The correct answer is 87th Anniversary.

Key Points

• National Defence Day is observed annually in India to honor the sacrifices and contributions of the armed forces in safeguarding the nation's security and sovereignty.
• The year 2025 marked the 87th anniversary of National Defence Day, which traces its roots back to significant military events in 1938.
• This day is dedicated to recognizing the valor, dedication, and commitment of personnel from the Army, Navy, and Air Force.
• National Defence Day also serves as a platform to spread awareness about the importance of a robust defense system in maintaining peace and security.
• Various ceremonies, parades, and tributes are organized across the country to commemorate the occasion.

Additional Information

• Indian Armed Forces
• India's armed forces consist of three main branches: the Army, Navy, and Air Force, along with auxiliary organizations like the Coast Guard.
• The President of India serves as the Supreme Commander of the Indian Armed Forces.
• India has one of the largest and most powerful military forces in the world, with a focus on modernization and self-reliance in defense production.
• Historical Significance
• The establishment of National Defence Day is tied to key milestones in India's military history, including contributions during pre-independence and post-independence periods.
• It is a day to remember the martyrs who laid down their lives in service to the nation.
• Important Military Operations
• India's armed forces have participated in several notable operations, including the Indo-Pak Wars (1947, 1965, 1971, and 1999), the Sino-Indian War (1962), and peacekeeping missions under the United Nations.
• They play a crucial role in disaster relief, internal security, and maintaining strategic stability in the region.
• Key Military Institutions
• India has premier institutions like the National Defence Academy (NDA), Indian Military Academy (IMA), and Defence Research and Development Organisation (DRDO) to train and equip its armed forces.
• These institutions contribute significantly to the development of military strategies, technology, and leadership.

The correct answer is Kuno National Park.

Key Points

• In February 2025, five cheetahs were released into Kuno National Park, located in Madhya Pradesh, India.
• This release is part of India's ambitious Cheetah Reintroduction Project, aimed at reintroducing cheetahs in the country after their extinction nearly 70 years ago.
• The cheetahs were translocated from Africa as part of a collaborative effort between India and countries like Namibia and South Africa.
• Kuno National Park was selected for this project due to its suitable habitat, abundant prey base, and minimal human-wildlife conflict.
• This effort is a step toward restoring ecological balance and ensuring the conservation of endangered species in India.

Additional Information

• Kuno National Park
• Located in the Sheopur district of Madhya Pradesh, Kuno was declared a national park in 2018.
• The park spans over an area of approximately 748 square kilometers and is known for its diverse flora and fauna.
• Kuno was originally considered a potential site for relocating Asiatic lions from Gir National Park in Gujarat.
• Cheetah Reintroduction in India
• Cheetahs were declared extinct in India in 1952 due to habitat loss, hunting, and human interference.
• The current reintroduction plan is the first time wild cheetahs have been translocated across continents.
• The project involves collaborative efforts with Namibia and South Africa, where the cheetahs were sourced.
• Ecological Importance of Cheetahs
• Cheetahs are apex predators, playing a critical role in maintaining the balance of ecosystems.
• Their presence helps control herbivore populations, promoting the growth of vegetation and biodiversity.
• Challenges of the Project
• Ensuring the survival and adaptation of cheetahs to their new environment is a significant challenge.
• Potential risks include poaching, human-wildlife conflict, and insufficient prey base in the area.
• Continuous monitoring, habitat management, and public awareness are crucial for the project's success.

The logic followed here is:

                                                                                                                                                                                                                                                                

Thus, the missing term in the series is 912.

Hence, the correct answer is "Option 2";

Shortcut Trick Ratio of Selling Price (SP) to Cost Price (CP) can be derived directly: 10 × SP = 16 × CP. SP/CP = 16/10 = 8/5. Here, SP (8 units) > CP (5 units), so there is a gain. Gain% = (Difference ÷ CP) × 100 = (8 − 5) ÷ 5 × 100 = 3/5 × 100 = 60%. ∴ The correct answer is 60% gain.

Alternate Method Given → SP of 10 books = CP of 16 books. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

⇒ Let the Cost Price (CP) of 1 book be Re. 1. ⇒ Then, CP of 16 books = Rs. 16. ⇒ According to the question, SP of 10 books = CP of 16 books = Rs. 16. ⇒ CP of 10 books = Rs. 10. ⇒ Gain = SP − CP = 16 − 10 = Rs. 6. ⇒ Gain% = (6 ÷ 10) × 100 = 60%. ∴ The correct answer is 60% gain.

Additional Information Profit and Loss on Quantity When the CP of 'x' articles equals the SP of 'y' articles, the profit or loss percentage is given by [(x − y) ÷ y] × 100. If positive, it is a gain; if negative, it is a loss. Relation between SP and CP If SP > CP, there is a profit. If CP > SP, there is a loss. Percentage is always calculated on the Cost Price unless specified otherwise.

BODMAS Rule:

According to the question, the letters are interchanged as follows:

We need to find which option results in 50 after interchanging the symbols.

Let's evaluate each option:

1) 24 P 4 S 28 R 12 Q 6

After interchanging the signs: 24 ÷ 4 − 28 + 12 × 6

⇒ 24 ÷ 4 − 28 + 12 × 6

⇒ 6 − 28 + 72

⇒ −22 + 72

⇒ 50

2) 24 S 4 Q 28 P 12 R 6

After interchanging the signs: 24 − 4 × 28 ÷ 12 + 6

⇒ 24 − 4 × 28 ÷ 12 + 6

⇒ 24 − 4 × (7/3) + 6

⇒ 24 − 28/3 + 6

⇒ (72 − 28)/3 + 6

⇒ 44/3 + 6

⇒ (44 + 18)/3

⇒ 62/3

3) 24 Q 4 R 28 S 12 P 6

After interchanging the signs: 24 × 4 + 28 − 12 ÷ 6

⇒ 24 × 4 + 28 − 12 ÷ 6

⇒ 24 × 4 + 28 − 2

⇒ 96 + 28 − 2

⇒ 124 − 2

⇒ 122

4) 24 R 4 P 28 Q 12 S 6

After interchanging the signs: 24 + 4 ÷ 28 × 12 − 6

⇒ 24 + 4 ÷ 28 × 12 − 6

⇒ 24 + 12/7 − 6

⇒ (168 + 12)/7 − 6

⇒ 180/7 − 6

⇒ (180 − 42)/7

⇒ 138/7

Hence, the correct answer is "Option 1".

Shortcut Trick

When a sheet is rolled along its width, the width becomes the circumference (C) and the length becomes the height (h).

C = 22 cm ⇒ 2πr = 22 ⇒ r = 11/π cm

Volume = πr²h = π × (11/π)² × 17

Volume = π × (121/π²) × 17 = 2057/π cm³

∴ The correct answer is 2057/π cm³.

Alternate Method

Given: Length of rectangular sheet (l) = 17 cm, Width (w) = 22 cm.

Formula Used: Volume of cylinder = πr²h; Circumference = 2πr

⇒ When rolled along the width, the circumference of the base of the cylinder = 22 cm.

⇒ 2 × π × r = 22

⇒ r = 22 / (2π) = 11/π cm

⇒ The height (h) of the cylinder = 17 cm

⇒ Volume = π × (11/π)² × 17

⇒ Volume = π × (121/π²) × 17

⇒ Volume = (121 × 17) / π

⇒ Volume = 2057/π cm³

∴ The correct answer is 2057/π cm³.

Additional Information

Cylinder Rolling Rules

If rolled along length 'L', then 2πr = L and h = width. If rolled along width 'W', then 2πr = W and h = length.

Surface Area of Cylinder

Curved Surface Area (CSA) = 2πrh. Total Surface Area (TSA) = 2πr(h + r).

Volume of Cylinder

Volume = Base Area × Height = πr²h.

The given code language is:

Thus, 'I' is coded as '2'.

Hence, the correct answer is "Option 2".

The correct answer is National Girl Child Day.

Key Points

• National Girl Child Day is celebrated in India every year on 24th January to promote awareness about the rights, education, and health of girl children.
• It was first initiated by the Ministry of Women and Child Development in 2008 to highlight the issues faced by girls in India and to empower them.
• The day emphasizes addressing gender-based discrimination and promoting gender equality in all aspects of society.
• Various campaigns and events are organized across the country to spread awareness about the importance of saving, educating, and empowering the girl child.
• The celebration aligns with the goals of government schemes like Beti Bachao Beti Padhao, which focuses on improving the welfare and status of girls in India.

Additional Information

• Beti Bachao Beti Padhao (BBBP):
• Launched in 2015, it aims to address declining Child Sex Ratio (CSR) and promote the survival, protection, and education of the girl child.
• The campaign is a tri-ministerial effort involving the Ministries of Women and Child Development, Health and Family Welfare, and Education.
• Sukanya Samriddhi Yojana (SSY):
• A government-backed savings scheme aimed at securing the future of girl children.
• Parents can open an account for a girl child below 10 years, with benefits like tax exemptions and high-interest rates.
• Gender Inequality in India:
• India has faced challenges like female infanticide, child marriage, and gender-based violence, which these initiatives aim to address.
• Promoting girl child education and empowerment is pivotal to achieving societal progress and economic development.
• United Nations International Day of the Girl Child:
• Celebrated globally on 11th October, it complements India's National Girl Child Day by advocating for girls' rights worldwide.
• The focus is on issues like education, healthcare access, and ending child marriage.

The correct answer is State List.

Key Points

• Co-operative societies are classified under the State List of the Indian Constitution as per Entry 32 of List II in the Seventh Schedule.
• This classification empowers state governments to legislate on matters related to co-operative societies within their respective jurisdictions.
• The 97th Constitutional Amendment Act, 2011 added a new Part IXB to the Indian Constitution, exclusively dealing with co-operative societies.
• Part IXB provides for the promotion, management, and governance of co-operative societies, ensuring their autonomy and democratic functioning.
• Although primarily under the State List, certain aspects of co-operative societies may also be addressed under the Concurrent List, especially post the 97th Amendment.

Additional Information

• Seventh Schedule of the Indian Constitution
• The Seventh Schedule divides the powers between the Union and State governments into three lists: Union List, State List, and Concurrent List.
• The Union List contains subjects on which only the Parliament can legislate, such as defense and foreign affairs.
• The State List contains subjects on which state legislatures can legislate, including police, public health, and agriculture.
• The Concurrent List contains subjects on which both Parliament and state legislatures can legislate, like education and forest conservation.
• 97th Constitutional Amendment Act, 2011
• This amendment introduced the concept of co-operative societies into the Constitution.
• It added the term "co-operatives" in Article 19(1)(c), allowing citizens the right to form co-operative societies.
• It mandated states to enact laws ensuring the autonomous and democratic functioning of co-operative societies.
• Co-operative Societies in India
• Co-operative societies are voluntary associations formed for mutual benefit and operate on democratic principles.
• They play a vital role in sectors like agriculture, banking, housing, and consumer goods.
• Examples include milk co-operatives like Amul and co-operative banks providing financial services to rural communities.
• Concurrent List and Co-operatives
• Post the 97th Amendment, aspects of co-operatives such as their governance and management can be legislated under the Concurrent List.
• This ensures both the states and the central government can collaborate to strengthen co-operative societies.

The correct answer is National Agro-forestry Policy, 2014.

Key Points

• The National Agro-forestry Policy, 2014 was introduced by the Government of India to promote agro-forestry practices across the country.
• This policy aims to integrate trees and agriculture on farmland, enhancing productivity, livelihoods, and environmental sustainability.
• The policy encourages farmers to grow trees alongside crops on their farmland, ensuring a balance between agricultural and forestry practices.
• It emphasizes the relaxation of regulatory constraints related to tree felling, transportation, and marketing of agro-forestry produce.
• The National Agro-forestry Policy, 2014, aligns with India's commitments to increasing forest cover and promoting sustainable agricultural practices.

Additional Information

• Agro-forestry:
• Agro-forestry is a land-use system that integrates trees and shrubs with crops and livestock on the same land.
• It helps in improving soil fertility, water retention, and biodiversity while also providing economic benefits to farmers.
• Common agro-forestry practices include alley cropping, silvopasture, and windbreaks.
• Benefits of Agro-forestry:
• It enhances carbon sequestration, contributing to climate change mitigation.
• Agro-forestry reduces soil erosion and improves soil health, ensuring sustainable farming practices.
• It provides additional income through timber, fruits, and other forest-based products.
• National Forest Policy, 1988:
• The National Forest Policy of 1988 emphasizes maintaining ecological balance and preserving biodiversity.
• The policy aims to increase forest and tree cover to 33% of India's geographical area.
• India's Agro-forestry Mission:
• The National Agro-forestry Policy, 2014, is implemented under the ambit of the Ministry of Agriculture & Farmers' Welfare.
• It aligns with India's National Action Plan on Climate Change and Sustainable Development Goals (SDGs).

The correct answer is Two.

Key Points

• The Chandrayaan-4 mission by the Indian Space Research Organisation (ISRO) is planned to have two launches using the LVM-3 rocket.
• The LVM-3 (Launch Vehicle Mark-3) is ISRO's heaviest and most advanced launch vehicle, capable of carrying payloads up to 8,000 kg to Low Earth Orbit (LEO).
• The two launches will ensure the deployment of the required mission components, which may include an orbiter, lander, and rover, depending on the mission design.
• The Chandrayaan-4 mission is expected to build on the advancements made during the Chandrayaan-2 and Chandrayaan-3 missions, focusing on lunar exploration and scientific research.
• ISRO uses the LVM-3 rocket for critical missions due to its high reliability and capability to handle complex payloads.

Additional Information

• LVM-3 Rocket (Launch Vehicle Mark-3):
• The LVM-3, previously known as GSLV Mk-III, is a three-stage heavy-lift launch vehicle developed by ISRO.
• It has a lift-off mass of approximately 640 tons and stands 43.5 meters tall.
• The rocket uses a combination of solid, liquid, and cryogenic propulsion systems.
• LVM-3 is also the launch vehicle for India’s human spaceflight program, Gaganyaan.
• Chandrayaan Missions:
• Chandrayaan-1 (2008): India’s first lunar mission focused on mapping the Moon’s surface and detecting water molecules.
• Chandrayaan-2 (2019): Aimed at soft-landing a rover on the lunar south pole, though the lander lost communication during descent.
• Chandrayaan-3 (2023): Successfully demonstrated soft-landing and deployed a rover for lunar surface exploration.
• Scientific Objectives of Chandrayaan-4:
• To further explore the lunar surface, particularly the unexplored south pole region.
• To conduct advanced experiments on lunar geology, topography, and surface composition.
• To test new technologies for future interplanetary missions.
• ISRO's Lunar Exploration Roadmap:
• ISRO plans to establish a strong presence in lunar exploration as part of its long-term goals.
• Future missions include more advanced lunar landers and potential collaboration with international space agencies.

Given: 

Raghav starts from Point A and drives 8 km towards South.

He then takes a left turn, drives 6 km, turns left and drives 11 km.

He then takes a left turn and drives 12 km. He takes a final left turn, drives 3 km and stops at Point P.

Thus, He should derive  6 km to the east in order to reach Point A again.

Hence, the correct answer is "Option 4".

Given:

$\frac{7^2 \times 7^3}{\sqrt{49} \times \sqrt{2401}}$

Formula Used:

Exponent Rules: $a^m × a^n = a^{m+n}$

Square Root Simplification: √a² = a

Calculation:

$\frac{7^2 \times 7^3}{\sqrt{49} \times \sqrt{2401}}$

⇒ $\frac{7^2 \times 7^3}{\sqrt{7^2} \times \sqrt{7^4}}$

⇒ $\frac{7^2 \times 7^3}{7 \times 7^2}$

⇒ 7²

⇒ 49

∴ Option 1 is the correct answer.

The correct answer is Access speed decreases and cost per bit decreases.

Key Points

• As we move down the memory hierarchy—from registers to secondary storage—the access speed decreases. Registers are the fastest, while secondary storage devices like hard drives are significantly slower.
• The cost per bit of storage decreases as we move from registers to secondary storage. Registers and cache are expensive due to their high-speed performance and small size.
• Registers are located within the CPU, offering nanosecond-level access times, whereas secondary storage devices like HDDs or SSDs have access times in milliseconds or microseconds.
• Secondary storage devices, such as hard drives, offer much larger storage capacity at a lower cost per bit but are slower in terms of data retrieval compared to primary memory.

Additional Information

• Memory Hierarchy in Computers
• It refers to the arrangement of memory types based on speed, cost, and capacity.
• It typically includes registers, cache, main memory (RAM), and secondary storage (HDD/SSD).
• Registers and cache are the fastest but have the smallest capacity, while secondary storage is slower but offers large capacity.
• Access Time
• Access time is the time taken by the CPU to retrieve data from memory.
• Registers have the shortest access time, measured in nanoseconds, while secondary storage access time is measured in milliseconds or microseconds.
• Cost per Bit
• Cost per bit refers to the expense incurred for storing one bit of data.
• Registers and cache have the highest cost per bit, while secondary storage devices have the lowest cost per bit.
• Secondary Storage
• Includes devices like HDDs, SSDs, and optical disks.
• It is non-volatile and provides persistent storage for data even when the system is powered off.
• Registers
• Smallest and fastest memory located directly within the CPU.
• Used to temporarily store data that is actively being processed by the CPU.

The correct answer is Promotion of Hindi language as a medium of expression.

Key Points

• Part IV of the Indian Constitution deals with the Directive Principles of State Policy (DPSP), which provides guidelines for the establishment of a just society.
• The promotion of Hindi language as a medium of expression is not explicitly mentioned in Part IV of the Constitution.
• Article 51 of Part IV mentions the promotion of international peace and security as one of the Directive Principles.
• Other provisions under Part IV include the organisation of agricultural and animal husbandry (Article 48) and the provision for free and compulsory education for children (Article 45).
• The Directive Principles aim to create social and economic conditions under which citizens can lead a good life, ensuring equality and welfare for all.

Additional Information

• Part IV - Directive Principles of State Policy:
• Directive Principles are non-justiciable guidelines for governance provided to the State.
• These principles are inspired by the Irish Constitution and aim to achieve socio-economic justice.
• They are categorized into economic and social, Gandhian, and international principles.
• Article 51 (Promotion of International Peace):
• The State shall promote international peace and security.
• It aims to maintain just and honorable relations between nations and encourage settlement of international disputes by arbitration.
• Article 45 (Education for Children):
• The Constitution mandates free and compulsory education for children until they reach the age of 14 years.
• This was later reinforced by the Right to Education Act, 2009.
• Article 48 (Agriculture and Animal Husbandry):
• The State shall endeavor to organize agriculture and animal husbandry on modern and scientific lines.
• It also aims to preserve and improve breeds and prohibit the slaughter of cows, calves, and other milch and draught cattle.
• Promotion of Hindi Language:
• Provisions related to the promotion of Hindi language are covered under Part XVII (Articles 343-351) of the Constitution.
• It emphasizes the development of Hindi as the official language and its enrichment by assimilating elements from other Indian languages.

Shortcut Trick

Net efficiency = Fill rate − Empty rate = 1/18 − 1/24 = (4 − 3)/72 = 1/72 unit/hr.

Time to fill full tank = 72 hours.

Time to fill 3/4^th tank = 72 × 3/4 = 18 × 3 = 54 hours.

∴ The correct answer is 54 hours.

Alternate Method

Given: Filling Tap (A) = 18 hours, Emptying Tap (B) = 24 hours.

Formula Used: Total Work = LCM of time; Efficiency = Work ÷ Time.

⇒ Combined Efficiency of (A + B) = 4 − 3 = 1 unit/hr

⇒ Target Work = 3/4 × Total Work = 3/4 × 72 = 54 units

⇒ Time Required = Target Work ÷ Combined Efficiency = 54 ÷ 1 = 54 hours

∴ The correct answer is 54 hours.

Additional Information

Net Work Done

When one pipe fills (x) and another empties (y), net work in 1 hour = (1/x − 1/y). If the result is positive, the tank fills; if negative, it empties.

Pipes and Cisterns vs Time and Work

The logic is identical to Time and Work, but the emptying tap (outlet) is treated as having negative efficiency.

Partial Filling

To find time for a fraction (k) of the tank, use: Time = (k × Total Capacity) ÷ Net Efficiency.

The logic followed here is:

                                                                                                                                                                                                                                                                                                                                                               

Thus, the missing term in the series is 87.

Hence, the correct answer is "Option 4";

The correct answer is Swami Vivekananda.

Key Points

• National Youth Day is celebrated annually on 12th January to commemorate the birth anniversary of Swami Vivekananda.
• The Government of India declared Swami Vivekananda's birthday as National Youth Day in 1984 to honor his contributions towards inspiring youth.
• Swami Vivekananda, a key figure in introducing Indian philosophies like Vedanta and Yoga to the Western world, believed in the power of youth for nation-building.
• His teachings focused on self-confidence, self-reliance, and spirituality, making him an ideal role model for Indian youth.
• Various programs, including speeches, seminars, cultural performances, and competitions, are organized across India on National Youth Day to spread awareness about his life and ideals.

Additional Information

• Swami Vivekananda:
• Born on 12th January 1863 in Kolkata, India, he was originally named Narendranath Datta.
• He was a disciple of Ramakrishna Paramahamsa and went on to establish the Ramakrishna Mission in 1897.
• Swami Vivekananda is best known for his speech at the 1893 Parliament of the World's Religions in Chicago, where he introduced Hinduism to the global audience.
• His famous quote, "Arise, awake, and stop not till the goal is reached," continues to inspire millions worldwide.
• National Youth Day Themes:
• Every year, National Youth Day is celebrated with a particular theme to engage the youth in constructive activities.
• The themes are centered around topics like youth empowerment, innovation, and spirituality.
• Significance of National Youth Day:
• The day serves to highlight the role of youth in shaping the future of the nation.
• It encourages young people to imbibe the teachings of Swami Vivekananda and work towards self-development and societal progress.
• Global Recognition:
• Swami Vivekananda's ideas on religious harmony, universal brotherhood, and the empowerment of youth resonate globally.
• His contributions to philosophy and spirituality have earned him recognition as one of India's greatest cultural ambassadors.

The correct answer is Touch Screen.

Key Points

• A touch screen is an electronic display that can act as both an input and output device.
• As an input device, it allows users to interact with the system by touching the screen using a finger or stylus.
• As an output device, it displays visual content, such as text, images, or videos, similar to a regular screen or monitor.
• Touch screens are commonly used in smartphones, tablets, ATMs, interactive kiosks, and other digital devices.
• They employ various technologies such as resistive, capacitive, infrared, or surface acoustic wave to detect and process touch inputs.

Additional Information

• Resistive Touch Screen:
• It uses two electrically conductive layers separated by a small gap.
• When pressure is applied to the screen, the layers come into contact, registering the touch input.
• Commonly used in older devices and ATM machines.
• Capacitive Touch Screen:
• It works by sensing the electrical conductivity of the user's finger.
• Capacitive screens are more responsive and support multi-touch gestures.
• They are widely used in smartphones and modern tablets.
• Infrared Touch Screen:
• This technology uses infrared light beams to detect touch.
• It does not require physical contact; even proximity can register input.
• Typically found in interactive kiosks and large touch displays.
• Surface Acoustic Wave (SAW) Touch Screen:
• SAW screens rely on ultrasonic waves that pass over the touch screen surface.
• When the screen is touched, the waves are absorbed, allowing the location of the touch to be determined.
• They provide high clarity and durability but are sensitive to external contaminants.
• Applications of Touch Screens:
• Touch screens are widely used in retail stores, healthcare, education, gaming, and industrial automation.
• They enable intuitive user experiences, reducing the need for external peripherals like keyboards or mice.

The logic followed here is:

1. First to Second Cluster: Both letters in the first cluster shift +2 positions forward in the English alphabetical order.
2. Second to Third Cluster: The first letter shifts +4 positions forward, and the second letter shifts +9 positions forward in the English alphabetical order.

IF : KH : OQ

KH : MJ : QS

Now, let's apply this combined logic to the given options to find the triad that follows the same pattern:

Option 1: MJ-OL-SU

This option follows the pattern.

Option 2: NJ-OL-SV

This option does NOT follow the pattern.

Option 3: NJ-OK-SV

This option does NOT follow the pattern.

Option 4: MJ-OL-SV

This option does NOT follow the pattern. 

Hence, the correct answer is "Option 1".

The correct answer is Mandatory quarterly CSR reporting accompanied by independent audits.

Key Points

• In 2024, the Indian government amended the Companies Act to improve Corporate Social Responsibility (CSR) transparency.
• The amendment introduced mandatory quarterly CSR reporting for eligible companies to ensure regular updates on CSR activities.
• Independent audits of the CSR reports were made compulsory to enhance credibility and accountability.
• The change aims to address issues of non-compliance, misuse of CSR funds, and ensure alignment of CSR activities with their intended social objectives.
• This step is part of broader efforts to encourage responsible corporate governance and increase trust among stakeholders.

Additional Information

• Corporate Social Responsibility (CSR):
• CSR refers to the practices where businesses voluntarily contribute to sustainable development by delivering economic, social, and environmental benefits.
• In India, Section 135 of the Companies Act, 2013 mandates CSR spending for companies meeting certain financial thresholds.
• Eligible companies must spend at least 2% of their average net profit of the last 3 years on CSR activities.
• Independent Audits:
• Independent audits involve third-party examination of financial or operational processes to ensure compliance and accuracy.
• In the context of CSR, these audits validate the effectiveness and alignment of CSR projects with prescribed norms.
• CSR Reporting:
• CSR reporting involves documenting and disclosing information about a company’s CSR activities, expenditures, and outcomes.
• Quarterly reporting ensures transparency and provides regular updates to stakeholders about the company’s contribution to social development.
• Impact of CSR Amendments:
• Improves corporate accountability and stakeholder confidence.
• Encourages companies to align their CSR initiatives with national development goals.
• Addresses misuse or underutilization of CSR funds by ensuring stricter compliance.

The correct answer is Assam.

Key Points

• 'Jhum' is the local name for shifting cultivation practiced predominantly in the northeastern states of India, including Assam.
• It involves clearing a patch of forest land, burning the vegetation, and using the ash as fertilizer to grow crops.
• After cultivating the land for a few years, farmers leave it fallow to allow the soil to regain its fertility.
• Jhum cultivation is a traditional practice among tribal communities and is deeply rooted in their culture and livelihood.
• This agricultural method is also practiced in other northeastern states like Nagaland, Meghalaya, and Arunachal Pradesh, but Assam remains one of the prominent regions for Jhum cultivation.

Additional Information

• Shifting Cultivation: It is an agricultural practice where land is cultivated temporarily, then abandoned to allow natural vegetation to regenerate.
• Environmental Concerns: Jhum cultivation has been criticized for causing deforestation, soil erosion, and loss of biodiversity in the northeastern states.
• Sustainable Alternatives: The Indian government and various NGOs promote sustainable agricultural practices like terrace farming as alternatives to Jhum cultivation.
• Historical Significance: Shifting cultivation has been practiced for centuries by indigenous communities, who rely on it for subsistence farming.
• Government Initiatives: Programs like the National Mission for Sustainable Agriculture (NMSA) aim to provide support to farmers transitioning from Jhum cultivation to more sustainable methods.

Shortcut Trick

If two quadratic equations have both roots in common, their corresponding coefficients must be proportional.

Equation 1: 1x² + 3x + 2 = 0

Equation 2: ax² + bx + c = 0

Proportionality: a/1 = b/3 = c/2 = k (where k is a constant)

⇒ ax² + bx + c = k(x² + 3x + 2)

∴ The correct answer is ax² + bx + c must be a multiple of x² + 3x + 2.

Alternate Method

Given:

First equation: x² + 3x + 2 = 0

Second equation: ax² + bx + c = 0

Formula Used:

A quadratic equation with roots α and β can be expressed as k(x − α)(x − β) = 0, where k is a non-zero constant.

Calculations:

⇒ First, we find the roots of x² + 3x + 2 = 0:

⇒ x² + 2x + x + 2 = 0

⇒ x(x + 2) + 1(x + 2) = 0

⇒ (x + 1)(x + 2) = 0

⇒ The roots are x = −1 and x = −2.

⇒ Since ax² + bx + c = 0 also has these same roots, it must be of the form:

⇒ ax² + bx + c = k(x − (−1))(x − (−2))

⇒ ax² + bx + c = k(x + 1)(x + 2)

⇒ ax² + bx + c = k(x² + 3x + 2)

⇒ This confirms that the polynomial ax² + bx + c is a constant multiple of x² + 3x + 2.

∴ The correct answer is ax² + bx + c must be a multiple of x² + 3x + 2.

Additional Information

Condition for Two Common Roots

For equations a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0 to have both roots in common: a₁/a₂ = b₁/b₂ = c₁/c₂.

Condition for One Common Root

If only one root is common, the condition is (c₁a₂ − c₂a₁)² = (a₁b₂ − a₂b₁)(b₁c₂ − b₂c₁).

Relationship between Roots and Coefficients

For ax² + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

Shortcut Trick

The Mean Proportional (MP) between two numbers a and b is given by √(a × b).

Given a = (13 + 8√5) and b = (10 − 2√5).

Product = 13(10 − 2√5) + 8√5(10 − 2√5) = 130 − 26√5 + 80√5 − 16(5).

Product = 130 + 54√5 − 80 = 50 + 54√5.

MP = √(50 + 54√5).

∴ The correct answer is √(50 + 54√5).

Alternate Method

Mean Proportional Formula x = √(a × b)

a = 13 + 8√5 b = 10 − 2√5

Given:

First term (a) = (13 + 8√5)

Second term (b) = (10 − 2√5)

Formula Used:

⇒ Mean Proportional = √(a × b)

Calculations:

⇒ Mean Proportional = √[(13 + 8√5) × (10 − 2√5)]

⇒ Let Product (P) = 13(10) − 13(2√5) + 8√5(10) − 8√5(2√5)

⇒ P = 130 − 26√5 + 80√5 − (16 × 5)

⇒ P = 130 + 54√5 − 80

⇒ P = 50 + 54√5

⇒ Mean Proportional = √(50 + 54√5)

∴ The correct answer is √(50 + 54√5).

Additional Information

Mean Proportional

If a, b, and c are in continued proportion such that a:b = b:c, then b is the mean proportional where b² = ac or b = √ac.

Third Proportional

The third proportional to two numbers a and b is c, such that a:b = b:c, which gives c = b²/a.

Fourth Proportional

The fourth proportional to three numbers a, b, and c is d, such that a:b = c:d, which gives d = (b × c)/a.

Shortcut Trick

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

Here, a = 6x² and b = 18xy.

Third Proportional = (18xy) × (18xy) ÷ (6x²)

⇒ (324x²y²) ÷ (6x²) = 54y².

∴ The correct answer is 54y².

Alternate Method

6x² :

18xy ::

c Ratio: a : b :: b : c

Given: First term (a) = 6x², Second term (b) = 18xy.

Formula Used: If c is the third proportional to a and b, then a : b = b : c.

⇒ a/b = b/c

⇒ c = b² / a

⇒ c = (18xy)² / 6x²

⇒ c = (324x²y²) / 6x²

⇒ c = 54y²

∴ The correct answer is 54y².

Additional Information

Mean Proportional

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

Fourth Proportional

For three numbers a, b, and c, the fourth proportional d is calculated using a : b = c : d, which means d = (b × c) / a.

Continued Proportion

Numbers a, b, c are in continued proportion if a/b = b/c, implying b² = ac.

The correct answer is Introduction of western sciences.

Key Points

• The Charter Act of 1813 allowed for the promotion of Western education in India, including sciences and literature.
• This act sanctioned a sum of ₹1 lakh annually for the education of Indians to encourage the introduction of Western knowledge.
• The Act ended the monopoly of the East India Company in trade, except for trade in tea and trade with China, which indirectly supported the spread of education and knowledge.
• It laid the foundation for modern education in India by emphasizing the need for institutions to teach Western sciences and languages.
• Missionaries were allowed under the Act to propagate Christianity, which also contributed to the spread of English education in India.

Additional Information

• Charter Act of 1813
• This Act was passed by the British Parliament to renew the charter of the East India Company.
• It marked a shift in British policy by introducing measures for the advancement of education in India.
• It also aimed to protect the rights of Indian subjects and bring changes in administrative governance.
• Western Education in India
• The Charter Act of 1813 was the first official step toward the establishment of English education in India.
• Western sciences and literature were introduced as part of a broader effort to modernize Indian education.
• It provided the groundwork for future educational reforms such as the Macaulay Minute of 1835.
• Missionary Activities
• The Act allowed Christian missionaries to enter India and propagate their religion.
• Missionaries were instrumental in establishing schools and colleges that taught Western sciences and languages.
• Impact on Indian Society
• The introduction of Western sciences and literature helped Indians gain knowledge in various fields such as medicine, engineering, and law.
• It also contributed to the rise of a new educated middle class in India.

Given Expression: M ÷ N + O × P – Q

M ÷ N: M is the father of N.

N + O: N is the sister of O.

O × P: O is the wife of P.

P – Q: P is the brother of Q.

According to the given information Family Tree Representation:

Therefore, M is Brother's Wife's Father of Q.

Hence, the correct answer is "Option 3"

Given series:

(Left) * 4 * 2 9 @ @ 8 3 £ $ 6 4 £ * 4 8 £ % 9 8 8 (Right)

Condition to be checked:

Symbols which are immediately preceded by a number and also immediately followed by a symbol.

Number → Symbol → Symbol

• 4 * 2 9 @ @ 8 3 £ $ 6 **4 £ *** 4 8 £ % 9 8 8

Thus, here is the 4 pairs which satisfy the conditions.

Hence,"4" is the correct answer.

Mistake Points

Immediately preceded by means immediately before or to come just before.

Immediately followed by means immediately after or to come just after.

Shortcut Trick Convert each ratio to its decimal equivalent for a quick comparison. (1) 27/57 ≈ 0.473 | (2) 27/54 = 0.5 | (3) 30/49 ≈ 0.612 | (4) 18/57 ≈ 0.315 The value 0.612 is the largest among all calculated decimals. ∴ The correct answer is 30 : 49. Alternate Method Given: Ratios are 27/57, 27/54, 30/49, and 18/57.

⇒ Compare (1) 27/57 and (2) 27/54: Since numerators are same, the one with smaller denominator is greater. ∴ 27/54 > 27/57. ⇒ Compare (1) 27/57 and (4) 18/57: Since denominators are same, the one with larger numerator is greater. ∴ 27/57 > 18/57. ⇒ Now compare (2) 27/54 = 1/2 = 0.5 with (3) 30/49. ⇒ For 30/49, half of 49 is 24.5. Since 30 > 24.5, then 30/49 > 0.5. ⇒ 30/49 ≈ 0.612. ∴ The correct answer is 30 : 49. Additional Information Comparing Fractions with Same Numerators If numerators are equal, the fraction with the smaller denominator is the larger value. Comparing Fractions with Same Denominators If denominators are equal, the fraction with the larger numerator is the larger value. Cross-Multiplication Method To compare a/b and c/d, check the products (a × d) and (b × c). If (a × d) > (b × c), then a/b > c/d.

The correct answer is Paris, France.

Key Points

• The 2024 International Conference of NGOs under UNESCO was organized in Paris, France, where UNESCO’s headquarters are located.
• This conference is a biennial event that brings together UNESCO’s official NGO partners to discuss and align strategies for global development and cooperation.
• Paris has hosted numerous key UNESCO events, emphasizing its role as a global center for education, culture, and science.
• The conference primarily focuses on strengthening collaboration between UNESCO and NGOs to address global challenges like education, heritage preservation, and sustainable development.
• The event serves as a platform to review and strategize UNESCO’s partnership frameworks with non-governmental organizations (NGOs).

Additional Information

• UNESCO (United Nations Educational, Scientific and Cultural Organization)
• Established in 1945, UNESCO aims to promote international collaboration in education, science, and culture.
• Its headquarters is situated in Paris, France.
• UNESCO is known for its World Heritage Sites program, which recognizes culturally and naturally significant locations worldwide.
• Other key focus areas include education for all, freedom of expression, and fostering scientific cooperation.
• International Conference of NGOs
• This conference is held every two years and involves UNESCO’s official NGO partners.
• It aims to assess the collective impact of NGOs in UNESCO’s priority areas and discuss future collaborations.
• The conference also provides a platform to share best practices and innovative solutions for global challenges.
• It helps in aligning NGO activities with UNESCO’s objectives for sustainable development.
• NGOs in partnership with UNESCO
• UNESCO collaborates with over 400 NGOs worldwide to achieve its goals in education, science, and culture.
• These NGOs play a critical role in implementing grassroots programs and providing technical expertise.
• Partnerships are based on a framework agreement that outlines specific areas of cooperation.
• UNESCO’s Sustainable Development Goals (SDGs)
• UNESCO actively contributes to achieving the UN’s 2030 Agenda for Sustainable Development.
• Its work focuses on Quality Education (SDG 4), Gender Equality (SDG 5), and Climate Action (SDG 13), among others.
• Partnerships with NGOs are vital for mobilizing resources and implementing SDG-related initiatives.

Given: Each of C, D, E, F, S, T and U has an exam on a different day of a week, starting from Monday and ending on Sunday of the same week.

1. F has the exam on Thursday.

2. C has the exam after S and before E.

3. U has the exam after T and before D.

4. T has the exam after F.

From (1) and (4), T can be on Friday, Saturday, or Sunday.

Let’s assume T is on Friday → U can be on Saturday → D on Sunday.

Now place S before C and E after C. Let S on Monday, C on Tuesday, and E on Wednesday.

Now, how many people have exams between U (Saturday) and C (Tuesday)?

→ Wednesday (E), Thursday (F), Friday (T) → Total = Three persons between U and C.

Hence, the correct answer is "Option 4".

The correct answer is Parliament.

Key Points

• The authority to make laws for multi-state co-operative societies is vested in the Parliament of India.
• Multi-state co-operative societies are governed by the Multi-State Co-operative Societies Act, 2002, which was enacted by Parliament.
• Multi-state co-operative societies operate in more than one state, and hence, come under the purview of the Union List of the Indian Constitution.
• Article 246 of the Constitution assigns legislative powers over subjects in the Union List exclusively to Parliament.
• The Department of Co-operation, under the Ministry of Co-operation, oversees the implementation and regulation of laws concerning multi-state co-operative societies.

Additional Information

• Multi-State Co-operative Societies Act, 2002:
• It regulates the functioning of co-operative societies that operate across multiple states in India.
• The Act emphasizes democratic management, accountability, and transparency in co-operative societies.
• It provides provisions for registration, management, and dissolution of multi-state co-operative societies.
• Union List:
• The Union List is one of the three lists under the Seventh Schedule of the Indian Constitution.
• It contains subjects on which only Parliament has the exclusive power to legislate.
• Examples include defense, foreign affairs, atomic energy, and multi-state co-operative societies.
• Ministry of Co-operation:
• Established in July 2021 to promote and strengthen co-operative societies across India.
• Its responsibilities include formulating policies and implementing programs related to co-operatives.
• The ministry also aims to streamline processes for multi-state co-operative societies.
• Article 246 of the Indian Constitution:
• Defines the distribution of legislative powers between Parliament and state legislatures.
• Subjects listed under the Union List are exclusively under Parliament’s jurisdiction.
• Co-operative societies operating across multiple states fall under Parliament's legislative domain due to their inclusion in the Union List.

Given: Seven people, I, J, K, L, O, P and Q are sitting in a row, facing north.

No one sits to the right of Q.

Only three people sit between I and J.

L sits to the immediate left of J.

Only two people sit between Q and L.

K sits to the immediate right of P.

Thus, Only two people sit between O and K.

Hence, the correct answer is "Option 3".

The correct answer is 0.685.

Key Points

• India's Human Development Index (HDI) value for 2025 is projected to be 0.685, as per the Human Development Index Report.
• The HDI is a composite index measuring average achievement in three basic dimensions of human development: health, education, and standard of living.
• India's HDI has been steadily improving due to consistent progress in life expectancy, literacy rates, and per capita income.
• India is classified as a country with medium human development, given its HDI value falls between 0.550 and 0.699.
• Despite improvements, India continues to face challenges such as inequality, regional disparities, and low gender equality, which impact its overall HDI ranking.

Additional Information

• Human Development Index (HDI)
• HDI is published annually by the United Nations Development Programme (UNDP) in its Human Development Report.
• The index focuses on three dimensions: health (life expectancy), education (mean years of schooling and expected years of schooling), and standard of living (GNI per capita).
• It ranges from 0 to 1, where a higher value indicates better human development outcomes.
• India's HDI Trends
• India's HDI value has seen consistent growth over the last few decades due to government initiatives in health, education, and poverty alleviation.
• For instance, India's HDI value was 0.645 in 2019, and it has shown an upward trend despite challenges like the COVID-19 pandemic.
• Inequality-adjusted HDI (IHDI)
• IHDI accounts for inequality in the distribution of each dimension of HDI.
• India's IHDI value is typically lower than its HDI value, highlighting inequality in education, health, and income.
• Global HDI Context
• In the latest Human Development Report, countries like Norway, Ireland, and Switzerland rank highest in HDI.
• India's HDI ranking is typically around the 130-140 range, reflecting its medium level of human development compared to global peers.

Given:

: OLM :: HEF : %

Analysis of Options:

Option 1) # = POP, % = EUC

For # (POP) to OLM : : HEF to % (EUC)

 

 

Since the pattern for POP to OLM (-1, -3, -3) is not the same as the pattern for HEF to EUC (-3, +16, -3), Option 1 is incorrect.

Option 2) # = RVP, % = EQZ

For # (RVP) to OLM : :  HEF to % (EQZ)

 

Option 3) # = RUI, % = ESA

For # (RUI) to OLM : : HEF to % (ESA)

 

 

Option 4) # = ROP, % = EBC

For # (ROP) to OLM : : HEF to % (EBC)

 

Thus, the analogy holds true only for Option 4 where the pattern (-3, -3, -3) is consistent for both pairs.

Hence, the correct answer is "Option 4".

Given:  A, B, C, D, G, H and I are sitting around a circular table facing the centre of the table.

Only one person sits between D and G when counted from the left of G.

H sits third to the right of I. C sits third to the left of A.

H sits to the immediate right of C. B is not an immediate neighbour of C.

Thus, Only three people sit between B and G when counted from the right of B.

Hence, the correct answer is  "Option 4".

Shortcut Trick

The edge of the cube (a) = 42 m.

Volume = a³ = 42 × 42 × 42.

Unit digit check: 2 × 2 × 2 = 8. The answer must end in 8.

Checking options, only 74,088 ends with 8.

∴ The correct answer is 74,088 m³.

Alternate Method

Given:

Edge of the cube (a) = 42 m

Formula Used:

Volume of a cube = (Side)³

Calculations:

⇒ Volume = 42³

⇒ Volume = 42 × 42 × 42

⇒ Volume = 1,764 × 42

⇒ Volume = 74,088 m³

∴ The correct answer is 74,088 m³.

Additional Information

Surface Area of a Cube

The Total Surface Area (TSA) of a cube is 6a² and the Lateral Surface Area (LSA) is 4a².

Diagonal of a Cube

The length of the longest diagonal that can fit inside a cube is given by a√3.

Units of Volume

Volume is always expressed in cubic units (m³, cm³, etc.) as it involves three dimensions of length.

The correct answer is Limited industrial activity, mainly concentrated in a few cities like Calcutta and Bombay.

Key Points

• During the colonial period, India's industrial development was largely limited due to the exploitative economic policies of the British government.
• Industrial activity was mainly concentrated in a few urban centers like Bombay (now Mumbai), Calcutta (now Kolkata), and Madras (now Chennai).
• Heavy industries and large-scale manufacturing units were almost absent, with small-scale industries such as textiles and jute dominating the industrial landscape.
• India's domestic capital goods industry was virtually non-existent, forcing reliance on imports from Britain.
• The rural areas of India were primarily agrarian, with little to no industrial activity, leading to regional imbalances in economic development.

Additional Information

• Drain of Wealth Theory: Proposed by Dadabhai Naoroji, it highlighted how colonial policies drained India's wealth to Britain, leaving limited resources for industrial development.
• Deindustrialization: The British systematically destroyed India's traditional handicrafts and small industries to promote British industrial goods, leading to widespread unemployment and poverty.
• Economic Exploitation: Colonial policies prioritized raw material exports (like cotton and jute) over domestic industrial growth, benefiting British industries at the expense of Indian economy.
• Railways and Ports: While infrastructure like railways and ports was developed, it primarily served colonial interests of transporting raw materials and finished goods rather than fostering industrial growth.
• Post-Independence Scenario: After independence, India focused on building a strong industrial base through initiatives like the Five-Year Plans and establishment of public sector enterprises.

The correct answer is Switches to the next tab.

Key Points

• Ctrl + Tab is a commonly used keyboard shortcut to switch to the next open tab in applications that support multiple tabs, such as web browsers, code editors, and document processors.
• It cycles through tabs in the order they are listed, moving from left to right.
• This shortcut is universally recognized across major web browsers like Google Chrome, Mozilla Firefox, Microsoft Edge, and Safari.
• In contrast, the shortcut Ctrl + Shift + Tab allows users to switch to the previous tab (from right to left).
• Using keyboard shortcuts like Ctrl + Tab significantly enhances productivity by eliminating the need to manually click on tabs with a mouse.

Additional Information

• Keyboard Shortcuts in Browsers:
• Ctrl + T: Opens a new tab.
• Ctrl + W: Closes the current tab.
• Ctrl + Shift + T: Reopens the last closed tab.
• Ctrl + 1 to Ctrl + 8: Navigates directly to a specific tab (e.g., Ctrl + 1 goes to the first tab).
• Ctrl + 9: Jumps to the last tab, regardless of its position.
• Tab Management in Applications:
• Tabbed interfaces are widely used in software applications to improve workflow and organization.
• Examples include web browsers, text editors, and spreadsheet programs.
• Switching between tabs using shortcuts saves time, especially for power users who work with multiple tabs simultaneously.
• Other Useful Shortcuts:
• Alt + Tab: Switches between open applications on Windows.
• Cmd + Tab: Switches between open applications on macOS.
• Ctrl + F4: Closes the current tab or window in applications.
• Accessibility and Efficiency:
• Keyboard shortcuts are designed to make computing faster and more accessible for all users.
• They reduce reliance on the mouse, which can be especially helpful for individuals with repetitive strain injuries.

The correct answer is Central Pollution Control Board.

Key Points

• In 2024, the Central Pollution Control Board (CPCB) was given enhanced powers to enforce penalties and ensure compliance with environmental regulations in India.
• The CPCB operates under the Ministry of Environment, Forest and Climate Change (MoEF&CC) and is the apex body for pollution control in the country.
• The amendments empowered the CPCB to impose stricter fines and oversee the implementation of green clearances to address environmental violations effectively.
• As part of its expanded role, the CPCB was tasked with ensuring adherence to environmental standards by industries, urban bodies, and other entities.
• The move aimed to strengthen India's capacity to tackle air, water, and soil pollution, ensuring sustainable development.

Additional Information

• Central Pollution Control Board (CPCB):
• Established in 1974 under the Water (Prevention and Control of Pollution) Act.
• It also functions under the Air (Prevention and Control of Pollution) Act, 1981.
• The CPCB advises the central government on environmental policies and coordinates with state pollution control boards.
• Environmental Clearances in India:
• Green clearances are required for activities that may have significant environmental impacts.
• These include projects in sectors like mining, infrastructure, and energy.
• The process is overseen by the Ministry of Environment, Forest and Climate Change (MoEF&CC) and the CPCB.
• Pollution in India:
• India faces challenges related to air pollution, water contamination, and waste management.
• According to the World Air Quality Report, several Indian cities rank among the most polluted globally.
• Sustainable Development Goals (SDGs):
• Goal 13 focuses on climate action, while Goal 15 emphasizes sustainable use of terrestrial ecosystems.
• Strengthening environmental regulations aligns with India's commitment to achieving these goals.

Shortcut Trick

Let the HCF be x.

Numbers are 2x, 1x, and 5x.

LCM of (2, 1, 5) × HCF = LCM of numbers.

10 × x = 5380

x = 538

∴ The correct answer is 538.

Alternate Method

Given:

Ratio of three numbers = 2 : 1 : 5

LCM of the numbers = 5380

Formula Used:

If the ratio of numbers is a : b : c and their HCF is H, then the numbers are aH, bH, and cH.

LCM of (aH, bH, cH) = H × LCM(a, b, c)

Calculations:

⇒ Let the numbers be 2H, 1H, and 5H, where H is the HCF.

⇒ LCM of 2, 1, and 5 = 10 (since they are prime/co-prime to each other).

⇒ LCM of (2H, 1H, 5H) = 10 × H

⇒ 10H = 5380

⇒ H = 5380 ÷ 10

⇒ H = 538

∴ The correct answer is 538.

Additional Information

HCF and LCM Relation

For two numbers A and B, A × B = HCF(A, B) × LCM(A, B). Note: This does not directly apply to three numbers.

Ratio and Multiples

If numbers are in ratio x : y : z, then the numbers can be expressed as kx, ky, and kz, where k is their HCF.

LCM of Fractions

LCM = LCM of Numerators ÷ HCF of Denominators.

Shortcut Trick

Time taken by Filling Tap (A) = 8 hours

Time taken by Emptying Hole (B) = 10 hours

Combined Time = (A × B) ÷ (B − A)

Net Time = (8 × 10) ÷ (10 − 8) = 80 ÷ 2 = 40 hours

∴ The correct answer is 40 hr.

Alternate Method

Given: Filling time = 8 hr, Emptying time = 10 hr.

Formula: Total Work = LCM(8, 10) = 40 units.

⇒ Efficiency of Filling Tap = 40 ÷ 8 = +5 units/hr

⇒ Efficiency of Emptying Hole = 40 ÷ 10 = −4 units/hr

⇒ Combined Efficiency = 5 − 4 = +1 unit/hr

⇒ Time taken to fill = Total Work ÷ Combined Efficiency = 40 ÷ 1 = 40 hours

∴ The correct answer is 40 hr.

Additional Information

Net Efficiency Rule

When one pipe fills (rate x) and another empties (rate y), the net work done per hour is (1/x − 1/y) if x < y.

Pipes and Cisterns vs Time and Work

The concepts are identical, but in cisterns, work done by an outlet/leak is taken as negative work.

The correct answer is Option 2: 1, 2 and 3.

Key Points

• National Manufacturing Policy 2011: It highlights that every job created in the manufacturing sector leads to the creation of 2-3 additional jobs in related activities, emphasizing the multiplier effect of manufacturing employment.
• Transformational Sector: Industries add value to raw materials and enhance the skill set of workers, which is why the industrial sector is considered a transformational sector in economic development.
• Employment & Poverty Eradication: Industrial development plays a critical role in generating employment and is a precondition for eradicating poverty and unemployment in India.
• The industrial sector contributes significantly to the Gross Domestic Product (GDP) and serves as a backbone for the economic progress of the country.
• Policies like Make in India and National Manufacturing Policy aim to boost industrial growth and employment generation in India.

Additional Information

• Industrial Sector Overview:
• The industrial sector includes manufacturing, construction, mining, and utilities.
• It is a key driver of economic growth, accounting for approximately 25-30% of India’s GDP.
• National Manufacturing Policy (NMP) 2011:
• Aimed at increasing the share of manufacturing in GDP to 25% by 2022.
• Focuses on skill development, technology upgrades, and creation of National Investment and Manufacturing Zones (NIMZs).
• Make in India Initiative:
• Launched in September 2014 to promote manufacturing and attract foreign investments.
• Targets 25 priority sectors including automobiles, pharmaceuticals, and textiles.
• Employment in Industrial Sector:
• Accounts for a large segment of formal and informal employment in India.
• Industrial policies aim to reduce unemployment through job creation in manufacturing and allied sectors.
• Challenges in Industrial Development:
• Infrastructure bottlenecks, skill gaps, and regulatory hurdles.
• Low levels of research and development (R&D) and technological innovation.

The correct answer is All ministers share full responsibility for government decisions.

Key Points

• Collective executive responsibility is a principle enshrined in Article 75(3) of the Indian Constitution, which states that the Council of Ministers is collectively responsible to the Lok Sabha (House of the People).
• This principle ensures that all members of the Council of Ministers, including the Prime Minister, act as a single entity and take joint responsibility for the actions and policies of the government.
• If a decision is taken by the government, all ministers are expected to defend it publicly, even if they personally disagree with it.
• If a minister disagrees with a decision and is unwilling to defend it, the convention is that they must resign from their position.
• The principle of collective responsibility strengthens the unity of the executive and maintains the stability of the government by ensuring accountability to the legislature.

Additional Information

• Article 75(3): This article specifies that the Council of Ministers shall be collectively responsible to the Lok Sabha, ensuring that they act as a unified body in matters of governance.
• Individual Responsibility: While collective responsibility exists, each minister is also individually responsible for their respective departmental actions and policies.
• No-Confidence Motion: If the Lok Sabha passes a no-confidence motion against the Council of Ministers, the entire Council, including the Prime Minister, is required to resign, demonstrating collective accountability.
• Parliamentary Democracy: The principle of collective responsibility is a cornerstone of parliamentary democracy, ensuring that the executive remains accountable to the legislature.
• Westminster Model: India’s collective responsibility principle is inspired by the Westminster model of governance, which emphasizes the unity and accountability of the executive branch.

Shortcut Trick

The relationship between Mean, Median, and Mode is defined by the ratio of their differences.

Using the empirical formula: (Mode − Median) = 2/3 × (Mode − Mean)

Given: (Mode − Mean) = 37.8

Calculation: (Mode − Median) = 2/3 × 37.8 = 2 × 12.6 = 25.2

∴ The correct answer is 25.2.

Alternate Method

Given: Mode − Mean = 37.8

Formula Used: Mode = 3 × Median − 2 × Mean

⇒ Mode − Mean = 37.8

⇒ Mean = Mode − 37.8

⇒ Mode = 3 × Median − 2 × (Mode − 37.8)

⇒ Mode = 3 × Median − 2 × Mode + 75.6

⇒ 3 × Mode − 3 × Median = 75.6

⇒ 3(Mode − Median) = 75.6

⇒ Mode − Median = 75.6 ÷ 3 = 25.2

∴ The correct answer is 25.2.

Additional Information

The correct answer is Deccan.

Key Points

• The Rashtrakutas were a prominent dynasty that ruled large parts of the Deccan region of India from the 8th to 10th century CE.
• They established their capital at Manyakheta (modern-day Malkhed in Karnataka).
• The Rashtrakutas were known for their patronage of art and architecture, most notably the Kailasa temple at Ellora, which is a UNESCO World Heritage site.
• Under rulers like Amoghavarsha I, the Rashtrakutas achieved significant cultural, economic, and military prosperity in the Deccan region.
• Their empire extended over vast areas including parts of Maharashtra, Karnataka, Andhra Pradesh, and Tamil Nadu.

Additional Information

• Rashtrakutas Origin:
• The Rashtrakutas claimed descent from the Yadava lineage and were originally based in the Lattaluru region (modern-day Latur in Maharashtra).
• Kailasa Temple:
• This temple, carved out of a single rock, is considered an architectural marvel of the Rashtrakuta period.
• It reflects the technological and artistic prowess of ancient Indian artisans.
• Amoghavarsha I:
• One of the greatest Rashtrakuta rulers, he authored the Kannada classic Kavirajamarga.
• His reign marked the peak of Rashtrakuta cultural achievements.
• Decline of the Rashtrakutas:
• The empire eventually fell to the Chalukyas of Kalyani in the late 10th century CE.
• Their decline marked the end of one of the most influential dynasties in the Deccan.

Given:

Expression to evaluate: 30 - [30 - {30 - (30 - 30 × 3)}]

Formula Used:

Follow BODMAS (Bracket, Order, Division/Multiplication, Addition/Subtraction) rules to evaluate the expression.

Calculation:

30 - [30 - {30 - (30 - 30 × 3)}]

⇒ 30 - [30 - {30 - (30 - 90)}]

⇒ 30 - [30 - {30 - (-60)}]

⇒ 30 - [30 - {30 + 60}]

⇒ 30 - [30 - 90]

⇒ 30 - [-60]

⇒ 30 + 60

⇒ 90

∴ Option 4 is the correct answer.

Shortcut Trick

Let the total salary be 100%.

Spending on rent = 30%. Remaining salary = 70%.

Total amount except rent = 751 + 8481 + 715 = ₹9,947.

Since this amount represents the remaining 70%, then 70% = 9947.

100% = 9947 ÷ 70 × 100 = 14210.

∴ The correct answer is ₹14,210.

Alternate Method

Given:

House Rent = 30% of Salary

Conveyance = ₹751

Grocery = ₹8,481

Savings = ₹715

Let Total Monthly Salary be 'S'.

⇒ Total Expenditure and Savings (excluding rent) = 751 + 8481 + 715

⇒ Sum = ₹9,947

⇒ Percentage of salary excluding rent = 100% − 30% = 70%

⇒ 70% of S = 9947

⇒ (70 ÷ 100) × S = 9947

⇒ S = (9947 × 100) ÷ 70

⇒ S = 142.1 × 100

⇒ S = ₹14,210

∴ The correct answer is ₹14,210.

Additional Information

Percentage Expenditure

Total Salary = Expenditure + Savings. If expenses are given as percentages, ensure the base is the same (Total Salary) unless 'of the remaining' is specified.

Successive Percentage

When spending occurs on the 'remaining' amount, use the formula: Final = Initial × (1 − r₁/100) × (1 − r₂/100).

Base Change Rule

To find the total value from a partial percentage: Total = (Partial Value ÷ Partial Percentage) × 100.

The given code language is:

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

Hence, the correct answer is "Option 1".

The pattern followed here is.

Thus, the missing term in the series is NU48.

Hence, the correct answer is Option 4.

The correct answer is Albert Einstein.

Key Points

• Albert Einstein critically examined the foundations of Newtonian mechanics and introduced revolutionary concepts that led to the development of modern physics.
• His theory of special relativity (1905) challenged Newtonian mechanics by introducing the constancy of the speed of light and the relativity of simultaneity.
• Einstein’s work revealed that Newtonian mechanics fails at speeds approaching the speed of light and in strong gravitational fields, leading to the development of general relativity (1915).
• The equivalence principle, a cornerstone of general relativity, contradicted Newton’s concept of absolute space and time.
• Einstein’s contributions fundamentally reshaped the understanding of space, time, and energy, pushing science beyond the classical framework established by Newton.

Additional Information

• Newtonian Mechanics:
• A classical physics framework developed by Sir Isaac Newton, describing motion using laws of inertia, force, and action-reaction.
• It assumes absolute space and time, which Einstein later challenged.
• Special Relativity:
• Developed by Albert Einstein in 1905, it introduced concepts like time dilation, length contraction, and E=mc².
• It applies to objects moving at constant speeds close to the speed of light.
• General Relativity:
• Published by Einstein in 1915, it describes gravity as the curvature of spacetime caused by mass and energy.
• It replaced Newton’s law of universal gravitation in explaining phenomena like black holes and cosmic expansion.
• Equivalence Principle:
• A concept in general relativity stating that gravitational force and acceleration are indistinguishable.
• It played a key role in Einstein’s departure from Newtonian mechanics.
• Impact on Modern Physics:
• Einstein’s work laid the foundation for quantum mechanics, cosmology, and advancements in theoretical physics.
• His discoveries opened new avenues in understanding the universe at both macroscopic and microscopic scales.

The correct answer is Improved ability to handle and execute multiple separate processes concurrently.

Key Points

• Multi-core processors allow multiple cores to work independently, enabling efficient execution of multiple independent tasks simultaneously.
• This architecture reduces bottlenecks caused by task switching in single-core systems, improving overall system performance.
• Each core operates as a separate processing unit, facilitating better multitasking and parallel processing capabilities.
• Multi-core systems are especially advantageous in environments requiring concurrent execution of multiple processes, such as servers or multimedia applications.
• While clock speed remains the same, multiple cores ensure more tasks are processed in parallel, leading to better utilization of system resources.

Additional Information

• Core: A core is a processing unit within a CPU that performs computational tasks. Multi-core CPUs contain multiple cores in a single chip.
• Parallel Processing: The simultaneous execution of multiple processes or tasks by dividing them across multiple cores to improve efficiency.
• Hyper-threading: A technology used in some processors to enable a single core to handle multiple threads, though it does not replace the advantages of physical multi-core systems.
• Single-core vs Multi-core: Single-core processors execute one thread at a time, whereas multi-core processors can execute multiple threads or tasks concurrently.
• Applications: Multi-core processors are widely used in high-performance computing, gaming, video editing, and server systems requiring multitasking and parallel workloads.

The correct answer is Bronze.

Key Points

• The 'Dancing Girl' statue is a significant artifact from the Indus Valley Civilization, which dates back to around 2500 BCE.
• It is made of bronze using the lost-wax casting technique, showcasing advanced metallurgical skills of the civilization.
• The statue is approximately 4 inches tall and depicts a young girl in a confident, relaxed pose.
• This artifact was discovered in Mohenjo-daro, one of the major urban centers of the Indus Valley Civilization.
• The 'Dancing Girl' is celebrated for its realistic portrayal of human anatomy and artistic sophistication.

Additional Information

• Indus Valley Civilization: It is one of the world's oldest urban civilizations, flourishing between 2500 BCE and 1900 BCE in regions of present-day Pakistan and northwest India.
• Lost-Wax Casting Technique: This is a method of metal casting where a wax model is covered with clay and fired to create a mold. Molten metal is then poured into the mold to create the artifact.
• Mohenjo-daro: An archaeological site in Sindh, Pakistan, and a major urban center of the Indus Valley Civilization known for its advanced city planning and architecture.
• An alloy primarily consisting of copper and tin, widely used in ancient civilizations for making tools, weapons, and artifacts due to its durability and workability.
• Artistic Significance: The 'Dancing Girl' is considered a masterpiece of ancient Indian art, reflecting the cultural and artistic achievements of the Indus Valley Civilization.

The correct answer is Diwan-i-Khas.

Key Points

• Diwan-i-Khas was a private hall used by Islamic rulers, specifically for confidential meetings and royal audiences.
• It served as a venue where the emperor met his ministers, nobles, and other important officials to discuss state affairs privately.
• The design of Diwan-i-Khas reflected grandeur and exclusivity, symbolizing the ruler’s authority and status.
• Famous examples of Diwan-i-Khas can be found in Mughal architecture, such as the Red Fort in Delhi and Fatehpur Sikri.
• Unlike Diwan-i-Aam (Hall of Public Audience), which was open to the general public, Diwan-i-Khas was highly restricted and accessible only to select individuals.

Additional Information

• Sarai: Sarais were rest houses or inns constructed along trade routes to provide lodging and essential facilities to travelers, traders, and pilgrims.
• Katra: Katras were market complexes or caravanserais often used for commercial purposes. They were designed to accommodate traders and store goods.
• Bridges: Bridges constructed during the Islamic reign were primarily for public use, facilitating transportation and trade over rivers and other obstacles.
• Diwan-i-Aam: Unlike Diwan-i-Khas, the Diwan-i-Aam was a public hall where the emperor addressed grievances and petitions from common people.
• Architectural Significance: Structures like Diwan-i-Khas exemplify the blend of Persian, Islamic, and Indian architectural styles, showcasing intricate designs, inlaid marble work, and decorative arches.

Given series:

(Left) * 6 8 @ 1 £ 9 5 3 @ $ 9 © @ 7 9 £ @ 9 1 £ 6 (Right)

Condition to be checked:

Symbols which are immediately preceded by a number and also immediately followed by a number.

Number → Symbol → Number

• 6 8 @ 1 £ 9 5 3 @ $ 9 © @ 7 9 £ @ 9 1 £ 6

 

Hence, "3" is the correct answer.

Mistake Points

Immediately preceded by means immediately before or to come just before.

Immediately followed by means immediately after or to come just after.

Statements:

 All boys are handsome.

 Some handsome are cars.

 Some cars are grey.

The least possible Venn Diagram is given:

<br>

 Conclusions:

 (I) All handsome are boys - False(because all boys are handsome is given. it implies that some handsome are boys not all).

 (II) All cars are handsome - False(some handsome are cars, so it can be possible only).

Thus, Neither conclusion (I) nor (II) follows.

Hence, the correct answer is "Option 1".

The correct answer is 30 June 2025.

Key Points

• The Ministry of Corporate Affairs (MCA) in India extended the deadline for private companies to dematerialise their securities to 30 June 2025.
• Dematerialisation is a process wherein physical certificates of securities are converted into electronic form.
• This extension was announced in February 2025 to provide private companies with adequate time to comply with regulations.
• The previous deadline for dematerialisation of securities was set earlier but has been extended for better implementation and compliance.
• Private companies are required to ensure their securities are held in electronic form through a depository participant registered with SEBI.

Additional Information

• Dematerialisation of Securities:
• Dematerialisation eliminates the risks associated with holding physical certificates, such as loss, theft, or forgery.
• Securities in electronic format are managed through depositories like NSDL (National Securities Depository Limited) and CDSL (Central Depository Services Limited).
• It facilitates easier transfer, trading, and monitoring of securities.
• Depository Participant:
• A Depository Participant (DP) acts as an intermediary between the investor and the depository.
• Registered with SEBI, DPs provide services like opening demat accounts, transferring securities, and holding securities electronically.
• SEBI's Role:
• The Securities and Exchange Board of India (SEBI) regulates securities markets in India and ensures compliance with dematerialisation guidelines.
• SEBI mandates dematerialisation to promote transparency and efficiency in the trading of securities.
• Benefits of Dematerialisation:
• Ensures safe storage and easy transfer of securities.
• Helps reduce paperwork and administrative costs associated with physical certificates.
• Enhances market liquidity and facilitates faster settlement of transactions.

The correct answer is $200 billion annually for biodiversity conservation.

Key Points

• During the extended session of COP16 in Rome, member nations agreed to allocate $200 billion annually for biodiversity conservation.
• This financial commitment aims to address the ongoing global biodiversity crisis, including habitat loss, species extinction, and ecosystem degradation.
• The funding will support initiatives like restoration of ecosystems, protection of endangered species, and sustainable management of natural resources.
• The decision aligns with the objectives of the Convention on Biological Diversity (CBD) to protect 30% of the planet's land and marine areas by 2030, also known as the "30x30" target.
• Countries were encouraged to mobilize resources from both public and private sectors to meet this ambitious goal.

Additional Information

• Convention on Biological Diversity (CBD):
• An international treaty adopted in 1992 at the Earth Summit in Rio de Janeiro.
• Aims to conserve biodiversity, promote sustainable use of its components, and ensure fair sharing of benefits arising from genetic resources.
• The CBD has been ratified by 196 nations, making it a globally recognized framework for biodiversity protection.
• 30x30 Target:
• A global initiative to protect at least 30% of Earth's land and ocean areas by 2030.
• Proposed under the Global Biodiversity Framework to halt and reverse biodiversity loss.
• Focuses on safeguarding key biodiversity hotspots and ecosystems critical for climate regulation.
• Global Biodiversity Crisis:
• According to the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES), over 1 million species are at risk of extinction.
• Major drivers include deforestation, climate change, pollution, and overexploitation of natural resources.
• Urgent action is necessary to prevent irreversible damage to ecosystems and biodiversity.
• Funding Mechanisms:
• Countries are urged to mobilize financial resources through mechanisms like green bonds, biodiversity trust funds, and public-private partnerships.
• International organizations like the Global Environment Facility (GEF) and Green Climate Fund (GCF) play a pivotal role in financing biodiversity initiatives.

Given:

 Mr. K starts from Point Z and drives 6 km towards the north.

He then takes a right turn, drives 3 km, turns right and drives 11 km.

He then takes a right turn and drives 10 km.

He then takes a final right turn, drives 5 km and stops at Point B. 

Thus,  he should drive 7 km towards the east in order to reach Point Z again.

Hence, the correct answer is "Option 1".

Given interchange rules:

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

The given equation is:

186 ÷ 5 + 189 × 3 − 2 = ?

Replace the operators with their corresponding new meanings:

186 × 5 − 189 ÷ 3 + 2 = ?

Now, we solve the equation following the BODMAS rule:

= 186 × 5 − 189 ÷ 3 + 2

= 930 − 63 + 2

= 867 + 2

= 869

Hence, the correct answer is "Option 4".

The logic followed in this pattern involves consistent alphabetical shifts for the letters and an arithmetic operation for the number:

• For the first letter, it shifts +2 positions forward in the English alphabetical order.
• For the second letter, it shifts +3 positions forward in the English alphabetical order.
• For the number, it increases by +9.

Let's verify this logic with the given examples:

For 'NW -19' related to 'PZ -10':

For 'RD -12' related to 'TG -3':

The consistent pattern observed is: First letter +2, Second letter +3, Number +9.

Similarly,  'WU -2':

Thus, 'WU -2' is related to YX 7.

Hence, The correct answer is "Option 1"

The correct answer is Option 1: 2 : 2.

Key Points

• The balanced chemical equation for the reaction is: 2Al + 3Cl₂ → 2AlCl₃.
• In the reaction, two moles of aluminium (Al) react with three moles of chlorine gas (Cl₂) to produce two moles of aluminium chloride (AlCl₃).
• The mole ratio of aluminium (Al) to aluminium chloride (AlCl₃) is 2:2, which simplifies to 1:1.
• This ratio indicates that for every two moles of aluminium, two moles of aluminium chloride are formed.
• The correct option is Option 1: 2 : 2, as it directly reflects the stoichiometric coefficients in the balanced equation.

Additional Information

• Stoichiometry: The branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction.
• Mole Ratio: Derived from the coefficients of the balanced chemical equation and represents the proportional relationship between substances involved in the reaction.
• Balanced Equation: Ensures the conservation of mass, where the number of atoms for each element is the same on both sides of the equation.
• Reaction Details: Aluminium reacts with chlorine gas to form aluminium chloride, an ionic compound commonly used in chemical synthesis and industrial processes.
• Limiting Reactant Concept: In practical scenarios, the reactant present in a lower stoichiometric quantity may limit the amount of product formed, but this does not affect the mole ratio derived from the balanced equation.

The logic followed in the given sets is:

Logic: Middle number = (First number - Last number) × 2.

(41, 34, 24)

→ (41 - 24) × 2

→ 17 × 2 = 34 

(63, 80, 23)

→ (63 - 23) × 2

→ 40 × 2 = 80 

Now, let's apply this logic to the given options:

1) (17, 2, 19)

→ (17 - 19) × 2

→ -2 × 2 = -4 ≠ 2. Incorrect.

2) (46, 86, 24)

→ (46 - 24) × 2

→ 22 × 2 = 44 ≠ 86. Incorrect.

3) (43, 40, 23)

→ (43 - 23) × 2

→ 20 × 2 = 40 = 40. This holds.

4) (17, 14, 11)

→ (17 - 11) × 2

→ 6 × 2 = 12 ≠ 14. Incorrect.

Hence, the correct answer is "Option 3".

The correct answer is a Muslim sovereignty in Deccan.

Key Points

• The Nizam of Hyderabad ruled one of the largest princely states in India, and his administration projected Muslim sovereignty in the Deccan, emphasizing Islamic traditions.
• The Nizam's dynasty traced its origins to the Mughal Empire and sought to maintain its cultural and political identity within the predominantly Hindu-majority region of the Deccan.
• The Nizam focused on protecting and promoting Islamic culture while maintaining a stable governance structure in his territory.
• Hyderabad became a hub for Islamic scholarship, architecture, and cultural preservation during the Nizam’s reign.
• Despite projecting Islamic sovereignty, the Nizam's administration included significant interactions with the British colonial powers to ensure political stability and economic trade benefits.

Additional Information

• Hyderabad State:
• Hyderabad was the largest princely state in India during British rule, covering areas of present-day Telangana, Karnataka, and Maharashtra.
• The state was ruled by the Nizam and known for its wealth, cultural diversity, and strategic importance.
• Nizam's Dynasty:
• The Nizam of Hyderabad belonged to the Asaf Jah dynasty, which was established in 1724.
• The dynasty maintained strong ties with the Mughal Empire and later with the British colonial rulers.
• British Protectorate:
• While the Nizam projected Islamic sovereignty, Hyderabad operated as a British protectorate under the subsidiary alliance system.
• The British provided military protection to the Nizam in exchange for control over the state's foreign affairs.
• Cultural Contributions:
• The Nizam's rule contributed to significant architectural landmarks like the Charminar and Mecca Masjid in Hyderabad.
• Hyderabad emerged as a center for Urdu literature, Islamic education, and cultural synthesis during this period.

Shortcut Trick

Convert rate to fraction: Rate (R) = 10% = 1/10.

For 3 years, let Principal = 10³ = 1000 units.

Difference (D) between CI and SI = 3(10) + 1 = 31 units.

Given 31 units = ₹186 ⇒ 1 unit = ₹6.

Principal = 1000 units × 6 = ₹6000.

∴ The correct answer is ₹6000.

Alternate Method

Given: Time (T) = 3 years, Rate (R) = 10% p.a., Difference (D) = ₹186.

Formula Used: Difference (D) = P × (R/100)² × (3 + R/100)

Calculations:

⇒ 186 = P × (10/100)² × (3 + 10/100)

⇒ 186 = P × (1/100) × (3.1)

⇒ 186 = P × (3.1 / 100)

⇒ P = (186 × 100) ÷ 3.1

⇒ P = 18600 ÷ 3.1

⇒ P = 186000 ÷ 31

⇒ P = ₹6000.

∴ The correct answer is ₹6000.

Additional Information

2-Year Difference Formula

The difference between Compound Interest and Simple Interest for 2 years is D = P × (R/100)².

Effective Rate of Interest

For a 10% Rate, the Effective CI Rate for 3 years is 33.1%, while the SI Rate is 30%.

Compound Interest Ratio Method

CI for 2 years follows the ratio 2:1 and for 3 years follows 3:3:1 on the calculated interest steps.

Shortcut Trick

Use the relation between Marked Price (MP) and Cost Price (CP): MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Ratio of MP to CP is 122 : 100 based on the 22% markup.

122 ÷ 100 = (100 + 7) ÷ (100 − D).

122 × (100 − D) = 107 × 100 ⇒ 12200 − 122D = 10700.

122D = 1500 ⇒ D = 1500 ÷ 122 ≈ 12.295%.

∴ The correct answer is 12.30%.

Alternate Method

Given → Marked Price (MP) = ₹668, Markup = 22%, Profit = 7%.

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

⇒ Let Cost Price (CP) be x. Since MP is 22% above CP, 1.22x = 668 ⇒ x = 668 ÷ 1.22 ≈ 547.54.

⇒ Selling Price (SP) = CP × (107 ÷ 100) = 547.54 × 1.07 ≈ 585.87.

⇒ Discount Amount = MP − SP = 668 − 585.87 = 82.13.

⇒ Discount Percentage = (82.13 ÷ 668) × 100 ≈ 12.295%.

∴ The correct answer is 12.30%.

Additional Information

Relation between CP, MP, Profit and Discount

The most efficient way to solve such problems is the ratio MP/CP = (100 + P%)/(100 - D%) which bypasses the need for actual currency values.

Marked Price

It is the price displayed on the product. Discounts are always calculated on the Marked Price, while profit or loss is calculated on the Cost Price.

Shortcut Trick

Total distance = 819 + 1476 + 1053 = 3348 km

Total time = Total distance ÷ Average speed = 3348 ÷ 54 = 62 hours

Time for 1st and 3rd parts = (819 ÷ 63) + (1053 ÷ 81) = 13 + 13 = 26 hours

Time for 2nd part = 62 − 26 = 36 hours

x = 1476 ÷ 36 = 41 km/hr

∴ The correct answer is 41 km/hr.

Alternate Method

Given:

Distances: D₁ = 819 km, D₂ = 1476 km, D₃ = 1053 km

Speeds: S₁ = 63 km/hr, S₂ = x km/hr, S₃ = 81 km/hr

Average Speed (V_avg) = 54 km/hr

Formula Used:

Average Speed = Total Distance ÷ Total Time

Time = Distance ÷ Speed

Calculations:

⇒ Total Distance = 819 + 1476 + 1053 = 3348 km

⇒ Total Time (T) = 3348 ÷ 54 = 62 hours

⇒ T₁ = 819 ÷ 63 = 13 hours

⇒ T₃ = 1053 ÷ 81 = 13 hours

⇒ T₂ = T − (T₁ + T₃) = 62 − (13 + 13) = 62 − 26 = 36 hours

⇒ Speed x = D₂ ÷ T₂ = 1476 ÷ 36

⇒ x = 41 km/hr

∴ The correct answer is 41 km/hr.

Additional Information

Average Speed for Equal Distances

If two equal distances are covered at speeds u and v, then Average Speed = 2uv ÷ (u + v).

Relative Speed

In the same direction, relative speed = S₁ − S₂. In the opposite direction, relative speed = S₁ + S₂.

Unit Conversion

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

Shortcut Trick

Initial Average of 36 numbers = 45.

Sum of discarded numbers = 37 + 53 = 90.

Average of the two discarded numbers = 90 ÷ 2 = 45.

If the average of the discarded items is equal to the group average, the average of the remaining items does not change.

∴ The correct answer is 45.

Alternate Method

Given:

Total numbers = 36 | Initial Average = 45

Numbers to be discarded = 37 and 53

Formula Used:

Average = Total Sum ÷ Number of Observations

Calculations:

⇒ Total Sum of 36 numbers = 36 × 45 = 1620

⇒ Sum of discarded numbers = 37 + 53 = 90

⇒ Remaining Sum = 1620 − 90 = 1530

⇒ Remaining Numbers = 36 − 2 = 34

⇒ New Average = 1530 ÷ 34

⇒ New Average = 45

∴ The correct answer is 45.

Additional Information

Constant Removal Property

If the average of discarded items is exactly equal to the original average, the mean of the remaining data set remains constant.

Weighted Average Formula

Average_combined = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂), where n is the count and A is the average.

Deviation Method

The sum of deviations of all observations from their mean is always zero. If discarded items have zero net deviation from the mean, the average stays the same.

The correct answer is Heraka Movement - West Bengal.

Key Points

• The Heraka Movement was not based in West Bengal but originated in the Naga Hills of Assam and Nagaland.
• This socio-religious movement was led by Jadonang and later Rani Gaidinliu with the aim of reviving Naga traditions and customs.
• The movement also sought to oppose British colonial rule and Christian missionary influence in the region.
• Heraka, meaning "pure," was a reformist movement that sought to consolidate the indigenous Naga religious practices and reject foreign influence.

Additional Information

• Ramosi Rebellion
• The Ramosi Rebellion (1822-1841) took place in Maharashtra.
• It led by Chittur Singh and Umaji Naik, was a response to British annexation policies in the Western Ghats.
• The Ramosis were a tribal community employed as hill police during Maratha rule but were marginalized under British rule.
• Lushai Revolt
• This revolt occurred in the present-day Mizoram (then part of Assam) during the 19th century.
• The Lushai tribes resisted British interference in their territory and culture.
• The British eventually subdued the rebellion and brought the region under their control.
• Kol Rebellion
• The Kol Rebellion (1831-1832) was centered in Jharkhand.
• The rebellion was led by the Kol tribal community against exploitative landlords and moneylenders.
• It was a significant tribal uprising during British colonial rule.
• Heraka Movement Leadership
• Jadonang was the founder of the Heraka Movement and sought to preserve Naga culture.
• After his execution by the British, Rani Gaidinliu became the leader and continued the fight for Naga identity and freedom.
• Rani Gaidinliu is remembered as a freedom fighter and was posthumously awarded the Padma Bhushan.

Shortcut Trick

Total cost: 10 bags + 10 pens = ₹1310 ⇒ 1 bag + 1 pen = ₹131.

Multiply by 2: 2 bags + 2 pens = ₹262.

Compare with first case: (2 bags + 11 pens) − (2 bags + 2 pens) = 505 − 262 ⇒ 9 pens = ₹243.

Cost of 1 pen = ₹27, and 1 bag = 131 − 27 = ₹104.

Difference for 8 units = 8 × (104 − 27) = 8 × 77 = ₹616.

∴ The correct answer is ₹616.

Alternate Method

Given:

2B + 11P = 505 (Equation 1)

10B + 10P = 1310 (Equation 2)

From Equation 2, simplify by dividing by 10:

⇒ B + P = 131 ⇒ B = 131 − P

Substitute B in Equation 1:

⇒ 2(131 − P) + 11P = 505

⇒ 262 − 2P + 11P = 505

⇒ 9P = 505 − 262

⇒ 9P = 243 ⇒ P = 27

Now, find the cost of the bag:

⇒ B = 131 − 27 = 104

Calculate the required difference:

⇒ 8B − 8P = 8(B − P)

⇒ 8(104 − 27) = 8 × 77

⇒ 8 × 77 = 616

∴ The correct answer is ₹616.

Additional Information

Linear Equations in Two Variables

These are equations of the form ax + by = c. They can be solved using elimination, substitution, or cross-multiplication methods.

Cost Difference Logic

The difference of costs for multiple items n(B − P) is always n times the difference of single item costs (B − P).

Substitution Method

Express one variable in terms of the other from the simpler equation and substitute it into the complex one to reduce the system to a single variable.

Shortcut Trick

Total interest for 2 years = ₹4,000

Interest for 1 year = 4,000 ÷ 2 = ₹2,000

Rate (x) = (Interest for 1 year ÷ Principal) × 100

x = (2,000 ÷ 16,000) × 100 = 1/8 × 100 = 12.5%

∴ The correct answer is 12.5.

Alternate Method

Given:

Principal (P) = ₹16,000

Simple Interest (SI) = ₹4,000

Time (T) = 2 years

Rate of Interest (R) = x% per annum

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ 4,000 = (16,000 × x × 2) ÷ 100

⇒ 4,000 = 160 × 2 × x

⇒ 4,000 = 320 × x

⇒ x = 4,000 ÷ 320

⇒ x = 400 ÷ 32

⇒ x = 100 ÷ 8

⇒ x = 12.5

∴ The correct answer is 12.5.

Additional Information

Simple Interest Formula

SI = (P × R × T) / 100, where P is Principal, R is Rate, and T is Time.

Amount in Simple Interest

Amount (A) = Principal (P) + Simple Interest (SI). It represents the total money repaid.

Rate of Interest Definition

The Rate of Interest is the percentage of the principal charged as interest for a specific period (usually per annum).

The correct answer is Lucknow.

Key Points

• As per Census of India 2001, Million Plus Urban Agglomerations Cities are those urban areas with a population exceeding one million.
• Lucknow, the capital city of Uttar Pradesh, was identified as one of the Million Plus Urban Agglomerations Cities in the Census 2001.
• Lucknow's population crossed the one million mark during the 2001 census, making it eligible for this classification.
• Other notable cities like Chandigarh also fall under this category, but Lucknow specifically satisfies the criteria for the given question.
• Million Plus Cities are significant for urban planning and resource allocation by the government.

Additional Information

• Urban Agglomeration:
• An Urban Agglomeration (UA) consists of a core city and its adjoining areas forming a continuous urban spread.
• It includes the main city, towns, and outgrowths (like railway colonies, university campuses, etc.) linked to the urban core.
• Million Plus Cities:
• These cities have populations exceeding one million as per Census data.
• Such cities are key focus areas for infrastructure development under schemes like Smart Cities Mission.
• Census of India:
• The Census is conducted every 10 years to collect demographic, social, and economic data.
• Census 2001 was the 14th National Census exercise conducted in India.
• Importance of Million Plus Cities:
• These cities are crucial for economic activities, governance, and urban development.
• They often serve as hubs for trade, education, healthcare, and employment opportunities.

The correct answer is Malwa.

Key Points

• The Malwa Plateau is located in the central part of India and lies between the Aravali and Vindhya ranges.
• It is primarily spread across the states of Madhya Pradesh and Rajasthan, with some portions extending into Gujarat.
• The plateau is characterized by black soil, which is highly fertile and suitable for agriculture, particularly for crops like wheat, cotton, and soybean.
• This region is also known for its geological significance, being a part of the Deccan Traps, which are made up of volcanic basalt rock.
• Key rivers such as the Chambal, Kali Sindh, and Parbati originate or flow through the Malwa Plateau, enriching the region's agriculture.

Additional Information

• Aravali Range:
• One of the oldest mountain ranges in the world, running diagonally across Rajasthan and parts of Haryana and Gujarat.
• It acts as a natural barrier, influencing the climate and biodiversity of the region.
• Vindhya Range:
• A mountain range running parallel to the Narmada River, forming the southern boundary of the Malwa Plateau.
• It is geologically younger than the Aravali range and influences the northern boundary of the Deccan Plateau.
• Deccan Traps:
• A large igneous province in west-central India, formed due to volcanic activity around 66 million years ago.
• The basaltic rock formations contribute to the region's black soil, which is ideal for agriculture.
• Key Cities:
• Important cities located in the Malwa Plateau include Indore, Ujjain, Ratlam, and Neemuch.
• Ujjain is a major religious and cultural hub, known for the Mahakaleshwar Jyotirlinga.
• Economic Significance:
• The plateau is rich in mineral resources like limestone and is a hub for cement production.
• It also plays a crucial role in agriculture, being one of the most fertile regions in central India.

Given series:

(Left) * 1 * $2 3 7 £ 1 7 @ 4 9 9 * 6 * 3$ 1 $ @ (Right)

Condition to be checked:

Numbers which are immediately preceded by a symbol and also immediately followed by a symbol.

Symbol → Number → Symbol

*** 1 *** $ 2 3 7 £ 1 7 @ 4 9 9 *** 6** * 3 $1$ @

• 1 * 
  

 * 6 *

• 3 $

​$1$

Hence, "4" is the correct answer.

Mistake Points

Immediately preceded by means immediately before or to come just before.

Immediately followed by means immediately after or to come just after.

Shortcut Trick

Use the ratio-unitary method based on Selling Price (SP) percentage.

Given Gain% = 34%, so SP = 134% of Cost Price (CP).

If 134% ⇒ ₹3,417, then 1% ⇒ 3,417 ÷ 134 = ₹25.5.

Profit is 34%, so Profit = 34 × 25.5 = ₹867.

∴ The correct answer is ₹867.

Alternate Method

Given: Sales proceeds (SP) = ₹3,417, Gain% = 34%. Formulas: CP = [SP × 100] ÷ [100 + Gain%] | Profit = SP − CP.

⇒ Let Cost Price (CP) be x.

⇒ Selling Price (SP) = x + 34% of x = 1.34x.

⇒ 1.34x = 3,417 ⇒ x = 3,417 ÷ 1.34 = ₹2,550.

⇒ Profit = SP − CP = 3,417 − 2,550 = ₹867.

∴ The correct answer is ₹867.

Additional Information

Relation between SP, CP and Profit

Profit is always calculated on the Cost Price unless stated otherwise. Profit = (Profit% ÷ 100) × CP.

Fractional Method

34% can be written as 34/100 or 17/50. Here, 50 is CP and 17 is Profit, making SP = 67 units.

Given: Seven boxes, A, B, C, D, E, F, and G, are kept one over the other but not necessarily in the same order.

1. Only two boxes are kept between G and B.

2. Only A is kept above F → A is at the top, F is second from the top.

3. No box is kept below B → B is at the bottom (7th position).

4. E is kept in some place below C but in some place above D → C > E > D.

E is at position 5 → Boxes above E = A, F, C, G → Total = 4 boxes.

Hence, the correct answer is "Option 2".

Let's verify this logic with the given examples:

For 'IL 17' related to 'LN 12':

For 'MN 12' related to 'PP 7':

The consistent pattern observed is: First letter +3, Second letter +2, Number -5.

Similarly, 'VR 4':

Thus, 'VR 4' is related to YT -1.

Hence, the correct answer is "Option 2".

The correct answer is Bitra.

Key Points

• According to the 2011 Census, Bitra is the smallest inhabited island in the Lakshadweep archipelago in terms of population.
• The population of Bitra was recorded as only 271 people, making it the least populous among all islands in Lakshadweep.
• Bitra is geographically the smallest inhabited island, covering an area of approximately 0.105 square kilometers.
• The island serves primarily as a fishing village, with a small number of families residing there.
• The nearest inhabited island to Bitra is Chetlat, which is located approximately 50 kilometers away.

Additional Information

• About Lakshadweep:
• It is a union territory of India consisting of 36 islands, of which only 10 are inhabited.
• Lakshadweep is located in the Arabian Sea, about 200-440 km off the southwestern coast of India.
• The islands are known for their coral atolls, reefs, and lagoons, which make them ecologically and economically significant.
• Census in India:
• The Census of India is conducted every 10 years, with the latest available data from the 2011 Census.
• It provides vital information on population, demographics, literacy, and socioeconomic parameters.
• Bitra's Unique Demographics:
• Bitra has the highest sex ratio among all islands in Lakshadweep, with 1,384 females per 1,000 males as per the 2011 Census.
• The small population size makes it a closely-knit community.
• Economic Activities in Lakshadweep:
• The primary livelihood of the inhabitants is fishing, followed by coconut cultivation.
• The region also promotes sustainable tourism to preserve its fragile ecosystem.

Given number: '3518642'

Condition to be applied:

• If the digit is odd, add 1.
• If the digit is even, subtract 2.

After applying the condition to each digit:

 

Now, the digits second from the left and second from the right in the new number are:

• Second from the left: 6
• Second from the right: 2

Sum of 6 and 2 is: 8.

Hence, the correct answer is "Option 3".

The logic followed here is:

Option (1) 'NT – QL':

Option (2) 'GM – JE':

Option (3) 'RX – VP':

Here, it does not follow.

Option (4) 'AG – DY':

Hence, the correct answer is "Option 3" .