Given: Each of T, U, V, W, X, Y and Z has an exam on a different day of a week,

Starting from Monday and ending on Sunday of the same week.

1. X has an exam on the third day of the week.

2. Only three people have an exam between X and T.

3. Z has an exam immediately after V, and Y has an exam immediately after Z.

4. W does not have an exam on Monday.

Thus, the V has an exam on "Thursday."

The correct answer is "Option 4".

The correct answer is Humayun.

Key Points

• Humayun, the second Mughal emperor, regained his lost kingdom after defeating the successors of Sher Shah Suri in 1555.
• He recaptured Delhi and Agra from the Afghan rulers, marking the end of the Second Afghan Empire.
• Humayun's return to power was aided by strategic alliances, including support from the Persian ruler Shah Tahmasp.
• His victory restored the Mughal Empire's presence in India, laying the foundation for the reign of his son, Akbar the Great.
• Humayun's return to the throne was short-lived, as he passed away in 1556, shortly after regaining power.

Additional Information

• Second Afghan Empire:
• It was established by Sher Shah Suri, who overthrew Humayun in 1540 and ruled until his death in 1545.
• Sher Shah's successors were unable to maintain control, leading to Humayun's return.
• Shah Tahmasp's Support:
• Humayun sought refuge in Persia after losing his kingdom and received military assistance from Shah Tahmasp.
• This alliance was pivotal in Humayun's successful campaign against the Afghan rulers.
• Mughal Empire:
• The Mughal Empire was one of the largest and most influential empires in Indian history, known for its cultural and architectural contributions.
• Humayun's restoration strengthened the Mughal dynasty, which reached its zenith under Akbar.
• Humayun's Tomb:
• Built by Humayun's widow, Bega Begum, it is one of the first examples of Mughal architecture in India.
• Located in Delhi, it is a UNESCO World Heritage Site and inspired later architectural marvels like the Taj Mahal.

The correct answer is To enhance the efficiency and safety of solid rocket motor manufacturing.

Key Points

• The vertical planetary mixer developed by ISRO in February 2025 is designed to enhance the efficiency and safety in the production of solid rocket motors.
• This technology supports precise mixing of propellant ingredients, ensuring consistent quality and composition for better performance of rockets.
• Solid rocket motors are critical components in many launch vehicles, including those used for satellite deployment and interplanetary missions.
• The mixer integrates advanced mechanical design and automation features to reduce human intervention, minimizing risks associated with hazardous materials.
• ISRO has been focusing on innovations to streamline the manufacturing process of solid propulsion systems, which are vital for India’s space missions.

Additional Information

• Solid Rocket Motors:
• Solid rocket motors use a solid propellant mixture that is ignited to produce thrust.
• They are simpler and more reliable compared to liquid propulsion systems but require meticulous manufacturing processes for consistent results.
• Propellant mixtures generally include oxidizers, fuel, and binders.
• Planetary Mixers:
• Planetary mixers are specialized machines designed for mixing viscous materials uniformly.
• They are widely used in industries like food, chemical, and aerospace manufacturing.
• The "vertical" design enhances efficiency by reducing material settling and ensuring thorough mixing.
• ISRO’s Advancements in Propulsion:
• ISRO has developed several propulsion technologies, including cryogenic engines and solid rocket boosters.
• Solid propulsion systems are used in the PSLV and GSLV series for launching satellites into orbit.
• Continuous advancements aim to improve reliability, safety, and cost-effectiveness.
• Safety Considerations in Propellant Manufacturing:
• Propellant manufacturing involves handling hazardous chemicals and explosive materials.
• Automation and specialized equipment like vertical planetary mixers reduce the risks associated with human errors.
• Safety protocols and advanced designs are integral to ensuring worker safety and environmental protection.

The correct answer is To manage hardware and software resources.

Key Points

• An operating system acts as an intermediary between hardware and software, enabling them to function together seamlessly.
• Its primary role is to manage system resources, such as CPU, memory, storage, and input/output devices.
• The operating system provides a user interface (e.g., command line or graphical user interface) to interact with the system.
• It oversees tasks like process scheduling, ensuring efficient execution of multiple programs.
• Popular operating systems include Windows, macOS, Linux, and Chrome OS, each designed to optimize resource utilization and user experience.

Additional Information

• Kernel:
• The kernel is the core component of an operating system, responsible for managing system resources and facilitating communication between hardware and software.
• It handles essential functions like memory management, process management, and device control.
• File System:
• The operating system organizes and stores data using a file system, enabling efficient retrieval and management.
• Popular file systems include NTFS, FAT32, ext4, and APFS.
• Multitasking:
• Modern operating systems support multitasking, allowing multiple processes to run simultaneously.
• This is achieved through process scheduling techniques like time-sharing and priority-based execution.
• Security:
• Operating systems implement security measures like user authentication, access control, and firewalls to protect data and resources.
• Regular updates are provided to address vulnerabilities and enhance security.
• Virtualization:
• Operating systems can support virtualization, allowing multiple virtual environments to run on a single physical machine.
• It is widely used in cloud computing and server management for resource optimization.

The logic followed here is:

Hence, the correct answer is "Option 4".

The correct answer is Shifting agriculture.

Key Points

• Shifting agriculture, also known as Jhum cultivation, is a traditional farming method practiced in Northeast India, particularly in states like Assam, Nagaland, and Mizoram.
• Farmers clear forested land by cutting and burning vegetation (slash-and-burn method) and use the ash as fertilizer for crops.
• This practice leads to severe soil erosion due to the removal of vegetation cover, exposing the soil to heavy rainfall and wind.
• Shifting agriculture results in the loss of soil nutrients over time, leading to the degradation of land and reduced agricultural productivity.
• After a few years, the land is abandoned, and farmers move to another area, repeating the cycle, which further contributes to deforestation and environmental concerns.

Additional Information

• Soil Erosion:
• It refers to the removal of the topsoil layer due to natural forces like wind and water or human activities such as deforestation and farming.
• Soil erosion reduces fertility, destroys agricultural land, and affects water quality in nearby rivers and streams.
• Terrace Farming:
• This is a sustainable agricultural practice where crops are grown on stepped terraces built into hillsides to prevent soil erosion and water runoff.
• It is widely practiced in hilly regions, such as in Himachal Pradesh and Uttarakhand, but is not the main method used in Northeast India.
• Mixed Farming:
• Involves growing crops and raising livestock simultaneously on the same farm.
• It does not involve practices that lead to significant soil erosion.
• Deforestation:
• Shifting agriculture contributes to deforestation as large areas of forests are cleared for farming.
• Deforestation leads to loss of biodiversity, disruption of ecosystems, and increased carbon emissions.

The correct answer is Ravi.

Key Points

• Ravi is one of the major rivers of the Indus basin system, flowing through India and Pakistan.
• The river originates in the Kullu hills of Himachal Pradesh, India, and flows westward before entering Pakistan.
• It is an important tributary of the Indus River and plays a significant role in the irrigation systems in both countries.
• The Ravi River is historically significant, being mentioned in ancient texts like the Rigveda and associated with the region of Punjab.
• Under the Indus Waters Treaty (1960), the Ravi is allocated to India for utilization of its waters.

Additional Information

• Indus River System
• The Indus River System consists of six main rivers: Indus, Jhelum, Chenab, Ravi, Beas, and Sutlej.
• These rivers originate in the Himalayas and serve as lifelines for agriculture in northern India and Pakistan.
• The system is governed by the Indus Waters Treaty (1960), signed between India and Pakistan.
• Indus Waters Treaty (1960)
• The treaty was brokered by the World Bank to resolve water-sharing disputes between India and Pakistan.
• Under the treaty, India has control over the eastern rivers (Ravi, Beas, and Sutlej), while Pakistan controls the western rivers (Indus, Jhelum, and Chenab).
• Punjab Region
• The name "Punjab" translates to "Land of Five Rivers," referring to Ravi, Beas, Sutlej, Chenab, and Jhelum.
• The region is agriculturally rich, largely due to the extensive irrigation supported by the Indus River System.
• Ravi River's Historical Significance
• The Ravi River was central to the ancient Indus Valley Civilization.
• It flows near the historic city of Lahore, Pakistan, and has cultural importance in the region.

Shortcut Trick

By the standard degree measure theorem of circles, the angle subtended by an arc or chord at the centre is always twice the angle subtended by it at any point on the remaining part of the circumference.

Let the angle subtended at the circumference be θ.

Then, the angle subtended at the centre is 2θ.

Required Ratio = Angle at Centre : Angle at Circumference = 2θ : θ = 2 : 1.

∴ The correct answer is 2 : 1.

Alternate Method

Given:

⇒ A circle with centre O.

⇒ A chord AB subtending an angle ∠AOB at the centre O.

⇒ The same chord subtends an angle ∠ACB at point C on the circumference.

Theorem Used:

The angle subtended by an arc at the centre of a circle is twice the angle subtended by it at any point on the circumference.

Calculations:

⇒ Let the angle subtended at the circumference be ∠ACB = θ

⇒ According to the theorem, the angle subtended at the centre is ∠AOB = 2 × ∠ACB

⇒ ∠AOB = 2θ

⇒ Required Ratio = ∠AOB : ∠ACB

⇒ Ratio = 2θ : θ

⇒ Ratio = 2 : 1

Explanation of Incorrect Options:

⇒ Option (1) 3 : 1 is incorrect because the central angle is exactly double, not triple, the inscribed angle.

⇒ Option (2) 1 : 3 is incorrect because the central angle must be larger than the inscribed angle, making a ratio less than 1 impossible.

⇒ Option (3) 1 : 2 is incorrect because this represents the ratio of the angle at the circumference to the angle at the centre, which is the reverse of the requested order.

∴ The correct answer is 2 : 1.

Additional Information

Angle in a Semicircle

An angle subtended by a diameter at any point on the circumference is always a right angle (90°), which is half of the 180° straight angle at the centre.

Angles in the Same Segment

Angles subtended by the same chord or arc at different points on the same segment of the circumference are always equal.

Cyclic Quadrilateral Property

The opposite angles of a cyclic quadrilateral always sum up to 180° (they are supplementary).

The correct answer is Their Indian citizenship ends automatically.

Key Points

• As per the Indian Citizenship Act, 1955, Indian citizenship is automatically terminated when an Indian citizen voluntarily acquires the citizenship of another country.
• India follows the principle of single citizenship, meaning that dual citizenship is not allowed under Indian law.
• An individual acquiring foreign citizenship must surrender their Indian passport as it becomes invalid after acquiring foreign nationality.
• The government of India issues an Overseas Citizen of India (OCI) card to eligible individuals of Indian origin, which provides certain privileges but is not equivalent to dual citizenship.
• Section 9(1) of the Indian Citizenship Act explicitly states that Indian citizenship ceases automatically upon acquiring foreign citizenship voluntarily.

Additional Information

• Indian Citizenship Act, 1955
• This act governs the acquisition, termination, and supplementary provisions of Indian citizenship.
• It provides five modes of acquiring citizenship: by birth, descent, registration, naturalization, and incorporation of territory.
• It also lays down the grounds for the termination and deprivation of citizenship under specific conditions.
• Overseas Citizen of India (OCI) Card
• The OCI card is issued to foreign nationals of Indian origin, allowing them to visit, live, or work in India indefinitely.
• It is not equivalent to Indian citizenship, and OCI cardholders cannot vote, hold government office, or purchase agricultural land in India.
• The scheme was introduced in 2005 to strengthen the bond between India and its diaspora.
• Dual Citizenship
• Dual citizenship refers to a situation where an individual is a legal citizen of two countries simultaneously.
• India does not allow dual citizenship; instead, it provides the OCI card as an alternative for individuals of Indian origin.
• Surrender Certificate
• Indian citizens who acquire foreign nationality must obtain a surrender certificate for their Indian passport.
• This certificate is required for availing of consular services and applying for an OCI card.

Shortcut Trick

Identify the coefficients: a = 1, b = −2, and c = 13.

Apply the Discriminant formula: D = b² − 4ac.

D = (−2)² − 4 × 1 × 13 = 4 − 52 = −48.

Since D < 0, the equation has no real roots.

∴ The correct answer is −48, No real roots.

Alternate Method

Given quadratic equation: x² − 2x + 13 = 0

Comparing with the standard form ax² + bx + c = 0, we get:

⇒ a = 1

⇒ b = −2

⇒ c = 13

The Discriminant (D) is calculated as:

⇒ D = b² − 4ac

⇒ D = (−2)² − 4 × (1) × (13)

⇒ D = 4 − 52

⇒ D = −48

Nature of roots based on Discriminant value:

⇒ As D = −48, which is less than zero (D < 0), the roots are imaginary/non-real.

∴ The correct answer is −48, No real roots.

Additional Information

Nature of Roots

If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Quadratic Formula

The roots of ax²+bx+c=0 are given by x = (−b ± √D) / 2a.

Sum and Product of Roots

For a quadratic equation, Sum of roots = −b/a and Product of roots = c/a.

The logic followed here is: 

Hence, the correct answer is "Option 1".

The correct answer is Increasing atomic mass.

Key Points

• Dmitri Mendeleev arranged the elements in his periodic table based on their increasing atomic mass.
• He grouped elements with similar chemical properties into vertical columns called groups.
• Mendeleev left gaps in his periodic table to predict the existence of undiscovered elements and their properties.
• The periodic table was published in 1869, marking a significant advancement in the study of chemistry.
• Although atomic mass was the primary criterion, Mendeleev occasionally altered the arrangement to ensure elements with similar properties were aligned correctly.

Additional Information

• Periodic Table:
• A tabular arrangement of chemical elements organized by their atomic number, electron configuration, and recurring chemical properties.
• The modern periodic table is based on the Moseley’s concept of increasing atomic number, rather than atomic mass.
• Atomic Mass:
• The total mass of protons and neutrons in an atom's nucleus.
• Mendeleev used atomic mass as a criterion because atomic numbers were unknown at the time.
• Predictions Made by Mendeleev:
• Mendeleev successfully predicted the properties of elements like gallium (eka-aluminum) and germanium (eka-silicon).
• These predictions were later confirmed with the discovery of these elements.
• Limitations of Mendeleev’s Table:
• Some elements were placed out of order based on atomic mass to align with chemical properties.
• The periodic table did not account for the existence of isotopes, which have the same atomic number but different atomic masses.

The logic followed here is:

Given: # : AND :: RWX : %

Option 1) # = XQB, % = UTZ

Here, it does follow the pattern.

Option 2)  # = LCT, % = XQB

Option 3)  # = OZV, % = LCT

Option 4) # = UTZ, % = OZV

Hence, the correct answer is "Option 1".

Given: DIE CUP BOX ASK

According to the question:

In each of the words, each vowel is changed to the letter immediately following it in the English alphabetical order and each consonant is changed to the letter immediately preceding in the English alphabetical order.

Now, changing each letter in the words:

DIE: D → C, I → J, E → F

CUP: C → B, U → V, P → O

BOX: B → A, O → P, X → W

ASK: A → B, S → R, K → J

Thus, the new clusters formed are:

DIE → CJF

CUP → BVO

BOX → APW

ASK → BRJ

In these clusters, the ones without any vowel (A, E, I, O, U) are:

CJF, BVO, APW, BRJ

Thus, 2 cluster of letter without any vowel CJF,  BRJ

Hence, the correct answer is "Option 1".

The correct answer is Annpurna Devi.

Key Points

• Annpurna Devi, Union Minister of State for Education, represented India at the 69th Session of the United Nations Commission on the Status of Women (UNCSW).
• The session was held at the United Nations Headquarters in New York in March 2023.
• The theme for the 69th Session of UNCSW was "Innovation and technological change, and education in the digital age for achieving gender equality and the empowerment of all women and girls."
• Annpurna Devi emphasized India's commitment to gender equality and empowerment through technology and innovation.
• The session focused on global discussions regarding the role of technology in bridging gender gaps and promoting inclusivity in education and innovation.

Additional Information

• United Nations Commission on the Status of Women (UNCSW):
• UNCSW is a functional commission of the United Nations Economic and Social Council (ECOSOC).
• Its primary focus is on advancing gender equality and the empowerment of women globally.
• It convenes annually at the UN Headquarters in New York to discuss progress, challenges, and strategies related to women's rights.
• India's Efforts in Digital Education:
• India has launched several initiatives like PM eVIDYA, DIKSHA (Digital Infrastructure for Knowledge Sharing), and SWAYAM to enhance digital education.
• These programs aim to provide inclusive and equitable access to education, especially for marginalized groups.
• Role of Technology in Gender Equality:
• Technology and innovation play a crucial role in bridging the digital divide and promoting women's participation in education and workforce.
• Global discussions focus on ensuring equal access to digital resources and addressing challenges such as online safety and digital literacy.
• India's Global Representation:
• India actively participates in global forums like UNCSW to showcase its efforts in gender equality and sustainable development.
• Such participation reflects India's commitment to achieving the Sustainable Development Goals (SDGs), particularly SDG 5 (Gender Equality).

Given:

 

 

Now, the group of numbers and symbols is: 2 # @ 7 9

Here, 2nd condition applies (If the first element is an even number and the last an odd number, the first and last elements are to be coded as ©

Hence, the code for 2 # @ 7 9 is → © P Z L ©

Therefore, the correct answer is "Option 3".

Given: (Left) 956 521 251 156 335 (Right)

The second digit of the highest number is: 5 (956)

And, 

The first digit of the lowest number is: 1 (156)

So, the addition of the second digit of the highest number and the first digit of the lowest number is:

→ 5 + 1 = 6.

The correct answer is "Option 1".

Shortcut Trick

Total items = 8. Let all 8 be suits: Total cost = 8 × 1,000 = ₹8,000.

Difference from actual cost = 10,000 − 8,000 = ₹2,000.

Price difference per saree = 1,500 − 1,000 = ₹500.

Number of sarees = 2,000 ÷ 500 = 4.

Number of suits = 8 − 4 = 4.

∴ The correct answer is 4 sarees and 4 suits.

Alternate Method

Given → Total Cost = ₹10,000, Total Quantity = 8, Saree Price = ₹1,500, Suit Price = ₹1,000. Formulas: Total Cost = (Price_Saree × Qty_Saree) + (Price_Suit × Qty_Suit)

⇒ Let the number of sarees be x and suits be (8 − x). ⇒ Equation: 1,500x + 1,000(8 − x) = 10,000. ⇒ 1,500x + 8,000 − 1,000x = 10,000. ⇒ 500x = 2,000. ⇒ x = 4 (Sarees). ⇒ Suits = 8 − 4 = 4.

∴ The correct answer is 4 sarees and 4 suits.

Additional Information

Linear Equations in Two Variables

Problems involving two types of items can be solved using x and y where x + y = Total Quantity.

Alligation Method

The ratio of quantities can be found by (Average Price − Price 1) : (Price 2 − Average Price).

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

Only two people sit between A and H when counted from the right of A. Only two people sit between H and D.

Only two people sit between H and D. Only three people sit between A and B. C sits to the immediate left of I.

Thus, I sits third to the left of G.

Hence, the correct answer is "Option 3".

Given: Each of P, Q, R, S, T, U and V has an exam on a different day of a week,

Starting from Monday and ending on Sunday of the same week.

1. P has the exam on Thursday.

2. U has the exam on one of the days after R and on one of the days before T.

3. V has the exam on one of the days after S but on one of the days before Q.

4. S has the exam on one of the days after P.

Thus, the number of the person before V is 5.

Hence, the correct answer is "Option 2".

Given: 6154932

By adding 2 in the even digits and subtracting 1 from the odd digits, we will get,

 

The new number formed is: 8046842

Here, the digits that appear more than once are 4 and 8.

So, the number of digits that appear more than once is: 2

Hence, the correct answer is "Option 4".

Given symbol mappings:

• ‘S’ stands for ‘−’
• ‘Q’ stands for ‘×’
• ‘R’ stands for ‘÷’
• ‘P’ stands for ‘+’

The given equation is:

1 P 45 R 2 Q 2 S 4 = ?

⇒ 1 + 45 ÷  2 × 2 - 4 = ?

⇒ 1 + 45 - 4 = ?

⇒ 46 - 4 = 42.

Hence, the correct answer is "Option 4".

Shortcut Trick

Base radius (r) = 100 ÷ 2 = 50 cm.

Slant height (l) = CSA ÷ (πr) = 6500π ÷ (50π) = 130 cm.

Using Pythagorean triplet (5, 12, 13) scaled by 10 → (50, 120, 130).

Height (h) = 120 cm.

∴ The correct answer is 120 cm.

Alternate Method

Given:

Curved Surface Area (CSA) = 6500π cm²

Diameter (d) = 100 cm ⇒ Radius (r) = 50 cm

Formula Used:

Curved Surface Area of cone = πrl

Relationship between height (h), radius (r), and slant height (l): l² = r² + h²

Calculations:

⇒ π × 50 × l = 6500π

⇒ 50 × l = 6500

⇒ l = 6500 ÷ 50

⇒ l = 130 cm

⇒ h² = l² − r²

⇒ h² = 130² − 50²

⇒ h² = 16900 − 2500

⇒ h² = 14400

⇒ h = √14400 = 120 cm

∴ The correct answer is 120 cm.

Additional Information

Total Surface Area (TSA) of a Cone

It is the sum of the curved surface area and the base area: TSA = πr(l + r).

Volume of a Cone

The amount of space occupied by a cone: V = (1/3)πr²h.

Pythagorean Triplets

Standard sets like (3, 4, 5), (5, 12, 13), and (8, 15, 17) help solve right-triangle geometry problems quickly by scaling.

The correct answer is Jat-Jatin.

Key Points

• Jat-Jatin is a popular folk dance of Bihar, often performed during the monsoon season.
• The dance is a symbolic representation of the love and quarrels of a married couple, portraying their emotional dynamics.
• It is widely performed in the Mithila region of Bihar and adjoining areas, showcasing the cultural richness of the state.
• The dance is accompanied by traditional folk songs that narrate the stories of Jat (husband) and Jatin (wife).
• Jat-Jatin serves as a form of entertainment and a medium for expressing the daily lives and struggles of rural communities.

Additional Information

• Folk Dances of Bihar:
• Some other famous folk dances of Bihar include Sohar-Khilouna, Bidesia, Jhijhiya, and Kajari.
• These dances are deeply rooted in the traditions and practices of rural Bihar, celebrating various aspects of life.
• Mithila Region:
• The Mithila region is known for its unique cultural heritage, including folk art, music, and dance.
• It is also famous for the world-renowned Madhubani paintings.
• Music in Jat-Jatin:
• The music accompanying the Jat-Jatin dance typically uses traditional instruments such as dholak, harmonium, and manjira.
• The lyrics focus on themes of rural life, love, and hardships faced by couples.
• Cultural Significance:
• Jat-Jatin reflects the social and emotional aspects of relationships in rural Bihar.
• It provides insights into the challenges faced by couples due to migration, poverty, and societal norms.

The correct answer is Sixth Schedule.

Key Points

• The Sixth Schedule of the Indian Constitution provides for the administration of tribal areas in the states of Assam, Meghalaya, Tripura, and Mizoram.
• It allows for the establishment of Autonomous District Councils (ADCs), which are empowered to make laws and govern certain aspects of administration in tribal areas.
• The ADCs are authorized to create village councils or courts for handling disputes and cases involving tribal individuals, ensuring their customary laws and practices are preserved.
• This schedule provides a legal framework to protect the rights and culture of tribal communities while granting them self-governance.
• The Sixth Schedule seeks to empower tribal regions by granting them autonomy in areas such as land use, resource management, and administration of justice.

Additional Information

• Autonomous District Councils (ADCs):
• ADCs are created under the Sixth Schedule to administer tribal areas and protect tribal rights.
• They have the authority to legislate on matters such as land, forests, water, customs, and inheritance.
• ADCs are composed of members both elected and nominated by the Governor of the respective state.
• Tribal Courts:
• Village councils or courts established under ADCs are empowered to handle cases involving tribal individuals in accordance with customary laws.
• These courts aim to ensure quick and culturally sensitive resolution of disputes within tribal communities.
• Other Schedules Related to Tribals:
• The Fifth Schedule of the Indian Constitution deals with the administration and control of Scheduled Areas and Scheduled Tribes in other states (excluding the Sixth Schedule states).
• The Sixth Schedule, however, provides a more autonomous framework for certain northeastern states.
• Importance of the Sixth Schedule:
• It preserves the unique cultural identity and traditions of tribal communities.
• It ensures self-governance and participatory democracy within tribal areas.

Shortcut Trick

Spending = 40% ⇒ Savings = 100% − 40% = 60%.

Given Savings = ₹18,000.

60% → ₹18,000

1% → ₹18,000 ÷ 60 = ₹300

100% → 300 × 100 = ₹30,000

∴ The correct answer is ₹30,000.

Alternate Method

Given:

Expenditure percentage = 40%

Total Savings amount = ₹18,000

Formula Used:

Income = Expenditure + Savings

Income = (Savings ÷ Savings %) × 100

Calculations:

⇒ Let Total Income be 'I'.

⇒ Savings % = 100% − 40% = 60%

⇒ 60% of I = 18,000

⇒ (60 ÷ 100) × I = 18,000

⇒ I = (18,000 × 100) ÷ 60

⇒ I = 300 × 100

⇒ I = 30,000

∴ The correct answer is ₹30,000.

Additional Information

Percentage Change

Increase or decrease in income is calculated as: (Change ÷ Original Value) × 100.

Ratio Method

If Expenditure : Savings = 40 : 60 = 2 : 3, then Income corresponds to 5 units. If 3 units = 18,000, then 1 unit = 6,000 and 5 units = 30,000.

Successive Changes

If Income increases by x% and then y%, the net effective change is (x + y + xy/100)%.

The logic followed here is:

Logic: 1st number + 2 = 2nd number × 2 = 3rd number + 2 - 4th number.

For, 3 - 5 - 10 - 12

⇒ 3 + 2 = 5 × 2 = 10 + 2 = 12.

For, 8 - 10 - 20 - 22

⇒ 8 + 2 = 10 × 2 = 20 + 2 = 22.

Option 1) 4 - 6 - 12 - 24

⇒ 4 + 2 = 6 × 2 = 12 + 2 = 14 ≠ 24. 

Option 2) 28 - 30 - 60 - 64

⇒ 28 + 2 = 30 × 2 = 60 + 2 = 62 ≠ 64. 

Option 3) 6 - 10 - 12 - 24

⇒ 6 + 2 = 8 × 2 = 16 + 2 = 18 ≠ 24. 

Option 4) 18 - 20 - 40 - 42

⇒ 18 + 2 = 20 × 2 = 40 + 2 = 42.

Hence, the correct answer is "Option 4".

Shortcut Trick

Distance Ratio: Covered : Remaining = 4 : 3

Total units = 7 units → 37 km ∴ 1 unit = 37/7 km

Distance Covered = 4 units = 4 × (37/7) = 148/7 km

Time = 1 hr 5 min = 13/12 hr

Speed = (148/7) ÷ (13/12) = 1776/91 ≈ 19.5 km/hr

∴ The correct answer is 19.5 km/hr.

Alternate Method

Given:

Total Distance = 37 km

Time = 1 hour 5 minutes

Relationship: Distance covered = 4/3 × Remaining distance

Calculations:

⇒ Let the remaining distance be x km.

⇒ Distance covered = 4/3 x km.

⇒ Total Distance = x + 4/3 x = 7/3 x = 37 km

⇒ x = (37 × 3) / 7 = 111/7 km

⇒ Distance covered = 4/3 × (111/7) = 148/7 km

⇒ Time = 1 + 5/60 = 1 + 1/12 = 13/12 hours

⇒ Speed = Distance ÷ Time = (148/7) ÷ (13/12)

⇒ Speed = (148 × 12) / (7 × 13) = 1776 / 91

⇒ Speed ≈ 19.516 km/hr

∴ The correct answer is 19.5 km/hr.

Additional Information

Speed, Distance, and Time Relation

The basic formula is Speed = Distance ÷ Time. Ensure all units are consistent (e.g., km and hours) before calculation.

Unit Conversion

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

Average Speed

If a journey is divided into parts, Average Speed = Total Distance ÷ Total Time. Do not simply average the speeds.

Given:

Sunil starts from Point A and drives 11 km towards the south.

He then takes a left turn, drives 3 km, turns left and drives 4 km.

He then takes a left turn and drives 12 km.

He takes a final right turn, drives 7 km and stops at Point P. 

Thus, 9 km to the east he should drive in order to reach Point A.

Hence, the correct answer is "Option 4".

Statements:

Some cars are buses.

All buses are trucks.

Some buses are ships.

The least possible venn diagram is:

<br>

Conclusions:

(I) Some ships are cars - False(because, there is no direct relation id given so, it can be possible only).

(II) All trucks are cars - False(because, All bus are truck and some care are bus, it implies thar some truck are car, so it can be possible only).

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

Hence, the correct answer is "Option 4".

Shortcut Trick

For numbers a, b, c, d to be in proportion after adding x: x = (ad − bc) ÷ ((a + d) − (b + c)).

Here a = 26, b = 40, c = 22, d = 34.

x = (26 × 34 − 40 × 22) ÷ ((26 + 34) − (40 + 22)) = (884 − 880) ÷ (60 − 62) = 4 ÷ (−2) = −2.

Mean proportional y² = 4x × (7x − 6) ⇒ y² = 4(−2) × (7(−2) − 6) = −8 × (−20) = 160. (Check values: 26−2=24, 40−2=38, 22−2=20, 34−2=32. 24/38 ≠ 20/32).

Correcting calculation: x = (bc − ad) ÷ ((a+d) − (b+c)) = (880 − 884) ÷ (60 − 62) = −4 ÷ −2 = 2. x = 2. Then y² = 4(2) × (7(2) − 6) = 8 × 8 = 64 ⇒ y = 8.

∴ The correct answer is 8.

Alternate Method

Given: Numbers 26, 40, 22, 34. Added value is x. Resulting numbers are in proportion.

Formula: (a+x)/(b+x) = (c+x)/(d+x)

⇒ (26 + x) × (34 + x) = (22 + x) × (40 + x)

⇒ 884 + 26x + 34x + x² = 880 + 22x + 40x + x²

⇒ 884 + 60x = 880 + 62x

⇒ 62x − 60x = 884 − 880

⇒ 2x = 4 ⇒ x = 2

⇒ Given 4x : y :: y : (7x − 6)

⇒ y² = 4x × (7x − 6)

⇒ y² = 4(2) × (7 × 2 − 6)

⇒ y² = 8 × (14 − 6)

⇒ y² = 8 × 8 = 64

⇒ y = √64 = 8 (as y > 0)

∴ The correct answer is 8.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(ab). It is also written as a : b :: b : c where b² = ac.

Proportion Rule

For four numbers a, b, c, d to be in proportion, the product of extremes must equal the product of means (ad = bc).

Third Proportional

If a, b, c are in continued proportion, then c is the third proportional to a and b, calculated as c = b² ÷ a.

The correct answer is 90%.

Key Points

• According to the Annual Report 2024-25 published by the Ministry of Rural Development, around 90% of rural families rely on agriculture, livestock, and Non-Timber Forest Products (NTFP) for their livelihoods.
• This data underscores the significant dependency of rural households on these sectors for both income generation and food security.
• Non-Timber Forest Products (NTFP) include resources like bamboo, honey, medicinal plants, and other forest-derived materials that are crucial for rural livelihoods.
• Livelihood diversification in rural areas is often centered around a combination of agriculture, livestock rearing, and forest-based activities.
• Such dependency also highlights the vulnerability of rural families to climate change, economic disruptions, and environmental degradation.

Additional Information

• Agriculture in Rural India:
• Agriculture is the primary source of livelihood for rural households, contributing significantly to India's GDP.
• Small and marginal farmers constitute the majority, with holdings of less than 2 hectares.
• Seasonal crops and monsoon dependence make rural agriculture vulnerable to climatic variations.
• Livestock in Rural Livelihoods:
• Livestock rearing provides supplementary income and acts as a risk mitigation strategy during crop failures.
• India is the largest producer of milk globally, with livestock being a key contributor to rural economies.
• Livestock products like milk, eggs, and meat are crucial for nutritional security in rural areas.
• Non-Timber Forest Products (NTFP):
• NTFPs include bamboo, lac, resin, honey, medicinal plants, and other forest-based resources.
• These products are especially significant for tribal communities and forest-dwelling populations.
• NTFPs contribute to both sustenance and income generation, with many rural families relying on them for daily needs.
• Challenges for Rural Livelihoods:
• Climate change, deforestation, and over-exploitation of natural resources pose threats to sustainability.
• Lack of market access, infrastructure, and financial support hinders income growth for rural families.
• Government initiatives like MGNREGA and rural development schemes aim to address these challenges.

The logic followed here is:

Given:  # : FLN :: TXB : %

Option 1)  # = BPJ, % = XTF

Here, it does follow the logic.

Option 2)  # = LFT, % = BPJ

Option 3) # = PBX, % = XTF

Option 4)  # = XTF, % = PBX

Hence, the correct answer is "Option 1".

Given:  ‘M + N − O ÷ P × Q’

Decoding the signs:

It  means that M is the mother of N, N is the brother of O, O is the father of P, P is the wife of Q.

Thus, M is the Wife's father's mother of Q.

Hence, the correct answer is "Option 2".

The correct answer is Cooperatives Build Prosperity for All.

Key Points

• The ICA Global Cooperative Conference in November 2024 had the theme "Cooperatives Build Prosperity for All."
• It emphasized the role of cooperatives in fostering inclusive economic growth and equitable development across communities.
• The conference brought together cooperative leaders, policymakers, and stakeholders from around the globe to discuss strategies for achieving prosperity through cooperative models.
• This theme aligns with the International Cooperative Alliance's mission to promote sustainable development and solidarity within the cooperative movement.
• The conference showcased examples of cooperative initiatives successfully improving livelihoods and creating opportunities for marginalized groups.

Additional Information

• International Cooperative Alliance (ICA)
• The ICA is a global organization representing cooperatives worldwide, founded in 1895.
• Its mission is to unite, represent, and serve cooperatives, advocating their role in sustainable development.
• The ICA defines cooperatives as autonomous associations of people united voluntarily to meet common economic, social, and cultural needs.
• It works towards promoting cooperative values such as self-help, equality, equity, and democracy.
• Role of Cooperatives in Economic Growth
• Cooperatives play a critical role in local economic development by generating employment and supporting small-scale enterprises.
• They empower individuals and communities, fostering financial inclusion and social equity.
• Cooperatives operate on the principle of shared ownership and democratic decision-making, ensuring accountability and fairness.
• Global Cooperative Movement
• The cooperative movement is recognized as an essential force for sustainable development and poverty reduction globally.
• It is supported by international bodies such as the United Nations, which declared the International Year of Cooperatives in 2012.
• Cooperatives contribute significantly to achieving the United Nations' Sustainable Development Goals (SDGs), including zero hunger and reduced inequalities.
• Sustainable Development through Cooperatives
• Cooperatives focus on long-term benefits for members and communities, rather than short-term profits.
• They promote environmentally friendly practices and support green initiatives in sectors like agriculture and energy.
• By engaging communities, cooperatives help build resilience against social and economic challenges.

Given: 

Uday starts from Point A and drives 3 km towards south.

He then takes a right turn, drives 2 km, turns left and drives 5 km.

He then takes a right turn and drives 3 km.

He takes a final right turn, drives 8 km and stops at Point P.

Thus,  he drive5 km; East in order to reach Point A again.

Hence, the correct answer "Option 3".

The correct answer is Opens the Run Command dialog box.

Key Points

• Alt + F2 is a keyboard shortcut commonly used in the Linux GNOME desktop environment to open the "Run Command" dialog box.
• The "Run Command" dialog box allows users to quickly launch applications or execute commands without opening a terminal.
• This feature is designed for advanced users who prefer keyboard shortcuts for efficiency and speed.
• When the dialog box opens, users can type the name of an application, a command, or a script to execute it directly.
• It is a widely supported feature in most Linux desktop environments, including GNOME, KDE, and others, with slight variations in functionality.

Additional Information

• GNOME Desktop Environment
• GNOME is a popular open-source desktop environment used in many Linux distributions.
• It provides a graphical user interface (GUI) for managing files, applications, and system settings.
• GNOME is known for its simplicity, user-friendliness, and modern design.
• Keyboard Shortcuts in Linux
• Keyboard shortcuts are combinations of keys that perform specific functions, improving productivity and accessibility.
• Linux environments often allow customization of shortcuts to suit user preferences.
• Examples include Ctrl + Alt + T to open a terminal and Alt + Tab to switch between open windows.
• Run Command Dialog Box
• The "Run Command" dialog box is a lightweight tool for launching applications or commands without navigating through menus.
• It is particularly useful for experienced users who are familiar with application names or specific commands.
• Commands entered in this dialog box are executed in the background, without requiring a terminal window.
• Other Common Shortcuts in GNOME
• Alt + Tab: Switch between open windows.
• Ctrl + Alt + T: Open the terminal.
• Super (Windows key): Open the Activities Overview.
• Alt + F4: Close the current window.

The correct answer is 1 year.

Key Points

• The 97th Constitutional Amendment introduced reforms to promote the autonomy and democratic functioning of cooperative societies in India.
• Under this amendment, state laws inconsistent with the provisions of the amendment can remain in force for a maximum period of 1 year from the commencement of the amendment.
• This period allows states to make necessary modifications to their cooperative laws to comply with the amendment.
• The amendment aimed to make cooperative societies more accountable, transparent, and member-driven.
• It also added a new part, Part IXB, to the Constitution of India to specifically deal with cooperative societies.

Additional Information

• 97th Constitutional Amendment:
• The amendment was passed in 2011 and came into effect on February 15, 2012.
• It added Article 43B to the Directive Principles of State Policy, encouraging states to promote voluntary formation, democratic functioning, and professional management of cooperative societies.
• Part IXB of the Constitution:
• This part specifically deals with cooperative societies and outlines provisions for their governance.
• It includes provisions for the composition, election, and tenure of the board of cooperative societies.
• Objective of the Amendment:
• To improve the functioning of cooperative societies and ensure their accountability to members.
• To protect the interests of members and prevent misuse of funds and powers.
• Legal Framework:
• States were required to amend their cooperative society laws to comply with the constitutional provisions within one year.
• Any inconsistent state law beyond this period would cease to have effect.

The correct answer is Tana Bhagats.

Key Points

• The Santhal Rebellion (1855-56) was led by tribal leaders Sidhu, Kanho, Chand, and Bhairav Murmu to resist British colonial oppression and exploitation by landlords and moneylenders.
• The rebellion primarily took place in the Rajmahal Hills of present-day Jharkhand, where the Santhal tribes united against oppressive policies.
• Tana Bhagats, a tribal group from the Oraon community, were not part of the Santhal Rebellion. They emerged later in 1914, as followers of Mahatma Gandhi's non-violent principles.
• The Santhal Rebellion was one of the significant tribal uprisings against British rule, marked by violent resistance to reclaim tribal autonomy and land rights.
• The rebellion was ultimately crushed by the British forces, but it led to the creation of the Santhal Pargana district in 1856 to address tribal grievances.

Additional Information

• Santhal Rebellion (1855-56):
• Also known as the Hul Rebellion, it was a tribal uprising led by the Santhal community against British rule and exploitation by zamindars and moneylenders.
• The rebellion marked a significant resistance movement before the Indian Revolt of 1857.
• Tana Bhagats Movement (1914):
• Founded by Jatra Oraon, the Tana Bhagats were a tribal reformist group inspired by Gandhian ideals of non-violence and self-purification.
• They opposed British taxes and participated in the Civil Disobedience Movement.
• Sidhu and Kanho Murmu:
• They were the key leaders of the Santhal Rebellion, who mobilized thousands of tribal people in the fight against colonial oppression.
• Their leadership remains a symbol of tribal resistance in Indian history.
• Impact of Santhal Rebellion:
• It highlighted the grievances of tribal communities under British rule, especially regarding land alienation and exploitation.
• It led to administrative changes, including the establishment of the Santhal Pargana district.

The correct answer is 33%.

Key Points

• The 106th Amendment Act of the Indian Constitution proposed 33% reservation for women in Lok Sabha and State Legislative Assemblies.
• This amendment aimed to ensure gender equality in political representation and decision-making bodies.
• The reservation was to apply to both directly elected seats and seats reserved for Scheduled Castes (SCs) and Scheduled Tribes (STs).
• The bill to enact this amendment was commonly referred to as the Women's Reservation Bill.
• Though widely discussed and debated, the bill has not been implemented as of the latest updates.

Additional Information

• Women's Reservation Bill:
• Introduced in Parliament in 1996, it aimed to reserve 33% of seats for women in Lok Sabha and State Legislative Assemblies.
• The bill was passed in the Rajya Sabha in 2010 but has not been passed in the Lok Sabha.
• The aim was to enhance women’s participation in governance and policy-making.
• Importance of Women's Representation:
• Increased representation of women ensures diverse perspectives in decision-making.
• It promotes gender equality and empowers women politically, socially, and economically.
• Current Status of Women's Representation:
• As of 2023, women constitute approximately 14% of the Lok Sabha and 10% of the State Assemblies.
• India ranks relatively low in the global Gender Gap Index in terms of political empowerment.
• Global Examples:
• Countries like Rwanda and Sweden have implemented effective gender quotas in their legislatures.
• Rwanda has over 60% representation of women in its Parliament, the highest in the world.

Shortcut Trick

Net profit percentage = a − b − (a × b) ÷ 100, where a is the markup percentage and b is the discount percentage.

Here, markup percentage (a) = 25% and discount percentage (b) = 4%.

Net Profit% = 25 − 4 − (25 × 4) ÷ 100

Net Profit% = 21 − 100 ÷ 100 = 21 − 1 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given: Marked Price (MP) = ₹7,725, Markup = 25%, Discount = 4%. Formulas: Profit% = ((SP − CP) ÷ CP) × 100 | SP = MP × (100 − D%) ÷ 100 | CP = MP × 100 ÷ (100 + Markup%)

⇒ Let Cost Price (CP) be 100 units. ⇒ Marked Price (MP) = 100 + 25% of 100 = 125 units. ⇒ Selling Price (SP) = MP − 4% of MP = 125 − (4 ÷ 100 × 125) = 125 − 5 = 120 units. ⇒ Profit = SP − CP = 120 − 100 = 20 units. ⇒ Profit Percentage = (20 ÷ 100) × 100 = 20%.

∴ The correct answer is 20%.

Additional Information

Relationship between CP and MP

The ratio of CP to MP can be calculated as CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%).

Successive Percentage Change

Profit% is the resultant of markup (increase) and discount (decrease) applied successively on the Cost Price.

The correct answer is To store frequently accessed data for quick retrieval.

Key Points

• Cache memory is a small-sized, high-speed memory located close to the CPU, designed to store frequently accessed data and instructions.
• It reduces the time required to access data from the main memory (RAM), thereby improving system performance.
• Cache operates at a much faster speed compared to RAM, enabling the CPU to retrieve essential data quickly without delays.
• Modern processors often include multiple levels of cache, such as L1, L2, and L3 cache, each with varying speeds and sizes for optimized performance.
• By minimizing the need for frequent access to slower main memory, cache memory plays a crucial role in enhancing processing efficiency.

Additional Information

• Levels of Cache Memory:
• L1 Cache: Closest to the CPU, the smallest and fastest type of cache.
• L2 Cache: Larger and slightly slower than L1, typically located on the CPU chip.
• L3 Cache: Shared among CPU cores, larger but slower than L1 and L2.
• Cache Hit and Miss:
• A cache hit occurs when the CPU finds the required data in the cache, resulting in faster access.
• A cache miss happens when the data is not in the cache, forcing the CPU to retrieve it from main memory.
• Cache Replacement Policies:
• Techniques like Least Recently Used (LRU), First In First Out (FIFO), and Random Replacement determine which data to replace in cache when it's full.
• Difference Between Cache and RAM:
• Cache memory is faster but smaller in size compared to RAM.
• RAM stores larger data temporarily, while cache focuses on frequently accessed data for rapid retrieval.
• Modern Applications:
• Cache memory is crucial in applications like gaming, video editing, and database management systems for enhancing processing speeds.

The logic followed here is:

Hence, the correct answer is "Option 4".

Shortcut Trick

Net work per minute = (1 ÷ filling time) − (1 ÷ emptying time)

Net filling rate = (1 ÷ 10) − (1 ÷ 20) = 1 ÷ 20

Time taken = Reciprocal of net rate = 20 minutes

∴ The correct answer is 20 minutes.

Alternate Method

⇒ Combined Efficiency = 2 − 1 = 1 unit/min

⇒ Time required = Total Capacity ÷ Combined Efficiency

⇒ Time = 20 ÷ 1 = 20 minutes

∴ The correct answer is 20 minutes.

Additional Information

Inlet and Outlet Rule

Work done by an inlet pipe is always considered positive, while work done by an outlet (leak) is negative.

Total Capacity (LCM Method)

The Least Common Multiple (LCM) of the individual times provides the most convenient value for total tank capacity.

Net Time Formula

If pipe A fills in 'x' and pipe B empties in 'y' (y > x), time taken together = (x × y) ÷ (y − x).

Given symbol mappings:

• ‘+’ means ‘−’
• ‘−’ means ‘×’
• ‘×’ means ‘÷’
• ‘÷’ means ‘+’

The given equation is:

502 ÷ 78 + 2 − 258 × 2 = ?

Replace the operators with their corresponding new meanings:

502 + 78 − 2 × 258 ÷ 2 = ?

⇒ 502 + 78 − 258 = ?

⇒ 580 - 250 = 322.

hence, the correct answer is "Option 1".

Shortcut Trick

Total Profit = Profit from Pen 1 + Profit from Pen 2.

Pen 1: CP = 630, SP before discount = 630 × 1.70. Final SP = (630 × 1.70) × 0.91.

Pen 2: CP = 722, Profit = 722 × 71% = 512.62.

Total Profit = [630 × 1.70 × 0.91 − 630] + 512.62.

Total Profit = 344.61 + 512.62 = 857.23.

∴ The correct answer is ₹857.23.

Alternate Method

Given → CP₁ = ₹630, CP₂ = ₹722, Profit%₁ = 70%, Discount₁ = 9%, Profit%₂ = 71%. Formulas: Profit = SP − CP | SP = CP × (100 + P%) ÷ 100 | Final SP = Marked Price × (100 − D%) ÷ 100.

⇒ Pen 1 MP = 630 + (70% of 630) = 630 + 441 = ₹1071. ⇒ Pen 1 Final SP = 1071 − (9% of 1071) = 1071 − 96.39 = ₹974.61. ⇒ Pen 1 Net Profit = 974.61 − 630 = ₹344.61. ⇒ Pen 2 Profit = 71% of 722 = (71 × 722) ÷ 100 = ₹512.62. ⇒ Total Profit = 344.61 + 512.62 = ₹857.23.

∴ The correct answer is ₹857.23.

Additional Information

Markup and Discount Relationship

When a profit percentage is applied and then a discount is given, the effective multiplier is (1 + Profit%_initial) × (1 − Discount%).

Profit Calculation

Total profit is the sum of individual profits from each article: Total Profit = ∑ (SP_i − CP_i).

The correct answer is Bhupinder Singh of Patiala.

Key Points

• Maharaja Bhupinder Singh of Patiala was a notable patron of the Sikh community and played a key role in preserving Sikh religious and cultural heritage.
• He contributed significantly to the construction and renovation of Sikh religious shrines, including the Golden Temple in Amritsar.
• The Maharaja supported Sikh institutions, including funding for educational initiatives and religious activities to promote Sikhism.
• He was a key figure in the Sikh community during the early 20th century and maintained close ties with the Shiromani Gurdwara Parbandhak Committee (SGPC).
• Maharaja Bhupinder Singh is also remembered for his efforts to preserve Sikh traditions and for promoting unity within the Sikh community.

Additional Information

• Golden Temple (Harmandir Sahib):
• The Golden Temple, located in Amritsar, Punjab, is the holiest shrine in Sikhism.
• It was founded by the fourth Sikh Guru, Guru Ram Das, and later completed by Guru Arjan Dev.
• The temple represents Sikh values of equality, unity, and service to humanity.
• Shiromani Gurdwara Parbandhak Committee (SGPC):
• The SGPC is an organization responsible for managing Sikh gurdwaras and promoting Sikh religious activities.
• It plays a vital role in preserving Sikh history, culture, and traditions.
• Princely States of India:
• During British rule, princely states were semi-autonomous regions governed by local monarchs under British suzerainty.
• Patiala was one of the largest princely states in Punjab.
• Bhupinder Singh's Legacy:
• Apart from his contributions to Sikhism, Maharaja Bhupinder Singh is also remembered for his progressive reforms in Patiala, including modern infrastructure and military advancements.
• He was an influential leader and diplomat, representing India in international arenas, such as the League of Nations.

Shortcut Trick

Net increase in the sum = (10 × 12.5) + (10 × 15) + (5 × 0)

Net increase = 125 + 150 + 0 = 275

Increase in mean = Total Increase ÷ Total Numbers = 275 ÷ 25 = 11

New arithmetic mean = Old Mean + Increase = 110 + 11 = 121

∴ The correct answer is 121.

Alternate Method

Given:

Total numbers (n) = 25

Initial Arithmetic Mean = 110

Formula Used:

New Mean = (Original Sum + Total Change) ÷ Total Numbers

Calculations:

⇒ Original Sum of 25 numbers = 25 × 110 = 2750

⇒ Increase from first 10 numbers = 10 × 12.5 = 125

⇒ Increase from next 10 numbers = 10 × 15 = 150

⇒ Total Increase = 125 + 150 + (5 × 0) = 275

⇒ New Total Sum = 2750 + 275 = 3025

⇒ New Arithmetic Mean = 3025 ÷ 25

⇒ New Arithmetic Mean = 121

∴ The correct answer is 121.

Additional Information

Linear Property of Mean

If a constant k is added to every observation in a data set, the new mean is the original mean + k.

Total Sum Formula

The sum of all observations is always equal to Mean × Number of observations (Sum = x¯ × n).

Weighted Average

When groups are changed differently, the net change in mean is (Σ n_i × c_i) ÷ N, where c_i is the change in each group.

The logic followed here is:

The code "V" is "6".

Hence, the correct answer is "Option 2".

The logic followed here is:

Option 1) KL - FG

Option 2) XY - ST

Option 3) HK - LP

Option 4) OP - JK

  

Hence, the correct answer is "Option 3".

The correct answer is Anne Michaels.

Key Points

• Anne Michaels is a Canadian poet and novelist known for her profound exploration of themes like memory, loss, and identity.
• Her novel 'Held', shortlisted for the Booker Prize 2024, continues her tradition of blending poetic language with compelling storytelling.
• Anne Michaels previously gained global recognition with her novel 'Fugitive Pieces', which won multiple prestigious awards, including the Orange Prize for Fiction.
• 'Held' has been praised by critics for its intricate narrative and emotionally resonant prose, solidifying her status as a literary powerhouse.
• Michaels’ works are widely celebrated for their ability to delve into universal human experiences while maintaining a personal and intimate tone.

Additional Information

• Booker Prize:
• One of the most prestigious literary awards, established in 1969, recognizing outstanding original novels written in English.
• The award is open to authors of any nationality, provided the work is published in the UK or Ireland.
• Past winners include literary greats such as Salman Rushdie, Margaret Atwood, and Kazuo Ishiguro.
• Anne Michaels’ Writing Style:
• Her works often blend poetry and prose to create rich, textured narratives.
• Michaels is known for her meticulous attention to language, crafting sentences that resonate deeply with readers.
• Recurring themes in her work include history, memory, trauma, and the enduring nature of human connection.
• Fugitive Pieces:
• Anne Michaels’ debut novel, which explores the Holocaust through the lens of memory and survival.
• The book has been translated into over 20 languages and adapted into a feature film.
• It won several awards, including the Orange Prize for Fiction and the Guardian Fiction Prize.
• Booker Prize 2024:
• The shortlisted works for this edition of the prize represent diverse voices and innovative storytelling.
• It demonstrates the global reach and influence of contemporary English literature.
• The winner will be announced later in the year, with the shortlisted novels gaining immense critical and commercial attention.

Shortcut Trick

Ratio of Men : Women : Children = 20 : 50 : (100 − 70) = 2 : 5 : 3.

Average weight = [(2 × 45) + (5 × 60) + (3 × 20)] ÷ (2 + 5 + 3)

Average weight = [90 + 300 + 60] ÷ 10 = 450 ÷ 10 = 45 kg.

∴ The correct answer is 45 kg.

Alternate Method

Given:

Percentage of Men = 20%, Women = 50%, Children = 30%

Average weight of Men = 45 kg, Women = 60 kg, Children = 20 kg

Formula Used:

Total Weight = (Average Weight × Number of People)

Average Weight of Group = Total Weight of all ÷ Total Number of People

Calculations:

⇒ Let the total number of people in the group be 100.

⇒ Number of Men = 20, Women = 50, Children = 100 − (20 + 50) = 30.

⇒ Total weight of Men = 20 × 45 = 900 kg.

⇒ Total weight of Women = 50 × 60 = 3000 kg.

⇒ Total weight of Children = 30 × 20 = 600 kg.

⇒ Total weight of the group = 900 + 3000 + 600 = 4500 kg.

⇒ Average weight of the group = 4500 ÷ 100 = 45 kg.

∴ The correct answer is 45 kg.

Additional Information

Weighted Average Formula

Used when different groups have different sizes and averages: Avg = (n₁A₁ + n₂A₂ + ...) ÷ (n₁ + n₂ + ...).

Deviation Method

Assume an average (say 40) and calculate net deviation: Total deviation = [Σ(Actual − Assumed) × Weight]. Avg = Assumed + (Total Deviation ÷ Total Weight).

Ratio Simplification

In problems involving percentages, always simplify the quantities into the smallest possible ratios to reduce calculation time.

Shortcut Trick

∠BEF = 180° − ∠PEB = 180° − 56° = 124° (Linear pair)

∠GEF = ∠BEF − ∠BEG = 124° − 32° = 92°

In ▵EGF, sum of angles = 180°

∠EGF = 180° − (∠GEF + ∠GFE) = 180° − (92° + 47°) = 41°

∴ The correct answer is 41°.

Alternate Method

Given: AB || CD, transversal PQ intersects them at E and F. ∠PEB = 56°, ∠BEG = 32°, and ∠GFE = 47°.

Formula Used: Linear pair property (sum = 180°) and Angle Sum Property of a triangle (sum = 180°).

⇒ Since PQ is a straight line, ∠PEB + ∠BEF = 180° (Linear pair)

⇒ 56° + ∠BEF = 180°

⇒ ∠BEF = 180° − 56° = 124°

⇒ From the figure, ∠BEF = ∠BEG + ∠GEF

⇒ 124° = 32° + ∠GEF

⇒ ∠GEF = 124° − 32° = 92°

⇒ In ▵EGF, ∠GEF + ∠GFE + ∠EGF = 180°

⇒ 92° + 47° + ∠EGF = 180°

⇒ 139° + ∠EGF = 180°

⇒ ∠EGF = 180° − 139° = 41°

∴ The correct answer is 41°.

Additional Information

Parallel Lines and Transversals

When two parallel lines are intersected by a transversal, corresponding angles are equal, and alternate interior angles are equal.

Angle Sum Property

The sum of the interior angles of any triangle is always 180°.

Linear Pair Axiom

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.

Shortcut Trick

Radius (r) = 144 ÷ 2 = 72 cm

CSA = πrl ⇒ 5400π = π × 72 × l

l = 5400 ÷ 72 = 75 cm

Using Pythagorean triplet (7, 24, 25) × 3 → (21, 72, 75)

∴ The correct answer is 21 cm.

Alternate Method

Given:

Curved Surface Area (CSA) = 5400π cm²

Diameter = 144 cm ⇒ Radius (r) = 72 cm

Formula Used:

CSA of Cone = πrl

Slant height (l) = √(h² + r²)

Calculations:

⇒ π × 72 × l = 5400π

⇒ l = 5400 ÷ 72

⇒ l = 75 cm

⇒ h² = l² − r²

⇒ h² = 75² − 72²

⇒ h² = (75 − 72)(75 + 72)

⇒ h² = 3 × 147

⇒ h² = 441

⇒ h = √441 = 21 cm

∴ The correct answer is 21 cm.

Additional Information

Total Surface Area of Cone

TSA = πr(l + r), which includes the curved area and the circular base area.

Volume of Cone

Volume = (1/3)πr²h, which is exactly one-third the volume of a cylinder with the same radius and height.

Slant Height Relation

In a right circular cone, l² = h² + r² based on the Pythagoras Theorem.

The correct answer is 70%.

Key Points

• The Budget Estimates (BE) for the Smart Cities Mission in 2024-25 show a decrease of 70% compared to the Revised Estimates (RE) for 2023-24.
• The Smart Cities Mission is a flagship program launched by the Government of India in 2015 to enhance urban infrastructure and development.
• The reduction in allocation reflects the government’s reprioritization of urban development funding or the nearing completion of key projects under the mission.
• The allocation adjustments are typically influenced by factors such as project progress, expenditure efficiency, and broader fiscal constraints.
• For 2024-25, the focus may shift toward other urban infrastructure schemes or consolidation of ongoing Smart Cities projects.

Additional Information

• Smart Cities Mission:
• Launched on 25 June 2015, the mission aims to promote sustainable and inclusive cities.
• It is implemented by the Ministry of Housing and Urban Affairs and has a target of developing 100 smart cities across the country.
• The focus areas include urban mobility, sanitation, energy efficiency, digital governance, and affordable housing.
• Budget Estimates vs. Revised Estimates:
• Budget Estimates represent the initial allocation for a financial year.
• Revised Estimates reflect adjustments based on actual spending trends and fiscal priorities during the year.
• Changes between BE and RE indicate the government’s dynamic resource allocation strategy.
• Challenges in Urban Development:
• Urban areas face issues such as overcrowding, inadequate infrastructure, pollution, and resource constraints.
• Smart Cities aim to address these by leveraging technology, innovation, and sustainable practices.
• Fiscal Management in India:
• The government balances funding across competing priorities such as health, education, defense, and infrastructure.
• Changes in allocation reflect efforts to optimize spending and improve project outcomes.

Given: ACT BUS CAR DAD

According to the question:

In each of the words, each vowel is changed to the letter immediately following it in the English alphabetical order and each consonant is changed to the letter immediately preceding in the English alphabetical order.

Now, changing each letter in the words:

ACT: A → B, C → B, T → S

BUS: B → A, U → V, S → R

CAR: C → B, A → B, R → Q

DAD: D → C, A → B, D → C

Thus, the new clusters formed are:

ACT → BBS

BUS → AVR

CAR → BBQ

DAD → CBC

In these clusters, the ones without any vowel (A, E, I, O, U) are:

BBS, BBQ, CBC

Hence, the number of letter clusters where no vowel appears is: 3

Therefore, the correct answer is "Option 3".

The correct answer is 30 per 1000 live births.

Key Points

• According to the Sample Registration System (SRS) 2019, the Infant Mortality Rate (IMR) in India was 30 per 1000 live births.
• IMR represents the number of deaths of infants under one year of age per 1000 live births in a given year.
• India has witnessed a consistent decline in IMR over the years due to improvements in healthcare, sanitation, and immunization coverage.
• The IMR in rural areas was higher at 34 per 1000 live births compared to urban areas, which recorded 20 per 1000 live births.
• This decline in IMR aligns with the government’s efforts under programs like National Health Mission (NHM) and Intensified Mission Indradhanush.

Additional Information

• Sample Registration System (SRS):
• SRS is a demographic survey conducted in India by the Registrar General and Census Commissioner.
• It provides reliable annual estimates of birth rates, death rates, and other fertility and mortality indicators.
• Neonatal Mortality Rate (NMR):
• NMR refers to the number of deaths of newborns within the first 28 days of life per 1000 live births.
• India’s NMR in 2019 stood at 22 per 1000 live births, as per SRS data.
• National Health Mission (NHM):
• The NHM aims to improve healthcare access and outcomes, particularly for women and children.
• It includes initiatives like Janani Suraksha Yojana (JSY) and Janani Shishu Suraksha Karyakaram (JSSK).
• Intensified Mission Indradhanush (IMI):
• IMI aims to achieve full immunization coverage for children under two years and pregnant women.
• It targets unvaccinated and partially vaccinated children in underserved areas.
• Sustainable Development Goals (SDG):
• India is committed to reducing IMR and NMR in alignment with SDG 3, which focuses on ensuring healthy lives and promoting well-being for all at all ages.

The correct answer is Justice B R Gavai; 52nd Chief Justice of India.

Key Points

• Justice Sanjiv Khanna, the 51st Chief Justice of India, retired in May 2025, as per the standard retirement age of 65 for Supreme Court judges.
• Justice B R Gavai has been named as his successor, making him the 52nd Chief Justice of India upon appointment.
• Justice B R Gavai is known for his significant contributions to the judiciary and has been part of several landmark judgments during his tenure in the Supreme Court.
• He will be the second Chief Justice of India from the Scheduled Caste community, following Justice K G Balakrishnan, who served as the 37th CJI.
• The appointment of the Chief Justice of India is made by the President of India based on seniority among the Supreme Court judges and recommendations from the outgoing CJI.

Additional Information

• Chief Justice of India (CJI):
• The Chief Justice of India is the head of the judiciary system and the Supreme Court, the highest constitutional court in India.
• The CJI plays a vital role in upholding the Constitution, interpreting laws, and maintaining checks and balances between the three branches of government.
• Eligibility for the CJI:
• Must be a citizen of India.
• Must have served as a judge in a High Court for at least five years or as an advocate in a High Court for at least ten years, or be a distinguished jurist in the President's opinion.
• Appointment Process:
• The President of India appoints the CJI based on seniority among the judges of the Supreme Court.
• The outgoing CJI recommends their successor in consultation with other senior judges of the Supreme Court.
• Retirement Age:
• Supreme Court judges, including the CJI, retire at the age of 65.
• High Court judges, by comparison, retire at the age of 62.
• Historical Significance:
• Justice H J Kania was the first Chief Justice of India, serving from 1950 to 1951.
• Justice Fathima Beevi was the first woman to be appointed as a Supreme Court judge in India, paving the way for greater representation in the judiciary.

Given:

Solve: 70 + (72/6) + 29 - 30

Formula used:

Use BODMAS (Bracket, Order, Division/Multiplication, Addition/Subtraction) rule to solve.

Calculation:

70 + (72/6) + 29 - 30

⇒ 70 + 12 + 29 - 30

⇒ 70 + 12 + 29 = 111

⇒ 111 - 30 = 81

∴ The correct answer is option (2).

The correct answer is 100%.

Key Points

• The Jal Jeevan Mission aims to provide 100% functional household tap connections (FHTCs) to all rural households by 2024.
• Launched by the Ministry of Jal Shakti in August 2019, the mission focuses on water supply infrastructure in rural areas.
• Under this initiative, 55 liters of water per person per day is targeted to be supplied to every household.
• It emphasizes community participation and involves local bodies like Gram Panchayats in the implementation process.
• The scheme aligns with the United Nations Sustainable Development Goal-6, which ensures access to clean water and sanitation for all.

Additional Information

• Jal Jeevan Mission Key Components:
• Ensures piped water supply to households in rural areas.
• Promotes decentralized service delivery models, including rainwater harvesting and greywater management.
• Focuses on water quality monitoring and testing to prevent contamination.
• Community Participation:
• Village Water and Sanitation Committees (VWSCs) play a crucial role in planning and executing projects.
• Capacity-building programs are conducted for local communities to ensure efficient water resource management.
• Financial Allocation:
• The scheme operates on a cost-sharing model between the central and state governments.
• Significant funds have been allocated to states based on their requirement and progress.
• Challenges Addressed:
• Addresses issues like water scarcity, contamination, and poor infrastructure.
• Encourages sustainable practices to ensure long-term water security.

The correct answer is First effective antibiotic against bacterial infections.

Key Points

• Penicillin, discovered by Alexander Fleming in 1928, was the first antibiotic that proved to be highly effective against bacterial infections.
• The discovery marked the beginning of the modern era of antibiotics, revolutionizing the treatment of bacterial diseases such as pneumonia, syphilis, and strep throat.
• During World War II, penicillin was mass-produced and saved countless lives by treating infections in wounded soldiers.
• Penicillin works by inhibiting bacterial cell wall synthesis, making it effective against a wide range of Gram-positive bacteria.
• Its discovery earned Alexander Fleming, Howard Florey, and Ernst Boris Chain the Nobel Prize in Physiology or Medicine in 1945.

Additional Information

• Antibiotics:
• Substances that kill or inhibit the growth of bacteria without harming the host organism.
• Penicillin was the first antibiotic discovered, followed by others like streptomycin, tetracycline, and erythromycin.
• Overuse or misuse of antibiotics can lead to antibiotic resistance, a significant global health concern.
• Alexander Fleming's Discovery:
• Fleming observed that a mold, later identified as Penicillium notatum, inhibited bacterial growth on a petri dish.
• This serendipitous discovery laid the foundation for the development of antibiotics.
• Mass Production of Penicillin:
• During World War II, efforts led by Howard Florey and Ernst Chain enabled large-scale production of penicillin.
• This breakthrough ensured the availability of the drug for treating battlefield infections and saving civilian lives.
• Impact on Medicine:
• Penicillin reduced mortality rates from bacterial infections and transformed medical practices worldwide.
• It is considered one of the most significant discoveries in medical history.

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. Only two people have the exam before T.

2. Only one person has the exam after D.

3. Only three people have the exam between T and F.

4. Only one person has the exam between E and C.

5. U has the exam immediately before E.

 

Thus, S has the exam on Friday.

Hence, the correct answer is "Option 4".

Shortcut Trick

Combine ratios: x : y : z = (2 × 4) : (5 × 4) : (5 × 7) = 8 : 20 : 35.

Total units = 8 + 20 + 35 = 63 units.

Value of 1 unit = 15,120 ÷ 63 = ₹240.

Amounts: x = 8 × 240 = ₹1,920; y = 20 × 240 = ₹4,800; z = 35 × 240 = ₹8,400.

∴ The correct answer is 1,920, 4,800 and 8,400.

Alternate Method

Given: x : y = 2 : 5 and y : z = 4 : 7. Total Amount = ₹15,120.

⇒ To equalize y: x : y = (2×4) : (5×4) = 8 : 20

⇒ y : z = (4×5) : (7×5) = 20 : 35

⇒ Combined Ratio x : y : z = 8 : 20 : 35

⇒ Total Share = 8k + 20k + 35k = 63k

⇒ 63k = 15,120 ⇒ k = 15,120 ÷ 63 = 240

⇒ x = 8 × 240 = ₹1,920

⇒ y = 20 × 240 = ₹4,800

⇒ z = 35 × 240 = ₹8,400

∴ The correct answer is 1,920, 4,800 and 8,400.

Additional Information

Ratio Combination Rule

To combine a:b and b:c, multiply the terms so that the common variable 'b' has the same numerical value in both ratios.

Proportional Division

If a total amount T is divided in ratio a:b:c, the share of the first part is [a / (a+b+c)] × T.

Verification Tip

Always ensure that the sum of calculated individual shares equals the total given amount (1,920 + 4,800 + 8,400 = 15,120).

The correct answer is Execute instructions and process data.

Key Points

• The CPU (Central Processing Unit) is the primary component of a computer system responsible for executing instructions provided by software programs.
• It performs the essential task of processing data, which includes arithmetic operations, logic operations, control functions, and input/output operations.
• The CPU consists of three key components: the Arithmetic Logic Unit (ALU), Control Unit (CU), and registers, which help in executing instructions efficiently.
• The CPU operates based on the fetch-decode-execute cycle, where it retrieves instructions from memory, decodes them, and performs the required operations.
• Modern CPUs are equipped with multiple cores, enabling parallel processing and significantly improving performance for multitasking and complex computations.

Additional Information

• Arithmetic Logic Unit (ALU):
• The ALU is a fundamental part of the CPU responsible for performing arithmetic operations (e.g., addition, subtraction) and logical operations (e.g., comparisons).
• It acts as the computational powerhouse of the CPU.
• Control Unit (CU):
• The CU directs the operation of the processor by interpreting instructions and ensuring that data flows correctly between the CPU and other components.
• It coordinates the fetch-decode-execute cycle.
• Registers:
• Registers are small, high-speed storage areas within the CPU that temporarily store data and instructions during processing.
• They facilitate quick access to frequently used data.
• Clock Speed:
• Clock speed, measured in GHz (gigahertz), represents the number of cycles a CPU can perform per second.
• Higher clock speeds generally result in faster processing but are also influenced by the CPU architecture and core count.
• Multi-Core Processors:
• Modern CPUs often include multiple cores, enabling them to perform multiple tasks simultaneously.
• Multi-core processors enhance performance in applications that support parallel computing, such as video editing and gaming.

Shortcut Trick

When the Mode is exactly equal to the Lower Limit of a class interval, the frequency of the preceding class must be equal to the frequency of the modal class in the formula numerator.

Given Mode = 140, which is the boundary between the classes 135−140 and 140−145.

Using the modal class 140−145, the formula gives Mode = L only when f₁ − f₀ = 0.

⇒ x − 33 = 0 ⇒ x = 33.

∴ The correct answer is 33.

Alternate Method

Given: Mode = 140, Class Width (h) = 5.

Formula: Mode = L + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h

125-130 130-135 135-140 140-145 145-150 30 30 33 x 31

Shortcut Trick

In a 30°-60°-90° triangle, the ratio of sides opposite to these angles is 1 : √3 : 2.

Side opposite to 60° (Base) = 48 m.

√3 units = 48 m ⇒ 1 unit = 48/√3 m.

Height (side opposite to 30°) = 1 unit = 16√3 m.

∴ The correct answer is 16√3 m.

Alternate Method

Given: Distance from foot (Base) = 48 m, Angle of elevation (θ) = 30°.

Formula Used: tan θ = Perpendicular / Base

⇒ tan 30° = h / 48

⇒ 1/√3 = h / 48

⇒ h = 48 / √3

⇒ h = (48 × √3) / (√3 × √3)

⇒ h = 48√3 / 3 = 16√3 m

∴ The correct answer is 16√3 m.

Additional Information

Trigonometric Ratios

Standard values: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3.

Angle of Elevation and Depression

The angle of elevation from an observer's eye to an object above is equal to the angle of depression from the object to the observer due to alternate interior angles.

Pythagoras Theorem

In any right-angled triangle, Hypotenuse² = Base² + Perpendicular².

The correct answer is Low water availability.

Key Points

• Dryland farming refers to agricultural practices in regions where rainfall is insufficient, typically less than 750 mm annually, making water availability a critical constraint.
• The primary challenge in dryland farming is low soil moisture due to minimal rainfall, which limits crop growth and productivity.
• Crops grown in such areas are primarily drought-resistant varieties, such as millets, sorghum, and pulses, as they can survive with limited water.
• Dryland farming areas are also prone to soil erosion, which further reduces the land's capacity to retain water.
• Efficient water management techniques, such as rainwater harvesting and mulching, are critical to overcoming water scarcity in these regions.

Additional Information

• Dryland Farming:
• It is a type of farming practiced in arid and semi-arid regions with low rainfall.
• Relies on moisture conservation techniques like deep plowing, contour farming, and minimal tillage to retain soil moisture.
• Crops such as pearl millet, chickpeas, and groundnuts are commonly grown in dryland farming systems.
• Soil Moisture Management:
• Techniques like mulching (covering soil with organic matter) help conserve moisture and prevent evaporation.
• Use of micro-irrigation systems, such as drip irrigation, ensures precise water delivery to crops.
• Rainwater Harvesting:
• Collecting and storing rainwater for agricultural use is a common practice in dryland regions.
• Helps supplement water availability during dry spells.
• Drought-Resistant Crops:
• These crops have evolved to survive with minimal water, making them ideal for dryland farming.
• Examples include millets, sorghum, pigeon peas, and certain oilseeds like sesame.

The correct answer is Hyderabad.

Key Points

• The two-day Chintan Shivir was organized in Hyderabad on 7-8 March 2025.
• The event was held to discuss India’s preparations for hosting the 2028 and 2036 Olympics.
• Hyderabad, known for its modern infrastructure and technological advancements, was chosen as the venue for the brainstorming session.
• Senior officials, sports experts, and stakeholders participated in the event to strategize and plan for India’s Olympic ambitions.
• The Shivir focused on collaboration between government bodies, private sectors, and international organizations to bolster India's sports ecosystem.

Additional Information

• Olympics Hosting Process:
• The International Olympic Committee (IOC) selects host cities through a competitive bidding process.
• Countries submit detailed proposals showcasing infrastructure, budget, and legacy plans for hosting the Games.
• Emphasis is placed on sustainability, inclusivity, and long-term benefits for the host city.
• India's Olympic Aspirations:
• India has been working towards enhancing its sports infrastructure and training facilities.
• The government and private sectors are collaborating to boost athletes' performance on the global stage.
• Hosting the Olympics would showcase India’s organizational capabilities and promote sports culture nationwide.
• Hyderabad as a Venue:
• Hyderabad is one of India’s leading cities in terms of infrastructure and connectivity.
• It has hosted several international events, showcasing its ability to organize large-scale gatherings.
• The city’s advanced IT ecosystem and modern facilities make it an ideal location for strategic discussions.
• India and the Olympics:
• India first participated in the Olympics in 1900.
• India has won medals in various disciplines, including hockey, wrestling, and athletics.
• Efforts are ongoing to improve India’s medal tally and overall performance in the Games.

Shortcut Trick

At constant expenditure, the Quantity is inversely proportional to the Price per unit.

Profit = 40% ⇒ Ratio of CP : SP = 100 : 140 = 5 : 7.

Therefore, the ratio of Quantity (CP) : Quantity (SP) = 7 : 5.

Given: Selling quantity = 5 chocolates for &8377;1.

Since 5 units = 5 chocolates, then 7 units = 7 chocolates.

∴ The correct answer is 7.

Alternate Method

Given: Selling Price (SP) of 5 chocolates = &8377;1 | Gain% = 40%.

Formulas: CP = [SP × 100] ÷ [100 + Gain%]

⇒ SP of 1 chocolate = &8377;1/5 = &8377;0.20.

⇒ CP of 1 chocolate = [0.20 × 100] ÷ [100 + 40] = 20 ÷ 140 = &8377;1/7.

⇒ Number of chocolates bought for &8377;1 = 1 ÷ (1/7) = 7.

∴ The correct answer is 7.

Additional Information

Price and Consumption Relationship

When the total Expenditure remains constant, the Price is inversely proportional to the Quantity. Price × Quantity = Expenditure.

Profit Percentage

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

The correct answer is 28,275.

Key Points

• 28,275 youth were trained in vocational skills under the Nehru Yuva Kendra Sangathan (NYKS) initiatives as of February 2025.
• The Nehru Yuva Kendra Sangathan is an autonomous body under the Ministry of Youth Affairs and Sports, Government of India.
• NYKS works to promote and develop the personality and leadership qualities of rural youth through skill development and vocational training programs.
• The training programs aim to make youth employable by equipping them with market-relevant skills.
• These initiatives contribute to the government's focus on empowering youth and enhancing their employability through skill-building efforts.

Additional Information

• Nehru Yuva Kendra Sangathan (NYKS)
• Established in 1972, NYKS is one of the largest youth organizations in the world.
• Its primary goal is to involve rural youth in the nation-building process and provide opportunities for skill development.
• It organizes diverse programs such as vocational training, sports, cultural activities, and awareness campaigns.
• Vocational Training
• Vocational training refers to education that focuses on providing students with practical skills and knowledge required for a specific trade or profession.
• It is critical for enhancing employability, especially among youth, in both formal and informal sectors.
• Skill Development Initiatives in India
• The Government of India has introduced various programs such as Skill India Mission, Pradhan Mantri Kaushal Vikas Yojana (PMKVY), and Deen Dayal Upadhyaya Grameen Kaushalya Yojana (DDU-GKY) to bridge the skill gap in the country.
• These programs aim to train millions of youth in industry-specific skills, ensuring their employability and contribution to economic growth.
• Ministry of Youth Affairs and Sports
• The Ministry is responsible for overseeing youth development and sports activities in India.
• It supports initiatives like NYKS, National Service Scheme (NSS), and Khelo India to nurture talent and promote holistic development.

Shortcut Trick

To find the maximum volume of identical containers, we must find the HCF (Highest Common Factor) of the given quantities.

Quantities: 156 and 256.

HCF(156, 256) ⇒ Difference = 256 − 156 = 100.

Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. Checking the largest factor that divides both 156 and 256.

156 is divisible by 4, and 256 is divisible by 4. Larger factors of 100 do not divide 156.

∴ The correct answer is 4 litres.

Alternate Method

Given:

Volume of Oil A = 156 litres

Volume of Oil B = 256 litres

Calculation:

To find the maximum capacity of each container, calculate the HCF of 156 and 256.

Prime factorization of 156:

⇒ 156 = 2 × 2 × 3 × 13 = 2² × 3 × 13

Prime factorization of 256:

⇒ 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁸

HCF is the product of the lowest powers of common prime factors:

⇒ HCF = 2²

⇒ HCF = 4

∴ The correct answer is 4 litres.

Additional Information

Highest Common Factor (HCF)

HCF is the greatest number that divides two or more numbers without leaving a remainder. It is also known as GCF or GCD.

Least Common Multiple (LCM)

LCM is the smallest non-zero common multiple of two or more numbers. Relationship: Product of two numbers = HCF × LCM.

Application in Partitioning

When items need to be divided into the largest possible equal groups or containers without mixing, HCF is always the required value.

The correct answer is 2020.

Key Points

• India and China suspended direct passenger flights in 2020 due to the outbreak of the COVID-19 pandemic.
• The suspension of flights was part of global measures to curb the spread of the coronavirus, which disrupted international air travel.
• Discussions to resume flights began in April 2025, signaling efforts to normalize ties and strengthen bilateral relations.
• Several countries including India and China implemented travel restrictions in 2020, affecting passenger movement across borders.
• The resumption of flights is expected to enhance people-to-people connectivity and foster economic collaboration between the two nations.

Additional Information

• COVID-19 Pandemic and Air Travel:
• The COVID-19 pandemic caused widespread disruption in global air travel starting in early 2020.
• Many countries imposed travel bans and restrictions to prevent the spread of the virus.
• Passenger flights were suspended between India and China as a precautionary measure.
• Restoring international flights required coordination between governments, airlines, and health authorities.
• India-China Relations:
• India and China are major trading partners, with bilateral trade exceeding $100 billion annually.
• Resuming flights is expected to improve ties and facilitate business and cultural exchanges.
• Both nations have faced challenges in their relationship, including border tensions.
• Efforts to resume flights reflect a step toward normalization and cooperation.
• Impact of Flight Suspensions:
• Suspending flights disrupted tourism, trade, and student movement between countries.
• China is a popular destination for Indian students pursuing higher education, particularly in medicine.
• Indian businesses rely on imports from China, which were affected by the travel restrictions.
• Restoring flights can help mitigate the economic impact of prolonged disruptions.
• International Travel Resumption Post-Pandemic:
• Many countries gradually resumed international air travel starting in 2021 with strict health protocols.
• Mandatory testing, quarantine, and vaccination requirements became commonplace.
• Airlines adapted to new guidelines to ensure passenger safety and compliance.
• Resumption of flights between India and China marks a significant milestone in post-pandemic recovery.

The correct answer is Acting as the core interface between applications and the system hardware.

Key Points

• The kernel is the central component of an operating system and serves as the core interface between the system's hardware and its applications.
• It manages critical tasks such as CPU scheduling, memory management, and device control.
• The kernel ensures that multiple programs and processes can run simultaneously by handling resource allocation and process isolation.
• It provides low-level system services such as hardware abstraction and ensures secure and efficient communication between the hardware and software.
• Popular kernel types include monolithic kernels (e.g., Linux) and microkernels (e.g., MINIX), each with distinct advantages in terms of performance and modularity.

Additional Information

• Kernel Modes:
• Modern operating systems use two modes: User Mode (for running applications) and Kernel Mode (for executing system-level tasks).
• The kernel operates in Kernel Mode, with unrestricted access to hardware resources and memory.
• Types of Kernels:
• Monolithic Kernel: All OS services run in a single large process, providing better performance but less modularity.
• Microkernel: Only essential services run in the kernel, while others run in user space, enhancing modularity and fault isolation.
• Memory Management:
• The kernel handles memory allocation and ensures that processes do not interfere with each other.
• Techniques such as virtual memory allow efficient memory utilization.
• Hardware Abstraction:
• The kernel provides a hardware abstraction layer (HAL) to shield applications from hardware-specific details.
• This abstraction makes the OS adaptable to different hardware platforms.
• Process Management:
• The kernel creates, schedules, and terminates processes.
• It ensures fairness in CPU time distribution and prevents deadlocks through mechanisms like semaphores and mutexes.

Shortcut Trick

For proportions a : b :: c : d, the product of extremes equals the product of means.

3.5 × x = 17.4 × 14

x = 17.4 × (14 ÷ 3.5)

x = 17.4 × 4 = 69.6

∴ The correct answer is 69.6.

Alternate Method

Given: 3.5 : 17.4 :: 14 : x

Formula Used: a/b = c/d

⇒ 3.5 ÷ 17.4 = 14 ÷ x

⇒ x = (14 × 17.4) ÷ 3.5

⇒ x = (140 × 17.4) ÷ 35

⇒ x = 4 × 17.4

⇒ x = 69.6

∴ The correct answer is 69.6.

Additional Information

Fourth Proportional

In the proportion a : b :: c : d, d is called the fourth proportional to a, b, and c. It is calculated as d = (b × c) ÷ a.

Third Proportional

If a, b, c are in continued proportion such that a : b :: b : c, then c is the third proportional where c = b² ÷ a.

Mean Proportional

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

Given equation: 63 ÷ 12 − 98 × 7 + 35 = ?

After interchanging ‘+’ and ‘−’ and ‘×’ and ‘÷’, we get:

63 × 12 + 98 ÷ 7 − 35 = ?

Following the BODMAS/PEMDAS rule:

= 63 × 12 + 98 ÷ 7 − 35

= 756 + 14 − 35

= 770 − 35

= 735

Hence, the correct answer is "735".

Shortcut Trick

Apply the Difference of Squares identity: a² − b² = (a + b)(a − b).

Let a = 2x + 3 and b = x + 1.

Sum (a + b) = 2x + 3 + x + 1 = 3x + 4.

Difference (a − b) = 2x + 3 − (x + 1) = x + 2.

Multiply factors: (3x + 4)(x + 2) = 3x² + 6x + 4x + 8 = 3x² + 10x + 8.

∴ The correct answer is 3x² + 10x + 8.

Alternate Method

Given: The expression to simplify is (2x + 3)² − (x + 1)².

Formula Used: (a + b)² = a² + 2ab + b²

⇒ Expand the first term: (2x + 3)² = (2x)² + 2(2x)(3) + 3² = 4x² + 12x + 9

⇒ Expand the second term: (x + 1)² = x² + 2(x)(1) + 1² = x² + 2x + 1

⇒ Substitute back: (4x² + 12x + 9) − (x² + 2x + 1)

⇒ Distribute the negative sign: 4x² + 12x + 9 − x² − 2x − 1

⇒ Combine like terms: (4x² − x²) + (12x − 2x) + (9 − 1)

⇒ Result: 3x² + 10x + 8

∴ The correct answer is 3x² + 10x + 8.

Additional Information

Algebraic Identities

Standard identities like (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b² are essential for polynomial expansion.

Difference of Squares

The formula a² − b² = (a − b)(a + b) is often faster for simplifying subtractions of two squared terms.

Like Terms

Polynomial simplification requires grouping terms with the same exponent and variable (e.g., all x² terms together).

Shortcut Trick

For a period of 2 years, the difference between Compound Interest (CI) and Simple Interest (SI) is given by the formula:

Difference (D) = P × (R/100)²

D = 47,100 × (9/100) × (9/100)

D = 471 × 81 / 100 ⇒ 38,151 / 100 = 381.51

∴ The correct answer is ₹381.51.

Alternate Method

Given:

Principal (P) = ₹47,100

Rate of Interest (R) = 9% per annum

Time (T) = 2 years

Step 1: Calculate Simple Interest (SI)

⇒ SI = (P × R × T) / 100

⇒ SI = (47,100 × 9 × 2) / 100

⇒ SI = 471 × 18 = ₹8,478

Step 2: Calculate Compound Interest (CI)

⇒ Amount (A) = P × (1 + R/100)^T

⇒ A = 47,100 × (1 + 9/100)²

⇒ A = 47,100 × (1.09)²

⇒ A = 47,100 × 1.1881 = ₹55,959.51

⇒ CI = Amount − Principal = 55,959.51 − 47,100 = ₹8,859.51

Step 3: Calculate the Difference

⇒ Difference = CI − SI

⇒ Difference = 8,859.51 − 8,478 = ₹381.51

∴ The correct answer is ₹381.51.

Additional Information

CI − SI Difference for 3 Years

The formula for the difference between CI and SI for 3 years is D = [P × (R/100)² × (300 + R) / 100].

Effective Rate Method

For 2 years, the effective CI rate is [x + y + (xy/100)]%. The difference between effective CI and SI rates is exactly (R²/100)%.

Compounding Periods

If interest is compounded half-yearly, the rate is halved (R/2) and the time is doubled (2T) for calculation purposes.

The correct answer is 851 km.

Key Points

• The Mahanadi River has a total length of 851 km, making it one of the major rivers in central and eastern India.
• It originates from Sihawa in Chhattisgarh and flows through Odisha before emptying into the Bay of Bengal.
• The river is known for its vast delta and extensive irrigation network, playing a vital role in agriculture and water resources in the region.
• It is an important source of water for Hirakud Dam, which is one of the largest dams in India and provides irrigation, flood control, and hydroelectric power.
• The Mahanadi drainage basin spreads across several states, including Chhattisgarh, Odisha, Jharkhand, and Maharashtra.

Additional Information

• Hirakud Dam
• Located on the Mahanadi River, it is the longest earthen dam in India.
• It was constructed in 1957 and plays a key role in flood control, irrigation, and hydroelectric power generation.
• The reservoir created by the dam spans an area of approximately 743 sq. km.
• Mahanadi Basin
• The Mahanadi Basin covers an area of approximately 141,600 sq. km.
• It includes tributaries such as the Seonath, Mand, Ib, and Hasdeo rivers.
• The basin supports agriculture and industries in Chhattisgarh and Odisha.
• Delta Formation
• The Mahanadi forms a wide delta at its mouth near Cuttack in Odisha.
• The delta is fertile and heavily cultivated, supporting rice farming and other crops.
• It houses several cities and towns, including Paradip Port, which is a key trading hub.
• Environmental Significance
• The Mahanadi River is home to rich biodiversity, including several freshwater fish and aquatic species.
• Efforts are being made to address pollution and over-extraction of water from the river.
• Conservation initiatives focus on maintaining the ecological balance of the river and its surroundings.

The logic followed here is:

Option 1) KGE

Option 2) DAX

Here, it does not follow the logic.

Option 3) WSQ

Option 4) SOM

Hence, the correct answer is "Option 2".

Shortcut Trick

Monthly Salary = 10,000

Monthly Expenditure = 6,000 + 2,500 = 8,500

Monthly Savings = 10,000 − 8,500 = 1,500

Yearly Savings (excluding birthday month) = 1,500 × 11 = 16,500

∴ The correct answer is ₹16,500.

Alternate Method

Given:

Monthly Salary = ₹10,000

House Rent = ₹6,000

Bills = ₹2,500

Calculations:

⇒ Total Monthly Expenses = 6,000 + 2,500 = ₹8,500

⇒ Monthly Savings = 10,000 − 8,500 = ₹1,500

⇒ Since he spends his savings in the birthday month, he only saves for 11 months.

⇒ Yearly Savings = 1,500 × 11

⇒ Yearly Savings = ₹16,500

∴ The correct answer is ₹16,500.

Additional Information

Savings Formula

Basic relation: Savings = Income − Expenditure. Net annual savings is the sum of savings across all 12 months.

Percentage Change in Savings

If income increases by x% and expenditure increases by y%, the new savings are calculated using the updated values of both.

Given:

194 + [6 × (1 - 6 + 5)] ÷ 12

Calculation:

194 + [6 × (1 - 6 + 5)] ÷ 12

⇒ 194 + [6 × (0)] ÷ 12

⇒ 194 + 0 ÷ 12

⇒ 194 + 0

⇒ 194

∴ The correct answer is option (4).

The correct answer is Charter Act of 1793.

Key Points

• The Charter Act of 1793 was instrumental in reinforcing the power of the Governor-General of India in certain critical matters.
• It authorised the Governor-General to override the decisions of his council in cases where the interests of the British Empire in India were at stake.
• This act was an extension of the Regulating Act of 1773 and Pitt’s India Act of 1784, further centralising power in the hands of the Governor-General.
• The provision was seen as a measure to ensure the efficient administration of British interests in India without unnecessary delays caused by council disagreements.
• The act also renewed the East India Company’s charter for another 20 years, maintaining its monopoly over trade with India.

Additional Information

• Charter Act of 1813:
• This act ended the East India Company’s trade monopoly in India, except for trade in tea and trade with China.
• It allowed Christian missionaries to propagate their religion in India.
• It allocated funds for the promotion of education in India.
• Regulating Act of 1773:
• This was the first attempt by the British Parliament to regulate the affairs of the East India Company in India.
• It created the position of the Governor-General of Bengal and established a council to assist him.
• Pitt's India Act of 1784:
• This act established a system of dual control by creating a Board of Control in Britain to supervise the East India Company’s administration in India.
• It distinguished between the company’s commercial and political functions.
• Centralisation of Power:
• The Charter Act of 1793 was part of the broader British strategy to centralise administrative power in India for better governance and control.
• This trend continued in subsequent acts, culminating in the complete transfer of power to the British Crown under the Government of India Act 1858.

The correct answer is Babur.

Key Points

• Babur, the founder of the Mughal Empire in India, died in 1530, leaving behind a vast empire.
• The empire stretched across northern India—from the Indus River in the west to Bihar in the east, and from the Himalayas in the north to Gwalior in the south.
• Babur defeated Ibrahim Lodi in the First Battle of Panipat (1526), which marked the establishment of the Mughal Empire.
• He was a descendant of Timur on his father's side and Genghis Khan on his mother's side, which gave legitimacy to his rule.
• Babur's autobiography, "Baburnama," provides detailed accounts of his life, campaigns, and the socio-political conditions of his time.

Additional Information

• Mughal Empire:
• The Mughal Empire ruled most of India and Pakistan from the early 16th to the mid-18th century.
• It is known for its significant contributions to art, architecture, culture, and centralized governance.
• Notable Mughal rulers include Akbar, Jahangir, Shah Jahan, and Aurangzeb.
• Babur's military tactics:
• Babur introduced modern artillery and gunpowder to Indian warfare during his campaigns.
• He employed the "Tulughma" strategy, dividing his army into flanking, center, and reserve units for better maneuverability.
• Baburnama:
• Babur wrote his autobiography, "Baburnama," in Chagatai Turkish, which was later translated into Persian.
• The book provides insights into Babur's thoughts, personal life, and the cultural landscape of his era.
• First Battle of Panipat:
• Fought in 1526 between Babur and Ibrahim Lodi, the Sultan of Delhi.
• This battle marked the end of the Delhi Sultanate and the beginning of Mughal rule in India.