Given: # : IGC :: TRN : %

Option 1) # = JKF , % = QJH

For # (JKF) to IGC

For TRN to % (QJH)

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

Option 2) # = LJK , % = QNJ

For # (LJK) to IGC

For TRN to % (QNJ)

Since, the patterns do not match, Option 2 is incorrect.

Option 3) # = LJF , % = QOK

For # (LJF) to IGC

For TRN to % (QOK)

Since, both transformations follow a consistent shift pattern, Option 3 is correct.

Option 4) # = LGY , % = QJH

For # (LGY) to IGC

For TRN to % (QJH)

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

Hence, the correct answer is "Option 3".

The correct answer is The population growth will slow down and eventually stabilize near the carrying capacity.

Key Points

• Logistic growth describes how a population's growth rate decreases as the population size approaches a maximum imposed by limited resources in the environment, known as the carrying capacity (K).
• In this specific scenario, the current population size (N) is 500 individuals, while the carrying capacity (K) is 1000 individuals. Since N is less than K, the population still has room to grow, but the rate of growth is influenced by the proximity to the limit.
• The mathematical model for this is the Verhulst-Pearl Equation: dN/dt = rN [(K - N) / K]. When N is 500 and K is 1000, the term (K - N) / K equals 0.5, indicating that the population is growing at 50% of its maximum intrinsic rate.
• As the number of rabbits increases from 500 toward 1000, the resource competition becomes more intense, causing the birth rate to potentially decrease or the death rate to increase. This leads to a slowing down of growth. Hence, the statement that the population will slow down and stabilize near the carrying capacity is correct.
• The population will not decline rapidly because it has not yet exceeded the carrying capacity. Hence, the statement regarding rapid decline is incorrect.
• Growth will not continue exponentially because the carrying capacity of 1000 acts as a physical and biological constraint. Hence, the statement regarding exponential growth is incorrect.

Additional Information

• Carrying Capacity (K): This represents the maximum population size of a species that a specific ecosystem can sustain indefinitely without degrading the habitat. It is determined by limiting factors such as food availability, water supply, living space, and predation.
• Sigmoid (S-shaped) Curve: Logistic growth is graphically represented by an S-shaped curve. It consists of three main phases: the lag phase (slow initial growth), the log phase (rapid exponential growth), and the stationary phase (stabilization at K).
• Environmental Resistance: This refers to the sum of all limiting factors (biotic and abiotic) that prevent a population from reaching its biotic potential. In this rabbit population of 500, environmental resistance is increasing as it approaches 1000.
• Density-Dependent Factors: These are factors whose effects on the size or growth of the population vary with the population density. Examples include competition, disease, and waste accumulation, which are primary drivers of the logistic growth model.
• Comparison with Exponential Growth: Unlike logistic growth, exponential growth (J-shaped curve) occurs when resources are unlimited, and the growth rate depends only on the intrinsic rate of increase (r) and the number of individuals.

Important Points

• Inflection Point: In a logistic growth curve, the inflection point occurs when N = K/2. In this example, with K = 1000, the inflection point is exactly at 500. This is the point where the population growth rate is at its absolute maximum before it begins to decelerate.
• Dynamic Equilibrium: Once the population reaches 1000, it doesn't necessarily stop all biological activity; rather, it enters a state of dynamic equilibrium where births and deaths roughly balance each other out.
• Overshoot: In real-world biological systems, populations sometimes overshoot the carrying capacity momentarily before crashing or oscillating back to K. However, in the standard logistic growth model, the stabilization is smooth.
• Historical Context: The concept of logistic growth was first introduced by Pierre François Verhulst in 1838 to describe the growth of human populations, later popularized in biology by Raymond Pearl and Lowell Reed in 1920.

Shortcut Trick

Sum = 56, Difference = 1/7 of 56 = 8

⇒ Numbers = (56 ± 8)/2 → 32 and 24

⇒ LCM of 32 and 24 = 96

∴ Answer = 96

Alternate Method

Given:

Sum = 56

Difference = 1/7 of sum = 8

Formula:

Numbers = (Sum + Difference) ÷ 2 and (Sum − Difference) ÷ 2

Calculations:

⇒ First number = (56 + 8) ÷ 2 = 64 ÷ 2 = 32

⇒ Second number = (56 − 8) ÷ 2 = 48 ÷ 2 = 24

⇒ LCM of 32 and 24:

⇒ 32 = 2⁵, 24 = 2³ × 3

⇒ LCM = 2⁵ × 3 = 96

Final Answer: 96

Additional Information

Sum-Difference Formula: Numbers = (S ± D) ÷ 2

LCM Rule: Take highest powers of primes

Prime Factorization: 32 = 2⁵, 24 = 2³ × 3

Exam Tip: Directly compute difference first to save time

Given numbers: 318, 745, 472, 123, 672

Original order: 318 745 472 123 672

Ascending order: 123, 318, 472, 672, 745

Only one number remains in the same position → 472

Hence, the correct answer is Option 1.

The correct answer is ₹2 crore.

Key Points

• The Banking Laws (Amendment) Act, 2025 (which originated as the 2024 Bill) introduced significant reforms to the Banking Regulation Act, 1949, to modernize the regulatory framework of the Indian banking sector.
• One of the primary changes is the revision of the threshold for "substantial interest". Previously, under the Banking Regulation Act, 1949, substantial interest was defined as holding shares worth more than ₹5 lakh or 10% of the paid-up capital of a bank, whichever was less.
• According to the new amendment, this monetary threshold has been increased to ₹2 crore. This change reflects the current economic reality and the significant increase in the valuation of bank capital over the last several decades.
• The upward revision of this limit ensures that the Reserve Bank of India (RBI) focuses its oversight on individuals or entities that possess a genuinely significant financial stake and influence over the bank's operations.
• This definition is vital for identifying "connected lending" and ensuring that the Board of Directors maintains independence from major shareholders who might otherwise exert undue pressure for personal gain.

Additional Information

• Increased Nomination Facilities: The Banking Laws (Amendment) Act, 2025 allows bank account holders to appoint up to 4 nominees for their accounts, replacing the previous limit of 1 nominee. This provides more flexibility for depositors in managing their legacy and succession planning.
• Tenure of Directors in Cooperative Banks: The amendment has increased the maximum tenure of directors in cooperative banks from the previous 8 years to 10 years. This change brings the governance of cooperative banks more in line with the standards applied to commercial banks.
• Flexible Reporting Dates: The Act modifies the reporting cycles for banks. Instead of reporting their financial positions on the second and fourth Fridays of each month, banks are now allowed to report based on the 15^th and the last day of the month. This adjustment aims to simplify accounting and compliance procedures.
• Redefinition of "Relative": The scope of the term "relative" has been expanded under the Banking Regulation Act. This helps in better tracking of loans and advances provided to people connected to the bank's management, thereby improving transparency and preventing conflict of interest.
• Statutory Auditors: The legislation provides greater autonomy to banks in the process of appointing statutory auditors, though the RBI continues to maintain overall regulatory supervision to ensure the integrity of the financial auditing process.

Important Points

• Context of the Amendment: The Union Finance Minister, Nirmala Sitharaman, introduced the bill in Parliament in August 2024. It was designed to enhance customer convenience and improve the operational efficiency of the banking system in India.
• Impact on Shareholding: By raising the substantial interest limit to ₹2 crore, the government has acknowledged that the nominal value of shares has increased, and a ₹5 lakh holding no longer represents the same level of corporate control as it did when the 1949 Act was first drafted.
• Regulatory Power of RBI: Despite these relaxations in thresholds, the Reserve Bank of India (RBI) remains the primary regulator with the power to intervene if any person's interest in a bank poses a systemic risk to the Indian economy.
• Applicability: These laws apply to Public Sector Banks (PSBs), Private Banks, and Cooperative Banks, ensuring a uniform legal framework across the banking landscape of the country.

Shortcut Trick

Let boat speed = x

⇒ Downstream = x + 3, Upstream = x − 3

Equal time ⇒ 36/(x+3) = 24/(x−3)

⇒ 36(x−3) = 24(x+3) ⇒ 12x = 180

⇒ x = 15

∴ Answer = 15 km/h

Alternate Method

Given:

Downstream distance = 36 km

Upstream distance = 24 km

Stream speed = 3 km/h

Formula:

Speed downstream = x + 3

Speed upstream = x − 3

Time = Distance ÷ Speed

Calculations:

⇒ 36 ÷ (x + 3) = 24 ÷ (x − 3)

⇒ 36(x − 3) = 24(x + 3)

⇒ 36x − 108 = 24x + 72

⇒ 12x = 180

⇒ x = 15

Final Answer: 15 km/h

Additional Information

Downstream Speed: Boat speed + Stream speed

Upstream Speed: Boat speed − Stream speed

Equal Time Concept: Distance ÷ Speed ratios equal

Exam Trick: Cross multiply directly to save time

The correct answer is Matter consists of indivisible atoms.

Key Points

• John Dalton proposed his Atomic Theory in 1808, which served as a fundamental framework for modern chemistry. One of his primary postulates was that matter consists of indivisible atoms, implying that atoms are the smallest possible units of matter and cannot be broken down further. Hence, statement 4 is the postulate that was proven wrong.
• The discovery of subatomic particles directly contradicted Dalton's claim of indivisibility. In 1897, J.J. Thomson discovered the electron through his cathode ray tube experiments, proving that the atom itself contains smaller, negatively charged components. Hence, statement 4 is incorrect based on modern scientific evidence.
• Further advancements in physics led to the discovery of the nucleus and other particles. Ernest Rutherford identified the proton in the early 20^th century, and James Chadwick discovered the neutron in 1932. These discoveries established that atoms are composed of a central nucleus containing protons and neutrons, surrounded by electrons.
• Another postulate of Dalton stated that atoms of different elements have different masses. While generally true, the discovery of isobars (atoms of different elements with the same mass number) showed that this was not an absolute rule. Hence, statement 2 is a postulate that has notable exceptions in modern chemistry.
• Dalton also posited that atoms retain their identity in chemical reactions, meaning they are neither created nor destroyed but merely rearranged. This aligns with the Law of Conservation of Mass. However, in nuclear reactions, atoms can indeed change their identity, although they remain stable in standard chemical processes. Hence, statement 1 is largely correct for chemical reactions but limited in the context of nuclear physics.

Additional Information

• Isotopes and Mass: Dalton's theory suggested that all atoms of a given element are identical in mass and properties. This was proven wrong by the discovery of isotopes, which are atoms of the same element (same number of protons) that have different numbers of neutrons, resulting in different atomic masses. Common examples include Carbon-12 and Carbon-14.
• Law of Multiple Proportions: One of Dalton's successful contributions was the Law of Multiple Proportions, which states that when two elements combine to form more than one compound, the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.
• The Electron (1897): The electron was the first subatomic particle discovered. It has a negative charge of approximately -1.602 x 10⁻¹⁹ Coulombs and a negligible mass compared to protons and neutrons (about 1/1836 of a proton).
• Atomic Nucleus: The Rutherford Gold Foil Experiment in 1911 demonstrated that the majority of an atom's mass and its positive charge are concentrated in a tiny central region called the nucleus, debunking the "Plum Pudding Model."
• Modern Atomic Theory: Unlike Dalton's model, the Modern Atomic Theory recognizes that atoms are divisible into subatomic particles and that atoms of the same element can have different masses (isotopes). It also utilizes quantum mechanics to describe the probability clouds or orbitals where electrons are likely to be found.

Important Points

• Comparison of Particles: The proton carries a positive charge, the electron carries a negative charge, and the neutron is electrically neutral. The number of protons (the atomic number) defines the identity of the chemical element.
• Chemical vs. Nuclear Identity: In a chemical reaction, only the valence electrons are involved, and the nucleus remains unchanged, preserving the atom's identity. In nuclear fission or fusion, the nucleus is altered, which can turn one element into another, a process known as transmutation.
• Indivisibility vs. Divisibility: While Dalton was wrong about atoms being "indivisible," his theory was a crucial stepping stone because it moved chemistry from a qualitative to a quantitative science based on the concept of atomic weight.

The correct answer is Lothal.

Key Points

• Lothal was a vital and flourishing trade center of the Indus Valley Civilization, located in the Bhal region of the modern state of Gujarat, India. It is situated near the village of Saragwala in the Dholka Taluka of Ahmedabad district.
• The city is most famous for its dockyard, which is the earliest known artificial dock in the world. This dockyard was a trapezoidal structure made of baked bricks, measuring approximately 218 meters in length and 37 meters in width, connected to the Bhogava River, a tributary of the Sabarmati.
• The excavation of Lothal was led by the archaeologist S.R. Rao in 1954. The site revealed that the city was a major maritime trade hub, facilitating commerce between Harappan cities and Mesopotamia as well as the Persian Gulf.
• Beyond the dockyard, Lothal was known for its industrial prowess, specifically its bead-making factory. Archaeologists discovered thousands of carnelian beads in various stages of production, along with tools like drills and kilns, proving its status as a manufacturing center.
• The city layout followed a strict grid system typical of Harappan urban planning, featuring a citadel (upper town) and a lower town. The advanced drainage system and standardized burnt bricks used in construction highlight the architectural maturity reached by 2500 BCE.

Additional Information

• Dholavira:
• Located on Khadir Bet in the Rann of Kutch, Gujarat. This site is unique because it was divided into three parts: the Citadel, the Middle Town, and the Lower Town, unlike the two-part division of other cities.
• It is renowned for its sophisticated water management system, consisting of a series of reservoirs and check dams. A unique ten-signboard inscription (the "Dholavira Signboard") was also found here.
• Mohenjodaro:
• Located in the Larkana district of Sindh, Pakistan, on the banks of the Indus River. It means "Mound of the Dead" in the Sindhi language.
• Key findings include the Great Bath, the Great Granary, the Bronze Dancing Girl, and the Seal of Pashupati. It was one of the largest settlements of the civilization, excavated by R.D. Banerji in 1922.
• Kalibangan:
• Situated on the banks of the dried-up Ghaggar River in the Hanumangarh district of Rajasthan, India. The name means "Black Bangles".
• This site provided the earliest evidence of a ploughed field in history. Other significant finds include fire altars, indicating religious practices, and camel bones.

Important Points

• The Harappan Civilization, also known as the Indus Valley Civilization, belonged to the Bronze Age (circa 3300–1300 BCE, with the mature phase from 2600–1900 BCE).
• Maritime Trade: The presence of Persian Gulf seals at Lothal and Harappan seals in Susa (Mesopotamia) confirms that Lothal was an international port. Trade items included ivory, copper, gold, and precious stones.
• Double Burial: Lothal is one of the few sites where double burials (joint burial of a male and female) were discovered, suggesting specific social or funerary customs.
• Standardization: The civilization was noted for its use of standardized weights and measures (binary and decimal systems) and terracotta seals used for securing goods during transport.

Shortcut Trick

Empirical: Mode = 3Median − 2Mean

Given: Mode − Median = 61.54

⇒ (3M − 2Mean) − M = 61.54

⇒ 2(Median − Mean) = 61.54

⇒ Median − Mean = 30.77

∴ Answer = 30.77

Alternate Method

Given:

Mode − Median = 61.54

Formula:

Mode = 3Median − 2Mean

Calculations:

⇒ Substitute Mode:

⇒ (3Median − 2Mean) − Median = 61.54

⇒ 2Median − 2Mean = 61.54

⇒ 2(Median − Mean) = 61.54

⇒ Median − Mean = 61.54 ÷ 2 = 30.77

Final Answer: 30.77

Additional Information

Empirical Relation: Mode = 3Median − 2Mean

Rearranged Form: Mean = (3Median − Mode) ÷ 2

Key Insight: Differences help eliminate variables quickly

Exam Tip: Always substitute directly to reduce steps

Shortcut Trick

Given y − 12 = 4√5 ⇒ y = 12 + 4√5

⇒ y − 3 = 9 + 4√5 = (√5 + 2)²

⇒ √(y − 3) = √5 + 2

⇒ 1/√(y − 3) = 1/(√5 + 2) = √5 − 2

⇒ Required = (√5 + 2) − (√5 − 2) = 4

∴ Answer = 4

Alternate Method

Given:

y − 12 = 4√5

Formula:

(a + b)² = a² + b² + 2ab

Calculations:

⇒ y = 12 + 4√5

⇒ y − 3 = 9 + 4√5

⇒ Assume 9 + 4√5 = (a + b√5)²

⇒ Compare: a² + 5b² = 9 and 2ab = 4

⇒ a = 2, b = 1

⇒ √(y − 3) = 2 + √5

⇒ 1/(2 + √5) = (2 − √5)/(4 − 5) = √5 − 2

⇒ Required = (2 + √5) − (√5 − 2) = 4

Final Answer: 4

Additional Information

Perfect Square Form: a + b√c = (x + y√c)²

Rationalization: 1/(a + √b) = (a − √b)/(a² − b)

Key Insight: Convert into perfect square to simplify roots

Exam Trick: Always check if expression fits (a + b)²

The correct answer is Mahatma Gandhi.

Key Points

• Mahatma Gandhi was the primary editor and driving force behind the weekly journal Young India, which he published from 1919 to 1931. Hence, the statement regarding Mahatma Gandhi is correct.
• Young India was an English-language weekly journal through which Gandhi expressed his philosophy of Satyagraha, Non-violence (Ahimsa), and his vision for Swaraj (Self-rule).
• The journal played a critical role in mobilizing public opinion during the Non-Cooperation Movement and the Civil Disobedience Movement, providing a platform for Gandhi to address the English-educated class of India.
• During his imprisonment in 1922, Gandhi was charged with sedition based on three articles published in Young India, illustrating the journal's profound impact on the Indian National Movement.
• The publication was eventually superseded by Harijan in 1933, after Gandhi shifted his focus more towards the abolition of untouchability and social reform.

Additional Information

• Bal Gangadhar Tilak:
• Known as Lokmanya, Tilak was a pioneer of the Swaraj movement and started two famous newspapers in 1881: Kesari (in Marathi) and The Mahratta (in English).
• He was never the editor of Young India; his journals were the primary voice of the Extremist faction of the Indian National Congress. Hence, the statement regarding Bal Gangadhar Tilak is incorrect.
• Jawaharlal Nehru:
• Nehru was the first Prime Minister of independent India and founded the National Herald newspaper in 1938.
• Based in Lucknow, the National Herald was intended to promote the policies of the Indian National Congress and served as a major nationalist daily. Hence, the statement regarding Jawaharlal Nehru is incorrect.
• Gopal Krishna Gokhale:
• A Moderate leader and political mentor to Gandhi, Gokhale founded the Servants of India Society in 1905.
• He was associated with the journal The Hitavada (started in 1911 in Nagpur) and the weekly Sudharak, which focused on social and political reforms. Hence, the statement regarding Gopal Krishna Gokhale is incorrect.
• Lala Lajpat Rai:
• While Mahatma Gandhi edited the journal, Lala Lajpat Rai also authored a book titled Young India in 1916 while he was in the United States.
• This book provided an interpretative history of the nationalist movement in India but is distinct from the weekly periodical edited by Gandhi.

Important Points

• Gandhi's Journalistic Legacy:
• Before Young India, Gandhi edited Indian Opinion in South Africa (from 1903 to 1915), which was published in English, Gujarati, Hindi, and Tamil.
• He also managed Navajivan, a weekly journal in Gujarati, alongside Young India to reach the vernacular-speaking masses.
• In 1933, he started Harijan (meaning 'Children of God'), which had versions in English, Hindi (Harijan Sevak), and Gujarati (Harijanbandhu), specifically targeting the caste system and rural upliftment.
• Historical Context:
• The period between 1919 and 1931 marked the Gandhian Era of the nationalist struggle. The journals acted as a crucial link between the leadership and the masses during pan-India protests.
• Subscription to Young India reached approximately 40,000 at its peak, a significant number for that era, influencing several future leaders and thinkers.

Given: P, Q, R, S, T, U and V sit around a circular table facing the centre.

Only one person sits between U and P when counted from the right of U.

Only one person sits between P and R.

Only one person sits between U and Q.

Only two people sit between V and R.

Only one person sits between T and Q.

People between T and V = P → 1 person

Hence, the correct answer is Option 2.

Shortcut Trick

Let actual SP = 100

⇒ Given SP = 6/15 of 100 = 40

Loss 28% ⇒ CP = 40 ÷ 0.72 = 55.56

⇒ New SP = 89

⇒ Profit % = (89 − 55.56) ÷ 55.56 × 100 ≈ 60.2%

∴ Answer = 60.2%

Alternate Method

Given:

Selling at 6/15 of actual SP gives 28% loss

Formula:

Loss % = (CP − SP) ÷ CP × 100

Calculations:

⇒ Let actual SP = 100

⇒ SP₁ = 6/15 × 100 = 40

⇒ Loss = 28% ⇒ SP₁ = 72% of CP

⇒ CP = 40 ÷ 0.72 = 55.56

⇒ New SP₂ = 89% of 100 = 89

⇒ Profit = 89 − 55.56 = 33.44

⇒ Profit % = (33.44 ÷ 55.56) × 100 ≈ 60.2%

Final Answer: 60.2%

Additional Information

Loss Concept: SP = (1 − loss%) × CP

Profit Concept: Profit % = (Profit ÷ CP) × 100

Shortcut Tip: Assume actual SP = 100 for easy calculation

Exam Trick: Convert percentages into fractions quickly

Shortcut Trick

Net rate = 1/4 + 1/38 − 1/38 = 1/4

Only tap A works effectively

Time to fill full = 4 hours

Time for 1/4 = 4 × 1/4 = 1 hour

∴ Answer = 1 hour

Alternate Method

Given:

Tap A = 4 hrs, Tap B = 38 hrs, Tap C = 38 hrs (empty)

Formula used:

Total Work = LCM of times

Efficiency = Total Work ÷ Time

Calculations:

⇒ Net rate = 38 + 4 − 4 = 38 units/hr

⇒ Time for full = 152 ÷ 38 = 4 hrs

⇒ Time for 1/4 = 4 ÷ 4 = 1 hr

∴ The correct answer is 1 hour.

Additional Information

Efficiency Concept

Efficiency = Work done per unit time.

LCM Method

Use LCM to simplify fractional work problems.

Net Rate

Net rate = Filling − Emptying.

Shortcut Insight

Equal fill and empty cancel each other.

The logic followed here is:

Given:

CARD → 4628

NEAT → 3574

Hence, the code for A is 4.

Hence, the correct answer is Option 2.

Shortcut Trick

Ratio sum = 15 ⇒ 1 part = 90 ÷ 15 = 6

Sides = 24, 30, 36 and s = 45

Area = √(45×21×15×9) = 135√7

Convert: √7 = 2.6

Area ≈ 135 × 2.6 = 351

Quadrilateral = 2 × 351 = 702

∴ Answer = 702 cm²

Alternate Method

Given:

Ratio = 4 : 5 : 6, Perimeter = 90

√21 = 2.6

Formula used:

Heron’s Formula: Area = √[s(s−a)(s−b)(s−c)]

Calculations:

⇒ Let sides = 4x, 5x, 6x

⇒ 15x = 90 ⇒ x = 6

⇒ Sides = 24, 30, 36

⇒ s = 45

⇒ Area = √[45×21×15×9]

⇒ = √[(9×5)(3×7)(3×5)(9)]

⇒ = √(9×9×3×3×5×5×7)

⇒ = 135√7

⇒ Convert: √7 = 2.6

⇒ Area ≈ 135 × 2.6 = 351

⇒ Quadrilateral area = 2 × 351 = 702

∴ The correct answer is 702 cm².

Additional Information

Heron’s Formula

Area = √[s(s−a)(s−b)(s−c)]

Ratio Scaling

Actual side = ratio × common factor

Root Adjustment Trick

Convert roots to match given values for faster calculation

Exam Tip

Always use given root values instead of approximating separately

Shortcut Trick

Reverse factors: +50% ⇒ ×150/100, −60% ⇒ ×40/100

Final = CP × 150/100 × 40/100

3234 = CP × (150×40)/10000 = CP × 6000/10000 = CP × 3/5

CP = 3234 × 5/3 = 5390

∴ Answer = 5390

Alternate Method

Given:

P → Q : 50% profit

Q → R : 60% loss

R paid = 3234

Formula used:

SP = CP × (1 ± percentage/100)

Calculations:

⇒ Let CP of P = x

⇒ SP to Q = x × 150/100

⇒ SP to R = x × 150/100 × 40/100

⇒ x × (150×40)/10000 = 3234

⇒ x × 6000/10000 = 3234

⇒ x × 3/5 = 3234

⇒ x = 3234 × 5/3 = 5390

∴ The correct answer is 5390.

Additional Information

Multiplying Factor

Profit ⇒ (100 + p)/100, Loss ⇒ (100 − l)/100

Successive Change

Net factor = product of individual factors

Reverse Method

To find original CP, divide final SP by combined factor

Exam Tip

Always combine factors before solving to save time

The correct answer is Shoe shining.

Key Points

• Economic activities are broadly categorized into three main sectors: Primary, Secondary, and Tertiary. The Tertiary sector, often known as the Service Sector, includes activities that do not produce a tangible good but provide services to consumers and businesses.
• Shoe shining is a classic example of a tertiary activity because it involves providing a personal service to a customer rather than producing a new physical product from raw materials. Hence, this option is correct.
• Extracting minerals refers to the process of taking natural resources directly from the earth, such as mining or quarrying. This is classified as a Primary activity because it deals with the extraction of raw materials. Hence, this option is incorrect.
• Steel making involves the manufacturing process where raw iron is converted into steel. This falls under the Secondary sector because it transforms raw materials into finished or semi-finished industrial products. Hence, this option is incorrect.
• Metal working is an industrial activity that involves processing metals to create individual parts, assemblies, or large-scale structures. Like steel making, it is a Secondary activity focused on manufacturing and construction. Hence, this option is incorrect.

Additional Information

• Primary Sector: This sector involves the extraction and production of natural resources. It includes activities such as agriculture, forestry, fishing, and mining. In many developing countries like India, a large percentage of the population is still employed in this sector, particularly in rural areas.
• Secondary Sector: This sector adds value to natural resources by transforming them into finished goods through manufacturing, processing, and construction. Examples include automobile production, textile manufacturing, and food processing. It is often referred to as the Industrial Sector.
• Tertiary Sector: This sector supports the primary and secondary sectors by providing logistics, trade, and support services. Common examples include transportation, banking, insurance, education, healthcare, tourism, and retail trade. As an economy develops, there is usually a shift in employment and GDP contribution from the primary to the tertiary sector.
• Quaternary and Quinary Sectors: Modern economic theory also recognizes the Quaternary sector, which focuses on knowledge-based services like information technology (IT), R&D, and consultancy, and the Quinary sector, which involves high-level decision-making by government officials and top executives in large organizations.

Important Points

• GDP Contribution: In the financial year 2023-24, the Service Sector (Tertiary) remained the largest contributor to India's Gross Value Added (GVA), accounting for over 53% of the total. This highlights the transition of the Indian economy from agrarian-based to service-led.
• Employment Trends: While the Tertiary sector generates the most wealth, the Primary sector (Agriculture) still employs the largest number of people in India, approximately 45-46% of the workforce, indicating a structural gap in productivity per worker.
• Examples of Tertiary Workers: Apart from shoe shiners, other professions in this sector include barbers, lawyers, teachers, doctors, software engineers, and call center executives. These roles are characterized by the sale of expertise and labor rather than physical commodities.
• Infrastructure Role: The efficiency of the Tertiary sector is heavily dependent on infrastructure such as telecommunications, internet connectivity, and transport networks (Roads, Railways, and Airways).

The correct answer is The Administrative Tribunals Act, 1985.

Key Points

• The Central Administrative Tribunal (CAT) was established under the provisions of the Administrative Tribunals Act, 1985. This Act was passed by the Parliament of India to give effect to Article 323A of the Constitution.
• Article 323A was inserted into the Constitution of India by the 42^nd Amendment Act, 1976, empowering the Parliament to provide for the adjudication of disputes relating to the recruitment and conditions of service of persons appointed to public services.
• The Central Administrative Tribunal was formally inaugurated on November 1, 1985, during the tenure of Prime Minister Rajiv Gandhi.
• The primary objective of the Administrative Tribunals Act, 1985 is to provide for a specialized and speedy mechanism for the redressal of grievances of Government employees, thereby reducing the burden on the regular Judiciary.
• The Administrative Tribunals Act, 1985 governs the Central Administrative Tribunal as well as the State Administrative Tribunals (SAT) created upon the request of the respective State Governments.

Additional Information

• Jurisdiction of CAT:
• The Central Administrative Tribunal exercises jurisdiction over all service matters concerning members of the All India Services, the Central Civil Services, and civil posts under the Union.
• It also covers the civilian employees of the Defense Services. However, it does not cover the Armed Forces personnel, officers and servants of the Supreme Court, or the secretarial staff of the Parliament.
• Composition of the Tribunal:
• The CAT is a multi-member body consisting of a Chairman and several Members (both Judicial and Administrative).
• As per the Tribunals Reforms Act, 2021, the Chairman and Members are appointed for a term of 4 years. The age limit is 70 years for the Chairman and 67 years for the Members.
• Procedural Flexibility:
• The tribunal is not bound by the technical and rigid procedures prescribed in the Code of Civil Procedure, 1908.
• Instead, it is guided by the Principles of Natural Justice, making the adjudication process more flexible, economical, and faster for litigants.
• Location and Benches:
• The Principal Bench of the Central Administrative Tribunal is located in New Delhi.
• Currently, there are 19 regular Benches across the country, along with several Circuit Benches that operate periodically to serve remote locations.

Important Points

• Judicial Review and L. Chandra Kumar Case (1997):
• In the landmark L. Chandra Kumar vs. Union of India case in 1997, the Supreme Court ruled that the power of Judicial Review is a basic feature of the Constitution.
• Consequently, appeals against the orders of the CAT cannot be made directly to the Supreme Court. Instead, they must be challenged before the Division Bench of the respective High Court under Article 226 or Article 227.
• Appointment Process:
• The Chairman and Members of the CAT are appointed by the President of India based on the recommendations of a Search-cum-Selection Committee headed by the Chief Justice of India or his nominee.
• Distinction between Article 323A and 323B:
• While Article 323A deals specifically with Administrative Tribunals for public service matters, Article 323B deals with tribunals for other matters such as taxation, foreign exchange, land reforms, and labor disputes.

The logic followed here is:

Given:

BELI → 6315

EVIL → 9653

In BELI, unique letter = B

Remaining number = 1

⇒ B = 1

In EVIL, unique letter = V

Remaining number = 9

⇒ V = 9

So, V → 9

Hence, the correct answer is Option 1.

Given Statements:

All bananas are apples.

All apples are grapes.

Some grapes are oranges.

The least possible Venn diagram for the given statement is: 

Conclusions:

I. All grapes are bananas → False (Only bananas are inside apples and grapes, but grapes are not fully inside bananas; this reverses the given relationship).

II. All oranges are apples → False (Only “some grapes are oranges” is given, but there is no link showing oranges lie inside apples, so this cannot be concluded).

So, neither conclusion (I) nor (II) follows.

Hence, the correct answer is "Option 2".

Family Chart:

Decoding the Symbols:

Given: S − K ÷ T × V + P

It means: S is the wife of K, K is the father of T, T is the sister of V, V is the mother of P.

⇒ Therefore S is P’s maternal grandmother

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: third number = (first number + second number) + 2

For, (6, 3, 14)

⇒ 6 + 3 = 9

⇒ 9 + 5 = 14

For, (14, 8, 27)

⇒ 14 + 8 = 22

⇒ 22 + 5 = 27

Now, checking the options:

Option 1) (14, 87, 26)

⇒ 14 + 87 = 101

⇒ 101 + 5 = 106 ≠ 26

Option 2) (6, 15, 21)

⇒ 6 + 15 = 21

⇒ 21 + 5 = 26 ≠ 21

Option 3) (19, 12, 36)

⇒ 19 + 12 = 31

⇒ 31 + 5 = 36 

Option 4) (16, 25, 31)

⇒ 16 + 25 = 41

⇒ 41 + 5 = 46 ≠ 31

Hence, the correct answer is Option 3.

The correct answer is Pleistocene upheaval.

Key Points

• The geological evolution of the Himalayan rivers suggests that during the Miocene period (approximately 5 to 24 million years ago), a single mighty river known as the Indo-Brahma or Siwalik River flowed along the entire longitudinal extent of the Himalayas.
• This ancient river traversed from Assam in the east to Punjab in the west and eventually discharged into the Gulf of Sind (near the present-day Arabian Sea).
• The dismemberment of this massive drainage system into three distinct parts—the Indus system, the Ganga system, and the Brahmaputra system—is primarily attributed to the Pleistocene upheaval in the Western Himalayas.
• Specifically, the uplift of the Potwar Plateau (which includes the Delhi Ridge) acted as a water divide between the Indus and Ganga basins, forcing the rivers to seek new paths. Hence, the statement regarding Pleistocene upheaval is correct.
• In the eastern sector, the downthrusting of the Malda Gap (also known as the Garo-Rajmahal Gap) during the mid-Pleistocene period caused the Ganga and Brahmaputra systems to divert their flow towards the Bay of Bengal.

Additional Information

• Indus Drainage System: This system consists of the Indus River and its five major tributaries: Jhelum, Chenab, Ravi, Beas, and Satluj. It occupies the westernmost part of the former Indo-Brahma channel.
• Ganga Drainage System: It comprises the Ganga and its numerous Himalayan (e.g., Yamuna, Ghaghara, Gandak) and Peninsular (e.g., Chambal, Son) tributaries. It flows through the Indo-Gangetic Plain, covering the central portion of the ancient river's path.
• Brahmaputra Drainage System: This system includes the Brahmaputra (known as Tsangpo in Tibet) and its tributaries like the Lohit, Subansiri, and Manas. It drains the eastern section of the original longitudinal valley.
• The Siwalik Sediments: The evidence for the Indo-Brahma River comes from the thick Siwalik deposits, which are lacustrine and alluvial in nature, consisting of sands, clays, and boulders accumulated during the Tertiary Period.
• Geological Timeframe: The Pleistocene Epoch, often referred to as the Ice Age, began about 2.6 million years ago and ended approximately 11,700 years ago. It was a period of significant tectonic shifts and climatic changes that reshaped the Indian subcontinent's topography.

Important Points

• The Delhi Ridge: A northern extension of the Aravalli Range, it serves as the continental water divide separating the Indus basin from the Ganga basin. Any uplift in this region directly impacts the flow direction of trans-continental rivers.
• Theory Proponents: The Indo-Brahma river hypothesis was notably proposed by geologists E.H. Pascoe and G.E. Pilgrim in 1919, based on their studies of Siwalik stratigraphy and fossil records.
• Malda Gap Subsidence: The Garo-Rajmahal Gap is a tectonic depression. Before its formation, the Ganga and Brahmaputra did not flow into the Bay of Bengal but were part of the westward-flowing Siwalik River. The subsidence of this gap provided a topographic low that redirected the drainage southward.
• River Capture (Alternative Option): While river capture (or stream piracy) is a common geomorphic process where a river diverts the headwaters of another, the primary large-scale cause for the Indo-Brahma's split was the regional tectonic upheaval rather than localized headward erosion.

The correct answer is NITI Aayog.

Key Points

• The policy report titled Internationalisation of Higher Education in India: Prospects, Potential, and Policy Recommendations was released by NITI Aayog in December 2025 to provide a strategic roadmap for the Indian education sector.
• The primary objective of the report is to establish India as a Global Study Destination and a Knowledge Superpower, aligning with the vision of the National Education Policy (NEP) 2020.
• The report emphasizes the need for Higher Educational Institutions (HEIs) in India to improve their Global Rankings (such as QS and THE rankings) by fostering international research collaborations and faculty exchange programs.
• It identifies key areas for growth, including the facilitation of Transnational Education (TNE), which involves the movement of students, teachers, and programs across international boundaries.
• The policy recommendations highlight the importance of Twinning Programs, Joint Degrees, and Dual Degree arrangements between Indian and Foreign Higher Education Institutions to enhance the employability of students.

Additional Information

• NITI Aayog (National Institution for Transforming India):
• It was established on January 1, 2015, replacing the Planning Commission.
• It serves as the apex public policy Think Tank of the Government of India, focusing on Cooperative Federalism and sustainable development goals.
• The Prime Minister of India is the Ex-officio Chairperson, while the Vice-Chairperson and CEO handle administrative and strategic functions.
• National Education Policy (NEP) 2020:
• Launched in July 2020, it aims to transform India's education system by 2040.
• The policy promotes the entry of Top 100 Foreign Universities to set up campuses in India, facilitating Foreign Direct Investment (FDI) in the education sector.
• University Grants Commission (UGC):
• A statutory body established by the UGC Act, 1956, under the Ministry of Education.
• In 2023, the UGC released regulations allowing Foreign Higher Educational Institutions (FHEIs) to establish and operate campuses in India, which is a major step toward Internationalisation.
• Study in India (SII) Programme:
• A flagship project launched by the Ministry of Education in 2018.
• It aims to double the market share of international students coming to India by providing fee waivers and a centralized admission portal for over 160 selected Indian institutes.
• GIFT City Initiatives:
• The Gujarat International Finance Tec-City (GIFT City) in Gandhinagar is the first International Financial Services Centre (IFSC) in India to permit foreign universities like Deakin University and University of Wollongong from Australia to open independent campuses.

Important Points

• The report suggests regulatory reforms to reduce bureaucratic hurdles for international students, such as simplifying visa processes (e-FRRO) and granting post-study work permits.
• Internationalisation at Home: This concept mentioned in the report refers to integrating international and intercultural dimensions into the curriculum for all students, even those who do not travel abroad.
• Economic Impact: By attracting 5,00,000 international students by 2030, India can significantly boost its Foreign Exchange Earnings and improve the Global Soft Power index of the country.

Shortcut Trick

Take total work = 48 units ⇒ P=6, Q=3, R=2 per hour

First 9 hrs (P,Q,R cycle): (6+3+2)=11 per 3 hrs ⇒ 3 cycles ⇒ 33 units

Remaining = 48 − 33 = 15 units

Q+R cycle (2 hrs) = 5 units ⇒ 3 cycles ⇒ 6 hrs

∴ Answer = 6 hours

Alternate Method

Given:

P = 8 hrs, Q = 16 hrs, R = 24 hrs

Work in turns, P stops after 9 hrs

Formula used:

Total Work = LCM(8,16,24) = 48

Efficiency = Work ÷ Time

Calculations:

⇒ 3-hour cycle (P+Q+R) = 6+3+2 = 11

⇒ In 9 hrs ⇒ 3 cycles ⇒ work = 33

⇒ Remaining = 48 − 33 = 15

⇒ Q+R (2 hrs) = 3+2 = 5

⇒ Time = 15 ÷ 5 × 2 = 6 hrs

∴ The correct answer is 6 hours.

Additional Information

LCM Method

Use LCM to convert work into integer units.

Cyclic Work

If work repeats in pattern, calculate per cycle.

Efficiency

Efficiency = Total Work ÷ Time

Exam Tip

Solve alternating work using cycle method to save time.

The correct answer is Microprocessors.

Key Points

• The fourth generation of computers is defined by the use of Microprocessors, which started around 1971 and continues to the present day. These computers use Very Large Scale Integration (VLSI) technology, where thousands of transistors are integrated onto a single silicon chip.
• Vacuum tubes were the primary technology for the first generation of computers (1940-1956). They were large, expensive, and generated significant heat, leading to frequent malfunctions. Hence, this option is incorrect.
• Transistors characterized the second generation of computers (1956-1963). They replaced vacuum tubes, allowing computers to become smaller, faster, cheaper, and more energy-efficient. Hence, this option is incorrect.
• Integrated circuits (ICs) were the hallmark of the third generation of computers (1964-1971). By placing many transistors on a single chip, the speed and efficiency of computers increased significantly. Hence, this option is incorrect.
• Microprocessors allowed for the creation of the Personal Computer (PC). In 1971, the Intel 4004 chip was developed, locating all the components of the computer—from the central processing unit (CPU) and memory to input/output controls—on a single chip. Hence, this option is correct.

Additional Information

• Evolution of Hardware: The shift from LSI (Large Scale Integration) to VLSI enabled the miniaturization of circuits. This advancement allowed computers that once occupied entire rooms to fit on a desktop or even a palm.
• Software and Interface: The fourth generation saw the rise of Graphical User Interfaces (GUI), the mouse, and handheld devices. Operating systems like MS-DOS and later Windows and Apple Macintosh revolutionized how users interacted with machines.
• Networking: This era witnessed the birth and rapid expansion of the Internet. Computers became linked together to form networks, which eventually led to the global connectivity we see today.
• Memory and Storage: During this generation, semiconductor memory replaced magnetic core memory. Storage capacities increased exponentially with the development of hard disks and optical disks.
• Examples: Notable computers of this generation include the IBM PC, Apple II, STAR 1000, and CRAY-1 (supercomputer).

Important Points

• VLSI Technology: This technology allowed the integration of about 10,000 to 100,000 components on a single chip, drastically reducing the size and cost of manufacturing.
• The First Microprocessor: The Intel 4004, released in November 1971, is credited as the world's first commercially available microprocessor. It was a 4-bit CPU.
• Fifth Generation Transition: While the fourth generation is still prevalent, the fifth generation is emerging, characterized by Ultra Large Scale Integration (ULSI) and Artificial Intelligence (AI), focusing on natural language processing and self-learning capabilities.
• Impact on Society: The fourth generation made computing accessible to the general public, leading to the Digital Revolution and changing how data is processed across the globe.

The logic followed here is:

So, 'LFW 23' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

Shortcut Trick

572 is 30 less than 28% ⇒ 28% = 572 + 30 = 602

Total = 602 × 100 ÷ 28 = 2150

Friend % = 473 × 100 ÷ 2150

= 22%

∴ Answer = 22%

Alternate Method

Given:

Girish marks = 572

Short by 30 from 28% of total

Friend marks = 473

Formula used:

Total marks = (Given value × 100) ÷ Percentage

Percentage = (Marks × 100) ÷ Total

Calculations:

⇒ 28% of total = 572 + 30 = 602

⇒ Total marks = 602 × 100 ÷ 28

⇒ = 2150

⇒ Friend % = 473 × 100 ÷ 2150

⇒ = 22%

∴ The correct answer is 22%.

Additional Information

Reverse Percentage

If x is p% of total, then total = x × 100 ÷ p

Percentage Formula

Percentage = (Part ÷ Whole) × 100

Adjustment Trick

If short by value, add it before forming percentage

Exam Tip

Solve percentage questions by reversing conditions first

The correct answer is Robir Kiran.

Key Points

• Robir Kiran is a renowned cultural and musical organization that focuses on the promotion and preservation of Rabindra Sangeet (the songs of Rabindranath Tagore).
• The group was founded in the year 2015, making December 2025 the landmark occasion for its 10^th anniversary celebrations.
• It is led by the celebrated Rabindra Sangeet exponent Srabani Sen, who has been instrumental in training hundreds of students in the traditional and soulful renditions of Tagore's compositions.
• The 10^th-anniversary event in 2025 serves as a significant milestone for the cultural landscape of Kolkata, highlighting a decade of dedication to Bengali music and heritage.
• The organization operates primarily in Kolkata, West Bengal, and has expanded its reach through various digital platforms and international performances over the last number 10 years.

Additional Information

• Rabindra Sangeet: It refers to the body of 2,230 songs written and composed by the Nobel Laureate Rabindranath Tagore. These songs are a distinctive genre in the music of India and Bangladesh.
• Srabani Sen: She is a leading vocalist from the Srabani Sen Music Academy and Robir Kiran. She belongs to a prestigious musical lineage, being the daughter of the legendary singer Sumitra Sen and the sister of Indrani Sen.
• Kala Mandir: While mentioned as an option, Kala Mandir is actually a prestigious concert hall and auditorium located in Kolkata, which was established in 1968. It frequently hosts events for groups like Robir Kiran but is not a musical group itself celebrating a 10^th anniversary in 2025.
• Satyajit Ray Society: This organization was founded in 1994 to preserve and promote the legacy of the Oscar-winning filmmaker Satyajit Ray. Given its founding year, it does not align with a 10^th-anniversary celebration in 2025.
• Cultural Impact: Groups like Robir Kiran play a vital role in maintaining the UNESCO Intangible Cultural Heritage standards by passing down traditional art forms to the younger generation through structured pedagogy and public performances.

Important Points

• Establishment Year: The group Robir Kiran started its journey in May 2015, coinciding with the birth anniversary of Rabindranath Tagore (Pachishe Boishakh).
• Location: The primary base of operations and the 10^th-anniversary venue is Kolkata, often regarded as the Cultural Capital of India.
• Functions: The group serves dual functions: it acts as a music school for aspirants and a professional performing troupe for national and international festivals.
• Numerical Value: The 10-year journey of Robir Kiran has seen the documentation and performance of various Parjay (categories) of Tagore's songs, including Puja, Prakriti, and Prem.

The correct answer is Jharkhand.

Key Points

• The slash and burn agriculture is a primitive method of farming where forest land is cleared by cutting trees and burning the vegetation. In the state of Jharkhand, this practice is locally known as Kuruwa. Hence, the option Jharkhand is correct.
• In Madhya Pradesh, the slash and burn practice is known as Bewer or Dahiya. It is traditionally used by tribal communities like the Baigas. Hence, the option Madhya Pradesh is incorrect for the name Kuruwa.
• In Rajasthan, specifically in the South Eastern parts, the practice is known as Valre or Waltre. This method is often associated with the Bhil tribes of the Aravalli region. Hence, the option Rajasthan is incorrect.
• In Arunachal Pradesh and other North-Eastern states of India, slash and burn is famously known as Jhumming. It involves the cyclic movement of cultivators from one forest patch to another. Hence, the option Arunachal Pradesh is incorrect.
• The Kuruwa method in Jharkhand is primarily practiced by the Mal Paharia tribe in the Santal Pargana division to grow crops like maize and pulses.

Additional Information

• Regional Names in India:
• In the state of Odisha, this agricultural practice is identified by various names such as Pama Dabi, Koman, or Bringa.
• Across the Western Ghats, especially in Kerala and Karnataka, it is called Kumari.
• In the Himalayan belt, extending through Himachal Pradesh and Uttarakhand, it is referred to as Khil.
• In Andhra Pradesh and Telangana, the practice is popularly known as Podu or Penda.
• In Manipur, it is called Pamlou, and in the Bastar district of Chhattisgarh, as well as the Andaman and Nicobar Islands, it is known as Dipa.
• Global Nomenclature:
• In Mexico and Central America, the slash and burn system is known as Milpa.
• In Brazil (South America), it is referred to as Roca, while in Venezuela, it is called Conuco.
• In Central Africa, the term used is Masole.
• In Southeast Asia, it is called Ladang in Indonesia and Malaysia, and Ray in Vietnam.

Important Points

• Environmental Impact: While slash and burn agriculture is a traditional practice, it has come under scrutiny due to its contribution to deforestation, soil erosion, and loss of biodiversity. However, it is an integral part of the cultural identity and subsistence of many indigenous groups.
• Mechanism of Cultivation: The process relies on natural regeneration. After a harvest, the land is left fallow for several years (the fallow period can range from 5 to 20 years) to regain its soil fertility before the farmers return to burn and plant again.
• Government Regulations: In India, the National Forest Policy and various state-level guidelines have been formulated to discourage shifting cultivation and encourage settled agriculture to protect forest cover.

Shortcut Trick

Let Anil = A, Ashok = B

Equal amounts: A(1.1)¹⁵ = B(1.1)¹⁶

⇒ A = 1.1B

⇒ A + B = 1407 ⇒ 1.1B + B = 2.1B = 1407

⇒ B = 1407 ÷ 2.1 = 670

∴ Answer = 670

Alternate Method

Given:

Total = 1407

Rate = 10% per annum

Formula:

A = P(1 + r/100)ⁿ

Calculations:

⇒ Let Anil = A, Ashok = B

⇒ A(1.1)¹⁵ = B(1.1)¹⁶

⇒ Divide both sides by (1.1)¹⁵

⇒ A = B(1.1)

⇒ A + B = 1407

⇒ 1.1B + B = 1407

⇒ 2.1B = 1407

⇒ B = 1407 ÷ 2.1 = 670

Final Answer: 670

Additional Information

Compound Interest: A = P(1 + r/100)ⁿ

Key Insight: Cancel common powers to simplify equation

Ratio Concept: A : B = 1.1 : 1

Exam Trick: Convert decimal into fraction for faster division

The correct answer is Mining & Quarrying.

Key Points

• The National Statistical Office (NSO), under the Ministry of Statistics and Programme Implementation (MoSPI), released the Gross Value Added (GVA) data for the first quarter (Q1) of the financial year. While most sectors showed resilience, the Mining & Quarrying sector is often highlighted due to its high volatility and specific monthly contractions reported within the fiscal year.
• During the August 2024 period (which falls within the early data cycle for the current fiscal), the Index of Industrial Production (IIP) showed that the mining sector contracted by 4.3%. This negative growth was primarily attributed to heavy rainfall hindering mining operations in several parts of the country.
• The Agriculture and Allied sector recorded a growth rate of 2.0% in Q1 FY 2024-25, which was a significant slowdown compared to previous years but remained in positive territory. Hence, the statement regarding agriculture showing negative growth is incorrect.
• The Construction sector emerged as one of the fastest-growing segments, recording a robust growth of 10.5% in Q1. This growth was driven by the Government of India’s continued focus on infrastructure and capital expenditure. Hence, the statement regarding construction having negative growth is incorrect.
• The Tertiary Sector (Services), specifically the 'Financial, Real Estate & Professional Services' segment, grew by 7.1%, while 'Trade, Hotels, Transport, and Communication' grew by 5.7%. These sectors maintained a steady upward trajectory. Hence, the statement regarding the tertiary sector showing negative growth is incorrect.
• In the Q1 FY 2024-25 report, the Real GVA at basic prices was estimated at ₹40.73 lakh crore, showing a growth rate of 6.8% over the previous year. Mining & Quarrying, though growing 7.2% in the specific Q1 GVA data, faced the sharpest monthly decline later in the cycle, marking it as the sector with specific negative growth intervals in 2024.

Additional Information

• Gross Value Added (GVA):
• GVA is a measure of the total value of goods and services produced in an economy. It is defined as GDP minus net taxes (taxes on products minus subsidies on products).
• It provides a sector-specific picture of the economy, helping policymakers understand which industries (like Manufacturing or Services) are driving growth.
• National Statistical Office (NSO):
• The NSO was formed by the merger of the National Sample Survey Office (NSSO) and the Central Statistics Office (CSO) on May 23, 2019.
• It functions under MoSPI and is responsible for conducting large-scale surveys and releasing critical economic data like CPI (Consumer Price Index) and IIP.
• Index of Industrial Production (IIP):
• The IIP is an index that tracks the growth rates in different industry groups of the economy. The Base Year for IIP in India is currently 2011-12.
• It comprises three broad sectors: Mining (14.37% weight), Manufacturing (77.63% weight), and Electricity (7.99% weight).
• Economic Trends in FY 2024-25:
• The Real GDP growth for Q1 FY 2024-25 was recorded at 6.7%, slightly lower than the 8.2% recorded in the same quarter of the previous year.
• External factors such as global supply chain disruptions and internal factors like monsoon variability significantly influence the Agriculture and Mining sectors in India.

Important Points

• Mining Sector Challenges: The negative growth in monthly output for Mining in mid-2024 was a result of excessive rainfall in coal-bearing areas like Jharkhand, Odisha, and Chhattisgarh, which stalled the extraction of natural resources.
• Sectoral Contributions: The Secondary Sector (including Manufacturing and Electricity) showed the highest growth in the first quarter of 2024-25, with the Electricity, Gas, and Water Supply segment growing at a massive 10.4%.
• Data Frequency: While GVA data is released on a quarterly basis, IIP data is released monthly, providing a more granular look at industrial health.

Shortcut Trick

Let son = x ⇒ Sharad = 3x, daughter = x − 3

3 years ago total = 63 ⇒ present total = 63 + 9 = 72

⇒ 3x + x + (x − 3) = 72

⇒ 5x − 3 = 72 ⇒ x = 15

⇒ Sharad = 3x = 45

∴ Answer = 45

Alternate Method

Given:

Sharad = 3 × son

Daughter = son − 3

Sum 3 years ago = 63

Formula:

Present age = Past age + 3

Calculations:

⇒ Let son = x

⇒ Sharad = 3x, daughter = x − 3

⇒ Sum 3 years ago:

(3x − 3) + (x − 3) + (x − 6) = 63

⇒ 5x − 12 = 63

⇒ 5x = 75 ⇒ x = 15

⇒ Sharad = 3x = 45

Final Answer: 45

Additional Information

Age Concept: Sum increases by 3 × number of persons every 3 years

Linear Relation: Express all ages in one variable

Shortcut Tip: Convert past sum to present sum quickly

Exam Trick: Avoid long equations using total adjustment

Given number: 15762349

Logic:

Arrange the digits in ascending order and compare their original positions with the new arrangement.

Original number: 1 5 7 6 2 3 4 9

Ascending order:  1, 2, 3, 4, 5, 6, 7, 9

Digits unchanged in position: 1 and 9 → 2 digits

Hence, the correct answer is Option 4.

Shortcut Trick

Total members = 78 + 22 + 34 = 134

⇒ Ratio = 78:22:34 = 39:11:17

⇒ Weighted avg = (39×136 + 11×383 + 17×457) ÷ 67

⇒ = (5304 + 4213 + 7769) ÷ 67 = 17286 ÷ 67 = 258

∴ Answer = 258

Alternate Method

Given:

A: 78 members, avg = 136

B: 22 members, avg = 383

C: 34 members, avg = 457

Formula:

Overall avg = (Σ (n × avg)) ÷ Σ n

Calculations:

⇒ Total amount A = 78 × 136 = 10608

⇒ Total amount B = 22 × 383 = 8426

⇒ Total amount C = 34 × 457 = 15538

⇒ Total amount = 10608 + 8426 + 15538 = 34572

⇒ Total members = 134

⇒ Average = 34572 ÷ 134 = 258

Final Answer: 258

Additional Information

Weighted Average: (Σ n_ix_i) ÷ Σ n_i

Ratio Trick: Simplify group sizes before calculation

Concept: Larger group dominates overall average

Exam Tip: Use reduced ratio to save time

Given: (Left) © 3 @ 8 5 1 £ 1 6 1 5 7 2 8 # € £ © € © 1 3 (Right)

Now,

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

So, Needed pattern is: Symbol - Number - Symbol.

(Left) © 3 @ 8 5 1 £ 1 6 1 5 7 2 8 # € £ © € © 1 3 (Right)

Only one number satisfies the condition.

Hence, the correct answer is 'Option 1'.

The correct answer is Lieutenant Governor.

Key Points

• According to Article 239 of the Constitution of India, every Union Territory is administered by the President acting, to such extent as he thinks fit, through an administrator appointed by him with such designation as he may specify.
• In the Union Territories of Andaman and Nicobar Islands, Puducherry, Delhi, Jammu and Kashmir, and Ladakh, the administrators are specifically designated as the Lieutenant Governor.
• The Lieutenant Governor serves as the representative or agent of the President of India and functions as the constitutional head of the respective Union Territory.
• In Puducherry and Delhi, the Lieutenant Governor operates with a Legislative Assembly and a Council of Ministers, whereas in Andaman and Nicobar Islands, there is no such legislature, and the Lieutenant Governor holds direct administrative authority.
• This designation distinguishes these territories from other Union Territories like Chandigarh, Lakshadweep, or Dadra and Nagar Haveli and Daman and Diu, where the head is simply termed the Administrator.

Additional Information

• Andaman and Nicobar Islands: This territory is located in the Bay of Bengal and consists of a group of 572 islands. The capital is Port Blair. It was declared a Union Territory in 1956. It falls under the jurisdiction of the Calcutta High Court.
• Puducherry: Formerly known as Pondicherry, it was a French colonial settlement until 1954. It comprises four non-contiguous districts: Puducherry, Karaikal, Mahe, and Yanam. Under Article 239A, it was granted a Legislative Assembly and a Council of Ministers in 1963.
• Governor vs. Lieutenant Governor: A Governor is the constitutional head of a State (under Article 153) and possesses independent constitutional powers, whereas a Lieutenant Governor is an administrator appointed by the President and acts as his delegate.
• Union Territories without Legislatures: Territories like Lakshadweep and Chandigarh do not have their own Legislative Assemblies. In Chandigarh, the Governor of Punjab is generally appointed as the Administrator.

Important Points

• The 7^th Constitutional Amendment Act of 1956 led to the reorganization of states and the formal creation of the category of Union Territories.
• The President can also appoint the Governor of an adjoining State as the administrator of a Union Territory, and in such cases, the Governor exercises his functions independently of his Council of Ministers.
• While the Parliament has the power to make laws on any subject in the State List for Union Territories, the President can make regulations for the peace, progress, and good government of certain UTs like Andaman and Nicobar and Lakshadweep.
• The Ministry of Home Affairs (MHA) is the nodal ministry for all matters of Union Territories relating to legislation, appointments of administrators, and budgetary allocations.

The correct answer is March 2024.

Key Points

• The India-European Free Trade Association (EFTA) signed the historic Trade and Economic Partnership Agreement (TEPA) on March 10, 2024. This marks a milestone in India's economic relations with the European bloc. Hence, the statement regarding the signing month is correct.
• The agreement was signed between India and the four EFTA member states, which include Iceland, Liechtenstein, Norway, and Switzerland. These nations are not part of the European Union (EU) but maintain high standards of economic development.
• For the first time in the history of Free Trade Agreements (FTAs), a legal commitment has been made for Foreign Direct Investment (FDI). The EFTA countries have committed to investing $100 billion in India over the next 15 years.
• The TEPA is expected to generate approximately 1 million direct jobs in India through these committed investments, significantly boosting the manufacturing and services sectors.
• The agreement consists of 14 chapters, covering various aspects such as Trade in Goods, Rules of Origin, Trade in Services, Investment Promotion, and Intellectual Property Rights (IPR).

Additional Information

• European Free Trade Association (EFTA):
• It was founded in 1960 through the Stockholm Convention as an alternative for states that did not wish to join the then European Economic Community.
• Its current headquarters is located in Geneva, Switzerland.
• The EFTA countries are among the most competitive and innovative economies globally, with high GDP per capita.
• Trade in Goods and Market Access:
• Under the TEPA, India is offering 92.2% of its tariff lines to EFTA exporters, which covers 99.6% of EFTA exports to India.
• Conversely, EFTA is offering 92.7% of its tariff lines, covering 99% of India's exports.
• Specifically, India will benefit from 100% market access for its non-agricultural products in EFTA countries.
• Services and Digital Trade:
• The deal includes provisions for Mutual Recognition Agreements (MRAs) in professional services like Nursing, Chartered Accountancy, and Architectural Services.
• It facilitates easier Visa norms for Indian professionals (Mode 4 supply of services) to work in EFTA nations.
• Strategic Significance:
• The signing in 2024 reflects India's strategy to diversify its trade partners and integrate more deeply into Global Value Chains (GVCs).
• The TEPA serves as a template for India’s future negotiations with other major blocs like the UK and the EU.

Important Points

• Key Figures: The agreement was finalized after 21 rounds of negotiations that spanned over 15 years, having initially started in 2008.
• Sectors Involved: Major sectors expected to benefit include Pharmaceuticals, Machinery, Watches, Chemicals, and Food Processing.
• Ratification Process: While the signing took place in March 2024, the agreement requires ratification by the Parliaments of all involved nations before it formally comes into force, as seen with the target date of 1 October 2025 mentioned in the query.
• Intellectual Property: Switzerland, being a global hub for Innovation, ensured high standards for IPR protection, which aligns with India's evolving Intellectual Property regime$.

The logic followed here is:

Logic: The second number is obtained by multiplying the first number by 2 and adding three times the third number.

For, (20, 46, 2)

⇒ 20 × 2 = 40

⇒ 2 × 3 = 6

⇒ 40 + 6 = 46

For, (32, 136, 24)

⇒ 32 × 2 = 64

⇒ 24 × 3 = 72

⇒ 64 + 72 = 136

Now, checking the options using the same pattern:

Option 1) (6, 42, 10)

⇒ 6 × 2 = 12

⇒ 10 × 3 = 30

⇒ 12 + 30 = 42

Option 2) (13, 25, 1)

⇒ 13 × 2 = 26

⇒ 1 × 3 = 3

⇒ 26 + 3 = 29 ≠ 25

Option 3) (32, 93, 11)

⇒ 32 × 2 = 64

⇒ 11 × 3 = 33

⇒ 64 + 33 = 97 ≠ 93

Option 4) (17, 78, 16)

⇒ 17 × 2 = 34

⇒ 16 × 3 = 48

⇒ 34 + 48 = 82 ≠ 78

Hence, the correct answer is Option 1.

The correct answer is Bangladesh and Pakistan.

Key Points

• India shares its land boundaries with seven countries. According to the Ministry of Home Affairs, the total length of India's land border is approximately 15,106.7 km.
• The length of the border with China is 3,488 km, which is the second-longest border India shares with any neighbor.
• The border with Bangladesh is the longest at 4,096.7 km, while the border with Pakistan is 3,323 km. When combined, the total land border for Bangladesh and Pakistan stands at 7,419.7 km, which is significantly longer than China's border. Hence, statement 1 is correct.
• The border with Bhutan is 699 km and with Afghanistan is 106 km. Combined, they equal 805 km, which is much less than China's 3,488 km. Hence, statement 2 is incorrect.
• The border with Nepal is 1,751 km and with Myanmar is 1,643 km. Combined, they equal 3,394 km. This is slightly shorter than the border with China. Hence, statement 3 is incorrect.
• The border with Pakistan (3,323 km) and Nepal (1,751 km) totals 5,074 km. While this is longer than China's border, the combination of Bangladesh and Pakistan represents a much larger aggregate. Hence, statement 4 is incorrect in the context of being the primary comparison pair for land length extremes.

Additional Information

• Bangladesh Border: It is the fifth-longest land border in the world. It passes through five Indian states: West Bengal, Assam, Meghalaya, Tripura, and Mizoram. The boundary was determined by the Radcliffe Line in 1947.
• China Border (Line of Actual Control): This border is divided into three sectors: Western (Ladakh), Middle (Himachal Pradesh and Uttarakhand), and Eastern (Sikkim and Arunachal Pradesh). The McMahon Line, determined in 1914, serves as the effective boundary in the Eastern sector.
• Pakistan Border: This border runs along the states of Gujarat, Rajasthan, Punjab, and the Union Territories of Jammu and Kashmir and Ladakh. It includes the International Border (IB), the Line of Control (LoC), and the Actual Ground Position Line (AGPL) in the Siachen region.
• Nepal and Myanmar Borders: The border with Nepal is an open border, shared by Uttarakhand, Uttar Pradesh, Bihar, West Bengal, and Sikkim. The Myanmar border runs along the four northeastern states: Arunachal Pradesh, Nagaland, Manipur, and Mizoram.

Important Points

• Shortest Border: India shares its shortest land boundary with Afghanistan (106 km) in the Wakhan Corridor, touching the Union Territory of Ladakh.
• Maritime Neighbors: Apart from land borders, India has maritime boundaries with Sri Lanka (separated by the Palk Strait and Gulf of Mannar) and the Maldives.
• Border Guarding Forces: Different paramilitary forces guard these borders: the Border Security Force (BSF) guards the Bangladesh and Pakistan borders; the Indo-Tibetan Border Police (ITBP) guards the China border; and the Sashastra Seema Bal (SSB) guards the Nepal and Bhutan borders.
• Tri-junctions: India has several critical tri-junctions, such as the one between India, China, and Bhutan at Doklam and the one between India, China, and Afghanistan in the north.

Shortcut Trick

Cube side = 8 m, cylinder h = 4 m ⇒ layers = 8/4 = 2

Base: diameter = 1 m ⇒ 8 ÷ 1 = 8 cylinders per side

⇒ Total cylinders = 8 × 8 × 2 = 128

Surface area (1 cyl) = 2πr(h + r) = 2 × 22/7 × 0.5 × 4.5 = 99/7

⇒ Total cost = 128 × 99/7 × 14 = 25344

∴ Answer = 25344

Alternate Method

Given:

Cube side = 8 m

Cylinder: diameter = 1 m ⇒ r = 0.5 m, height = 4 m

Rate = ₹14/m²

Formula:

Number of cylinders = (8 ÷ 1)² × (8 ÷ 4)

Total surface area = 2πr(h + r)

Calculations:

⇒ Cylinders per layer = 8 × 8 = 64

⇒ Layers = 2

⇒ Total cylinders = 64 × 2 = 128

⇒ Surface area of 1 cylinder:

= 2 × 22/7 × 0.5 × (4 + 0.5)

= 2 × 22/7 × 0.5 × 4.5

= 99/7

⇒ Total area = 128 × 99/7

⇒ Cost = 128 × 99/7 × 14 = 25344

Final Answer: ₹25344

Additional Information

Cylinder Count: Floor packing = (side ÷ diameter)² × layers

Total Surface Area: 2πr(h + r)

Optimization: Use full packing to maximize number

Exam Trick: Cancel π early to simplify calculations

Shortcut Trick

Assume mean ≈ 60

Deviation method:

⇒ Σfd = (21×15 + (-25)×4 + 13×3 + (-4)×16 + 0×?) = 315 -100 +39 -64 = 190

⇒ Total f = 38

⇒ Mean ≈ 60 + (190/38) = 60 + 5 = 65

∴ Answer = 65

Alternate Method

Given:

Values (x): 81, 35, 73, 56

Frequencies (f): 15, 4, 3, 16

Formula:

Mean = Σ(fx) ÷ Σf

Calculations:

⇒ 81×15 = 1215

⇒ 35×4 = 140

⇒ 73×3 = 219

⇒ 56×16 = 896

⇒ Σfx = 1215 + 140 + 219 + 896 = 2470

⇒ Σf = 15 + 4 + 3 + 16 = 38

⇒ Mean = 2470 ÷ 38 = 65

Final Answer: 65

Additional Information

Mean Formula: Mean = Σ(fx) ÷ Σf

Shortcut Method: Assumed mean reduces calculation load

Deviation Method: Mean = A + (Σfd ÷ Σf)

Exam Tip: Choose central value as assumed mean

Shortcut Trick

Regular hexagon = 6 equilateral triangles

Area = 6 × (√3/4 × a²)

= (3√3/2) × a²

a = 14√3 ⇒ a² = 588

Area = (3√3/2) × 588 = 882√3

∴ Answer = 882√3 cm²

Alternate Method

Given:

Side of hexagon a = 14√3 cm

Formula used:

Area of regular hexagon = (3√3/2) × a²

Regular Hexagon (6 equal sides) a = 14√3

Calculations:

⇒ a = 14√3

⇒ a² = (14√3)² = 196 × 3 = 588

⇒ Area = (3√3/2) × 588

⇒ = 3 × 294 × √3

⇒ = 882√3

∴ The correct answer is 882√3 cm².

Additional Information

Hexagon Property

A regular hexagon can be divided into 6 equilateral triangles.

Equilateral Triangle Area

Area = (√3/4) × a²

Direct Formula

Area of hexagon = (3√3/2) × a²

Exam Tip

Always square side first to simplify quickly.

The correct answer is To promote trade and investment.

Key Points

• The primary objective of the high-level discussions held in New Delhi on 16 October 2025 between India and MERCOSUR representatives was to promote trade and investment by expanding the scope of the existing Preferential Trade Agreement (PTA). Hence, the statement regarding promoting trade and investment is correct.
• The India–MERCOSUR PTA is a limited-scope agreement designed to reduce tariffs on a specific list of goods, thereby enhancing bilateral commercial ties between the South Asian giant and the South American trade bloc.
• During the 2025 talks, both parties aimed to increase the number of tariff lines (products) included in the agreement, which currently covers around 450 to 500 items, to a much larger basket to reflect current economic realities.
• The discussions did not pertain to defense policies or military coordination, as these fall under separate bilateral security frameworks rather than a trade agreement. Hence, the statement regarding defense policies is incorrect.
• Standardizing education systems or establishing a common currency (similar to the Euro) were not on the agenda, as MERCOSUR and India maintain distinct sovereign monetary policies and educational standards. Hence, statements regarding education systems and common currency are incorrect.

Additional Information

• What is MERCOSUR?:
• MERCOSUR (Southern Common Market) is a regional trade bloc established in 1991 by the Treaty of Asunción.
• The full members of this organization are Argentina, Brazil, Paraguay, and Uruguay. Bolivia has also undergone the process of becoming a full member.
• The headquarters of MERCOSUR is located in Montevideo, Uruguay.
• History of India-MERCOSUR PTA:
• A Framework Agreement was signed in June 2003 at Asunción to create a free trade area.
• The actual Preferential Trade Agreement was signed on 25 January 2004 and became fully operational in June 2009.
• The agreement provides for tariff concessions ranging from 10% to 100% on agreed-upon goods.
• Trade Basket:
• India’s major exports to MERCOSUR include refined petroleum, organic chemicals, pharmaceuticals, and machinery.
• India’s major imports from the bloc include crude oil, vegetable oils (soybean), sugar, and mining products.

Important Points

• Expansion Efforts: India has been keen on expanding the PTA to include up to 3,000 tariff lines to tap into the vast potential of the Latin American market.
• South-South Cooperation: This agreement is a landmark in South-South Cooperation, allowing developing economies to build resilient supply chains independent of traditional Western markets.
• Economic Impact: In recent fiscal years, bilateral trade has fluctuated between $10 billion and$15 billion, with the 2025 discussions aiming to push this figure significantly higher through deregulation and investment protection clauses.
• Legal Framework: Any expansion of the PTA requires a Protocol of Amendment to be ratified by the Parliaments of all involved sovereign nations before coming into force.

The correct answer is Regulation of market prices and rationing.

Key Points

• Alauddin Khilji (reigned 1296–1316) was the most powerful ruler of the Khilji Dynasty of the Delhi Sultanate. He is famously known for his radical administrative and economic reforms.
• One of his most significant innovations was the Regulation of market prices. He fixed the prices of all essential commodities, ranging from food grains, cattle, and horses to slaves and cloth. Hence, this option is the correct attribution to his reign.
• To ensure the success of these price controls, he established a rationing system. During times of scarcity or famine, grain was released from government granaries, and no individual was allowed to buy more than a specified quantity. Hence, the statement regarding market regulation and rationing is correct.
• He appointed a dedicated officer known as the Shahna-i-Mandi to supervise the grain market and ensured that merchants complied with the state-fixed rates.
• The primary objective of these market reforms was to maintain a massive standing army at a low cost to defend the empire against Mongol invasions.

Additional Information

• Creation of the Mansabdari System:
• The Mansabdari system was an administrative and military system introduced by the Mughal Emperor Akbar in 1571. It was not a Khilji innovation. Hence, this statement is incorrect.
• Under this system, every officer was assigned a rank (Mansab), which determined their status, salary, and the number of cavalrymen they were required to maintain.
• Foundation of Diwan-i-Arz:
• The Diwan-i-Arz (the Military Department) was originally established by Ghiyasuddin Balban of the Slave Dynasty to improve military organization. Hence, this statement is incorrect.
• While Alauddin Khilji significantly strengthened this department and introduced cash salaries for soldiers, he was not its founding creator.
• Establishment of the Iqta System:
• The Iqta system was a practice of granting revenue-yielding land to officers in lieu of cash salaries. It was formalized and expanded by Shamsuddin Iltutmish. Hence, this statement is incorrect.
• Interestingly, Alauddin Khilji acted against this system by abolishing small Iqtas and converting them into Khalisa land (crown land) to increase state revenue.

Important Points

• Military Reforms: Alauddin introduced the system of Dagh (branding of horses) and Chehra (descriptive roll of soldiers) to prevent corruption and proxy soldiers in the army.
• Revenue Administration: He was the first Sultan to insist that land revenue be based on the measurement of land (Paimaish). He also introduced the Ghari (house tax) and Chari (pasture tax).
• Centralization: He prohibited the social gatherings of nobles and the use of liquor to prevent conspiracies against the throne.
• Geographical Expansion: His general Malik Kafur led successful expeditions into South India, reaching as far as Madurai, and extracting tributes from the Yadavas, Kakatiyas, and Hoysalas.

The logic followed here is:

So, '92' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

The correct answer is Business and Commerce.

Key Points

• Business and Commerce is the primary sector that utilizes computers for online transactions, which involve the buying and selling of goods and services over the internet through E-commerce platforms.
• Computers in this sector facilitate payroll processing, an essential function where software calculates employee salaries, tax deductions, insurance premiums, and allowances automatically, ensuring 100% accuracy and timely payments.
• Inventory control is managed using computerized systems like ERP (Enterprise Resource Planning) and Inventory Management Software to track stock levels, orders, sales, and deliveries, thereby preventing overstocking or stockouts.
• Data analysis in business involves using computational tools to process big data, identify market trends, and understand consumer behavior. This helps organizations in strategic planning and decision-making.
• The integration of Information Technology (IT) in Business and Commerce has led to the development of Digital Marketing, Customer Relationship Management (CRM), and Supply Chain Management (SCM), making operations more efficient and cost-effective.

Additional Information

• Manufacturing Plants:
• In the manufacturing sector, computers are used for CAD (Computer-Aided Design) and CAM (Computer-Aided Manufacturing) to design products and control automated assembly lines.
• They monitor real-time production data, manage quality control, and oversee Robotic Process Automation (RPA) to increase productivity and reduce human error.
• Research:
• The Research and Development (R&D) sector uses Supercomputers and High-Performance Computing (HPC) for complex simulations, scientific modeling, and data crunching.
• In fields like Space Research (e.g., ISRO or NASA), computers are used for satellite tracking and launch vehicle control. In Healthcare Research, they aid in genomic sequencing and drug discovery.
• Service Industry:
• This sector includes Banking, Hospitality, Healthcare, and Transportation.
• In Banking, computers handle Core Banking Solutions (CBS), ATM operations, and Internet Banking. In Healthcare, computers manage Electronic Health Records (EHR) and control advanced diagnostic equipment like MRI and CT scan machines.

Important Points

• Historical Context: The use of computers in business dates back to the 1950s with the UNIVAC I, which was used for census data and payroll. By the 1980s, the introduction of the Personal Computer (PC) revolutionized small business operations.
• Economic Impact: The transition to digital commerce (Digital India initiative launched in 2015) has significantly contributed to the GDP by enabling paperless transactions and increasing transparency.
• Security Measures: With the rise of online transactions, businesses implement Cybersecurity protocols such as SSL encryption, Two-Factor Authentication (2FA), and Firewalls to protect sensitive financial data from cyber threats.

Family Chart:

Decoding the Symbols:

Given: E + R @ D % N # B

It means: E is the wife of R, R is the son of D, D is the father of N, N is the sister of B.

 

Here, E is B’s brother’s wife

Hence, the correct answer is "Option 3".

The logic followed here is:

Option 1) UWR

Option 2) SUP

Option 3) KMG

Option 4) EGB

Now, KMG follows a different pattern.

Hence, the correct answer is Option 3.

BODMAS Table: 

Given expression: 20 D 8 A 2 C 1 B 5 = ?

Now, if the operations are interchanged as: D → −, A → ÷, C → +, B → ×

⇒ 20 − 8 ÷ 2 + 1 × 5 = ?

⇒ 20 − 4 + 1 × 5 = ?

⇒ 20 − 4 + 5 = ?

⇒ 16 + 5 = 21

Hence, the correct answer is "Option 4".

Shortcut Trick

Both equations have same roots ⇒ coefficients proportional

(8A+4) : B : (4A−8) = (6A+3) : K : (3A−6)

Compare first & third ⇒ ratio = 4/3

⇒ B/K = 4/3

⇒ 9B² − 16K² = 0

∴ Answer = 0

Alternate Method

Given:

Two quadratic equations have same roots

Formula used:

If roots are same ⇒ coefficients are proportional

Calculations:

⇒ First equation: (8A+4)x² + Bx + (4A−8)

⇒ Second equation: (6A+3)x² + Kx + (3A−6)

⇒ Ratio = (8A+4)/(6A+3)

⇒ Factor ⇒ 4(2A+1)/3(2A+1) = 4/3

⇒ So B/K = 4/3

⇒ ⇒ 3B = 4K

⇒ 9B² − 16K²

⇒ = (3B)² − (4K)²

⇒ = (3B − 4K)(3B + 4K)

⇒ = 0

∴ The correct answer is 0.

Additional Information

Common Roots Rule

If two quadratic equations have same roots, their coefficients are proportional.

Factorization Trick

Factor expressions to identify common ratios quickly.

Difference of Squares

a² − b² = (a − b)(a + b)

Exam Tip

Always compare leading coefficients first for quick ratio.

Given: A, B, C, D, E and F live on six different floors of the same building. The lowermost floor is numbered 1 and the topmost floor is numbered 6.

Only two people live below C.

Only two people live between B and C.

A lives above E but below C.

F does not live above D.

Now, the person immediately below B (floor 6) is D.

Hence, the correct answer is Option 3.

The correct answer is Portuguese.

Key Points

• The Portuguese were the first European power to arrive in India and also the last European power to leave India. Hence, option 3 is correct.
• Vasco da Gama, a Portuguese explorer, reached Calicut (Kozhikode) in 1498 through the sea route around the Cape of Good Hope.
• The Portuguese established their first Indian colony at Goa in 1510 under the leadership of Afonso de Albuquerque.
• Although the British left India in 1947, the Portuguese continued to control territories such as:
• Goa
• Daman
• Diu

until 1961, when these territories were integrated into India through Operation Vijay.

• Option-wise Analysis:
• Americans – Did not establish colonial rule in India.
• Dutch – Arrived after the Portuguese and left earlier.
• Portuguese – First to arrive and last to leave India. Correct.
• French – Controlled settlements like Puducherry but left before the Portuguese.
• Hence, the correct answer is Portuguese.

Additional Information

• Major European powers that came to India during the medieval and colonial period include:
• Portuguese – 1498
• Dutch – 1605
• English – 1608
• French – 1664
• The Portuguese introduced several new items and practices in India such as:
• Tobacco
• Cashew
• Printing Press
• Goa became a Union Territory after its liberation in 1961 and later attained statehood in 1987.
• The Portuguese were mainly interested in controlling the spice trade and maritime commerce in the Indian Ocean.
• Operation Vijay was the military operation conducted by India in December 1961 to end Portuguese rule in India.

Important Points

• Vasco da Gama reached India during the reign of Zamorin of Calicut.
• Questions related to European trading companies, colonial history, important dates, and freedom movement are frequently asked in competitive examinations.

Shortcut Trick

Opposite direction ⇒ relative speed = 60 + 84 = 144 km/hr

Convert: 144 × 5/18 = 40 m/s

Distance = speed × time = 40 × 30

= 1200 m

∴ Answer = 1200 m

Alternate Method

Given:

Speed of train 1 = 60 km/hr

Speed of train 2 = 84 km/hr

Time = 30 sec

Formula used:

Distance = Relative Speed × Time

Calculations:

⇒ Relative speed = 60 + 84 = 144 km/hr

⇒ Convert to m/s = 144 × 5/18 = 40 m/s

⇒ Distance = 40 × 30 = 1200 m

∴ The correct answer is 1200 m.

Additional Information

Relative Speed

Opposite direction ⇒ speeds add.

Unit Conversion

km/hr to m/s ⇒ multiply by 5/18

Train Crossing

Distance covered = sum of lengths of trains

Exam Tip

Always convert speed before multiplying with time

Shortcut Trick

Z = 5 parts = 23000 ⇒ 1 part = 4600

X = 4 parts = 18400, Y = 2 parts = 9200

X time-adjusted = 6 + 3 = 9 months

Ratio ⇒ X:Y:Z = (4×9):(2×12):(5×12) = 36:24:60

Difference (X−Y) = 12 parts ⇒ 12/120 × 37000

∴ Answer = 3700

Alternate Method

Given:

Ratio = 4 : 2 : 5

Z investment = 23000

Total profit = 37000

Formula used:

Profit ∝ Capital × Time

Calculations:

⇒ Total ratio = 36 + 24 + 60 = 120

⇒ Difference (X−Y) = 36 − 24 = 12

⇒ Profit difference = 12/120 × 37000

⇒ = 3700

∴ The correct answer is 3700.

Additional Information

Profit Sharing Rule

Profit ∝ Capital × Time

Capital Change

If capital changes, split time accordingly

Ratio Conversion

Convert all into same time base before comparing

Exam Tip

Work directly with ratios to avoid large calculations

The correct answer is New Zealand.

Key Points

• India defeated New Zealand in the 2025 ICC Champions Trophy final in Dubai to secure their seventh ICC men’s senior cricket title.
• This marked India's third Champions Trophy title and their second consecutive ICC win.
• Rohit Sharma led from the front, scoring 76 runs off 83 balls, and was named Player of the Match.
• This was India's seventh ICC senior men's title and their second consecutive ICC trophy following the 2024 T20 World Cup.
• New Zealand's Rachin Ravindra was honored for his consistent performance throughout the series.

 

Additional Information

• India’s ICC Trophy History:
• India has now won a total of seven major ICC titles: the 1983 Cricket World Cup, the 2002 ICC Champions Trophy (shared with Sri Lanka), the 2007 ICC T20 World Cup, the 2011 Cricket World Cup, the 2013 ICC Champions Trophy, the 2024 ICC T20 World Cup, and the 2025 ICC Champions Trophy.
• With this win, Rohit Sharma became one of the most successful captains in Indian history, leading the team to back-to-back global trophies in 2024 and 2025.
• Tournament Format and Context:
• The 2025 ICC Champions Trophy was the 9^th edition of the tournament, featuring the top 8 teams based on their rankings in the 2023 ODI World Cup.
• The tournament was hosted using a hybrid model; while Pakistan was the official host, several matches, including the Final, were moved to Dubai due to administrative and security considerations.

Important Points

• Key Statistics:
• Shubman Gill finished the tournament as one of the leading run-getters, while Jasprit Bumrah was instrumental with the ball, maintaining an economy rate of under 4.5 throughout the event.
• The win elevated India to the Number 1 spot in the ICC ODI Team Rankings, surpassing Australia.
• Venue Details:
• The Dubai International Stadium, known for its "Ring of Fire" floodlights, hosted the final with a capacity crowd of over 25,000 spectators.
• The pitch for the final was a balanced track, offering assistance to spinners in the first innings and becoming better for batting under lights.

Shortcut Trick

Take a = 2, b = 3

Numerator = 7×8 − 2×27 = 56 − 54 = 2

Denominator = 27 − 8 = 19

∴ Answer = 2 : 19

Alternate Method

Given:

a : b = 2 : 3

Formula used:

If a : b = m : n ⇒ a = mx, b = nx

Calculations:

⇒ Let a = 2x, b = 3x

⇒ a³ = 8x³, b³ = 27x³

⇒ Numerator = 7a³ − 2b³

⇒ = 7×8x³ − 2×27x³

⇒ = 56x³ − 54x³ = 2x³

⇒ Denominator = b³ − a³

⇒ = 27x³ − 8x³ = 19x³

⇒ Ratio = 2x³ : 19x³

⇒ = 2 : 19

∴ The correct answer is 2 : 19.

Additional Information

Ratio Substitution

Replace variables using given ratio to simplify expressions.

Power Handling

Apply powers to both numerator and denominator terms carefully.

Common Factor

Cancel common terms like x³ to simplify ratio.

Exam Tip

Use direct substitution (a=2, b=3) for fastest solving.

Shortcut Trick

Apply BODMAS:

⇒ (-56) ÷ (-14) = 4

⇒ (-4) × 7 = -28

⇒ Expression = -9 - 4 - 28

⇒ = -41

∴ Answer = -41

Alternate Method

Given:

(-9) - (-56) ÷ (-14) + (-4) × 7

Formula:

BODMAS Rule

Calculations:

⇒ (-56) ÷ (-14) = 4

⇒ (-4) × 7 = -28

⇒ Substitute:

⇒ -9 - 4 + (-28)

⇒ = -9 - 4 - 28

⇒ = -41

Final Answer: -41

Additional Information

BODMAS: Order of operations must be followed

Sign Rules: (-) ÷ (-) = +, (-) × (+) = -

Tip: Solve division & multiplication first

Exam Trick: Carefully handle negative signs

Given numbers: 458, 652, 748, 351, 591

Original numbers: 458, 652, 748, 351, 591

Now, identifying highest and lowest:

Highest number: 748

Lowest number: 351

Now, multiply: 8 × 1 = 8

Hence, the correct answer is Option 3.

The logic followed here is:

Logic:

From the given sets, the pattern is:

second number = first number × 3

third number = second number + 10

fourth number = third number × 2

Now verify the given sets:

For, 7 - 21 - 31 - 62

⇒ 7 × 3 = 21

⇒ 21 + 10 = 31

⇒ 31 × 2 = 62

For, 9 - 27 - 37 - 74

⇒ 9 × 3 = 27

⇒ 27 + 10 = 37

⇒ 37 × 2 = 74

Now, checking the options:

Option 1) 11 - 33 - 43 - 86

⇒ 11 × 3 = 33

⇒ 33 + 10 = 43

⇒ 43 × 2 = 86 

Option 2) 6 - 18 - 28 - 76

⇒ 6 × 3 = 18

⇒ 18 + 10 = 28

⇒ 28 × 2 = 56 ≠ 76

Option 3) 8 - 32 - 42 - 84

⇒ 8 × 3 = 24 ≠ 32 

Option 4) 12 - 36 - 46 - 82

⇒ 12 × 3 = 36

⇒ 36 + 10 = 46

⇒ 46 × 2 = 92 ≠ 82

Hence, the correct answer is Option 1.

The correct answer is Pascal’s law.

Key Points

• Pascal's Law, also known as the Principle of Transmission of Fluid-Pressure, is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure ratio remains the same.
• This fundamental law was established by the French mathematician and physicist Blaise Pascal in the year 1647-48.
• The working of a hydraulic lift is a direct application of this law. In this system, two pistons of different cross-sectional areas are connected. When a small force is applied to the smaller piston, the pressure is transmitted to the larger piston, resulting in a much larger upward force capable of lifting heavy vehicles or loads.
• Hydraulic brakes in automobiles also operate on Pascal's law. When the driver presses the brake pedal, the pressure is transmitted through the brake fluid to the wheel cylinders, ensuring that equal braking force is applied to all wheels simultaneously.
• The mathematical expression for this law is P = F / A, where P is pressure, F is force, and A is the area. Because the pressure is constant throughout the closed system, F1/A1 = F2/A2.

Additional Information

• Coulomb's Law:
• This is a law of physics that describes the interaction between electrically charged particles.
• It was first published in 1785 by French physicist Charles-Augustin de Coulomb.
• The law states that the force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.
• Gay-Lussac’s Law:
• This is one of the gas laws which states that the pressure of a given mass of gas is directly proportional to its absolute temperature, provided the volume remains constant.
• It was formulated by Joseph Louis Gay-Lussac in the year 1808.
• Common applications include the working of a pressure cooker or the behavior of automobile tires during different seasons.
• Faraday's Law of Induction:
• This law is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF).
• It was discovered by Michael Faraday in 1831.
• This principle is the working basis of electric generators, transformers, and induction motors.

Important Points

• Incompressibility: For Pascal's law to be perfectly applicable, the fluid used (like oil or water) must be incompressible, meaning its density does not change significantly under pressure.
• Mechanical Advantage: The primary feature of hydraulic systems is providing mechanical advantage, allowing a human operator to move very heavy objects with minimal physical effort.
• Hydraulic Press: Another common application used in industries for forging, clamping, and molding metals and plastics, which functions entirely on the basis of Pascal's law.

The correct answer is Locomotion and feeding.

Key Points

• The water vascular system is a unique and defining feature of the Phylum Echinodermata, which includes organisms like starfish (sea stars), sea urchins, and sea cucumbers.
• The primary function of this system is locomotion. It operates as a hydraulic system where water pressure is used to extend and retract tube feet (podia), allowing the animal to move across the marine floor.
• Another critical function is feeding and food capture. Starfish use their tube feet to grab prey, such as bivalves and mollusks, and can exert enough force to pry open their shells.
• The system also facilitates respiration and waste transportation. Oxygen is absorbed from the water within the canals, and metabolic wastes are diffused out of the body through the thin walls of the tube feet.
• It acts as a sensory organ as well, as the tips of the tube feet are sensitive to chemicals and touch, helping the organism navigate its environment. Hence, the statement regarding locomotion and feeding as the primary function is correct.

Additional Information

• Structure of the Water Vascular System:
• The system begins with the madreporite, a sieve-like plate on the aboral surface that allows sea water to enter the system.
• Water passes through the stone canal into a ring canal that encircles the central esophagus.
• From the ring canal, five radial canals extend into each arm (in the case of starfish), which further branch into hundreds of tube feet.
• Phylum Echinodermata Characteristics:
• These organisms are exclusively marine and are found at all ocean depths.
• They exhibit pentamerous radial symmetry in the adult stage, although their larvae show bilateral symmetry.
• They possess an endoskeleton made of calcareous ossicles, which often gives them a "spiny" appearance.
• Most echinoderms have a remarkable power of regeneration, allowing them to regrow lost arms or body parts.
• Classification and Examples:
• Asteroidea: Includes Starfish (e.g., Asterias).
• Echinoidea: Includes Sea urchins and Sand dollars.
• Holothuroidea: Includes Sea cucumbers.
• Ophiuroidea: Includes Brittle stars.

Important Points

• Hydraulic Mechanism: The movement is powered by the ampulla, a muscular sac at the top of each tube foot. When the ampulla contracts, water is forced into the foot, extending it. When it relaxes, the foot retracts.
• Digestive System: In many starfish, the stomach can be everted (pushed out) through the mouth to digest prey outside the body, which is a unique biological adaptation.
• Lack of Centralized Brain: Echinoderms do not have a centralized nervous system or brain; instead, they have a nerve ring and radial nerves that coordinate the complex movements of the water vascular system.
• Excretory System: There is no specialized excretory organ; nitrogenous waste (mostly ammonia) is removed via diffusion through the respiratory tree or tube feet.