Shortcut Trick

Total distance = 39 km. Ratio of Covered Distance to Remaining Distance = 5 : 4.

Total units = 5 + 4 = 9 units → 39 km. Covered distance = (5/9) × 39 = 21.666 km.

Time taken = 5 hours 5 minutes = 5 + 5/60 = 5 + 1/12 = 61/12 hours.

Speed = Distance ÷ Time = 21.666 ÷ (61/12) ≈ 4.26 km/hr.

∴ The correct answer is 4.3 km/hr.

Alternate Method

Given: Total distance = 39 km, Time = 5 hours 5 minutes, Covered distance = 5/4 × Remaining distance.

Let the remaining distance be x km.

⇒ Covered distance = 5x/4 km.

⇒ Total Distance = 5x/4 + x = 9x/4

⇒ 9x/4 = 39

⇒ x = (39 × 4) ÷ 9 = 156/9 = 52/3 km.

⇒ Covered Distance = 39 − 52/3 = (117 − 52)/3 = 65/3 km.

⇒ Time = 5 hours + 5/60 hours = 305/60 = 61/12 hours.

⇒ Speed = Distance ÷ Time = (65/3) ÷ (61/12) = (65/3) × (12/61) = 260/61 km/hr.

⇒ Speed ≈ 4.262 km/hr ≈ 4.3 km/hr.

∴ The correct answer is 4.3 km/hr.

Additional Information

Speed, Distance, and Time Relationship

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

Unit Conversion

To convert minutes to hours, divide by 60. To convert km/hr to m/s, multiply by 5/18.

Rounding Off Rules

If the second decimal digit is 5 or more, increase the first decimal digit by 1. Here, 4.26 becomes 4.3.

The Correct answer is ₹10 lakh crore.

Key Points

• The Asset Monetization Plan 2025-30 is a continuation of the government’s initiative to unlock value from its public sector assets and reinvest the proceeds in new infrastructure projects.
• The plan focuses on raising ₹10 lakh crore through the monetization of core assets in sectors like transportation, energy, and urban infrastructure.
• Monetization is carried out by leasing or selling assets, while the ownership of land and other strategic assets remains with the government.
• This initiative aligns with the government’s broader objective of fostering economic growth and infrastructure development.
• The revenue generated from this plan will be reinvested into new projects under the National Infrastructure Pipeline (NIP), which aims to modernize and expand India’s infrastructure.
• The focus is on public-private partnerships (PPPs), which help bring private sector efficiency and expertise to the management of these assets.
• The government had earlier announced the National Monetization Pipeline (NMP) for 2021-24, and this plan is an extension of that initiative.
• Through this plan, the government aims to achieve fiscal consolidation while boosting infrastructure investment.

Additional Information

• ₹25 lakh crore
• This amount might be considered for larger-scale plans or a longer timeline, but for the 2025-30 Asset Monetization Plan, the focus is on ₹10 lakh crore.
• ₹15 lakh crore
• Although plausible for other government initiatives, this is not the allocated amount for the Asset Monetization Plan 2025-30.
• ₹20 lakh crore
• Similar to the above, this amount does not correspond to the specified plan but could be part of a different financial strategy or target.

Shortcut Trick

Calculate the square of the difference: (a − b)² = (a² + b²) − 2ab = 132 − 72 = 60.

Calculate the square of the sum: (a + b)² = (a² + b²) + 2ab = 132 + 72 = 204.

Find the ratio of these squares: ((a − b)/(a + b))² = 60 / 204 = 5 / 17.

Take the square root to find the required value: (a − b) / (a + b) = √(5 / 17).

∴ The correct answer is √5/17.

Alternate Method

Given: a² + b² = 132, ab = 36, and a > b.

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

⇒ First, we find the numerator (a − b):

⇒ (a − b)² = a² + b² − 2ab = 132 − 2(36) = 132 − 72 = 60

⇒ Since a > b, (a − b) = √60

⇒ Next, we find the denominator (a + b):

⇒ (a + b)² = a² + b² + 2ab = 132 + 2(36) = 132 + 72 = 204

⇒ Assuming (a + b) is positive, (a + b) = √204

⇒ The required ratio is (a − b) / (a + b):

⇒ ((a − b) / (a + b)) = √60 / √204 = √(60 / 204)

⇒ Simplifying the fraction: 60 / 204 = (60 ÷ 12) / (204 ÷ 12) = 5 / 17

⇒ Ratio = √(5 / 17) = √5 / √17

∴ The correct answer is √5/17.

Additional Information

Algebraic Identity for Product

The relationship between the sum, difference, and product of two numbers is given by: (a + b)² − (a − b)² = 4ab.

Sum of Squares Identity

The sum of the squares of the sum and difference is: (a + b)² + (a − b)² = 2(a² + b²).

Square Root of Fractions

When taking the square root of a ratio, √(x/y) = √x / √y, where y ≠ 0.

The Correct answer is Satpura Hills.

Key Points

• The Narmada River originates from the Amarkantak Plateau, which is located in the Satpura Hills of Madhya Pradesh, India.
• The Narmada is the fifth-largest river in India and the largest west-flowing river in the country.
• It flows through the states of Madhya Pradesh, Maharashtra, and Gujarat before emptying into the Arabian Sea.
• The river is often referred to as the "Lifeline of Madhya Pradesh and Gujarat" due to its significance in providing water for agriculture, drinking, and electricity generation.
• It is also known for its cultural and religious significance, with many temples and ghats located along its banks.
• One of the prominent landmarks on the river is the Sardar Sarovar Dam, which is a multipurpose project aimed at irrigation, hydropower, and water supply.
• The Narmada Valley is rich in biodiversity and is home to a variety of flora and fauna, some of which are endemic to the region.

Additional Information

• Western Ghats
• The Western Ghats are a mountain range that runs parallel to the western coast of India.
• They are known for their rich biodiversity and have been declared a UNESCO World Heritage Site.
• Some major rivers originating from the Western Ghats include the Godavari, Krishna, and Kaveri.
• Vindhyachal
• The Vindhyachal range is a mountain range in central India, separating the northern and southern parts of the country.
• It is not the origin of the Narmada River but plays a significant role in Indian geography by forming a natural boundary.
• Aravalli
• The Aravalli Hills are one of the oldest mountain ranges in the world, located in western India.
• The range extends across Rajasthan, Haryana, and Gujarat.
• It is not related to the origin of the Narmada River but is known for its mineral deposits and ecological significance.

The Correct answer is Five Writs.

Key Points

• The Constitution of India empowers the Supreme Court (under Article 32) and the High Courts (under Article 226) to issue five types of writs for the enforcement of Fundamental Rights.
• The five writs mentioned in the Constitution are:
• Habeas Corpus: A writ to produce a person detained or imprisoned before the court to examine the legality of their detention.
• Mandamus: A writ issued to a public official, body, corporation, or government to perform a duty they are legally obligated to perform.
• Prohibition: A writ directed at a lower court or tribunal, preventing it from exceeding its jurisdiction or acting contrary to the law.
• Certiorari: A writ by which a higher court orders a lower court or tribunal to transfer a case for review or quashes its decision if it acted beyond its jurisdiction.
• Quo Warranto: A writ to challenge the legality of a person holding a public office without proper authority.
• These writs are significant tools to ensure the protection of Fundamental Rights under Part III of the Indian Constitution.
• The Supreme Court's power to issue writs is primarily for the enforcement of Fundamental Rights, making it a guardian of these rights.
• The High Courts, however, have a broader jurisdiction and can issue writs for other legal rights in addition to Fundamental Rights.

Additional Information

• Four Writs
• The concept of issuing writs is derived from the English Common Law, which initially included only four primary writs. However, the Indian Constitution explicitly mentions five writs.
• Four writs would exclude the writ of Quo Warranto, which is essential in ensuring that public offices are not held unlawfully.
• Six Writs
• The Indian Constitution does not mention six writs. The concept of writs in India is limited to the five types specifically listed in the Constitution under Article 32 and Article 226.
• Seven Writs
• The Constitution of India does not authorize the issuance of seven writs. The writs are limited to the five defined types, and the addition of extra writs is not part of the constitutional framework.

Shortcut Trick

Ratio of A : B : C : D = 10 : 4 : 8 : 5

Difference between C and B in units = 8 − 4 = 4 units

Given, 4 units = ₹24 ⇒ 1 unit = ₹6

A's share = 10 units = 10 × ₹6 = ₹60

∴ The correct answer is ₹60.

Alternate Method

Given: Ratio A:B:C:D = 10 : 4 : 8 : 5 and C − B = ₹24

Formula: Value of one unit = (Actual Difference) ÷ (Difference in Ratio parts)

⇒ Let the shares be 10x, 4x, 8x, and 5x.

⇒ 8x − 4x = 24

⇒ 4x = 24

⇒ x = 24 ÷ 4 = 6

⇒ Amount received by A = 10x = 10 × 6 = 60

∴ The correct answer is ₹60.

Additional Information

Concept of Ratio and Proportion

A ratio compares values. To find the actual value, multiply the ratio part by a constant 'x' which represents the value of a single unit.

Total Sum Calculation

Total Sum = (Sum of all ratio parts) × value of one unit. In this case: (10+4+8+5) × 6 = 27 × 6 = ₹162.

Proportional Division

If a sum S is divided in ratio a:b, then first part = [a/(a+b)] × S and second part = [b/(a+b)] × S.

Shortcut Trick

Weight of B = [Sum of (A + B) + Sum of (B + C)] − Sum of (A + B + C)

Weight of B = (2 × 39) + (2 × 48) − (3 × 45)

Weight of B = 78 + 96 − 135 = 174 − 135

Weight of B = 39 kg

∴ The correct answer is 39 kg.

Alternate Method

Given:

Average weight of A, B, and C = 45 kg

Average weight of A and B = 39 kg

Average weight of B and C = 48 kg

Formula Used:

Sum of values = Average × Number of observations

Calculations:

⇒ Total weight of A + B + C = 3 × 45 = 135 kg

⇒ Total weight of A + B = 2 × 39 = 78 kg

⇒ Total weight of B + C = 2 × 48 = 96 kg

⇒ Sum of (A + B) and (B + C) = 78 + 96 = 174 kg

⇒ This sum can be written as: (A + B + C) + B = 174 kg

⇒ 135 + B = 174

⇒ B = 174 − 135

⇒ B = 39 kg

∴ The correct answer is 39 kg.

Additional Information

Definition of Average

The average is the central value of a set of numbers, calculated by dividing the sum of all values by the total number of values.

Overlap Principle

When two sub-groups (like A&B and B&C) are combined and they share a common member (B), that member is added twice in the total sum of sub-groups.

Deviation Method

Averages can also be solved by checking the net deviation from the actual average. Sum of deviations from the mean is always zero.

The Correct answer is They won the title for the third time in seven seasons.

Key Points

• Vidarbha's performance in the Ranji Trophy 2024-25 was remarkable as they secured the title for the third time in seven seasons.
• This achievement highlights Vidarbha's consistent dominance and growing reputation in domestic cricket.
• The Ranji Trophy is India’s premier first-class cricket tournament, and winning it multiple times showcases the team's strong cricketing infrastructure and player development.
• Vidarbha’s earlier wins in the Ranji Trophy occurred in 2017-18 and 2018-19, making this their third overall title.
• Their success is attributed to the contributions of seasoned players, a strong domestic structure, and effective coaching staff.
• Vidarbha’s cricket board has invested in youth development and fostering new talent, which has paid off in the form of consistent performances.
• The team’s ability to perform under pressure and deliver in crucial matches is a testament to their mental strength and preparation.

Additional Information

• They won the title for the first time
• This option is incorrect as Vidarbha had already won the Ranji Trophy before, in the 2017-18 and 2018-19 seasons.
• Their first title win in 2017-18 was a historic moment for the team, marking their emergence on the domestic cricket scene.
• They lost the final to Kerala
• This option is incorrect as Vidarbha did not lose the final to Kerala in the 2024-25 season.
• In fact, they emerged as the champions, showcasing their dominance in domestic cricket.
• They did not qualify for the final
• This option is incorrect as Vidarbha not only qualified for the final but also went on to win the title.
• Their consistent performances throughout the tournament ensured their place in the final.

The Correct answer is Tuberculosis.

Key Points

• Tuberculosis (TB) is a highly contagious infectious disease caused by the bacterium Mycobacterium tuberculosis.
• The disease primarily affects the lungs, but it can also impact other parts of the body, such as the spine, kidneys, and brain.
• TB is one of the oldest known diseases in human history and continues to be a major cause of illness and death worldwide.
• It is typically spread through airborne particles when an infected person coughs, sneezes, or speaks.
• Symptoms of TB include persistent cough, fever, night sweats, weight loss, and fatigue.
• TB can be treated and cured with a combination of antibiotics, usually taken over a course of six months or longer.
• Efforts to combat TB include public health initiatives such as vaccination with the BCG vaccine and widespread screening programs.
• In 2025, John Green’s book likely explores the historical impact of TB, including its role in shaping public health systems and its representation in literature and culture.

Additional Information

• Influenza
• Influenza, commonly known as the flu, is caused by the influenza virus.
• It primarily affects the respiratory system and spreads through airborne droplets or contact with contaminated surfaces.
• Influenza pandemics, such as the Spanish Flu of 1918, have caused widespread fatalities.
• Vaccination is the primary method of prevention, and antiviral medications are used for treatment.
• Malaria
• Malaria is caused by parasites of the genus Plasmodium, transmitted through the bites of infected Anopheles mosquitoes.
• It is prevalent in tropical and subtropical regions, especially in Sub-Saharan Africa.
• Symptoms include fever, chills, headache, and vomiting.
• Malaria can be prevented with the use of mosquito nets, insect repellents, and antimalarial drugs.
• Cholera
• Cholera is an acute diarrheal disease caused by the bacterium Vibrio cholerae.
• It is commonly transmitted through contaminated water or food.
• Symptoms include severe dehydration, watery diarrhea, and vomiting.
• Improving access to clean water and sanitation is critical for preventing cholera outbreaks.

Decoding symbols:

Given: E + F – G x H ÷ K

E + F → E is the son of F.

F – G → F is the sister of G.

G x H → G is the wife of H.

H ÷ K → H is the father of K.

Thus, E is K's mother's sister's son.

Hence, the correct answer is "Option 1"

The Correct answer is Annie Besant and Bal Gangadhar Tilak.

Key Points

• The Home Rule Movement in India was started during World War I (1914-1918).
• The movement was pioneered by two prominent leaders: Annie Besant and Bal Gangadhar Tilak.
• The primary aim of the movement was to achieve self-government within the framework of the British Empire.
• Annie Besant founded the Home Rule League in September 1916 in Madras (now Chennai).
• Bal Gangadhar Tilak established his own Home Rule League in April 1916, focusing on Maharashtra, Karnataka, and central provinces.
• The movement sought to mobilize Indians for self-rule through constitutional means, promoting political education and awareness.
• Annie Besant, a British national, played a significant role in spreading the ideas of self-rule and garnered massive support through her writings in newspapers like "New India" and "Commonweal."
• Tilak, known as the “Father of Indian Unrest,” brought his strong nationalist ideals to the movement, emphasizing the need for India’s autonomy.
• The movement laid the foundation for future struggles for India's independence, inspiring widespread political consciousness.

Additional Information

• Mahatma Gandhi and Gopal Krishna Gokhale
• Mahatma Gandhi became a prominent leader in Indian politics later, especially during the Non-Cooperation Movement (1920-22) and the Civil Disobedience Movement (1930-34).
• Gopal Krishna Gokhale was a moderate leader and mentor to Gandhi but was not associated with the Home Rule Movement. He passed away in 1915, before the movement began.
• Lala Lajpat Rai and Bipin Chandra Pal
• Lala Lajpat Rai, known as the Lion of Punjab, was a part of the Lal-Bal-Pal trio but was not directly involved in the Home Rule Movement.
• Bipin Chandra Pal, a staunch nationalist, focused on the Swadeshi movement and other activities, rather than the Home Rule Movement.
• Jawaharlal Nehru and Subhas Chandra Bose
• Jawaharlal Nehru emerged as a major leader during the 1930s, especially in the context of the Indian National Congress.
• Subhas Chandra Bose became a significant figure in the Indian freedom struggle during the 1940s and was associated with the Indian National Army (INA).

The Correct answer is To shift the cursor to the next field or tab position.

Key Points

• The Tab key is a standard key on most computer keyboards, primarily used to move the cursor to the next field, section, or tab stop in a document or form.
• It is highly useful for navigating between input fields in online forms or applications, simplifying data entry tasks.
• In word processors like Microsoft Word, pressing the Tab key moves the cursor forward by a fixed indentation space, typically equivalent to five spaces or a predefined tab stop.
• The Tab key is also critical in programming, as it helps to create structured code by inserting indents for better readability and organization.
• Many software applications use the Tab key to cycle through interactive elements, such as buttons, menus, or text boxes, improving navigation and accessibility.
• In spreadsheets like Microsoft Excel, pressing the Tab key moves the active cell to the next column, facilitating horizontal data entry.
• The Tab key often works alongside the Shift key to move backward through fields or tabs, offering flexibility in navigation.
• On graphical user interfaces, the Tab key enhances user experience by allowing rapid movement between focusable elements without using a mouse.

Additional Information

• Option 1: To insert a forward slash
• The forward slash is typically inserted using the ‘/’ key, not the Tab key.
• This key is often used in URLs, file paths, and programming for division operations or directory navigation.
• Option 2: To remove text
• Text removal is generally performed using the Backspace or Delete keys, not the Tab key.
• The Backspace key deletes text to the left of the cursor, while the Delete key removes text to the right.
• Option 3: To close the active application
• Closing an active application is commonly done using keyboard shortcuts like Alt + F4 in Windows or Cmd + Q in macOS.
• The Tab key does not have any functionality related to application closure.

The Correct answer is ₹3,790 crore.

Key Points

• The Union Budget for 2025 allocated a total of ₹3,790 crore to the Ministry of Youth Affairs and Sports.
• This allocation reflects the government's commitment to promoting sports and youth development in India.
• The budget aims to enhance the implementation of initiatives under schemes such as Khelo India and Fit India Movement.
• It also focuses on strengthening infrastructure development for sporting activities across the country.
• The allocation will help in boosting sports facilities, athlete training programs, and youth engagement initiatives.
• The Ministry of Youth Affairs and Sports plays a pivotal role in fostering talent and promoting a sporting culture among the youth.
• Increased funding ensures better opportunities for India's representation in international sports events, including the Olympics, Commonwealth Games, and Asian Games.

Additional Information

• Key Focus of Union Budget 2025
• The Union Budget 2025 emphasized inclusive growth, with significant investments in healthcare, education, and sports.
• It prioritized human resource development by allocating funds for schemes promoting youth skill development and employment generation.
• Increased funding for the sports sector aligns with India's vision of becoming a global leader in sports.
• Other Ministries' Allocations
• The Ministry of Education received a substantial allocation to further the goals of the National Education Policy (NEP) 2020.
• The Ministry of Health saw an increase in funds to boost public health infrastructure and combat future pandemics.
• Role of Khelo India Scheme
• The Khelo India Scheme aims to identify and nurture young talent through structured training programs.
• It provides funding for building sports infrastructure and organizing multi-disciplinary sports events.
• This scheme plays a crucial role in achieving the objectives of the Ministry of Youth Affairs and Sports.

Shortcut Trick

Check for divisibility by 11 as the volume involves π (22/7).

Option (1) 308: 3 + 8 − 0 = 11 (Divisible by 11)

Option (2) 300: 3 + 0 − 0 = 3 (Not divisible)

Option (3) 307: 3 + 7 − 0 = 10 (Not divisible)

Option (4) 314: 3 + 4 − 1 = 6 (Not divisible)

∴ The correct answer is 308 cm³.

Alternate Method

Given: Total Surface Area (TSA) = 396 cm², Radius (r) = 7 cm, π = 22/7.

Formula Used: TSA = 2πr(h + r); Volume (V) = πr²h

⇒ 396 = 2 × (22/7) × 7 × (h + 7)

⇒ 396 = 44 × (h + 7)

⇒ h + 7 = 396 ÷ 44 = 9

⇒ h = 2 cm

⇒ Volume = πr²h = (22/7) × 7 × 7 × 2

⇒ Volume = 22 × 7 × 2 = 154 × 2 = 308 cm³

∴ The correct answer is 308 cm³.

Additional Information

Curved Surface Area of Cylinder

The lateral surface area excluding the top and bottom circles is 2πrh.

Area of Base/Top

The area of each circular face is πr².

Total Surface Area relation

TSA = CSA + 2 × Base Area = 2πrh + 2πr².

Shortcut Trick

In any quadrilateral, the angle formed by the bisectors of two adjacent angles is equal to half the sum of the other two remaining angles.

∠TES = (∠Q + ∠R) ÷ 2

∠TES = (52° + 44°) ÷ 2

∠TES = 96° ÷ 2 = 48°

∴ The correct answer is 48°.

Alternate Method

Given:

In quadrilateral QRST:

∠Q = 52°

∠R = 44°

The bisectors of ∠S and ∠T meet at E.

Formula Used:

The sum of all interior angles of a quadrilateral is 360°.

The sum of all interior angles of a triangle is 180°.

Calculations:

In quadrilateral QRST:

⇒ ∠Q + ∠R + ∠S + ∠T = 360°

⇒ 52° + 44° + ∠S + ∠T = 360°

⇒ 96° + ∠S + ∠T = 360°

⇒ ∠S + ∠T = 360° − 96° = 264°

Dividing both sides by 2:

⇒ (∠S + ∠T) ÷ 2 = 264° ÷ 2 = 132°

⇒ ∠S/2 + ∠T/2 = 132°

Since SE and TE are the angle bisectors of ∠S and ∠T respectively:

⇒ ∠EST = ∠S/2 and ∠ETS = ∠T/2

⇒ ∠EST + ∠ETS = 132°

In triangle TES:

⇒ ∠TES + ∠EST + ∠ETS = 180°

⇒ ∠TES + 132° = 180°

⇒ ∠TES = 180° − 132° = 48°

∴ The correct answer is 48°.

Additional Information

Angle Bisector Theorem in Quadrilaterals

The angle formed by the bisectors of two adjacent angles of a quadrilateral is equal to half the sum of the other two remaining angles. For adjacent angles A and B, the angle of intersection of their bisectors is (∠C + ∠D) ÷ 2.

Sum of Interior Angles

For any n-sided polygon, the sum of interior angles is given by (n − 2) × 180°. For a quadrilateral (n = 4), the sum is always 360°.

Opposite Angle Bisectors

The angle between the bisectors of two opposite angles of a quadrilateral is equal to half the difference of the other two angles.

The Correct answer is Legal Services Authorities Act, 1987.

Key Points

• The National Legal Services Authority (NALSA) was constituted under the Legal Services Authorities Act, 1987.
• The primary aim of NALSA is to ensure free legal aid to weaker sections of society and promote justice on the basis of equal opportunity.
• It works to organize Lok Adalats, which are informal courts that resolve disputes through conciliation and settlement.
• The Act emphasizes providing legal services to marginalized groups such as women, children, Scheduled Castes, Scheduled Tribes, and other vulnerable communities.
• Under this Act, State Legal Services Authorities were also created to implement policies and organize legal aid programs at the state level.
• It is an important law for ensuring compliance with Article 39A of the Indian Constitution, which mandates free legal aid to economically weaker sections and promotes equality before the law.
• The Act also empowers NALSA to conduct legal awareness campaigns to educate citizens about their rights and duties.

Additional Information

• Public Interest Litigation Act, 1990
• There is no specific law called the Public Interest Litigation Act, 1990. Public Interest Litigation (PIL) refers to a judicial process under which cases can be filed for protecting public interests.
• PILs are governed by various provisions of the Indian Constitution, especially Articles 32 and 226, which allow individuals to approach the Supreme Court or High Courts.
• This concept was introduced in the 1980s and is not linked to a specific act but rather to judicial activism.
• Advocates Act, 1961
• The Advocates Act, 1961 governs the legal profession in India and provides for the establishment of the Bar Council of India and State Bar Councils.
• It regulates the standards of professional conduct, etiquette, and legal education for advocates.
• This Act focuses on the administration and organization of the legal profession rather than providing legal aid services.
• Indian Bar Council Act, 1926
• The Indian Bar Council Act, 1926 was enacted to provide for the establishment of Bar Councils in different provinces and regulate the legal profession.
• It was a precursor to the Advocates Act, 1961 and laid the foundation for the legal profession in India.
• This Act does not deal with legal aid or the organization of Lok Adalats.

Given series: (Left) % 3 £ 3 & © * 3 & 7 7 3 7 % 4 8 © * 1 * 9 9 (Right)

According to the question, 

Required condition: Symbol - Number - Symbol

(Left) % 3 £ 3 & © *** 3 &** 7 7 3 7 % 4 8 © *** 1 *** 9 9 (Right)

Thus, there are four such numbers which are immediately preceded by a symbol and also immediately followed by a symbol.

Hence, "Option 3" is the correct answer.

Shortcut Trick

Use the ratio formula: CP ÷ MP = (100 − Discount%) ÷ (100 + Gain%).

Ratio CP : MP = (100 − 53) : (100 + 41) = 47 : 141.

Simplify the ratio: 47 : 141 = 1 : 3.

Since 1 unit (CP) = ₹1,301, then 3 units (MP) = 1,301 × 3 = ₹3,903.

∴ The correct answer is ₹3,903.

Alternate Method

Given: Cost Price (CP) = ₹1,301, Discount = 53%, Gain = 41%.

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

⇒ Selling Price (SP) = 1,301 × (100 + 41) ÷ 100 = 1,301 × 1.41 = ₹1,834.41

⇒ Marked Price (MP) = SP ÷ (1 − 0.53) = 1,834.41 ÷ 0.47

⇒ Marked Price (MP) = ₹3,903

∴ The correct answer is ₹3,903.

Additional Information

Marked Price and Discount

The Marked Price (MP) is the price printed on an item. Discount is always calculated on the MP to arrive at the Selling Price (SP). SP = MP × (100 − D%) / 100.

Relation between CP and MP

When both Profit% and Discount% are known, the direct relation is CP / MP = (100 − D) / (100 + P).

Shortcut Trick

For any cubic equation ax³ + bx² + cx + d = 0, the product of roots is given by −d/a.

In the given equation kx³ − 5x² − 12x + k = 0, the coefficient of x³ (a) is k and the constant term (d) is k.

Product of roots = −k ÷ k = −1.

∴ The correct answer is -1.

Alternate Method

Given:

The cubic equation is kx³ − 5x² − 12x + k = 0.

Formula Used:

For a standard cubic equation ax³ + bx² + cx + d = 0 with roots α, β, and γ:

Product of roots (αβγ) = −(Constant Term) / (Coefficient of x³) = −d/a

Calculations:

Comparing the given equation kx³ − 5x² − 12x + k = 0 with ax³ + bx² + cx + d = 0, we get:

⇒ a = k

⇒ b = −5

⇒ c = −12

⇒ d = k

Now, applying the Vieta's formula for the product of roots:

⇒ Product = −d / a

⇒ Product = −k / k

⇒ Product = −1

∴ The correct answer is -1.

Additional Information

Sum of Roots

For a cubic equation, the sum of roots (α + β + γ) is given by −b/a, which is −(coefficient of x²) ÷ (coefficient of x³).

Sum of Product of Roots Taken Two at a Time

The sum of the products of roots taken in pairs (αβ + βγ + γα) is given by c/a, which is (coefficient of x) ÷ (coefficient of x³).

Quadratic Roots Product

For a quadratic equation ax² + bx + c = 0, the product of roots is simply c/a.

Degree and Roots

According to the Fundamental Theorem of Algebra, a polynomial of degree n will have exactly n roots (including real and complex roots).

Shortcut Trick

Sum of interior angles of a regular polygon with n sides is (n − 2) × 180°.

Given, (n − 2) × 180° = 1260° ⇒ n − 2 = 7 ⇒ n = 9 sides.

Number of diagonals = n × (n − 3) ÷ 2 = 9 × (9 − 3) ÷ 2 = 27.

∴ The correct answer is 27 diagonals.

Alternate Method

Given:

Sum of interior angles of a regular polygon = 1260°

Formula Used:

1. Sum of interior angles of an n-sided polygon = (n − 2) × 180°
2. Number of diagonals of an n-sided polygon = n × (n − 3) ÷ 2

Calculations:

Let the number of sides of the regular polygon be n.

⇒ (n − 2) × 180° = 1260°

⇒ n − 2 = 1260° ÷ 180°

⇒ n − 2 = 7

⇒ n = 7 + 2

⇒ n = 9

Thus, the polygon is a regular nonagon (9-sided polygon).

Now, we calculate the number of diagonals:

⇒ Number of diagonals = n × (n − 3) ÷ 2

⇒ Number of diagonals = 9 × (9 − 3) ÷ 2

⇒ Number of diagonals = 9 × 6 ÷ 2

⇒ Number of diagonals = 54 ÷ 2

⇒ Number of diagonals = 27

Option Analysis:

Option (1) 35: If diagonals = 35, then n × (n − 3) ÷ 2 = 35 ⇒ n × (n − 3) = 70 ⇒ n = 10 (decagon). Sum of interior angles would be (10 − 2) × 180° = 1440° ≠ 1260°.

Option (2) 27: This is the correct option as calculated above for a 9-sided polygon (nonagon).

Option (3) 20: If diagonals = 20, then n × (n − 3) ÷ 2 = 20 ⇒ n × (n − 3) = 40 ⇒ n = 8 (octagon). Sum of interior angles would be (8 − 2) × 180° = 1080° ≠ 1260°.

Option (4) 44: If diagonals = 44, then n × (n − 3) ÷ 2 = 44 ⇒ n × (n − 3) = 88 ⇒ n = 11 (hendecagon). Sum of interior angles would be (11 − 2) × 180° = 1620° ≠ 1260°.

∴ The correct answer is 27 diagonals.

Additional Information

Sum of Exterior Angles

The sum of the exterior angles of any convex polygon is always 360°.

Each Interior Angle of a Regular Polygon

For a regular polygon with n sides, each interior angle is equal to ((n − 2) × 180°) ÷ n.

Each Exterior Angle of a Regular Polygon

For a regular polygon with n sides, each exterior angle is equal to 360° ÷ n.

The Correct answer is South Africa.

Key Points

• South Africa will host the 2025 G20 Summit, marking the first time the summit will be held on the African continent.
• This decision aligns with the G20’s aim to promote global inclusivity and expand representation of regions like Africa in global decision-making forums.
• South Africa, being a member of the G20, is one of the most influential nations in Africa, known for its strong economy and significant political role in the region.
• The summit will provide an opportunity to highlight Africa’s developmental challenges and potential, including topics like poverty alleviation, climate change, infrastructure development, and economic growth.
• This event will also serve to strengthen South Africa’s diplomatic ties with other G20 nations and showcase its leadership on the global stage.
• The hosting of the summit reflects the G20’s recognition of the importance of Africa in the global economy and geopolitics.

Additional Information

• Egypt
• Egypt is located in North Africa and is known for its ancient civilization and landmarks such as the Pyramids of Giza.
• Though Egypt has played a significant role in African diplomacy, it is not hosting the 2025 G20 Summit.
• Egypt is a member of the African Union but is not a permanent G20 member.
• Nigeria
• Nigeria, located in West Africa, is the most populous country in Africa and has one of the continent’s largest economies.
• It is a leading oil-producing nation but is not part of the G20 group.
• Although Nigeria is influential in African affairs, it is not hosting the 2025 G20 Summit.
• Kenya
• Kenya is situated in East Africa and is renowned for its wildlife tourism and contributions to regional diplomacy.
• It has a growing economy and is a member of the African Union, but like Nigeria, it is not part of the G20 group.
• Kenya is not hosting the 2025 G20 Summit.

Shortcut Trick

Initial Speed = 23 km/hr for 4.5 hours.

Increased Speed = 23 + 11 = 34 km/hr for 1 hour.

Average Speed = (Total Distance) ÷ (Total Time)

Average Speed = [(23 × 4.5) + (34 × 1)] ÷ (4.5 + 1) = (103.5 + 34) ÷ 5.5 = 137.5 ÷ 5.5 = 25 km/hr.

∴ The correct answer is 25 km/hr.

Alternate Method

Given:

Speed₁ = 23 km/hr, Time₁ = 4.5 hr

Speed₂ = 23 + 11 = 34 km/hr, Time₂ = 1 hr

Formula Used:

Average Speed = (D₁ + D₂) ÷ (T₁ + T₂)

Calculations:

⇒ Distance₁ = 23 × 4.5 = 103.5 km

⇒ Distance₂ = 34 × 1 = 34 km

⇒ Total Distance = 103.5 + 34 = 137.5 km

⇒ Total Time = 4.5 + 1 = 5.5 hr

⇒ Average Speed = 137.5 ÷ 5.5

⇒ Average Speed = 25 km/hr

∴ The correct answer is 25 km/hr.

Additional Information

Average Speed (Equal Distances)

When a person travels equal distances at speeds x and y, the average speed is 2xy ÷ (x + y).

Relative Speed

If two objects move in the same direction, relative speed = s₁ − s₂. In opposite directions, relative speed = s₁ + s₂.

Unit Conversion

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

Given: F, G, H, K, L, and M live on six different floors of a building, numbered 1 to 6 from bottom to top.

1. L lives on floor number 5.

2. H lives on a floor above L.

Since L is on floor 5, H must be on floor 6.

3. Only K lives below M.

This implies that M lives on floor 2 and K lives on floor 1. No one else lives below M.

4. F lives on an even-numbered floor.

The remaining empty floors are 3 and 4. The remaining people are F and G. The only remaining even-numbered floor is 4.

So, F must live on floor 4. This leaves G to live on floor 3.

From the final arrangement, G lives on floor 3. The people living below G are M (on floor 2) and K (on floor 1).

Therefore, Two people live below G.

Hence, the correct answer is "Option 1".

The logic followed here is:                                                                                                                                                                                                                   

Thus, the missing term in the series is 83.

Hence, the correct answer is "Option 3".

Shortcut TrickCompare the fractions: 9/11 (≈ 0.818), 10/27 (≈ 0.370), 31/38 (≈ 0.815), and 11/11 (= 1.000).A ratio where antecedent equals consequent (1 : 1) represents a whole unit, which is greater than any proper fraction (where numerator < denominator).∴ The correct answer is 11 : 11.Alternate MethodGiven: Ratios (1) 9/11, (2) 10/27, (3) 31/38, (4) 11/11Formula: Convert each ratio to decimal form or compare with 1.⇒ Ratio 1: 9 ÷ 11 = 0.8181...⇒ Ratio 2: 10 ÷ 27 = 0.3703...⇒ Ratio 3: 31 ÷ 38 = 0.8157...⇒ Ratio 4: 11 ÷ 11 = 1.0000⇒ Comparing values: 1.000 > 0.8181 > 0.8157 > 0.3703∴ The correct answer is 11 : 11.Additional InformationComparison of RatiosTo compare a/b and c/d, check the products (a × d) and (b × c). If ad > bc, then a/b > c/d.Types of RatiosA ratio a:b is a ratio of greater inequality if a > b, lesser inequality if a < b, and equality if a = b.Cross Multiplication MethodFor quick comparison without division, cross-multiply numerators with denominators of other fractions.

The Correct answer is Modern Education among Muslims.

Key Points

• The Aligarh Movement was initiated by Sir Syed Ahmed Khan, an eminent scholar and reformer, during the late 19th century in India.
• The movement primarily focused on providing modern education to the Muslim community, which lagged behind in educational and socio-economic progress.
• Sir Syed Ahmed Khan believed that modern education, particularly in the fields of science, technology, and English, was necessary to empower Muslims to compete with other communities in colonial India.
• He established the Mohammedan Anglo-Oriental College (MAO College) in 1875, which later became Aligarh Muslim University (AMU).
• The movement emphasized the adoption of Western-style education, which was seen as crucial for the growth and development of Muslims in the colonial era.
• It aimed to build bridges between the Muslim community and the British authorities, promoting harmony and cooperation.
• The Aligarh Movement also worked to eliminate prejudices and foster better understanding between different communities in India.
• The movement's success contributed to the establishment of a modern educational infrastructure for Muslims and inspired many other reform initiatives across India.

Additional Information

• Women's Rights
• While the Aligarh Movement did not primarily focus on women's rights, it indirectly contributed to the cause by promoting education, which eventually extended to women.
• Educational reforms initiated under the movement laid the groundwork for greater awareness regarding women's empowerment and their access to education.
• Hindu Revivalism
• Hindu Revivalism was an entirely separate movement that aimed at rejuvenating and promoting Hindu culture, values, and traditions.
• It was led by reformers such as Swami Dayanand Saraswati and organizations like the Arya Samaj.
• This movement was not related to the objectives of the Aligarh Movement, which focused on Muslim education.
• Abolition of Sati
• The Abolition of Sati was a significant reform led by social reformers like Raja Ram Mohan Roy in the early 19th century.
• This practice involved the self-immolation of widows on their husbands' funeral pyres, and its abolition in 1829 was one of the key milestones in Indian social reform.
• While both the abolition of Sati and the Aligarh Movement aimed at societal improvement, their focus and contexts were entirely different.

Shortcut Trick

Ratio of CP to SP for A is 100 : 40 (60% loss) ⇒ 5 : 2.

Ratio of CP to SP for B is 100 : 125 (25% profit) ⇒ 4 : 5.

Combined ratio (A_CP : C_CP) = (5 × 4) : (2 × 5) = 20 : 10 = 2 : 1.

Since 1 unit (C's price) = 62,616, then 2 units (A's price) = 62,616 × 2 = 1,25,232.

∴ The correct answer is ₹1,25,232.

Alternate Method

Given → Loss of A = 60%, Profit of B = 25%, Final Price (C) = 62,616. Formulas: SP = CP × (100 − Loss%) ÷ 100 | SP = CP × (100 + Profit%) ÷ 100.

⇒ Let the cost price for A be x.

⇒ B's cost price = x × (100 − 60) ÷ 100 = 0.40x.

⇒ C's cost price = 0.40x × (100 + 25) ÷ 100 = 0.40x × 1.25.

⇒ 62,616 = 0.5x.

⇒ x = 62,616 ÷ 0.5 = 1,25,232.

∴ The correct answer is ₹1,25,232.

Additional Information

Successive Transactions

When an item is sold multiple times, the final cost price can be calculated as Initial CP × (1 ± r₁/100) × (1 ± r₂/100) ... = Final Price.

Profit and Loss Percentage

Profit% = (Profit ÷ CP) × 100 and Loss% = (Loss ÷ CP) × 100. Both are always calculated on the Cost Price (CP) unless stated otherwise.

The Correct answer is Manoj Kumar Dubey.

Key Points

• Manoj Kumar Dubey was appointed as the CEO of the Indian Railway Finance Corporation (IRFC) in October 2024.
• The Indian Railway Finance Corporation (IRFC) is the dedicated financing arm of the Indian Railways, responsible for raising financial resources for railway projects.
• Manoj Kumar Dubey has a strong background in finance and management, making him a suitable choice for this critical role.
• IRFC plays a crucial role in supporting the infrastructure development and modernization of Indian Railways.
• Under his leadership, it is expected that IRFC will continue to focus on innovative financing mechanisms and efficient resource mobilization.
• His appointment aligns with the government’s vision to further enhance the efficiency and growth of Indian Railways through robust financial planning and execution.
• The appointment was made following due processes, ensuring that the candidate’s qualifications and expertise aligned with the demands of the role.

Additional Information

• Ajit Kumar Saxena
• Ajit Kumar Saxena is known for his expertise in the field of administration and operations, particularly in the public sector.
• He has served in various important roles but was not appointed as the CEO of IRFC.
• Vijaya Kishore Rahatkar
• Vijaya Kishore Rahatkar is a prominent leader known for her contributions in the field of social and political development.
• She has been associated with various governmental and non-governmental organizations, but her role is unrelated to IRFC.
• Paramesh Sivamani
• Paramesh Sivamani is recognized for his work in the technical and engineering domains.
• While his expertise is significant, he was not selected for the role of CEO of IRFC.

Shortcut Trick

For any reciprocal algebraic expression, if x + 1/x = k, then x² + 1/x² = k² − 2.

Given: x + 1/x = 33

Here, k = 33.

x² + 1/x² = 33² − 2 = 1089 − 2 = 1087.

∴ The correct answer is 1087.

Alternate Method

Given:

x + 1/x = 33

Formula Used:

The Algebraic Identity: (a + b)² = a² + 2ab + b²

Calculations:

⇒ x + 1/x = 33

Squaring both sides of the equation:

⇒ (x + 1/x)² = 33²

⇒ x² + (1/x)² + 2 × x × (1/x) = 1089

⇒ x² + 1/x² + 2 = 1089

⇒ x² + 1/x² = 1089 − 2

⇒ x² + 1/x² = 1087

∴ The correct answer is 1087.

Additional Information

Negative Reciprocal Identity

If x − 1/x = k, then x² + 1/x² = k² + 2.

Cubic Reciprocal Identity

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k.

Square of a Binomial

(a − b)² = a² + b² − 2ab, which is used to derive relationships between sums and differences of squares.

Shortcut Trick

Divide 13874 by 67 and find the remainder.

13874 ÷ 67 → Quotient = 207, Remainder = 5.

Smallest number to be added = Divisor − Remainder.

Value = 67 − 5 = 62.

∴ The correct answer is 62.

Alternate Method

Given: Number = 13874, Divisor = 67.

Formula Used: Required Number to add = Divisor − (Number mod Divisor)

⇒ Long division of 13874 by 67:

⇒ 67 × 2 = 134

⇒ 138 − 134 = 4 (bring down 7 → 47)

⇒ 67 × 0 = 0 (bring down 4 → 474)

⇒ 67 × 7 = 469

⇒ 474 − 469 = 5 (Remainder)

⇒ Smallest number to add = 67 − 5 = 62.

∴ The correct answer is 62.

Additional Information

Division Algorithm

Dividend = (Divisor × Quotient) + Remainder. For exact divisibility, the remainder must be 0.

Number to Subtract

To find the smallest number to subtract to make a number divisible, the answer is simply the Remainder itself.

Divisibility Rule of 67

There is no simple shortcut for 67 as it is a prime number; long division or the (Divisor − Remainder) method is the most efficient.

The logic followed here is.

Option (1) 'IL - FI':

Option (2) 'MJ - DF':

Option (3) 'NQ - KN':

Option (4) 'MP - JM':

Thus, option 2 'MJ - DF' is odd one.

Hence, the correct answer is "Option 2".

The correct answer is Nagabhata I.

Key Points

• Nagabhata I was the founder of the Gurjara-Pratihara dynasty, which ruled parts of northern and western India.
• He established the dynasty in the 8th century CE and set the foundation for a powerful empire.
• Nagabhata I is known for defending his kingdom against the Arab invasions, particularly the Arab forces from Sindh, which were a significant threat during that period.
• The Gurjara-Pratihara dynasty played a crucial role in halting the spread of Arab influence into the Indian subcontinent.
• The capital of Nagabhata I’s kingdom was located at Ujjain, a prominent cultural and religious center.
• The dynasty later grew into a major power under successors like Bhoja I and others.
• The Gurjara-Pratiharas were known for their patronage of art, architecture, and culture, contributing significantly to the development of North Indian temples.

Additional Information

• Vatsaraja
• Vatsaraja was a ruler of the Gurjara-Pratihara dynasty, but he was not its founder.
• He is known for his significant military campaigns and ambitions to expand the empire.
• During his reign, he clashed with the Pala dynasty and the Rashtrakutas, which were other major powers at the time.
• Gopala
• Gopala was the founder of the Pala dynasty, not the Gurjara-Pratihara dynasty.
• He was elected as a king by the chiefs of Bengal in the 8th century CE and established the Pala rule.
• The Pala dynasty was known for its contribution to Buddhism and its patronage of the famous Vikramashila and Nalanda universities.
• Bhoja
• Bhoja was a later ruler of the Gurjara-Pratihara dynasty, known for expanding the empire to its zenith.
• He is often referred to as Bhoja I, and his reign marked the peak of the dynasty’s power and influence.
• Bhoja was a great patron of art and architecture, and he contributed to the development of temple architecture.

The Correct answer is Manipur.

Key Points

• Manipur came under President's Rule in January 2025 due to ongoing ethnic violence and the resignation of its Chief Minister.
• The ethnic violence in Manipur is primarily rooted in tensions between the Meitei community and the Kuki-Zomi tribes.
• Manipur is a state in northeastern India, known for its diverse cultural heritage and significant tribal population.
• The application of President's Rule is governed by Article 356 of the Indian Constitution, which allows the central government to take control of a state in case of a breakdown of constitutional machinery.
• During President's Rule, the Governor assumes responsibility for the administration, and the state legislature is either suspended or dissolved.
• Manipur has been a hotspot for ethnic and territorial disputes due to its complex socio-political landscape.
• The situation escalated further in 2025, necessitating intervention from the central government to restore law and order.
• The central government often uses President’s Rule as a measure of last resort to stabilize states facing severe crises.

Additional Information

• Tripura
• Tripura is a northeastern Indian state, known for its cultural diversity and large tribal population.
• It is bordered by Bangladesh and is recognized for its unique cultural and historical significance.
• Tripura has had a history of insurgency and ethnic tensions, but these have largely diminished in recent years.
• It is famous for its Unakoti sculptures and Tripura Sundari Temple.
• Assam
• Assam is known for its tea plantations and rich biodiversity, including the Kaziranga National Park.
• It has faced ethnic violence in the past, particularly related to migration and land disputes, but was not under President's Rule in January 2025.
• Assam is the gateway to the northeastern region of India, with significant importance in terms of its natural resources and strategic location.
• Nagaland
• Nagaland is another northeastern state, famous for its Hornbill Festival and vibrant tribal culture.
• The state has witnessed insurgency and ethnic conflicts, but it was not involved in the specific events of January 2025.
• Nagaland is known for its tribal diversity, with over 16 major tribes.
• It is a mountainous state with a rich tradition of crafts and community life.

Shortcut Trick

Ratio of Selling Prices: Loss 10% ⇒ 90 units and Profit 68% ⇒ 168 units.

Given: 90 units = &rupee;2,03,700.

Value of 1 unit = 2,03,700 ÷ 90 = 2,263.

Required SP = 168 units × 2,263 = &rupee;3,80,184 is not in options, recalculating: 20370 ÷ 9 = 2,263.33...

Multiplier method: SP = (2,03,700 ÷ 90) × 168 = 2,263.33... × 168 = &rupee;3,80,240.

∴ The correct answer is &rupee;3,80,240.

Alternate Method

Formulas: CP = [SP × 100] ÷ [100 − Loss%], New SP = [CP × (100 + Profit%)] ÷ 100.

⇒ Step 1: Find the Cost Price (CP) of the car.

⇒ CP = (2,03,700 × 100) ÷ (100 − 10) = 2,03,700 × 100 ÷ 90 = &rupee;2,26,333.33...

⇒ Step 2: Calculate the New Selling Price for 68% profit.

⇒ New SP = 2,26,333.33... × (168 ÷ 100) = 2,263.33... × 168.

⇒ New SP = &rupee;3,80,240.

∴ The correct answer is &rupee;3,80,240.

Additional Information

Cost Price & Selling Price Relationship

When an object is sold at two different conditions, CP remains constant. Ratio of SP₁:SP₂ = (100 ± P/L₁):(100 ± P/L₂).

Profit and Loss Percentages

Profit% and Loss% are always calculated on the Cost Price unless stated otherwise in the question.

Shortcut Trick

Effective CI rate for 2 years at 5% = 5 + 5 + (5 × 5) / 100 = 10.25%.

Effective SI rate for 2 years at 5% = 5 × 2 = 10%.

Given, 10.25% corresponds to ₹102.5.

⇒ 10% will correspond to (102.5 ÷ 10.25) × 10 = ₹100.

∴ The correct answer is ₹100.

Alternate Method

Given:

Rate (R) = 5% p.a.

Time (T) = 2 years

Compound Interest (CI) = ₹102.5

Formula Used:

CI = P × [(1 + R/100)^T − 1]

SI = (P × R × T) ÷ 100

Calculations:

⇒ 102.5 = P × [(1 + 5/100)² − 1]

⇒ 102.5 = P × [(1.05)² − 1]

⇒ 102.5 = P × [1.1025 − 1]

⇒ 102.5 = P × 0.1025

⇒ P = 102.5 ÷ 0.1025 = ₹1000

Now, calculate Simple Interest (SI):

⇒ SI = (1000 × 5 × 2) ÷ 100

⇒ SI = 10000 ÷ 100

⇒ SI = ₹100

∴ The correct answer is ₹100.

Additional Information

Difference between CI and SI

For a period of 2 years, the difference (D) between CI and SI is given by: D = P × (R/100)².

Effective Rate of Interest

For 2 years, effective CI rate = x + y + (xy/100)%, where x and y are rates for the 1st and 2nd years.

Compound Interest Formula

Amount (A) = P(1 + R/100)ⁿ, where CI = A − P.

The Correct answer is All India Muslim Personal Law Board.

Key Points

• The All India Muslim Personal Law Board (AIMPLB) was established in 1973.
• It is a non-governmental organization that aims to protect and promote the application of Islamic personal laws (Shariat) for Muslims in India.
• The organization played a pivotal role in the protests against the Waqf (Amendment) Act of 2025, terming it as "unconstitutional and undemocratic."
• AIMPLB has been actively involved in issues related to Muslim personal laws, inheritance, marriage, divorce, and maintenance under the purview of the Muslim Personal Law (Shariat) Application Act, 1937.
• It frequently advocates for the autonomy of Muslim institutions and opposes interference in religious matters by the government.
• The protests led by AIMPLB in 2025 were part of its broader mission to safeguard the rights and interests of the Muslim community in India.
• The organization comprises members from various schools of Islamic thought, including Sunnis, Shias, and other smaller sects, ensuring representation across the community.

Additional Information

• All India Shia Personal Law Board
• The All India Shia Personal Law Board (AISPLB) was formed in 2005 to address the specific issues of the Shia community in India.
• It operates independently of the AIMPLB and focuses on matters related to Shia jurisprudence, customs, and traditions.
• Although it advocates for Shia rights, it was not at the forefront of the protests against the Waqf (Amendment) Act.
• Imarat-e-Shariah
• The Imarat-e-Shariah is a socio-religious organization based in Patna, Bihar.
• It primarily works for the welfare of the Muslim community in states like Bihar, Jharkhand, and Odisha.
• It provides services such as Islamic education, dispute resolution, and welfare programs but was not involved in leading the nationwide protests in 2025.
• Jamiat Ulema-e-Hind
• The Jamiat Ulema-e-Hind is one of the oldest Islamic organizations in India, established in 1919.
• It primarily focuses on political and social issues affecting Muslims in India.
• While it has participated in various movements, the leadership of protests against the Waqf (Amendment) Act was not attributed to this organization.

Given: 

Mr. XYZ starts from Point A and drives 15 km towards the west.

He then takes a left turn, drives 11 km, turns left and drives 19 km.

He then takes a left turn and drives 16 km. He takes a final left turn, drives 4 km and stops at Point P.

Thus, he drive 5 km to the south in order to reach Point A again.

Hence, the correct answer is "Option 2".

Given: Seven people, A, B, L, M, N, S, and T are sitting in a row, facing north.

Only three people sit between A and S. M sits to the immediate left of S.

No one sits to the right of T. Only two people sit between T and M. N sits to the immediate right of L.

Thus, Only two people sit between B and N.

Hence, the correct answer is "option 1".

The Correct answer is high water table.

Key Points

• Sub-irrigation is a method of irrigation where water is supplied directly to the root zone by raising the water table.
• This technique is particularly beneficial in areas with a high water table, as it allows plants to access water naturally through capillary action.
• It minimizes water evaporation and runoff, making it more efficient and environmentally friendly.
• Regions with a high water table are ideal for sub-irrigation as water is readily available just below the surface.
• This method reduces the need for complex irrigation infrastructure and is suitable for crops that thrive with consistent moisture levels.
• India has several regions with high water tables, such as parts of the Indo-Gangetic Plain, where sub-irrigation can be effectively practiced.

Additional Information

• Sandy soil
• Sandy soil is characterized by large particles and poor water retention capacity.
• Sub-irrigation is not effective in sandy soils as water cannot be held near the root zone due to its high permeability.
• Crops in sandy soils usually require surface or sprinkler irrigation systems for optimal growth.
• Low soil fertility
• Low soil fertility refers to the lack of essential nutrients needed for plant growth.
• This condition is unrelated to the water table and sub-irrigation; it requires soil amendment techniques such as fertilizer application or organic matter incorporation.
• Low water table
• Areas with a low water table are unsuitable for sub-irrigation because water is not readily available near the surface.
• Such regions often require alternative irrigation methods like drip irrigation or canal irrigation.

Shortcut Trick

Assume a base Average Expenditure of ₹300.

Calculate deviations from ₹300: −50, 0, −25, +25, +50.

Sum of deviations = (−50 + 50) + (−25 + 25) + 0 = 0.

Net change in average = 0 ÷ 5 = 0.

Final Average = 300 + 0 = ₹300.

∴ The correct answer is ₹300.

Alternate Method

Given:

Expenditure on Monday = ₹250

Expenditure on Tuesday = ₹300

Expenditure on Wednesday = ₹275

Expenditure on Thursday = ₹325

Expenditure on Friday = ₹350

Formula Used:

Average = (Sum of all observations) ÷ (Total number of observations)

Calculations:

⇒ Total Expenditure = 250 + 300 + 275 + 325 + 350

⇒ Total Expenditure = ₹1500

⇒ Number of Days = 5

⇒ Average Daily Expenditure = 1500 ÷ 5

⇒ Average Daily Expenditure = ₹300

∴ The correct answer is ₹300.

Additional Information

Arithmetic Mean

The basic average, calculated by dividing the sum of a set of numbers by the count of those numbers. Formula: Average = Σx ÷ n.

Combined Average

The average of two or more groups combined. Formula: Combined Avg = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Average of Consecutive Numbers

For any sequence in Arithmetic Progression (AP), the average is simply (First Term + Last Term) ÷ 2.

The pattern followed in both pairs is a consistent shift of (+2, +2, -5).

For: ICK : KEF

For: HDW : JFR

Now let's check all the options with this pattern.

Option 1: GGP : IJK

Option 2: VJF : XLA

Option 3: KLR : MNN

Option 4: RFM : TIH

Hence, the correct answer is Option 2

The correct answer is Pushyamitra.

Key Points

• Pushyamitra was the founder of the Shunga Dynasty in ancient India.
• He is historically known for overthrowing the Mauryan dynasty and establishing his rule around 185 BCE.
• Pushyamitra Shunga was a Brahmin general in the Mauryan Empire before he ascended to power.
• He is believed to have engaged in conflicts with the Bactrian-Greek ruler Demetrius I, who invaded parts of northern India during his reign.
• Demetrius I's campaigns were aimed at expanding the Indo-Greek territories, leading to confrontations with local rulers, including Pushyamitra.
• The historical records, including texts like the Milindapanha and works by classical historians, suggest that these invasions were a significant challenge for the Shunga rulers.
• Pushyamitra's reign marked the decline of the Buddhist influence propagated by the Mauryan rulers and a resurgence of Brahmanical practices.

Additional Information

• Harsha
• Harsha was an emperor who ruled northern India during the 7th century CE.
• He is known for his reign of peace, prosperity, and revival of Hinduism and Buddhism.
• Harsha was not contemporary to Demetrius or Pushyamitra, as his rule occurred much later.
• Nahapana
• Nahapana was a ruler of the Western Kshatrapas, a dynasty of Indo-Scythian origin.
• He ruled during the early centuries of the Common Era, much after the time of Demetrius and Pushyamitra.
• Hence, there was no direct conflict between Nahapana and Demetrius.
• Simuka
• Simuka was the founder of the Satavahana Dynasty, ruling parts of South India.
• His reign was not contemporaneous with Demetrius, and his kingdom was geographically distant from the Indo-Greek territories.

The Correct answer is Green box.

Key Points

• The PM-KISAN scheme is a direct income support scheme launched by the Government of India to provide financial assistance to farmers.
• Under the World Trade Organization's (WTO) Agreement on Agriculture, subsidies are classified into different "boxes" based on their impact on trade and production.
• The Green Box includes subsidies that have minimal or no trade-distorting effects on production and are considered permissible under WTO rules.
• PM-KISAN falls under the Green Box because it involves direct income transfers to farmers without linking the payments to the production of any specific crop or agricultural output.
• The scheme provides Rs. 6,000 annually in three equal installments to eligible farmers, ensuring a steady source of income for agricultural households.
• Green Box subsidies are typically government-funded and do not involve price support, making them compliant with WTO regulations.
• This classification ensures that the PM-KISAN scheme does not violate international trade norms and supports farmers in a non-discriminatory manner.

Additional Information

• Red Box
• Red Box subsidies are prohibited under WTO rules as they have significant trade-distorting effects.
• These include measures such as export subsidies that directly affect global trade and production.
• Amber Box
• Amber Box subsidies are considered trade-distorting but are subject to reduction commitments under WTO.
• Examples include price support programs and subsidies linked to production levels.
• Blue Box
• Blue Box subsidies are a subset of Amber Box but are exempt from reduction commitments under specific conditions.
• These subsidies are linked to production-limiting programs and aim to reduce overproduction.

The Correct answer is 1530.

Key Points

• In 1530, Goa became the capital of the Portuguese commercial empire in India.
• The Portuguese first arrived in India in 1498, when Vasco da Gama landed on the Malabar coast.
• They established their presence in Goa after capturing it from the Sultan of Bijapur in 1510.
• Goa was strategically chosen as the capital due to its ideal location for maritime trade and its strong coastal defenses.
• The city of Goa became the hub of Portuguese administration, trade, and missionary activities in India during the colonial period.
• Under Portuguese rule, Goa flourished as a center for trade in spices, textiles, and other goods, connecting Europe and Asia.
• Goa remained the capital of Portuguese India until India's independence and the eventual liberation of Goa in 1961.
• Portuguese influence can still be seen in Goa's architecture, culture, and cuisine.

Additional Information

• Option 2 (1390)
• No significant historical events related to Goa's establishment as the Portuguese capital occurred in 1390.
• During this period, Goa was under the control of various Indian rulers, such as the Kadamba dynasty and later the Bahmani Sultanate.
• Option 3 (1659)
• By 1659, Goa had already been the Portuguese capital for over a century.
• This date is not relevant to the establishment of Goa as the Portuguese capital but may be associated with other historical events in Portuguese India.
• Option 4 (1410)
• In 1410, Goa was not under Portuguese control. It was ruled by local dynasties before being captured by the Sultan of Bijapur.
• The Portuguese arrived in India much later, in the late 15th century.

The Correct answer is 9 States and 4 Union Territories.

Key Points

• As per the Annual Report 2022-23 of the Ministry of Home Affairs, India has a coastline that is spread across 9 States and 4 Union Territories (UTs).
• The Indian coastline spans approximately 7,516.6 km, including the mainland and islands.
• The 9 coastal states are: Gujarat, Maharashtra, Goa, Karnataka, Kerala, Tamil Nadu, Andhra Pradesh, Odisha, and West Bengal.
• The 4 coastal Union Territories are: Andaman and Nicobar Islands, Lakshadweep, Puducherry, and Daman and Diu.
• Coastal regions play a significant role in India's economy, as they are hubs for port activities, fishing, tourism, and industries.
• The coastline also supports rich biodiversity, including mangroves, coral reefs, and marine ecosystems.
• Important ports along the Indian coastline include Mumbai Port, Chennai Port, Visakhapatnam Port, and Kochi Port.
• The Ministry of Home Affairs oversees the security of India's coastline through agencies such as the Indian Coast Guard and the Marine Police.

Additional Information

• 10 States and 5 Union Territories
• This is incorrect because India has only 9 coastal states, not 10.
• The number of coastal Union Territories is also limited to 4, not 5.
• 11 States and 6 Union Territories
• This option is incorrect as India does not have 11 coastal states, nor does it have 6 coastal Union Territories.
• 8 States and 3 Union Territories
• This is incorrect because the total number of coastal states is 9, not 8.
• Similarly, there are 4 coastal Union Territories, not 3.

The pattern can be summarized as (-5, -5, -5, -5)

For: YAGK : RTZD

For**: WYEI : PRXB**

Applying the same logic to BDJN:

Thus, BDJN is related to UWCG.

Hence, the correct answer is "Option 3".

Shortcut Trick

Let Total Capacity of the tank be 120 units (LCM of 60 and 40).

Efficiency of Pipe C = 2 units/min and Pipe D = 3 units/min.

Average efficiency for total time T = (Efficiency of D × 0.5) + (Efficiency of C+D × 0.5).

Average efficiency = (3 × 0.5) + (5 × 0.5) = 1.5 + 2.5 = 4 units/min.

Total Time = 120 ÷ 4 = 30 minutes.

∴ The correct answer is 30 min.

Alternate Method

Given: Filling time for Pipe C = 60 min, Pipe D = 40 min.

Let the total time taken to fill the tank be T minutes.

⇒ Time for which only Pipe D works = T/2

⇒ Time for which Pipes C and D work together = T/2

⇒ Work done = (Efficiency of D × T/2) + (Efficiency of C+D × T/2) = 120

⇒ (3 × T/2) + ((2 + 3) × T/2) = 120

⇒ 1.5T + 2.5T = 120

⇒ 4T = 120

⇒ T = 30 min

∴ The correct answer is 30 min.

Additional Information

Pipes and Cisterns Efficiency

The efficiency of a pipe is inversely proportional to the time it takes to fill a tank. Efficiency = Total Work ÷ Time.

Combined Pipe Formula

If two pipes fill a tank in x and y hours, the time taken together is (x × y) ÷ (x + y) hours.

Inlet and Outlet Pipes

Inlet pipes have positive efficiency, while outlet (leakage) pipes have negative efficiency when calculating net flow.

The Correct answer is For undiscovered elements.

Key Points

• Dmitri Mendeleev, the Russian chemist, is credited with the creation of the first widely recognized periodic table.
• Mendeleev arranged the elements in order of their increasing atomic weights and grouped them based on similar chemical properties.
• While arranging, he noticed gaps in the periodic table and intentionally left them for undiscovered elements.
• He predicted the existence of these elements and their properties, long before they were discovered.
• Examples of elements discovered later that fit into these gaps include gallium (Ga), scandium (Sc), and germanium (Ge).
• This approach demonstrated the predictive power of the periodic table and highlighted its importance in understanding chemical behavior.
• The gaps ensured the periodic table remained organized and followed the periodic law, which states that the properties of elements are periodic functions of their atomic weights (later modified to atomic numbers).

Additional Information

• To make the table look symmetrical
• Mendeleev did not leave gaps for aesthetic purposes or symmetry; his focus was on the scientific rationale behind the arrangement of elements.
• The periodic table's structure is determined by chemical properties and atomic weights (or atomic numbers), not symmetry.
• To include isotopes
• Mendeleev's periodic table was based on atomic weight, not isotopes. The concept of isotopes was introduced later by Frederick Soddy in the early 20th century.
• Isotopes are variants of elements with the same number of protons but different numbers of neutrons, and they were not part of Mendeleev's original table.
• To avoid repetition of elements
• Mendeleev's periodic table did not have repetition of elements; each element had a unique place based on its atomic weight and chemical properties.
• The gaps were for elements yet to be discovered, not to prevent repetition.

Shortcut Trick

The Mode is simply the value that appears most frequently in a data set.

Scan the data for repetitions: 43 appears 4 times, while 53 appears 3 times.

Other numbers like 42 and 54 appear only 2 times each.

Since 43 has the highest frequency, it is the mode.

∴ The correct answer is 43.

Alternate Method

Given: Data set = {53, 47, 43, 42, 52, 54, 54, 51, 42, 53, 53, 48, 46, 43, 43, 40, 43, 41}

Formula: Mode = Value with the maximum frequency.

To find the mode, we calculate the frequency of each observation:

⇒ Frequency of 40 = 1

⇒ Frequency of 41 = 1

⇒ Frequency of 42 = 2

⇒ Frequency of 43 = 4

⇒ Frequency of 46 = 1

⇒ Frequency of 47 = 1

⇒ Frequency of 48 = 1

⇒ Frequency of 51 = 1

⇒ Frequency of 52 = 1

⇒ Frequency of 53 = 3

⇒ Frequency of 54 = 2

⇒ The observation with the maximum frequency is 43 (frequency = 4).

∴ The correct answer is 43.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship between the three measures of central tendency is: Mode = 3 × Median − 2 × Mean.

Bimodal and Multimodal Data

If two values have the same maximum frequency, the data is bimodal. If more than two values have the same maximum frequency, it is multimodal.

Median

The Median is the middle value when data is sorted. For an even number of observations (n), it is the average of the (n/2)^th and (n/2 + 1)^th terms.

The pattern can be summarized as (-7, -7, -7, -7).

Pair 1: MQIL : FJBE

Pair 2: OSKN : HLDG

Applying the same logic to QUMP:

Thus, QUMP is related to JNFI.

Hence, the correct answer is "Option 4".

Given equation: 35 − 112 × 84 ÷ 48 + 75 = ?

According to the question, after '+' and '−' are interchanged and '×' and '÷' are interchanged:

35 − 112 × 84 ÷ 48 + 75 = ? ⇒ 35 + 112 ÷ 84 × 48 - 75 = ?

⇒ 35 + 112 ÷ 84 × 48 - 75 = ?

⇒ 35 + 1.33 × 48 - 75 = ?

⇒ 35 + 64 - 75 = ?

⇒ 99 - 75 = ?

⇒ 24 = ?

Hence, "Option 3" is the correct answer.

The pattern followed here is.

Thus, the missing term in the series is QIW 144.

Hence, the correct answer is Option 1.

The Correct answer is System of units.

Key Points

• The system of units is a standardized framework used for the measurement of physical quantities.
• It includes both base units (fundamental units) and derived units (units derived from the base units through mathematical relationships).
• The most widely used system of units is the International System of Units (SI), which is globally recognized.
• Base units in the SI system include the meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity).
• Derived units, such as newton (force), joule (energy), and watt (power), are formed by combining base units according to specific equations.
• Using a standardized system ensures consistency, accuracy, and ease of communication in scientific and technical fields worldwide.
• The system of units is essential for conducting research, industrial processes, and global trade where precise measurements are required.

Additional Information

• Scientific model
• A scientific model is a representation of a system, concept, or phenomenon used to explain and predict its behavior.
• Examples include the Bohr model of the atom, the standard model in particle physics, and the climate models used to study weather patterns.
• It is not directly related to the units of measurement.
• Universal constant system
• The term universal constant system is not a formally recognized concept in physics.
• However, there are universal constants, such as the speed of light (c), gravitational constant (G), and Planck's constant (h), which are fundamental to the laws of physics.
• These constants are utilized within the framework of the system of units but do not constitute a separate system.
• Measurement set
• The term measurement set is a generic phrase and does not represent a formalized concept in physics or metrology.
• It could refer to a collection of measured data or instruments, but it is not equivalent to the system of units.

Given:

60% of 40 and (3/5) of 15

Formula Used:

Percentage calculation: (X% of Y) = (X × Y) / 100

Fraction of a number: (P/Q) × N

Difference = Value 1 - Value 2

Calculation:

60% of 40 = (60 × 40) / 100

⇒ (60 × 40) / 100 = 2400 / 100 = 24

(3/5) of 15 = (3 × 15) / 5

⇒ (3 × 15) / 5 = 45 / 5 = 9

Difference = 24 - 9

⇒ 24 - 9 = 15

The difference is 15.

The correct answer is 4.93 out of 5.

Key Points

• The Data Governance Quality Index (DGQI) 2.0 is a tool developed to assess the data management practices of government departments.
• The Department of Rural Development achieved a remarkable score of 4.93 out of 5 in Q4 of 2023-24, indicating strong data governance practices.
• The DGQI framework evaluates departments on various parameters, including data quality, standards, security, integration, and accessibility.
• This high score reflects the department's commitment to efficient data management, transparency, and accountability in its operations.
• The Department of Rural Development plays a crucial role in implementing flagship programs like MGNREGS (Mahatma Gandhi National Rural Employment Guarantee Scheme) and PMAY-G (Pradhan Mantri Awaas Yojana - Gramin), which require robust data systems.
• Such scores are indicative of the department's efforts towards leveraging data-driven decision-making to improve service delivery and governance.
• DGQI assessments are part of the government's initiative to enhance e-governance and ensure better utilization of data across various schemes.

Additional Information

• Data Governance Quality Index (DGQI)
• The DGQI is a framework introduced by NITI Aayog to ensure that data is efficiently managed and utilized by government departments.
• The framework assesses departments on 6 key pillars: Data Quality, Data Standards, Data Security, Data Use Cases, Data Integration, and Data Accessibility.
• DGQI 2.0 builds on the earlier version and incorporates more advanced metrics for data governance.
• Department of Rural Development
• It is responsible for implementing major rural development schemes in India, including MGNREGS, PMAY-G, and NRLM (National Rural Livelihoods Mission).
• The department focuses on improving rural infrastructure, generating employment, and alleviating poverty.
• A strong data governance system helps the department track progress, identify gaps, and improve the efficiency of its programs.
• Importance of High DGQI Scores
• High scores reflect adherence to best practices in data governance, ensuring data reliability and security.
• They also signify the department's readiness for integrated digital systems and data-driven policy-making.
• Such scores can serve as benchmarks for other departments striving for better data governance.

Shortcut Trick

Net efficiency = Filling efficiency − Emptying efficiency.

Let Total Work = LCM(15, 40) = 120 units.

Efficiency: Pipe A = +8, Pipe B = −3 → Combined = +5 units/hr.

Required Work = 1/3 × 120 = 40 units.

Time = 40 ÷ 5 = 8 hours.

∴ The correct answer is 8 hours.

Alternate Method

Given: Filling time = 15 hours, Emptying time = 40 hours.

Formula Used: Efficiency = Total Work ÷ Time; Time = Work ÷ Efficiency.

⇒ Net efficiency of both pipes = 8 − 3 = 5 units/hr.

⇒ Capacity to be filled = 1/3 × 120 = 40 units.

⇒ Time required = 40 ÷ 5 = 8 hours.

∴ The correct answer is 8 hours.

Additional Information

Pipes and Cisterns Concept

Filling pipes have positive efficiency, while outlet or leakage pipes have negative efficiency. Total capacity is typically assumed as the LCM of individual times.

Net Work Formula

If pipe A fills in x hrs and pipe B empties in y hrs, net work done in 1 hr = (1/x − 1/y). Time to fill completely = (xy)/(y − x).

Shortcut Trick

Total Interest Percentage = (Interest ÷ Principal) × 100

Total Interest % = (700 ÷ 1400) × 100 = 50%

Rate of Interest per annum = Total Interest % ÷ Time

Rate (R) = 50% ÷ 5 = 10%

∴ The correct answer is 10%.

Alternate Method

Given:

Principal (P) = ₹1,400

Simple Interest (SI) = ₹700

Time (T) = 5 years

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ 700 = (1400 × R × 5) ÷ 100

⇒ 700 = 14 × R × 5

⇒ 700 = 70 × R

⇒ R = 700 ÷ 70

⇒ R = 10%

∴ The correct answer is 10%.

Additional Information

Simple Interest (SI)

It is the interest calculated only on the initial Principal amount for the entire period. Formula: SI = (P × R × T) ÷ 100.

Amount (A)

The total money (Principal + Interest) to be paid back after the time period. Formula: A = P + SI = P(1 + RT ÷ 100).

Rate of Interest (R)

The percentage of the Principal charged as interest per year. R = (SI × 100) ÷ (P × T).

The Correct answer is Large surface area combined with a thin alveolar-capillary barrier.

Key Points

• The alveoli in the lungs are designed to maximize gas exchange efficiency.
• Their structure provides a large surface area due to the presence of millions of alveoli, which increases the interface for oxygen and carbon dioxide exchange.
• The walls of the alveoli are composed of a single layer of thin epithelial cells, which minimizes the diffusion distance for gases.
• The adjacent capillaries also have thin walls, further facilitating the quick diffusion of gases.
• The thin alveolar-capillary barrier ensures rapid exchange of oxygen into the blood and carbon dioxide out of the blood.
• This structure is further supported by a layer of surfactant, which reduces the surface tension of the alveoli and prevents their collapse during exhalation.
• The combination of large surface area, thin barriers, and proximity of alveoli to capillaries is crucial for maintaining the efficiency of gas exchange.

Additional Information

• Thick epithelial lining to protect from pathogens
• While the alveoli have a thin epithelial lining for efficient gas exchange, other parts of the respiratory tract, such as the trachea, have thicker epithelial layers to provide protection from pathogens.
• These areas are also supported by mucus and cilia to trap and expel foreign particles.
• Abundance of mucus-secreting cells
• Mucus-secreting cells are prominent in the upper respiratory tract but are not a feature of alveoli, as mucus would impede gas exchange.
• Mucus primarily functions to trap dust, debris, and pathogens, preventing them from reaching the delicate alveoli.
• A robust elastic network to maintain alveolar shape
• The elastic fibers in the alveoli allow them to expand and recoil during breathing, but this feature alone does not directly enhance gas exchange efficiency.
• The elastic network supports the structural integrity of the alveoli rather than facilitating gas diffusion.

The Correct answer is The file will open in Compatibility Mode with limited functionality.

Key Points

• When an MS Excel file created in a newer version (e.g., Excel 2021) is opened in an older version (e.g., Excel 2010), it typically opens in Compatibility Mode.
• Compatibility Mode is a feature in Excel that ensures the file remains accessible in older versions, but some of the newer features and formatting may not be fully functional.
• This mode is used to maintain backward compatibility, allowing users to work on the file despite the version differences.
• Features introduced in the newer versions of Excel, such as dynamic arrays, new chart types, or advanced functions, may not be supported in older versions and will either be disabled or replaced with approximate alternatives.
• Users are often notified about the limitations when the file is opened in Compatibility Mode.
• To restore full functionality, users can either upgrade their Excel version or save the file in an older format compatible with their current version.
• Using Compatibility Mode ensures is maintained while allowing collaboration across different Excel versions.

Additional Information

• The file will be automatically converted to a PDF.
• This is incorrect as Excel does not automatically convert files to PDF. Users must manually choose to export or save the file as a PDF format.
• PDF conversion is an optional feature available in Excel, useful for creating non-editable versions of documents.
• MS Excel will display an error and refuse to open the file.
• Excel typically does not refuse to open files from newer versions. Instead, it uses Compatibility Mode to handle version differences.
• Errors may only occur in rare cases of file corruption or unsupported file formats.
• The file will open normally with all features intact.
• This is incorrect because newer features not available in the older version of Excel will lead to limited functionality.
• Older versions lack the ability to process certain advanced features or formatting introduced in later versions.

The Correct answer is Arunachal Pradesh.

Key Points

• Arunachal Pradesh is one of the northeastern states of India with a sparse population.
• The state is primarily characterized by its hilly terrain and dense forests, which make habitation and agricultural activities challenging.
• It is located in the Himalayan region, contributing to its rugged topography.
• Arunachal Pradesh has a total area of approximately 83,743 square kilometers, but the population density is very low due to the inaccessibility of many areas.
• The state is known for its tribal communities, who predominantly live in scattered villages rather than urban centers.
• Geographical factors such as steep slopes, heavy rainfall, and dense forest cover restrict large-scale development and settlement.
• Despite being sparsely populated, Arunachal Pradesh is rich in biodiversity, and it is home to various unique flora and fauna.
• It shares international borders with China, Bhutan, and Myanmar, which also add to its strategic significance.

Additional Information

• Odisha
• Odisha is located on the eastern coast of India and is known for its coastal plains and fertile lands.
• The state has a relatively higher population density, especially in areas like Bhubaneswar and Cuttack.
• Odisha is famous for its Chilika Lake and historical temples like the Konark Sun Temple.
• It is less affected by hilly terrain compared to Arunachal Pradesh.
• Tamil Nadu
• Tamil Nadu is located in southern India and has a high population density due to its fertile plains and developed urban areas.
• The state is known for its industries, agriculture, and cultural heritage.
• It is home to the Cauvery Delta, which is one of the most agriculturally productive regions in India.
• Hilly terrain exists in parts such as the Nilgiris, but it does not dominate the state's geography.
• Gujarat
• Gujarat is located in western India and is known for its industrial hubs, coastal areas, and plains.
• It has a relatively high population density due to urban centers like Ahmedabad, Surat, and Vadodara.
• Gujarat is famous for its Gir National Park, home to the Asiatic lion, and Rann of Kutch, a salt marsh.
• The state does not have widespread hilly terrain like Arunachal Pradesh.

The logic followed here is:

Thus, the missing term in the series is PIK.

Hence, the correct answer is "Option 3";

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

1. Only two boxes are kept between C and H.

2. Only F is kept above G.

3. Only one box is kept between G and C.

4. E is kept at some place below X but at some place above D.

After arranging the boxes, the number of boxes kept between X and D is 2.

Hence, the correct answer is "Option 2".

Shortcut Trick

Identify the modal class (highest frequency): 50−60 where f₁ = 37.

Apply the Mode formula: L + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h

Mode = 50 + [(37 − 34) ÷ (74 − 66)] × 10 = 50 + (3 ÷ 8) × 10

Mode = 50 + 3.75 = 53.75

∴ The correct answer is 53.75 years.

Alternate Method

Given:

Lower limit of modal class (L) = 50

Frequency of modal class (f₁) = 37

Frequency of preceding class (f₀) = 34

Frequency of succeeding class (f₂) = 32

Class width (h) = 10

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

⇒ Mode = 50 + [(37 − 34) ÷ (2 × 37 − 34 − 32)] × 10

⇒ Mode = 50 + [3 ÷ (74 − 66)] × 10

⇒ Mode = 50 + (3 ÷ 8) × 10

⇒ Mode = 50 + 0.375 × 1

The Correct answer is A new slide is inserted with the same layout as the previous slide.

Key Points

• When you press Ctrl + M in MS PowerPoint 365, it automatically inserts a new slide into the presentation.
• The new slide retains the same layout as the previously selected slide.
• This shortcut is particularly useful for creating a series of slides with a consistent design or layout, ensuring uniformity in the presentation.
• It saves time by eliminating the need to manually select and apply the layout for every new slide.
• The feature is part of PowerPoint's focus on enhancing workflow efficiency and improving the user experience.
• For example, if the previous slide had a Title and Content layout, the new slide will also inherit this layout when using Ctrl + M.
• This functionality is applicable across all modern versions of Microsoft PowerPoint, including PowerPoint 365.

Additional Information

• Option 1: The slide master view is opened
• The Slide Master view is used for editing the overall design of a presentation, such as font styles, placeholder positions, and backgrounds.
• This view can be accessed by navigating to the View tab on the ribbon and selecting Slide Master.
• It is not associated with the Ctrl + M shortcut.
• Option 2: A duplicate of the current slide is created
• To duplicate a slide in PowerPoint, the shortcut is generally Ctrl + D, not Ctrl + M.
• Duplicating a slide creates an identical copy, including all its content and layout.
• Option 4: A new blank slide is inserted regardless of the previous layout
• To insert a blank slide, users can choose the Blank layout manually from the Home tab.
• However, Ctrl + M inserts a slide with the same layout as the previous one, not a blank layout.

The Correct answer is To revolutionise high-speed transportation and reduce travel time.

Key Points

• The primary objective of the hyperloop test track launched by IIT Madras and Indian Railways in 2025 is to test and develop a system that can revolutionize high-speed transportation.
• The hyperloop aims to drastically reduce travel time by operating at speeds of up to 1200 km/h, which is much faster than conventional rail or air travel.
• This technology uses a system of low-pressure vacuum tubes through which pods travel, significantly minimizing air resistance and enabling such high speeds.
• The hyperloop system is considered a game-changing innovation in transportation due to its potential to connect cities and regions efficiently.
• India's investment in hyperloop technology aligns with its vision of modernizing infrastructure and creating future-ready transportation systems.
• The collaboration between IIT Madras and Indian Railways demonstrates India's commitment to advancing cutting-edge technologies and fostering research and development within the country.
• Hyperloop technology could significantly impact urban development, reduce congestion, and improve the overall quality of life by offering faster and more efficient travel options.

Additional Information

• To promote sustainable transportation solutions
• The concept of sustainable transportation focuses on reducing carbon emissions and promoting eco-friendly technologies.
• While hyperloop technology has the potential to reduce environmental impact, its primary objective is not specifically focused on sustainability but rather on achieving high-speed travel.
• To develop a new mode of transportation for goods
• Although hyperloop technology can be adapted for cargo transportation, the initial focus is on passenger travel to demonstrate the feasibility and efficiency of the technology.
• To test the feasibility of vacuum tube technology
• Hyperloop technology does rely on vacuum tube systems, but the objective of the test track is broader, aiming to revolutionize transportation speeds and reduce travel time on a large scale.

The logic followed here is:

Position of Hari from the right = 11

Position of Hari from the left = 38 - 11 + 1 = 28th

Position of Hema from the left = 14th

Now, the number of people between Hari and Hema is:

= Position of Hari from the left - Position of Hema from the left - 1

= 28 - 14 - 1

= 13.

Hence, the correct answer is "Option 4".

The Correct answer is Decreased from 5.4% to 5.1%.

Key Points

• The unemployment rate is a critical indicator of the health of an economy, as it reflects the percentage of people actively seeking work but unable to find it.
• For the fiscal year FY23 to FY24, the unemployment rate in usual status for persons aged 15 years and above in urban areas decreased from 5.4% to 5.1%.
• This decline shows an improvement in employment opportunities in urban areas, indicating a positive trend in the economic recovery or growth during this period.
• The term usual status refers to the employment status of individuals over a longer reference period, typically one year, offering insights into sustained employment trends.
• The data is sourced from the Department of Economic Affairs, which regularly monitors and reports economic indicators crucial for policy-making and analysis.
• Urban areas often have diverse sectors like services, manufacturing, and IT, which contribute to the employment dynamics captured in this report.
• This trend aligns with efforts by the government and other stakeholders to create jobs, boost industries, and enhance employability through various policies and programs.

Additional Information

• Increased from 4% to 5%
• This option is incorrect as the actual trend shows a decrease in the unemployment rate, not an increase.
• Decreased from 6% to 5%
• This option is incorrect since the unemployment rate did not start at 6% but at 5.4% in FY23.
• Remained stable at 5.0%
• This option is incorrect because the unemployment rate showed a decline rather than remaining stable.

Given number: 75246183

According to the question, 

So, digits that appeared more than once in the new number thus formed → 7, 3 and 5 = Three

Hence, "Option 4" is the correct answer.

Given: (Left) 815 497 460 637 147 (Right)

According to the question:

So,

Second digit of the highest number → 815 → 1

Third digit of the lowest number → 147 → 7

Thus, if the second digit of the highest number is subtracted from the third digit of the lowest number then the resultant will be → 7 - 1 → 6 

Hence, "Option 4" is the correct answer.

Given: Seven people D, E, F, G, L, M and N are sitting in a row, facing north.

Only two people sit to the left of L. Only three people sit between L and E.

G sits second to the right of L. Only two people sit between G and M.

D sits at some place to the right of N but at some place to the left of F. 

Thus, Only three people sit to the right of D.

Hence, the correct answer is "Option 4".

The logic followed here is:

Option (1): MSN

Option (2): HNI

Option (3): PVQ

Option (4): KQM

Thus, out of all 'KQM' is the odd one out.

Hence, the correct answer is "Option 4".

Given Table:

According to the given condition:

Given: OBAHMQ

Here, (ii) rule applies here i.e. first element is vowel and the fourth letter is a consonant.

O → coded as ©

B → coded as 1

A → coded as 6 

H → coded as ©

M → coded as 8

Q → coded as 9

So, OBAHMQ → Coded as ©16©89

Hence, "Option 2" is the correct answer.

Shortcut Trick

Let the Monthly Salary be 100%.

Rent = 50%, so the remaining 50% must cover Conveyance, Groceries, and Savings.

Remaining 50% = ₹780 + ₹9,800 + ₹110 = ₹10,690.

If 50% = ₹10,690, then 100% = ₹10,690 × 2 = ₹21,380.

∴ The correct answer is ₹21,380.

Alternate Method

Given:

Rent Expenditure = 50% of Salary

Conveyance = ₹780, Groceries = ₹9,800, Savings = ₹110

Formula: Total Salary = Rent + Conveyance + Groceries + Savings

⇒ Let Total Salary = S

⇒ S = 0.50S + 780 + 9,800 + 110

⇒ S − 0.50S = 10,690

⇒ 0.50S = 10,690

⇒ S = 10,690 ÷ 0.50

⇒ S = ₹21,380

∴ The correct answer is ₹21,380.

Additional Information

Percentage Base Change

When a value is split into percentages, the sum of all parts must equal 100% of the base value.

Savings Formula

Savings = Income − Total Expenditure. In percentage terms: Savings % = 100% − (Sum of all expenditure %).

Successive Percentage

If the question says 'percent of remaining', use the formula: Final = Initial × (1 − r₁/100) × (1 − r₂/100).

The logic followed here is:

Thus, the missing term in the series is 1472.

Hence, the correct answer is "Option 1".