SSC GD Constable 2026 Official Paper (Held On 22 May, 2026 Shift 1) (Previous Year Paper)

Logic followed here is:

Logic: The first letter of each term increases by a constant value, while the second letter decreases by a constant value in each successive term of the series.

 

The missing term in the series is JA.

Hence, the correct answer is "Option 2".

Logic followed here is.

Logic: The series consists of two patterns applied to the positional values of the first and second letters of each term in the English alphabetical series.

Therefore, the missing term is 'VO'.

 

Hence, the correct answer is "Option 3".

Logic followed here is that each term in the series follows a specific pattern for its first letter and second letter based on their positional values in the English alphabet.

 

Therefore, the missing term is 'YR'.

Hence, the correct answer is "Option 3".

The logic followed in these sets is based on constant alphabetical shifts for both the first and second letters of each cluster within the set.

For the set '(WA, AF, EK)':

For the set '(DS, HX, LC)':

Applying the same logic to the options:

In Option 4, the set '(BD, FI, JN)' follows the same pattern:

Thus, the set (BD, FI, JN) follows the identified logic of +4 for the first letter and +5 for the second letter.

Hence, the correct answer is 'Option 4'.

Concept:

The number of times a particular day occurs in a month depends on the total number of days in that month and the day of the week it starts on:

• A month with 30 days will have 5 of a specific day if the month starts on that day or the day before it (i.e., the day must fall on the 1^st or 2^nd of the month).
• A month with 31 days will have 5 of a specific day if the month starts on that day or up to two days before it (i.e., the day must fall on the 1^st, 2^nd, or 3^rd of the month).

Calculation:

The year 1916 is divisible by 4, making it a leap year. Therefore, February has 29 days.

First, we determine the day of the week for January 1, 1916. Using the calendar calculation, January 1, 1916, was a Saturday.

I. June 1916

June always has 30 days.

Total days from January 1 to June 1 = 31 (Jan) + 29 (Feb) + 31 (Mar) + 30 (Apr) + 31 (May) = 152 days.

Odd days = 152 ÷ 7 = 21 weeks and 5 odd days.

Day on June 1 = Saturday + 5 days = Thursday.

Since June starts on a Thursday, the Wednesdays fall on the 7^th, 14^th, 21^st, and 28^th. There are only 4 Wednesdays in June 1916.

II. December 1916

December always has 31 days.

Total days from June 1 to December 1 = 30 (Jun) + 31 (Jul) + 31 (Aug) + 30 (Sep) + 31 (Oct) + 30 (Nov) = 183 days.

Odd days = 183 ÷ 7 = 26 weeks and 1 odd day.

Day on December 1 = Thursday + 1 day = Friday.

Since December starts on a Friday, the Wednesdays fall on the 6^th, 13^th, 20^th, and 27^th. There are only 4 Wednesdays in December 1916.

Therefore, neither June nor December had 5 Wednesdays in the year 1916.

Therefore, the correct option is 4.

Alternate Method

We can use the day of the week formula: Day = (Date + Month Code + Year Code + Century Code + Leap Year Adjustment) mod 7.

For the year 1916: Year = 16, Leap Year count = 16 ÷ 4 = 4. Century Code (1900s) = 0.

For June 1 (Month Code = 4): (1 + 4 + 16 + 4 + 0) mod 7 = 25 mod 7 = 4 (Thursday).

For December 1 (Month Code = 5): (1 + 5 + 16 + 4 + 0) mod 7 = 26 mod 7 = 5 (Friday).

A 30-day month (June) needs to start on Tuesday or Wednesday to have 5 Wednesdays. A 31-day month (December) needs to start on Monday, Tuesday, or Wednesday to have 5 Wednesdays.

Since June started on Thursday and December started on Friday, neither month had 5 Wednesdays.

Hence, the correct answer is Neither I nor II.

Logic followed here is.

Logic: The numer of lines present on the left side combines to make a shape on the right side.

 

Hence, the correct answer is "Option 1".

Logic followed here is.

Logic: All the elements present are shifted 2 places in the clockwise direction.

Hence, the correct answer is "Option 1".

Given:

ZX212 : UW326 :: VT312 : ? :: LK420 : HI534

The relationship between the letter-number clusters is determined by shifting the letters and adding a constant to the whole number:

ZX212 : UW326 →

LK420 : HI534 →

VT312 : ? →

The resulting cluster is QS426.

Hence, the correct answer is 'Option 2'.

Given:

The relationship follows a specific pattern in each cluster:

First Letter-Number Cluster Relation (ZKP500 : WHM260):

Third Letter-Number Cluster Relation (LTJ700 : IQG460):

Applying the same logic to YXU600:

Thus, the missing cluster is VUR360.

Hence, the correct answer is 'Option 2'.

The logic followed here is:

Logic: Second Number = First Number − 54

For the first pair 1747 : 1693

⇒ 1747 − 54 = 1693

For the second pair 2564 : 2510

⇒ 2564 − 54 = 2510

Applying the same logic to the third pair

4929 : ?

⇒ 4929 − 54 = 4875

Hence, the correct answer is 'Option 2'.

The logic followed here is:

Logic: Second Number = First Number + 229

For the first pair 765 : 994

⇒ 765 + 229 = 994

Applying the same logic to the third pair

691 : 920

⇒ 691 + 229 = 920

Similarly, applying the logic to the second pair

942 : ?

⇒ 942 + 229 = 1171

Hence, the correct answer is 'Option 3'.

Logic followed here is:

Logic: The code for the word is obtained by adding or subtracting specific values from the positional values of the letters in a fixed sequence: +2, +5, −1, −4, and −5.

For AEGIS is coded as CJFEN:

For DELLS is coded as FJKHN:

Similarly, for the word BEAKS:

 

Therefore, BEAKS is coded as DJZGN.

Hence, the correct answer is "Option 2".

The logic followed here is that each term in the series (KP94, HT200, EX306, BB412, ?) is divided into three components: the first letter, the second letter, and the numerical part. Each component follows its own pattern.

Hence, the correct answer is "Option 1".

Logic followed here is.

Logic: Each term in the series consists of three letters and a number. The pattern for each component is determined by a constant increment or decrement from one term to the next.

Hence, the correct answer is "Option 3".

Concept:

Hour hand covers 3600 in 12 hours.

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

Angular distance covered by the hour hand in 1 minute = 30/60 = 0.50

Minute hand covers 3600 in 60 minutes.

Angular distance covered in 1 minute = 360/60 = 60

Calculation:

The given time is between 10 AM and 11 AM. Let the time be 10:M.

At 10:00 AM, the hour hand is at 10 × 300 = 3000 and the minute hand is at 00.

In M minutes:

Position of the hour hand = 3000 + 0.5 × M

Position of the minute hand = 6 × M

Angle between hands = |(300 + 0.5M) − 6M| = |300 − 5.5M|

Given the angle is 15 degrees:

Case 1:

300 − 5.5M = 15 ⇒ 5.5M = 285

M = 285 / 5.5 ≈ 51.81 minutes

Case 2:

300 − 5.5M = −15 ⇒ 5.5M = 315

M = 315 / 5.5 ≈ 57.27 minutes

The approximate time from Case 1 is 10:52 AM (since 51.81 ≈ 52).

Alternate Method

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

Here, H = 10 and Angle = 15.

15 = $|60 \times 10 - 11 \times M| \over 2$

30 = |600 − 11M|

600 − 11M = 30 ⇒ 11M = 570 ⇒ M = 51.818...

600 − 11M = −30 ⇒ 11M = 630 ⇒ M = 57.272...

The closest value to the options is 51.82, which is approximately 52 minutes.

Hence, the correct answer is 10:52

Concept:

The angle between the hour hand and the minute hand of a clock can be calculated using the following relationship:

Angle (θ) = |30H − 5.5M|

Where:

• H is the hour (in this case, 3).
• M is the minutes past the hour.

Alternatively, we can look at the relative speeds:

Speed of the minute hand = 6° per minute

Speed of the hour hand = 0.5° per minute

The relative speed between the two hands is 5.5° per minute.

Calculation:

We are looking for the time between 3 PM and 4 PM when the angle is 110 degrees.

Given H = 3 and θ = 110°.

Case 1: The minute hand is behind the hour hand (not possible for 110° starting from 3 PM, as 3:00 is only 90°).

Case 2: The minute hand is ahead of the hour hand.

110 = 5.5M − 30(3)

110 = 5.5M − 90

110 + 90 = 5.5M

200 = 5.5M

M = 200 ÷ 5.5

M = 400 ÷ 11

M = 36.3636...

Rounding to the nearest minute, we get M ≈ 36.

Therefore, the time is approximately 3:36 PM.

Alternate Method

At 3:00 PM, the angle between the hands is 90°.

To reach an angle of 110°, the minute hand must first cover the 90° to overlap the hour hand and then move 110° ahead of it.

Total relative distance to be covered = 90° + 110° = 200°

Time = Distance ÷ Relative Speed

Time = 200 ÷ 5.5

Time = 36.36 minutes

The approximate time is 3:36 PM.

Hence, the correct answer is 3:36.

The logic followed here is: In each step, the number of squares are increasing and number of circles are decreasing with the triangle flipping upside down in each step.

Hence, Option 4 is the correct answer.

The logic followed here is: The arrow inside the box rotates 45° clockwise at each step, while the entire box with the circle flips to the left.

Hence, Option 4 is the correct answer.

The logic followed in this series is: Moving of the entire object 45° in clockwise direction.

Hence, "Option 4" is the correct answer.

Given:

Present age ratio of M and S = 2 : 5

M is 9 years younger than S.

Calculation:

Let the present ages of M and S be 2x and 5x.

Difference = 5x − 2x = 9

3x = 9

x = 3

Present ages:

• M = 2 × 3 = 6 years
• S = 5 × 3 = 15 years

After 12 years:

M = 6 + 12 = 18 years

S = 15 + 12 = 27 years

Required ratio:

18 : 27 = 2 : 3

Hence, the correct answer is "Option 1".

The correct answer is Chandragupta II.

Key Points

• Kalidasa, widely regarded as the greatest poet and dramatist in the Sanskrit language, is historically associated with the court of Chandragupta II.
• He was celebrated as one of the Navaratnas (Nine Gems), a group of nine distinguished scholars and artists who graced the royal court of the Gupta Empire.
• Chandragupta II, who assumed the prestigious title of Vikramaditya, ruled from approximately 380 CE to 415 CE, marking the peak of the Gupta Golden Age.
• The poet's works, including the world-renowned drama Abhijnanashakuntalam and epic poems like Meghaduta and Kumarasambhava, reflect the cultural sophistication and religious harmony of the Gupta era.
• While the primary capital was Pataliputra, Chandragupta II maintained a secondary capital at Ujjain, which became a significant center for literary and scientific advancements where Kalidasa flourished.

 Additional Information

• Samudragupta:
• Often referred to as the Napoleon of India by historian V.A. Smith due to his extensive military conquests.
• He was a versatile genius and a poet himself, earning the title Kaviraja (King of Poets).
• Kumaragupta:
• The son and successor of Chandragupta II, his reign saw the establishment of the famous Nalanda University.
• He was a worshiper of Lord Kartikeya and performed the Ashvamedha sacrifice to assert his imperial authority.
• Skandagupta:
• Recognized as the last great Gupta Emperor, he is famous for successfully defending the empire against the Hunas (Huns).
• His achievements are inscribed on the Bhitari Pillar and the Junagarh Rock.

The correct answer is Mumbai.

Key Points

• According to the Census 2011 data, Mumbai (as an Urban Agglomeration) was the most populous metropolitan city in India, with a total population of approximately 18,414,288.
• The Mumbai Metropolitan Region (MMR) encompasses the Municipal Corporation of Greater Mumbai (MCGM) and several surrounding satellite towns like Thane, Navi Mumbai, and Kalyan-Dombivli.
• The city has a massive population density, often exceeding 20,000 persons per square kilometer in its core urban districts, making it one of the most densely populated regions globally.
• The demographic growth in Mumbai is largely driven by its status as the Economic Capital of India, housing the headquarters of major financial institutions like the Reserve Bank of India (RBI), BSE, and NSE.
• In the hierarchy of Indian cities during the 2011 Census, Mumbai held the top rank, followed by the National Capital Territory of Delhi and the city of Kolkata.

 Additional Information

• Delhi:
• As per the 2011 Census, it was the second largest metropolitan city with a population of about 16,314,838.
• It serves as the National Capital Territory (NCT) and is a major hub for administrative, political, and commercial activities in North India.
• Kolkata:
• It ranked third among metropolitan cities with a population of approximately 14,112,536.
• It was the former capital of the British Raj and remains the primary economic and cultural center of East India.
• Chennai:
• The city recorded a population of about 8,696,010 in its metropolitan area, placing it fourth among the major metros.
• Often referred to as the Detroit of Asia, it is a critical center for the automobile industry and health services.
• Census 2011 Overview:
• This was the 15^th National Census of India and the 7^th after independence.
• The Census defined a Metropolitan City or Mega City as one having a population of 4 million or more, while a Million-Plus City is one with at least 1 million residents.
• The census was conducted under the leadership of C. Chandramouli, the Registrar General and Census Commissioner of India.

The correct answer is Government of India Act, 1858.

Key Points

• The Government of India Act, 1858, also known as the Act for the Good Government of India, was enacted by the British Parliament on August 2, 1858, following the Revolt of 1857.
• This act formally terminated the rule of the East India Company and transferred the governance of India directly to the British Crown, marking the beginning of the British Raj.
• It abolished the system of Double Government by dissolving the Board of Control and the Court of Directors, centralizing authority under the British cabinet.
• A new political office, the Secretary of State for India, was created. This official was a member of the British Cabinet and was assisted by a 15-member body known as the Council of India.
• The title of the Governor-General of India was changed to the Viceroy of India. The Viceroy acted as the direct representative of the British Monarch in India; Lord Canning became the first Viceroy under this act.
• The act ensured that the Secretary of State had the power to send secret despatches to India without consulting the Council, effectively making the British Parliament the ultimate authority over Indian affairs.

 Additional Information

• Regulating Act, 1773:
• It was the first step taken by the British Government to control and regulate the affairs of the East India Company in India.
• It designated the Governor of Bengal as the Governor-General of Bengal and established a Supreme Court at Fort William, Calcutta.
• Charter Act, 1833:
• This act was the final step towards centralization in British India, making the Governor-General of Bengal the Governor-General of India.
• It ended the commercial activities of the East India Company, transforming it into a purely administrative body.
• Indian Councils Act, 1861:
• This act introduced the Portfolio System, where each member of the Viceroy's Council was put in charge of specific departments.
• It initiated the process of decentralization by restoring the legislative powers to the Bombay and Madras Presidencies.

The correct answer is Rs. 30000 crores.

Key Points

• The PM Dhan-Dhaanya Krishi Yojana (PM-DDKY) is a major agricultural reform initiative officially approved by the Union Cabinet in July 2025 to bolster the rural economy and ensure long-term food security.
• The scheme has been granted a substantial annual allocation of Rs. 30,000 crores, aimed at providing a comprehensive safety net and growth framework for the farming community across India.
• This budgetary provision is specifically designed to facilitate technological upgrades in farming, such as the adoption of precision agriculture, AI-driven crop monitoring, and the deployment of agricultural drones.
• The primary focus of the Rs. 30,000 crores fund is to support small and marginal farmers who constitute the majority of the Indian agricultural workforce, helping them transition toward high-value crops and sustainable farming practices.
• The scheme integrates various sub-components including soil health management, subsidized quality seeds, and direct benefit transfers (DBT) for essential farm inputs.

 Additional Information

• Strategic Objectives of PM-DDKY:
• Crop Diversification: Encouraging farmers to shift from water-intensive monocultures to nutri-cereals, pulses, and oilseeds to improve ecological balance.
• Post-Harvest Infrastructure: A portion of the Rs. 30,000 crores is earmarked for building cold storage facilities and warehouse hubs at the village level to reduce wastage.
• Irrigation Efficiency: Strengthening the Per Drop More Crop mission by providing incentives for drip and sprinkler irrigation systems.
• Implementation and Monitoring:
• The Ministry of Agriculture and Farmers Welfare serves as the lead agency for the execution of this scheme, utilizing the Digital General Platform for real-time tracking of fund utilization.
• The allocation is part of a broader vision of Viksit Bharat 2047, aiming to double the share of agriculture in the Gross Value Added (GVA) through systematic financial injections and policy reforms.
• Special emphasis is placed on Aspirational Districts and the North-Eastern Region to bridge the infrastructure gap in the primary sector.

The correct answer is 1960.

Key Points

• Mazagon Dock Shipbuilders Limited (MDL), situated in Mumbai, was originally incorporated as a public limited company in 1934.
• The Government of India took over the management of the dockyard in April 1960 to enhance the nation’s self-reliance in defense production.
• Following the nationalization, the shipyard was placed under the administrative control of the Ministry of Defence, specifically the Department of Defence Production.
• The primary objective of the takeover was to transform the facility into a premier warship building yard capable of meeting the strategic requirements of the Indian Navy.
• Since 1960, MDL has transitioned from a small ship repair yard into a sophisticated Defence Public Sector Undertaking (DPSU) that constructs destroyers, frigates, and submarines.

 Additional Information

• Historical Significance and Growth:
• Before the 1960 acquisition, the yard was owned by the British India Steam Navigation Company and the Peninsular and Oriental Steam Navigation Company.
• In 1968, the yard launched INS Nilgiri, the first Leander-class frigate built indigenously in India, which was commissioned in 1972.
• MDL is currently involved in high-profile projects such as Project 15B (Visakhapatnam-class destroyers) and Project 17A (Nilgiri-class stealth frigates).
• It is also the site for Project 75, responsible for the construction of Scorpene-class (Kalvari-class) submarines through a technology transfer agreement with Naval Group, France.
• The facility remains one of the few shipyards in the world capable of building both conventional submarines and heavy surface combatants.

The correct answer is Sub-tropical high pressure belt.

Key Points

• The Sub-tropical high pressure belt is located in both hemispheres between approximately 30°N to 35°N and 30°S to 35°S latitudes.
• This belt is also famously known as the Horse Latitudes due to the calm winds and high pressure that historically stalled sailing ships.
• The formation of this belt is primarily due to the subsidence of air; air that rises at the Equator (Hadley Cell) cools as it moves poleward and descends at these latitudes, creating high-pressure conditions at the surface.
• Characterized by anticyclonic conditions, this region experiences light winds, clear skies, and low humidity, which is why most of the world's hot deserts (like the Sahara and Arabian deserts) are located along these latitudes.
• The term Horse Latitudes originated because sailors, when becalmed for long periods, had to throw horses overboard to conserve drinking water for the crew.

 Additional Information

• Equatorial Low Pressure Belt:
• Located between 5°N and 5°S latitudes.
• Known as the Doldrums, it is a zone of convergence for trade winds and intense solar heating.
• Sub-polar Low Pressure Belt:
• Situated between 60° and 65° latitudes in both hemispheres.
• Formed by the convergence of warm Westerlies and cold Polar Easterlies, leading to the development of temperate cyclones.
• Polar High Pressure Belt:
• Located around the North and South Poles (80°−90°).
• Caused by extremely low temperatures which make the air dense, leading to constant high pressure and cold, dry conditions.

The correct answer is 3.

Key Points

• The Pradhan Mantri Dakshata Aur Kushalata Sampanna Hitgrahi (PM-DAKSH) Yojana is a Central Sector Scheme launched by the Ministry of Social Justice and Empowerment in 2020-21.
• The primary objective of this scheme is to increase the skill levels of the target youth by providing them short-term and long-term training, making them employable for both self-employment and wage-employment.
• The scheme specifically targets Scheduled Castes (SCs), Other Backward Classes (OBCs), Economically Backward Classes (EBCs), De-notified Tribes (DNTs), and Safai Karamcharis.
• According to the eligibility criteria, candidates belonging to the Other Backward Classes (OBC) category must have a total annual family income of less than Rs. 3 lakh to avail of the training benefits.
• For candidates under the Economically Backward Classes (EBC) category, the annual family income limit is even lower, stipulated at less than Rs. 1 lakh per annum.
• There is no income limit for candidates belonging to the Scheduled Castes (SC), De-notified, Nomadic and Semi-Nomadic Tribes (DNT), and Safai Karamcharis including waste pickers.

 Additional Information

• The scheme is implemented through three apex corporations under the Ministry:
• NSFDC: National Scheduled Castes Finance and Development Corporation.
• NBCFDC: National Backward Classes Finance and Development Corporation.
• NSKFDC: National Safai Karamcharis Finance and Development Corporation.
• Types of Training Programs:
• Up-skilling/Recognition of Prior Learning (RPL): Training duration ranges from 32 to 80 hours for artisans and sanitation workers.
• Short Term Training: Focuses on NSQF compliant job roles with a duration of 200 to 600 hours.
• Long Term Training: Covers courses for 6 months to 1 year in high-demand sectors.
• Entrepreneurship Development Program (EDP): Aimed at youth wanting to start their own micro-enterprises, usually lasting 80 to 90 hours.
• Benefits to Trainees:
• Training is provided free of cost to all eligible candidates.
• A stipend is provided to trainees with at least 80 percent attendance (e.g., Rs. 1,000 to Rs. 1,500 per month depending on the category and course).

The correct answer is West Bengal.

Key Points

• Gaudiya Nritya is a classical dance form that originated in the ancient region of Gaur (or Gauda), which served as the capital of Bengal during various historical periods.
• This dance form is deeply intertwined with the Gaudiya Vaishnavism tradition, which saw a major resurgence in the 16^th century under the spiritual leadership of Sri Chaitanya Mahaprabhu.
• The reconstruction and revival of Gaudiya Nritya as a classical discipline were spearheaded by Dr. Mahua Mukherjee through extensive research into the Natya Shastra, medieval literature, and Pala-Sena era temple sculptures.
• It is a composite art form that integrates elements of temple dancing, rhythmic Kirtan music, and folk traditions like Chhau and Nachni.
• The performance typically features themes from the Radha-Krishna lore and uses traditional instruments such as the Khol and Kartal.

 Additional Information

• Haryana:
• Common folk dances include Ghoomar, Phag, and Dhamal, primarily performed during agricultural festivals like Baisakhi.
• Jammu and Kashmir:
• Home to the Rouf dance, performed by women during Ramzan, and Bhand Pather, a traditional satirical folk theatre.
• Andhra Pradesh:
• Best known for Kuchipudi, a major Indian classical dance recognized for its blend of Nritta (pure dance) and Abhinaya (expression).

The correct answer is Madhya Pradesh.

Key Points

• The Panna Diamond Mine is located in the Panna district of Madhya Pradesh and is part of the larger Vindhyan Range geological formation.
• It is the only active, industrial-scale diamond mine in India, making Madhya Pradesh the leading producer of diamonds in the country.
• The National Mineral Development Corporation (NMDC) is the primary public sector enterprise responsible for the mechanized mining operations at the Majhgawan site in Panna.
• The diamonds in this region are found in Kimberlite pipes and conglomerate beds, which were formed millions of years ago through volcanic and sedimentary processes.
• The Panna belt extends approximately 240 kilometers and produces various categories of diamonds, including gem-quality, off-color, and industrial-grade stones.

 Additional Information

• Jharkhand:
• This state is the primary hub for Coal production in India, featuring the famous Jharia and Bokaro coalfields.
• It is also rich in Iron Ore (Singhbhum) and Copper (Ghatshila).
• Karnataka:
• Historically famous for Gold mining, particularly the Kolar Gold Fields (KGF) and the currently operational Hutti Gold Mines.
• It is also a major producer of Magnetite Iron Ore and Manganese.
• Gujarat:
• Renowned for its Petroleum and Natural Gas reserves located in the Ankleshwar and Cambay basins.
• It is the largest producer of Salt in India and holds significant deposits of Lignite and Fluorite.

The correct answer is Dol Purnima.

Key Points

• In West Bengal, the festival of Holi is celebrated with great fervor as Dol Purnima or Dol Jatra, marking the final full moon day of the Hindu lunar month of Phalguna.
• The festival is primarily dedicated to Lord Krishna and Radha. The deities are placed in a palanquin (the Dol) and carried in a procession around streets while devotees sing devotional songs and hymns.
• A cultural highlight of this festival is the Basanta Utsav (Spring Festival) held at Shantiniketan, a tradition established by the Nobel laureate Rabindranath Tagore to welcome spring through poetry, dance, and music.
• Participants primarily use dry colored powders known as Abir or Gulal rather than liquid colors, signifying the colors of the blossoming Spring (Basanta) season.
• This day is also of immense spiritual significance for the Gaudiya Vaishnava community as it marks the birth anniversary of Chaitanya Mahaprabhu, the 15^th-century saint who revitalized the Bhakti movement.

 Additional Information

• Bhai Phonta:
• Celebrated on the second day after Kali Puja (Diwali) in West Bengal, it is the regional equivalent of Bhai Dooj.
• Sisters perform a ritual where they apply a sandalwood paste mark on their brothers' foreheads to pray for their protection and longevity.
• Jagaddhatri Puja:
• Dedicated to Goddess Jagaddhatri (the Holder of the World), this festival occurs in the month of Kartik, typically four days after Durga Puja.
• It is celebrated with massive community pandals, particularly in Chandannagar and Krishnanagar, featuring colossal clay idols.
• Kalpataru Utsav:
• Observed every year on January 1^st, this festival commemorates the transformation of Sri Ramakrishna Paramahansa into a Kalpataru (wish-fulfilling tree) in 1886.
• The main celebrations take place at the Cossipore Garden House and Dakshineswar Kali Temple in Kolkata.

The correct answer is Vaporisation.

Key Points

• Vaporisation refers to the physical transition of a substance from the liquid phase to the gaseous phase.
• At atmospheric pressure, this change occurs when molecules in the liquid gain sufficient thermal energy to overcome the intermolecular attractive forces (such as hydrogen bonding or Van der Waals forces) that hold them in a condensed state.
• This process encompasses two distinct phenomena: evaporation, which is a surface-level transition occurring at any temperature, and boiling, which occurs throughout the bulk of the liquid at a specific boiling point.
• When a liquid reaches its boiling point at 1 atmospheric pressure (101.325 kPa), the vapour pressure of the liquid becomes equal to the external atmospheric pressure.
• The transition requires an input of energy known as the Latent Heat of Vaporisation, which increases the potential energy of the particles without raising the temperature during the phase change.

 Additional Information

• Solidification and Freezing:
• Solidification (often called freezing) is the phase change from liquid to solid.
• This process occurs when kinetic energy is removed, allowing particles to settle into a fixed, ordered crystalline lattice or an amorphous structure.
• Deposition:
• Deposition is a thermodynamic process where a substance transforms directly from a gas to a solid, bypassing the liquid state entirely.
• A common natural example is the formation of sub-freezing hoar frost on ground surfaces or the transformation of water vapour into snow in clouds.

The correct answer is 2005-2006.

Key Points

• Gender Budgeting was formally introduced in India during the Union Budget 2005-2006 under the leadership of the then Finance Minister P. Chidambaram.
• It is not a separate budget for women but a fiscal strategy and analytical tool used to examine the government budget through a gender lens to ensure equitable distribution of resources.
• The introduction featured the first Gender Budget Statement, originally known as Statement 20 (now Statement 13), which disclosed the allocations specifically targeting women.
• The process categorizes schemes into two parts: Part A, which includes schemes with 100% allocation for women, and Part B, which includes schemes where at least 30% of the allocation is earmarked for women.
• India became one of the pioneering developing nations to institutionalize Gender Responsive Budgeting (GRB) to address gender gaps in education, health, and economic opportunities.

 Additional Information

• Institutional Mechanisms:
• The Ministry of Women and Child Development (MWCD) is the nodal agency for the implementation and monitoring of gender budgeting across various sectors.
• Following the 2005-2006 mandate, Gender Budget Cells (GBCs) were established within various central ministries and departments to facilitate gender-sensitive planning and evaluation.
• The National Institute of Public Finance and Policy (NIPFP) provided the initial analytical framework that helped the government transition from a general budget to a gender-sensitive one.
• Evolution and Background:
• The groundwork was laid during the Ninth Five-Year Plan (1997-2002), which introduced the Women's Component Plan (WCP) to ensure that 30% of funds from all ministries were directed toward women.
• In 2004, an Expert Group was constituted to recommend a classification system for government expenditure to track pro-women allocations effectively.
• While it started with only 10 ministries in its inaugural year, the scope of the Gender Budget Statement has expanded significantly, now covering over 30 ministries and departments.

Therefore, the correct answer is 2005-2006.

The correct answer is 1983.

Key Points

• India secured its maiden ICC Men's Cricket World Cup title in 1983 by defeating the formidable West Indies, who were the two-time defending champions.
• The final match was contested at the iconic Lord's Cricket Ground in London on 25^th June 1983.
• Under the inspirational leadership of captain Kapil Dev, India defended a modest total of 183 runs, successfully bowling out the West Indies for 140 runs.
• Mohinder Amarnath was adjudged the Man of the Match for his critical all-round performance, contributing 26 runs and taking 3 wickets for 12 runs.
• This historic victory is widely regarded as the defining moment that transformed cricket into a mass obsession in India and shifted the game's financial center to South Asia.

 Additional Information

• 1975 World Cup:
• This was the inaugural edition of the tournament, officially known as the Prudential Cup, held in England.
• The West Indies won the title by defeating Australia in the final.
• 1996 World Cup:
• Officially called the Wills World Cup, it was co-hosted by India, Pakistan, and Sri Lanka.
• Sri Lanka claimed their first championship by defeating Australia in the final at Gaddafi Stadium, Lahore.
• 1999 World Cup:
• The event was primarily hosted by England, with secondary venues in Scotland, Ireland, Wales, and the Netherlands.
• Australia emerged victorious after defeating Pakistan in a one-sided final.

The correct answer is Both I and II.

Key Points

• Critical minerals such as Lithium, Cobalt, Nickel, and Graphite are considered the foundational components of a modern economy because they are essential for the production of advanced technologies, including semiconductors, telecommunications equipment, and defense systems. Hence, statement I is correct.
• As the world undergoes a massive shift from hydrocarbons to green energy, these minerals are increasingly described as the 'oil of the 21^st century' because they serve as the primary fuel for the energy transition, powering Electric Vehicles (EVs) and renewable energy storage systems. Hence, statement II is correct.

 Additional Information

• Characteristics and Global Significance:
• Definition: A mineral is classified as 'critical' when it is essential for economic growth and national security, while its supply chain is prone to disruption due to geological scarcity or geopolitical factors.
• Rare Earth Elements (REEs): A group of 17 minerals used in permanent magnets for wind turbines and EV motors, currently dominated by China in terms of mining and processing.
• Indian Context: The Ministry of Mines released a list of 30 critical minerals in 2023, including Beryllium, Germanium, and Titanium, to bolster the Atmanirbhar Bharat initiative and secure domestic manufacturing.
• International Alliances: India has joined the Mineral Security Partnership (MSP), a US-led initiative aimed at accelerating the development of diverse and sustainable critical energy minerals supply chains globally.
• Supply Chain Vulnerability: Unlike oil, which is traded on a liquid global market, critical minerals often have highly concentrated production sites, leading to strategic dependencies and the need for bilateral trade agreements.

The correct answer is 20.

Key Points

• The 20^th Asian Games, officially known as the XX Asiad, is a major multi-sport event scheduled to be held in Japan from September 19 to October 4, 2026.
• The games will be co-hosted by the Aichi Prefecture and its capital city, Nagoya, marking the third time Japan has hosted this prestigious continental competition.
• Previous Japanese host cities include Tokyo in 1958 and Hiroshima in 1994, highlighting the country's long-standing tradition of organizing large-scale sporting events.
• The hosting rights were officially awarded by the Olympic Council of Asia (OCA) during their 35^th General Assembly held in Danang, Vietnam, in September 2016.
• The Aichi-Nagoya 2026 edition aims to be cost-effective and sustainable by utilizing existing sports infrastructure and venues across the prefecture.
• The event is expected to feature over 40 sports, including traditional Olympic disciplines and sports popular across the Asian continent.

 Additional Information

• 19^th Asian Games:
• This edition was held in Hangzhou, China. Initially scheduled for 2022, it was postponed to September–October 2023 due to the global COVID-19 pandemic.
• 18^th Asian Games:
• Held in 2018, this was the first time the games were co-hosted by two cities, Jakarta and Palembang, in Indonesia.
• 17^th Asian Games:
• This event took place in Incheon, South Korea, in 2014, featuring approximately 439 events in 36 sports.
• Future Hosting Roadmap:
• Following Aichi-Nagoya 2026, the 21^st Asian Games are scheduled for Doha, Qatar, in 2030, and the 22^nd Asian Games will be hosted in Riyadh, Saudi Arabia, in 2034.

The correct answer is 3.

Key Points

• The Secretary-General of the Shanghai Cooperation Organisation (SCO) is the highest administrative official of the organization, responsible for directing the Secretariat and representing the SCO in international forums.
• According to the SCO Charter (specifically Article 19), the Secretary-General is appointed for a fixed tenure of 3 years.
• The appointment is made by the Council of Heads of State (CHS), which is the supreme decision-making body of the organization, based on the recommendation of the Council of Foreign Ministers.
• The position of Secretary-General rotates among the member states in the Russian alphabetical order of the names of the member states.
• The term of the Secretary-General is non-renewable, ensuring that different member states have the opportunity to lead the administrative wing of the organization periodically.
• The Secretary-General is tasked with implementing the decisions of the Council of Heads of State and the Council of Heads of Government, as well as managing the organization’s budget and reports.

 Additional Information

• Shanghai Cooperation Organisation (SCO) Overview:
• Founded on June 15, 2001, in Shanghai, China, the organization was established by the leaders of China, Russia, Kazakhstan, Kyrgyzstan, Tajikistan, and Uzbekistan.
• The SCO Secretariat is the permanent executive body and is headquartered in Beijing, China.
• The Regional Anti-Terrorist Structure (RATS), another permanent organ of the SCO, is headquartered in Tashkent, Uzbekistan, and its Director also serves a 3-year term.
• The organization expanded in 2017 to include India and Pakistan as full members during the Astana Summit.
• The official working languages of the organization are Russian and Chinese, reflecting the linguistic heritage of its primary founding members.
• As of recent developments, Iran became a full member in 2023, and Belarus joined as the tenth full member in July 2024.

The correct answer is Both I and II.

Key Points

• Mass Transport is one of the seven engines identified under the PM Gati Shakti initiative, focusing on enhancing urban connectivity through projects like Metro Rail, Regional Rapid Transit Systems (RRTS), and integrated bus services to reduce congestion. Hence, statement I is correct.
• Logistics Infrastructure is a fundamental engine designed to integrate supply chains, develop Multi-Modal Logistics Parks (MMLPs), and create a seamless network for the movement of goods and services across the country. Hence, statement II is correct.
• The PM Gati Shakti National Master Plan is powered by a total of seven engines, which include Roads, Railways, Airports, Ports, Mass Transport, Waterways, and Logistics Infrastructure.
• The primary objective of these engines is to facilitate multi-modal connectivity, ensuring that different modes of transport are integrated to provide last-mile connectivity for people and goods.

 Additional Information

• PM Gati Shakti Master Plan:
• Launched in October 2021, it is a Rs 100 lakh crore project aimed at holistic infrastructure development.
• It incorporates 16 Ministries onto a single digital platform to ensure synchronized planning and avoid departmental silos.
• The platform was developed by BISAG-N (Bhaskaracharya National Institute for Space Applications and Geo-informatics) using GIS-based spatial planning tools.
• The initiative seeks to reduce India’s logistics costs from the current 13-14 percent of GDP to approximately 8 percent, aligning with global standards.
• It identifies six pillars: Comprehensiveness, Prioritization, Optimization, Synchronization, Analytical, and Dynamic.
• Key targets include increasing the National Highway network to 2 lakh kilometers and creating 400 new-generation Vande Bharat trains by 2024-25.

The correct answer is Both I and II.

Key Points

• The Breaststroke is a swimming style in which the swimmer is on their chest and the torso does not rotate. It is characterized by simultaneous arm movements on a horizontal plane and a frog-like kick (whip kick). It is widely regarded as the oldest and slowest of the four competitive strokes. Hence, statement I is correct.
• The Backstroke (or back crawl) is unique because it is the only competitive stroke performed with the swimmer lying on their back. It involves alternating arm movements and a flutter kick. A key advantage of this stroke is that it allows for easy breathing, though swimmers cannot see where they are going. Hence, statement II is correct.
• Both Breaststroke and Backstroke are officially recognized by World Aquatics (formerly FINA) as standard competitive disciplines in international events like the Olympic Games and World Championships.

 Additional Information

• Apart from the strokes mentioned above, there are two other primary competitive swimming strokes:
• Freestyle (Front Crawl):
• It is the fastest and most efficient swimming stroke.
• Characterized by an alternating overhand arm motion and a continuous flutter kick.
• Swimmers breathe by rotating their heads to the side.
• Butterfly Stroke:
• Regarded as the most physically demanding and technically difficult stroke.
• Features a simultaneous overhead arm recovery and a dolphin kick where the legs move together.
• It was developed as a variation of the breaststroke before becoming its own category in 1952.
• Individual Medley (IM):
• A single swimmer performs all four strokes in a specific order: Butterfly, Backstroke, Breaststroke, and Freestyle.

The correct answer is 58.

Key Points

• The Environmental Performance Index (EPI) 2024 provides a data-driven summary of the state of sustainability worldwide, ranking 180 countries on their environmental efforts.
• In the 2024 framework, the index utilized a total of 58 performance indicators to provide a granular and comprehensive assessment of national environmental performance.
• These 58 indicators are systematically organized into 11 issue categories, which address specific environmental challenges such as Air Quality, Biodiversity, and Waste Management.
• The indicators are further grouped into three overarching policy objectives: Climate Change, Environmental Health, and Ecosystem Vitality.
• The EPI is a biennial report published by the Yale Center for Environmental Law & Policy and the Center for International Earth Science Information Network at Columbia University.

 Additional Information

• Core Policy Objectives:
• Climate Change: Focuses on progress toward net-zero emissions by 2050, tracking greenhouse gas emission growth rates and projected targets.
• Environmental Health: Evaluates factors directly impacting human well-being, including Sanitation & Drinking Water, Air Quality, and exposure to Heavy Metals like Lead.
• Ecosystem Vitality: Measures the health of natural systems, covering Forestry, Fisheries, Agriculture, and Biodiversity & Habitat protection.
• Significance of Indicators:
• The 58 indicators allow for a sophisticated analysis of how close countries are to established environmental policy targets.
• By using standardized data, the EPI helps identify leaders and laggards in environmental sustainability, facilitating the sharing of best practices among nations.

The correct answer is CPCB.

Key Points

• The Comprehensive Environmental Pollution Index (CEPI) is a framework developed to evaluate the environmental quality of industrial clusters and to identify areas that require immediate attention.
• It was designed and published by the Central Pollution Control Board (CPCB) in collaboration with the Indian Institute of Technology (IIT), Delhi in 2009.
• The primary purpose of CEPI is to categorize industrial clusters into Critically Polluted Areas (CPA), Severely Polluted Areas (SPA), and Other Polluted Areas (OPA) based on a scoring system.
• A CEPI score above 70 denotes a Critically Polluted Area, which often leads to a moratorium on new industrial activities in that region, while a score between 60 and 70 identifies a Severely Polluted Area.
• The assessment methodology considers the scale of industrial activity, the nature of pollutants (relative toxicity), the scale of exceedance of environmental standards, and the impact on human health.
• The index evaluates three environmental components: Air, Water, and Land, integrating them into a single score that reflects the overall environmental stress in a geographical area.

 Additional Information

• Central Pollution Control Board (CPCB):
• A statutory organization established in 1974 under the Water (Prevention and Control of Pollution) Act to provide technical support to the Ministry of Environment, Forest and Climate Change.
• National Green Tribunal (NGT):
• Established on October 18, 2010, under the NGT Act for the effective and expeditious disposal of cases relating to environmental protection and conservation of forests.
• Central Ground Water Board (CGWB):
• Operating under the Ministry of Jal Shakti, it is the national apex body responsible for managing, monitoring, and researching groundwater resources across India.
• NITI Aayog:
• The National Institution for Transforming India, created in January 2015 as a successor to the Planning Commission, serves as the premier policy think tank of the Indian government.

Shortcut Trick

Solve the bracket and multiplication first: (38 + 21) × 2 = 59 × 2 = 118.

Rewrite the expression: 67 + 89 − 53 + 118 − 96.

Group the terms: (67 + 89 + 118) − (53 + 96) = 274 − 149 = 125.

∴ The correct answer is 125.

Alternate Method

Given:

67 + 89 − 53 + (38 + 21) × 2 − 96

Applying the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction):

Step 1: Solve the bracket (B).

⇒ 67 + 89 − 53 + 59 × 2 − 96

Step 2: Perform multiplication (M).

⇒ 67 + 89 − 53 + 118 − 96

Step 3: Perform addition and subtraction (A and S) from left to right.

⇒ 156 − 53 + 118 − 96

⇒ 103 + 118 − 96

⇒ 221 − 96

⇒ 125

∴ The correct answer is 125.

Additional Information

BODMAS Rule

It is the standard order of operations used to solve mathematical expressions: Brackets first, then Orders (exponents/roots), followed by Division and Multiplication (from left to right), and finally Addition and Subtraction (from left to right).

Associative Property

While solving only addition and subtraction, the terms can be grouped together (e.g., all positives together and all negatives together) to simplify the calculation process.

Shortcut Trick

Solve (19 of 2) = 38 and 42 ÷ 6 = 7.

The expression becomes: 96 + 38 − 38 + 7 + 28 − 16.

Notice that +38 and −38 cancel each other out directly.

Remaining: 96 + 7 + 28 − 16 = 115.

∴ The correct answer is 115.

Alternate Method

Given: 96 + (19 of 2) − 38 + 42 ÷ 6 + 28 − 16

Follow VBODMAS rule: Vinculum, Bracket, Of, Division, Multiplication, Addition, Subtraction.

⇒ 96 + (19 × 2) − 38 + 42 ÷ 6 + 28 − 16

⇒ 96 + 38 − 38 + (42 ÷ 6) + 28 − 16

⇒ 96 + 38 − 38 + 7 + 28 − 16

⇒ (96 + 38 + 7 + 28) − (38 + 16)

⇒ 169 − 54

⇒ 115

∴ The correct answer is 115.

Additional Information

VBODMAS Rule

This acronym helps remember the order of operations: Vinculum (Bar), Brackets ((), {}, []), Of, Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Precedence of 'Of'

In mathematical expressions, the 'Of' operator is equivalent to multiplication but must be performed before division and general multiplication.

Shortcut Trick

Convert the range and options into decimals for quick comparison.

Range: 2 1/4 = 2.25 and 2 3/4 = 2.75.

Option (1) 2.9 | Option (2) 2.625 | Option (3) 2.77 | Option (4) 2.83.

Only 2.625 lies between 2.25 and 2.75.

∴ The correct answer is 2 5/8.

Alternate Method

Given:

Lower Limit = 2 1/4

Upper Limit = 2 3/4

Calculations:

⇒ Lower Limit = 2 + 1/4 = 2 + 0.25 = 2.25

⇒ Upper Limit = 2 + 3/4 = 2 + 0.75 = 2.75

⇒ Option (1): 2 9/10 = 2 + 0.9 = 2.9 (Outside range)

⇒ Option (2): 2 5/8 = 2 + 0.625 = 2.625 (Inside range)

⇒ Option (3): 2 7/9 = 2 + 0.777... ≈ 2.78 (Outside range)

⇒ Option (4): 2 5/6 = 2 + 0.833... ≈ 2.83 (Outside range)

⇒ Comparing 2.25 < 2.625 < 2.75.

∴ The correct answer is 2 5/8.

Additional Information

Comparing Rational Numbers

To compare fractions, either convert them to decimals or bring them to a common denominator by finding the LCM of denominators.

Mixed Fraction Conversion

A mixed fraction A b/c is converted to an improper fraction using the formula (A × c + b) / c.

Density Property

Between any two rational numbers, there are infinitely many rational numbers that can be found by taking their average or interpolating between them.

Shortcut Trick

Directly calculate the square roots: √169 = 13, √121 = 11, and √64 = 8.

Apply the calculation: X = (13 × 11) + 8 = 143 + 8 = 151.

Find the required value: 2X = 2 × 151 = 302.

∴ The correct answer is 302.

Alternate Method

Given:

X = √169 × √121 + √64

Method Used:

Apply the BODMAS rule and Square Root simplification.

Calculations:

⇒ X = 13 × 11 + 8

⇒ X = 143 + 8

⇒ X = 151

⇒ 2X = 2 × 151

⇒ 2X = 302

∴ The correct answer is 302.

Additional Information

BODMAS Rule

It stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction. Operations must be performed in this specific sequence.

Perfect Squares

Squares of numbers from 11 to 15: 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225.

Multiplication Trick

To multiply any two-digit number by 11, add the two digits and place the sum in between them (e.g., 13 × 11 → 1, (1+3), 3 → 143).

Shortcut Trick

For a square, the Perimeter is four times its Side.

Side = Perimeter ÷ 4

Side = 40 ÷ 4 = 10 cm

∴ The correct answer is 10 cm.

Alternate Method

Given:

Perimeter of the square = 40 cm

Formula Used:

Perimeter of a square = 4 × Side (a)

Calculations:

⇒ Let the side of the square be a cm.

⇒ 4 × a = 40

⇒ a = 40 ÷ 4

⇒ a = 10 cm

∴ The correct answer is 10 cm.

Additional Information

Area of Square

The total surface area covered by the square is Area = Side × Side = a².

Diagonal of Square

The length of the diagonal connecting two opposite vertices is Diagonal = a√2.

Properties of Square

In a square, all four sides are equal, and each interior angle is exactly 90°.

Shortcut Trick

Area of a rectangle = Length × Breadth

⇒ Area = 9 × 4 = 36 cm²

∴ The correct answer is 36 cm².

Alternate Method

Given:

Length of the rectangle = 9 cm

Breadth of the rectangle = 4 cm

Formula Used:

Area = Length × Breadth

Calculations:

⇒ Area = 9 cm × 4 cm

⇒ Area = 36 cm²

∴ The correct answer is 36 cm².

Additional Information

Perimeter of a Rectangle

The total boundary length is given by Perimeter = 2 × (length + breadth).

Diagonal of a Rectangle

The distance between opposite vertices is Diagonal = √(length² + breadth²).

Properties of a Rectangle

All interior angles are 90°, opposite sides are equal and parallel, and diagonals bisect each other.

Shortcut Trick

Check divisibility of 4: Last two digits must be divisible by 4.

Check divisibility of 9: Sum of all digits must be divisible by 9.

Option 1: 4170 → 70 is not divisible by 4.

Option 2: 4128 → Sum of digits (4+1+2+8 = 15) is not divisible by 9.

Option 3: 4092 → Sum of digits (4+0+9+2 = 15) is not divisible by 9.

Option 4: 4032 → 32 ÷ 4 = 8 and Sum (4+0+3+2 = 9) is divisible by 9.

∴ The correct answer is 4032.

Alternate Method

Given: Numbers 4170, 4128, 4092, 4032.

Rules Applied: Divisibility rule of 4 (last two digits) and Divisibility rule of 9 (sum of digits).

⇒ Check 4170: Last two digits 70 ÷ 4 = 17.5 (Not divisible). Sum = 4+1+7+0 = 12 (Not divisible by 9).

⇒ Check 4128: Last two digits 28 ÷ 4 = 7 (Divisible). Sum = 4+1+2+8 = 15 (Not divisible by 9).

⇒ Check 4092: Last two digits 92 ÷ 4 = 23 (Divisible). Sum = 4+0+9+2 = 15 (Not divisible by 9).

⇒ Check 4032: Last two digits 32 ÷ 4 = 8 (Divisible). Sum = 4+0+3+2 = 9 (Divisible by 9).

∴ The correct answer is 4032.

Additional Information

Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is a multiple of 3.

Divisibility Rule of 8

A number is divisible by 8 if the last three digits of the number are divisible by 8.

Divisibility Rule of 6

A number is divisible by 6 if it is divisible by both 2 and 3 (i.e., it is an even number and its digit sum is divisible by 3).

Divisibility Rule of 11

The difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.

Shortcut Trick

√1156 = 34 (since 30² = 900 and 40² = 1600)

√0.36 = 0.6 (6² = 36, half the decimal places)

√0.0025 = 0.05 (5² = 25, half the decimal places)

Total Sum = 34 + 0.6 + 0.05 = 34.65

∴ The correct answer is 34.65.

Alternate Method

Given Expression: √1156 + √0.36 + √0.0025

Using Fractional Conversion for decimal terms:

⇒ √1156 = 34

⇒ √0.36 = √(36 ÷ 100) = 6 ÷ 10 = 0.6

⇒ √0.0025 = √(25 ÷ 10000) = 5 ÷ 100 = 0.05

⇒ Required Value = 34 + 0.6 + 0.05

⇒ Sum = 34.65

∴ The correct answer is 34.65.

Additional Information

Square Root of Decimals

When calculating the square root of a decimal, if the number has 2n decimal places, the result will have n decimal places.

Perfect Square Identification

A perfect square cannot end with the digits 2, 3, 7, or 8. Numbers ending in 6 will have square roots ending in either 4 or 6.

Squares Ending in 5

For any number (n5)², the result is always [n × (n+1)] followed by 25. Example: 35² = (3 × 4)25 = 1225.

Shortcut Trick

A number divisible by 36 must be divisible by both 4 and 9 (36 = 4 × 9).

Check the divisibility rule of 9 (sum of digits) for the options:

(1) 1036: 1+0+3+6 = 10 | (2) 1008: 1+0+0+8 = 9 | (3) 1016: 1+0+1+6 = 8 | (4) 1028: 1+0+2+8 = 11.

Only 1008 is divisible by 9 and its last two digits (08) are divisible by 4.

∴ The correct answer is 1008.

Alternate Method

Given:

Smallest 4-digit number = 1000

Divisor = 36

Method:

Divide the smallest 4-digit number by 36 to find the remainder, then adjust to find the next multiple.

Calculations:

⇒ 1000 ÷ 36

⇒ 36 × 27 = 972

⇒ Remainder = 1000 − 972 = 28

⇒ To find the next multiple, add (Divisor − Remainder) to the number.

⇒ Adjustment = 36 − 28 = 8

⇒ Smallest 4-digit multiple = 1000 + 8 = 1008

∴ The correct answer is 1008.

Additional Information

Divisibility Rule of 9

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

Divisibility Rule of 4

A number is divisible by 4 if its last two digits are divisible by 4 or are both zero.

Smallest n-digit Multiple

Smallest multiple = Smallest n-digit number + (Divisor − Remainder), where the remainder comes from dividing the smallest n-digit number by the divisor.

Shortcut Trick

The average (p) of any data set must be greater than or equal to the smallest number and less than or equal to the largest number.

Given the smallest number is 25, the average p ≥ 25 and the largest number ≥ 25.

Since the total number of elements and their specific values are unknown, p and the largest number can vary infinitely.

Fixed values like p = 27 or Largest = 35 are only specific possibilities, not universal truths.

∴ The correct answer is Neither I nor II.

Alternate Method

Given: Smallest value in the set = 25. Average of the set = p.

Formula Used: Average (p) = (Sum of all numbers) ÷ (Total count of numbers)

⇒ Let the set of numbers be {x₁, x₂, x₃, ..., x_n} where x₁ = 25.

⇒ If the set is {25, 25}, then Average p = 25. This contradicts Statement I (p = 27).

⇒ If the set is {25, 100}, then the largest number is 100. This contradicts Statement II (Largest = 35).

⇒ Since we can choose different sets that satisfy the condition (Smallest = 25), the average and largest values are not fixed.

⇒ Therefore, neither Statement I nor Statement II is always correct.

∴ The correct answer is Neither I nor II.

Additional Information

Properties of Arithmetic Mean

The average of a set of numbers always lies between the minimum and maximum values of the data set: Min ≤ Average ≤ Max.

Sum of Observations

The total sum of a data set can be calculated as Sum = Average × Number of observations.

Range of Data

The Range is the difference between the largest and the smallest value: Range = Max − Min.

Shortcut Trick

The smallest number is obtained by subtracting the increment from the LCM of the given divisors.

LCM of 5, 6, and 8 ⇒ 120.

Required number = LCM − 17.

Number = 120 − 17 = 103.

∴ The correct answer is 103.

Alternate Method

Given: Divisors are 5, 6, and 8. The number is increased by 17 to become divisible.

Formula Used: Required Number = [LCM(a, b, c)] − k (where k is the increment).

⇒ Prime factorization of divisors:

⇒ 5 = 5¹

⇒ 6 = 2 × 3

⇒ 8 = 2³

⇒ LCM(5, 6, 8) = 2³ × 3 × 5 = 8 × 3 × 5 = 120.

⇒ According to the problem: Number + 17 = 120

⇒ Number = 120 − 17

⇒ Number = 103.

∴ The correct answer is 103.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by each of the given numbers. It is used to find a common scale for different periodic events.

General Remainder Rule

If the number leaves a remainder 'r' when divided by a, b, and c, the smallest such number is LCM(a, b, c) + r.

Common Difference Rule

If the number leaves remainders r₁, r₂, r₃ such that (a−r₁) = (b−r₂) = (c−r₃) = k, then the number is LCM(a, b, c) − k.

HCF vs LCM Relation

For two numbers A and B: HCF(A, B) × LCM(A, B) = A × B.

Shortcut Trick

Find the LCM of 8 and 7 to get the smallest number divisible by both.

LCM(8, 7) = 8 × 7 = 56 (since they are co-prime).

The next multiple is 56 × 2 = 112, which is a 3-digit number.

Thus, the largest 2-digit number divisible by both is 56.

∴ The correct answer is 56.

Alternate Method

Given:

Divisors = 8 and 7

Target = Largest 2-digit number exactly divisible by both.

Formula Used:

A number divisible by multiple numbers is also divisible by their Least Common Multiple (LCM).

Calculations:

⇒ Step 1: Calculate the LCM of 8 and 7.

⇒ Prime factorization of 8 = 2 × 2 × 2

⇒ Prime factorization of 7 = 7

⇒ LCM(8, 7) = 2³ × 7 = 56

⇒ Step 2: List the multiples of 56 to find the largest 2-digit one.

⇒ 56 × 1 = 56

⇒ 56 × 2 = 112

⇒ Since 112 is a 3-digit number and the maximum 2-digit number is 99, 112 is excluded.

⇒ The largest 2-digit multiple is therefore 56.

∴ The correct answer is 56.

Additional Information

Least Common Multiple (LCM)

The smallest positive integer that is a multiple of two or more numbers. For co-prime numbers (numbers with HCF = 1), the LCM is always the product of the numbers.

Co-prime Numbers Property

If a and b are co-prime, then any number divisible by both a and b must also be divisible by their product (a × b).

Divisibility Rule of 8 and 7

A number is divisible by 8 if its last three digits are divisible by 8. For 7, subtract twice the last digit from the remaining number; if the result is divisible by 7, the original number is too.

Shortcut Trick

Ratio of A : B = 1 : 5

Value of B is 5 units and A is 1 unit.

Difference = 5 − 1 = 4 units.

Percentage less = (Difference ÷ Value of B) × 100 = (4 ÷ 5) × 100 = 80%.

∴ The correct answer is 80 percent.

Alternate Method

Given:

A = (1/5) × B

Calculation:

⇒ A / B = 1 / 5

⇒ Let B = 5x and A = 1x

⇒ Difference = B − A = 5x − 1x = 4x

⇒ Percentage less = (Difference ÷ B) × 100

⇒ Percentage less = (4x ÷ 5x) × 100

⇒ Percentage less = (4 ÷ 5) × 100 = 80%

∴ The correct answer is 80 percent.

Additional Information

Percentage Decrease Formula

Percentage Less = [(Reference Value − Target Value) ÷ Reference Value] × 100.

Fraction to Percentage Conversion

To convert any fraction x/y into percentage, multiply the fraction by 100 (e.g., 1/5 × 100 = 20%).

Complementary Percentages

If A is 20% of B, then A is (100% − 20%) = 80% less than B.

Shortcut Trick

Profit = 920 − 800 = ₹120

Profit % = (Profit ÷ CP) × 100

Profit % = (120 ÷ 800) × 100 = 15%

∴ The correct answer is 15%.

Alternate Method

Given:

Cost Price (CP) of the article = ₹800

Selling Price (SP) of the article = ₹920

Formula Used:

Profit = Selling Price (SP) − Cost Price (CP)

Profit Percentage = (Profit ÷ Cost Price (CP)) × 100

Calculations:

⇒ Profit = 920 − 800

⇒ Profit = ₹120

⇒ Profit Percentage = (120 ÷ 800) × 100

⇒ Profit Percentage = (12 ÷ 80) × 100

⇒ Profit Percentage = (3 ÷ 20) × 100

⇒ Profit Percentage = 3 × 5 = 15%

∴ The correct answer is 15%.

Additional Information

Loss Percentage

When the Cost Price (CP) is greater than the Selling Price (SP), a loss occurs. Loss% = [(CP − SP) ÷ CP] × 100.

Marked Price and Discount

Marked Price (MP) is the price printed on an item. Discount is always calculated on the MP. SP = MP − Discount.

Relation between CP and SP

SP = CP × [(100 + Profit%) ÷ 100] for profit cases, and SP = CP × [(100 − Loss%) ÷ 100] for loss cases.

Shortcut Trick

If both the Cost Price (CP) and Selling Price (SP) are multiplied or divided by the same factor (or decreased/increased by the same percentage), the ratio between them remains unchanged.

Since both CP and SP are decreased by 50%, they are both halved, keeping the ratio CP : SP constant.

Original ratio ⇒ CP : SP = 100 : 60 (for a 40% loss).

New ratio ⇒ 50 : 30 = 100 : 60.

Because the ratio is unchanged, the loss percentage remains 40%.

∴ The correct answer is 40 percent.

Alternate Method

Given: Initial Loss % = 40%, Reduction in CP and SP = 50%.

Formula Used: Loss % = [(CP − SP) ÷ CP] × 100

⇒ Let the initial Cost Price (CP₁) = 100.

⇒ Initial Selling Price (SP₁) = CP₁ − 40% of CP₁ = 100 − 40 = 60.

⇒ New Cost Price (CP₂) = 100 − 50% of 100 = 50.

⇒ New Selling Price (SP₂) = 60 − 50% of 60 = 30.

⇒ New Loss Amount = CP₂ − SP₂ = 50 − 30 = 20.

⇒ New Loss Percentage = (New Loss ÷ CP₂) × 100

⇒ New Loss Percentage = (20 ÷ 50) × 100 = 40%.

∴ The correct answer is 40 percent.

Additional Information

Profit and Loss % Invariance

The profit or loss percentage remains unchanged if both the Cost Price and Selling Price are multiplied or divided by the same non-zero constant (constant ratio).

Loss Percentage Formula

Loss % is calculated as (Loss ÷ CP) × 100. It measures the loss relative to the initial investment (CP).

Successive Changes in CP and SP

If CP changes by x% and SP changes by y%, the new profit/loss % must be calculated using the new values: New % = [(SP × (1+y/100) − CP × (1+x/100)) ÷ (CP × (1+x/100))] × 100.

Shortcut Trick

Ratio of marks P : Q : R = 80 : 100 : 50 = 8 : 10 : 5

Total sum of ratio units = 8 + 10 + 5 = 23 units

Given 23 units = 2300 → 1 unit = 100

Difference between Q and R = 10 − 5 = 5 units

Required difference = 5 × 100 = 500

∴ The correct answer is 500.

Alternate Method

Given:

Marks of P = Q − 20% of Q = 0.8Q

Marks of R = Q − 50% of Q = 0.5Q

Sum of marks (P + Q + R) = 2300

Calculations:

⇒ 0.8Q + 1.0Q + 0.5Q = 2300

⇒ 2.3Q = 2300

⇒ Q = 2300 ÷ 2.3 = 1000

⇒ R = 0.5 × 1000 = 500

⇒ Difference = Q − R = 1000 − 500 = 500

∴ The correct answer is 500.

Additional Information

Percentage to Ratio Conversion

Comparing values by converting percentages to units simplifies calculations significantly in competitive exams.

Percentage Change Formula

Final Value = Initial Value × (100 ± x)/100, where x is the percentage increase or decrease.

Difference between Values

The difference between two quantities can be found directly from their ratio parts without calculating individual values first: Difference = (Diff in parts ÷ Sum of parts) × Total Sum.

Shortcut Trick

Total work capacity = 25 men × 60 days = 1500 units.

Target work (50% work) = 1500 ÷ 2 = 750 units.

Days required for 15 men = 750 ÷ 15 = 50 days.

∴ The correct answer is 50 days.

Alternate Method

Given:

Initial men (M₁) = 25 men

Initial days (D₁) = 60 days

Target men (M₂) = 15 men

Work ratio = W₁ is 1, W₂ is 0.5 (50 percent)

Formula Used:

(M₁ × D₁) ÷ W₁ = (M₂ × D₂) ÷ W₂

Calculations:

⇒ (25 × 60) ÷ 1 = (15 × D₂) ÷ 0.5

⇒ 1500 = 30 × D₂

⇒ D₂ = 1500 ÷ 30

⇒ D₂ = 50 days

∴ The correct answer is 50 days.

Additional Information

Chain Rule Formula

Used to solve problems with multiple variables: (M₁×D₁×H₁)/W₁ = (M₂×D₂×H₂)/W₂, where M is men, D is days, H is hours, and W is work.

Work and Efficiency

Efficiency is inversely proportional to the time taken to complete the work (Efficiency ∝ 1/Time).

Man-Days Concept

Total work is the product of the number of workers and the time they work (Work = Men × Days).

Shortcut Trick

Ratio of total work done (and thus wages) is Efficiency × Days.

Ratio of shares (R : M : T) = (1 × 4) : (2 × 6) : (3 × 8) = 4 : 12 : 24 = 1 : 3 : 6.

Total units = 1 + 3 + 6 = 10 units → ₹540.

1 unit = ₹54 ∴ M's share = 3 units = 3 × ₹54 = ₹162.

∴ The correct answer is ₹162.

Alternate Method

Given:

Time worked by R = 4 days, M = 6 days, T = 8 days.

One day work (Efficiency) ratio R : M : T = 1 : 2 : 3.

Total amount distributed = ₹540.

Formula Used:

Individual Wage = (Efficiency × Number of Days worked)

Calculations:

⇒ Total work done by R = 1 × 4 = 4 units

⇒ Total work done by M = 2 × 6 = 12 units

⇒ Total work done by T = 3 × 8 = 24 units

⇒ Ratio of shares = 4 : 12 : 24

⇒ Simplify ratio by dividing by 4: 1 : 3 : 6

⇒ Let shares be x, 3x, and 6x

⇒ x + 3x + 6x = 540

⇒ 10x = 540

⇒ x = 54

⇒ Share of M = 3x = 3 × 54 = 162

∴ The correct answer is ₹162.

Additional Information

Work and Wages Concept

Wages are distributed in the ratio of the total work done by each person. Work Done = Efficiency × Time.

Efficiency and Time Relationship

If work is constant, Efficiency is inversely proportional to Time (E ∝ 1/T). However, for wages, we always use the actual units of work completed.

Ratio Distribution

To find a specific share from a total: Share = (Individual Ratio Part ÷ Sum of Ratio Parts) × Total Amount.

Shortcut Trick

Convert speed from km/hr to m/s: 72 × (5/18) = 20 m/s.

Total Distance = Train length + Platform length = 180 + 120 = 300 m.

Time taken = Total Distance ÷ Speed = 300 ÷ 20 = 15 sec.

∴ The correct answer is 15 sec.

Alternate Method

Given:

Speed of the train = 72 km/hr

Length of the train = 180 m

Length of the platform = 120 m

Formula Used:

Speed = Distance ÷ Time

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

Calculations:

⇒ Speed in m/s = 72 × (5/18)

⇒ Speed = 4 × 5 = 20 m/s

⇒ Total Distance to be covered = Length of train + Length of platform

⇒ Total Distance = 180 + 120 = 300 m

⇒ Time = Distance ÷ Speed

⇒ Time = 300 ÷ 20

⇒ Time = 15 sec

∴ The correct answer is 15 sec.

Additional Information

Unit Conversion

To convert Speed from km/hr to m/s, multiply by 5/18. To convert from m/s to km/hr, multiply by 18/5.

Crossing Stationary Objects

When a train crosses a stationary object with length (like a bridge or platform), the total distance is (Length of train + Length of object). For a point object (like a pole), distance equals the length of the train.

Relative Speed

When two objects move in the same direction, relative speed is (S₁ − S₂). In opposite directions, it is (S₁ + S₂).

Shortcut Trick

Total distance covered in 10 minutes at 60 km/hr = 60 × (10/60) = 10 km.

Total distance = 10,000 m.

Since the Length of the Train and the Platform are equal:

2 × Platform Length = 10,000 m.

Platform Length = 10,000 ÷ 2 = 5,000 m.

∴ The correct answer is 5000 m.

Alternate Method

Given:

Speed of Train = 60 km/hr

Time taken to cross = 10 minutes

Length of Train (L_t) = Length of Platform (L_p)

Formula Used:

Distance = Speed × Time

Total Distance = L_t + L_p

Calculations:

⇒ Let L_t = L_p = L

⇒ Total Distance = L + L = 2L

⇒ Speed in m/s = 60 × (5/18) = 50/3 m/s

⇒ Time in seconds = 10 × 60 = 600 s

⇒ Distance = (50/3) × 600

⇒ 2L = 50 × 200

⇒ 2L = 10,000

⇒ L = 5,000 m

∴ The correct answer is 5000 m.

Additional Information

Unit Conversion

To convert speed from km/hr to m/s, multiply by 5/18. To convert from m/s to km/hr, multiply by 18/5.

Relative Distance

When a train crosses a stationary object of length 'P', the total distance covered is (Length of train + P). If it crosses a point object (pole/man), the distance is just the Length of the train.

Time, Speed, and Distance

The fundamental relation is Distance = Speed × Time. Ensure all variables are in consistent units (e.g., metres and seconds, or km and hours) before calculating.

The correct answer is: under another's authoritarian control; continually forced to submit to another's will.

Key Points

• The idiom 'under the thumb of someone' refers to a person who is completely controlled or dominated by someone else, often in a way that limits their freedom. (किसी के पूर्ण नियंत्रण में होना)
• Example: Even after moving out, he remained under the thumb of his overbearing parents.
• The phrase 'under another's authoritarian control; continually forced to submit to another's will' accurately describes the state of being dominated or dictated to by another person or entity. (किसी दूसरे के सत्तावादी नियंत्रण में होना; किसी दूसरे की इच्छा के आगे झुकने के लिए निरंतर मजबूर होना)
• Example: The workers felt they were under another's authoritarian control, having no say in the new company policies.
• Hence, we can infer that the meaning of the idiom 'under the thumb of someone' is being under someone's authoritarian control.

Therefore, the correct answer is- under another's authoritarian control; continually forced to submit to another's will.

Additional Information

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

• To be viewed with suspicion, distrust, or disapproval (संदेह, अविश्वास या नामंजूरी की दृष्टि से देखा जाना): This is often described by the idiom 'under a cloud'.
• Example: Since the accounting error was discovered, the manager has been under a cloud of suspicion.
• To come under the protection, tutelage, nurture, or care of someone (किसी के संरक्षण, शिक्षा या देखभाल के अंतर्गत आना): This is often described by the idiom 'under someone's wing'.
• Example: The experienced professor took the young researcher under her wing to help him publish his first paper.
• To be controlled or afflicted by a magical enchantment (जादुई मंत्र या प्रभाव के वश में होना): This is often described by the phrase 'under a spell'.
• Example: In the legend, the knight was under a spell that made him sleep for a hundred years.

The correct answer is: Behave badly or show contempt toward.

Key Points

• The idiom 'treat like dirt' means to behave towards someone in a very mean, disrespectful, or insulting way, often as if they are worthless. (बहुत बुरा व्यवहार करना या तिरस्कार करना)
• Example: Despite her years of loyal service to the company, her manager continued to treat her like dirt in front of her colleagues.
• 'Behave badly or show contempt toward' refers to acting in an improper, offensive, or disrespectful manner towards another person, showing that you consider them beneath consideration or deserving of scorn. (बुरा व्यवहार करना या अवमानना दिखाना)
• Example: It is never acceptable to behave badly or show contempt toward people just because they have a different opinion.
• Hence, we can infer that the meaning of the idiom 'treat like dirt' is to 'behave badly or show contempt toward'.

Therefore, the correct answer is- Behave badly or show contempt toward.

Additional Information

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

• To discuss very private, personal matters, especially that which may be embarrassing, in public or with other people (सार्वजनिक रूप से निजी या शर्मनाक मामलों पर चर्चा करना): This describes the idiom 'wash one's dirty linen in public'.
• Example: The couple's argument escalated until they were washing all their dirty linen in public, much to the discomfort of their neighbors.
• To find negative information that has been concealed (छिपी हुई नकारात्मक जानकारी का पता लगाना): This describes the idiom 'dig up dirt'.
• Example: During the election, both parties hired private investigators to dig up dirt on their opponents' pasts.
• To discover or come upon something very, particularly, or abundantly valuable or useful, especially after a long or arduous search (कुछ बहुत मूल्यवान या उपयोगी खोजना): This is often associated with the phrase 'strike gold' or 'strike it rich'.
• Example: After years of unsuccessful attempts, the archaeologists finally struck gold when they found the hidden tomb.

The correct answer is: Nemesis.

Key Points

• The word 'Nemesis' refers to an inescapable agent of someone's or something's downfall, or a long-standing rival or arch-enemy. (अपरिहार्य दंड)
• Example: In the final chapter of the novel, the protagonist finally confronts his nemesis.
• 'Nemesis' is correctly spelled in this context and represents the standard English orthography for the noun meaning a persistent source of harm or failure. (सही वर्तनी)
• Example: The high-speed corners of the track proved to be the racing driver's nemesis.
• Hence, we can infer that among the given options, the word 'Nemesis' is correctly spelled.

Therefore, the correct answer is: Nemesis.

Additional Information

Here are the other options explained along with their meanings and correct spellings:

• Nascent (incorrectly spelled as Nasient) (विकासोन्मुख): Something that is just coming into existence and beginning to display signs of future potential.
• Example: The nascent space tourism industry is attracting a lot of global interest.
• Niche (उपयुक्त स्थान): A specialized segment of the market for a particular kind of product or service, or a comfortable position in life.
• Example: After years of searching, she finally found her niche in environmental law.
• Nuance (incorrectly spelled as Nuence) (सूक्ष्म अंतर): A subtle difference in or shade of meaning, expression, or sound.
• Example: He was able to capture every nuance of the character's complex emotions in his performance.

The correct answer is: Discover.

Key Points

• The word 'find' means to locate or encounter something or someone by chance or through a deliberate search. (खोजना/पाना)
• Example: It took me several hours to find the specific reference in the library.
• 'Discover' means to find something unexpectedly or to be the first to learn about its existence, which makes it the closest synonym to 'find'. (पता लगाना/खोजना)
• Example: The researchers were excited to discover a new species of flora in the rainforest.
• Hence, we can conclude that the word closest in meaning to 'find' is 'Discover'.

Therefore, the correct answer is- Discover.

Additional Information

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

• lose (खोना): To be deprived of or to be unable to find something you once had.
• Example: Please be careful not to lose your passport while traveling abroad.
• Hide (छिपाना): To put or keep something out of sight to prevent it from being found.
• Example: The child tried to hide the broken toy behind the sofa.
• Forget (भूलना): To fail to remember or recall something.
• Example: I often forget where I parked my car in large shopping malls.

The correct answer is Option (1) i.e. Zeastfu.

Key Points

• The word 'Zeastfu' is the misspelt word among the given options. There is no such word in the English language. (गलत वर्तनी)
• Example: The student realized that 'Zeastfu' was a typo and not a valid English word.
• 'Zestful' is the correct spelling of the intended word, which means to be full of energy, enthusiasm, or excitement. (उत्साहपूर्ण)
• Example: The children were zestful and eager to start their summer vacation.
• Hence, we can identify that 'Zeastfu' is incorrectly spelled.

Therefore, the correct answer is: Zeastfu.

Additional Information

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

• Zealously (उत्साहपूर्वक): Doing something with great energy or enthusiasm in pursuit of a cause or objective.
• Example: The activist zealously campaigned for better healthcare facilities in rural areas.
• Zoologist (प्राणीविज्ञानी): An expert who studies the behavior, physiology, and classification of animals.
• Example: As a zoologist, she spent years researching the social structures of African elephants.
• Zodiac (राशि-चक्र): A belt of the heavens within which the sun, moon, and planets move, divided into twelve signs.
• Example: Many people believe that their zodiac sign can influence their personality traits.

The correct answer is: Energetic.

Key Points

• The word 'Exhausted' refers to a state of being completely drained of physical or mental resources; feeling extremely tired or spent. (थका हुआ)
• Example: After the marathon, the runners were completely exhausted and needed immediate rest.
• 'Energetic' describes someone or something that has or shows great vitality, enthusiasm, or physical power; it is the opposite of being tired or drained. (ऊर्जावान)
• Example: She felt energetic and ready to tackle her new project after a refreshing vacation.
• Hence, we can infer that the opposite of 'Exhausted' is 'Energetic'.

Therefore, the correct answer is: Energetic.

Additional Information

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

• Tired (थका हुआ): In need of sleep or rest; weary.
• Example: He was too tired to continue reading his book.
• Fatigued (थका हुआ / क्लांत): Feeling overtired, with low energy and a strong desire to sleep.
• Example: The long journey across the desert left the travelers deeply fatigued.
• Weary (थका हुआ): Feeling or showing extreme tiredness, especially as a result of excessive exertion.
• Example: The weary soldiers finally returned home after months of service.

The correct answer is: Cosmopolitan.

Key Points

• The phrase 'One who regards the entire world as their country' refers to an individual who has a global outlook and does not limit their sense of belonging to a single nation or region. (वह व्यक्ति जो पूरी दुनिया को अपना देश मानता है)
• Example: With his deep understanding of various cultures, he lives his life as someone who considers the entire world his home.
• 'Cosmopolitan' describes a person who is familiar with and at ease in many different countries and cultures, reflecting a universal rather than a local perspective. (सर्वदेशीय)
• Example: A cosmopolitan traveler feels equally comfortable in the bustling streets of Tokyo as they do in the cafes of Paris.
• Hence, we can infer that the one-word substitution for the given phrase is 'cosmopolitan'.

Therefore, the correct answer is: Cosmopolitan.

Additional Information

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

• Convalescent (स्वास्थ्य-लाभ करनेवाला): A person who is recovering from an illness or medical operation.
• Example: The convalescent patient was moved to a quiet room to ensure a speedy recovery.
• Cynosure (आकर्षण का बिंदु): A person or thing that is the center of attention or admiration.
• Example: The magnificent diamond was the cynosure of the entire jewelry exhibition.
• Contemporary (समकालीन): A person or thing living or occurring at the same time as another.
• Example: Although they worked in different countries, the two scientists were contemporaries in the field of physics.

The correct answer is: stoic.

Key Points

• The phrase 'One who does not care about the pains and pleasures of life' refers to an individual who maintains a state of indifference or detachment towards emotional or physical distress as well as happiness. (दुख और सुख के प्रति उदासीन)
• Example: Ancient philosophers often practiced mindfulness to become individuals who do not care about the pains and pleasures of life.
• 'Stoic' describes a person who can endure pain or hardship without showing their feelings or complaining, remaining calm and indifferent to external circumstances. (वैरागी या सुख-दुख में समान रहने वाला)
• Example: Even after losing his business, he remained stoic and started working on a new plan immediately.
• Hence, we can infer that the one-word substitute for 'one who does not care about the pains and pleasures of life' is 'stoic'.

Therefore, the correct answer is: stoic.

Additional Information

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

• Epicure (चटोरा / स्वादलोलुप): A person who takes particular pleasure in fine food and drink.
• Example: My brother is a true epicure; he can identify every spice used in a dish just by tasting it.
• Fatalist (भाग्यवादी): A person who believes that all events are predetermined and therefore inevitable.
• Example: Being a fatalist, he believed that his failure in the exam was destined to happen regardless of his preparation.
• Coquette (नखरेबाज / मोहिनी): A woman who flirts with men to get their attention without having sincere feelings for them.
• Example: She was known as a coquette in the social circles for her playful and flirtatious behavior.

The correct answer is 'with'.

 

Key Points

• The verb comply means to act in accordance with a wish, command, rule, or law.
• In English grammar, comply is a prepositional verb that is followed by the fixed preposition with.
• The phrase comply with is used when referring to following the law, regulations, or orders.
• In the given sentence, the requirement is to follow the law of the land, so with is the appropriate choice.

Therefore, the correct answer is Option 2.

 

Complete Sentence: "Citizens ought to comply with the law of the land; otherwise, they must get ready for the consequences."

 

Additional Information

• Abide by: We use the preposition by with the verb abide to mean the same thing (e.g., abide by the law).
• Adhere to: We use the preposition to with the verb adhere (e.g., adhere to the rules).
• Options 1, 3, and 4 are incorrect because they do not form the standard idiomatic expression with the verb comply.

The correct answer is The new strategic plan for the company has been approved by the board..

Key Points

• The original sentence 'The board has approved the new strategic plan for the company' is in the Active Voice and utilizes the Present Perfect Tense.
• In an active sentence, the subject ('The board') performs the action, while in a passive sentence, the focus shifts to the Object ('The new strategic plan for the company') receiving the action.
• The specific grammatical rule for converting Present Perfect Tense into Passive Voice is: Object + has/have + been + V3 (Past Participle) + by + Subject.
• In this transformation, the singular object 'The new strategic plan' necessitates the use of the auxiliary verb 'has' followed by 'been' and the past participle 'approved'.
• The preposition 'by' is introduced to connect the action back to the original agent, 'the board'.
• By following these linguistic rules, the sentence maintains its original meaning and tense while correctly shifting the voice.

 Additional Information

• Understanding Tense Mismatches in Passive Voice:
• Past Perfect Passive: The phrase 'had been approved' is used only if the active sentence is in the Past Perfect Tense (Subject + had + V3).
• Simple Past Passive: The phrase 'was approved' is appropriate only for Simple Past Tense active sentences (Subject + V2).
• Present Continuous Passive: The construction 'is being approved' is reserved for the Present Continuous Tense (Subject + is/am/are + V1 + ing).
• Subject-Verb Agreement: When converting to passive voice, the auxiliary verb (has/have) must always agree with the new subject (the former object).

The correct answer is The director was conducting the final rehearsal when the chief guest unexpectedly arrived..

Key Points

• The original sentence is written in the Passive Voice of the Past Continuous Tense, as indicated by the construction was being conducted.
• In English grammar, the Passive Voice structure for the Past Continuous Tense is: Object + was/were + being + V3 (Past Participle) + by + Subject.
• To convert this into the Active Voice, the agent of the action (the director) must become the grammatical subject of the sentence.
• The Active Voice formula for the Past Continuous Tense is: Subject + was/were + V1 + ing (Present Participle) + Object.
• Following this rule, the verb phrase was being conducted transforms into was conducting to maintain the progressive nature of the past action.
• The original subject, the final rehearsal, moves to the object position in the active sentence, receiving the action of the verb.
• The subordinate clause when the chief guest unexpectedly arrived is already in the active voice (Simple Past) and serves as a temporal marker; therefore, it remains unchanged during the transformation.

 Additional Information

• Grammatical Tense Analysis:
• Simple Past Tense: Option 1 uses conducted, which implies a completed fact rather than an ongoing action interrupted by the arrival of the guest.
• Past Continuous Tense: This tense is specifically used to describe actions that were in progress at a certain point in the past, often interrupted by another event (indicated by the Simple Past in the when-clause).
• Past Perfect Tense: Option 3 uses had conducted, suggesting that the rehearsal was entirely finished before the guest arrived, which changes the original meaning of the sentence.
• Future Tense: Option 4 uses will conduct, which is logically and grammatically incompatible with the past tense clause arrived.
• Subject-Verb Agreement: Since the director is a singular noun, the auxiliary verb was is correctly utilized instead of were.

The correct answer is People are expecting that the meeting will finish by 5 p.m..

Key Points

• The given sentence is in the Passive Voice of the Present Continuous Tense, which is identified by the construction is being expected (is/am/are + being + V3).
• In English grammar, when a sentence is converted from passive to Active Voice, the tense must remain consistent. Therefore, the active form must also be in the Present Continuous Tense (is/am/are + V-ing).
• The original sentence uses a dummy subject It because the actual agent (the people doing the expecting) is not specified. When converting to active voice, we introduce a generic plural subject like People.
• Since People is a plural noun, it requires the plural auxiliary verb are followed by the present participle form of the main verb, which is expecting.
• The subordinate clause that the meeting will finish by 5 p.m. serves as the object of the verb and remains unchanged during the voice conversion process.

 Additional Information

• Analysis of Incorrect Options:
• Tense Mismatch: Option 2 uses the Simple Past Tense (expected), and Option 4 uses the Future Tense (will expect). Both options are incorrect because they change the original timeframe of the action.
• Subject-Verb Agreement: Option 3 uses expects, which is a singular verb form. In standard English, the noun People is always treated as plural and must take the plural verb form (expect or are expecting).
• Impersonal Passive Construction: The structure It is being + V3 + that... is an impersonal passive. It is commonly used for reporting opinions, beliefs, or rumors. The active counterpart generally begins with People/They + active reporting verb.
• Active to Passive Rule: For continuous tenses, the word being is the essential indicator in the passive voice. Removing it and returning the verb to its -ing form is the standard procedure for restoring the active voice.

The correct answer is Option 4.

 

Key Points

• The error lies in the fourth part of the sentence: 'the train is going to come to the station within five min.'
• In the context of transportation and scheduled timings, the verb 'arrive' is much more appropriate and idiomatic than the verb 'come'.
• Additionally, the verb 'arrive' is typically followed by the preposition 'at' when referring to a specific location like a station (e.g., 'arrive at the station').
• Since the train schedule is a fixed future event, using the present simple or present continuous tense (e.g., 'is arriving' or 'arrives') is often preferred over 'is going to come'.
• Therefore, the phrase should be corrected to 'the train is arriving at the station' or 'the train will arrive at the station'.

Therefore, the correct answer is 4.

 

Correct Sentence: 'It is 14:25 hr now and the arrival time of the train is 14:30 hr, so we have to wait for five more min, and the train is arriving at the station within five min.'

 

Additional Information

• Option 1 is grammatically correct as it sets the current time.
• Option 2 correctly defines the scheduled time and uses the conjunction 'so' to show result/consequence.
• Option 3 correctly uses the phrasal structure 'wait for' and the duration 'five more min'.