The correct answer is TRAI.

Key Points

• The Telecom Regulatory Authority of India (TRAI) was established in the year 1997 under the Telecom Regulatory Authority of India Act, 1997.
• TRAI was formed to regulate the telecommunication services in India and to promote fair competition in the telecom sector.
• The authority ensures that the interests of both service providers and consumers are protected. It also monitors the quality of service provided by the telecom operators.
• TRAI provides recommendations to the Government on matters related to licenses, spectrum allocation, and tariffs.
• The organization plays a pivotal role in the growth and development of the telecom industry in India, especially after the liberalization policies were implemented.
• It also aims at ensuring the availability of affordable telecom services to the common people, thus contributing to the telecom revolution in India.

Additional Information

• SEBI
• SEBI stands for the Securities and Exchange Board of India.
• It was established in 1988 and given statutory powers in 1992 under the SEBI Act, 1992.
• SEBI regulates the securities market in India to protect the interests of investors and to promote the development of the securities market.
• NABARD
• NABARD stands for National Bank for Agriculture and Rural Development.
• It was established in 1982 under the NABARD Act, 1981.
• NABARD focuses on providing credit and other facilities for the promotion of agriculture, small-scale industries, and rural development in India.
• IRDAI
• IRDAI stands for Insurance Regulatory and Development Authority of India.
• It was established in 1999 under the IRDA Act, 1999.
• The IRDAI regulates and promotes the insurance industry in India to protect the interests of policyholders.

The logic followed here is:

 

Thus, the missing term in the series is 539.

Hence, the correct answer is "Option 4";

The Correct answer is Surinder Kumar Choudhary, Jammu & Kashmir National Conference (JKNC).

Key Points

• Surinder Kumar Choudhary is a prominent political leader from Jammu & Kashmir, representing the Jammu & Kashmir National Conference (JKNC).
• Following the 2024 Jammu & Kashmir Assembly elections, he was appointed as the Deputy Chief Minister.
• The JKNC, one of the oldest political parties in Jammu & Kashmir, has historically played a significant role in the region's politics.
• Surinder Kumar Choudhary’s appointment reflects the party's focus on strengthening governance and addressing regional issues.
• The Deputy Chief Minister plays a crucial role in assisting the Chief Minister in administrative responsibilities and policy-making.
• His leadership is expected to bring attention to important matters such as development, infrastructure, and regional harmony.

Additional Information

• Ghulam Ahmad Mir
• Ghulam Ahmad Mir is a senior leader of the Indian National Congress (INC).
• He has served as the President of the Jammu & Kashmir Pradesh Congress Committee (JKPCC).
• Although a strong contender, he was not appointed as the Deputy Chief Minister following the 2024 Assembly elections.
• Ravinder Raina
• Ravinder Raina is associated with the Bharatiya Janata Party (BJP).
• He is known for his vocal stance on issues concerning Jammu & Kashmir.
• Ravinder Raina has previously served as the President of the BJP’s Jammu & Kashmir unit.
• Despite being influential, he was not selected for the Deputy Chief Minister’s position post-election.
• Indian National Congress (INC)
• The Indian National Congress (INC) is one of India’s oldest political parties, founded in 1885.
• It has a significant presence in Jammu & Kashmir but did not secure the Deputy Chief Minister’s position in the 2024 elections.

The Correct answer is Nana Saheb.

Key Points

• Nana Saheb, also known as Dhondu Pant, was one of the prominent leaders of the Indian Rebellion of 1857.
• He travelled to places like Bithoor, Kalpi, Delhi, and Lucknow to rally the support of native princes and leaders against British rule.
• He was the adopted son of Peshwa Baji Rao II, and his grievance with the British stemmed from their refusal to grant him the pension that was given to his father.
• Nana Saheb led the rebellion in Kanpur, where he played a significant role in the uprising against the British forces.
• He sought to unify Indian rulers and build a strong alliance to overthrow British authority during the revolt.
• His efforts were pivotal in orchestrating and sustaining the rebellion in key regions during the 1857 uprising.
• After the rebellion, he is believed to have escaped to Nepal, where his later life remains shrouded in mystery.

Additional Information

• Tantia Tope
• Tantia Tope was another prominent leader of the 1857 uprising, known for his guerrilla warfare tactics.
• He was a close associate of Nana Saheb and supported him in the rebellion.
• Tantia Tope led successful campaigns in regions like Kanpur, Gwalior, and central India.
• He was eventually captured and executed by the British in 1860.
• Bahadur Shah Zafar
• Bahadur Shah Zafar, the last Mughal emperor, was declared the symbolic leader of the 1857 revolt.
• He provided moral and symbolic support to the rebellion but had limited actual control over the uprising.
• After the revolt was suppressed, he was captured by the British and exiled to Rangoon (present-day Yangon, Myanmar).
• Rani of Jhansi
• Rani Lakshmibai, the Rani of Jhansi, was one of the most iconic figures of the 1857 revolt.
• She fought valiantly against the British forces to protect her kingdom of Jhansi.
• She is remembered for her bravery and leadership, especially in battles like the Siege of Jhansi and the defense of Gwalior.

Shortcut Trick

Net Profit or Loss percentage can be calculated using the Successive Percentage formula: a + b + (a × b) ÷ 100.

Here, a = 84 (Markup percentage) and b = −50 (Discount percentage).

Net effect = 84 − 50 + (84 × (−50)) ÷ 100.

Net effect = 34 − 4200 ÷ 100 = 34 − 42 = −8%.

The negative sign indicates a loss of 8%.

∴ The correct answer is 8% loss.

Alternate Method

Given: Markup % = 84%, Discount % = 50%.

Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100 | Loss% = (CP − SP) ÷ CP × 100.

⇒ Let the Cost Price (CP) be 100.

⇒ Marked Price (MP) = 100 + 84% of 100 = 184.

⇒ Selling Price (SP) = 184 − 50% of 184 = 184 − 92 = 92.

⇒ Loss = CP − SP = 100 − 92 = 8.

⇒ Loss % = (8 ÷ 100) × 100 = 8%.

∴ The correct answer is 8% loss.

Additional Information

Marked Price and Discount

The price listed on the label is the Marked Price. Discount is always calculated on the MP to arrive at the Selling Price.

Relationship Formula

MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%). This helps find any one value if the other three are known.

Shortcut Trick

Remaining distance = (1 − 2/3) × 549 = 1/3 × 549 = 183 km.

Remaining time = (1 − 3/4) × 8 = 1/4 × 8 = 2 hours.

Required Speed = Remaining Distance ÷ Remaining Time = 183 ÷ 2 = 91.5 km/hr.

∴ The correct answer is 91.5 km/hr.

Alternate Method

Given: Total distance = 549 km, Total time = 8 hours.

Formula Used: Speed = Distance ÷ Time

⇒ Distance covered = 2/3 × 549 = 366 km

⇒ Remaining distance = 549 − 366 = 183 km

⇒ Time taken = 3/4 × 8 = 6 hours

⇒ Remaining time = 8 − 6 = 2 hours

⇒ Required Speed = 183 ÷ 2 = 91.5 km/hr

∴ The correct answer is 91.5 km/hr.

Additional Information

Average Speed

Average Speed = Total Distance ÷ Total Time. If distances are equal, Average Speed = 2xy/(x+y).

Unit Conversion

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

Relative Speed

Same direction = S₁ − S₂ | Opposite direction = S₁ + S₂.

The Correct answer is Foreign Relations and Defence.

Key Points

• The Union Cabinet in India explicitly manages Foreign Relations and Defence as part of its coordinating functions.
• Under Article 73 of the Indian Constitution, the Union Government has exclusive powers to legislate on matters relating to foreign affairs and defence.
• Foreign Relations involve managing India’s diplomatic ties, treaties, trade agreements, and coordination with international organizations such as the United Nations.
• Defence encompasses the responsibility of ensuring national security, managing the armed forces (Army, Navy, and Air Force), and overseeing strategic operations.
• The Union Cabinet handles critical decisions such as signing international treaties, defense procurement, and deploying forces during crises.
• These areas are fundamental to maintaining the sovereignty, security, and global standing of India, which is why they are explicitly managed by the central government.
• The Ministry of External Affairs and the Ministry of Defence work in coordination with the Union Cabinet to implement policies in these domains.

Additional Information

• Agriculture and Labour
• Agriculture falls under the State List as per the Constitution of India, meaning that state governments primarily manage policies related to agriculture.
• Labour is included in the Concurrent List, which allows both the Union and State Governments to legislate on issues such as employment, wages, and industrial disputes.
• The Union Cabinet does intervene in labour matters for national-level policies, but these are not exclusively managed by the Union Cabinet.
• Tourism and Sports
• Tourism is primarily managed by the states, though the Union Government promotes national-level tourism campaigns and policies like Incredible India.
• Sports policies and development programs are largely coordinated by the Ministry of Youth Affairs and Sports, but these do not fall under the exclusive domain of the Union Cabinet.
• Education and Health
• Education is part of the Concurrent List, and both Union and State Governments can legislate on matters related to schools, universities, and other educational institutions.
• Health is also in the State List, meaning state governments have primary responsibility for healthcare policies, though the Union Government coordinates national health schemes like Ayushman Bharat.

The Correct answer is ₹1,500 crore.

Key Points

• The Indian Government introduced a ₹1,500 crore incentive scheme in March 2025 to encourage small-value UPI transactions during the financial year 2024-25.
• The primary aim of this initiative is to boost the adoption and usage of Unified Payments Interface (UPI), particularly for micro and small transactions.
• This incentive is part of the government's effort to accelerate digital payments and reduce reliance on cash-based transactions.
• UPI has become one of the most popular and widely used payment systems in India, significantly contributing to financial inclusion.
• The scheme reflects the government's commitment towards promoting a cashless economy and leveraging technology-driven financial solutions.
• Such initiatives encourage banks to focus on increasing the penetration of UPI, especially in rural and semi-urban areas where digital payment adoption is comparatively lower.
• This move aligns with India's vision of becoming a global leader in digital payments infrastructure.

Additional Information

• ₹1,700 crore
• The incentive amount of ₹1,700 crore might represent a higher allocation, but it is not the correct figure for the scheme introduced in March 2025.
• Higher allocations could indicate a more expansive effort towards promoting UPI transactions in future years.
• ₹1,800 crore
• ₹1,800 crore as an option may reflect government policies or schemes with larger budgets, but it does not correspond to the specific scheme for small-value UPI transactions in FY 2024-25.
• ₹1,600 crore
• The allocation of ₹1,600 crore could have been used for other financial or digital initiatives by the government, but it is not related to the scheme introduced in March 2025.

The logic followed here is:

Logic: 1^st number - 12 = 2^nd number - 12 = 3^rd number.

For, (88, 76, 64)

88 - 12 = 76 - 12 = 64.

Here, the logic followed.

For, (71, 59, 47)

 71 - 12 = 59 - 12 = 47.

Here, the logic followed.

Now, let's check the options based on this logic:

Option 1) (64, 52, 40)

 64 - 12 = 52 - 12 = 40. (Matches)

Here, logic followed.

Option 2) (40, 38, 36)

 40 - 12 = 28. (Given Second number is 38, 38 ≠ 28)

Here, logic not followed.

Option 3) (99, 77, 55)

⇒ First to Second: 99 - 12 = 87. (Given Second number is 77, 77 ≠ 87)

Here, logic not followed.

Option 4) (58, 46, 24)

⇒ First to Second: 58 - 12 = 46 - 12 = 34. (Given Third number is 24, 24 ≠ 34)

Here, logic not followed.

Hence, the correct answer is "Option 1".

Shortcut Trick

Equate Total Work: (3M + 14W) × 18 = (11M + 8W) × 12

Divide both sides by 6: (3M + 14W) × 3 = (11M + 8W) × 2

9M + 42W = 22M + 16W

26W = 13M ⇒ 2W = 1M

∴ The correct answer is 2.

Alternate Method

Given:

Case 1: 3 Men and 14 Women in 18 days.

Case 2: 11 Men and 8 Women in 12 days.

Formula Used:

Total Work = (Number of workers × Time taken)

Calculations:

⇒ Total Work = (3M + 14W) × 18 --- (i)

⇒ Total Work = (11M + 8W) × 12 --- (ii)

⇒ (3M + 14W) × 18 = (11M + 8W) × 12

⇒ 3(3M + 14W) = 2(11M + 8W)

⇒ 9M + 42W = 22M + 16W

⇒ 42W − 16W = 22M − 9M

⇒ 26W = 13M

⇒ 1M = 2W

∴ The correct answer is 2.

Additional Information

Man-Day Concept

Total work is constant and expressed as the product of efficiency and time. M₁D₁ = M₂D₂.

Work and Wages

Wages are distributed based on the ratio of work done, which is often the ratio of efficiencies when time is constant.

The given code language is:

 

Thus, 'H' is coded as '5'.

Hence, the correct answer is "Option 4".

The Correct answer is Laapataa Ladies.

Key Points

• Laapataa Ladies has been selected as India's official entry for the Oscar Awards 2025 in the Best International Feature Film category.
• The film is directed by Kiran Rao, who is known for her unique storytelling and creative approach to filmmaking.
• Laapataa Ladies is a Hindi-language drama that explores themes of gender, identity, and societal norms in rural India.
• The film is set in the 1990s and follows the story of two young brides who go missing during a train journey, leading to a search filled with humor and heartfelt moments.
• It is produced under the banner of Aamir Khan Productions, ensuring high production quality and wide reach.
• The movie premiered at the Toronto International Film Festival (TIFF) and received critical acclaim for its storytelling and performances.
• This selection highlights India's commitment to showcasing diverse narratives and promoting regional stories on the global stage.

Additional Information

• Jawan
• Jawan is a blockbuster action-thriller film directed by Atlee and starring Shah Rukh Khan.
• The film focuses on themes of vigilantism and social justice but was not selected for the Oscars as it primarily caters to a commercial audience.
• Animal
• Animal is an upcoming action-drama film directed by Sandeep Reddy Vanga and starring Ranbir Kapoor.
• The film explores complex relationships, especially between a father and son, but it is yet to be released and hence was not eligible for Oscar consideration.
• 12^th Fail
• 12^th Fail is an inspirational film directed by Vidhu Vinod Chopra, based on the struggles of a student preparing for competitive exams in India.
• Though it delivers a strong social message, it did not make it as India's official Oscar entry.

The given code language is:

Thus, 'R' is coded as '4'.

Hence, the correct answer is "Option 4".

The logic followed here is:

Thus, the missing number in the series is 220.

Hence, the correct answer is "Option 1".

The Correct answer is UNR Rao vs. Indira Gandhi, 1971.

Key Points

• The case of UNR Rao vs. Indira Gandhi, 1971, is a landmark judgment by the Supreme Court of India.
• In this case, the court ruled that the Council of Ministers does not cease to hold office even after the dissolution of the Lok Sabha.
• This judgment clarified that the Council of Ministers continues to function and assist the President of India in discharging their duties.
• The decision was based on the interpretation of Article 74 of the Indian Constitution, which provides for a Council of Ministers headed by the Prime Minister to aid and advise the President.
• This case established that the executive authority of the government does not come to a standstill with the dissolution of the Lok Sabha, ensuring continuity in governance.
• It highlights the importance of the principle of collective responsibility of the Council of Ministers to the Lok Sabha, as enshrined in the Constitution.

Additional Information

• Kesavananda Bharati vs. State of Kerala, 1973
• This case is famous for the Basic Structure Doctrine, which limits the power of Parliament to amend the Constitution.
• The court ruled that while Parliament can amend any part of the Constitution, it cannot alter its basic structure.
• This case is considered a cornerstone in the history of Indian constitutional law.
• Golaknath vs. State of Punjab, 1967
• This case ruled that Fundamental Rights cannot be amended by Parliament.
• It declared that the Constitution's Fundamental Rights were sacrosanct and inviolable.
• However, this decision was later overturned by the Kesavananda Bharati case.
• SR Bommai vs. Union of India, 1994
• This case is a landmark judgment in the context of the President's Rule under Article 356 of the Constitution.
• The court laid down the principles of judicial review of the imposition of President's Rule.
• It emphasized that the secular character of the Constitution is part of its basic structure.

Shortcut Trick

Perform prime factorization of 4232.

4232 = 2 × 2116 = 2 × 2 × 1058 = 2 × 2 × 2 × 529 = 2³ × 23²

Grouping into pairs: (2 × 2) × 2 × (23 × 23).

Only one 2 is left without a pair, so we must multiply by 2.

∴ The correct answer is 2.

Alternate Method

Given number is 4232.

To find the smallest number to multiply to make it a perfect square, we use the prime factorization method.

⇒ Prime factors of 4232 = 2 × 2 × 2 × 23 × 23

⇒ Grouping the prime factors in identical pairs: (2 × 2) × (23 × 23) × 2

⇒ The prime factor 2 does not have a pair.

⇒ Therefore, 4232 must be multiplied by 2 to make it a perfect square.

⇒ New number = 4232 × 2 = 8464 (which is 92²)

∴ The correct answer is 2.

Additional Information

Perfect Square Property

In the prime factorization of any perfect square, the exponent of every prime factor must be an even number.

Division Rule for Perfect Squares

The smallest number by which a number must be divided to make it a perfect square is also the unpaired factor (which is 2 in this case).

Given interchange rules:

• ‘+’ is replaced by ‘−’.
• ‘×’ and ‘÷’ are interchanged.

The given equation is:

44 ÷ 8 + 5 × 1 + 7 = ?

After applying the interchange rules, the equation becomes:

44 × 8 − 5 ÷ 1 − 7 = ?

Now, we solve the equation following the BODMAS rule:

= 44 × 8 − 5 ÷ 1 − 7

= 352 − 5 − 7

= 347 − 7

= 340

Hence, the correct answer is "Option 3".

Given: Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.

1. No one has the exam before V.

2. Only four people have exams between P and R.

3. Q has the exam immediately before R.

 4: T is after S but before U. The only available slots are Wednesday, Thursday, and Friday. So, S = Wednesday, T = Thursday, U = Friday.

Thus, To find how many people have exams between S (Wednesday) and R (Sunday): Thursday (T), Friday (U), Saturday (Q) → 3 people.

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

As per the question,

Given Numbers: 853 628 981 217 132

Rule: Add the second digit of the highest number to the first digit of the lowest number.

→ Highest number: 981

→ Second digit of the highest number: 8

→ Lowest number: 132

→ First digit of the lowest number: 1

(Second digit of highest) + (First digit of lowest)

8 + 1 = 9

Hence, the correct answer is "Option 3".

Given interchange rules:

• ‘÷’ and ‘−’ are interchanged.
• ‘×’ and ‘+’ are interchanged.

The given equation is:

522 × 708 − 59 + 19 ÷ 17 = ?

After applying the interchange rules, the equation becomes:

522 + 708 ÷ 59 × 19 − 17 = ?

Now, we solve the equation following the BODMAS rule:

= 522 + 708 ÷ 59 × 19 − 17

= 522 + 12 × 19 − 17

= 522 + 228 − 17

= 750 − 17

= 733

Hence, the correct answer is "Option 4".

The logic followed here is.

Option (1) DX – LE 

Option (2) VP – DX

Option (3) HB – PJ

Option (4) ZT – HB

Thus, option 1 is odd one.

Hence, the correct answer is "Option 1".

The Correct answer is Drip irrigation.

Key Points

• Drip irrigation is a micro-irrigation system designed to save water and nutrients by allowing water to drip slowly to the roots of plants.
• This system is ideal for arid and semi-arid regions, where water conservation is critical.
• The water is delivered through a network of valves, pipes, tubing, and emitters, ensuring precise delivery directly to the plant's root zone.
• It helps to minimize evaporation and runoff, making it a highly efficient method of irrigation.
• Drip irrigation is particularly beneficial for cultivating crops such as vegetables, fruits, and flowers, where water management is crucial for growth.
• This system reduces weed growth, as water is not dispersed widely across the field, but targeted only where needed.
• The Government of India promotes drip irrigation under the Pradhan Mantri Krishi Sinchayee Yojana (PMKSY) to encourage farmers to adopt water-efficient practices.
• It is recognized as one of the most effective irrigation techniques in regions like Rajasthan, Gujarat, and Maharashtra, where water scarcity is a major challenge.

Additional Information

• Canal irrigation
• Canal irrigation involves the distribution of water through a network of canals and is commonly used in areas with an abundant supply of surface water.
• It is widely used in northern India, especially in states like Punjab, Haryana, and Uttar Pradesh.
• Canal irrigation is less efficient than drip irrigation due to significant water loss through evaporation and seepage.
• Tank irrigation
• Tank irrigation involves storing water in tanks or reservoirs for later use in irrigation.
• This system is commonly found in southern India, especially in states like Tamil Nadu, Andhra Pradesh, and Karnataka.
• It is suitable for areas with uneven terrain where other methods like canal irrigation are not feasible.
• Sprinkler irrigation
• Sprinkler irrigation involves spraying water over crops using sprinklers, simulating rainfall.
• This method is suitable for undulating terrain and is commonly used for horticultural crops, lawns, and golf courses.
• Although efficient, sprinkler irrigation is less effective in arid regions due to water loss from evaporation.

The correct answer is Maharajadhiraja.

Key Points

• Chandragupta I was the founder of the Gupta Empire and reigned during the early 4^th century CE.
• He adopted the title of "Maharajadhiraja," meaning "King of Kings," to signify his authority over other rulers and his elevated status.
• The use of this title marked the rise of the Gupta Empire as a prominent and centralized political power in ancient India.
• This designation highlighted the imperial ambitions of Chandragupta I, as he sought to consolidate power and unify regions under his rule.
• The title "Maharajadhiraja" had been used by other rulers in ancient India, but its adoption by Chandragupta I signified the beginning of the Gupta dynasty's golden age.
• Under Chandragupta I's reign, the Gupta Empire expanded its influence, particularly in the Magadha region, which was a significant center of power.
• This era is considered a period of political stability, economic prosperity, and cultural advancements, laying the foundation for the Gupta Empire's future achievements.

Additional Information

• Maharaj
• The term "Maharaj" simply means "great king" but does not carry the same imperial connotation as "Maharajadhiraja."
• It was commonly used by rulers, including those who governed smaller kingdoms or regions, during ancient Indian history.
• Chakravartin
• The term "Chakravartin" refers to a "universal ruler" or someone who rules ethically and universally over the known world.
• It was a title often associated with rulers who adhered to Dharmic principles and was more symbolic than political.
• This title was not specifically used by Chandragupta I.
• Samrat
• The title "Samrat" means "emperor" and was used by rulers to denote supreme authority.
• While it is similar to "Maharajadhiraja," Chandragupta I specifically chose the latter to emphasize his superiority over other kings.

The logic followed here is:

Option (1): TPMH

Option (2): AWTO

 

                                                         

Option (3): NJGB

 

                                                         

Option (4): EAYS

                                                           

The letter-cluster that DOES NOT belong to the group is: EAYS.

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

The pattern followed here is.

Thus, the missing term in the series is OHK 63.

Hence, the correct answer is Option 2.

Shortcut Trick To find (a − b) / (a + b), we use the square identities: (a − b)2 = (a2 + b2) − 2ab and (a + b)2 = (a2 + b2) + 2ab. Numerator value: (a − b)2 = 163 − 2(27) = 163 − 54 = 109. Denominator value: (a + b)2 = 163 + 2(27) = 163 + 54 = 217. Taking the square root of both sides: (a − b) / (a + b) = √109 / √217 = √(109/217). ∴ The correct answer is √(109/217). Alternate Method Given: a2 + b2 = 163 a × b = 27 a > b Formula Used:

1. (a + b)2 = a2 + b2 + 2ab
2. (a − b)2 = a2 + b2 − 2ab

Calculations: ⇒ 2ab = 2 × 27 = 54 ⇒ (a + b)2 = 163 + 54 = 217 ⇒ a + b = √217 (Since a > b, sum is positive) ⇒ (a − b)2 = 163 − 54 = 109 ⇒ a − b = √109 (Since a > b, difference is positive) ⇒ (a − b) / (a + b) = √109 / √217 ⇒ (a − b) / (a + b) = √(109 / 217) ∴ The correct answer is √(109/217). Additional Information Algebraic Expansion of Square of Sum (a + b)2 = a2 + b2 + 2ab. This identity links the sum of squares, the product of terms, and the square of the sum. Algebraic Expansion of Square of Difference (a − b)2 = a2 + b2 − 2ab. This is used to find the difference between two variables when their squares and product are known. Difference of Two Squares a2 − b2 = (a + b)(a − b). This is a fundamental factoring identity used to simplify fractional algebraic expressions.

The Correct answer is Sunlight on the Broken Column.

Key Points

• Sunlight on the Broken Column is a novel written by Attia Hosain, published in the year 1961.
• The novel is set in the background of the Partition of India, which divided British India into two countries: India and Pakistan.
• It portrays the impact of Partition on a feudal family and explores themes of tradition, change, and personal identity.
• The protagonist, Laila, navigates her life amidst the upheaval of Partition, addressing issues such as patriarchy, familial expectations, and political turmoil.
• The novel is significant for its vivid depiction of the social and cultural transformation that accompanied the historical event of Partition.
• Attia Hosain, the author, was also a noted writer, broadcaster, and journalist, who brought a unique perspective to her writing as a member of the Muslim aristocracy in pre-Partition India.
• The novel is considered a classic piece of literature that offers an insightful portrayal of the socio-political challenges during a critical period in Indian history.

Additional Information

• Clear Light of Day
• Written by Anita Desai, this novel was published in 1980.
• It focuses on the dynamics of a middle-class family in Old Delhi and explores themes such as family relationships, memory, and time.
• Unlike "Sunlight on the Broken Column," it does not directly deal with the Partition.
• Ice Candy Man
• Written by Bapsi Sidhwa, this novel is also known as Cracking India.
• It depicts the Partition of India through the eyes of a young girl, Lenny, in Lahore.
• The novel is notable for its portrayal of communal violence and the human impact of Partition.
• Midnight’s Children
• Written by Salman Rushdie, this iconic novel was published in 1981.
• The book blends magical realism with historical fiction, narrating the story of India’s transition from British colonialism to independence and Partition.
• It is a celebrated work but is distinct in style and narrative from Attia Hosain's novel.

The Correct answer is 1 only.

Key Points

• The President of India can summon a joint sitting of both Houses of Parliament under Article 108 of the Constitution.
• This is applicable in cases of a legislative deadlock on an Ordinary Bill, where both Houses fail to agree on its passage.
• A joint sitting is presided over by the Speaker of the Lok Sabha, or in their absence, the Deputy Speaker.
• Joint sittings are convened to resolve disputes between the Lok Sabha and Rajya Sabha concerning an Ordinary Bill.
• The Money Bill and Constitutional Amendment Bill are excluded from this provision as they have distinct procedural requirements and do not fall under legislative deadlock scenarios.
• The joint sitting mechanism reflects the principle of resolving conflicts and ensuring the smooth functioning of the legislative process in a parliamentary democracy.

Additional Information

• Money Bill
• A Money Bill is specifically defined under Article 110 of the Indian Constitution.
• It primarily deals with matters related to the imposition, abolition, remission, alteration, or regulation of taxes, borrowing of money, expenditure from the Consolidated Fund of India, etc.
• The Lok Sabha has exclusive power to approve a Money Bill, while the Rajya Sabha can only recommend changes within a limited timeframe.
• No provision for a joint sitting exists for Money Bills, as the Lok Sabha holds greater authority in financial matters.
• Constitutional Amendment Bill
• A Constitutional Amendment Bill is governed under Article 368 of the Constitution.
• Such bills are passed with a special majority in both Houses of Parliament, and there is no provision for a joint sitting to resolve differences.
• These bills often require ratification by at least half of the State Legislatures for amendments impacting the federal structure.
• The procedural requirements for Constitutional Amendment Bills are distinct from Ordinary Bills and Money Bills.

The Correct answer is Flash Memory.

Key Points

• Flash Memory is a type of non-volatile storage, meaning it retains data even when the power is turned off.
• It is often referred to as solid-state storage because it has no moving parts, unlike traditional hard drives.
• This memory is widely used in devices such as USB flash drives, memory cards, solid-state drives (SSDs), and various embedded systems.
• It is based on NAND or NOR flash technology, which uses floating-gate transistors to store data.
• Flash memory is known for its high speed, durability, and compact size, making it suitable for modern computing and mobile devices.
• It enables the storage of data in a rewritable format, allowing users to repeatedly write and erase data.
• Flash memory is also highly energy-efficient compared to other storage technologies, making it ideal for portable devices.
• Common applications include smartphones, tablets, cameras, and solid-state drives (SSDs) in computers.

Additional Information

• Cache Memory
• Cache Memory is a high-speed memory that temporarily stores frequently accessed data for quick retrieval.
• It is located closer to the CPU and is used to improve processing speed.
• Cache memory is not considered solid-state storage because it is volatile and does not retain data when power is off.
• Crystal Storage
• Crystal Storage refers to experimental data storage technologies using crystals, such as quartz glass.
• It is not widely implemented and is different from flash memory.
• Primary Memory
• Primary Memory, also known as main memory, includes RAM and ROM.
• It is volatile in the case of RAM and does not qualify as solid-state storage.
• ROM, while non-volatile, is not rewritable like flash memory.

Shortcut Trick

Total interest percentage for 3 years at 20% = 20% × 3 = 60%.

Total amount percentage = Principal (100%) + Interest (60%) = 160%.

Given: 160% = ₹4,800 ⇒ 1% = 4800 ÷ 160 = ₹30.

Interest for 1 year at 20% = 20 × 30 = ₹600.

∴ The correct answer is ₹600.

Alternate Method

Given: Amount (A) = ₹4,800, Rate (R) = 20% p.a., Time (T) = 3 years.

Formula Used: Amount (A) = P + SI = P + (P × R × T) ÷ 100

⇒ 4,800 = P × (1 + (20 × 3) ÷ 100)

⇒ 4,800 = P × (1 + 0.6)

⇒ 4,800 = P × 1.6

⇒ P = 4,800 ÷ 1.6 = ₹3,000

⇒ Simple Interest for 1 year = (3000 × 20 × 1) ÷ 100

⇒ Simple Interest = 30 × 20 = ₹600

∴ The correct answer is ₹600.

Additional Information

Simple Interest (SI) formula

SI is calculated only on the Principal amount: SI = (P × R × T) ÷ 100, where P is principal, R is rate per annum, and T is time in years.

Amount in Simple Interest

The total Amount (A) is the sum of the Principal and Simple Interest: A = P + SI = P(1 + RT/100).

Annual Interest Constant

In Simple Interest, the interest earned remains constant every year because it is always calculated on the original principal.

Shortcut Trick

Total Volume = Volume of Cube + Volume of Cuboid

Total Volume = 5³ + (35 × 15 × 15) = 125 + 7875 = 8000 cm³

Number of new cubes = Total Volume ÷ Volume of New Cube

Number of new cubes = 8000 ÷ 10³ = 8000 ÷ 1000 = 8

∴ The correct answer is 8 cubes.

Alternate Method

Given:

Side of the first metal cube (a₁) = 5 cm

Dimensions of the metal cuboid = 35 cm × 15 cm × 15 cm

Side of the newly formed cubes (a₂) = 10 cm

Formula Used:

Volume of a Cube = (Side)³

Volume of a Cuboid = Length × Breadth × Height

Calculations:

⇒ Volume of small metal cube = 5 × 5 × 5 = 125 cm³

⇒ Volume of metal cuboid = 35 × 15 × 15 = 7875 cm³

⇒ Total volume of metal available = 125 + 7875 = 8000 cm³

⇒ Volume of one new cube = 10 × 10 × 10 = 1000 cm³

⇒ Number of cubes = Total Volume ÷ Volume of one new cube

⇒ Number of cubes = 8000 ÷ 1000 = 8

∴ The correct answer is 8 cubes.

Additional Information

Conservation of Volume

When one or more solid objects are melted and recast into new shapes, the total volume remains constant.

Cuboid Properties

Total Surface Area of cuboid = 2(lb + bh + hl) and Diagonal = √(l² + b² + h²).

Cube Properties

Total Surface Area of cube = 6a² and Diagonal = a√3.

The logic followed here is that each letter of the first term is shifted backward by 2 positions to get the second term. The pattern can be summarized as (-2, -2, -2, -2).

Pair 1: LIQM : JGOK

 

Pair 2: IFNJ : GDLH

Applying the logic to OLTP:

Thus, OLTP is related to MJRN.

Hence, the correct answer is "Option 4".

The Correct answer is Bombay Session, 1885.

Key Points

• The demand for Indianisation of higher administrative services, including the civil services, was first formally raised during the Bombay Session of the Indian National Congress (INC) in 1885.
• This session marked the foundation of the INC, which aimed to voice Indian aspirations and seek reforms from the British administration.
• One of the key demands during this session was to ensure greater representation of Indians in administrative services, as these services were dominated by British officials, leading to a lack of Indian involvement in decision-making processes.
• The demand for Indianisation was rooted in the belief that Indians were equally competent to serve in higher administrative roles and that their inclusion would lead to more effective governance.
• This issue was significant as it highlighted the growing nationalist sentiment and dissatisfaction with British policies that excluded Indians from key roles in governance.
• The Bombay Session was presided over by W.C. Bonnerjee, the first president of the INC, and laid the foundation for subsequent sessions to address various political and economic grievances.
• The demand for Indianisation of administrative services became a recurring theme in the early years of the INC and reflected the aspirations of educated Indians for equal opportunities under British rule.

Additional Information

• Allahabad Session, 1890
• The Allahabad Session of INC in 1890 was presided over by Pherozeshah Mehta.
• This session focused on broader issues like economic reforms and self-governance but did not specifically raise the demand for Indianisation of administrative services.
• Calcutta Session, 1886
• The Calcutta Session of 1886 was significant as it was presided over by Dadabhai Naoroji, one of the founding members of the INC.
• Although the session addressed issues related to economic exploitation by the British, Indianisation was not the central focus.
• Madras Session, 1887
• The Madras Session of 1887 was presided over by Badruddin Tyabji, the first Muslim president of the INC.
• This session was more focused on unity and communal harmony among Indians rather than administrative reforms.

The Correct answer is Partnership for Accelerating Sustainable Development and Climate Solutions.

Key Points

• The theme of the World Sustainable Development Summit (WSDS) 2025 is "Partnership for Accelerating Sustainable Development and Climate Solutions."
• The WSDS is an annual flagship event organized by The Energy and Resources Institute (TERI), headquartered in New Delhi, India.
• This theme highlights the importance of global partnerships to address challenges like climate change and achieve the Sustainable Development Goals (SDGs).
• The summit serves as a platform for policy-makers, researchers, and industry leaders to collaborate and discuss actionable strategies for a sustainable future.
• It emphasizes climate solutions through technological advancements, inclusive policies, and international cooperation.
• By accelerating sustainable development, the summit aims to ensure a balance between economic growth, environmental conservation, and social inclusion.
• The WSDS is aligned with global frameworks such as the Paris Agreement and the United Nations 2030 Agenda.

Additional Information

• Partnerships for Accessing Supportive Development and Climate Solutions
• This option incorrectly mentions "Accessing Supportive Development," which is not the focus of the summit's theme.
• The correct emphasis is on accelerating solutions rather than just accessing support.
• Partnership for Accessing Sustainable Development and Climate Solutions
• This option incorrectly uses the term "Accessing Sustainable Development."
• The summit theme focuses on speeding up (accelerating) development rather than merely accessing it.
• Partnership for Approaching Sustainable Development and Climate Change
• This option incorrectly uses the term "Approaching," which does not align with the dynamic and urgent nature of the summit's objectives.
• The focus is on action and acceleration, not just approaching the issues.

The Correct answer is Moral law.

Key Points

• The term 'Dhamma', as used in Ashoka's inscriptions, primarily refers to a set of ethical and moral principles that were intended to guide the behavior of individuals and the administration of the state.
• This concept of Dhamma was not limited to Buddhist teachings but was a broader moral code aimed at promoting social harmony, tolerance, and non-violence.
• The Dhamma included principles such as respect for elders, compassion towards all living beings, non-violence (Ahimsa), and truthfulness.
• Ashoka, after embracing Buddhism, adopted these moral principles and propagated them through his edicts, which were inscribed on rocks and pillars across his empire.
• The inscriptions reflect Ashoka's efforts to create a just and ethical society by emphasizing the importance of moral conduct over rituals and ceremonies.
• Ashoka’s Dhamma was not sectarian; it was designed to be universally acceptable, addressing the welfare of all people, including animals.
• The promotion of Dhamma was a key part of Ashoka's efforts to govern his empire based on the principles of righteousness and justice.

Additional Information

• Slogans of Buddha
• This option refers to the teachings or sayings of Buddha, which are known as Dhammapada or other Buddhist scriptures. However, Ashoka's Dhamma was broader than just Buddhist slogans; it was a universal moral code.
• Royal decree
• While Ashoka's inscriptions can be considered as royal decrees, the term 'Dhamma' specifically refers to the ethical and moral principles promoted through these decrees.
• Buddhist doctrine
• Though Ashoka was a follower of Buddhism, his concept of Dhamma was not confined to Buddhist doctrine. It was a more inclusive and universal set of principles.

The Correct answer is To integrate modern subjects alongside traditional teachings.

Key Points

• The primary objective of implementing a standardised curriculum in Himalayan Buddhist monasteries was to integrate modern education with traditional Buddhist teachings.
• This initiative aims to equip monks and students with knowledge in modern subjects like science, mathematics, and technology, alongside their spiritual and philosophical studies.
• The program also seeks to enhance the overall educational standards in monasteries and help the monastic community adapt to contemporary socio-economic challenges.
• Introducing modern subjects ensures that students in monasteries remain competitive and can contribute effectively to national development while preserving their cultural and spiritual heritage.
• This initiative reflects the Indian government's efforts to promote a more holistic and inclusive education system in remote areas, particularly in the Himalayan region.
• The move also aligns with India's broader aim of fostering educational equity and ensuring that all communities, including those in monasteries, receive access to quality education.

Additional Information

• To promote Chinese language education
• This option is incorrect because the initiative was focused on integrating modern subjects with traditional Buddhist teachings rather than promoting any specific foreign language like Chinese.
• Chinese language education is typically associated with China's efforts in cultural diplomacy through programs like Confucius Institutes, not India's monastic curriculum.
• To convert monasteries into secular schools
• This option is incorrect because the initiative aimed to enhance the existing monastic education system, not replace it with a secular school structure.
• The focus was on preserving traditional Buddhist teachings while complementing them with modern subjects.
• To reduce the number of monasteries in border areas
• This option is incorrect as the initiative was intended to support monasteries by upgrading their educational standards, not to reduce their presence.
• The monasteries play a crucial role in maintaining the cultural and spiritual identity of the Himalayan region.

The Correct answer is PL-480.

Key Points

• PL-480 stands for the Public Law 480, also referred to as the Food for Peace Program.
• This program was initiated by the United States in 1954 to provide food aid to countries facing food shortages.
• Under this program, India received substantial amounts of wheat and other grains during the 1950s and 1960s to address its chronic food insecurity.
• The dependency on PL-480 reduced significantly after the Green Revolution in India, which began in the late 1960s and led to an increase in agricultural production.
• This program was a form of economic assistance and was instrumental in building US-India relations during the initial years of India's independence.
• PL-480 not only supported India during its food crises but also laid the groundwork for the modernization of India's agricultural sector.

Additional Information

• KL-580
• KL-580 appears to be an arbitrary term with no specific historical or factual relevance to India's food aid or agricultural history.
• Marshall Plan
• The Marshall Plan was a post-World War II initiative by the United States to provide economic assistance for the reconstruction of Europe.
• This plan was not related to food aid in India but focused on rebuilding war-torn European economies during the late 1940s and early 1950s.
• Green Aid
• Green Aid does not correspond to any specific program or initiative associated with India's food aid or agricultural development.
• The term might be confused with the Green Revolution, which was a domestic Indian initiative to increase agricultural productivity.

The Correct answer is A combination of voltage-gated ion channels and active ion pumps.

Key Points

• Cardiomyocytes, or heart muscle cells, rely heavily on a combination of voltage-gated ion channels and active ion pumps to maintain their membrane potential and ensure proper contraction.
• Voltage-gated ion channels are specialized proteins that allow ions like sodium (Na⁺), potassium (K⁺), and calcium (Ca²⁺) to move across the membrane in response to changes in voltage.
• During the cardiac action potential, these channels facilitate the influx of sodium and calcium ions, which depolarize the cell membrane, while potassium ion efflux repolarizes it.
• Active ion pumps, such as the sodium-potassium pump (Na⁺/K⁺-ATPase), maintain the ionic gradients by actively transporting ions against their concentration gradients using ATP energy.
• The calcium pump and the sodium-calcium exchanger also play critical roles in regulating intracellular calcium levels, which directly influence the contractile function of cardiomyocytes.
• The precise coordination of these mechanisms ensures the rhythmic contraction and relaxation of the heart, which is essential for pumping blood effectively throughout the body.

Additional Information

• Passive diffusion through gap junctions only
• Gap junctions are specialized structures that allow direct communication between adjacent cardiomyocytes.
• While they are important for the propagation of electrical signals, they do not actively maintain the membrane potential or regulate ion gradients.
• Facilitated diffusion of nutrients exclusively
• Facilitated diffusion is a process by which certain molecules, such as glucose, are transported across cell membranes via protein channels.
• While important for providing energy to cardiomyocytes, this mechanism does not directly influence the membrane potential or contraction.
• Endocytosis of extracellular fluid
• Endocytosis is a process that involves the uptake of extracellular substances or fluid into the cell via vesicles.
• This is not a primary mechanism for maintaining the membrane potential or supporting the contractile function of cardiomyocytes.

The correct answer is Define New Multilevel List.

Key Points

• The Define New Multilevel List feature in MS Word 2019 allows users to create structured, multi-level numbered lists, such as 1, 1.1, 1.2, 2, etc.
• This tool is particularly useful for creating hierarchical documents, such as outlines, legal documents, or academic papers.
• Users can customize the number style (e.g., Arabic numerals, Roman numerals, or letters) for each level of the list.
• It also allows the user to specify the indentation for each level, making the document appear more organized and professional.
• To access this feature, navigate to the Home tab, click on the Multilevel List dropdown, and select Define New Multilevel List.
• Within the dialog box, users can define the numbering format, alignment, and linking of levels to styles.
• This feature improves document readability and ensures a consistent numbering scheme throughout the content.

Additional Information

• Change Styles option
• The Change Styles option in MS Word is used to quickly apply or modify document themes, including font styles, colors, and paragraph spacing.
• This feature is located under the Home tab and is more focused on formatting the document's appearance rather than managing lists.
• Format Painter
• The Format Painter is a tool used for copying and applying formatting (such as font type, size, and color) from one section of text to another.
• It does not handle list creation or numbering but is useful for maintaining consistency in text styling.
• Increase Indent button
• The Increase Indent button, available in the Paragraph group of the Home tab, is used to increase the indentation of a paragraph or text.
• It is not specifically designed for creating or modifying multilevel numbered lists, but it can adjust list levels within a predefined numbering scheme.

The given three-digit numbers are: 441, 317, 999, 155, 444.

Now,

The highest number is 999. Its third digit is 9.

The lowest number is 155. Its first digit is 1.

Perform the subtraction.

Subtract the third digit of the highest number 9 from the first digit of the lowest number 1.

1 - 9 = -8.

Hence, the correct answer is "Option 2".

The correct answer is Arti Sarin.

Key Points

• Arti Sarin has created history by becoming the first woman officer to take over as the Director General of the Armed Forces Medical Services (DG AFMS) in October 2024.
• This achievement marks a significant milestone for women in the Indian Armed Forces.
• The Armed Forces Medical Services (AFMS) is responsible for the medical care of armed forces personnel, and this is one of the highest ranks in the organization.
• Her appointment highlights the growing role of women in leadership positions in the defense forces.
• Arti Sarin is known for her outstanding contributions to the field of military medicine and has served in various critical roles during her career.
• This achievement reflects the progressive steps taken by the Indian Armed Forces towards promoting gender equality.

Additional Information

• Anju Rathi Rana
• Anju Rathi Rana is a well-known name in the Indian defense sector, but she has not been appointed as the Director General of AFMS.
• She has contributed significantly to the administrative and operational aspects of the armed forces.
• Vijaya Kishore Rahatkar
• Vijaya Kishore Rahatkar is a prominent Indian politician and social activist.
• She has been associated with the Bharatiya Janata Party (BJP) and served as the Chairperson of the Maharashtra State Commission for Women.
• Her work primarily focuses on women's empowerment and social reforms, not military services.
• Deena Mehta
• Deena Mehta is a distinguished figure in the Indian financial sector.
• She was the first woman president of the Bombay Stock Exchange (BSE).
• Her expertise lies in finance and stock market operations, not in the armed forces.

Given: A, B, C, D, R, S and T are sitting around a circular table facing the centre of the table.

Only one person sits between T and S when counted from the right of T.

Only one person sits between S and C. Only one person sits between T and R.

Only two people sit between A and C. Only one person sits between B and R. 

Thus, S sits third to the right of D.

Hence, the correct answer is "Option 3".

The Correct answer is Chamber of Princes.

Key Points

• The Chamber of Princes was established in the year 1921 as a deliberative and advisory body for the princely states in British India.
• It was set up by the British Government to provide a platform for the princely rulers to discuss and deliberate matters related to their states and their relationship with the British Crown.
• The Chamber of Princes was inaugurated by the then Duke of Connaught in 1921 at the Rashtrapati Bhavan (then known as the Viceroy's House).
• This body consisted of 108 members, including rulers of princely states and their representatives.
• The Chamber was a purely advisory body and had no legislative powers, functioning as a forum for princes to exchange ideas and communicate with the British Government.
• It was a part of the British Government's attempt to control and manage the princely states effectively.
• The Chamber ceased to exist after India’s independence in 1947 when princely states were integrated into the Indian Union.

Additional Information

• Indian Council
• The Indian Council, also known as the Council of India, was established under the Government of India Act 1858 to assist the Secretary of State for India.
• It was not a deliberative body for princes but instead an advisory body for the administration of British India.
• The members of the Indian Council were based in London and were responsible for advising on policy matters.
• Imperial Assembly
• The term Imperial Assembly does not refer to any specific institution in the context of British India.
• It may appear to suggest a legislative body, but such an assembly did not exist under this name during British rule in India.
• Royal Consultation Board
• The Royal Consultation Board is not a historically recognized institution under British rule in India.
• It does not relate to the Chamber of Princes or any similar body.

Shortcut Trick

Count the total number of observations, n = 11 (which is an odd number).

Arrange the data in ascending order: 16, 27, 32, 38, 41, 47, 67, 74, 85, 88, 98.

For odd n, the Median is the middle term: ((n + 1) ÷ 2)^th term.

Median = (12 ÷ 2)^th term = 6^th term = 47.

∴ The correct answer is 47.

Alternate Method

Given: Data set = {74, 85, 67, 27, 47, 16, 41, 32, 98, 38, 88}

Formula Used: Median = ((n + 1) ÷ 2)^th term, where n is the number of observations (when n is odd).

⇒ Total number of observations (n) = 11

⇒ Arranging the data in ascending order: 16, 27, 32, 38, 41, 47, 67, 74, 85, 88, 98

⇒ Median = ((11 + 1) ÷ 2)^th term

⇒ Median = 6^th term

⇒ Median = 47

∴ The correct answer is 47.

Additional Information

Median for Even Number of Terms

If n is even, the Median is the arithmetic mean of the (n/2)^th and (n/2 + 1)^th terms after arranging the data in order.

Mean (Arithmetic Average)

The Mean is the sum of all observations divided by the total number of observations: Σx ÷ n.

Mode

The Mode is the value that occurs most frequently in the given data set. A data set can have one mode, more than one mode, or no mode at all.

Shortcut Trick

For a Right-Angled Triangle, the sides often follow standard Pythagorean Triplets.

Given sides: (x − 10), (x − 5), and x. These represent sides with a constant difference of 5.

The only standard triplet with a constant difference is 3 : 4 : 5. Multiplying by 5, we get 15 : 20 : 25.

Check: 25 − 10 = 15 and 25 − 5 = 20. Thus, x = 25, Base = 15, Height = 20.

Area = 1/2 × Base × Height = 1/2 × 15 × 20 = 150 cm².

∴ The correct answer is 150 cm².

Alternate Method

Given: Sides of right triangle are (x − 10), (x − 5) and x.

Formula Used: Pythagoras Theorem: a² + b² = c², where c is the hypotenuse (longest side).

⇒ (x − 10)² + (x − 5)² = x²

⇒ (x² − 20x + 100) + (x² − 10x + 25) = x²

⇒ 2x² − 30x + 125 = x²

⇒ x² − 30x + 125 = 0

⇒ x² − 25x − 5x + 125 = 0

⇒ x(x − 25) − 5(x − 25) = 0

⇒ (x − 25)(x − 5) = 0

⇒ x = 25 or x = 5 (x=5 not possible as side x−5 would be 0 and x−10 would be negative)

⇒ Sides are: 25, (25−5)=20, (25−10)=15

⇒ Area = 1/2 × 15 × 20 = 150 cm²

∴ The correct answer is 150 cm².

Additional Information

Pythagorean Triplets

Sets of three integers that satisfy a² + b² = c², such as (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Area of Right Triangle

Area is calculated as 1/2 × base × height, where base and height are the two legs forming the 90° angle.

Hypotenuse Property

The hypotenuse is always the longest side of a right-angled triangle and is opposite the right angle.

Given:

Expression to solve: [525 ÷ {19 + 7 × (3 - 5)}]

Calculation:

[525 ÷ {19 + 7 × (3 - 5)}]}

⇒ [525 ÷ {19 + 7 × (-2)}]

⇒ [525 ÷ {19 - 14}]

⇒ [525 ÷ 5]

⇒ 105

∴ The correct answer is option (1).

Shortcut Trick

Calculate Total Frequency (N) = 14 + 37 + 28 + 39 + 12 = 130.

Find N/2 = 130 ÷ 2 = 65.

Identify Median Class by Cumulative Frequency (CF): 14, 51, 79... (65 falls in the 240-290 class).

Apply Median = L + [(N/2 − CF_p) ÷ f] × h = 240 + [(65 − 51) ÷ 28] × 50.

Median = 240 + [14 ÷ 28] × 50 = 240 + 25 = 265.

∴ The correct answer is 265.

Alternate Method

Given: Distribution of classes and their respective frequencies.

Formula Used: Median = L + [((N/2) − CF) ÷ f] × h

Where: L = Lower limit of median class, N = Total frequency, CF = Cumulative frequency of preceding class, f = Frequency of median class, h = Class width.

Step 1: Calculate Cumulative Frequencies (CF)

⇒ Class 140-190: f = 14, CF = 14

⇒ Class 190-240: f = 37, CF = 14 + 37 = 51

⇒ Class 240-290: f = 28, CF = 51 + 28 = 79

⇒ Class 290-340: f = 39, CF = 79 + 39 = 118

⇒ Class 340-390: f = 12, CF = 118 + 12 = 130

Step 2: Find Median Class

⇒ Total Frequency (N) = 130

⇒ N/2 = 130 ÷ 2 = 65

⇒ The CF just greater than 65 is 79, which corresponds to the Median Class 240-290.

Step 3: Apply Median Formula

⇒ L = 240, CF = 51, f = 28, h = 50

⇒ Median = 240 + [(65 − 51) ÷ 28] × 50

⇒ Median = 240 + [14 ÷ 28] × 50

⇒ Median = 240 + [0.5 × 50]

⇒ Median = 240 + 25 = 265

∴ The correct answer is 265.

Additional Information

Empirical Relationship

For a moderately skewed distribution: Mode = 3 Median − 2 Mean.

Mode of Grouped Data

Mode = L + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h, where f₁ is the frequency of the modal class.

Mean of Grouped Data

Mean (μ) = Σ(f_i × x_i) ÷ Σf_i, where x_i is the class mark (mid-point) of each interval.

The correct answer is Metallic character increases across a period from left to right.

Key Points

• Metallic character refers to the ability of an element to lose electrons and form positive ions (cations).
• Across a period in the periodic table (from left to right), the metallic character decreases. This is because the atomic radius decreases, and the effective nuclear charge increases, making it harder for atoms to lose electrons.
• The statement "Metallic character increases across a period from left to right" is incorrect because non-metallic character increases across a period instead.
• For example, in Period 3 of the periodic table, elements transition from metals (like sodium) to metalloids (like silicon) and finally to non-metals (like chlorine).
• In contrast, metallic character increases down a group as atomic size increases and the outer electrons become easier to lose due to a weaker hold by the nucleus.
• This trend is closely related to other periodic properties like ionization energy and electronegativity.
• Thus, the correct answer is the statement that contradicts this trend: "Metallic character increases across a period from left to right".

Additional Information

• Metallic character increases down a group
• As we move down a group, the atomic size increases, and the outermost electrons are farther from the nucleus.
• This reduces the effective nuclear charge experienced by the outermost electrons, making it easier for the atom to lose electrons and exhibit metallic character.
• For example, in Group 1, lithium is less metallic than cesium.
• Metallic character decreases across a period from left to right
• Across a period, the atomic radius decreases as the number of protons increases, resulting in a stronger nuclear pull on the electrons.
• This makes it harder for atoms to lose electrons, reducing their metallic character.
• For example, in Period 2, beryllium (metal) transitions to fluorine (non-metal).
• The change from metallic to non-metallic is gradual
• This statement is correct because elements transition from metals to metalloids and then to non-metals as we move from left to right across a period.
• For example, in Period 3, aluminum (metal) transitions to silicon (metalloid) and finally to sulfur (non-metal).

The Correct answer is Cossipore.

Key Points

• The first Ordnance Factory in India was established in Cossipore, Kolkata, in the year 1801.
• It is known as the Cossipore Gun & Shell Factory, and it is the oldest ordnance factory in India.
• The establishment of this factory marked the beginning of the Ordnance Factories Board (OFB), which is now part of India’s defense production sector.
• Ordnance Factories Day is observed on 18^th March every year to commemorate the foundation of this factory.
• The ordnance factories are responsible for the manufacture of arms, ammunition, and defense equipment for the Indian Armed Forces.
• The factory in Cossipore played a significant role in the defense preparedness of India during both World War I and World War II.
• It is under the administrative control of the Department of Defence Production, Ministry of Defence, Government of India.
• The factory is equipped with advanced manufacturing technologies and continues to produce a wide range of defense products.

Additional Information

• Pune
• Pune is a major industrial and educational hub in India, but it is not the location of India’s first ordnance factory.
• However, Pune is home to several defense-related institutions such as the Defence Institute of Advanced Technology (DIAT) and the National Defence Academy (NDA).
• Hyderabad
• Hyderabad is known for its contribution to the defense sector through establishments like the Defence Research and Development Laboratory (DRDL) and the Research Centre Imarat (RCI).
• It is not the location of India’s first ordnance factory.
• Jabalpur
• Jabalpur is another important center for defense production in India with facilities like the Gun Carriage Factory (GCF) and Vehicle Factory Jabalpur (VFJ).
• While significant, it is not the location of the first ordnance factory.

Given: Mr. Yanki starts from Point A and drives 17 km towards the South.

He then takes a right turn, drives 19 km, turns right and drives 29 km.

He then takes a right turn and drives 15 km, turns right drives 1 km.

He then takes a left turn drives 6 km.

He takes a final right turn, drives 11 km and stops at Point P.

Thus, he drive 2 km to the West in order to reach Point A again.

Hence, the correct answer is "Option 4".

Shortcut Trick

Given Cost Price (CP) = ₹285 and Marked Price (MP) = ₹1,140.

The ratio of CP to MP is 285 : 1140 = 1 : 4.

If MP = 100 units, then CP = 25 units.

Selling Price (SP) at 70% discount = 100 − 70 = 30 units.

Profit% = (SP − CP) ÷ CP × 100 = (30 − 25) ÷ 25 × 100 = 5 ÷ 25 × 100 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given: Cost Price (CP) = ₹285, Marked Price (MP) = ₹1,140, Discount = 70%.

Formulas: SP = MP × (100 − Discount%) ÷ 100 | Profit% = (SP − CP) ÷ CP × 100.

⇒ Step 1: Calculate Selling Price (SP) = 1140 × (100 − 70) ÷ 100

⇒ SP = 1140 × 30 ÷ 100 = 114 × 3 = ₹342

⇒ Step 2: Calculate Profit = SP − CP = 342 − 285 = ₹57

⇒ Step 3: Calculate Profit Percentage = (57 ÷ 285) × 100

⇒ Profit% = (1 ÷ 5) × 100 = 20%

∴ The correct answer is 20%.

Additional Information

Marked Price & Discount

Marked Price (MP) is the price printed on an article. Discount is always calculated on the MP to arrive at the Selling Price (SP). Formula: SP = MP − Discount.

Profit and CP Relationship

Profit or loss is always calculated on the Cost Price (CP) unless otherwise stated. Formula: Profit% = [(SP − CP) ÷ CP] × 100.

Shortcut Trick

The overall average of 30 students is 75.

The first 20 students have an average of 80, which is +5 more than the total average.

Total excess score = 20 × 5 = +100.

To balance this, the remaining 10 students must have a total deficit of −100.

Average of remaining 10 students = 75 + (−100 ÷ 10) = 65.

∴ The correct answer is 65.

Alternate Method

Given:

Total number of students = 30

Average score of class = 75

Average score of 20 students = 80

Formula Used:

Sum of values = Average × Number of observations

Calculations:

⇒ Total score of all 30 students = 30 × 75 = 2250

⇒ Total score of 20 students = 20 × 80 = 1600

⇒ Total score of remaining 10 students = 2250 − 1600 = 650

⇒ Average score of remaining 10 students = 650 ÷ 10 = 65

∴ The correct answer is 65.

Additional Information

Weighted Average Formula

When two groups with averages a₁ and a₂ and sizes n₁ and n₂ are combined, the new average is (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Net Deviation Rule

The sum of the deviations of all items in a set from their arithmetic mean is always zero.

Constant Change

If every value in a data set is increased or decreased by a constant 'k', the average of the set also increases or decreases by 'k'.

Shortcut Trick

Perimeter of a cuboid = 4 × (Length + Breadth + Height)

Sum of terms = (2x + 5x + x) + (−5y + 7y + y) + (3 − 7 + 3) = 8x + 3y − 1

Perimeter = 4 × (8x + 3y − 1) = 32x + 12y − 4

∴ The correct answer is (32x + 12y − 4) m.

Alternate Method

Given:

Length (l) = (2x − 5y + 3) m

Breadth (b) = (5x + 7y − 7) m

Height (h) = (x + y + 3) m

Formula Used:

Perimeter of Cuboid = 4(l + b + h)

Calculations:

⇒ Sum = (2x − 5y + 3) + (5x + 7y − 7) + (x + y + 3)

⇒ Sum = (2x + 5x + x) + (−5y + 7y + y) + (3 − 7 + 3)

⇒ Sum = 8x + 3y − 1

⇒ Perimeter = 4 × (8x + 3y − 1)

⇒ Perimeter = 32x + 12y − 4

∴ The correct answer is (32x + 12y − 4) m.

Additional Information

Total Surface Area of Cuboid

The total area of all six faces is given by 2(lb + bh + hl).

Volume of Cuboid

The space occupied by the cuboid is calculated as Length × Breadth × Height.

Diagonal of Cuboid

The longest rod that can be placed inside is √(l² + b² + h²).

Given: L is the mother of two sons, namely, P and J. F is the wife of P. Q is the daughter of J. 

Thus, L is the Father's mother of Q.

Hence, the correct answer is "Option 1".

The Correct answer is Modernisation and technology upgrade.

Key Points

• The Seventh Five-Year Plan (1985–90) in India was initiated under the leadership of Prime Minister Rajiv Gandhi.
• The focus of this plan was on modernisation, technology upgrade, and self-reliance.
• It aimed to improve industrial productivity through the adoption of advanced technologies and techniques.
• There was a strong emphasis on the use of modern technology in agriculture to increase yield and efficiency.
• This plan targeted economic growth by strengthening the infrastructure and fostering the development of sectors like energy, telecommunications, and transport.
• It also aimed to achieve sustainable development by balancing growth with environmental protection.
• The plan prioritized the reduction of regional disparities through balanced regional development and equitable distribution of resources.
• Special attention was given to employment generation and improving the living standards of the people.

Additional Information

• Liberalisation
• Liberalisation refers to the relaxation of government restrictions in areas like trade, investment, and industry.
• The concept became prominent in India during the economic reforms of 1991, not in the Seventh Five-Year Plan.
• It focuses on reducing trade barriers, tariffs, and regulations to encourage foreign investment and improve competitiveness.
• Structural reforms
• Structural reforms are comprehensive changes aimed at improving the functioning of an economy.
• In India, structural reforms were notably implemented during the 1991 economic liberalisation, focusing on sectors like banking, trade, and public enterprises.
• Privatisation
• Privatisation involves transferring ownership of public sector enterprises to private entities.
• Although some privatisation steps were taken earlier, it became a major policy focus during the post-1991 economic reforms.

The Correct answer is Right-clicking on the desktop and selecting 'New' → 'Folder'.

Key Points

• Creating a new folder on a Windows desktop can be easily achieved by right-clicking on the desktop space.
• After right-clicking, a context menu appears with several options such as 'View', 'Sort by', 'Refresh', 'New', etc.
• Select the 'New' option, which opens a secondary menu with options to create different items like Folder, Shortcut, Text Document, etc.
• Clicking on 'Folder' creates a new folder on the desktop, which appears with the default name 'New Folder'.
• The user can rename the folder immediately by typing the desired name or later by right-clicking on the folder and selecting 'Rename'.
• This method is a graphical user interface (GUI)-based approach, making it simple and intuitive for users of all skill levels.
• The process works on most Windows operating systems, including Windows 7, 8, 10, and 11.

Additional Information

• Alt + Tab
• Alt + Tab is a keyboard shortcut used to switch between open applications or windows on a computer.
• This shortcut does not relate to creating folders but enhances multitasking efficiency.
• Recycle Bin Icon
• Clicking on the Recycle Bin icon allows users to view deleted files and restore or permanently delete them.
• The Recycle Bin is part of Windows' file management system, but it cannot be used to create folders.
• Ctrl + F
• Ctrl + F is a shortcut used to find text or specific items within a document, webpage, or application.
• It is commonly used for searching content but has no function related to creating folders.

The Correct answer is Printed Circuit Board.

Key Points

• Printed Circuit Board (PCB) is a critical component used in electronic circuits to mechanically support and electrically connect electronic components.
• It is made of layers of conductive material (typically copper) and non-conductive substrate (such as fiberglass or epoxy resin).
• PCBs are designed using specialized software to create a precise layout of electrical connections between components.
• They are widely used in various applications such as computers, mobile phones, medical devices, automotive electronics, and industrial equipment.
• PCBs eliminate the need for complex wiring by embedding the circuitry directly onto the board, making them compact and efficient.
• PCB manufacturing involves multiple steps, including designing, etching, drilling, soldering, and assembly.
• The primary types of PCBs include single-sided, double-sided, and multi-layer boards, depending on the complexity of the circuit.
• Advanced PCBs may also include components like integrated circuits (ICs), resistors, capacitors, and connectors.
• PCBs are critical for ensuring the reliability, performance, and scalability of electronic systems.

Additional Information

• Peripheral Circuit Bridge
• This term does not exist as a standard concept in electronics or electrical circuits.
• The word Peripheral commonly refers to external devices connected to a computer, such as printers, keyboards, and mice, but does not relate to PCBs.
• Programmed Control Base
• This term could refer to a component or system used for automation or control in industrial applications, but it is not related to PCBs.

Programmable Logic Controllers (PLCs) are often used for programmed control, but these are separate devices and not synonymous with PCBs.

• Process Control Board
• Process control systems are used in industries to monitor and control production processes. However, this term is not a standard replacement for Printed Circuit Board.
• Process control boards may contain PCBs, but they refer to a specific application rather than the general concept of a PCB.

The Correct answer is Sovereign borrowing.

Key Points

• Sovereign borrowing refers to the process where a government borrows money, typically through the issuance of bonds or loans, to finance its expenditures or development projects. It is not considered a form of privatisation, as privatisation involves transferring ownership or control of government assets to private entities.
• Privatisation is a key element of the New Economic Policy of 1991, which aimed to reduce the role of the government in economic activities and promote private sector participation. However, sovereign borrowing does not align with this objective, as it does not involve transferring ownership or management to private players.
• Sovereign borrowing is primarily used to bridge fiscal deficits, fund infrastructure projects, or manage economic crises, and does not involve selling or monetising government-owned assets.
• The term "privatisation" is typically associated with methods like strategic sale, disinvestment, and asset monetisation, all of which involve reducing government control or ownership in public enterprises or assets.
• In contrast, sovereign borrowing is a financial mechanism, not a structural reform like privatisation.

Additional Information

• Strategic Sale
• A strategic sale involves selling a significant portion of a government-owned enterprise to a private entity, usually with the transfer of management control.
• It is a form of privatisation, as it reduces government ownership and promotes private sector efficiency.
• An example is the sale of Air India to the Tata Group in 2021.
• Disinvestment
• Disinvestment refers to the process where the government reduces its stake in a public sector enterprise, often by selling shares to private investors.
• It is a common method of privatisation and helps raise funds for the government while increasing private sector participation.
• An example is the disinvestment in companies like Bharat Petroleum Corporation Limited (BPCL).
• Asset Monetisation
• Asset monetisation involves leasing or selling government-owned assets like roads, railways, or airports to private entities to generate revenue.
• It is considered a form of privatisation as it allows private players to manage and utilise public assets while reducing government control.
• For example, the National Monetisation Pipeline (NMP) launched in India aims to monetise assets worth ₹6 lakh crore.

The Correct answer is COP29.

Key Points

• COP29 refers to the 29^th annual Conference of the Parties under the United Nations Framework Convention on Climate Change (UNFCCC).
• The event is scheduled to take place in Baku, Azerbaijan, in November 2024.
• COP29 serves as a significant platform where world leaders, policymakers, and environmental experts come together to address climate change and discuss strategies for mitigating its effects.
• The focus of COP29 will likely include discussions on implementing the Paris Agreement, setting new targets for reducing greenhouse gas emissions, and advancing climate finance mechanisms for developing nations.
• These conferences are crucial for achieving a global consensus on climate-related issues and for ensuring that countries are held accountable for their commitments.
• The UNFCCC, established in 1992 during the Earth Summit in Rio de Janeiro, oversees these conferences as part of its efforts to combat climate change globally.
• Azerbaijan's hosting of COP29 underscores its increasing role in global climate diplomacy and its efforts to integrate sustainable practices within its development framework.

Additional Information

• COP28
• COP28 refers to the 28^th Conference of the Parties under the UNFCCC and is scheduled to take place in Dubai, United Arab Emirates (UAE), in 2023.
• The COP28 agenda focuses on achieving the Global Stocktake, a critical assessment of global progress toward meeting climate goals set out in the Paris Agreement.
• Earth Summit 2024
• The term "Earth Summit" typically refers to the 1992 United Nations Conference on Environment and Development (UNCED) held in Rio de Janeiro, Brazil.
• While no event titled Earth Summit 2024 is officially recognized under UNFCCC proceedings, such summits historically address sustainable development and environmental protection.
• Global Climate Forum
• The Global Climate Forum is a platform for researchers and stakeholders to collaboratively address climate-related challenges.
• Although it plays a significant role in shaping climate policies and research, it is distinct from the COP conferences under the UNFCCC.

Given: Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.

1. T has an exam on Friday.

2. Exactly 3 people have an exam between P and U, neither of whom has an exam on Sunday.

3. V has an exam immediately before U.

 

4. S has an exam immediately after Q.

Thus, People after S (Wednesday) → Thursday (V), Friday (T), Saturday (U), Sunday (empty) → 3 people have exams after S.

Hence, the correct answer is 3 (Option 1).

Shortcut Trick

For a 3-year period, the difference (D) between Compound Interest and Simple Interest is given by the formula:

D = P × (r/100)² × (3 + r/100)

Given: D = ₹228 and r = 4%.

⇒ 228 = P × (4/100)² × (3 + 4/100)

⇒ 228 = P × (1/625) × (304/100)

⇒ P = (228 × 625 × 100) / 304 = 46875

∴ The correct answer is ₹46,875.

Alternate Method

Given:

Time (T) = 3 years

Rate (R) = 4% per annum

Difference (CI − SI) = ₹228

Let the Principal be P.

Simple Interest (SI) for 3 years:

⇒ SI = (P × R × T) / 100

⇒ SI = (P × 4 × 3) / 100 = 12P / 100

Compound Interest (CI) for 3 years:

⇒ Amount (A) = P(1 + R/100)^T

⇒ A = P(1 + 4/100)³ = P(1 + 1/25)³ = P(26/25)³

⇒ A = P(17576 / 15625)

⇒ CI = A − P = P(17576/15625 − 1) = 1951P / 15625

According to the question, CI − SI = 228:

⇒ 1951P / 15625 − 12P / 100 = 228

⇒ (1951P × 4 − 12P × 625) / 62500 = 228

⇒ (7804P − 7500P) / 62500 = 228

⇒ 304P / 62500 = 228

⇒ P = (228 × 62500) / 304

⇒ P = 3/4 × 62500 = 3 × 15625 = 46875

∴ The correct answer is ₹46,875.

Additional Information

Difference for 2 years

The difference between CI and SI for a 2-year period is given by D = P(r/100)².

Effective Rate Method

For CI of 2 years, effective rate = r + r + (r×r)/100. For 3 years, apply the successive formula again.

Simple Interest Property

Simple Interest remains the same for every year if the principal and rate are constant.

The Correct answer is West to east.

Key Points

• In winter, the jet streams influencing the Indian climate typically flow from west to east.
• Jet streams are fast-moving air currents found in the upper levels of the atmosphere, mainly in the troposphere.
• These streams play a vital role in shaping the weather patterns, especially during winter months.
• The western jet stream influences the Indian subcontinent, bringing cold weather conditions and impacting the western disturbances.
• The western disturbances, driven by these jet streams, are responsible for the winter rainfall in the northwestern parts of India.
• The direction of jet streams is primarily governed by the rotation of the Earth and the temperature contrast between the equator and poles.
• During winter, the position of the jet streams shifts southward, influencing the weather over South Asia, including India.
• The west-to-east flow of jet streams also impacts the movement of cyclonic systems in the region, contributing to the formation of rain-bearing clouds.
• These jet streams have a significant effect on agriculture, as winter rainfall supports the Rabi crop season.

Additional Information

• East to west
• Jet streams typically do not flow from east to west due to the Earth's rotation and the temperature gradient between the poles and the equator.
• This direction would contradict the general movement of atmospheric circulation in the Northern Hemisphere.
• Southwest to northeast
• This direction is commonly associated with the movement of the Southwest Monsoon winds in India during the summer season, not winter.
• The monsoon winds are influenced by the heating of the Indian Ocean and the Himalayas, which is distinct from the jet streams.
• Southeast to northwest
• Jet streams in this direction are unusual and do not align with the typical atmospheric circulation observed in the Indian subcontinent.
• This option is not relevant for the Indian winter climate influenced by jet streams.

Shortcut Trick

Identify Radius (r) = 102 ÷ 2 = 51 cm.

Using CSA = πrl ⇒ 4335π = π × 51 × l ⇒ Slant height (l) = 85 cm.

Apply Pythagorean Triplet (8, 15, 17) scaled by 5 × 17 = 85, 3 × 17 = 51, 4 × 17 = 68.

∴ The height is 68 cm.

∴ The correct answer is 68 cm.

Alternate Method

Given: Curved Surface Area (CSA) = 4335π cm², Diameter (d) = 102 cm.

Formula Used: CSA = πrl and l² = r² + h²

⇒ Radius (r) = 102 ÷ 2 = 51 cm.

⇒ π × r × l = 4335π

⇒ 51 × l = 4335

⇒ l = 4335 ÷ 51 = 85 cm.

⇒ h² = l² − r²

⇒ h² = 85² − 51² = (85 − 51)(85 + 51)

⇒ h² = 34 × 136 = 4624

⇒ h = √4624 = 68 cm.

∴ The correct answer is 68 cm.

Additional Information

Total Surface Area of Cone

The total surface area includes the CSA and the Base Area: TSA = πr(l + r).

Volume of Cone

The capacity of a cone is exactly one-third the volume of a cylinder with the same base and height: V = (1/3)πr²h.

Relation between l, r, and h

In a right circular cone, the slant height (l), vertical height (h), and radius (r) form a Right-Angled Triangle: l² = r² + h².

Shortcut Trick

Net percentage increase for two successive decades of 20% each = 20 + 20 + (20 × 20)/100 = 44%.

Population in 1988 = 4,85,000 × (144/100).

Population in 1988 = 4,850 × 144 = 6,98,400.

∴ The correct answer is 6,98,400.

Alternate Method

Given: Initial population (1968) = 4,85,000. Increase per decade = 20%. Time period = 1968 to 1988 = 2 decades.

Formula: Final Population = P × (1 + R/100)ⁿ

⇒ Population in 1978 = 4,85,000 × (120/100) = 5,82,000

⇒ Population in 1988 = 5,82,000 × (120/100)

⇒ Population in 1988 = 5,820 × 120

⇒ Population in 1988 = 6,98,400

∴ The correct answer is 6,98,400.

Additional Information

Successive Percentage Change

If a value changes by x% and then by y%, the effective change is (x + y + xy/100)%.

Population Growth Formula

Similar to compound interest, growth is calculated as A = P(1 + r/100)^t, where r is growth rate per period.

Base Change Property

In successive growth, the second percentage increase is applied to the new base (the value after the first increase).

The correct answer is Only 1 and 2.

Key Points

• In the 2024 Haryana Assembly Elections, the Bharatiya Janata Party (BJP) formed the government for the third consecutive term in the state. Hence, Statement 1 is correct.
• The Indian National Lok Dal (INLD) secured 2 seats in the Haryana Legislative Assembly elections. Hence, Statement 2 is correct.
• Independent candidates did not secure more than 5 seats in the election. Hence, Statement 3 is incorrect.
• The Haryana Legislative Assembly has a total of 90 seats, and the majority mark required to form the government is 46 seats, not 48. Hence, Statement 4 is incorrect.
• Statement-wise Analysis:
• 1. BJP formed the government for a third consecutive term – Correct.
• 2. INLD secured 2 seats – Correct.
• 3. Independent candidates secured more than 5 seats – Incorrect.
• 4. Majority mark was 48 seats – Incorrect.
• Hence, the correct answer is Only 1 and 2.

Additional Information

• Haryana Legislative Assembly is a unicameral legislature consisting of 90 elected members.
• The term of the Haryana Assembly is generally 5 years unless dissolved earlier.
• Chandigarh serves as the capital of both Haryana and Punjab.
• Indian National Lok Dal (INLD) is a regional political party mainly active in Haryana and was founded by Devi Lal.
• The Election Commission of India (ECI) conducts Assembly elections under the provisions of the Constitution of India.

Important Points

• The majority mark in any legislative assembly is calculated as more than half of the total seats.
• Questions related to recent elections, constitutional bodies, political parties, and state legislatures are frequently asked in competitive examinations.

Shortcut Trick

Total weight of all 4 people = 65 × 4 = 260 kg.

Let the average weight of the 3 friends be x kg.

M's weight = x + 8 kg.

Sum of weights = 3x + (x + 8) = 260 ⇒ 4x = 252 ⇒ x = 63 kg.

M's weight = 63 + 8 = 71 kg.

∴ The correct answer is 71 kg.

Alternate Method

Given:

Average weight of M and 3 friends (Total 4 people) = 65 kg.

Difference between M's weight and the average of 3 friends = 8 kg.

Formula Used:

Total Sum = Average × Number of entities

Calculations:

⇒ Total weight of M + 3 friends = 4 × 65 = 260 kg

⇒ Let the average weight of 3 friends be A kg.

⇒ Weight of M = A + 8 kg

⇒ Sum of weight of 3 friends = 3 × A

⇒ Total Weight = (Sum of 3 friends) + (Weight of M)

⇒ 260 = 3A + (A + 8)

⇒ 260 = 4A + 8

⇒ 4A = 260 − 8

⇒ 4A = 252

⇒ A = 252 ÷ 4 = 63 kg

⇒ M's weight = A + 8 = 63 + 8 = 71 kg

∴ The correct answer is 71 kg.

Additional Information

Weighted Average

When groups with different averages are combined, the total average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Average Deviation

The sum of deviations of all observations from their arithmetic mean is always zero.

Arithmetic Mean

Mean = (Sum of all observations) ÷ (Total number of observations).

The Correct answer is Department of Design and Manufacturing.

Key Points

• The Department of Design and Manufacturing at the Indian Institute of Science (IISc) focuses on cutting-edge research in the areas of design, manufacturing, and engineering systems.
• In the context of the 2025 research project on synthetic image generation for Magnetic Resonance (MR) applications, the department played a critical role in developing innovative technologies to enhance medical imaging.
• The research aimed to improve MR imaging quality using synthetic image generation techniques, which are essential for better diagnostics and treatment planning.
• The department leverages advanced technologies such as machine learning, computer vision, and optimization algorithms to design systems that meet specific requirements of industries, including healthcare.
• The team likely collaborated with experts from other interdisciplinary fields to ensure the successful application of synthetic image generation in MR systems.
• The department is well-known for its focus on innovative solutions in engineering design and manufacturing processes, which makes it a key contributor to projects requiring technical expertise and precision.
• This project highlights the department’s capability to merge engineering design principles with modern technological advancements.

Additional Information

• Department of Artificial Intelligence
• This department primarily focuses on machine learning, deep learning, and other AI-related technologies.
• While AI plays a role in synthetic image generation, the Department of Design and Manufacturing was specifically involved due to the engineering and manufacturing aspects of the project.
• AI applications are more general and cross-disciplinary, but this project required expertise in the integration of design principles with manufacturing systems.
• Department of Computer Science
• The Department of Computer Science specializes in theoretical and applied computer science, including algorithms, data structures, and computational systems.
• Although computer science techniques such as image processing might have been used in the project, the focus on design and manufacturing systems made the Department of Design and Manufacturing more suitable for leadership in this context.
• Department of Mechanical Engineering
• The Department of Mechanical Engineering is more focused on traditional engineering disciplines, such as thermodynamics, fluid mechanics, and structural analysis.
• While it contributes significantly to engineering projects, this specific research on synthetic image generation for MR applications required expertise in design systems and manufacturing technologies, making the Department of Design and Manufacturing a better fit.

The Correct answer is The entire Council of Ministers must resign.

Key Points

• A No-Confidence Motion is a parliamentary motion moved against the Union Government, indicating that the ruling government no longer holds the confidence of the majority of members in the Lok Sabha, as per Article 75(3) of the Indian Constitution.
• If the motion is passed, it leads to a loss of majority for the ruling government in the Lok Sabha, thereby mandating the resignation of the entire Council of Ministers, including the Prime Minister.
• The Prime Minister and the Council of Ministers collectively hold office during the pleasure of the President, but this is contingent upon the government maintaining the confidence of the Lok Sabha.
• It is a crucial legislative mechanism to ensure the accountability of the government to the elected representatives of the people.
• Once the Council of Ministers resigns, the President may invite the leader of another party or coalition that can prove majority support to form the new government, or may call for fresh general elections.
• The process of a No-Confidence Motion ensures the stability and democratic functioning of India's parliamentary system.

Additional Information

• The Prime Minister is given a chance to reorganise the Cabinet.
• This option is incorrect because a No-Confidence Motion does not provide the Prime Minister with an opportunity to reorganize the Cabinet. Instead, the motion directly challenges the authority and legitimacy of the entire government.
• The motion signifies loss of majority support, making it mandatory for the entire Council of Ministers to resign.
• Only the dissenting ministers resign.
• In the parliamentary system, the Council of Ministers functions as a collective entity. Hence, resignation due to a No-Confidence Motion applies to the entire Council of Ministers, not just dissenting members.
• Individual resignations do not address the fundamental issue of lack of majority support in the Lok Sabha.
• A re-election is triggered.
• While a No-Confidence Motion may eventually lead to fresh elections, it is not an automatic outcome of the motion being passed.
• The President can invite another party or coalition with a proven majority in the Lok Sabha to form the government before considering general elections.

The Correct answer is Terai.

Key Points

• The Terai region is a marshy and humid zone located in the Great Indian Plains, situated along the foothills of the Himalayas.
• It is characterized by high groundwater levels due to frequent seepage from rivers descending from the Himalayas.
• The region is known for its dense forests and fertile land, making it an agriculturally productive area.
• The climatic conditions in the Terai are humid, with significant rainfall, contributing to its marshy characteristics.
• The Terai serves as an important wildlife habitat, home to species like the Bengal tiger, rhinoceros, and elephants, particularly in areas like the Terai Arc Landscape.
• It is a transitional area between the plains and the mountains, and its geographical features play a critical role in the hydrology of northern India.

Additional Information

• Bhabar
• The Bhabar zone lies just above the Terai region, at the foothills of the Himalayas.
• It is characterized by a porous and rocky terrain, which causes rivers to disappear underground.
• The soil in this region is less fertile, and agriculture is limited.
• Bhangar
• Bhangar refers to the older alluvial soil found in the Great Indian Plains.
• This area is slightly elevated and less fertile compared to the newer alluvial soil (Khadar).
• It is primarily used for pasture and settlement rather than intensive agriculture.
• Delta
• The Delta region is located at the mouths of major rivers like the Ganga and Brahmaputra.
• It is characterized by extremely fertile soil, making it one of the most productive agricultural zones in India.
• This region often experiences flooding and is rich in biodiversity.

Shortcut Trick

For two numbers a and b, the third proportional is given by b²/a.

Given: a = 81, b = Z, and Third Proportional = 9.

⇒ Z² / 81 = 9

⇒ Z² = 81 × 9 = 729

⇒ Z = √729 = 27

∴ The correct answer is 27.

Alternate Method

Given: First number = 81, Second number = Z, Third proportional = 9.

Formula Used: If a, b, c are in continued proportion, then a : b = b : c, where c is the third proportional.

⇒ 81 : Z = Z : 9

⇒ 81 / Z = Z / 9

⇒ Z × Z = 81 × 9

⇒ Z² = 729

⇒ Z = √729

⇒ Z = 27

∴ The correct answer is 27.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Fourth Proportional

If a : b = c : d, then d is the fourth proportional, calculated as d = (b × c) / a.

Continued Proportion

Three numbers a, b, c are in continued proportion if a/b = b/c, which implies b² = ac.

The correct answer is Puducherry.

Key Points

• The Fourteenth Amendment Act of 1962 enabled the integration of the Union Territory of Puducherry (formerly known as Pondicherry) into India.
• Puducherry was a former French colony, and its integration into India was formalized through a treaty between India and France signed in 1956.
• The treaty was ratified by the French Parliament, and Puducherry officially became part of India on 16^th August 1962.
• The Union Territory of Puducherry includes four regions: Pondicherry, Karaikal, Mahe, and Yanam, which are geographically separated but collectively administered.
• Puducherry’s inclusion in India was a significant step towards consolidating the country’s territorial integrity post-independence.
• The region is known for its unique French heritage, architecture, and culture, which continue to influence its identity.
• Puducherry is governed under the provisions of Article 239 of the Indian Constitution, which deals with the administration of Union Territories.

Additional Information

• Goa
• Goa was annexed by India from Portuguese control in 1961 through a military operation called Operation Vijay.
• It became a Union Territory initially but achieved statehood on 30^th May 1987.
• Daman and Diu
• Daman and Diu were also liberated from Portuguese control in 1961, along with Goa.
• It remained a Union Territory until it was merged with Dadra and Nagar Haveli to form a new Union Territory in 2020.
• Lakshadweep
• Lakshadweep is a group of islands in the Arabian Sea, which became a Union Territory of India in 1956.
• The islands are known for their biodiversity, coral reefs, and tourism potential.

The logic followed here is:

GF 7 is related to EA -10

UG 14 is related to SB -3

Similarly,

LN 2 is related to ?

Hence, the correct answer is "Option 1".

Given:

: IKO :: TVZ : %

Option 1) # = EGK , % = YZD

For # (EGK) to IKO

The pattern derived from EGK to IKO is: (+4, +4, +4).

For TVZ to % (YZD)

The pattern derived from TVZ to YZD is: (+5, +4, +4).

Since the patterns do not match, Option 1 is incorrect.

Option 2) # = EGK , % = XZD

For # (EGK) to IKO

The pattern derived from EGK to IKO is: (+4, +4, +4).

For TVZ to % (XZD)

The pattern derived from TVZ to XZD is: (+4, +4, +4).

Since the patterns for both pairs match, Option 2 is the correct answer.

Option 3) # = ELK , % = XZD

For # (ELK) to IKO

The pattern derived from ELK to IKO is: (+4, -1, +4).

For TVZ to % (XZD)

The pattern derived from TVZ to XZD is: (+4, +4, +4).

Since the patterns do not match, Option 3 is incorrect.

Option 4) # = FGK , % = XZD

For # (FGK) to IKO

The pattern derived from FGK to IKO is: (+3, +4, +4).

For TVZ to % (XZD)

The pattern derived from TVZ to XZD is: (+4, +4, +4).

Since the patterns do not match, Option 4 is incorrect.

Thus,  # = EGK , % = XZD

Hence, the correct answer is "Option 2".