SSC CGL 2025 (Held On: 12 Sept, 2025 Shift 3) (Previous Year Paper)

The logic followed here is:

So, 'QUY' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

The logic followed here is:

So, 'QAK' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

The logic followed here is:

thus, "182" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

The logic followed here is:

Logic: Next term = (Previous term)² + 1

thus, "458330" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

The logic followed here is:

thus, "26" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

Given Statement: While the world is moving towards automation, it is essential to ensure that ethical frameworks evolve alongside technological advancements to prevent misuse.

Now, 

Assumptions:

I. Automation can lead to ethical dilemmas - Implicit (If there were no ethical risks, there would be no need to evolve ethical frameworks to prevent misuse)

II. Ethical frameworks must be updated to keep pace with technological advancements - Implicit  (The statement directly argues that ethical frameworks should evolve alongside technology.)

III. Automation will eventually replace human labor in all sectors - Not Implicit (The statement only discusses automation increasing, not complete replacement of human labor.)

Here, Only I and II are implicit

Hence, the correct answer is "Option 1".

Given word: 'DEVELOP'

After arranged in alphabetical order:

After arranged in alphabetical order: D, E, E, L, O, P, V

Thus,Two letters remain in the same position.

Hence, the correct answer is "Option 1".

The address given in the problem is,

No. 45, First Avenue, Raja Annamalaipuram, Chennai, Tamil Nadu - 600028

Let's match this address with the given options one by one to figure out which one is exactly the same.

So, the address that is exactly the same as the given address is in option (2).

Hence, the correct option is "option (2)".

Let’s check each option,

1) CANCEL → cannot be formed as there is  No A in INTELLIGENCE.

2) NEGLECT→ can be formed as INTELLIGENCE

3) GENTLE → can be formed as INTELLIGENCE

4) INCITE → can be formed as  INTELLIGENCE

Hence, “CANCEL” can’t be formed.

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

Given: Eight persons A, B, C, D, E, F, G, and H are sitting around a circle facing the center.

1.C is second to the right of A.

2.E is opposite C.

3.F is to the immediate left of E.

4.B is to the immediate right of A.

5.G is to the immediate left of D.

Thus, F is sitting to the right of D.

Hence, the correct answer is "Option 4".

The logic followed here is :-

COUNTRY : FRXQWUB 

Similarly,

EXAMINE : ?

Hence, the correct answer is "HADPLQH".

Thus, the correct answer is Optrion 2.

The logic followed here is :-  

​Logic: Split into two equal halves and interchange them (block shifting).

Given, KITCAT : CATTIK 

Break KITCAT into two equal blocks: KIT | CAT

Now reverse the order of the two blocks: CAT | KIT

So, CATTIK

Similarly,

Split into two equal halves: PEN | TOP

Reverse their order: TOP | PEN

Result → TOP + NEP = TOPNEP

Correct answer: TOPNEP (Option 2)

Hence, the correct answer is Option 2.

The logic followed here is:

Logic: Letter ↓1, Number ↑1

Now, checking the options, we get:

Option 1) Z1# : Y2@ : X3$

Option 2) W4% : V5^ : U6&

Option 3) T7* : S8( : R9)

Option 4) Q10_ : P9@ : O8$

Here, numbers are decreasing, while in all other options numbers are increasing.

Hence, the one which is odd from the rest is "Option 4."

The logic followed here is:

Given:

dream focus build skill → trq, xnz, hmd, clv

focus logic dream → trq, jkp, xnz

trust logic build dream → xnj, clv, jkp, trq

Similarly,

build skill logic trust is codded as clv, hmd, jkp, xnj

Hence, the one which is odd from the rest is "Option 1."

Given:

x + 2y = 14

x − y = 5

Calculations:

From the second equation:

x = 5 + y

Substitute into the first equation:

5 + y + 2y = 14

5 + 3y = 14

3y = 9

y = 3

Now substitute back:

x = 5 + 3

x = 8

∴ The correct answer is 'Option 3.'

The logic followed here is:

Given:

If 6 $ 2 = 20, 

⇒ 6 x 2 = 12

⇒ 6 + 2 = 8

⇒ 12 + 8 = 20

and 4 $ 3 = 19,

⇒ 4 x 3 = 12

⇒ 4 + 3 = 7

⇒ 12 + 7 = 19

Similarly, 5 $ 2 = ?

⇒ 5 x 2 = 10

⇒ 5 + 2 = 7

⇒ 10 + 7 = 17

Hence, the correct answer is "Option 2."

The logic followed here is:

Given:

'SAVE' is coded as '★3#5', 

S → ★

A → 3

V → #

E → 5

and  'VASE' as '#3★5',

V → # 

A → 3 

S → ★ 

E → 5 

Similarly, for  'EVAS'

E → 5

V → #

A → 3

S → ★

Here, the code for EVAS is 5#3★

Hence, the correct answer is "Option 4."

Given:

Let the two numbers be 3x and 5x (since ratio is 3 : 5).

Their sum is given as 64.

3x + 5x = 64

8x = 64

x = 8

Calculations:

Now find the numbers:

3x = 3 × 8 = 24

5x = 5 × 8 = 40

So, the two numbers are 24 and 40.

∴ The correct answer is "Option 1."

The logic followed here is:

Logic: the pattern is a @ b = a² + b

Given:

If 5 @ 3 = 28 , 

⇒ 5² + 3 = 25 + 3 = 28

and  4 @ 2 = 18,

⇒ 4² + 2 = 16 + 2 = 18 

Similarly,  6 @ 4 = ?

⇒ 6 @ 4 = 6² + 4

= 36 + 4

= 40

Hence, the correct answer is "Option 1."

Family Chart:

Given: 

"She is the daughter of my mother's only son."

→ My mother’s only son = I (the man himself).

So, The girl is his daughter.

Hence, the correct answer is "Option 1".

Family Chart:

Given:

P is the maternal uncle of Q.

Maternal uncle means mother’s brother.

So, P is Q’s mother’s brother.

Possible relation:

Since the information provided doesn't specify which sister we are talking about. So we can not extinguish the relation between them.

Hence, the correct answer is "Cannot be determined".

BODMAS Table: 

Given:

interchanging + & × and 3 & 9 

Now,checking the given equations, 

Option 1) (3+5)×9=48

⇒ (9×5)+3

= (45)+3

= 48

Option 2) (9+2)×3=10

⇒ (3×2)+9

= 6+9

= 15 ≠ 10

Option 3) (3+7)×9=60

⇒ (9×7)+3

= 63+3

= 66 ≠ 60

Option 4) (9+1)×3=15

⇒ (3×1)+9

= 3+9

= 12 ≠ 15

Hence, the correct answer is "Option 1".

Given: a % b = 37, where a % b = a + 2b,

Now,checking the given equations, 

Option 1) 25,5

⇒ 25 + 2×5 = 25 + 10 = 35 (Not correct)

Option 2) 27, 5

⇒ 27 + 2×5 = 27 + 10 = 37 (Correct)

Option 3) 16, 10

⇒ 16 + 2×10 = 16 + 20 = 36 (Not correct)

Option 4) 27, 10

⇒ 27 + 2×10 = 27 + 20 = 47 (Not correct)

Hence, the correct answer is "Option 2".

BODMAS Table: 

Given equation: 10 + 2 - 4 × 2 = ?

Now, if ‘+’, ‘-’, and ‘×’ are interchanged as:

= ×, - = +, × = ÷, then:

⇒ 10 × 2 + 4 ÷ 2 = ?

⇒ 20 + 2 = ?

⇒ 22

Hence, the correct answer is "Option 3".

Given:

In a tournament of 7 players, each player plays every other player once. 

Formula used:

When each player plays every other player once, the number of matches is given by:

Number of matches = n(n − 1) / 2

Where n = number of players

Calculations: 

Here, n = 7

Substitute the value:

Number of matches = 7(7 − 1) / 2

= 7 × 6 / 2

= 42 / 2

= 21

So, the total number of matches = 21

∴ The correct answer is "Option 1."

The correct answer is 1 - 3 - 4 - 2.

Key Points

• Bharatanatyam is considered one of the oldest classical dance forms of India, with references dating back to ancient texts such as the Natyashastra, written by Bharata around 200 BCE to 200 CE. It originated in Tamil Nadu and was initially performed in temples as a form of religious expression.
• Kathak, a classical dance form from North India, traces its roots to the storytelling tradition of ancient India. It evolved during the Mughal era and incorporates influences from both Hindu and Muslim cultures. Its historical references date back to the Bhakti movement, which emerged between the 15th and 17th centuries.
• Manipuri, originating from Manipur, is closely linked to the Vaishnavite traditions and the worship of Lord Krishna. Manipuri dance developed during the medieval period, particularly under King Bhagyachandra's reign in the 18th century.
• Mohiniyattam, a classical dance from Kerala, has relatively later references compared to the other forms. It gained prominence during the 18th century, particularly under the patronage of the rulers of Travancore.

Additional Information

• Bharatanatyam:
• Originated in Tamil Nadu, Bharatanatyam was performed in temples as a form of devotional offering.
• It is deeply rooted in the Natyashastra, which is an ancient treatise on drama and performance arts.
• The dance form is known for its graceful movements, expressions, and intricate footwork.
• It is performed to classical Carnatic music and often depicts stories from Hindu mythology.
• Kathak:
• Developed in North India, Kathak is known for its storytelling roots, derived from the Sanskrit word "Katha" meaning story.
• It reflects a blend of Hindu and Muslim cultural influences, especially during the Mughal era.
• Kathak dancers emphasize spins, facial expressions, and intricate rhythmic patterns.
• It is accompanied by classical Hindustani music and tabla or pakhawaj for rhythm.
• Manipuri:
• It emerged in the Vaishnavite traditions of Manipur.
• The dance form is notable for its soft and graceful movements, often depicting stories of Lord Krishna and Radha.
• Manipuri dancers typically wear traditional costumes, including a cylindrical skirt and intricate jewelry.
• The dance is performed to folk music and devotional songs.
• Mohiniyattam:
• Originated in Kerala, Mohiniyattam is known as the dance of the enchantress.
• It is characterized by gentle and flowing movements, complementing the lasya (feminine) aspect of dance.
• The dance form is performed to classical Carnatic music and often narrates mythological stories.
• It gained prominence under the rulers of Travancore during the 18th century.

Important Points

• Chronological Order:
• Bharatanatyam: Oldest, references in the Natyashastra (200 BCE - 200 CE).
• Kathak: Developed during the Bhakti movement and flourished under the Mughals.
• Manipuri: Evolved under the Vaishnavite traditions in the 18th century.
• Mohiniyattam: Gained prominence in Kerala during the 18th century.
• These classical dances are integral to India's cultural heritage and reflect the country's diverse traditions.
• The Natyashastra serves as the foundational text for most classical dance forms in India.

The correct answer is Phamsana — slabs rising to a point, straight incline.

Key Points

• Phamsana style roofs are characterized by slabs rising upwards in a straight slope toward a central point, forming a pyramidal appearance. Hence, this pair is correctly matched.
• Latina is the most common type of Nagara temple shikhara, marked by a tall curvilinear tower that curves inward gradually toward the top. Therefore, it is not rectangular or wagon-shaped.
• Valabhi roofs are rectangular and wagon-vault shaped, resembling the roof of a barrel vault. Hence, the pair mentioning Valabhi as “tall, curving inward sharply” is incorrect.
• Latina temples are not low and broad with stepped roofing; such stepped or pyramidal forms are associated more with other temple roof styles.
• Option-wise Analysis:
• Latina — rectangular, wagon-shaped – Incorrect.
• Phamsana — slabs rising to a point, straight incline – Correct.
• Valabhi — tall, curving inward sharply – Incorrect.
• Latina — low and broad with stepped roofing – Incorrect.
• Hence, the correct answer is Phamsana — slabs rising to a point, straight incline.

Additional Information

• Nagara Style: The dominant temple architecture style of North India, identified by curving towers called Shikharas.
• Latina Shikhara: Simple curvilinear tower with smooth vertical projection, commonly found in early Nagara temples.
• Phamsana Roof: Usually broader and shorter than Latina towers, often used for mandapas (assembly halls).
• Valabhi Style: Features a wagon-vault roof, similar to ancient Buddhist chaitya hall roofing patterns.
• Temple Architecture Period: Major developments in Nagara architecture occurred between the 5th century CE and 13th century CE.

Important Points

• Latina, Phamsana, and Valabhi are important classifications of Nagara temple superstructures.
• Wagon-vaulted roofs are strongly associated with Valabhi architecture, while curvilinear towers are associated with Latina.

The correct answer is Rangkhothak.

Key Points

• The Pongtu Festival is a significant cultural celebration of the Tutsa tribe in Arunachal Pradesh. This festival marks the post-sowing season and is celebrated primarily before the millet harvesting period.
• The festival is observed to seek blessings from the deity Rangkhothak. The deity is revered for ensuring a bountiful harvest and protecting the crops from natural calamities and pests.
• The Tutsa people express gratitude and hope for prosperity through their rituals and prayers during the festival. Hence, the correct answer is Rangkhothak.
• The Pongtu Festival is characterized by traditional dances, feasts, and offerings to the deity, which are performed to honor the divine forces that influence agriculture.
• It is an integral part of the cultural identity of the Tutsa tribe, symbolizing unity, gratitude, and their connection with nature and agricultural practices.

Additional Information

• About the Pongtu Festival:
• The Pongtu Festival generally lasts for a few days, during which various community activities are organized.
• It involves the consumption of traditional food, such as rice beer and millet-based dishes, which are staples for the Tutsa tribe.
• The festival also includes traditional dance and music performances that showcase the rich cultural heritage of the tribe.
• Role of Rangkhothak:
• Rangkhothak is regarded as the guardian deity of agricultural prosperity among the Tutsa tribe.
• Rituals performed during the Pongtu Festival are specifically aimed at seeking the deity's blessings for a good harvest and overall well-being.
• The deity is also believed to protect the crops from natural disasters and ensure a steady agricultural yield.
• Other Cultural Aspects of the Tutsa Tribe:
• The Tutsa tribe is one of the indigenous tribes of Arunachal Pradesh, known for their rich traditions and agricultural lifestyle.
• They practice shifting cultivation, which is a common agricultural method in the region.
• Their festivals, such as Pongtu, play a vital role in maintaining their cultural heritage and fostering community bonding.
• Comparison with Other Tribes:
• Unlike the Tutsa tribe, other tribes in Arunachal Pradesh, such as the Nyishi and Apatani, have their unique festivals and deities associated with agriculture and nature.
• For instance, the Nyishi tribe celebrates the Nyokum Festival to seek blessings from nature spirits for harmony and prosperity.

Important Points

• About Arunachal Pradesh:
• Arunachal Pradesh is often referred to as the "Land of the Rising Sun" in India.
• The state is home to numerous indigenous tribes, each with its unique culture, language, and festivals.
• Agriculture is a primary source of livelihood in Arunachal Pradesh, with festivals like Pongtu reflecting the agrarian lifestyle of its people.
• Significance of Tribal Festivals:
• Tribal festivals are not just religious events; they play a crucial role in preserving the cultural identity of indigenous communities.
• These festivals act as a platform for intergenerational knowledge transfer, ensuring the continuity of traditions and customs.
• They also promote unity and cooperation within the community, fostering a sense of belonging and shared purpose.

The correct answer is 9.

Key Points

• Teen Taal is one of the most popular and foundational taals (rhythmic cycles) in Hindustani Classical Music. It consists of 16 matras (beats).
• The structure of Teen Taal is divided into four vibhags (sections), each containing four matras. These divisions are essential for understanding and performing the taal rhythmically.
• The Khali, or the "empty beat," is a significant aspect of Teen Taal. It is marked with a wave of the hand instead of a clap, signifying a moment of rhythmic void or lightness.
• In Teen Taal, the Khali is placed on the 9th matra. This placement divides the taal into two halves, creating a balance between the claps (taali) and the wave (khali).
• The sequence of Teen Taal is represented as 1 (Sam), 2, 3, Taali on 5, 6, 7, 8, Khali on 9, 10, 11, 12, and Taali on 13, 14, 15, 16. This cyclic pattern is repeated throughout the composition.

Additional Information

• Structure of Teen Taal:
• Teen Taal has 16 beats divided into four sections of four beats each.
• Its notation is represented as + 2 0 3, where "+" denotes the first clap (Sam), "2" is the second clap (Taali on the 5th matra), "0" is the Khali (empty beat on the 9th matra), and "3" is the third clap (Taali on the 13th matra).
• Importance of Khali:
• The Khali, marked by a wave of the hand, provides contrast and adds a sense of lightness to the rhythm cycle.
• It helps distinguish between sections of the taal and guides the performer in maintaining proper rhythm.
• Applications of Teen Taal:
• Teen Taal is widely used in classical music compositions, including khayal, dhrupad, and instrumental music.
• It is also a foundation for tabla solos and accompaniment, where intricate rhythmic patterns are explored.
• Comparison with Other Taals:
• Teen Taal is distinguished by its 16-beat cycle, whereas other taals like Dadra have 6 beats and Ek Taal has 12 beats.
• This versatility makes Teen Taal suitable for a variety of compositions and improvisations.

Important Points

• Sam: The first beat of a taal, denoted by a clap, is called Sam. It is the most emphasized beat and serves as the starting and ending point of the rhythmic cycle.
• Taali: The clapping points in the taal, such as those on the 5th and 13th matras in Teen Taal, are called Taali. They help emphasize specific beats.
• Khali: The wave of the hand on the 9th matra indicates the Khali or empty beat. It provides a sense of contrast and balance within the taal cycle.
• Matra: A matra is a unit of time in Indian rhythm, similar to a beat in Western music. The number of matras determines the length of the rhythmic cycle.

The correct answer is Variations affect bounce, swing, and fairness on standard pitches.

Key Points

• Regulation by ICC: The International Cricket Council (ICC) strictly regulates the weight and circumference of cricket balls in official matches to maintain uniformity and fairness across all formats of the game.
• Impact on performance: Variations in weight and size significantly affect the bounce, swing, and spin of the ball. These factors are crucial in determining the outcome of matches and ensuring equal opportunities for both bowlers and batsmen.
• Standard pitches: Standard pitches are designed with specific dimensions and characteristics. Cricket balls must conform to regulated specifications to ensure predictable behavior on these pitches, contributing to a balanced contest.
• Consistency in gameplay: Uniformity in ball specifications helps ensure consistency in gameplay across different venues and conditions, fostering fair competition.
• Quality assurance: Strict regulations ensure that cricket balls are produced with high-quality materials and standardized manufacturing processes, preventing any unfair advantages or discrepancies.

Additional Information

• Specifications for Cricket Balls:
• The weight of a cricket ball must be between 156 grams and 163 grams as per ICC regulations.
• The circumference should be between 22.4 cm and 22.9 cm.
• Red balls are used in Test matches, while white balls are used in ODIs and T20s.
• Different ball brands such as Kookaburra, Dukes, and SG are used globally, with slight variations in seam and finish.
• Impact of Ball Variations:
• Heavier balls may offer more swing, while lighter balls might favor batsmen due to less movement.
• The seam plays a critical role in generating spin and swing, affecting bowler performance.
• Changes in ball dimensions can disrupt the balance between batting and bowling, leading to unfair outcomes.
• Role of ICC in Cricket:
• The ICC is the governing body for international cricket, responsible for standardizing rules, regulations, and equipment specifications.
• Its guidelines ensure uniformity in gameplay across various formats and tournaments.
• ICC also monitors ball manufacturing to uphold these standards.
• Red vs. White Balls:
• Red balls: Used in longer formats, they have a pronounced seam for better swing and spin.
• White balls: Used in limited-overs formats, they are treated for durability under floodlights.
• White balls tend to deteriorate faster, affecting their performance over time.

Important Points

• Advantages of Standardized Cricket Balls:
• Ensures fair gameplay and equal opportunities for all players.
• Maintains consistency across matches played in different regions and conditions.
• Helps bowlers and batsmen strategize effectively based on predictable ball behavior.
• Examples of ICC Regulations:
• In Test cricket, only red balls conforming to ICC specifications are permitted.
• In ODIs and T20s, white balls are used, but they must meet the same weight and circumference standards as red balls.
• Special cases like pink balls are used for day-night Test matches but are also regulated for consistency.

The correct answer is Harvinder Singh.

Key Points

• Harvinder Singh created history by becoming the first Indian archer to win a Paralympic gold medal at the Paris 2024 Paralympic Games.
• He won the gold medal in the Men's Individual Recurve Open Archery event, marking a landmark achievement for Indian para-sports.
• Harvinder defeated Poland's Lukasz Ciszek in the final and showcased exceptional consistency throughout the tournament.
• Before winning gold at Paris 2024, Harvinder Singh had won a bronze medal at the Tokyo 2020 Paralympics, becoming India's first Paralympic medalist in archery.
• This achievement was India's first-ever Paralympic gold medal in archery, making it a historic moment in Indian sporting history.
• Hence, Harvinder Singh is the correct answer.

Additional Information

• Harvinder Singh:
• Born in Haryana.
• Competes in Para Archery.
• Won Bronze Medal at the Tokyo 2020 Paralympics.
• Won Gold Medal at the Paris 2024 Paralympics.
• Sheetal Devi:
• India's first international armless archer.
• Won medals at the Asian Para Games 2023.
• Did not win India's first Paralympic gold in archery.
• Rakesh Kumar:
• Indian para-archer who competes in compound events.
• Represented India at multiple international competitions.
• Preethi Pal:
• Indian para-athlete specializing in track events.
• Won medals in athletics at the Paris 2024 Paralympics.
• She is not associated with archery.
• Paris 2024 Paralympics:
• Held in Paris, France.
• India recorded its best-ever Paralympic performance.
• Indian athletes achieved several historic milestones across different sports.

Important Points

• Sport: Para Archery
• Event: Men's Individual Recurve Open
• Paralympics: Paris 2024
• Historic Achievement: India's first-ever Paralympic gold medal in archery
• Gold Medal Winner: Harvinder Singh

Mistake Points

Sheetal Devi is not the correct answer for this specific question because of the distinction between winning a medal and winning the first-ever gold.

Sheetal Devi won a Bronze medal (Mixed Team Compound) at the Paris 2024 Paralympics. Harvinder Singh is the correct answer because he won the Gold medal (Men's Individual Recurve), marking India's first-ever gold in the sport.

Hence, the correct answer is "Harvinder Singh".

The correct answer is Pretoria, South Africa.

Key Points

• The Meeting of BRICS Ministers of Foreign Affairs was held in Pretoria, South Africa on 4 June 2018.
• The meeting aimed to strengthen cooperation among the BRICS nations (Brazil, Russia, India, China, South Africa) in areas such as economics, trade, and diplomacy.
• South Africa hosted the meeting as part of its role as the chair of BRICS for the year 2018.
• Discussions during the meeting focused on international peace, economic reforms, and strategies to promote sustainable development among member countries.
• BRICS is an important platform for emerging economies, and South Africa plays a significant role as the only African member of this group.

Additional Information

• BRICS Overview:
• BRICS is an acronym for Brazil, Russia, India, China, and South Africa, representing five major emerging economies.
• These countries collectively account for about 40% of the global population and nearly 25% of the world's GDP.
• It was formed in 2006, initially as BRIC, and South Africa joined in 2010.
• South Africa’s Role in BRICS:
• South Africa joined BRICS in 2010, bringing an African perspective to the grouping.
• It hosted the 6th BRICS Summit in Durban in 2013 and chaired BRICS meetings in 2018.
• South Africa emphasizes issues like sustainable development, African integration, and socio-economic growth within BRICS discussions.
• Significance of BRICS Meetings:
• BRICS meetings provide a platform for member countries to coordinate on global governance reforms, economic policies, and international diplomacy.
• The grouping works towards a multipolar world order and aims to reduce the dominance of traditional Western powers.
• Key outcomes often include resolutions on trade, investment, technology sharing, and geopolitical challenges.
• Other BRICS Summits:
• The first BRICS Summit was held in Yekaterinburg, Russia in 2009.
• India hosted the 8th BRICS Summit in Goa in 2016.
• China hosted the 9th BRICS Summit in Xiamen in 2017.

Important Points

• BRICS Goals:
• Promoting economic growth and development in member countries.
• Fostering cooperation on issues like climate change, terrorism, and global governance reforms.
• Enhancing trade, investment, and technological collaboration among member states.
• South Africa’s Contribution:
• South Africa advocates for African regional integration within BRICS discussions.
• It supports infrastructure development and promotes economic opportunities in Africa.

The correct answer is A collection of modern Indian plays on social issues.

Key Points

• "Hot Stage" is a book that brings together a collection of modern Indian plays, focusing on various social issues.
• The book highlights the cultural diversity and social dynamics of India through theatrical works, making it a reflection of contemporary Indian society.
• It aims to use the medium of drama to address societal problems such as inequality, gender discrimination, corruption, and poverty.
• Plays included in the book are written by modern Indian playwrights who contribute to creating awareness and stimulating thought among readers and audiences.
• Hence, the theme of the book aligns directly with social issues portrayed in a theatrical format.

Additional Information

• Role of Theatre in India:
• Theatre has been a powerful medium for storytelling and addressing social issues since ancient times.
• Modern Indian theatre often focuses on themes like poverty, gender issues, caste discrimination, and political corruption.
• Notable playwrights such as Girish Karnad, Mahesh Dattani, and Vijay Tendulkar have significantly contributed to Indian theatre addressing social concerns.
• Social Issues in Indian Plays:
• Plays often serve as a mirror to society, showcasing issues such as domestic violence, economic inequality, and societal norms.
• They act as an educational tool for audiences, creating awareness about the struggles faced by marginalized communities.
• Other Themes in Indian Literature:
• While "Hot Stage" deals with social issues, Indian literature also explores themes of mythology, history, and travel.
• For example, novels like "The Palace of Illusions" delve into ancient Indian mythology, while books like "Freedom at Midnight" focus on historical events such as India's independence movement.
• Difference Between Social Plays and Other Genres:
• Social plays often focus on real-life societal challenges, aiming to drive change through art.
• In contrast, plays based on mythology or history tend to showcase traditional values or revisit the past.

Important Points

• Option 2: "A historical account of India's independence movement" refers to works like "Freedom at Midnight" but does not align with the theme of "Hot Stage."
• Option 3: "A novel about ancient Indian mythology" focuses on works like "The Palace of Illusions" and is unrelated to social issues portrayed in modern plays.
• Option 4: "A travelogue about the Himalayas" pertains to books such as "Into Thin Air", focusing on adventure and exploration rather than societal themes.

The correct answer is Soil pH.

Key Points

• Weather elements are the characteristics used to describe and measure atmospheric conditions. These commonly include temperature, humidity, wind, pressure, and precipitation. Soil pH, however, is related to soil science rather than atmospheric conditions.
• Temperature: It is one of the primary weather elements, indicating the heat level in the atmosphere. It affects human activities, ecosystems, and weather patterns. Hence, temperature is considered a weather element.
• Humidity: It refers to the amount of water vapor in the air and is crucial for understanding precipitation, fog, and dew formation. Thus, humidity is considered a weather element.
• Wind: Wind represents the movement of air from high to low pressure areas and significantly impacts climate and weather. Therefore, wind is a weather element.
• Soil pH: This is a measure of the acidity or alkalinity of soil and pertains to soil science. It impacts agriculture and plant growth but is not relevant to weather patterns or atmospheric studies. Hence, soil pH is not considered a weather element.

Additional Information

• Temperature:
• Measured in units such as Celsius, Fahrenheit, or Kelvin.
• Affects evaporation, condensation, and the overall climate.
• Monitoring temperature is crucial for weather forecasting and studying climate change.
• Temperature can vary significantly based on location, altitude, and time of day.
• Humidity:
• Measured using instruments like hygrometers or psychrometers.
• Relative humidity is expressed as a percentage, indicating the air's moisture content relative to its capacity.
• High humidity can lead to discomfort, while low humidity can cause dryness in the atmosphere.
• It influences weather phenomena such as rainfall, snow, and storms.
• Wind:
• Measured using anemometers and wind vanes.
• Wind direction and speed are crucial for understanding weather systems.
• Global wind patterns are influenced by Earth's rotation and temperature differences.
• Strong winds can result in cyclones, hurricanes, and tornadoes.
• Soil pH:
• Measured using pH meters or litmus paper.
• Ranges from 0 to 14, with 7 being neutral. Below 7 is acidic, and above 7 is alkaline.
• Affects nutrient availability and microbial activity in the soil.
• Important for agriculture, as different crops require specific pH ranges for optimal growth.

Important Points

• Instruments used for weather elements:
• Thermometers for temperature.
• Hygrometers for humidity.
• Anemometers for wind speed.
• Barometers for atmospheric pressure.
• Applications:
• Weather forecasting relies on the accurate measurement of weather elements.
• Agriculture benefits from understanding weather patterns, such as rainfall and temperature.
• Climate studies use weather data to predict long-term changes in the atmosphere.

The correct answer is Option 1.

Key Points

• Statement 1: Grandmaster (GM) Karthik Venkataraman won the 61st National Chess Championship held in Gurgaon and received a prize money of ₹6 lakh. This is correct as per official sources.
• Statement 2: International Master (IM) Neelash Saha finished second in the championship but lost to Surya Sekhar Ganguly in a tiebreak game. This is incorrect because there is no record of such a tiebreak game in the championship between these players.
• The championship was organized under the aegis of the All India Chess Federation (AICF), which is the governing body for chess in India.
• The event witnessed participation from several top-rated players in the country, showcasing their strategic and intellectual prowess in the game.
• The final standings were determined based on performance over multiple rounds, and the monetary rewards were distributed accordingly to the winners.

Additional Information

• Karthik Venkataraman:
• Karthik Venkataraman is a renowned Indian chess Grandmaster.
• He has represented India in various international chess tournaments and is known for his aggressive playing style.
• Winning the 61st National Chess Championship is one of the significant milestones in his career.
• All India Chess Federation (AICF):
• AICF is the official body for managing and promoting chess in India.
• The federation organizes various national-level chess tournaments, including the National Chess Championship.
• AICF is affiliated with the World Chess Federation (FIDE).
• Chess Tournaments:
• National chess championships are conducted annually to identify the best players in the country.
• These events follow a Swiss format or round-robin system to ensure fair competition.
• The winners often get the opportunity to represent India in international events such as the Chess Olympiad.
• Monetary Rewards in Chess:
• Prize money serves as an incentive for players to perform their best in competitions.
• For the 61st National Chess Championship, the total prize pool was substantial, with the winner receiving ₹6 lakh.
• It helps in the financial and professional growth of chess players in India.

Important Points

• Grandmaster vs International Master:
• The title of Grandmaster (GM) is the highest title awarded by FIDE to chess players, while International Master (IM) is a lower title.
• Achieving the GM title requires fulfilling specific performance criteria, such as earning three GM norms and a rating of at least 2500 Elo.
• IM titleholders are considered elite players but have not yet reached the GM level.
• Chess in India:
• India has produced many renowned chess players, including Viswanathan Anand, a former World Chess Champion.
• The popularity of chess has grown significantly in India, with increasing participation in tournaments at the grassroots level.
• Initiatives by the government and private organizations aim to promote chess as a mind sport.
• Chess Olympiad 2022:
• The 44th Chess Olympiad was held in Chennai, Tamil Nadu, India.
• It showcased the country's capability to host international chess events successfully.

The correct answer is Suraksha Shakti safety mascot.

Key Points

• Suraksha Shakti safety mascot was launched by Shri Shripad Naik, the Minister of State for Power and New & Renewable Energy, on Electrical Safety Day in 2025.
• This mascot aims to promote awareness about electrical safety among citizens and reduce accidents caused by electrical hazards.
• The initiative is part of the government’s efforts to enhance public safety and encourage the adoption of safe electrical practices.
• The mascot is designed to be an engaging and interactive symbol, targeting individuals of all age groups to understand the importance of electrical safety.
• This campaign complements other government programs focused on sustainable energy and safe electricity usage.

Additional Information

• Electrical Safety Day:
• Electrical Safety Day is observed annually to raise awareness about safe electrical practices and the prevention of accidents due to electrical faults.
• This day highlights the importance of adhering to standard safety protocols in residential, industrial, and commercial settings.
• Importance of Electrical Safety:
• Electrical accidents can lead to severe injuries, fatalities, and damage to property.
• Adopting measures such as using certified equipment, regular maintenance, and proper insulation can significantly reduce such incidents.
• Government Efforts for Electrical Safety:
• The Ministry of Power regularly conducts campaigns, workshops, and training sessions to educate the public about safe electricity usage.
• Programs like the National Energy Conservation Campaign also emphasize electrical safety as part of energy conservation efforts.
• Suraksha Shakti Mascot Features:
• The mascot serves as a visual representation of electrical safety and is designed to appeal to children and adults alike.
• It is often integrated into digital campaigns, social media outreach, and public events to maximize its impact.

Important Points

• National Fire Safety Code: This option refers to a set of guidelines for fire safety in buildings and industries, but it was not launched on Electrical Safety Day 2025.
• Smart Meter Adoption Program: This program focuses on the installation of smart meters to improve energy efficiency, but it is unrelated to the safety mascot initiative.
• Digital Grid Optimization Tool: This tool is used for optimizing grid operations and energy distribution; however, it was not part of the Electrical Safety Day 2025 launch.

The correct answer is A is true, but R is false.

Key Points

• Assertion (A): The Chotanagpur Plateau is considered an eastern extension of the Central Highlands.
• The Chotanagpur Plateau lies in the eastern part of India, primarily in the state of Jharkhand, and spreads over parts of Odisha, West Bengal, Bihar, and Chhattisgarh.
• Geologically, it is a part of the Peninsular Plateau region and is considered an extension of the Central Highlands due to its similar topography and geological structure.
• It is composed of Precambrian rocks, rich in mineral resources like coal, mica, and iron ore, making it an important industrial region in India.
• Hence, the assertion is correct.
• Reason (R): The Chotanagpur Plateau is drained primarily by the Chambal and Betwa rivers.
• This statement is incorrect, as the Chotanagpur Plateau is drained by rivers like the Damodar, Subarnarekha, Koel, and Barakar.
• The Chambal and Betwa rivers, on the other hand, flow through the Malwa Plateau and the Bundelkhand region, located in the Central Highlands of India.
• The Damodar River, known as the "Sorrow of Bengal," is the most significant river that drains this region, contributing to its unique drainage pattern.
• Hence, the reason is false.
• The reason given does not correctly explain the assertion, as it mentions rivers that do not drain the Chotanagpur Plateau.
• Therefore, the correct answer is: A is true, but R is false.

Additional Information

• Chotanagpur Plateau:
• Located in the eastern part of India, covering an area of approximately 65,000 sq. km.
• Divided into various smaller plateaus, the most prominent being the Ranchi Plateau, Hazaribagh Plateau, and Palamau Plateau.
• It is a rich source of minerals like coal, iron ore, copper, bauxite, and mica, contributing significantly to India's industrial development.
• Known for its unique terraced landscapes and abundant forest cover.
• The plateau is an important watershed for rivers like Damodar, Subarnarekha, Koel, and Barakar.
• Central Highlands:
• Part of the Peninsular Plateau of India, located to the north of the Narmada River.
• Includes regions like the Malwa Plateau, Bundelkhand, and Baghelkhand.
• Drained by rivers such as the Chambal, Betwa, Son, and Ken.
• Composed of ancient igneous and metamorphic rocks.
• Rivers of the Chotanagpur Plateau:
• Damodar River: Flows through Jharkhand and West Bengal, known for its coal deposits.
• Subarnarekha River: Originates near Ranchi and flows through Jharkhand, Odisha, and West Bengal.
• Koel River: A tributary of the Son River, originating in Jharkhand.
• Barakar River: A tributary of the Damodar River, important for industrial activities.
• Difference between Chambal and Betwa Rivers:
• Both rivers are part of the Yamuna River system and flow through the Central Highlands.
• The Chambal River is famous for its ravines and is a sanctuary for the gharials and other aquatic species.
• The Betwa River flows through Madhya Pradesh and Uttar Pradesh, with historical significance due to its proximity to Bundelkhand.

Important Points

• Mineral Importance: The Chotanagpur Plateau is often called the "Storehouse of Minerals" in India due to its rich deposits of coal, iron ore, mica, and other minerals.
• Drainage Pattern: Rivers of the Chotanagpur Plateau exhibit a radial drainage pattern, flowing in various directions from the plateau's elevated areas.
• Geological Structure: Composed of Precambrian rocks, these are some of the oldest rocks on Earth, dating back over 540 million years.
• Industrial Significance: The presence of mineral resources has led to the development of industries like steel plants in Bokaro and Jamshedpur.
• Flora and Fauna: The plateau is home to several forest reserves, including Betla National Park, which shelters tigers, elephants, and leopards.

The correct answer is 2028.

Key Points

• The Bharatiya Antariksh Station (BAS) is India’s ambitious plan to establish its own independent space station, marking significant progress in its space program.
• The Indian Space Research Organisation (ISRO) has announced that the first module of the BAS is scheduled for launch in the year 2028.
• The BAS is expected to serve as a platform for conducting long-term space experiments, including microgravity research, biological studies, and material science experiments.
• ISRO plans to develop a 20-tonne modular space station capable of hosting astronauts for up to 20 days at a time.
• The decision to launch the BAS aligns with India’s increasing focus on advancing human spaceflight capabilities, particularly after the success of the Gaganyaan mission scheduled for completion by 2024.

Additional Information

• 2030:
• While 2030 is not the planned year for the launch of the BAS, it is seen as a significant year for global space programs, with many countries aiming to achieve advancements in space exploration and technology by this time.
• The European Space Agency (ESA) and NASA have outlined ambitious plans for lunar exploration and Mars missions by the year 2030.
• 2035:
• 2035 is not the target year for the BAS launch, but it is a year often associated with long-term space exploration goals.
• China, for instance, has set goals for its lunar base and deep space exploration missions to be fully operational by 2035.
• 2040:
• 2040 is not the correct year for the BAS launch, but it is projected as a significant period for advanced space exploration.
• Many space-faring nations, including the United States and China, aim to establish permanent bases on the Moon or Mars by 2040.
• Main Theme:
• The Bharatiya Antariksh Station (BAS) reflects India’s growing capabilities in space exploration, aiming to establish a foothold in human spaceflight and independent research in low Earth orbit.
• India’s focus on developing its space infrastructure, including the success of Chandrayaan and Mangalyaan missions, has laid the foundation for this ambitious project.

The correct answer is India has rich reserves vital for major industries..

Key Points

• Non-metallic minerals such as limestone, mica, gypsum, and dolomite are abundant in India and form the backbone of many industries like cement, glass, ceramics, and fertilizers.
• India is one of the world's largest producers of mica, a mineral critical for electrical equipment and thermal insulation.
• The availability of non-metallic minerals plays a vital role in supporting the construction, agriculture, and chemical industries, contributing significantly to economic growth.
• Gypsum reserves in India are crucial for the cement industry, which is a key sector in infrastructure development.
• Contrary to the statement that India lacks reserves or that they are minimally used, the country’s non-metallic minerals are extensively used in both domestic industries and exports.

Additional Information

• Characteristics and Applications of Non-Metallic Minerals:
• Limestone: Found abundantly in states like Madhya Pradesh, Rajasthan, and Andhra Pradesh. It is a primary raw material for the cement industry and is also used in steel production and agriculture.
• Mica: India is the largest producer of sheet mica, primarily found in states like Jharkhand, Bihar, and Andhra Pradesh. It is used in electrical appliances, cosmetics, and paints.
• Gypsum: Found in Rajasthan and Tamil Nadu. It is essential for the production of cement, plaster of Paris, and fertilizers.
• Dolomite: Used in the iron and steel industry as a flux material. It is also used in the glass and ceramics industries.
• Importance of Non-Metallic Minerals in Economic Development:
• These minerals are essential for infrastructure development, including the construction of buildings, roads, and bridges.
• They contribute to foreign exchange earnings through exports.
• Their utilization in industries supports the Make in India initiative by providing raw materials for manufacturing.
• Comparison with Metallic Minerals:
• Non-metallic minerals are lighter and more abundant, whereas metallic minerals are often heavier and more limited in reserves.
• Non-metallic minerals are widely used in industries like agriculture, construction, and energy production, unlike metallic minerals which are mainly used for machinery and tools.
• Regional Distribution:
• Major non-metallic mineral belts include the Vindhyan, Aravalli, and Himalayan regions.
• States like Rajasthan, Madhya Pradesh, Odisha, and Andhra Pradesh are rich in non-metallic mineral reserves.

Important Points

• National Mineral Policy 2019: This policy emphasizes the sustainable and efficient utilization of mineral resources, including non-metallic minerals, to ensure long-term industrial growth.
• Export Contributions: Non-metallic minerals like mica contribute significantly to India’s export earnings. India accounts for over 60% of global mica production.
• Global Standing: India is among the top five producers of several non-metallic minerals like mica and limestone.
• Challenges: Despite the abundance, challenges like illegal mining, environmental concerns, and lack of advanced technology hinder optimal utilization.

The correct answer is 1.

Key Points

• A Proclamation of National Emergency in India is issued under Article 352 of the Constitution of India.
• Once the Proclamation of National Emergency is made, it must be approved by both Houses of Parliament within a period of 1 month from the date of its issue.
• If approved, the emergency remains in force for an initial period of six months and can be extended further by parliamentary approval.
• The approval requires a special majority, meaning the resolution must be passed by a majority of the total membership of each House and by a majority of not less than two-thirds of the members present and voting.
• If the Proclamation is not approved within 1 month, it automatically ceases to operate. This is a constitutional safeguard to prevent misuse of emergency powers.

Additional Information

• Article 352:
• It empowers the President to proclaim a National Emergency when the security of India or a part of it is threatened by war, external aggression, or armed rebellion.
• This article has been amended by the 44th Constitutional Amendment Act, 1978, which made the proclamation of emergency subject to stricter parliamentary control.
• Prior to the amendment, the proclamation could remain in force for two months without parliamentary approval, but this was reduced to 1 month.
• Types of Emergencies in India:
• National Emergency under Article 352.
• President’s Rule (State Emergency) under Article 356.
• Financial Emergency under Article 360.
• Approval and Revocation:
• For approval of a National Emergency, the resolution must pass both Houses of Parliament with a special majority.
• The Proclamation can be revoked at any time by the President, and it does not require parliamentary approval for revocation.
• Impact of National Emergency:
• Fundamental Rights under Article 19 are automatically suspended.
• The Parliament acquires the power to legislate on state subjects during the emergency.
• The distribution of revenues between the Centre and states can be modified by the President during the emergency.

Important Points

• The 44th Amendment introduced several changes to prevent the misuse of emergency powers. For instance, the term "internal disturbance" was replaced with armed rebellion as a ground for proclaiming emergency under Article 352.
• The President can proclaim a National Emergency only after receiving a written recommendation from the Cabinet (not merely the Prime Minister).
• During a National Emergency, the state legislatures continue to function, but the Parliament can make laws on subjects enumerated in the State List.

The correct answer is Both A and R are true, and R is the correct explanation of A.

Key Points

• Assertion (A): The Polar Satellite Launch Vehicle (PSLV) is widely recognized as the workhorse launch vehicle of the Indian Space Research Organisation (ISRO). This statement is true as PSLV has been instrumental in launching numerous satellites for a variety of purposes since its inception.
• Reason (R): PSLV is highly versatile, capable of launching a diverse range of payloads into different Earth orbits, including Earth Observation satellites, small Geosynchronous satellites, and Navigation satellites. Additionally, PSLV boasts an exceptionally high mission success rate across its different variants. This statement is also true, and it explains why PSLV is regarded as ISRO’s workhorse.
• PSLV was first launched on September 20, 1993, and has since been used for multiple missions, including interplanetary missions such as the Mars Orbiter Mission (Mangalyaan).
• The PSLV is known for its reliability and flexibility, having launched satellites into Low Earth Orbit (LEO), Polar Sun-Synchronous Orbit, and Geostationary Transfer Orbit (GTO).
• The statement "Both A and R are true, and R is the correct explanation of A" aptly explains the significance and versatility of PSLV in ISRO's space programs.

Additional Information

• Polar Satellite Launch Vehicle (PSLV):
• The PSLV is a four-stage launch vehicle developed by ISRO, with alternate solid and liquid propulsion systems.
• It has launched satellites not only for India but also for international customers, making it a globally recognized launch vehicle.
• PSLV-C37 set a world record by successfully launching 104 satellites in a single mission on February 15, 2017.
• The PSLV has variants such as PSLV-XL, PSLV-G, and PSLV-CA, each designed for specific payload capacities and mission requirements.
• ISRO:
• ISRO, established in 1969, is India’s space agency responsible for space exploration and satellite development.
• It has developed multiple launch vehicles, including the GSLV (Geosynchronous Satellite Launch Vehicle) and SSLV (Small Satellite Launch Vehicle).
• ISRO’s achievements include missions like Chandrayaan-1, Mangalyaan, and Chandrayaan-3, demonstrating its technological prowess.
• Satellite Launch Missions:
• PSLV has launched satellites for applications like remote sensing, navigation, communication, and climate monitoring.
• Examples include the Cartosat series for Earth observation and NavIC satellites for navigation.
• International Collaboration:
• PSLV has launched satellites for countries like USA, Germany, Canada, and Japan, strengthening ISRO’s global footprint.
• This has contributed to ISRO’s reputation as a cost-effective and reliable space agency.

Important Points

• PSLV Variants:
• PSLV-XL: Extended configuration used for heavier payloads.
• PSLV-CA: Core-alone version without strap-on boosters, suitable for smaller payloads.
• PSLV-G: Standard configuration designed for medium payloads.
• Mars Orbiter Mission (Mangalyaan):
• Launched on November 5, 2013, using PSLV-C25.
• India became the first nation to reach Mars in its maiden attempt.
• The mission showcased PSLV’s capability to carry out interplanetary missions.
• World Record:
• PSLV’s ability to launch 104 satellites in one mission highlights its efficiency and versatility.

The correct answer is The provision was abolished by the 104th Constitutional Amendment..

Key Points

• The Anglo-Indian representation in the Lok Sabha and State Legislative Assemblies was provided under Article 331 and Article 333 of the Indian Constitution, respectively.
• The 104th Constitutional Amendment Act, 2019, abolished the provision for the nomination of Anglo-Indian members to the Lok Sabha and State Legislative Assemblies. This amendment came into effect on January 25, 2020.
• The provision for Anglo-Indian representation was initially introduced to provide political representation to a small minority community in India. However, the government reasoned that the Anglo-Indian population had significantly decreased, and there was no longer a need for this special representation.
• Governors of states were earlier empowered to nominate one Anglo-Indian member to the State Legislative Assemblies under Article 333, but this provision was removed by the 104th Amendment.
• Statements in the question:
• Statement 1: "The Governor still nominates one Anglo-Indian member to the Assembly." – Incorrect, as this provision was abolished by the 104th Constitutional Amendment.
• Statement 2: "The provision was abolished by the 42nd Constitutional Amendment." – Incorrect, as the 42nd Amendment (1976) did not deal with Anglo-Indian representation.
• Statement 3: "The provision was abolished by the 104th Constitutional Amendment." – Correct.
• Statement 4: "Anglo-Indian members are elected through proportional representation." – Incorrect, as they were nominated and not elected.

Additional Information

• Anglo-Indian Community:
• Anglo-Indians are a small community in India that originated during the British colonial period, with mixed Indian and European ancestry.
• The community played an important role in India's administration, railways, and education system during British rule.
• 104th Constitutional Amendment Act:
• It abolished the special representation of Anglo-Indians in the Lok Sabha and State Legislative Assemblies.
• It also extended the reservation for Scheduled Castes (SC) and Scheduled Tribes (ST) in the Lok Sabha and State Assemblies for another 10 years.
• Historical Context:
• The Anglo-Indian representation was initially a safeguard for a minority community to voice their concerns in legislative bodies.
• Over time, with the decline in the population of Anglo-Indians and their assimilation into mainstream society, this provision was deemed unnecessary.
• Other Reserved Categories in India:
• Seats are reserved for Scheduled Castes (SC) and Scheduled Tribes (ST) in legislative bodies under Articles 330 and 332 of the Constitution.
• These reservations aim to ensure the political representation of historically disadvantaged communities.

Important Points

• The 42nd Constitutional Amendment Act (1976) is often referred to as the "Mini-Constitution" because it introduced significant changes but did not address Anglo-Indian representation.
• The 104th Constitutional Amendment was passed in December 2019 and came into effect on January 25, 2020.
• Currently, no seats are reserved for Anglo-Indians in either the Lok Sabha or State Legislative Assemblies.
• This amendment highlights the dynamic nature of the Constitution, which adapts to social and demographic changes.

The correct answer is Video-recorded confessions.

Key Points

• Bharatiya Nagarik Suraksha Samhita (BNSS) replaces the Code of Criminal Procedure (CrPC), focusing on modernizing criminal procedure laws in India to align with contemporary requirements.
• The introduction of video-recorded confessions ensures transparency and enhances the reliability of evidence presented in courts. This provision aims to eliminate coercion and safeguard the rights of the accused.
• The initiative reflects a move toward digitization and technological integration in judicial processes, ensuring accountability and reducing malpractices.
• BNSS does not include provisions like presumption of guilt or scrapping of bail rights, as these would violate fundamental rights under the Constitution of India. Hence, these statements are incorrect.
• BNSS does not replace all IPC sections. It specifically deals with procedures rather than substantive criminal laws. Hence, this statement is also incorrect.
• Hence, the correct answer is video-recorded confessions.

Additional Information

• Bharatiya Nagarik Suraksha Samhita (BNSS):
• The BNSS, enacted in 2023, aims to enhance efficiency in criminal procedures and ensure justice delivery in a time-bound manner.
• The law emphasizes digital integration, including the use of technology for evidence recording, case management, and monitoring judicial processes.
• The BNSS also facilitates victim-centric justice by ensuring their active participation in the legal process and introducing provisions for victim compensation.
• Video-recorded confessions:
• This provision is aligned with global best practices, enhancing the credibility of the judicial system and ensuring compliance with Article 21 of the Constitution, which guarantees the right to life and personal liberty.
• It addresses concerns related to custodial torture or forced confessions by ensuring that statements are recorded in a transparent and impartial manner.
• Key Principles of Criminal Procedure:
• The principles of criminal procedure emphasize fair trial, presumption of innocence, and adherence to fundamental rights.
• BNSS retains these principles, reinforcing the importance of due process and equality before the law.
• Indian Penal Code (IPC):
• The IPC, enacted in 1860, is the primary criminal code in India, addressing substantive criminal law.
• BNSS focuses exclusively on procedures, ensuring streamlined processes for investigation, trial, and sentencing.
• Constitutional Provisions:
• Article 22 protects against arbitrary arrest and detention, ensuring safeguards for the accused during criminal proceedings.
• BNSS aligns with constitutional mandates to uphold justice, transparency, and the rule of law.

Important Points

• Digitization in Criminal Justice:
• The use of technology, such as video recording, reduces the scope for manipulation and ensures transparency in judicial proceedings.
• India's judicial reforms, including BNSS, aim to integrate digital tools to expedite case disposal and improve access to justice.
• International Best Practices:
• Several countries, including the United States and United Kingdom, have implemented video-recorded confessions to ensure the integrity of legal processes.
• India's adoption of such practices reflects its commitment to modernizing its judicial system in line with global standards.
• Victim-Centric Justice:
• BNSS incorporates provisions to ensure timely justice for victims and safeguard their rights during legal proceedings.
• Compensation mechanisms under BNSS aim to reduce the financial burden on victims and their families.

The correct answer is**(IPPB.**.

Key Points

• India Post Payments Bank (IPPB) was launched by the Government of India to provide financial inclusion services through the extensive network of post offices across the country.
• IPPB operates under the Department of Posts, Ministry of Communications, and was formally inaugurated by Prime Minister Narendra Modi on September 1, 2018.
• IPPB leverages the services of postmen and Gramin Dak Sevaks to deliver banking and financial services at the doorstep of citizens, especially in rural and remote areas.
• The bank offers services such as savings accounts, money transfers, bill payments, recharges, and insurance products in a secure and seamless manner.
• IPPB is aimed at making financial services accessible to the unbanked population, enhancing financial literacy, and promoting digital banking in India.
• The bank uses a QR code-based biometric authentication system, ensuring secure transactions for customers.

Additional Information

• Services offered by IPPB:
• Savings accounts: IPPB provides savings accounts with no minimum balance requirement. Customers can open a regular savings account or a digital savings account.
• Money transfer: The bank facilitates domestic money transfers and payments using mobile banking and doorstep banking services.
• Utility bill payments: Customers can pay their utility bills such as electricity, water, and gas through IPPB’s platform.
• Insurance products: IPPB partners with insurance providers to offer life insurance and other products to rural customers.
• Micro-ATM services: Postmen equipped with micro-ATMs deliver financial services to citizens’ doorsteps.
• IPPB and rural outreach:
• IPPB has a presence in over 1.55 lakh post offices across India, with more than 1.35 lakh post offices in rural areas.
• It employs Gramin Dak Sevaks and postmen as banking agents to reach underserved sections of society.
• These agents use mobile devices to process transactions, ensuring ease of access for customers.
• Technology and security:
• IPPB uses Aadhaar-enabled Payment Systems (AePS) and QR code-based systems for transactions, ensuring security and transparency.
• Its platform integrates with the Unified Payments Interface (UPI), enabling seamless digital payments.
• Other related schemes:
• Pradhan Mantri Jan Dhan Yojana (PMJDY): This financial inclusion scheme provides basic banking services like savings accounts and credit facilities to the unbanked population.
• Aadhaar Payments Bridge System (APBS): This system helps in the direct transfer of government subsidies to beneficiaries through Aadhaar-linked accounts.

Important Points

• Role of IPPB in financial inclusion:
• IPPB plays a crucial role in bridging the gap between urban and rural banking infrastructure.
• It enhances the reach of banking services to the last mile, ensuring accessibility for rural populations.
• The bank also assists in implementing government-sponsored schemes, such as Direct Benefit Transfers (DBT), ensuring subsidies reach beneficiaries without leakages.
• Key facts about IPPB:
• IPPB started with 650 branches across India at the time of launch.
• It is 100% owned by the Government of India under the Department of Posts.
• IPPB operates on a model of paperless banking, promoting digital transactions and financial literacy.

The correct answer is Snakes.

Key Points

• Kalbelia Dance is a traditional folk dance performed by the Kalbelia community of Rajasthan, India, primarily known for their expertise in snake charming.
• The movements of the dancers in Kalbelia mimic the graceful and fluid movements of a snake. This is in line with the community’s traditional association with snake charming.
• It is performed by women wearing traditional black swirling skirts that are embroidered with silver ribbons, representing the color and movement of snakes.
• The music accompanying the dance is provided by male members of the community using traditional instruments like the pungi (a wind instrument traditionally used by snake charmers), the dholak (a type of drum), and the khanjari (a tambourine-like instrument).
• In 2010, Kalbelia dance was included in the UNESCO Representative List of the Intangible Cultural Heritage of Humanity, recognizing its cultural significance.

Additional Information

• Kalbelia Community:
• The Kalbelias are a semi-nomadic community traditionally involved in snake charming and trading snake venom.
• Their livelihood has historically revolved around their deep connection with snakes, which is reflected in their art forms like dance and music.
• In modern times, the Kalbelia community has shifted from snake charming due to legal restrictions and has focused more on preserving their cultural heritage through dance and music.
• Costumes:
• The dancers wear black skirts that are embroidered with silver or white patterns resembling snake skin.
• Their jewelry is elaborate, often including headpieces, necklaces, and bangles, complementing the vibrant and dynamic dance movements.
• Musical Instruments:
• The pungi is the primary instrument, traditionally used by snake charmers to control snakes.
• Other instruments like the dholak and khanjari add rhythm and vibrancy to the performance, creating a lively and captivating atmosphere.
• Performance Style:
• The dance is characterized by intricate footwork, swirling movements, and graceful gestures, all mimicking the sinuous and undulating motion of a snake.
• The performers often incorporate storytelling elements into their dance, narrating tales of their heritage and connection to nature.
• UNESCO Recognition:
• Kalbelia dance was recognized by UNESCO in 2010 as part of the Intangible Cultural Heritage of Humanity.
• This recognition has helped in preserving and promoting the dance on global platforms, highlighting its cultural significance and artistic value.

Important Points

• Kalbelia Dance and Indian Culture:
• The Kalbelia dance is a significant representation of India’s diverse cultural heritage, showcasing the unique traditions of a marginalized community.
• Its inclusion in UNESCO’s list has brought attention to the need for preserving endangered cultural practices and supporting the communities that sustain them.
• Connection with Wildlife:
• The dance reflects the Kalbelia community’s historical relationship with wildlife, particularly snakes, and their environment.
• Their cultural practices highlight the importance of coexistence with nature and respecting biodiversity.
• Tourism and Cultural Preservation:
• Kalbelia dance has become a popular attraction in Rajasthan’s cultural festivals and tourism events, contributing to the local economy and cultural preservation.
• Efforts are being made by the government and NGOs to promote and support the Kalbelia community in preserving their cultural identity.

The correct answer is Infrastructure.

Key Points

• Switzerland secured the 1st position in Infrastructure in the IMD World Competitiveness Ranking for both 2024 and 2025, reflecting its consistent excellence in this domain.
• The Infrastructure dimension in the IMD ranking evaluates factors such as technology infrastructure, scientific research capabilities, education systems, healthcare facilities, and environmental sustainability.
• Switzerland’s robust education system, advanced healthcare infrastructure, and commitment to environmental sustainability significantly contribute to its top rank in this category.
• The country is widely recognized for its technological innovation, with substantial investments in R&D and a thriving ecosystem for scientific research.
• This achievement reaffirms Switzerland’s position as a leader in providing world-class facilities and fostering a conducive environment for its citizens and businesses.

Additional Information

• IMD World Competitiveness Ranking:
• This ranking is published annually by the International Institute for Management Development (IMD), based in Lausanne, Switzerland.
• The ranking assesses the competitiveness of countries based on four key dimensions: Economic Performance, Government Efficiency, Business Efficiency, and Infrastructure.
• The evaluation incorporates data from various sources and surveys, ensuring a comprehensive analysis of each country’s performance.
• Switzerland’s Infrastructure Strengths:
• Switzerland boasts a highly developed public transport system, including its renowned rail network, which is among the most efficient globally.
• The country’s education system emphasizes innovation and scientific research, supported by world-class institutions such as ETH Zurich and EPFL.
• Its healthcare system is consistently ranked as one of the best in the world, offering universal coverage and top-tier medical facilities.
• Switzerland prioritizes environmental sustainability, with policies aimed at reducing carbon emissions and promoting renewable energy sources.
• Other Dimensions of IMD Competitiveness Ranking:
• Economic Performance: Evaluates macroeconomic indicators, international trade, and employment.
• Government Efficiency: Assesses the quality of governance, public services, and regulatory framework.
• Business Efficiency: Focuses on labor market conditions, productivity, and business practices.
• Global Competitiveness:
• Switzerland’s position in global rankings highlights its ability to attract foreign investments and foster economic growth.
• Its infrastructure is a key factor that drives innovation, enhances productivity, and supports sustainable development.

Important Points

• Switzerland’s Educational Institutions:
• ETH Zurich and EPFL are globally renowned for their contributions to scientific research and technological innovation.
• These institutions attract international students and researchers, fostering a diverse and dynamic academic environment.
• Environmental Policies:
• Switzerland is committed to achieving carbon neutrality by 2050, with strategies focusing on renewable energy and energy efficiency.
• The country’s policies aim to balance economic growth with sustainability, ensuring long-term benefits for its citizens.
• Public Transport:
• The Swiss rail network is considered one of the most punctual and efficient globally, providing seamless connectivity across the country.
• This infrastructure supports economic activities and enhances the quality of life for residents and visitors.

The correct answer is Maharashtra.

Key Points

• The Mangrove Cell initiative was launched in Maharashtra to promote conservation, restoration, and sustainable management of mangrove ecosystems within the state.
• Maharashtra is home to approximately 320 sq. km of mangrove forests, which are ecologically significant for protecting coastal areas and supporting biodiversity.
• The state government established the Mangrove Cell under its Forest Department in 2012 to address growing concerns about mangrove destruction due to urbanization and industrialization.
• The initiative focuses on activities such as afforestation, enforcement of laws against mangrove destruction, and creating awareness among local communities about the importance of mangroves.
• Maharashtra’s Mangrove Cell is actively involved in research and collaboration with organizations like the UNDP and Wetlands International to implement effective conservation strategies.

Additional Information

• Importance of Mangroves:
• Mangroves act as a natural barrier against coastal erosion and protect shorelines during storms and tsunamis.
• They are crucial for maintaining marine biodiversity, providing breeding grounds for fish, shrimp, and other aquatic species.
• Mangroves play a role in carbon sequestration, helping to mitigate climate change by absorbing large amounts of carbon dioxide.
• Maharashtra's Mangrove Coverage:
• The state has significant mangrove forests spread across areas like Thane, Mumbai, Raigad, and Sindhudurg.
• The mangroves in Maharashtra belong to species such as Avicennia, Rhizophora, and Sonneratia.
• The Mithi River and areas around Mumbai are particularly known for dense mangrove ecosystems.
• Threats to Mangroves:
• Mangrove ecosystems face threats from urbanization, pollution, deforestation, and encroachment for agricultural and industrial purposes.
• Illegal dumping of debris and construction activities in coastal areas have led to substantial mangrove loss in Maharashtra.
• Government Initiatives:
• The Maharashtra Mangrove Cell conducts regular surveys to map mangrove forests and prevent illegal encroachments.
• It works on restoring degraded mangrove habitats through afforestation programs and public awareness campaigns.
• The cell has also introduced eco-tourism initiatives to promote sustainable interaction with mangrove ecosystems.

Important Points

• Mangrove Cell Achievements:
• The cell has successfully conserved over 15,000 hectares of mangroves in Maharashtra.
• It has received recognition for its efforts in protecting mangrove ecosystems from encroachments and destruction.
• Partnerships with organizations such as UNDP and local NGOs have enhanced the effectiveness of its conservation programs.
• Global Mangrove Conservation Efforts:
• Globally, organizations like IUCN and WWF are working towards mangrove conservation as part of climate action initiatives.
• International treaties such as the Ramsar Convention emphasize the protection of wetlands, including mangrove ecosystems.

The correct answer is A is true, but R is false.

Key Points

• Assertion (A): Iron and steel is considered a heavy industry.
• The assertion is true. The iron and steel industry is classified as a heavy industry because it involves large-scale operations, significant capital investment, and the handling of heavy raw materials like iron ore, coal, and limestone.
• Heavy industries primarily focus on producing materials that serve as the foundation for other industries, and iron and steel are crucial for sectors like construction, manufacturing, and transportation.
• Reason (R): It requires lightweight raw materials like cotton and rubber.
• The reason is false. The iron and steel industry does not use lightweight raw materials like cotton and rubber.
• Instead, it heavily relies on iron ore, coal, and limestone, which are bulky and heavy raw materials, making the reasoning incorrect.
• Relationship between Assertion (A) and Reason (R):
• While the assertion is true, the reason provided is not valid as it does not align with the requirements or characteristics of the iron and steel industry.
• Hence, the correct explanation for the assertion is not the one given in the reason.

Additional Information

• Iron and Steel Industry Overview:
• The iron and steel industry is a key component of the global economy, serving as the backbone of modern infrastructure development.
• The main raw materials for the industry include iron ore, coal, limestone, and scrap steel.
• It is highly energy-intensive and requires large setups for smelting, refining, and producing steel products.
• Characteristics of Heavy Industry:
• Involves large-scale production and significant capital investment.
• Requires heavy raw materials and machinery for operations.
• Examples include the iron and steel industry, shipbuilding, and heavy machinery manufacturing.
• Lightweight Raw Materials in Industries:
• Lightweight raw materials like cotton and rubber are primarily used in light industries such as textiles, garment production, and rubber manufacturing.
• Light industries typically involve consumer goods and have smaller-scale operations compared to heavy industries.
• Importance of the Iron and Steel Industry:
• It is critical for sectors like construction, infrastructure, and transportation.
• Major steel-producing countries include China, India, Japan, and the United States.
• The industry contributes significantly to the GDP of industrialized nations and supports economic growth through job creation and trade.

Important Points

• Global Production Statistics:
• As of 2023, China is the largest producer of steel, accounting for more than 50% of global production.
• India is the second-largest producer, playing a crucial role in meeting domestic and international demand.
• Environmental Concerns:
• The iron and steel industry is a major contributor to carbon dioxide emissions, prompting the need for sustainable practices.
• Technological advancements like hydrogen-based steelmaking are being explored to reduce environmental impact.
• Applications of Steel:
• Steel is used in building skyscrapers, bridges, automobiles, railways, and household appliances.
• It is also essential for the production of machinery and tools in various industries.

The correct answer is Only 1 and 2 are correct.

Key Points

• Statement 1: The MISHTI scheme aims at mangrove plantation using scientific methods. The primary objective of the scheme is to protect and restore India’s coastal ecosystems, particularly mangroves, which play a critical role in combating climate change and protecting coastal areas. Hence, this statement is correct.
• Statement 2: The MISHTI scheme was announced as part of the Union Budget 2023-24 by Finance Minister Nirmala Sitharaman. It was introduced under the Green Growth initiative to promote sustainable development and environmental conservation. Hence, this statement is correct.
• Statement 3: The scheme does not include commercial leasing of mangrove forests. The focus is on restoration and conservation, not exploitation for commercial purposes. This statement is incorrect as it contradicts the environmental conservation aspect of the scheme. Hence, this statement is incorrect.

Additional Information

• About the MISHTI Scheme:
• MISHTI stands for Mangrove Initiative for Shoreline Habitats and Tangible Incomes.
• It is a central government initiative to promote mangrove plantation along India’s coastlines and wetlands, ensuring long-term environmental sustainability.
• The scheme is aligned with India’s commitments to global environmental goals such as the Paris Agreement and UN Sustainable Development Goals.
• Importance of Mangroves:
• Mangroves play a critical role in carbon sequestration, helping to mitigate climate change by absorbing significant amounts of carbon dioxide.
• They act as a natural barrier against coastal erosion and protect coastal communities from natural disasters like storms and tsunamis.
• Mangroves also provide habitats for diverse flora and fauna, supporting biodiversity conservation.
• Budget 2023-24 and Green Growth:
• The Union Budget 2023-24 introduced several initiatives aimed at achieving sustainable and inclusive development, including the MISHTI scheme.
• Other initiatives under the Green Growth initiative include PM-PRANAM for reducing chemical fertilizer use and the Amrit Dharohar scheme for wetland conservation.
• Global Initiatives Related to Mangroves:
• The Global Mangrove Alliance is an international initiative to restore and protect mangrove ecosystems worldwide.
• India is also a signatory to the Ramsar Convention, which promotes the conservation and sustainable use of wetlands, including mangroves.

Important Points

• India’s Mangrove Cover:
• According to the India State of Forest Report (ISFR) 2021, India’s mangrove cover is around 4,992 sq. km, accounting for approximately 0.15% of the country’s total geographical area.
• West Bengal has the largest mangrove cover, particularly in the Sundarbans region, followed by Gujarat and Andaman & Nicobar Islands.
• Key Threats to Mangroves:
• Deforestation due to urbanization, agriculture, and aquaculture activities.
• Climate change impacts such as rising sea levels and increasing frequency of extreme weather events.
• Pollution from industrial and agricultural runoff.
• Conservation Efforts:
• Programs such as the National Coastal Mission have been launched to protect coastal ecosystems, including mangroves.
• Community-based initiatives and awareness campaigns play a vital role in mangrove conservation.

The correct answer is Presidential Order under Article 370(3).

Key Points

• Article 370 granted special status to Jammu and Kashmir, providing autonomy over its internal matters except for defense, foreign affairs, finance, and communications.
• The abrogation of Article 370 was executed using a Presidential Order issued under Article 370(3), which allowed the President of India to make modifications or exceptions to Article 370.
• The Presidential Order C.O. 272, issued on 5th August 2019, replaced the previous Presidential Order from 1954, extending all provisions of the Indian Constitution to Jammu and Kashmir.
• The Jammu and Kashmir Reorganization Act, 2019, was passed by Parliament, bifurcating Jammu and Kashmir into two Union Territories: Jammu and Kashmir and Ladakh.
• The procedure involved obtaining the concurrence of the Jammu and Kashmir Legislative Assembly, which was absent at the time due to President's Rule. Consequently, the concurrence was given by the Governor, who was acting on behalf of the state legislature.

Additional Information

• Article 370:
• Article 370 was part of the Indian Constitution that provided special autonomy to Jammu and Kashmir.
• It was incorporated as a temporary provision under Part XXI of the Constitution, which deals with “Temporary, Transitional, and Special Provisions.”
• Under Article 370, the state had its own Constitution and decision-making rights in all matters except defense, foreign affairs, finance, and communications.
• It also allowed Jammu and Kashmir to have a separate flag and denied property rights to outsiders.
• Presidential Order and Article 370(3):
• Article 370(3) empowered the President of India to declare Article 370 inoperative or modify it, provided the recommendation of the Constituent Assembly of Jammu and Kashmir was obtained.
• Since the Constituent Assembly of Jammu and Kashmir ceased to exist in 1957, the Indian government used the provision of President's Rule in the state to bypass this requirement.
• The Presidential Order issued on 5th August 2019 extended all provisions of the Indian Constitution to Jammu and Kashmir, effectively nullifying its special status.
• Jammu and Kashmir Reorganization Act, 2019:
• Passed on 6th August 2019, this Act reorganized the state of Jammu and Kashmir into two Union Territories: Jammu and Kashmir (with a Legislative Assembly) and Ladakh (without a Legislative Assembly).
• The Act came into effect on 31st October 2019.
• The bifurcation aimed to improve governance and integrate the region fully with the rest of India.
• Impact of Abrogation:
• The abrogation of Article 370 has led to the extension of all Indian laws and provisions to Jammu and Kashmir.
• It has sparked debates on federalism, autonomy, and the rights of states under the Indian Constitution.
• While some argue it has brought greater integration, others highlight concerns over political representation and regional identity.

Important Points

• Article 368: This article pertains to the power of Parliament to amend the Constitution, including fundamental rights. However, it was not used for the abrogation of Article 370.
• Article 356: This article allows the imposition of President's Rule in a state due to the failure of constitutional machinery. While President's Rule was in effect in Jammu and Kashmir, Article 356 was not directly used for the abrogation.
• Ordinance by the President: Ordinances are temporary laws issued by the President when Parliament is not in session. This mechanism was not employed for abrogating Article 370.
• It is important to understand that the abrogation of Article 370 followed a unique constitutional process, combining Presidential Orders and Parliamentary legislation.

Shortcut Trick

Given: 60% of A = 0.3 of B = 1/6 of C

⇒ (3/5)A = (3/10)B = (1/6)C

Take the LCM of the numerators (3, 3, 1) = 3.

Divide the entire equation by 3 to get direct denominators:

⇒ A / 5 = B / 10 = C / 18

∴ The correct answer is 5 : 10 : 18.

Alternate Method

Given:

60% of A = 0.3 of B = 1/6 of C

5 A

10 B

18 C

Ratio Comparison of A, B, and C

Calculations:

⇒ 60% of A = 0.3 of B = 1/6 of C

⇒ (60/100) × A = (3/10) × B = (1/6) × C

⇒ (3/5) × A = (3/10) × B = (1/6) × C

Let (3/5)A = (3/10)B = (1/6)C = k

⇒ A = 5k / 3

⇒ B = 10k / 3

⇒ C = 6k = 18k / 3

Now, finding the ratio A : B : C by substituting the values:

⇒ A : B : C = (5k / 3) : (10k / 3) : (18k / 3)

⇒ A : B : C = 5 : 10 : 18

∴ The correct answer is 5 : 10 : 18.

Additional Information

Ratio of Equalities

If pA = qB = rC, then the ratio A : B : C is calculated as (1/p) : (1/q) : (1/r) or by dividing each term by the LCM of numerators p, q, and r.

Compound Ratio

The compound ratio of two individual ratios a:b and c:d is generated by multiplying the antecedents and consequents respectively, given by (a × c) : (b × d).

Invertendo

If a : b = c : d, then applying invertendo property gives b : a = d : c.

Shortcut Trick

Convert the total time into minutes: 1 hour 45 minutes = 105 minutes.

Since the distance covered in 1 minute is 0.875 km, directly multiply the distance by the total time.

Total Distance = 0.875 × 105 = 91.875 km.

∴ The correct answer is 91.875 km.

Alternate Method

Given:

Distance covered in 1 minute = 0.875 km

Total time traveled = 1 hour 45 minutes

Formula Used:

Distance = Speed × Time

0 min 1 min 105 min

0 km 0.875 km ? km

1 min gap

× 105 multiplier

Calculations:

⇒ First, convert the total time strictly into minutes.

⇒ Total Time = 1 hour + 45 minutes

⇒ Total Time = 60 minutes + 45 minutes = 105 minutes

⇒ The car's speed is effectively 0.875 km per minute.

⇒ Distance in 105 minutes = 0.875 × 105

⇒ Distance = 0.875 × (100 + 5)

⇒ Distance = 87.5 + 4.375

⇒ Distance = 91.875 km

∴ The correct answer is 91.875 km.

Additional Information

Unitary Method

The unitary method involves finding the value of a single base unit and then multiplying it by the necessary number of units to determine the final total value.

Speed & Distance Formula

Distance is always calculated as the product of Speed and Time (Distance = Speed × Time). Here, the car's speed acts directly as the rate per minute.

Unit Matching

Before executing a multiplication, ensure all parameters share the same base dimension. In this case, converting hours to minutes allowed a direct multiplication with the given rate.

Shortcut Trick

Combine the first two fractional terms directly by cross-multiplying their denominators.

Sum = [(7 − √2) + (7 + √2)] ÷ [(7 + √2) × (7 − √2)]

Sum = 14 ÷ (49 − 2)

Notice that the third term is exactly identical to this sum.

Expression = [14 ÷ (49 − 2)] − [14 ÷ (49 − 2)] = 0

∴ The correct answer is 0.

Alternate Method

Given:

Expression = [1 / (7 + √2)] + [1 / (7 − √2)] − [14 / (49 − 2)]

Formula Used:

(a + b)(a − b) = a² − b²

Calculations:

⇒ First, add the first two fractions by taking the LCM of their denominators.

⇒ LCM = (7 + √2)(7 − √2) = 7² − (√2)² = 49 − 2 = 47

⇒ Numerator = (7 − √2) + (7 + √2) = 14

⇒ Sum of first two terms = 14 / 47

⇒ Now, evaluate the third term individually:

⇒ Third term = 14 / (49 − 2) = 14 / 47

⇒ Substitute these simplified values back into the overall expression:

⇒ Result = 14 / 47 − 14 / 47

⇒ Result = 0

∴ The correct answer is 0.

Additional Information

Rationalization of Surds

To rationalize a denominator of the form a + √b, multiply both the numerator and denominator by its conjugate a − √b. This simplifies the surd expression into standard integers.

Algebraic Identities

The difference of squares formula (a + b)(a − b) = a² − b² is the primary mathematical tool used to eliminate square roots from denominators.

Simplification Rules

When simplifying complex fractional expressions, always check if combining certain elements directly reduces the equation to a common base value, which often results in zero or one.

Shortcut Trick

Using the weighted average method for net percentage change:

Net % Change = [ (2 × −10%) + (4 × 5%) + (4 × −15%) ] ÷ (2 + 4 + 4)

Net % Change = ( −20% + 20% − 60% ) ÷ 10

Net % Change = −60% ÷ 10 = −6%

The negative sign represents a decrease.

∴ The correct answer is 6% decrease.

Alternate Method

Given:

Ratio of expenditure on Food, Clothing, and Entertainment = 2 : 4 : 4

Let actual initial expenditures be a convenient multiple of the ratio, such as 200, 400, and 400.

Food200−10%Clothing400+5%Entertainment400−15%−20+20−60Net Change = −60 out of Total 1000 = −6%

Calculations:

⇒ Total initial expenditure = 200 + 400 + 400 = 1000

⇒ New expenditure on Food = 200 − (10% of 200) = 200 − 20 = 180

⇒ New expenditure on Clothing = 400 + (5% of 400) = 400 + 20 = 420

⇒ New expenditure on Entertainment = 400 − (15% of 400) = 400 − 60 = 340

⇒ Total new expenditure = 180 + 420 + 340 = 940

⇒ Net change in expenditure = 940 − 1000 = −60

⇒ Percentage change = (Net change ÷ Total initial expenditure) × 100

⇒ Percentage change = (−60 ÷ 1000) × 100 = −6%

The negative value implies a decrease of 6%.

∴ The correct answer is 6% decrease.

Additional Information

Weighted Average in Percentages

When a quantity is divided into specific parts, the net percentage change is the sum of (part ratio × % change) divided by the total ratio sum.

Base Shifting Technique

Assuming a convenient base value like 100 or a multiple of 10 for abstract ratio amounts makes calculating percentage increases or decreases purely integer-based and minimizes error.

Net Percentage Change

A negative final percentage signifies an overall decrement (loss/fall), while a positive percentage denotes an increment (gain/rise).

Shortcut Trick

Profit ratio A : B = (1,20,000 × 10) : (1,60,000 × 7) = 15 : 14.

Total profit units = 15 + 14 = 29 units.

Given B's share (14 units) = ₹16,800.

Value of 1 unit = 16,800 ÷ 14 = ₹1,200.

Total profit (29 units) = 29 × 1,200 = ₹34,800.

∴ The correct answer is ₹34,800.

Alternate Method

Given:

Investment by A = ₹1,20,000

Investment by B = ₹1,60,000

Time period for A = 10 months

Time period for B = 7 months

B's profit share = ₹16,800

Formula Used:

Profit Ratio = (Capital of A × Time of A) : (Capital of B × Time of B)

Partner A1.2L × 10 monthsProfit: 15 UnitsPartner B1.6L × 7 monthsProfit: 14 Units14 Units = ₹16,800 → 29 Units = ₹34,800

Calculations:

⇒ Profit Ratio of A : B = (1,20,000 × 10) : (1,60,000 × 7)

⇒ Profit Ratio = 12,00,000 : 11,20,000

⇒ By simplifying, we get Profit Ratio = 120 : 112 = 15 : 14

⇒ Let A's profit be 15x and B's profit be 14x.

⇒ Total profit = 15x + 14x = 29x

⇒ We are given that B's profit share is ₹16,800.

⇒ 14x = 16,800

⇒ x = 16,800 ÷ 14 = 1,200

⇒ Total profit = 29 × 1,200 = 34,800

∴ The correct answer is ₹34,800.

Additional Information

Partnership Profit Ratio

When investments are made for different time periods, the profit is distributed in the ratio of the product of capital and time. P₁ : P₂ = (C₁ × T₁) : (C₂ × T₂).

Active vs Sleeping Partner

A sleeping partner only invests capital, while an active partner also manages the business. An active partner may receive a fixed salary or percentage from total profit before the remainder is split.

Joining Mid-way

If a partner joins x months after the start of a year, their investment time period will be calculated as (12 − x) months for the annual profit distribution.

Shortcut Trick

Convert all animals to equivalent cows to find the total grazing units.

1 horse = 5/3 cows and 1 sheep = 3/5 cows.

A's total grazing = (21 × 5/3 × 6) + (15 × 2) = 210 + 30 = 240 cow-months.

B's total grazing = (15 × 6) + (40 × 3/5 × 7.5) = 90 + 180 = 270 cow-months.

A's rent portion = 240 ÷ (240 + 270) = 240 ÷ 510 = 8/17.

∴ The correct answer is 8/17.

Alternate Method

Given:

A places 21 horses for 6 months and 15 cows for 2 months.

B places 15 cows for 6 months and 40 sheep for 7.5 months.

Food equality: 3 horses = 5 cows and 6 cows = 10 sheep.

Formula Used:

Total Usage = Equivalent Number of Animals × Time Period

240 Units Ratio: 8 270 Units Ratio: 9 A's Rent Share B's Rent Share

Calculations:

⇒ First, convert all animals into equivalent cow units for calculation consistency.

⇒ 3 horses = 5 cows ⇒ 1 horse = 5/3 cows

⇒ 6 cows = 10 sheep ⇒ 1 sheep = 6/10 = 3/5 cows

⇒ Total grazing consumption for A = (21 × 5/3 × 6) + (15 × 2)

⇒ Total equivalent units for A = 210 + 30 = 240 cow-months

⇒ Total grazing consumption for B = (15 × 6) + (40 × 3/5 × 7.5)

⇒ Total equivalent units for B = 90 + 180 = 270 cow-months

⇒ The total rent will be distributed in the ratio of their total grazing consumption.

⇒ Ratio of rent share (A : B) = 240 : 270 = 8 : 9

⇒ Total ratio parts = 8 + 9 = 17 parts

⇒ Portion of the rent A should cover = 8 / 17

∴ The correct answer is 8/17.

Additional Information

Partnership / Joint Rent Ratio

When multiple partners invest in a business or rent a shared resource, the profit or expense is distributed in the exact ratio of the product of their investment (or resource usage) and the time period. Ratio = (Usage₁ × Time₁) : (Usage₂ × Time₂).

Proportional Division

To divide a total quantity representing fractions of a whole into a given ratio a:b, the individual fractional parts are calculated directly as [a / (a+b)] and [b / (a+b)] respectively.

Shortcut Trick

Convert cows to equivalent sheep: 4 cows = 8 sheep ⇒ 1 cow = 2 sheep.

A's equivalent sheep-months = (16 × 2 × 3) + (20 × 4) = 96 + 80 = 176.

B's equivalent sheep-months = 30 × 6 = 180.

Ratio of A's rent to B's rent = 176 : 180 = 44 : 45.

A's portion out of the total rent = 44 ÷ (44 + 45) = 44/89.

∴ The correct answer is 44/89.

Alternate Method

Given:

A uses 16 cows for 3 months and 20 sheep for 4 months.

B uses 30 sheep for 6 months.

Equivalence: 4 cows = 8 sheep.

Formula Used:

Rent Share Ratio = Total equivalent animal-months of A : Total equivalent animal-months of B

Rent Sharing Proportion

A: 176 units

B: 180 units Ratio = 44 Ratio = 45

Calculations:

⇒ First, find the sheep equivalent for A's cows.

⇒ 4 cows = 8 sheep → 1 cow = 2 sheep.

⇒ A's 16 cows = 16 × 2 = 32 sheep.

⇒ Total equivalent sheep-months for A = (32 sheep × 3 months) + (20 sheep × 4 months).

⇒ Total for A = 96 + 80 = 176 sheep-months.

⇒ Total equivalent sheep-months for B = 30 sheep × 6 months.

⇒ Total for B = 180 sheep-months.

⇒ Rent Ratio (A : B) = 176 : 180 = 44 : 45.

⇒ Total proportion parts = 44 + 45 = 89.

⇒ A's portion of the rent = 44/89.

∴ The correct answer is 44/89.

Additional Information

Partnership Basic Rule

When resources are used for different time periods, the profit or rent sharing ratio is directly proportional to the product of capital (or equivalent resource) and time period. Formula: Ratio = C₁×T₁ : C₂×T₂.

Compound Partnership

When individuals invest different amounts in different phases, their effective capital is calculated by multiplying each invested amount by its respective time period and summing them up.

Equivalent Units Principle

In scenarios involving different entities (like cows, sheep, or men, women), a common unit ratio must first be established to calculate the total effective capital or work completed before determining any proportions.

Shortcut Trick

Assume the overall average is 20 years (the middle value).

Calculate net deviation: (18 − 20)×2 + (20 − 20)×3 + (22 − 20)×5

⇒ Net deviation = (−4) + 0 + 10 = +6

Average deviation per student = +6 ÷ (2 + 3 + 5) = +0.6

Overall average = Assumed Average + Average Deviation = 20 + 0.6 = 20.6

∴ The correct answer is 20.6 years.

Alternate Method

Given:

Average ages of three groups = 18, 20, and 22

Ratio of number of students in the groups = 2 : 3 : 5

Formula Used:

Weighted Average = (N₁A₁ + N₂A₂ + N₃A₃) ÷ (N₁ + N₂ + N₃)

Ratio: 2 Avg: 18

Ratio: 3 Avg: 20

Ratio: 5 Avg: 22

Total Ratio Sum = 10 Combined Average = 20.6

Calculations:

Let the exact number of students in the three groups be 2x, 3x, and 5x respectively.

⇒ Total sum of ages = (18 × 2x) + (20 × 3x) + (22 × 5x)

⇒ Total sum = 36x + 60x + 110x = 206x

⇒ Total number of students = 2x + 3x + 5x = 10x

⇒ Overall average age = 206x ÷ 10x

⇒ Overall average age = 20.6 years

∴ The correct answer is 20.6 years.

Additional Information

Weighted Average

It is used when different subsets of data have different frequencies or sample sizes. Formula: A_w = (N₁A₁ + N₂A₂ + ... + N_nA_n) ÷ (N₁ + N₂ + ... + N_n).

Net Deviation Method

This shortcut simplifies heavy calculations by selecting an assumed central mean. The true average is obtained using the relation: True Average = Assumed Mean + (Sum of Net Deviations ÷ Total Frequency).

Key Property of Averages

If every observation in a specific dataset is increased, decreased, multiplied, or divided by a constant 'k', the overall average of that dataset will automatically reflect the exact same mathematical operation.

Shortcut Trick

Using the deviation method from the total average (68):

Total deviation = 5 × (63 − 68) + 5 × (72 − 68)

Total deviation = −25 + 20 = −5

To balance the sum to zero, the 6th number must offset this deviation: 68 − (−5) = 73.

∴ The correct answer is 73.

Alternate Method

Given:

Average of 11 numbers = 68

Average of the first 5 numbers = 63

Average of the last 5 numbers = 72

First 5 Avg = 63

Last 5 Avg = 72

6th ?

Total 11 Numbers (Avg = 68)

Formula Used:

Sum of items = Average × Number of items

6th Number = Total Sum − (Sum of first 5 + Sum of last 5)

Calculations:

⇒ Total sum of 11 numbers = 11 × 68 = 748

⇒ Sum of the first 5 numbers = 5 × 63 = 315

⇒ Sum of the last 5 numbers = 5 × 72 = 360

⇒ Sum of these 10 numbers = 315 + 360 = 675

⇒ 6th Number = 748 − 675

⇒ 6th Number = 73

∴ The correct answer is 73.

Additional Information

Weighted Average

When combining groups with different averages, the overall average is (N₁A₁ + N₂A₂) ÷ (N₁ + N₂).

Deviation Method

The sum of deviations of all observations from their true average is exactly zero. This principle provides a powerful shortcut to compute an unknown item dynamically.

Overlapping Groups

If the given groups overlap on a central item (e.g., first 6 and last 6 out of 11), that central item can be found directly using: Overlapping Item = (Sum of Group 1 + Sum of Group 2) − Total Sum.

Shortcut Trick The numbers exactly divisible by 13 form an Arithmetic Progression (AP). For any AP, the average is simply the midpoint of the first and last terms. First multiple of 13 after 300 = 24 × 13 = 312. Last multiple of 13 before 450 = 34 × 13 = 442. Average = (312 + 442) ÷ 2 = 754 ÷ 2 = 377. ∴ The correct answer is 377.

Alternate Method Given: Range = 300 to 450 Divisor = 13 Formula Used: Average of an Arithmetic Progression (AP) = (First term + Last term) ÷ 2

300 450

312 442 377 Average (Midpoint)

Avg = (312 + 442) ÷ 2

Calculations: ⇒ First integer > 300 divisible by 13: 300 ÷ 13 ≈ 23.07 → 24 × 13 = 312 ⇒ Last integer < 450 divisible by 13: 450 ÷ 13 ≈ 34.61 → 34 × 13 = 442 ⇒ The sequence of numbers forms an AP: 312, 325, 338, ..., 442 ⇒ First term (a) = 312 ⇒ Last term (l) = 442 ⇒ Average = (312 + 442) ÷ 2 ⇒ Average = 754 ÷ 2 ⇒ Average = 377 ∴ The correct answer is 377.

Additional Information Arithmetic Progression (AP) An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. Example: 312, 325, 338, ... with a common difference of 13. Average of an Arithmetic Progression The average of an equally spaced series (AP) is strictly the midpoint, which equals (First Term + Last Term) ÷ 2. Finding the Number of Terms To find the total terms 'n' in an AP, use the formula: n = [(Last term − First term) ÷ Common difference] + 1.

Shortcut Trick

Memorize common percentage to fraction conversions for faster calculation.

12 ¹/₂% = 1/8 and 66 ²/₃% = 2/3

⇒ Expression = (1/8) × 560 + (2/3) × 240

⇒ Expression = 70 + 160 = 230

∴ The correct answer is 230 km.

Alternate Method

Given:

12 ¹/₂% of 560 km + 66 ²/₃% of 240 km

Calculation:

⇒ 12 ¹/₂% = 25/2 % = (25/2) × (1/100) = 25/200 = 1/8

⇒ 66 ²/₃% = 200/3 % = (200/3) × (1/100) = 200/300 = 2/3

Substituting the fractional values into the original expression:

⇒ (1/8 × 560) + (2/3 × 240)

⇒ 70 + 160

⇒ 230

∴ The correct answer is 230 km.

Additional Information

Common Percentage-Fraction Equivalents

Memorizing standard equivalents saves calculation time: 16 ²/₃% = 1/6, 14 ²/₇% = 1/7, 33 ¹/₃% = 1/3, and 37 ¹/₂% = 3/8.

BODMAS Rule

Always follow the order of operations: Brackets, Orders, Division/Multiplication (left to right), Addition/Subtraction (left to right). The word 'of' indicates multiplication and is solved before division.

Percentage Reversibility

X% of Y is always equal to Y% of X. This property can be used interchangeably to make calculations easier when numbers are reversed.

Shortcut Trick

Daily commission from shirts = 3 × (2% of 500) = 3 × 10 = ₹30

Daily commission from ties = 4 × (12% of 150) = 4 × 18 = ₹72

Total daily commission = 30 + 72 = ₹102

Total commission earned in 30 days = 102 × 30 = ₹3060

∴ The correct answer is ₹3060.

Alternate Method

Given:

Price of a shirt = ₹500, Commission on a shirt = 2%

Price of a tie = ₹150, Commission on a tie = 12%

Items sold per day = 3 shirts and 4 ties

Total days = 30

Shirts Price: ₹500 | Comm: 2% Comm/item: ₹10 Daily (x3): ₹30

Ties Price: ₹150 | Comm: 12% Comm/item: ₹18 Daily (x4): ₹72

Total in 30 Days = ₹3060

Calculations:

⇒ Commission earned on one shirt = 2% of 500 = (2 ÷ 100) × 500 = ₹10

⇒ Commission earned on 3 shirts per day = 3 × 10 = ₹30

⇒ Commission earned on one tie = 12% of 150 = (12 ÷ 100) × 150 = ₹18

⇒ Commission earned on 4 ties per day = 4 × 18 = ₹72

⇒ Total commission earned per day = 30 + 72 = ₹102

⇒ Total commission earned in 30 days = 102 × 30 = ₹3060

∴ The correct answer is ₹3060.

Additional Information

Percentage Application

Percentage implies 'out of 100'. Thus, x% of y is calculated as (x ÷ 100) × y. In practical applications like commissions, discounts, or taxes, the percentage is applied directly to the base value.

Commission and Base Amount

Commission is generally paid as a percentage of the total sales value. If multiple items are sold with varying commission rates, they must be calculated individually before summation.

Unitary Method

Finding the value for a single unit and then multiplying it by the total number of units required is called the unitary method. It is highly effective for scaling daily quantities to monthly or annual values.

Shortcut Trick

Let the Cost Price (CP) of 100 units of apples be ₹100.

Selling Price (SP) at a claimed 5% loss = ₹95.

Actual weight used is 20% less, so the seller gives only 80 units (True CP = ₹80).

Profit earned by the seller = SP − CP = 95 − 80 = ₹15.

Total Profit % = (15 ÷ 80) × 100 = 18.75%.

∴ The correct answer is 18.75%.

Alternate Method

Given:

Loss percentage on Cost Price = 5%

False weight used = 20% less than actual weight

Formula Used:

Profit % = (Profit ÷ Cost Price) × 100

Actual CP800 gm = ₹800Selling Price1000 gm claimed = ₹950Profit = ₹150Profit % = (150 ÷ 800) × 100 = 18.75%

Calculations:

⇒ Let the cost price of 1000 gm of apples be ₹1000.

⇒ Selling price at a 5% loss = 1000 − (5% of 1000) = 1000 − 50 = ₹950.

⇒ The seller uses a false weight that is 20% less than the actual weight.

⇒ Actual weight given by the seller = 1000 − (20% of 1000) = 1000 − 200 = 800 gm.

⇒ Actual cost price incurred by the seller (for 800 gm) = ₹800.

⇒ Profit earned = Selling Price − Actual Cost Price

⇒ Profit = 950 − 800 = ₹150.

⇒ Total Profit % = (Profit ÷ Cost Price) × 100

⇒ Total Profit % = (150 ÷ 800) × 100 = 18.75%.

∴ The correct answer is 18.75%.

Additional Information

Dishonest Dealer (Selling at Cost Price)

If a trader professes to sell his goods at cost price but uses false weights, then his Profit % = [Error ÷ (True Value − Error)] × 100.

Successive Percentage Method

The overall profit can be evaluated using successive percentages. Giving 20% less weight means a gain of (20 ÷ 80) × 100 = 25%. Combined with a 5% loss on price, the Net % = 25 − 5 − (25 × 5)÷100 = 20 − 1.25 = 18.75%.

Ratio Method for Dishonest Dealer

Write the price ratio and quantity ratio separately. Price ratio (SP:CP) = 95:100. Quantity given ratio (SP:CP) = 100:80. Net Ratio = (95 × 100) : (100 × 80) = 95 : 80, which results in a profit of 15 on a base of 80.

Shortcut Trick

If the profit at one selling price equals the loss at another, the Cost Price is exactly halfway between them.

CP = (SP₁ + SP₂) ÷ 2

CP = (2200 + 1800) ÷ 2 = ₹2000

New SP = ₹2050 ⇒ Profit = 2050 − 2000 = ₹50

Profit % = (50 ÷ 2000) × 100 = 2.5%

∴ The correct answer is Profit of 2.5%.

Alternate Method

Given:

Selling Price 1 (SP₁) = ₹2200

Selling Price 2 (SP₂) = ₹1800

Profit at SP₁ = Loss at SP₂

Formula Used:

Profit = SP − CP

Loss = CP − SP

Profit % = (Profit ÷ CP) × 100

₹1800 CP = ₹2000 ₹2200

New SP = ₹2050

Loss (L)

Profit (P = L)

Profit = ₹50

Calculations:

Let the cost price of the item be CP.

⇒ Profit at SP₁ = Loss at SP₂

⇒ 2200 − CP = CP − 1800

⇒ 2CP = 2200 + 1800

⇒ 2CP = 4000

⇒ CP = ₹2000

Now, the item is sold for a new SP = ₹2050.

⇒ Profit = New SP − CP = 2050 − 2000 = ₹50

⇒ Profit % = (50 ÷ 2000) × 100

⇒ Profit % = 2.5%

∴ The correct answer is Profit of 2.5%.

Additional Information

Marked Price and Successive Discount

Successive discounts of a% and b% are equivalent to a single net discount of (a + b − (a × b) ÷ 100)%.

Relation between CP and MP

The exact ratio of Cost Price to Marked Price is directly proportional to the discount and profit given: CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%).

Dishonest Dealer

If a dealer claims to sell goods at cost price but uses a false weight, the actual profit percentage is (Error ÷ False Weight) × 100.

Shortcut Trick

Cost Price (CP) to Selling Price (SP1) ratio at 20% profit = 100 : 120 = 5 : 6.

Assuming CP = 5 units, then initial SP1 = P = 6 units.

Given the festive Marked Price (MP) = 1.5P ⇒ MP = 1.5 × 6 = 9 units.

A discount of 10% is given, so New SP = 9 × 0.9 = 8.1 units.

Profit % = [(New SP − CP) ÷ CP] × 100 = [(8.1 − 5) ÷ 5] × 100 = 62%.

∴ The correct answer is 62% (or 0.62).

Alternate Method

Given:

Initial Selling Price = ₹P

Initial Profit = 20%

New Marked Price (MP) = 1.5P

Festive Discount = 10%

Formula Used:

CP = SP × [100 ÷ (100 + Profit%)]

New SP = MP × [100 − Discount%] ÷ 100

Profit % = [(New SP − CP) ÷ CP] × 100

CP 5P/6 SP1 P SP2 1.35P MP 1.5P +20% -10% New Profit = 62%

Calculations:

⇒ CP = P × (100 ÷ 120) = 5P/6

⇒ New SP = 1.5P × (90 ÷ 100) = 1.35P = 27P/20

⇒ Profit = New SP − CP = (27P/20) − (5P/6)

⇒ LCM of 20 and 6 is 60.

⇒ Profit = (81P − 50P) ÷ 60 = 31P/60

⇒ Profit % = [(31P/60) ÷ (5P/6)] × 100

⇒ Profit % = (31/60) × (6/5) × 100

⇒ Profit % = (31/50) × 100 = 62%

⇒ Expressed as a decimal fraction, it is 0.62.

∴ The correct answer is 62% (or 0.62).

Additional Information

Successive Percentage Change

When a value undergoes two successive changes of a% and b%, the net percentage change is given by: Net Change = a + b + (a × b) ÷ 100.

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). The Selling Price is derived as: SP = MP × [100 − Discount%] ÷ 100.

Relationship between CP, MP, Profit and Discount

A direct relationship ratio is given by: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Shortcut Trick

Using the effective successive percentage change formula:

Net Profit % = M − D − (M × D) / 100

Where Markup (M) = 25% and Discount (D) = 10%

⇒ Profit % = 25 − 10 − (25 × 10) / 100

⇒ Profit % = 15 − 2.5 = 12.5%

∴ The correct answer is 12.50%.

Alternate Method

Given:

Markup = 25% above Cost Price (CP)

Discount = 10% on Marked Price (MP)

CP = 100

SP = 112.5

MP = 125

+25% Markup

−10%

+12.5% Profit

Calculations:

⇒ Let the Cost Price (CP) = 100

⇒ Marked Price (MP) = CP + 25% of CP = 100 + 25 = 125

⇒ Discount = 10% of MP = (10 / 100) × 125 = 12.5

⇒ Selling Price (SP) = MP − Discount = 125 − 12.5 = 112.5

⇒ Profit = SP − CP = 112.5 − 100 = 12.5

⇒ Profit Percentage = (Profit / CP) × 100 = (12.5 / 100) × 100 = 12.5%

∴ The correct answer is 12.50%.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). The formula is: Selling Price (SP) = MP − Discount.

Successive Percentage Rule

When a value is increased by A% and then decreased by B%, the effective change percentage is given by the formula: A − B − (A × B) / 100.

Profit & Loss Basics

Profit or Loss percentage is always calculated on the original Cost Price (CP) unless specifically stated otherwise.

Shortcut Trick

Let CP = 100%. Then Marked Price (MP) = 160% (as it is 60% above CP).

Selling Price (SP) after 25% discount = 160% − (25% of 160%) = 120%.

Actual Final SP = 100% + 14% profit = 114%.

Difference in SPs = 120% − 114% = 6%, which corresponds to the ₹150 cash discount.

⇒ 6% of CP = 150 ⇒ CP = 150 × 100 ÷ 6 = ₹2500.

∴ The correct answer is ₹2500.

Alternate Method

Given:

Markup = 60% above Cost Price

Discount = 25%

Additional Cash Discount = ₹150

Overall Profit = 14%

Formula Used:

Selling Price (SP) = Marked Price × (100 − Discount%) ÷ 100

Final SP = Cost Price × (100 + Profit%) ÷ 100

CP = 100%

+60%

MP = 160%

-25%

SP = 120%

+14% Profit

Final SP = 114%

• ₹150

120% - 114% = 6% → ₹150   ∴ 100% = ₹2500

Calculations:

⇒ Let the Cost Price (CP) be 100x.

⇒ Marked Price (MP) = 100x + (60% of 100x) = 160x.

⇒ Selling Price before cash discount = 160x − (25% of 160x) = 160x − 40x = 120x.

⇒ Final Selling Price = 120x − 150.

⇒ Based on the profit percentage, Final SP = CP + (14% of CP) = 114x.

⇒ Equating both values of Final SP:

⇒ 120x − 150 = 114x

⇒ 120x − 114x = 150

⇒ 6x = 150

⇒ x = 25

⇒ Cost Price = 100x = 100 × 25 = ₹2500.

∴ The correct answer is ₹2500.

Additional Information

Marked Price & Discount

Discount is exclusively given on the Marked Price (MP), never on Cost Price. It is simply a reduction in price directly impacting the Selling Price. Formula: SP = MP × (100 − Discount%) ÷ 100.

Direct Formula for CP and MP

When Profit% and Discount% are known, the direct ratio between Cost Price and Marked Price is efficiently calculated as CP / MP = (100 − Discount%) / (100 + Profit%).

Successive Discounts

When multiple flat discounts x% and y% are given sequentially, the single equivalent discount percentage is evaluated using: (x + y − x × y ÷ 100)%.

Shortcut Trick

First, find the Cost Price (CP) of the mixture from its Selling Price (SP) and Gain %.

CP of mixture = SP ÷ (1 + Gain%) = 43.70 ÷ 1.15 = ₹38/kg

Using Alligation, Ratio of quantities = (38 − 32) : (45 − 38) = 6 : 7

Since 7 parts correspond to 25 kg, 6 parts will correspond to: (25 ÷ 7) × 6 = 150 ÷ 7 ≈ 21.43 kg

∴ The correct answer is 21 kg.

Alternate Method

Given:

CP of first type of sugar = ₹45/kg

CP of second type of sugar = ₹32/kg

Quantity of second type of sugar = 25 kg

SP of mixture = ₹43.70/kg

Profit on mixture = 15%

Formula Used:

CP = SP × [100 ÷ (100 + Gain%)]

Sugar 1 (₹45)Sugar 2 (₹32)₹3838 − 32 = 645 − 38 = 7Quantity Ratio = 6 : 7

Calculations:

⇒ Mean CP of mixture = 43.70 × [100 ÷ (100 + 15)]

⇒ Mean CP = (43.70 × 100) ÷ 115

⇒ Mean CP = 4370 ÷ 115 = ₹38/kg

⇒ Using the rule of alligation (as shown in the diagram), the ratio of the quantities is:

⇒ (Mean CP − CP₂) : (CP₁ − Mean CP) = (38 − 32) : (45 − 38) = 6 : 7

⇒ Let the required quantity of the first type of sugar be x kg.

⇒ x ÷ 25 = 6 ÷ 7

⇒ x = (25 × 6) ÷ 7

⇒ x = 150 ÷ 7 ≈ 21.43 kg

⇒ Therefore, approximately 21 kg of the first type of sugar must be mixed.

∴ The correct answer is 21 kg.

Additional Information

Rule of Alligation

It is a fast cross-calculation method used to find the ratio in which two ingredients at given unit prices must be mixed to produce a mixture of a desired target price. The target price must always lie exactly between the two given prices.

Mean Price Requirement

The central value placed in the alligation cross is called the Mean Price. It must always be the Cost Price (CP) of the mixture. Never place Selling Price (SP) in the alligation diagram.

Cost Price from Selling Price

When Selling Price (SP) and Gain Percentage (P%) are given, Cost Price (CP) is computed backwards using the relation: CP = [100 ÷ (100 + P%)] × SP.

Shortcut Trick

In a right circular cone, the height, base radius, and slant height always form a right-angled triangle.

Using the common Pythagorean triplet (7, 24, 25), where the two legs are 7 and 24, the hypotenuse is directly 25.

Since the given radius is 7 cm and the height is 24 cm, the slant height is directly 25 cm.

∴ The correct answer is 25 cm.

Alternate Method

Given:

Radius of the base (r) = 7 cm

Height of the cone (h) = 24 cm

Formula Used:

Slant height (l) = √(r² + h²)

h = 24 cm r = 7 cm l = ?

Calculations:

⇒ l = √(7² + 24²)

⇒ l = √(49 + 576)

⇒ l = √(625)

⇒ l = 25 cm

∴ The correct answer is 25 cm.

Additional Information

Volume of a Cone

The volume is one-third of the volume of a cylinder with the same base and height: V = (1 ÷ 3) × π × r² × h.

Curved Surface Area (CSA)

The area of the curved surface alone is calculated using the slant height: CSA = π × r × l.

Total Surface Area (TSA)

The total surface area includes both the base area and the curved surface area: TSA = π × r × (r + l).

Shortcut Trick

Equivalent principal for 1 year = (5000 × 2) + (3000 × 4) = 10000 + 12000 = 22000

Total Simple Interest received = 2200

Rate = (Total Interest ÷ Equivalent Principal) × 100

Rate = (2200 ÷ 22000) × 100

Rate = 10%

∴ The correct answer is 10%.

Alternate Method

Given:

Principal lent to B = ₹5000, Time = 2 years

Principal lent to C = ₹3000, Time = 4 years

Total simple interest = ₹2200

Formula Used:

Simple Interest (SI) = Principal × Rate × Time

(where Rate is taken as a decimal fraction r)

Lent to B₹5000 × 2 yrsLent to C₹3000 × 4 yrsTotal SI = ₹2200

Calculations:

⇒ Interest from B = 5000 × r × 2 = 10000r

⇒ Interest from C = 3000 × r × 4 = 12000r

⇒ Total Interest = 10000r + 12000r

⇒ 22000r = 2200

⇒ r = (2200 ÷ 22000) × 100

⇒ r = 10%

∴ The correct answer is 0.1 per annum.

Additional Information

Simple Interest (SI) Formula

SI = (P × R × T) ÷ 100, where P is Principal, R is Rate in %, and T is Time in years.

Decimal vs Percentage Rate

When solving equations, the percentage rate R can be expressed directly as a decimal r (where r = R ÷ 100) making the SI calculation simply P × r × T.

Equivalent Principal

When multiple investments are made at the same simple interest rate, the overall principal equivalent to a 1-year term is the sum of the products of each Principal and its respective Time period.

Shortcut Trick

Volume of any prism is directly proportional to its height when the base area is constant.

Original volume = 25 × 10 = 250 cm³

Since the height increases by 20%, the volume also increases by exactly 20%.

New volume = 250 × 1.2 = 300 cm³

∴ The correct answer is 300 cm³.

Alternate Method

Given:

Base area of the triangular prism = 25 cm²

Original height = 10 cm

Increase in height = 20%

Formula Used:

Volume of a prism = Base Area × Height

        Original h = 10 cm New h = 12 cm   Base Area = 25 cm² New Volume = 25 × 12 = 300 cm³

Calculations:

⇒ New height = 10 + (20% of 10)

⇒ New height = 10 + 2 = 12 cm

⇒ New volume = Base Area × New height

⇒ New volume = 25 × 12 = 300 cm³

∴ The correct answer is 300 cm³.

Additional Information

Volume of a Prism

The volume of any regular prism (triangular, rectangular, hexagonal, etc.) is always the product of its uniform base area and its vertical height: V = Base Area × h.

Proportionality in 3D Shapes

If only a single dimension (like height) of a 3D figure changes by x%, the total volume also undergoes an exact x% change, provided all other dimensions remain constant.

Total Surface Area of Prism

The Total Surface Area (TSA) is calculated as: TSA = Lateral Surface Area + (2 × Base Area) = (Perimeter of Base × Height) + (2 × Base Area).

Shortcut Trick

For a circular disc, Area ∝ (Radius)².

The net percentage change can be calculated using the successive change formula: x + y + (x × y) ÷ 100.

Since the radius is decreased by 10%, we substitute x = −10 and y = −10.

Net Change = −10 − 10 + [(−10) × (−10)] ÷ 100 = −20 + 1 = −19%.

The negative sign indicates a 19% decrease in the overall area.

∴ The correct answer is 19%.

Alternate Method

Given:

The radius of the circular disc is decreased by 10%.

Formula Used:

Area of a circle = π × r²

Percentage Decrease = [(Initial Area − Final Area) ÷ Initial Area] × 100

r Initial Area = 100%

− 10% Radius

0.9r Final Area = 81%

Net Decrease in Area = 19%

Calculation:

⇒ Let the original radius of the disc be 10 units.

⇒ Initial Area = π × 10² = 100π sq. units.

⇒ New radius = 10 − (10% of 10) = 10 − 1 = 9 units.

⇒ New Area = π × 9² = 81π sq. units.

⇒ Decrease in Area = 100π − 81π = 19π sq. units.

⇒ Percentage Decrease = (19π ÷ 100π) × 100 = 19%.

∴ The correct answer is 19%.

Additional Information

Successive Percentage Change

When a value is subjected to two successive percentage changes of x% and y%, the overall net change is calculated using the formula: Net Change = x + y + (xy ÷ 100). Use negative values for any decrease.

Volumetric Percentage Changes

For 3D shapes like spheres or cubes, if the radius or side changes by x%, the volume change is determined by applying the successive percentage formula twice consecutively to account for all three dimensions.

Constant Expenditure Rule

If the price of an item increases by R%, the consumption must be reduced by [R ÷ (100 + R)] × 100% to keep the total expenditure constant.

Shortcut Trick

For any given perimeter, the ratio of the area of a circle to a square is the constant 4 : π.

Ratio = 4 / π ≈ 4 ÷ 3.1416

Ratio ≈ 1.27 : 1

The total wire length of 100 m is not needed to find this ratio.

∴ The correct answer is 1.27:1.

Alternate Method

Given:

Total length of wire = Perimeter of circle = Perimeter of square = 100 m

Formula Used:

Circumference of circle = 2×π×r, Area of circle = π×r²

Perimeter of square = 4×a, Area of square = a²

r Circle Perimeter = 100 m

a Square Perimeter = 100 m

Calculations:

⇒ Circumference of the circle = 2×π×r = 100

⇒ Radius (r) = 50/π m

⇒ Area of circle = π×(50/π)² = 2500/π m²

⇒ Perimeter of the square = 4×a = 100

⇒ Side (a) = 25 m

⇒ Area of square = 25² = 625 m²

⇒ Ratio of areas = (2500/π) ÷ 625

⇒ Ratio = 4 / π

⇒ Ratio ≈ 4 ÷ 3.1416 = 1.2732...

⇒ Approximate ratio = 1.27 : 1

∴ The correct answer is 1.27:1.

Additional Information

Isoperimetric Theorem

For any given perimeter, the circle is the 2D shape that encloses the maximum possible area among all geometric figures.

Area Ratio for Same Perimeter

If a circle, a square, and an equilateral triangle all have the exact same perimeter, their respective areas are in the approximate ratio of 1 : 0.785 : 0.604.

Minimum Perimeter for Fixed Area

Conversely, if a fixed area must be enclosed, the circle is the shape that requires the absolute minimum perimeter (or boundary length) to do so.

Shortcut Trick

By the principle of displacement, Volume of oil raised = Volume of immersed hemisphere.

⇒ π × R² × h = ²⁄₃ × π × r³

⇒ R² × 3 = ²⁄₃ × 7³

⇒ R² = 686 ÷ 9

⇒ R = √686 ÷ 3 ≈ 26.19 ÷ 3 ≈ 8.73 cm

∴ The correct answer is 8.73 cm.

Alternate Method

Given:

Radius of the hemispherical stone (r) = 7 cm

Rise in the oil level (h) = 3 cm

Formula Used:

Volume of a cylinder = πR²h

Volume of a hemisphere = ²⁄₃πr³

R = ?

r = 7 cm

h = 3 cm

Rise in Level Original Level

Volume Displaced = Volume of Hemisphere

Calculations:

When the stone is immersed completely, the volume of the oil displaced equals the volume of the stone.

⇒ Volume of displaced oil = Volume of hemisphere

⇒ π × R² × h = ²⁄₃ × π × r³

⇒ π × R² × 3 = ²⁄₃ × π × 7³

Cancelling π from both sides:

⇒ 3 × R² = ²⁄₃ × 343

⇒ R² = 686 ÷ 9

⇒ R = √(686 ÷ 9) = √686 ÷ 3

⇒ R ≈ 26.19 ÷ 3

⇒ R ≈ 8.73 cm

∴ The correct answer is 8.73 cm.

Additional Information

Displacement Principle

When a solid object is fully immersed in a liquid, the volume of the displaced liquid is exactly equal to the volume of the object.

Volume of Cylinder

The total space occupied by a right circular cylinder is calculated as V = πR²h.

Volume of Hemisphere

A hemisphere is half of a sphere. Its volume is given by V = ²⁄₃πr³.

Shortcut Trick

Convert the central angle of the second sector from radians to degrees to easily compare them.

Angle in degrees = (2π ÷ 3) × (180° ÷ π) = 120°.

Both sectors belong to the same circle (radius = 7 cm) and have equal central angles of 120°.

Since both the radius and the central angles are identical, their areas must be exactly equal.

∴ The correct answer is 1:1.

Alternate Method

Given:

Radius of the circle (r) = 7 cm

Central angle of the first sector (θ₁) = 120°

Central angle of the second sector (θ₂) = 2π/3 radians