shortcut Trick

The extra time taken by the train is solely to cover the length of the platform.

Extra time = 75 s − 25 s = 50 s.

Extra distance = Length of platform = 500 m.

Speed of train = Distance ÷ Time = 500 ÷ 50 = 10 m/s.

∴ The correct answer is 10 m/s.

Alternate Method

Given:

Time to cross pole (T₁) = 25 s

Time to cross platform (T₂) = 75 s

Length of platform (P) = 500 m

Formula Used:

Speed = Total Distance ÷ Total Time

Let the length of the train be L metres and its speed be S m/s.

When crossing a pole, distance = L.

⇒ S = L ÷ 25 — (Equation 1)

When crossing a platform, distance = L + 500.

⇒ S = (L + 500) ÷ 75 — (Equation 2)

Equating Equation 1 and Equation 2:

⇒ L ÷ 25 = (L + 500) ÷ 75

⇒ 3 × L = L + 500

⇒ 2L = 500

⇒ L = 250 m

Now, calculate speed using Equation 1:

⇒ Speed = 250 ÷ 25

⇒ Speed = 10 m/s

∴ The correct answer is 10 m/s.

Additional Information

Relative Speed Concept

When two objects move in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Unit Conversion

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

Crossing Objects

For a point object (pole, man), Distance = Length of train. For a lengthy object (bridge, tunnel), Distance = Length of train + Length of object.

The correct answer is: Take someone down a peg or two.

Key Points

• The phrase 'Make someone realize that they are less talented or important than they think they are' means to humble a person who is acting in an arrogant or overconfident manner. (किसी को यह अहसास कराना कि वह उतना महत्वपूर्ण या प्रतिभाशाली नहीं है जितना वह खुद को समझता है)
• Example: After he started bragging about his minor promotion, his boss decided to humble him by assigning him a basic task.
• 'Take someone down a peg or two' is an idiom used to describe the act of reducing someone's high opinion of themselves or making them feel less proud. (किसी का घमंड चूर करना या किसी को उसकी औकात दिखाना)
• Example: The new champion was so boastful that the veteran player felt it was time to take him down a peg or two on the court.
• Hence, we can infer that the idiom that matches the given meaning is 'Take someone down a peg or two'.

Therefore, the correct answer is: Take someone down a peg or two.

Additional Information

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

• Peg away at (किसी काम में जुटे रहना): To continue working hard at a difficult or tedious task over a long period.
• Example: If you peg away at your revision every night, you will surely get an A in the exam.
• Square peg (अनुपयुक्त व्यक्ति): Usually used in the phrase 'a square peg in a round hole', referring to a person who is not suitable for the job or situation they are in.
• Example: He felt like a square peg in a round hole working in a high-pressure finance firm because he preferred painting.
• Peg back (बढ़त कम करना या रोकना): To reduce the lead of an opponent in a game or to prevent someone from making progress.
• Example: The opposition team managed to peg back the champions with a sudden counter-attack goal.

The correct answer is: Unpleasant things will happen to someone.

Key Points

• The idiom 'Woe betide' is an archaic expression used to warn someone that they will be in trouble or that something bad will happen to them if they do (or fail to do) a particular thing. (किसी का बुरा होना या मुसीबत आना)
• Example: Woe betide anyone who forgets to lock the front door tonight.
• 'Unpleasant things will happen to someone' is the direct interpretation of this idiom, as it signifies a state of misfortune or negative consequences befalling an individual. (किसी के साथ अप्रिय घटनाएँ घटित होंगी)
• Example: If you ignore the safety warnings, unpleasant things will happen to you during the trek.
• Hence, we can infer that the correct meaning of the idiom is that negative or undesirable outcomes are expected for someone.

Therefore, the correct answer is: Unpleasant things will happen to someone.

Additional Information

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

• Pleasant things will happen to someone (किसी के साथ अच्छी चीज़ें होंगी): This refers to positive, enjoyable, or favorable events occurring, which is the opposite of 'woe'.
• Example: After all his hard work, he felt that pleasant things would happen in his career.
• Unprecedented success to someone (किसी को अभूतपूर्व सफलता): This refers to a level of success that has never happened or been experienced before.
• Example: The athlete achieved unprecedented success by winning five gold medals in a single event.
• Feeling jealous of someone (किसी से ईर्ष्या करना): This refers to feeling unhappy or angry because you want to have what someone else has.
• Example: Instead of being happy for her sister, she was feeling jealous of her new car.

The correct answer is trepidation.

Key Points

• The term trepidation is a noun that refers to a feeling of fear, alarm, or agitation about something that may happen in the future.
• The spelling trepidition provided in the original sentence is incorrect because it uses the vowel i in the third syllable instead of the correct vowel a.
• The correct spelling, trepidation, follows the standard English orthographic pattern where the suffix -ation is used to form nouns indicating a state or condition.
• In the context of the sentence, the word describes the nervousness or apprehension felt by the individual as she enters an interview room, which is a common scenario for such psychological distress.

 Additional Information

• Etymological Roots:
• The word is derived from the Latin word trepidatio, which means trembling or alarm, coming from the root trepidare (to tremble).
• It was first recorded in the English language during the late 15th century.
• Contextual Synonyms:
• Apprehension: Specifically refers to anxiety or fear that something bad or unpleasant will happen.
• Consternation: A feeling of anxiety or dismay, typically at something unexpected.
• Perturbation: A state of mental disquiet, disturbance, or agitation.
• Usage in Literature and Formal Writing:
• Trepidation is frequently used in formal communication and literature to convey a deep-seated dread or hesitation before a significant or daunting event.
• An antonym for this term would be equanimity or composure, representing a state of mental calmness.

The correct answer is: complain.

Key Points

• The word grumble means to complain about something in a bad-tempered way, or to make a low rumbling sound. (बड़बड़ाना)
• Example: The passengers began to grumble about the delay of the flight.
• complain refers to the act of expressing dissatisfaction, pain, uneasiness, or resentment. It is the closest in meaning to grumble as both involve expressing discontent. (शिकायत करना)
• Example: You have every right to complain if the service is not up to the mark.
• Hence, we can infer that the synonym of grumble is complain.

Therefore, the correct answer is- complain

Additional Information

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

• Whisper (फुसफुसाना): To speak very softly using one's breath without using the vocal cords.
• Example: She leaned closer to whisper the secret in his ear.
• Shout (चिल्लाना): To speak or cry out in a very loud voice, often due to anger, excitement, or to be heard from a distance.
• Example: Don't shout at me; I am standing right next to you.
• Agree (सहमत होना): To have the same opinion as someone else or to accept a suggestion.
• Example: I totally agree with your decision to start a new business.

The correct answer is: Privilage.

Key Points

• The word 'Privilage' is incorrectly spelled; it is the misspelt version of the word 'Privilege'. (गलत वर्तनी)
• Example: The editor pointed out that the word privilage was spelled incorrectly in the first draft.
• The correct word 'Privilege' refers to a special right, advantage, or immunity granted or available only to a particular person or group. (विशेषाधिकार)
• Example: It was a privilege to witness the historic event in person.
• Hence, we can infer that 'Privilage' is the misspelt word among the given options.

Therefore, the correct answer is: Privilage.

Additional Information

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

• Occurrence (घटना): An incident or event that takes place.
• Example: The occurrence of solar eclipses is a fascinating astronomical event.
• Apparent (स्पष्ट): Clearly visible or understood; obvious.
• Example: The apparent reason for the delay was the heavy snowfall.
• Parallel (समांतर): Side by side and having the same distance continuously between them.
• Example: The two main streets of the town run parallel to each other.

The correct answer is: Reasonable.

Key Points

• The word 'Expensive' refers to something that costs a lot of money and is not cheap or affordable for everyone. (महँगा)
• Example: Maintaining a luxury sports car is extremely expensive due to high fuel and repair costs.
• 'Reasonable' refers to a price that is fair, moderate, and not excessive; it suggests that the cost is appropriate for the value received, making it the antonym of expensive. (उचित/किफायती)
• Example: The local cafeteria provides healthy and delicious meals at a very reasonable price.
• Hence, we can infer that the opposite of 'expensive' is 'reasonable'.

Therefore, the correct answer is: Reasonable.

Additional Information

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

• Costly (कीमती/महँगा): Something that results in a high price or involves a great expenditure.
• Example: The delay in the shipment proved to be a costly mistake for the company.
• Pricey (महँगा): An informal term used to describe something that is expensive.
• Example: Real estate in the downtown area is becoming increasingly pricey.
• Valuable (मूल्यवान): Something that is worth a great deal of money or is extremely useful and important.
• Example: The museum houses many valuable artifacts from the ancient era.

The correct answer is: Raconteur.

Key Points

• The phrase 'one who tells anecdotes in a skilful and amusing way' refers to a person who has a special talent for telling stories and keeping an audience entertained. (वह व्यक्ति जो कुशलतापूर्वक और मनोरंजक तरीके से किस्से सुनाता है)
• Example: Her grandfather was a wonderful storyteller, a true raconteur who could keep the children entertained for hours with his life experiences.
• 'Raconteur' means a person who excels in telling anecdotes and stories in a skillful and amusing manner. (किस्सागो / गल्पकार)
• Example: Being a natural raconteur, he could turn even the most mundane daily event into a hilarious and engaging story.
• Hence, we can infer that the one-word substitute for 'one who tells anecdotes in a skilful and amusing way' is 'raconteur'.

Therefore, the correct answer is- Raconteur.

Additional Information

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

• Sybarite (विलासी): A person who is self-indulgent in their fondness for sensuous luxury and pleasure.
• Example: The billionaire lived like a sybarite, surrounded by gold-plated furniture and private chefs.
• Martinet (कठोर अनुशासनवादी): A person who demands complete obedience and is a very strict disciplinarian.
• Example: The drill sergeant was known as a martinet who would punish the recruits for even the slightest uniform imperfection.
• Epicurean (भोगवादी): A person devoted to sensual enjoyment, especially derived from fine food and drink.
• Example: His epicurean lifestyle involved traveling across Europe in search of the finest wines and rare cuisines.

The correct answer is: Forfeiture.

Key Points

• The phrase 'The loss or giving up of something as a penalty for wrongdoing' refers to the legal or contractual consequence where an individual must surrender property, money, or a right due to a crime or failure to fulfill an obligation. (दंड के रूप में किसी वस्तु का त्याग या हानि)
• Example: The contract included a clause for the forfeiture of the down payment if the buyer backed out.
• 'Forfeiture' means the act of losing or being deprived of property or a right as a punishment for an offense or breach of duty. (ज़ब्ती/दंडस्वरूप समर्पण)
• Example: The court ordered the forfeiture of all assets gained through the illegal trade.
• Hence, we can infer that the most suitable one-word substitution for the given phrase is 'forfeiture'.

Therefore, the correct answer is: Forfeiture.

Additional Information

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

• Embezzlement (ग़बन): The fraudulent misappropriation or theft of funds placed in one's trust or belonging to one's employer.
• Example: He was sentenced to five years in prison for the embezzlement of company funds.
• Extradition (प्रत्यर्पण): The formal process where one country or state surrenders an individual to another for prosecution or punishment for a crime.
• Example: The two countries are currently negotiating an extradition treaty to deal with cross-border crime.
• Interdiction (पाबंदी/निषेध): The action of prohibiting or forbidding something, or the movement to intercept and prevent something from reaching a destination.
• Example: The coast guard's primary mission is the interdiction of illegal drug shipments.

The correct answer is 'without'.

 

Key Points

• The word 'without' is a preposition used to indicate the absence of something or a condition that has not been met.
• When a preposition is followed by a verb, that verb must be in the gerund form (verb + -ing). In this sentence, 'bringing' is the gerund following the preposition.
• The sentence implies that if the action of bringing identity proof is not performed, the result is that the person cannot apply for the job.
• Options 1, 2, and 4 are grammatically or contextually incorrect for this specific structure.

Therefore, the correct answer is Option 3.

 

Complete Sentence: 'Without bringing your identity proof, you cannot apply for the job.'

 

Additional Information

• Option 1: 'Apart from' is a preposition meaning 'besides' or 'in addition to', which does not fit the conditional logic of the sentence.
• Option 2: 'Unless' is a conjunction and must be followed by a clause (subject + verb), such as 'Unless you bring...'. It cannot be followed directly by a gerund.
• Option 4: 'Except' is used to show exclusion and usually requires 'for' (Except for bringing...) when used as a preposition before a gerund.

The correct answer is Eight suspects had been rounded up by the police before the press conference..

Key Points

• The original sentence is written in the Active Voice and follows the Past Perfect Tense structure, which consists of Subject (The police) + had + Past Participle (rounded up) + Object (eight suspects).
• To convert a Past Perfect sentence into Passive Voice, the standard grammatical formula is: New Subject (Object of Active) + had + been + Past Participle (V3) + by + New Object (Subject of Active).
• The Object of the active sentence, eight suspects, becomes the Subject of the passive sentence as it is the entity receiving the action.
• The auxiliary verb been must be inserted between had and the main verb rounded up to correctly denote the Passive state of the Perfect Tense.
• The agent, by the police, identifies the performer of the action, and the adverbial phrase of time, before the press conference, remains at the end to provide the necessary temporal context.

 Additional Information

• Grammatical Variations and Errors:
• Simple Past Passive: This uses were + V3 (e.g., were rounded up). While grammatically correct in isolation, it fails to preserve the Past-in-the-Past relationship established by the original had.
• Morphological Accuracy: The word being is used for Continuous Tenses. Combining had with being (as in had being rounded up) results in a Morphological Error as it violates the rules of English auxiliary verb sequencing.
• Semantic Shift: Maintaining the Active Voice but swapping the Subject and Object (e.g., suspects had rounded up the police) causes a Semantic Shift, reversing the meaning of the original statement.
• Past Perfect Utility: This tense is specifically used to show that an action (the arrest) was completed before another event in the past (the press conference).

The correct answer is Will the volunteers make the necessary arrangements before the guests reach the venue?.

Key Points

• The original sentence is in the Passive Voice of the Simple Future Tense in an interrogative form. The structure is: Will/Shall + Object + be + V3 (Past Participle) + by + Subject?
• To convert this into the Active Voice, the agent of the action (the volunteers) must become the subject of the sentence, and the receiver of the action (the necessary arrangements) must become the object.
• The conversion rule for the Simple Future Active Voice (Interrogative) is: Will/Shall + Subject + V1 (Base Form) + Object?
• The auxiliary be is omitted in the active voice, and the past participle made is converted to its base form make.
• The secondary clause before the guests reach the venue is already in the active voice and serves as a temporal modifier; thus, it remains unchanged in the final conversion.
• Applying these steps, the volunteers (subject) performs the action make (verb) on the necessary arrangements (object), resulting in the correct active construction.

 Additional Information

• Simple Future Tense Structure:
• Active: Subject + will/shall + V1 + Object.
• Passive: Object + will/shall + be + V3 + by + Subject.
• Identifying Incorrect Tense Conversions:
• Simple Present: Uses Do/Does as seen in Option 1. This is incorrect because the original sentence refers to a future intent.
• Simple Past: Uses Did as seen in Option 2. This is incorrect because it implies the action was already completed in the past.
• Present Perfect: Uses Has/Have + V3 as seen in Option 4. This is incorrect as it describes a completed action with present relevance, rather than a future one.

The correct answer is Someone guards the secret documents day and night.

Key Points

• The original sentence is in the Passive Voice using the Simple Present Tense, identifiable by the construction is/am/are + V3 (past participle).
• When converting from passive to active voice, the agent or performer of the action (found after the preposition by) becomes the subject of the active sentence. Here, someone becomes the new subject.
• The subject of the passive sentence (the secret documents) shifts to the object position in the active voice sentence.
• The verb are guarded must be changed to the active form of the Simple Present Tense. Since someone is an indefinite pronoun and is treated as singular, the base verb guard takes the -s suffix to become guards.
• The time-related phrase day and night is an adverbial adjunct and remains at the end of the sentence to maintain the original context and meaning.

 Additional Information

• Tense Variations in Active Voice:
• Present Perfect Tense: Used in option 2 (has guarded), this tense indicates an action that happened at an unspecified time in the past or has recently concluded. The passive form would be have been guarded.
• Present Continuous Tense: Used in option 3 (is guarding), this indicates an action currently in progress. The passive form would require the addition of being (e.g., are being guarded).
• Past Continuous Tense: Used in option 4 (was guarding), this describes an action that was ongoing at a specific point in the past. Its passive equivalent would be were being guarded.
• Active vs. Passive Voice Rules:
• In Active Voice, the subject performs the action (e.g., Subject + Verb + Object).
• In Passive Voice, the subject receives the action (e.g., Object + be verb + V3 + by + Subject).
• The tense must never change when converting between voices; only the structure and emphasis are altered.

The correct answer is crowded by millions of devotees.

 

Key Points

• The primary error in the sentence is the incorrect use of the preposition 'by' after the word 'crowded'.
• In English grammar, the adjective 'crowded' is typically followed by the preposition 'with' to indicate what is filling a particular space.
• The phrase 'crowded with' is an idiomatic expression used to describe a place that is full of people or things.
• Thus, the correct phrasing should be 'crowded with millions of devotees' instead of 'crowded by millions of devotees'.

Therefore, the correct answer is Option 2.

 

Correct Sentence: 'The Golden Temple was crowded with millions of devotees from all around the world on the day of Baisakhi.'

 

Additional Information

• Option 1: 'The Golden Temple was' – This part is grammatically sound, acting as the subject and the auxiliary verb in the passive construction.
• Option 3: 'from all around the world' – This prepositional phrase correctly describes the origin of the devotees.
• Option 4: 'on the day of Baisakhi' – This part correctly uses the preposition 'on' for a specific day or occasion.

The correct answer is 'upon'.

 

Key Points

• The word dilate, when followed by the preposition upon (or on), forms a phrasal verb meaning to speak or write at length or in great detail about a subject.
• In the given sentence, the student leaders are elaborating or providing a detailed discussion regarding political issues.
• The construction 'dilate upon' is the standard idiomatic usage for this context.

Therefore, the correct answer is Option 3.

 

Complete Sentence: 'The student leaders dilated upon the political issues.'

 

Additional Information

• Option 1: into is generally used to indicate movement toward the interior of something or a change in state, which does not fit the verb dilate here.
• Option 2: onto usually indicates movement to a position on a surface.
• Option 4: over can be used with verbs like 'talk' or 'ponder', but it is not the conventional preposition used with dilate to mean 'elaborate'.