SSC GD Constable 2026 Official Paper (Held On 29 May, 2026 Shift 1) (Previous Year Paper)

The logic followed here is,

67 + 7 = 74

74 + 7 = 81

81 = 7 = 88

88 + 7 = 95

95 + 7 = 102

102 + 7 = 109

109 + 7 = 116

Hence, the correct answer is 'Option 2';

Logic followed here is,

(−12 × 2) − 1 = −24 − 1 = −25

(−25 × 2) − 2 = −50 − 2 = −52

(−52 × 2) − 3 = −104 − 3 = −107

(−107 × 2) − 1 = −214 − 1 = −215

(−215 × 2) − 2 = −430 − 2 = −432

(−432 × 2) − 3 = −864 − 3 = −867

(−867 × 2) − 1 = −1734 − 1 = −1735

Missing term is -12.

Hence, the correct answer is “Option 2”.

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Pattern followed here is,

Hence, the correct answer is “Option 2”.

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Pattern followed here is,

Hence, the correct answer is “Option 2”.

Given that there are 5 cars A, B, M, S and T with different speeds.

From the clues, we can deduce the following relationships:

1. Speed of only three cars is more than A.

→ A is faster than only one car, so A is the 4th fastest.

→ _ > _ > _ > A > _

2. Speed of S is more than at least four cars.

→ S is faster than all the other four cars, so S is the fastest.

→ S > _ > _ > A > _

3. Speed of T is less than M and S. Speed of T is not the least.

→ Since A is already 4th, T cannot be 5th (least) and cannot be 4th (occupied by A).

→ Therefore, T must be the 3rd fastest.

→ S > _ > T > A > _

4. M is faster than T.

→ M must occupy the only remaining position above T.

→ S > M > T > A > B

Combining all these facts gives the final order from fastest to slowest:

→ S > M > T > A > B

Thus, M is faster than 3 cars (T, A and B).

Hence, the correct answer is "Option 3".

Given that there are 6 circles A, B, C, D, E and F with different diameters.

From the clues, we can deduce the following relationships:

1. Diameter of A is more than only E.

→ Only E has a smaller diameter than A.

→ A > E

2. Diameter of C is more than F but less than B.

→ B > C > F

3. Diameter of D is not more than F.

→ D < F

→ B > C > F > D

4. Since A is more than only E, all other circles (B, C, D and F) must have diameters greater than A.

→ B > C > F > D > A > E

Combining all these facts gives the final order from largest to smallest diameter:

→ B > C > F > D > A > E

Thus, the circle having the smallest diameter is E.

Hence, the correct answer is "Option 4".

Given that there are 6 girls P, Q, R, S, T and U with different marks.

From the clues, we can deduce the following relationships:

1. Marks of P are not less than anyone.

→ P has the highest marks.

2. Marks of U and R are both more than both S and T but less than Q.

→ P > Q > R, U > S, T

3. Marks of U = 300 and R = 400.

→ Since R has 400 marks and U has 300 marks, R > U.

Combining all these facts gives the final order from highest to lowest marks:

→ P > Q > R > U > S > T

Girls having more marks than R are:

→ P and Q

Therefore, the number of girls having more marks than R is 2.

Hence, the correct answer is "Option 3".

Family chart,

Family tree,

D is the Sister of C.

Hence, the correct answer is 'Option 1'.

Dictionary order of given word:

5. Drone
6. Drop
7. Dross
8. Drove
9. Drown

Correct order is: 53421

Hence, the correct answer is “Option 1”.

Dictionary order of given words,

4. Structure
5. Struggle
6. Strumatic
7. Strumpet
8. Strung

Correct order is: 41532

Hence, the correct answer is “Option 4”.

The logic followed here is:

Logic: Second Number = First Number − 49

For the first pair 5394 : 5345

⇒ 5394 − 49 = 5345.

Similarly, for the third pair 84 : 35

⇒ 84 − 49 = 35.

Applying the same logic to the second pair

3516 : ?

⇒ 3516 − 49 = 3467.

Hence, the correct answer is 'Option 1'.

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Pattern followed here is,

Hence, the correct answer is “Option 4”.

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Pattern followed here is,

Hence, the correct answer is “Option 3”.

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Pattern followed here is,

Hence, the correct answer is “Option 3”.

At 8:00 PM, the minute hand is at 0° and the hour hand is at 8 × 30° = 240°.

Let the hands be opposite to each other at M minutes past 8.

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

Angle covered by the hour hand in M minutes = 240 + 0.5 × M

For the hands to be opposite:

(240 + 0.5M) − 6M = 180

240 − 180 = 6M − 0.5M

60 = 5.5M

M = 60 / 5.5 = 120 / 11

M ≈ 10.91 minutes

Rounding to the nearest minute, we get 11 minutes.

Hence, the hands will be opposite at approximately 8:11 PM.

Alternate Method

The angle θ between the hour hand and minute hand is given by the formula:

$\theta = |{60H - 11M \over 2}|$

Where H = hours and M = minutes.

Given H = 8 and θ = 180°:

180 = |(60 × 8 − 11 × M) / 2|

360 = |480 − 11M|

Case 1: 360 = 480 − 11M

11M = 480 − 360

11M = 120

M = 120 / 11 ≈ 10.91

Case 2: −360 = 480 − 11M

11M = 480 + 360 = 840

M = 840 / 11 ≈ 76.36 (This value is greater than 60, so it is ignored).

Therefore, the time is approximately 8:11 PM.

Hence, the correct answer is 8:11.

Important Points

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 60 minutes = 30°

Angular distance covered by the hour hand in 1 minute = 30/60 = 1/2° (0.5°)

The minute hand covers 360° in 60 minutes.

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

Hands are opposite to each other when the angle between them is 180°.

The duration from 6:30 AM to 6:30 PM is 12 hours.

Initially, the clock is 8 minutes slow.

Finally, the clock is 4 minutes fast.

Total time gained by the clock = 8 minutes + 4 minutes = 12 minutes.

The clock gains 12 minutes in a total duration of 12 hours.

Gain per hour = 12 minutes ÷ 12 hours = 1 minute per hour.

For the clock to show the correct time, it must gain the 8 minutes it was initially slow.

Time required to gain 8 minutes = 8 minutes ÷ 1 minute/hour = 8 hours.

The time at which it shows the correct time = Start time + 8 hours.

Correct time = 6:30 AM + 8 hours = 2:30 PM.

Hence, the correct answer is 2:30.

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

The correct answer is Heavy industry.

Key Points

• The Second Five-Year Plan of India, covering the period from 1956 to 1961, was primarily focused on the development of the public sector and rapid industrialization.
• It was based on the Mahalanobis Model, formulated by the renowned Indian statistician Prasanta Chandra Mahalanobis, which emphasized the growth of capital goods to achieve long-term economic self-reliance.
• The plan shifted the national priority from agriculture, which was the focus of the First Plan, to heavy and basic industries like iron, steel, chemicals, and heavy engineering.
• The strategy aimed at import substitution, where India would produce its own industrial machinery and equipment rather than relying on foreign imports, thereby strengthening the domestic industrial base.
• Investment in this sector was intended to create a multiplier effect, generating employment and providing the necessary infrastructure for other sectors of the economy to grow.

 Additional Information

• Industrial Policy Resolution of 1956:
• This resolution was adopted to support the Second Plan's objectives, classifying industries into three categories and giving the State a leading role in industrial development.
• It led to the establishment of massive hydroelectric power projects and five new steel plants in Bhilai, Durgapur, and Rourkela with assistance from the USSR, UK, and West Germany respectively.
• Other Sectors in Context:
• Agriculture: While it was the top priority during the First Five-Year Plan (1951−1956) to address food shortages, it received a lower relative allocation in the Second Plan, which later led to a food crisis in the 1960s.
• Small-scale enterprises: The Karve Committee (1955) highlighted their importance for rural development, but the main budgetary thrust of the Second Plan remained on large-scale heavy industries.
• Services: This sector became a dominant driver of the Indian economy much later, particularly following the LPG reforms in 1991 and the Eighth Five-Year Plan.
• Atomic Energy Commission: Founded during this era under the leadership of Homi J. Bhabha, it marked India's early entry into high-technology industrial research.

The correct answer is Former Soviet Union.

Key Points

• The concept of Five-Year Plans (FYPs) in India was borrowed from the Union of Soviet Socialist Republics (USSR), commonly known as the Former Soviet Union.
• The Soviet Union was the first country in the world to implement a centralized economic plan, initiated by Joseph Stalin in 1928 to achieve rapid industrialization.
• Following India's independence, the first Prime Minister, Jawaharlal Nehru, who was deeply impressed by the socialist economic model and the success of centralized planning in the USSR, spearheaded the adoption of this system.
• To facilitate this, the Planning Commission of India was established on March 15, 1950, as a non-constitutional and advisory body to formulate the developmental strategies.
• The First Five-Year Plan was launched for the period 1951-1956, focusing primarily on the agricultural sector to ensure food security and address the refugee crisis and food shortages after partition.
• This planning model aimed at the balanced growth of the economy through the public sector, regulating resources to meet national priorities over five-year cycles.

 Additional Information

• Constitutional Borrowings from other Nations:
• United Kingdom: India adopted the Parliamentary form of government, the Rule of Law, Single Citizenship, and the Bicameralism system.
• United States of America: The Indian Constitution borrowed Fundamental Rights, Judicial Review, the Preamble, and the process of Removal of Supreme Court and High Court judges.
• France: The ideals of Liberty, Equality, and Fraternity inscribed in the Preamble and the Republican structure were taken from the French Constitution.
• Transition to NITI Aayog:
• The era of Five-Year Plans ended with the Twelfth Five-Year Plan (2012-2017).
• On January 1, 2015, the Planning Commission was replaced by the NITI Aayog (National Institution for Transforming India) to promote Cooperative Federalism and a Bottom-up approach.

The correct answer is Shifting cultivation.

Key Points

• The Gonds are one of the largest tribal communities in India, traditionally inhabiting the vast forested region known as Gondwana, which covers parts of Madhya Pradesh, Chhattisgarh, Maharashtra, and Odisha.
• Historically, the Gonds primarily practiced shifting cultivation, a traditional agricultural method where patches of forest land are cleared by felling trees and burning them.
• This practice is locally known by various names such as bewar, penda, or podu; the resulting ash acts as a natural fertilizer, providing essential nutrients like potash to the soil.
• Seeds are scattered in the ashes after the first monsoon rains, and the land is cultivated for a few years until the soil fertility declines significantly.
• Once the yield decreases, the Gond farmers abandon the current plot and move to a new area of the forest, allowing the previous land to lie fallow and recover its natural vegetation over several years.
• This mobile system of agriculture was central to their social structure and communal land ownership, where the village community managed the forest resources collectively under a Raja or Chieftain.

 Additional Information

• Terrace cultivation:
• Commonly practiced in mountainous regions like the Himalayas or the Western Ghats.
• It involves carving flat steps or terraces into steep slopes to create arable land and prevent soil erosion.
• Permanent farming:
• Also known as settled agriculture, where farmers cultivate the same piece of land year after year.
• While the Gonds were traditionally shifting cultivators, many transitioned to settled farming during the British colonial period due to changes in forest laws.
• Irrigation-based farming:
• A system that relies on the artificial application of water through canals, wells, or dams.
• This intensive method is typical of alluvial plains and was not the primary mode of the forest-dwelling Gond economy.

The correct answer is Executive power of the Union.

Key Points

• Article 53 of the Constitution of India establishes the framework for the Union Executive, declaring that the executive power shall be vested in the President.
• According to Article 53(1), this power is exercised by the President either directly or through officers subordinate to him, adhering strictly to the provisions of the Indian Constitution.
• The Supreme Command of the Defence Forces (Army, Navy, and Air Force) is formally vested in the President under Article 53(2), though its exercise is regulated by law passed by Parliament.
• While the legal authority is vested in the President, Article 74 necessitates that the President acts on the aid and advice of the Council of Ministers, headed by the Prime Minister.
• This article effectively makes the President the De jure (titular) head of the state, while the actual executive administration is managed by the Cabinet.
• Article 53(3) clarifies that the vesting of power in the President does not prevent Parliament from conferring by law functions on authorities other than the President, nor does it transfer powers already held by State Governments.

 Additional Information

• Term of office of President:
• Under Article 56, the President holds office for a term of five years from the date of assumption of duties.
• The President can resign by writing to the Vice-President or be removed via impeachment for violating the Constitution under Article 61.
• Qualifications for election as President:
• Article 58 prescribes that a person must be a citizen of India, have completed 35 years of age, and be qualified for election as a member of the Lok Sabha.
• The individual must not hold any office of profit under the Government of India, State Governments, or any local authority.
• Election of President:
• Article 54 mandates that the President is elected by an electoral college consisting of elected members of both Houses of Parliament and elected members of the Legislative Assemblies (MLAs) of the States and Union Territories (Delhi and Puducherry).
• The election follows the system of proportional representation by means of a single transferable vote.

The correct answer is Ministry of Housing and Urban Affairs.

Key Points

• The Atal Mission for Rejuvenation and Urban Transformation (AMRUT) was launched by the Government of India in June 2015, with the Ministry of Housing and Urban Affairs (MoHUA) serving as the nodal ministry.
• The mission aims to provide basic services like water supply, sewerage, and urban transport to households and build amenities in cities to improve the quality of life, focusing specifically on the poor and disadvantaged.
• The mission initially targeted 500 cities across India, covering approximately 60 percent of the urban population.
• The initiative emphasizes Green Spaces and parks, Stormwater drainage to reduce flooding, and Non-motorized Urban Transport such as cycling and pedestrian facilities.
• In October 2021, AMRUT 2.0 was launched to make cities water secure and provide 100 percent coverage of water supply to all households in around 4,700 statutory towns.

 Additional Information

• Ministry of Housing and Urban Affairs (MoHUA):
• This ministry was formed by merging the Ministry of Urban Development and the Ministry of Housing and Urban Poverty Alleviation in July 2017.
• It administers other major schemes like the Smart Cities Mission, Swachh Bharat Mission-Urban (SBM-U), and Pradhan Mantri Awas Yojana-Urban (PMAY-U).
• Ministry of Jal Shakti:
• Created in May 2019 by merging the Ministry of Water Resources, River Development and Ganga Rejuvenation, and the Ministry of Drinking Water and Sanitation.
• It manages the Jal Jeevan Mission, which primarily focuses on providing Functional Household Tap Connections (FHTC) in rural India.
• Funding Mechanism:
• AMRUT is a Centrally Sponsored Scheme where the Central Government provides a significant portion of the funds, while the rest is shared by State Governments and Urban Local Bodies (ULBs) based on city population.

The correct answer is Only I.

Key Points

• Article 27 of the Indian Constitution explicitly states that no person shall be compelled to pay any taxes, the proceeds of which are specifically appropriated in payment of expenses for the promotion or maintenance of any particular religion or religious denomination. This provision ensures the secular nature of the Indian State by prohibiting the use of public funds for the advancement of one religion over others. Hence, statement I is correct.
• Article 28 pertains to the freedom as to attendance at religious instruction or religious worship in certain educational institutions. It prohibits religious instruction in any educational institution wholly maintained out of State funds, while providing specific guidelines for institutions administered by the State but established under any endowment or trust. Hence, statement II is incorrect.

 Additional Information

• Right to Freedom of Religion (Articles 25−28):
• Article 25: Guarantees the freedom of conscience and the right to freely profess, practice, and propagate religion to all citizens, subject to public order, morality, and health.
• Article 26: Grants every religious denomination the right to establish and maintain institutions for religious and charitable purposes and to manage its own affairs in matters of religion.
• Right against Exploitation (Articles 23−24):
• Article 23: Prohibits traffic in human beings, begar, and other similar forms of forced labour. It is this specific article that covers the description erroneously attributed to Article 28 in the question.
• Article 24: Prohibits the employment of children below the age of 14 years in any factory, mine, or other hazardous employment to ensure their safety and education.
• Educational Institution Categories under Article 28:
• Wholly State Maintained: Religious instruction is strictly prohibited.
• State Recognized or State-Aided: Religious instruction is voluntary and requires the consent of the individual or their guardian.
• Administered by State but established under Trust: Religious instruction is permitted as per the requirements of the trust.

The correct answer is The relief is highly even..

Key Points

• The Peninsular Plateau is a tableland located to the south of the Northern Plains, extending up to the southern tip of the Indian mainland. Hence, statement 1 is correct.
• The plateau is broadly triangular in shape, with its base aligned with the southern edge of the Indo-Gangetic plains and its apex at Kanniyakumari. Hence, statement 2 is correct.
• The relief of the Peninsular Plateau is not even; it is highly rugged and undulating, characterized by numerous plateaus, hill ranges, and deep river valleys. Hence, statement 3 is incorrect.
• The Aravalli Hills, which are among the oldest fold mountains in the world, form the north-western boundary of the plateau. Hence, statement 4 is correct.

 Additional Information

• Peninsular Plateau:
• Geological Origin: It was formed due to the breaking and drifting of the Gondwana land, making it one of the oldest and most stable landmasses of the Earth crust.
• Major Divisions: It is primarily divided into two parts: the Central Highlands (north of the Narmada river) and the Deccan Plateau (south of the Narmada river).
• Rock Composition: The region is composed of crystalline, igneous, and metamorphic rocks, featuring rounded hills and wide valleys.
• Black Soil Area: One of the distinct features of this plateau is the Deccan Trap, which is a region of volcanic origin characterized by black soil suitable for cotton cultivation.
• Aravalli Range: These hills are highly eroded and appear as broken hills, extending from Gujarat through Rajasthan to Delhi.

The correct answer is Both I and II.

Key Points

• Pradhan Mantri Anusuchit Jaati Abhyuday Yojana (PM-AJAY) is a comprehensive scheme launched to uplift the socio-economic status of the Scheduled Castes (SC) population by merging three existing initiatives: Pradhan Mantri Adarsh Gram Yojana (PMAGY), Special Central Assistance to Scheduled Castes Sub Plan (SCA to SCSP), and Babu Jagjivan Ram Chhatrawas Yojana (BJRCY). It focuses on reducing poverty through infrastructure development, skill training, and income-generating schemes. Hence, statement I is correct.
• The SMILE (Support for Marginalized Individuals for Livelihood and Enterprise) scheme is a central sector initiative formulated by the Ministry of Social Justice and Empowerment. It provides a legal and social framework for the comprehensive rehabilitation of two specific groups: Transgender Persons and individuals engaged in the act of begging. Hence, statement II is correct.

 Additional Information

• Ministry of Social Justice and Empowerment: This is the nodal ministry for implementing both the PM-AJAY and SMILE schemes, ensuring inclusive growth for the most marginalized sections of Indian society.
• PM-AJAY Components:
• Adarsh Gram: Aims to provide essential infrastructure in villages having an SC population of 50% or more.
• Grant-in-Aid: Financial assistance for district-level projects that promote livelihood and socio-economic development.
• SMILE Sub-schemes:
• Rehabilitation of Transgender Persons: Includes provisions for Scholarships, Skill Development, and Garima Greh (shelter homes) to provide a safe space for the community.
• Rehabilitation for Begging: Focuses on survey and identification, medical facilities, and re-integration into mainstream society through vocational training.

The correct answer is Obligation of States and the Union.

Key Points

• Article 256 of the Indian Constitution stipulates that the executive power of every State shall be so exercised as to ensure compliance with the laws made by Parliament and any existing laws which apply in that State.
• It explicitly outlines the Obligation of States and the Union, where the Union executive is empowered to give such directions to a State as may appear to the Government of India to be necessary for the purpose of ensuring legal compliance.
• This provision serves as a fundamental pillar of Administrative Relations between the Centre and the States, ensuring that the federal structure functions harmoniously under the supremacy of Central legislation.
• The article is located within Part XI of the Constitution, which governs the Relations between the Union and the States, specifically under Chapter II regarding Administrative Relations.
• Non-compliance with the directions issued under Article 256 can invoke Article 365, which empowers the President to conclude that the State government cannot be carried on in accordance with the Constitution.

 Additional Information

• Article 258:
• Relates to the Power of the Union to confer powers, etc., on States in certain cases.
• It allows the President, with the consent of the State government, to entrust either conditionally or unconditionally to that Government functions in relation to any matter to which the executive power of the Union extends.
• Article 260:
• Relates to the Jurisdiction of the Union in relation to territories outside India.
• It permits the Government of India to undertake any executive, legislative, or judicial functions of a territory not being part of India by agreement with the Government of that territory.
• Article 258A:
• Relates to the Power of the States to entrust functions to the Union.
• This was inserted by the 7th Constitutional Amendment Act, 1956, allowing the Governor of a State, with the consent of the Government of India, to entrust functions to the Union.
• Article 257:
• Deals with the Control of the Union over States in certain cases, particularly regarding the maintenance of means of communication of national or military importance.

The correct answer is Meghalaya.

Key Points

• The Nongkrem dance is a vital religious festival of the Khasi tribe, one of the three major matrilineal ethnic groups in Meghalaya.
• The festival is officially referred to as Ka Pom-Blang Nongkrem and is celebrated annually at Smit, the cultural and administrative headquarters of the Hima Khyrim (Khyrim Syiemship).
• It is performed to appease the Goddess Ka Blei Synshar to seek her blessings for a bountiful harvest, peace, and the general prosperity of the community.
• The event spans five days and involves a ritualistic sacrifice of goats, known as Pomblang, which is conducted by the Syiem (the traditional administrative head) and the high priest.
• The dance performance features young Khasi women in the inner circle performing small, synchronized steps, while men dance in the outer circle holding swords and white yak-hair whisks (called Symphiah), symbolizing protection and strength.

 Additional Information

• Meghalaya (Tribal Festivals):
• Wangala Dance: Also known as the Hundred Drums Festival, it is the most important harvest festival of the Garo tribe.
• Laho Dance: A popular folk dance of the Jaintia tribe, performed during the Behdienkhlam festival where men and women dance together in a rhythmic pattern.
• Gujarat:
• Garba: A vibrant circular dance performed during the nine nights of Navratri to honor the feminine form of divinity.
• Dandiya Raas: A traditional folk dance involving decorated wooden sticks, often associated with the life of Lord Krishna.
• West Bengal:
• Chhau Dance: A semi-classical dance with martial and tribal roots; the Purulia Chhau variant is famous for its elaborate masks and acrobatic movements.
• Brita Dance: A traditional votive folk dance performed primarily by women to seek divine intervention for children or recovery from illness.
• Ladakh:
• Shondol Dance: Historically known as the Royal Dance, it was performed to honor the King of Ladakh on special occasions.
• Jabro: A folk dance performed by the nomadic people of Tibetan origin inhabiting the Changthang high-altitude plateaus.

The correct answer is Goa.

Key Points

• Ranmale is a traditional ritualistic folk theater and dance form predominantly practiced in the Sattari and Sanguem talukas of Goa, as well as parts of neighboring Sindhudurg in Maharashtra.
• It is traditionally performed by the agricultural and forest-dwelling communities, primarily the Zorman community, during the Shigmo festival, which marks the arrival of spring.
• The performance is a fusion of dance, drama, and music, where participants enact stories from the Indian epics, specifically the Ramayana and the Mahabharata.
• Historically, Ranmale served as a medium of entertainment and socio-religious expression for the rural population residing in the Western Ghats region.
• The musical elements are vital to the performance, featuring traditional instruments like the Ghumat (a terracotta pot drum), Shamel, and Cymbals to provide a rhythmic base for the dancers.
• The dance takes place in a sacred community space known as the Mand, often performed under the illumination of traditional oil torches or lamps.

 Additional Information

• Telangana:
• Home to the Perini Shivatandavam, an ancient dance form known as the Dance of Warriors, which flourished during the Kakatiya dynasty.
• Lambadi is another prominent folk dance performed by the nomadic Banjara tribes of the state.
• Manipur:
• Famous for Manipuri, one of the eight classical dances of India, which often focuses on the Raas Leela (the divine love of Radha and Krishna).
• The state also features Pung Cholom, a unique dance involving acrobatic movements and the use of the Pung drum.
• Jammu and Kashmir:
• Known for the Rouf dance, a popular folk dance performed by women during festive occasions like Eid and the harvesting season.
• Bacha Nagma and Dumhal are other traditional performances deeply rooted in the cultural fabric of the Kashmir Valley.

Concept:

The Western Ghats is a globally recognized biodiversity hotspot where new species are frequently discovered. Taxonomic classification helps identify these species based on their morphological and genetic characteristics, which is essential for wildlife conservation.

Given

Discovery Year: 2025

Species Name: Zographetus mathewi

Region: Western Ghats

Information

In early 2025, researchers identified a new species named Zographetus mathewi. This species belongs to the Hesperiidae family, which comprises skippers, a group of butterflies. The discovery was made in the Aralam Wildlife Sanctuary, located in the Kannur district of Kerala. Commonly referred to as the Aralam Forest Hopper, the species is named in honor of Mathew P. John for his significant contributions to the field of lepidopterology (the study of butterflies and moths). Given its biological classification within the genus Zographetus, it is categorized as a butterfly.

Final Answer: ✅ butterfly

The correct answer is Kerala.

Key Points

• The Thumba Equatorial Rocket Launching Station (TERLS) is a premier spaceport operated by the Indian Space Research Organisation (ISRO).
• It is located in Thumba, a suburb of Thiruvananthapuram, which is the capital city of Kerala.
• The facility was established on November 21, 1963, marking the birth of the Indian Space Programme.
• Thumba was chosen for its strategic geographical location, as it lies very close to the Earth magnetic equator (dip equator), making it ideal for ionospheric and electrojet research.
• The first rocket launched from this station was a Nike-Apache sounding rocket, which was provided by NASA in the United States.
• In 1968, the station was formally dedicated to the United Nations to facilitate international scientific cooperation in aeronomy and upper atmospheric physics.

 Additional Information

• Vikram Sarabhai Space Centre (VSSC):
• TERLS eventually evolved into the Vikram Sarabhai Space Centre, the lead ISRO center for the development of satellite launch vehicles like PSLV, GSLV, and LVM3.
• It was renamed in honor of Dr. Vikram Sarabhai, who is widely regarded as the Father of the Indian Space Programme.
• Karnataka:
• This state hosts the ISRO Headquarters and the U R Rao Satellite Centre (URSC) in Bengaluru, where major satellite technology developments occur.
• Gujarat:
• Home to the Space Applications Centre (SAC) in Ahmedabad, focusing on remote sensing, communications, and satellite navigation payloads.
• Maharashtra:
• Includes significant scientific institutions like the Indian Institute of Geomagnetism (IIG) in Mumbai, which researches geomagnetic fields relevant to space science.

The correct answer is Friction can be decreased by making the surface rough..

Key Points

• Static Friction occurs when surfaces are at rest relative to each other, allowing microscopic irregularities to interlock deeply. Once movement begins, the surfaces slide over each other without sufficient time for deep interlocking, making Sliding Friction generally lower than the maximum static friction. Hence, statement 1 is correct.
• Frictional force is directly proportional to the Normal Force. If the force pressing the two surfaces together increases, the interlocking between the irregularities becomes more intense, thereby increasing the resistance to motion. Hence, statement 2 is correct.
• Friction is vital for fundamental daily tasks such as walking (providing grip on the ground), writing (allowing the lead or ink to stick to paper), and braking (enabling vehicles to stop safely). Hence, statement 3 is correct.
• Friction arises from the interlocking of surface imperfections. Increasing the roughness of a surface adds more hills and valleys, which heightens the degree of interlocking and subsequently increases friction rather than decreasing it. Hence, statement 4 is incorrect.

 Additional Information

• Types of Friction:
• Static Friction: The opposing force that prevents the initiation of motion between two surfaces.
• Sliding Friction: Also known as kinetic friction, it acts when one surface is actually sliding over another.
• Rolling Friction: Occurs when an object rolls over a surface; it is significantly weaker than sliding friction, which is why Wheels and Ball Bearings are used in machinery.
• Fluid Friction: Often called Drag, it is the resistance offered by liquids and gases to objects moving through them.
• Methods to Modify Friction:
• Lubrication: Applying substances like Oil, Grease, or Graphite fills the surface irregularities, creating a thin layer that reduces direct contact.
• Polishing: Making surfaces smoother to minimize the height of microscopic bumps.
• Treading: Tires and shoes are designed with Treads and Spikes specifically to increase friction for better grip.

The correct answer is Bijak.

Key Points

• Saint Kabir was a legendary 15th-century mystic poet and saint of the Bhakti movement whose teachings fundamentally influenced the religious landscape of Northern India and the foundation of Sikhism.
• The Bijak is considered the most authentic and authoritative compilation of Kabir’s verses, serving as the primary holy scripture for the Kabir Panth sect.
• It is traditionally divided into three distinct sections: Sakhi (witnessing couplets teaching moral truths), Shabda (hymns meant for singing), and Ramaini (longer poems dealing with metaphysical and spiritual doctrines).
• Kabir utilized a unique linguistic style known as Sadhukkari Bhasha, which integrated elements of Awadhi, Braj, Bhojpuri, and Punjabi to communicate with the common masses.
• His poetry strongly advocated for Nirguna Bhakti (devotion to a formless God) and criticized organized religious rituals, the caste system, and the hypocrisy of the clergy in both Hinduism and Islam.
• Beyond the Bijak, a significant number of his verses are preserved in the Kabir Granthavali (Rajasthan tradition) and the Guru Granth Sahib, which contains over 500 verses attributed to him.

 Additional Information

• Padavali
• This refers to a genre of devotional songs, most famously the Vidyapati Padavali composed by the 14th-century poet Vidyapati in the Maithili language.
• The verses primarily revolve around the divine and romantic love between Radha and Lord Krishna.
• Gitagovinda
• A renowned 12th-century Sanskrit work composed by the poet Jayadeva, who served in the court of the Sena dynasty in Bengal.
• It describes the intricate relationship and the emotional pangs of separation between Krishna and the Gopis, particularly Radha.
• Prabandha Chintamani
• A semi-historical Sanskrit text authored by the Jain scholar Merutunga in 1304 CE.
• It provides valuable historical anecdotes and biographical accounts of medieval Indian kings, including Bhoja of the Paramara dynasty and Siddharaja Jaisimha of Gujarat.

The correct answer is Yellow.

Key Points

• A candle flame is divided into three distinct regions based on the availability of oxygen and the extent of combustion: the innermost, middle, and outer zones.
• The middle zone is the region where partial combustion (or incomplete combustion) occurs because the supply of air is limited in this central area.
• In this zone, the wax vapors do not burn completely, leading to the formation of unburnt carbon particles.
• These tiny carbon particles get heated to a high temperature and begin to glow, a process known as incandescence, which gives the flame its characteristic yellow color.
• Due to the emission of light from these glowing particles, the middle zone is also referred to as the luminous zone of the flame.
• Temperature-wise, the middle zone is considered moderately hot, sitting between the temperature extremes of the innermost and outermost layers.

 Additional Information

• Outer Zone of Complete Combustion:
• This is the hottest part of the candle flame where there is an abundant supply of oxygen.
• It undergoes complete combustion, resulting in a blue color flame that is non-luminous.
• Goldsmiths often use this part of the flame with a metallic blowpipe to melt gold and silver.
• Innermost Zone of Unburnt Vapors:
• This area immediately surrounds the wick and contains unburnt wax vapors.
• It appears black in color and is the coolest part (least hot) of the entire flame.
• Chemical Composition:
• Candle wax is primarily composed of hydrocarbons like paraffin wax.
• The process of burning involves the vaporization of liquid wax through capillary action up the wick.

The correct answer is APSARA-U.

Key Points

• APSARA-U (Apsara-Upgraded) is a high-performance swimming pool-type research reactor designed and built indigenously at the Bhabha Atomic Research Centre (BARC), Trombay.
• The reactor achieved its first criticality on September 10, 2018, making it the first research reactor in India to operate successfully using Low Enriched Uranium (LEU) fuel.
• The core of APSARA-U utilizes indigenously developed Uranium silicide (U₃Si₂) fuel dispersed in an Aluminum matrix, with U-235 enrichment kept below 20 percent to meet international non-proliferation standards.
• It replaces the original Apsara reactor, which was Asia’s first research reactor (commissioned in 1956) and previously functioned using Highly Enriched Uranium (HEU) fuel supplied by the United Kingdom.
• This upgraded facility provides a significantly higher thermal neutron flux, which is critical for the production of medical radioisotopes (such as Iodine-131), advanced neutron activation analysis, and material science research.

 Additional Information

• DHRUVA:
• Commissioned at Trombay in 1985, it is India’s largest research reactor and uses Natural Uranium as fuel with Heavy Water (D₂O) as the moderator and coolant.
• KAMINI:
• Located at the Indira Gandhi Centre for Atomic Research (IGCAR), it is the only reactor in the world currently using Uranium-233 fuel derived from Thorium.
• PURNE (PURNIMA Series):
• The PURNIMA (Plutonium Reactor for Neutron Investigations in Multiplying Assemblies) reactors were experimental fast reactors at BARC; PURNIMA-I achieved criticality in 1972 using Plutonium oxide fuel.

The correct answer is 5.

Key Points

• At the Olympic Games, the team event in table tennis is conducted as a best-of-five matches competition, where the first team to win three individual matches wins the overall tie.
• The team event format was officially introduced at the 2008 Beijing Olympics, replacing the separate doubles competition that had been a part of the program since 1988.
• Each team consists of three athletes. A match tie begins with a doubles match, which is immediately followed by a series of singles matches until a winner is decided.
• The standard order of play in the Olympic format is: Match 1 (Doubles), Match 2 (Singles), Match 3 (Singles), and if no team has won three matches yet, Match 4 (Singles) and Match 5 (Singles) are played.
• This best-of-five system ensures a balance between individual skill and team strategy, requiring players to be versatile in both singles and doubles formats.

 Additional Information

• Match and Game Structure:
• In the team event, each individual match (both singles and doubles) is typically played as a best-of-five games, whereas individual singles events at the Olympics are often best-of-seven games.
• A game is won by the first player or pair to reach 11 points, provided there is at least a two-point margin of lead.
• ITTF Regulations:
• The International Table Tennis Federation (ITTF) is the world governing body that regulates the rules and equipment standards, including the 40mm diameter ball and the polymer (plastic) material used in modern competition.
• Table tennis was first included in the Olympic program at the 1988 Seoul Games.

The correct answer is 3.66.

Key Points

• In Field Hockey, the dimensions of the goal are strictly regulated by the International Hockey Federation (FIH) to ensure global standardization of the sport.
• The distance between the inner edges of the vertical goalposts is precisely 3.66 metres, which is equivalent to 4 yards in the imperial system.
• The goalposts and the crossbar must have a rectangular cross-section with a width or thickness of 50 mm (5 cm).
• The goalposts are positioned centrally on the backlines, and they must be white in color to provide maximum visibility against the playing surface.
• The measurement is taken between the inner faces of the posts, meaning the actual gap the ball must pass through is 3.66 metres wide.

 Additional Information

• Other Goal Dimensions:
• The height of the crossbar from the ground (lower edge) is 2.14 metres (7 feet).
• The goal nets are attached to the posts and crossbar at intervals not exceeding 150 mm to prevent the ball from passing through.
• Sideboards and backboards within the goal are 460 mm high and are typically painted a dark color.
• Comparison with Football (Soccer):
• The value 2.44 (metres) mentioned in the options is the standard height of an Association Football goal (8 feet).
• A standard Football goal is much wider than a hockey goal, measuring 7.32 metres (8 yards) between the posts.
• Field Dimensions:
• A standard hockey pitch is 91.40 metres long and 55.00 metres wide.
• The striking circle (D-area) is a semi-circle with a radius of 14.63 metres measured from the inner front corner of the goalposts.

The correct answer is 3rd.

Key Points

• India secured the 3rd position in the final medal standings at the 2018 Commonwealth Games, which took place in Gold Coast, Queensland, Australia.
• Indian athletes delivered a stellar performance, clinching a total of 66 medals, comprising 26 Gold, 20 Silver, and 20 Bronze medals.
• This achievement stood as India's third-best demonstration in Commonwealth Games history, trailing behind the performances of the 2010 Delhi Games and the 2002 Manchester Games.
• Shooting emerged as the most successful sport for India, yielding 16 medals (including 7 Gold), followed closely by Wrestling with 12 medals and Weightlifting with 9 medals.

 Additional Information

• Overview of other top-performing countries at the 2018 Games:
• Australia dominated the tournament and finished in the 1st position with a massive collection of 198 medals (80 Gold, 59 Silver, and 59 Bronze).
• England took the 2nd position on the leaderboard, accumulating 136 medals (45 Gold, 45 Silver, and 46 Bronze).
• Canada finished in the 4th position; despite winning 82 total medals, they stood behind India due to a lower gold medal count of 15 Gold.

Shortcut Trick

Solve the expression using the BODMAS rule by processing the bracket and multiplication first.

87 − 43 + 92 − (55) + 82

Group positive and negative terms: (87 + 92 + 82) − (43 + 55)

261 − 98 = 163

∴ The correct answer is 163.

Alternate Method

Given: 87 − 43 + 92 − (38 + 17) + 41 × 2

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

⇒ Solve the bracket part: (38 + 17) = 55

⇒ Perform the multiplication: 41 × 2 = 82

⇒ The expression becomes: 87 − 43 + 92 − 55 + 82

⇒ Perform addition of positive terms: 87 + 92 + 82 = 261

⇒ Perform addition of negative terms: 43 + 55 = 98

⇒ Final subtraction: 261 − 98 = 163

∴ The correct answer is 163.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets, Of (powers/roots), Division, Multiplication, Addition, and Subtraction.

Grouping Technique

When dealing with multiple addition and subtraction terms, summing all positive numbers and all negative numbers separately before the final subtraction reduces calculation errors.

Shortcut Trick

Substitute a = 2 and b = 5 directly into the expression.

(a + b)⁵ = 7⁵ = 16807 and (a − b)³ = (−3)³ = −27.

Numerator = 16807 − (−27) = 16807 + 27 = 16834.

Denominator = 4 × 2 × 5 = 40.

Expression = 16834 ÷ 40 = 420.85.

∴ The correct answer is 420.85.

Alternate Method

Given:

Variable a = 2

Variable b = 5

Expression to evaluate: [(a + b)⁵ − (a − b)³] ÷ (4ab)

Step-by-step Calculation:

⇒ First, find the values of (a + b) and (a − b):

⇒ (a + b) = 2 + 5 = 7

⇒ (a − b) = 2 − 5 = −3

⇒ Calculate the powers:

⇒ (7)⁵ = 7 × 7 × 7 × 7 × 7 = 16807

⇒ (−3)³ = (−3) × (−3) × (−3) = −27

⇒ Substitute these into the numerator:

⇒ Numerator = 16807 − (−27) = 16807 + 27 = 16834

⇒ Calculate the denominator:

⇒ 4ab = 4 × 2 × 5 = 40

⇒ Divide the numerator by the denominator:

⇒ Result = 16834 ÷ 40 = 420.85

∴ The correct answer is 420.85.

Additional Information

BODMAS Rule

This rule dictates the order of operations: Brackets, Of, Division, Multiplication, Addition, and Subtraction.

Negative Base Exponents

A negative base raised to an odd power remains negative, e.g., (−x)³ = −x³, while an even power makes it positive, e.g., (−x)² = x².

Powers of 7

Knowing common powers like 7² = 49, 7³ = 343, 7⁴ = 2401, and 7⁵ = 16807 helps in quick simplification.

Shortcut Trick

Convert the base fraction 13/24 into its decimal equivalent: 13 ÷ 24 ≈ 0.5416.

Compare the decimal values of the given options:

(1) 26/51 ≈ 0.509 | (2) 27/50 = 0.540 | (4) 7/13 ≈ 0.538

(3) 25/46 ≈ 0.5434

Since 0.5434 is greater than 0.5416, the fraction 25/46 is the largest.

∴ The correct answer is 25/46.

Alternate Method

Given: Base fraction = 13/24

Method: We use the cross-multiplication rule to compare fractions. For two fractions a/b and c/d, if a × d > b × c, then a c/d.

Step-by-step Comparison:

⇒ Comparing 13/24 and 26/51: 13 × 51 = 663 and 24 × 26 = 624. Since 663 > 624 ⇒ 13/24 > 26/51.

⇒ Comparing 13/24 and 27/50: 13 × 50 = 650 and 24 × 27 = 648. Since 650 > 648 ⇒ 13/24 > 27/50.

⇒ Comparing 13/24 and 25/46: 13 × 46 = 598 and 24 × 25 = 600. Since 600 > 598 ⇒ 25/46 > 13/24.

⇒ Comparing 13/24 and 7/13: 13 × 13 = 169 and 24 × 7 = 168. Since 169 > 168 ⇒ 13/24 > 7/13.

∴ The correct answer is 25/46.

Additional Information

Cross-Multiplication Rule

To compare a/b and c/d, find the products ad and bc. If ad > bc, then a c/d; if ad < bc, then a/b < c/d.

Decimal Comparison Method

Converting fractions to decimals is often faster when the denominators are easy to divide or when denominators are close to powers of 10.

Same Numerator Rule

If two fractions have the same numerator, the one with the smaller denominator is the larger fraction (e.g., 13/24 > 13/25).

Shortcut Trick

Solve the numerator and denominator separately using basic arithmetic.

Numerator = (0.25 × 0.25) + 0.015 = 0.0625 + 0.015 = 0.0775.

Denominator = (0.2 × 0.2) + 0.01 = 0.04 + 0.01 = 0.05.

Result = 0.0775 ÷ 0.05 = 7.75 ÷ 5 = 1.55.

∴ The correct answer is 1.55.

Alternate Method

Given: (0.25 × 0.25 + 0.015) ÷ (0.2 × 0.2 + 0.01)

Method Used: BODMAS and Decimal Simplification

⇒ (0.0625 + 0.015) ÷ (0.04 + 0.01)

⇒ 0.0775 ÷ 0.05

⇒ 775/10000 ÷ 5/100

⇒ 775/10000 × 100/5

⇒ 775 ÷ (100 × 5)

⇒ 775 ÷ 500

⇒ 1.55

∴ The correct answer is 1.55.

Additional Information

BODMAS Rule

Always prioritize Multiplication before Addition as per the rule: Brackets, Orders, Division/Multiplication, Addition/Subtraction.

Decimal Multiplication

When multiplying decimals, the result contains a number of decimal places equal to the sum of decimal places in the multipliers (e.g., 0.25 × 0.25 = 0.0625).

Simplification Tip

To divide by 0.05, multiply the numerator by 100 and then divide by 5 to simplify fractional calculations.

Shortcut Trick

The remainder of any number when divided by 9 is equal to the sum of its digits (reduced to a single digit if necessary).

For the number 1200, the sum of digits = 1 + 2 + 0 + 0 = 3.

Since 3 is less than 9, the remainder is 3.

∴ The correct answer is 3.

Alternate Method

Given: Dividend = 1200, Divisor = 9

Formula: Dividend = (Divisor × Quotient) + Remainder

⇒ 1200 ÷ 9

⇒ 1200 = 1197 + 3

⇒ 1200 = (9 × 133) + 3

⇒ Quotient = 133

⇒ Remainder = 3

∴ The correct answer is 3.

Additional Information

Divisibility Rule of 9

A number is perfectly divisible by 9 if and only if the sum of its digits is divisible by 9. This sum also determines the remainder for non-divisible numbers.

Concept of Digital Root

The digital root is the single-digit value obtained by repeatedly adding digits until a single digit remains. If the digital root is 9, the remainder is 0; otherwise, the digital root is the remainder when divided by 9.

Divisibility Rule of 3

Similar to 9, a number is divisible by 3 if the sum of its digits is divisible by 3. For 1200, 1+2+0+0 = 3, which is divisible by 3, so the remainder when divided by 3 is 0.

Shortcut Trick

For a square park of side s having an inside path of width w:

Area of Path = 4w(s − w)

Given s = 15 cm and w = 3 cm:

Area = 4 × 3 × (15 − 3) = 12 × 12 = 144 cm²

∴ The correct answer is 144 cm².

Alternate Method

Given:

Side of the outer square park (S) = 15 cm

Width of the internal path (w) = 3 cm

Formula Used:

Area of a square = side × side

Area of path = Area of outer square − Area of inner square

Calculations:

⇒ Area of outer square = 15 × 15 = 225 cm²

⇒ Side of inner square = Outer Side − (2 × Width of path)

⇒ Side of inner square = 15 − (2 × 3) = 15 − 6 = 9 cm

⇒ Area of inner square = 9 × 9 = 81 cm²

⇒ Area of the path = 225 − 81 = 144 cm²

∴ The correct answer is 144 cm².

Additional Information

Path Outside a Square

If a path of width w is built outside a square of side s, the area of the path is given by 4w(s + w).

Cross Paths in a Square

When two paths of width w cross each other at right angles in the center of a square park of side s, the area of the paths is w(2s − w).

Path Inside a Rectangle

For a rectangle with length L and breadth B, an inside path of width w has an area = 2w(L + B − 2w).

Shortcut Trick

In a Rectangle, the sum of Length and Breadth is always half of the Perimeter.

L + B = 50 ÷ 2 = 25 cm.

Since L = 15 cm, B = 25 − 15 = 10 cm.

Area = L × B = 15 × 10 = 150 cm².

∴ The correct answer is 150 cm².

Alternate Method

Given:

Perimeter of the rectangle = 50 cm

Length (L) of the rectangle = 15 cm

Formula Used:

Perimeter = 2 × (Length + Breadth)

Area = Length × Breadth

Calculations:

⇒ 2 × (15 + B) = 50

⇒ 15 + B = 50 ÷ 2

⇒ 15 + B = 25

⇒ B = 25 − 15

⇒ B = 10 cm

Now, calculate the Area:

⇒ Area = 15 × 10

⇒ Area = 150 cm²

∴ The correct answer is 150 cm².

Additional Information

Diagonal of a Rectangle

The distance between opposite corners is given by d = √(L² + B²).

Properties of Rectangle

Opposite sides are equal and parallel, and every internal angle is exactly 90°.

Circumradius of a Rectangle

The radius of a circle passing through all vertices is half of the diagonal: R = d ÷ 2.

Shortcut Trick

The perimeter of a rectangle is twice the sum of its length and breadth.

Sum of (Length + Breadth) = Perimeter ÷ 2

Sum = 40 ÷ 2 = 20 cm

∴ The correct answer is 20 cm.

Alternate Method

Given: Perimeter = 40 cm, Length = 12 cm

Formula Used: Perimeter = 2 × (Length + Breadth)

⇒ 40 = 2 × (12 + Breadth)

⇒ 12 + Breadth = 40 ÷ 2

⇒ 12 + Breadth = 20

⇒ Breadth = 20 − 12 = 8 cm

⇒ Sum of length and breadth = 12 + 8 = 20 cm

∴ The correct answer is 20 cm.

Additional Information

Area of a Rectangle

The total space occupied by a rectangle is the product of its length and breadth: Area = Length × Breadth.

Diagonal of a Rectangle

The diagonal (d) is the longest line segment connecting opposite corners: d = √(Length² + Breadth²).

Perimeter of a Square

A square is a special rectangle where length = breadth = side (a). Its perimeter is 4 × a.

Shortcut Trick

Notice that x and y are reciprocal conjugates ($xy = 1$).

For $x = \frac{a+b}{a-b}$ and $y = \frac{a-b}{a+b}$, the sum $x+y = \frac{2(a^2+b^2)}{a^2-b^2}$.

Substitute $a=3$ and $b=\sqrt{8}$: $x+y = \frac{2(9+8)}{9-8} = 34$.

Applying the identity $x^2 + y^2 = (x + y)^2 − 2xy$.

Calculation: $34^2 − 2(1) = 1156 − 2 = 1154$.

∴ The correct answer is 1154.

Alternate Method

Given:

x = (3 + √8) ÷ (3 − √8)

y = (3 − √8) ÷ (3 + √8)

Formula Used:

x² + y² = (x + y)² − 2xy

Calculations:

⇒ Rationalizing x: x = [(3 + √8) × (3 + √8)] ÷ [(3 − √8) × (3 + √8)] ⇒ x = (9 + 8 + 6√8) ÷ (9 − 8) = 17 + 6√8 ⇒ Rationalizing y: y = [(3 − √8) × (3 − √8)] ÷ [(3 + √8) × (3 − √8)] ⇒ y = (9 + 8 − 6√8) ÷ (9 − 8) = 17 − 6√8 ⇒ x + y = (17 + 6√8) + (17 − 6√8) = 34 ⇒ xy = [(3 + √8) ÷ (3 − √8)] × [(3 − √8) ÷ (3 + √8)] = 1 ⇒ x² + y² = 34² − 2(1) ⇒ x² + y² = 1156 − 2 = 1154

∴ The correct answer is 1154.

Additional Information

Rationalization of Surds

To rationalize a denominator, multiply both numerator and denominator by the conjugate of the denominator to eliminate the radical.

Algebraic Identity for Sum of Squares

The sum of squares identity is x² + y² = (x + y)² − 2xy, which is extremely useful when the product xy is a simple integer like 1.

Reciprocal Conjugates

If the difference of the squares of two terms in a binomial surd is 1 (e.g., 3² − (√8)² = 1), then the expression and its conjugate are multiplicative inverses.

Shortcut Trick

Identify the number of terms (n): n = [(Last − First) ÷ Diff] + 1 = [(203 − 31) ÷ 2] + 1 = 87.

Find the average of the series: (First + Last) ÷ 2 = (31 + 203) ÷ 2 = 117.

Total Sum = Average × n = 117 × 87 = 10179.

∴ The correct answer is 10179.

Alternate Method

Given: The series is an Arithmetic Progression (AP) with first term a = 31, last term l = 203, and common difference d = 2.

Formula Used: Sum S_n = (n ÷ 2) × (a + l) and n = [(l − a) ÷ d] + 1.

⇒ First, calculate the number of terms (n):

⇒ n = [(203 − 31) ÷ 2] + 1

⇒ n = [172 ÷ 2] + 1 = 86 + 1 = 87

⇒ Now, calculate the sum (S_n):

⇒ S_n = (87 ÷ 2) × (31 + 203)

⇒ S_n = (87 ÷ 2) × 234

⇒ S_n = 87 × 117 = 10179

∴ The correct answer is 10179.

Additional Information

Sum of First n Odd Natural Numbers

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

General Term of an AP

The nth term of an Arithmetic Progression is defined as: a_n = a + (n − 1)d.

Alternate Sum Formula

The sum of an AP can also be calculated as: S_n = (n ÷ 2)[2a + (n − 1)d].

Shortcut Trick

Total Sum of three values = 30 × 3 = 90.

Ratio logic: Let the Third value = 3 units, so the First value = 1 unit.

The Second value = 3 units − 15.

Total units: 1 + 3 + (3 − 15) = 90 ⇒ 7 units = 105.

1 unit = 105 ÷ 7 = 15.

∴ The correct answer is 15.

Alternate Method

Given:

Average of three values = 30

First value = 1/3 of the Third value

Third value = Second value + 15

Formula Used:

Sum = Average × Total Number of Values

Calculations:

⇒ Total Sum = 30 × 3 = 90

⇒ Let the Third value be x.

⇒ First value = x/3

⇒ Second value = x − 15

⇒ x/3 + (x − 15) + x = 90

⇒ x/3 + 2x − 15 = 90

⇒ x/3 + 2x = 105

⇒ (x + 6x) / 3 = 105

⇒ 7x = 315

⇒ x = 315 ÷ 7 = 45

⇒ First value = 45 ÷ 3 = 15

∴ The correct answer is 15.

Additional Information

Basic Average Formula

The Average of n observations is calculated as the Sum of all observations divided by the total number of observations (n).

Relationship between Sum and Average

Total Sum = Average × Total number of entities. This is the most common starting point for solving word problems involving averages.

Ratio and Proportion in Averages

When values are linked by ratios (like 1/3), it is often easier to assign 'units' (e.g., 1x and 3x) to avoid complex fractions during algebraic substitution.

Shortcut Trick

To find the smallest number, we first calculate the Least Common Multiple (LCM) of the given divisors.

LCM of 6, 10, and 12 = 60.

Since the number is increased by 30 to be divisible, the original number is LCM − 30.

Required Number = 60 − 30 = 30.

∴ The correct answer is 30.

Alternate Method

Given:

Divisors = 6, 10, 12

Amount increased = 30

To find the LCM of 6, 10, and 12:

⇒ Prime factors of 6 = 2 × 3

⇒ Prime factors of 10 = 2 × 5

⇒ Prime factors of 12 = 2² × 3

⇒ LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60

Let the required number be x.

According to the problem, when x is increased by 30, it becomes a multiple of 60.

⇒ x + 30 = 60

⇒ x = 60 − 30

⇒ x = 30

∴ The correct answer is 30.

Additional Information

LCM Concept

The Least Common Multiple is the smallest positive integer that is perfectly divisible by every number in a given set.

General Form for Increased/Decreased Numbers

If a number N is increased by k to be divisible by a, b, c, then N = LCM(a, b, c) − k. If decreased by k, then N = LCM(a, b, c) + k.

Divisibility Rule for 12

A number is exactly divisible by 12 if it satisfies the divisibility rules for both 3 (sum of digits divisible by 3) and 4 (last two digits divisible by 4).

Shortcut Trick

The least number that leaves a common remainder when divided by several numbers is given by: LCM (Divisors) + Remainder.

Divisors: 9, 16, 30, 24 | Common Remainder: 6

LCM(9, 16, 30, 24) = 720

Required Number = 720 + 6 = 726

∴ The correct answer is 726.

Alternate Method

Given:

Divisors: 9, 16, 30, 24

Remainder: 6 in each case

Formula Used:

Least Number = LCM(x, y, z, ...) + R

Calculations:

⇒ Prime Factorization of divisors:

⇒ 9 = 3²

⇒ 16 = 2⁴

⇒ 30 = 2 × 3 × 5

⇒ 24 = 2³ × 3

⇒ LCM = 2⁴ × 3² × 5

⇒ LCM = 16 × 9 × 5 = 720

⇒ Least Number = 720 + 6

⇒ Least Number = 726

∴ The correct answer is 726.

Additional Information

Least Common Multiple (LCM)

The smallest number which is exactly divisible by all the given numbers.

Remainder Rule (Same Remainder)

Required Number = LCM(Divisors) + r, where 'r' is the common remainder.

Remainder Rule (Different Remainder)

If remainders are r₁, r₂ and (Divisor₁−r₁) = (Divisor₂−r₂) = k, then Number = LCM(Divisors) − k.

Shortcut Trick

Let the Total Income be I.

Remaining amount fraction = I × (100 − 30)% × (100 − 50)% = 3500

I × 0.70 × 0.50 = 3500

I × 0.35 = 3500

I = 3500 ÷ 0.35 = 10000

∴ The correct answer is Rs. 10000.

Alternate Method

Given:

Donation = 30% of Total Income

Bank Deposit = 50% of the remaining amount

Final Remainder = Rs. 3500

Let Total Income = 100 units

⇒ Donation = 30% of 100 = 30 units

⇒ Remaining after donation = 100 − 30 = 70 units

⇒ Bank Deposit = 50% of 70 = 35 units

⇒ Final Remaining Amount = 70 − 35 = 35 units

⇒ 35 units = Rs. 3500

⇒ 1 unit = 3500 ÷ 35 = Rs. 100

⇒ Total Income = 100 × 100 = Rs. 10000

∴ The correct answer is Rs. 10000.

Additional Information

Successive Percentage Change

When values are changed on a remainder basis, the final value is found by multiplying the initial value with successive decreasing factors: Final = Initial × (1 − r₁/100) × (1 − r₂/100).

Percentage to Fraction Conversion

Converting percentages to fractions (e.g., 50% = 1/2, 30% = 3/10) simplifies multi-step calculations by using simple multiplication.

Effective Reduction

A 30% reduction followed by a 50% reduction of the remainder results in an effective remaining part of (1 − 0.3) × (1 − 0.5) = 0.35 or 35% of the original.

Shortcut Trick

Ratio of Loss : Selling Price (SP) = 7 : 11

Since Loss = CP − SP, then Cost Price (CP) = 11 + 7 = 18 units

Loss Percentage = (Loss ÷ CP) × 100

Loss Percentage = (7 ÷ 18) × 100 = 38.888...% ≈ 38.89%

∴ The correct answer is 38.89%.

Alternate Method

Given:

Ratio of Loss to Selling Price = 7 : 11

Formula Used:

1. Cost Price (CP) = Selling Price (SP) + Loss

2. Loss Percentage = (Loss ÷ CP) × 100

Calculations:

⇒ Let the Loss be 7x and Selling Price (SP) be 11x.

⇒ Cost Price (CP) = 11x + 7x = 18x.

⇒ Loss Percentage = (7x ÷ 18x) × 100

⇒ Loss Percentage = (7 ÷ 18) × 100

⇒ Loss Percentage = 700 ÷ 18 = 38.888...%

⇒ Loss Percentage ≈ 38.89%

∴ The correct answer is 38.89%.

Additional Information

Profit and Loss Basics

Profit occurs when SP > CP, calculated as Profit = SP − CP. Loss occurs when CP > SP, calculated as Loss = CP − SP.

Profit/Loss Percentage

Both Profit Percentage and Loss Percentage are always calculated on the Cost Price (CP) unless stated otherwise in the question.

Marked Price and Discount

Marked Price (MP) is the labeled price. Discount is the reduction offered on MP, and SP = MP − Discount.

Shortcut Trick

Ratio of Loss to Selling Price = 5 : 7.

Cost Price = Selling Price + Loss = 7 + 5 = 12 units.

Loss Percentage = (Loss ÷ Cost Price) × 100.

Loss Percentage = (5 ÷ 12) × 100 = 41.67%.

∴ The correct answer is 41.67 percent.

Alternate Method

Given:

Ratio of Loss to Selling Price (SP) = 5 : 7.

Formula Used:

1. Cost Price (CP) = Selling Price (SP) + Loss
2. Loss Percentage = (Loss ÷ Cost Price) × 100

Calculations:

⇒ Let Loss = 5x and Selling Price = 7x.

⇒ Cost Price (CP) = 7x + 5x = 12x.

⇒ Loss % = (5x ÷ 12x) × 100.

⇒ Loss % = (5 ÷ 12) × 100 = 41.666...

⇒ Loss % ≈ 41.67%.

∴ The correct answer is 41.67 percent.

Additional Information

Profit Percentage

Profit occurs when Selling Price > Cost Price. Formula: Profit % = [(SP − CP) ÷ CP] × 100.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount. Discount % = (Discount ÷ MP) × 100.

Relationship between CP and SP

In case of Loss, SP = CP × (100 − Loss%) ÷ 100. In case of Profit, SP = CP × (100 + Profit%) ÷ 100.

Shortcut Trick

Total time for 100% filling = 80 min

Time for 25% filling = 80 ÷ 4 = 20 min

Convert to seconds: 20 × 60 = 1200 sec

∴ The correct answer is 1200 sec.

Alternate Method

Given:

Time to fill full tank = 80 min

Target portion = 25%

Formula:

Required Time = Total Time × Required fraction

Calculations:

⇒ Total time in seconds = 80 × 60 = 4800 sec

⇒ 25% of the total time = (25 ÷ 100) × 4800

⇒ Required time = 1/4 × 4800

⇒ Required time = 1200 sec

∴ The correct answer is 1200 sec.

Additional Information

Time and Work Relation

The time taken to complete a part of a work is directly proportional to the size of that part. Time = Work ÷ Efficiency.

Percentage to Fraction Conversion

To convert percentage to fraction, divide by 100. For example, 25% = 25/100 = 1/4.

Unit Conversion

To convert minutes to seconds, multiply by 60 (1 min = 60 sec). To convert seconds to minutes, divide by 60.

Shortcut Trick

Initial Speed = 12 ÷ (36/60) = 20 km/hr.

New Speed = 20 − 8 = 12 km/hr.

Since Distance is constant, Speed ratio 20 : 12 = 5 : 3 → Time ratio = 3 : 5.

3 units = 36 min ⇒ 1 unit = 12 min ⇒ 5 units = 60 min.

∴ The correct answer is 60 min.

Alternate Method

Given: Distance = 12 km, Initial Time = 36 min, Speed Decrease = 8 km/hr.

Formula Used: Speed = Distance ÷ Time | Time = Distance ÷ Speed

⇒ Initial Time in hours = 36 ÷ 60 = 0.6 hours.

⇒ Initial Speed = 12 ÷ 0.6 = 20 km/hr.

⇒ New Speed = 20 − 8 = 12 km/hr.

⇒ New Time = 12 ÷ 12 = 1 hour.

⇒ New Time in minutes = 1 × 60 = 60 min.

∴ The correct answer is 60 min.

Additional Information

Relationship between Speed, Time, and Distance

When Distance is constant, Speed is inversely proportional to Time (S₁/S₂ = T₂/T₁).

Unit Conversion

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

Average Speed

If a certain distance is covered at x km/hr and the same distance at y km/hr, the Average Speed = (2 × x × y) ÷ (x + y).

Shortcut Trick

Let Selling Price (SP) = 9 units.

Discount = 5/9 × 9 = 5 units ⇒ Marked Price (MP) = 9 + 5 = 14 units.

At 25% Loss, SP = 75% of CP ⇒ Cost Price (CP) = 9 ÷ 0.75 = 12 units.

Required percentage = (12/14) × 100 = 6/7 × 100 ≈ 85.71%.

∴ The correct answer is 85.71 percent.

Alternate Method

Given:

Loss percentage = 25%

Discount = (5/9) × Selling Price (SP)

Formula Used:

1. Marked Price (MP) = SP + Discount
2. Cost Price (CP) = SP ÷ (1 − Loss%)
3. Required % = (CP / MP) × 100

Calculations:

⇒ Let SP = 9x

⇒ Discount = (5/9) × 9x = 5x

⇒ MP = SP + Discount = 9x + 5x = 14x

⇒ Loss = 25% ⇒ SP = 75% of CP

⇒ 9x = (75/100) × CP

⇒ CP = (9x × 100) ÷ 75 = 12x

⇒ CP as % of MP = (12x / 14x) × 100

⇒ % = (6 / 7) × 100 = 85.7142...

∴ The correct answer is 85.71 percent.

Additional Information

Relationship between CP, SP, and MP

CP = SP − Profit or CP = SP + Loss. MP = CP + Markup. Discount is always calculated on Marked Price.

Profit and Loss Percentages

Profit % = (Profit / CP) × 100. Loss % = (Loss / CP) × 100. Discount % = (Discount / MP) × 100.

Successive Discounts

Equivalent discount for two successive discounts a% and b% = (a + b − ab/100)%.

Shortcut Trick

Ratio of articles = 18000 ÷ 600 = 30 times.

Total Marked Price for 18000 articles = 450 × 30 = ₹13500.

Since a 40% discount is given, Selling Price = 60% of Total MP.

Total SP = 60% of 13500 = 0.6 × 13500 = ₹8100.

∴ The correct answer is ₹8100.

Alternate Method

Given:

Total Marked Price (MP) of 600 articles = ₹450

Total articles to find SP for = 18000

Discount percentage = 40%

Formula Used:

Selling Price (SP) = MP − Discount

SP = MP × (100 − Discount %)/100

Calculations:

⇒ MP of 1 article = 450 ÷ 600 = ₹0.75

⇒ MP of 18000 articles = 18000 × 0.75

⇒ MP of 18000 articles = ₹13500

⇒ Discount on 18000 articles = 40% of 13500

⇒ Discount = (40/100) × 13500 = ₹5400

⇒ Selling Price = Total MP − Discount

⇒ Selling Price = 13500 − 5400 = ₹8100

∴ The correct answer is ₹8100.

Additional Information

Marked Price (MP)

It is the price printed on the article or the price at which the retailer intends to sell the product before offering any discount.

Successive Discounts

If two successive discounts of d1% and d2% are given, the equivalent single discount is given by (d1 + d2 − (d1 × d2)/100)%.

Profit and Loss Relation

The relationship between CP and MP is given by: CP/MP = (100 − Discount%)/(100 + Profit%).

The correct answer is 'affect'.

Key Points

• The passage discusses the vital role of sleep in human health and the repercussions of its deficiency.
• The blank requires a verb that describes how a lack of sleep influences or changes mood, memory, and physical health.
• 'Affect' means to have an effect on or to make a difference to. It is the most appropriate word to describe how health factors are influenced by external conditions like sleep deprivation.
• The phrase 'negatively affect' is a standard collocation used to describe an unfavorable influence on a system or state.

Therefore, the correct answer is 'Option 1'.

Complete Passage: Sleep is a vital part of human health and well-being. Lack of sleep can negatively 1. affect our mood, memory, and physical health. Experts recommend at least seven to eight hr of sleep for 2. average adults. During sleep, the body repairs tissues and the brain 3. processes information from the day. People with irregular sleep schedules may find it difficult to 4. function during the day. Creating a consistent bedtime routine can help 5. build better sleep habits.

Additional Information

• Destroy means to end the existence of something by damaging or attacking it; it is too extreme for describing the impact on mood.
• Damage means physical harm that impairs value or usefulness; while health can be damaged, 'affect' is more idiomatically versatile for mood and memory.
• Reflect means to throw back light or show an image, which does not fit the context of impact or influence.
• Note the difference: Affect is usually a verb (to influence), while Effect is usually a noun (the result).

The correct answer is 'average'.

Key Points

• The passage discusses the importance of sleep for human health and well-being.
• The sentence provides a general guideline for the amount of sleep needed by a standard representative of the population.
• The word 'average' is the most appropriate adjective here to describe the general adult population, for whom seven to eight hours of sleep is the standard medical recommendation.
• Using 'average' helps categorize the group without specifying individual variations like age or health conditions.

Therefore, the correct answer is 'Option 3'.

Complete Passage: Sleep is a vital part of human health and well-being. Lack of sleep can negatively (1) affect our mood, memory, and physical health. Experts recommend at least seven to eight hr of sleep for (2) average adults. During sleep, the body repairs tissues and the brain (3) processes information from the day. People with irregular sleep schedules may find it difficult to (4) function during the day. Creating a consistent bedtime routine can help (5) build better sleep habits.

Additional Information

• Typical: Refers to having the distinctive qualities of a particular type of person or thing.
• Common: Refers to something occurring, found, or done often.
• Normal: Refers to conforming to a standard or being usual/expected.

The correct answer is 'processes'.

Key Points

• The passage emphasizes the physiological and cognitive roles of sleep.
• The sentence explains what the brain does with the information gathered during the day while a person is sleeping.
• 'Processes' is the most appropriate verb in this context as it means to perform a series of operations on data or information to handle, organize, or consolidate it.
• In cognitive science, sleep is known as a time when the brain processes memories and information, which fits the sentence perfectly.

Therefore, the correct answer is 'Option 3'.

Complete Passage: Sleep is a vital part of human health and well-being. Lack of sleep can negatively 1. affect our mood, memory, and physical health. Experts recommend at least seven to eight hr of sleep for 2. average adults. During sleep, the body repairs tissues and the brain 3. processes information from the day. People with irregular sleep schedules may find it difficult to 4. function during the day. Creating a consistent bedtime routine can help 5. build better sleep habits.

Additional Information

• Earns: To receive money or rewards in return for work; this does not apply to the brain handling information.
• Saves: While the brain stores information, 'processes' is a more comprehensive term for what the brain does during sleep (sorting, consolidating, and handling data).
• Forgets: While some information is lost, the primary health-related function of sleep being described here is the beneficial handling (processing) of information.

The correct answer is 'function'.

Key Points

• The passage focuses on the importance of sleep for human health and the consequences of sleep deprivation.
• The sentence describes a difficulty people face during the day when their sleep schedules are irregular.
• 'Function' is the most appropriate verb as it means to work or operate in a proper or particular way, especially in the context of daily cognitive and physical performance.
• Other options ('relax', 'wake', 'speak') do not accurately describe the general daily impairment caused by a lack of restorative sleep.

Therefore, the correct answer is 'Option 1'.

Complete Passage: Sleep is a vital part of human health and well-being. Lack of sleep can negatively 1. affect our mood, memory, and physical health. Experts recommend at least seven to eight hr of sleep for 2. average adults. During sleep, the body repairs tissues and the brain 3. processes information from the day. People with irregular sleep schedules may find it difficult to 4. function during the day. Creating a consistent bedtime routine can help 5. build better sleep habits.

Additional Information

• Relax: To rest or engage in an enjoyable activity so as to become less tired or anxious.
• Wake: To emerge or cause to emerge from a state of sleep; stop sleeping.
• Speak: To say something in order to convey information, an opinion, or a feeling.

The correct answer is 'build'.

Key Points

• The passage focuses on the importance of sleep hygiene and maintaining healthy routines.
• The blank requires a verb that describes the action of developing or establishing better sleep habits.
• "Build" is the most appropriate choice as it means to develop or establish something (like a habit) over a period of time.
• Using a consistent routine is a proactive way to build or cultivate positive behavior.

Therefore, the correct answer is 'Option 1'.

Complete Passage: Sleep is a vital part of human health and well-being. Lack of sleep can negatively 1. affect our mood, memory, and physical health. Experts recommend at least seven to eight hr of sleep for 2. average adults. During sleep, the body repairs tissues and the brain 3. processes information from the day. People with irregular sleep schedules may find it difficult to 4. function during the day. Creating a consistent bedtime routine can help 5. build better sleep habits.

Additional Information

• Break: To stop or end a habit, usually a negative one (e.g., break a bad habit).
• CUE: A signal or prompt for something to happen; it does not fit the grammatical structure of 'helping to [verb] habits' in this context.
• Test: To examine or evaluate the quality or performance of something, which does not apply to the creation of habits here.

The correct answer is 'asleep at the switch'.

 

Key Points

• The idiom 'asleep at the switch' means to be inattentive to a duty or failing to react quickly to a situation.
• In the given sentence, it describes a bureaucracy that is failing to address the critical issue of youth unemployment.
• The origin of this phrase comes from the railroad industry, where a trainman might fail to change a track switch, leading to an accident.

Therefore, the correct answer is 'Option 3'.

Complete Sentence: When the youth are struggling with unemployment and the bureaucracy is asleep at the switch, how can a great nation be formed?

Additional Information

• The other options like 'asleep at the light', 'asleep at the board', and 'asleep at the cut-out' are incorrect variations and do not constitute standard English idioms.
• Common synonyms for being 'asleep at the switch' include negligent, remiss, and oblivious.

The correct answer is: Option (1) i.e. Dragged.

Key Points

• The word 'pulled' means to exert force on someone or something so as to cause movement towards oneself. (खींचना)
• Example: She pulled the door open to welcome the guests into the house.
• 'Dragged' refers to pulling someone or something along forcefully, especially with difficulty or along the ground; it is the closest synonym to the word 'pulled' in this context. (घसीटना)
• Example: The workers dragged the heavy sacks of cement across the construction site.
• Hence, we can infer that the synonym of 'pulled' is 'dragged'.

Therefore, the correct answer is: Dragged.

Additional Information

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

• Pushed (धक्का देना): To exert force on someone or something in order to move them away from oneself.
• Example: He pushed the cart through the narrow aisle of the supermarket.
• Stopped (रुकना / रोकना): To come to an end or to cause something to cease moving or operating.
• Example: The driver stopped the bus at the designated stop.
• Rejected (अस्वीकार करना): To dismiss as inadequate, inappropriate, or not meeting certain standards.
• Example: The university rejected his application because it was submitted after the deadline.

Choose the word that is the most appropriate synonym of the word 'deceive'.

The correct answer is 'Option (4)' i.e. 'Trick'.

Key Points

• The word 'deceive' means to deliberately cause someone to believe something that is not true, especially for personal gain or to hide the truth. (धोखा देना)
• Example: The salesman tried to deceive the customers by misrepresenting the quality of the product.
• 'Trick' refers to an act or scheme intended to deceive or outwit someone; it is the most appropriate synonym as it involves using cleverness or dishonesty to mislead others. (छल करना / चकमा देना)
• Example: The magician used a clever trick to make the coin disappear into thin air.
• Hence, we can infer that the most appropriate synonym of 'deceive' is 'trick'.

Therefore, the correct answer is- Trick.

Additional Information

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

• Help (मदद करना): To assist or aid someone in doing something.
• Example: It is always good to help those who are in need.
• Guide (मार्गदर्शन करना): To show someone the way or direct their movements or actions.
• Example: The tour leader will guide the group through the historical monuments of the city.
• Support (समर्थन करना): To provide assistance, encouragement, or approval for someone or something.
• Example: My parents always support my decisions regarding my career.

The correct answer is volatility.

Key Points

• In the given sentence, the word volatility is misspelled. It is often incorrectly written as volatality.
• The correct spelling of the term is v-o-l-a-t-i-l-i-t-y. It originates from the Latin word volatilis, which means flying or fleeting.
• The noun volatility describes the state of being unstable, highly changeable, or prone to unexpected and rapid shifts, especially in financial markets or chemical properties.
• All other underlined words in the sentence—dividend, shareholders, and remarkable—are spelled correctly and fit their respective grammatical contexts perfectly.

 Additional Information

• Dividend:
• Meaning: A distribution of a portion of a company's earnings, decided by the board of directors, paid to a class of its shareholders.
• Grammar: It is a noun, derived from the Latin word dividendum, which means thing to be divided.
• Shareholders:
• Meaning: Any person, company, or institution that owns at least one share of a company’s stock.
• Role: They are the actual owners of a corporation and have the right to vote on key corporate matters.
• Remarkable:
• Meaning: Worthy of attention, striking, or extraordinary.
• Word Class: It acts as an adjective modifying the noun rise in the provided sentence.

The correct answer is: False.

Key Points

• The word 'genuine' refers to something that is authentic, real, or true; it is not a fake or a counterfeit. (असली / वास्तविक)
• Example: The antique dealer confirmed that the signature on the painting was genuine.
• 'False' refers to something that is not real or genuine; it is intentionally untrue, fake, or artificial. (नकली / असत्य)
• Example: The witness was charged for providing false information to the police.
• Hence, we can infer that the most appropriate antonym of 'genuine' is 'false'.

Therefore, the correct answer is: False.

Additional Information

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

• Real (वास्तविक): Actually existing as a thing or occurring in fact; not imagined or supposed.
• Example: After years of searching, they finally found the real source of the river.
• Honest (ईमानदार): Free of deceit; truthful and sincere.
• Example: He is well-known for being an honest man who never breaks his promises.
• Original (मौलिक): Present or existing from the beginning; first or earliest.
• Example: The museum houses the original manuscript of the famous poet.

The correct answer is It is said that honesty is the best policy.

Key Points

• When an active sentence starts with an indefinite subject like They, People, or Someone followed by a reporting verb (e.g., say, think, believe) and a that-clause, the passive voice is often introduced by the dummy subject It.
• The active verb say is in the Present Indefinite Tense. To convert this into the passive voice, we use the structure: It + is + past participle (V3) + that-clause.
• In this specific sentence, They say becomes It is said. The conjunction that connects the passive introductory phrase to the rest of the statement.
• The phrase honesty is the best policy is a universal truth and a noun clause acting as the object. In such constructions, the content of the that-clause remains unchanged during the transformation.
• Therefore, the complete passive construction is It is said that honesty is the best policy.

 Additional Information

• Comparison of incorrect options:
• Honesty said to be the best policy: This is grammatically incomplete as it lacks the auxiliary verb (is) necessary to form the Passive Voice.
• They are said honesty is the best policy: This structure is logically and syntactically incorrect because the pronoun They cannot be the subject of the passive verb are said while simultaneously retaining the noun clause in this manner.
• Honesty was said to be the best policy: This is incorrect because it changes the tense of the original sentence. The reporting verb say is in the present tense, so the passive form must use is rather than the past tense was.
• Alternative Passive Structure:
• Such sentences can also be converted using the Subject + Verb (Passive) + To-infinitive pattern. For example: Honesty is said to be the best policy. This involves moving the subject of the noun clause to the start of the sentence.

The correct answer is Does the insurance company provide a complete health check-up every year?.

Key Points

• The original sentence is in the Passive Voice and follows the structure of an interrogative sentence in the Present Simple Tense. This is identified by the auxiliary verb 'Is' at the beginning and the Past Participle form of the verb 'provided'.
• The phrase 'every year' acts as an adverbial of frequency, which is a hallmark of the Present Simple Tense, indicating a habitual or routine action.
• To convert an interrogative sentence from passive to Active Voice in this tense, we use the formula: Do/Does + Subject + Base Verb (V1) + Object?.
• The Passive Agent 'the insurance company' becomes the Active Subject. Since 'the insurance company' is a singular third-person entity, the auxiliary verb 'Does' must be used.
• The Passive Subject 'a complete health check-up' becomes the Active Object, and the verb 'provided' reverts to its base form, 'provide'.

 Additional Information

• Understanding Tense Variations in Interrogative Sentences:
• Present Continuous Tense: Uses the structure 'Is/Am/Are + Subject + V-ing?'. It is used for actions happening at the moment of speaking.
• Past Simple Tense: Uses 'Did + Subject + V1?'. This is used to inquire about actions that were completed at a specific time in the past.
• Present Perfect Tense: Uses 'Has/Have + Subject + V3?'. This tense is typically used for actions where the time is not specific or the action has relevance to the present.
• Active Voice emphasizes the doer of the action, making the sentence more direct and clear, whereas Passive Voice emphasizes the recipient or the action itself.

The correct answer is 'in'.

 

Key Points

• The preposition 'in' is used to indicate a position within an enclosed space, a container, or a physical area with defined boundaries.
• Since a 'house' is a physical structure that provides an interior space for living, the preposition 'in' is the most appropriate choice to describe residing inside it.
• Common collocations for habitation include 'live in a house', 'live in an apartment', or 'live in a cottage'.

Therefore, the correct answer is Option 1.

 

Complete Sentence: 'The poor family lives in a small house near the forest of Similipal.'

 

Additional Information

• Option 2: 'on' is used for surfaces (e.g., 'on the roof') or being atop something, which does not fit the context of living inside a dwelling.
• Option 3: 'at' is typically used for specific points or locations in space (e.g., 'at the bus stop') or specific addresses.
• Option 4: 'by' means 'near' or 'beside' (e.g., 'a house by the woods'), which would imply living next to the house rather than inside it.

The correct answer is look into the matter.

Key Points

• The phrasal verb look into is the most appropriate choice here as it means to investigate, examine, or research the facts of a situation thoroughly.
• In the context of financial irregularities, a committee is expected to conduct a detailed inquiry or audit to identify errors or malpractices.
• The original phrase look onto is contextually incorrect because it refers to the physical direction or view a building or window has, such as a house that looks onto a park.
• By using look into, the sentence accurately conveys that the department is being subjected to a formal investigation regarding its monetary records.

 Additional Information

• Look over:
• This phrasal verb means to examine or inspect something quickly or superficially.
• It is typically used when checking for errors in a draft or reviewing a document before a meeting.
• Look after:
• This means to take care of, protect, or be responsible for someone or something.
• It is commonly applied to caregiving (looking after children) or supervising the maintenance of property.
• Phrasal Verbs with Look:
• Look up to: To admire or respect someone as a role model.
• Look down on: To consider someone as inferior or unimportant.
• Look out for: To be vigilant or watchful for potential danger or opportunities.