RRB NTPC CBT 1 2025 Question Paper with Answers & Explanations

Explanation

The Paika Rebellion (Paika Bidroha) was an armed uprising against British East India Company rule in Odisha in 1817. Led by Bakshi Jagabandhu Bidyadhar Mohapatra, the former military commander of the King of Khurda, the local militia known as Paikas revolted against extortionate British land revenue demands, harsh currency regulations, and salt monopoly policies that severely disrupted the traditional agrarian economy of Khurda.

Explanation

K. Sanjay Murthy, a 1989-batch IAS officer of the Himachal Pradesh cadre, assumed charge as the 15th Comptroller and Auditor General (CAG) of India on 21 November 2024. President Droupadi Murmu administered the oath of office to him at Rashtrapati Bhavan under Clause (1) of Article 148 of the Constitution of India. Prior to assuming this constitutional role, Murthy served as the Secretary in the Department of Higher Education under the Ministry of Education, where he oversaw the implementation of the National Education Policy 2020. He succeeded Girish Chandra Murmu as the head of the Supreme Audit Institution of India.

Explanation

Windows 10 is an operating system developed by Microsoft that manages hardware and software resources on desktop and laptop computers. It serves as the primary system software interface between the user, application software, and computer hardware, handling core functionality such as memory management, process scheduling, file system organization, and device input/output operations.

Explanation

To find numbers that are immediately preceded by a symbol and immediately followed by a symbol, search for the pattern Symbol - Number - Symbol in the sequence from left to right.

In the sequence, only the number 1 in the segment £ 1 % is immediately preceded by a symbol (£) and immediately followed by a symbol (%).

All other single-digit numbers in the series are either preceded by a number, followed by a number, or located at the end of the series, leaving a total count of 1.

Explanation

Bhopal, the capital city of Madhya Pradesh, is located at a latitude of approximately 23° 15′ N (23.25° N). Positioned just south of the Tropic of Cancer (23.5° N), it lies approximately 0.75° (around 83 km) south of the 24° N latitude line, making it the nearest state capital among the choices to this parallel.

Explanation

Town Area Committees are semi-municipal authorities created by a specific Act of the state legislature for the administration of small towns. They are entrusted with limited civic functions such as street lighting, drainage, conservancy, and local road maintenance. Their structural design and functional scope are tailored specifically to provide basic civic amenities in smaller urban areas without the full administrative apparatus of larger municipal bodies.

Explanation

Interchanging '+' with '-' and '×' with '÷', the given equation becomes:

38 × 21 - 436 ÷ 4 + 73 = ?

Following the BODMAS rule:

First, perform division: 436 ÷ 4 = 109

Next, perform multiplication: 38 × 21 = 798

Finally, perform subtraction and addition from left to right: 798 - 109 + 73 = 689 + 73 = 762

Explanation

Numbering the seven positions from 7 (top) to 1 (bottom):

Since no box is kept above F, F is at position 7. Only three boxes are kept between F and B, placing B at position 3. D is kept immediately above B, placing D at position 4. Only one box is kept between G and D, placing G at position 6. Only four boxes are kept between G and C, placing C at position 1. A is kept above E, so A is at position 5 and E is at position 2.

The arrangement from top to bottom is F, G, A, D, B, E, C. Box D is at position 4, so there are 3 boxes (B, E, and C) kept below D.

Explanation

In the Gender Inequality Index (GII) 2022, released by the United Nations Development Programme (UNDP) in its Human Development Report 2023/2024, India achieved a rank of 108 out of 193 countries with a score of 0.437. This marked an improvement of 14 positions from its rank of 122 in 2021. The GII evaluates gender-based disparities across three essential dimensions of human development: reproductive health, empowerment, and labor market participation.

Explanation

Pneumatophores are specialized aerial root structures (aerial organs of the root system) found in plants like mangroves that function primarily in gas exchange through lenticels or specialized pore structures. Disruption of these gas-exchange apparatuses on aerial roots severely hinders oxygen uptake without directly impairing the water-absorption capacity of the submerged or subterranean roots. In contrast, loss of root hairs or epiblema function (options C and D) directly reduces water uptake surface area and osmotic potential, while endodermal suberization (option A) regulates water and solute transport into the vascular cylinder.

Explanation

Burning wood is a chemical change because it involves a combustion reaction where cellulose and other organic compounds in wood react with atmospheric oxygen to form entirely new substances, such as carbon dioxide, water vapor, ash, and smoke. This chemical reaction involves breaking and forming chemical bonds, releasing heat and light, and cannot be reversed by physical means to recover the original wood.

Explanation

In user interfaces, pressing the Tab key advances keyboard focus sequentially to the next interactive element, such as text boxes, buttons, checkboxes, or dropdown menus. This enables smooth, hands-on-keyboard navigation through forms, dialog boxes, and menus without relying on a mouse.

Explanation

Let the smaller supplementary angle be x. The larger angle is x + 28°. Since the sum of two supplementary angles is always 180°:

x + (x + 28°) = 180° 2x + 28° = 180° 2x = 152° x = 76°

Explanation

Purananuru and Patirruppattu are two major Puram anthologies in the Ettuttokai collection of ancient Tamil Sangam literature. In Sangam poetic classification, Puram refers to the external or public aspects of human life. These works deal primarily with heroism, warfare, political statecraft, ethics, and the heroic deeds, conquests, and patronage of various rulers. Specifically, Purananuru contains 400 poems praising the bravery and righteousness of various kings, chieftains, and heroes, while Patirruppattu is a dedicated collection praising the valor and achievements of Chera monarchs.

Explanation

In Dravida (South Indian) temple architecture, the Vimana is the stepped, pyramidal tower constructed directly above the garbhagriha (sanctum sanctorum). It typically consists of multiple progressively smaller storeys (talas) rising upward and is capped at the top by a single stone block or dome-like cupola known as the shikhara.

Explanation

In the administrative system of the Gupta and post-Gupta periods, the empire was divided into several administrative units for governance. The largest administrative division directly below the central kingdom was the province, which was known as a 'Bhukti' or 'Desha'. Each Bhukti was governed by an official termed an 'Uparika' or 'Uparika-Maharaja', who was usually a prince or a high-ranking officer appointed by the monarch to oversee local administration, revenue collection, and law and order within the province.

Explanation

The Eastern Coastal Plains of India lie between the Eastern Ghats and the Bay of Bengal, extending from the Ganges delta in West Bengal in the north down to Kanyakumari in Tamil Nadu in the south. It spans across the eastern maritime states of West Bengal, Odisha, Andhra Pradesh, and Tamil Nadu, encompassing the fertile deltas of major rivers like the Mahanadi, Godavari, Krishna, and Kaveri.

Explanation

Let point A be at origin (0, 0) on a Cartesian plane, where the positive x-axis represents East and the positive y-axis represents North.

Starts at A (0, 0) and drives 12 km East: (12, 0) Turns left (North) and drives 9 km: (12, 9) Turns left (West) and drives 13 km: (12 - 13, 9) = (-1, 9) Turns left (South) and drives 11 km: (-1, 9 - 11) = (-1, -2) Turns left (East) and drives 1 km to reach P: (-1 + 1, -2) = (0, -2)

Point P is located at (0, -2), which is 2 km directly south of point A (0, 0). To reach point A from point P, he must drive 2 km towards the north.

Explanation

Using the net percentage change formula: Net % change = x + y + (x × y)/100

Here, x = -15 and y = +10.

Net % change = -15 + 10 + (-15 × 10)/100 = -5 - 1.5 = -6.5%

The negative sign represents a net reduction of 6.5% compared to the initial salary.

Explanation

The mean proportion between two numbers x and b is given by the formula √(x × b).

Given that the mean proportion between x and 338 is 260: √(x × 338) = 260

Squaring both sides: x × 338 = 260² x × 338 = 67,600 x = 67,600 / 338 x = 200

Explanation

A graphic card is an independent hardware component with its own dedicated processor, known as a Graphics Processing Unit (GPU), and its own memory (VRAM). It is mounted separately on the motherboard via an expansion slot (such as PCIe) to perform specialized display and video rendering tasks, operating distinctly from the Central Processing Unit.

Explanation

The weighted average formula is: Weighted Average = (n₁x₁ + n₂x₂) / (n₁ + n₂)

Here, n₁ = 12 students with average x₁ = 60, and n₂ = 30 - 12 = 18 students with average x₂ = 62.

Average score of the class = (12 × 60 + 18 × 62) / 30 = (720 + 1116) / 30 = 1836 / 30 = 61.2

Alternatively, using deviance from 60: Average = 60 + [18 × (62 - 60)] / 30 = 60 + 36 / 30 = 60 + 1.2 = 61.2

Explanation

The first 14 whole numbers form an arithmetic progression starting from 0 and ending at 13 (0, 1, 2, ..., 13).

The average of the first n whole numbers is given by the formula: Average = (n - 1) / 2

Substituting n = 14: Average = (14 - 1) / 2 = 13 / 2 = 6.5

Explanation

Each letter in the first cluster shifts to the corresponding letter in the second cluster following the pattern: first letter -2, second letter -3, third letter +2 in alphabetical positions.

For XHA : VEC: X - 2 = V H - 3 = E A + 2 = C

For BNW : ZKY: B - 2 = Z N - 3 = K W + 2 = Y

Both sides of the analogy maintain the exact same positional shift rule.

Explanation

Rajasthan is a landlocked state situated in northwestern India. It shares land borders with five Indian states—Punjab, Haryana, Uttar Pradesh, Madhya Pradesh, and Gujarat—and an international border with Pakistan to the west and northwest. Being entirely surrounded by land, it has no direct access to any ocean or sea.

Explanation

Surface area of a sphere = 4πr²

Given the diameter = 98 cm, the radius r = 98 / 2 = 49 cm.

Substituting the values: Surface area = 4 × (22/7) × 49 × 49 = 4 × 22 × 7 × 49 = 88 × 343 = 30,184 cm²

Explanation

Let the present age of Rahul's daughter be x years. Since Rahul's age is three times that of his daughter, Rahul's present age is 3x years.

After 8 years, daughter's age will be x + 8 years and Rahul's age will be 3x + 8 years.

According to the given condition: 3x + 8 = 2(x + 8) + 5 3x + 8 = 2x + 16 + 5 3x + 8 = 2x + 21 3x - 2x = 21 - 8 x = 13

Rahul's present age = 3x = 3 × 13 = 39 years.

Explanation

Position of Sunita from the left end = Gita's position from the left end + 21 = 16 + 21 = 37.

Position of a person from the right end = Total students - Position from the left end + 1.

Position of Sunita from the right end = 73 - 37 + 1 = 37.

Explanation

Muthoot Finance received approval from the Reserve Bank of India in February 2025 to open 115 new branches across India to expand its operational footprint and strengthen its gold loan business.

Explanation

Chandra's Surface Thermophysical Experiment (ChaSTE) is designed to measure the thermal conductivity and vertical temperature profile of the lunar topsoil (regolith) near the Moon's south polar region. Equipped with a thermal probe containing ten individual temperature sensors, it penetrates the lunar surface up to a depth of 10 centimeters to record precise temperature variations across different subsurface layers, providing crucial data on the insulation properties and thermal behavior of the lunar regolith.

Explanation

The Smart Cities Mission was launched by the Government of India on 25 June 2015 with the objective of developing 100 cities across the country into sustainable and citizen-friendly urban centres. The selection of these 100 cities was carried out through a nationwide competitive process called the City Challenge across multiple rounds between 2016 and 2018.

Explanation

Work rate of Varun and Ashish combined = 1/3 hall per day. Work rate of Varun alone = 1/7 hall per day.

Ashish's work rate = 1/3 − 1/7 = 4/21 hall per day.

Days required by Ashish alone to paint 4 halls = 4 ÷ (4/21) = 4 × (21/4) = 21 days.

Explanation

Speed of stream = ½ × (Downstream Speed − Upstream Speed)

Downstream Speed = 721 / 15 km/hr Upstream Speed = 721 / 42 km/hr

Speed of stream = ½ × (721 / 15 − 721 / 42) = ½ × 721 × (14 − 5) / 210 = ½ × 721 × 9 / 210 = 2163 / 140 = 15.45 km/hr

Explanation

Mumbai Indians won the Women's Premier League (WPL) 2025 title by defeating Delhi Capitals by 8 runs in the final held at the Brabourne Stadium, Mumbai. Captained by Harmanpreet Kaur, who top-scored with a 66-run knock off 44 balls, Mumbai Indians set a total of 149/7 before bowling out their opponents for 141/9. This victory marked the franchise's second WPL title, following their inaugural season win in 2023.

Explanation

The Takht-i-Bahi inscription, discovered near Mardan in Pakistan, belongs to the Indo-Parthian ruler Gondophares (Gondophenes). Written in the Kharosthi script, it records the 26th year of his reign and is dated to year 103 of the Vikrama Samvat era (46 CE). This inscription provides crucial epigraphic evidence for determining the precise historical chronology of the Indo-Parthian dynasty in northwestern India.

Explanation

The 97th Constitutional Amendment Act, 2011 inserted Article 43B into Part IV (Directive Principles of State Policy) of the Constitution of India. This article directs the State to endeavour to promote voluntary formation, autonomous functioning, democratic control, and professional management of co-operative societies.

Explanation

In this pattern, the second letter-cluster is formed by shifting each letter of the first letter-cluster forward by 2 positions in alphabetical order (+2 for the first letter, +2 for the second letter). In MU - KH, M (13) shifts backward by 2 positions to give K (11), and U (21) shifts backward by 13 positions to give H (8), which violates the +2 forward transformation rule.

Explanation

Raja Rammohan Roy founded Vedanta College in Calcutta in 1825 to synthesize traditional Indian knowledge with modern Western education. The college offered courses combining monotheistic Vedantic doctrines with Western physical and social sciences, reflecting his belief that an integration of Eastern spiritual philosophy and Western scientific learning was essential for India's social and intellectual modernization.

Explanation

The relationship between the letter-clusters in each pair is formed by shifting the positional value of each letter forward by 5 in the English alphabet (+5).

For the first pair, EGC to JLH: E (5) + 5 = J (10) G (7) + 5 = L (12) C (3) + 5 = H (8)

For the second pair, IKG to NPL: I (9) + 5 = N (14) K (11) + 5 = P (16) G (7) + 5 = L (12)

Explanation

Following the Jharkhand Assembly elections held in November 2024, Hemant Soren of the Jharkhand Mukti Morcha (JMM) assumed office as the Chief Minister of Jharkhand. He contested and won the election from the Barhait Assembly constituency (reserved for Scheduled Tribes) in Sahibganj district by a margin of 39,791 votes.

Explanation

Saving percentage = 100% - 45% = 55%

Income = (Savings / Saving percentage) × 100 Income = (66,000 / 55) × 100 Income = 1,200 × 100 = ₹1,20,000

Explanation

National Milk Day is celebrated in India every year on November 26 to commemorate the birth anniversary of Dr. Verghese Kurien, widely known as the Father of the White Revolution. The day honours his pioneering contributions to the country's dairy sector, which transformed India from a milk-deficient nation into the world's largest milk producer through Operation Flood.

Explanation

Cost price of the first dryer = 63,000 / 1.05 = ₹60,000 Cost price of the second dryer = 63,000 / 0.70 = ₹90,000

Total Cost Price = 60,000 + 90,000 = ₹1,50,000 Total Selling Price = 63,000 × 2 = ₹1,26,000

Total Loss = 1,50,000 - 1,26,000 = ₹24,000 Loss percentage = (24,000 / 1,50,000) × 100 = 16%

Explanation

For a period of 2 years, the difference between compound interest and simple interest is given by the formula:

Difference = P × (r / 100)²

where P is the principal sum and r is the annual rate of interest.

Substituting the given values into the formula: 797 = P × (16 / 100)² 797 = P × (4 / 25)² 797 = P × (16 / 625)

Solving for P: P = (797 × 625) / 16 P = 498,125 / 16 P = 31,132.8125

Rounding off to the nearest integer gives 31,133.

Explanation

The original number is 5217643. Adding 2 to both even and odd digits effectively means adding 2 to every digit in the number.

First digit from the left in the new number = 5 + 2 = 7 First digit from the right in the new number = 3 + 2 = 5

Sum = 7 + 5 = 12

Explanation

The Indian telecom sector was liberalised under the National Telecom Policy (NTP) 1994. It opened the telecommunications sector to private sector participation, allowing private operators to offer basic and cellular mobile services, thereby ending the state monopoly and laying the foundation for modern telecom expansion in India.

Explanation

To evaluate the expression, convert all terms to a common denominator of 16:

3/8 = 6/16 1/8 = 2/16 5/16 = 5/16 2/8 = 4/16 2 = 32/16

Substituting these into the expression:

(6/16) + (2/16) + (5/16) + (4/16) - (32/16) = (6 + 2 + 5 + 4 - 32) / 16 = (17 - 32) / 16 = -15/16

Explanation

When four numbers are in proportion, the product of the extremes equals the product of the means: (30 + x)(11 + x) = (15 + x)(21 + x)

Expanding both sides: 330 + 41x + x² = 315 + 36x + x² 5x = -15 x = -3

Given 6x : y :: y : (3x - 9), which implies y² = 6x(3x - 9).

Substituting x = -3: 6x = -18 3x - 9 = -18 y² = (-18) × (-18) = 324

Since y > 0: y = √324 = 18

Explanation

The diagonal AC divides quadrilateral ABCD into two triangles, ΔABC and ΔACD.

In ΔABC, with sides 8 cm, 15 cm, and 17 cm: 8² + 15² = 64 + 225 = 289 = 17² This satisfies the Pythagorean theorem, making ΔABC a right-angled triangle. Area of ΔABC = ½ × 8 × 15 = 60 cm²

In ΔACD, with sides 9 cm, 12 cm, and 15 cm: 9² + 12² = 81 + 144 = 225 = 15² This also satisfies the Pythagorean theorem, making ΔACD a right-angled triangle. Area of ΔACD = ½ × 9 × 12 = 54 cm²

Total area of quadrilateral ABCD = Area(ΔABC) + Area(ΔACD) = 60 + 54 = 114 cm²

Explanation

Simple interest (SI) is calculated as the difference between the total amount and the principal: SI = Amount - Principal = 2,280 - 1,200 = 1,080

Using the simple interest formula SI = (P × R × T) / 100: 1,080 = (1,200 × 4 × T) / 100 1,080 = 48 × T T = 1,080 / 48 = 22.5 years

Explanation

The Sabarmati River originates in the southern part of the Aravalli Hills, near Tepur village in the Udaipur district of Rajasthan. From its source, the river flows generally southwestward across Rajasthan and Gujarat over a total length of about 371 km before emptying into the Gulf of Khambhat in the Arabian Sea.

Explanation

The Digital Agriculture Mission, approved by the Union Cabinet in September 2024, focuses on establishing Digital Public Infrastructure (DPI) for the agriculture sector. Key components of this DPI include AgriStack, the Krishi Decision Support System (KDSS), and nationwide Soil Profile and Soil Fertility Mapping.

AgriStack comprises foundational registries—such as the Farmers' Registry, Geo-Referenced Village Maps, and the Crop Sown Registry—which are created, updated, and maintained by State Governments and Union Territories in coordination with the Central Government. By generating unique digital identities (Farmer IDs) linked to verified land and crop data, the mission enables seamless digital authentication for farmers to access financial and welfare services, including direct benefit transfers, subsidized credit, crop insurance, and government procurement.

Explanation

The series follows a pattern of subtracting consecutive odd numbers (1, 3, 5, 7, 9, ...) from each term:

701 - 1 = 700 700 - 3 = 697 697 - 5 = 692 692 - 7 = 685 685 - 9 = 676

Explanation

Virtual memory is a memory management technique that allows a computer system to compensate for physical RAM shortages by temporarily transferring data from main memory to secondary disk storage, such as a hard drive or solid-state drive. By allocating a portion of the disk space to act as a paging file or swap space, virtual memory effectively extends the address space beyond the physical RAM capacity, enabling the system to run larger applications and handle multitasking efficiently.

Explanation

Cost price of 1 lemon = 1/7

Selling price (SP) of 1 lemon = Cost Price × (100 + Profit%)/100 = (1/7) × (100 + 75)/100 = (1/7) × (175/100) = (1/7) × (7/4) = 1/4

Number of lemons to sell for 1 = 1 / SP = 1 / (1/4) = 4

Explanation

Ammonium chloride (NH4Cl) is a salt formed from a strong acid (HCl) and a weak base (NH4OH). In an aqueous solution, the ammonium cation (NH4+) undergoes cation hydrolysis by reacting with water molecules:

NH4+ + H2O ⇌ NH3 + H3O+

Since the conjugate acid of a weak base is acidic enough to donate protons to water, this reaction generates excess hydronium (H3O+) ions, making the solution slightly acidic with a pH less than 7.

Explanation

The series follows four distinct patterns for each component of the cluster:

First letter advances by 2 positions: O (+2) → Q (+2) → S (+2) → U (+2) → W. Second letter advances by 1 position: K (+1) → L (+1) → M (+1) → N (+1) → O. Third letter moves backward by 2 positions: I (-2) → G (-2) → E (-2) → C (-2) → A. Number increases by 4: 4 (+4) → 8 (+4) → 12 (+4) → 16 (+4) → 20.

Combining these gives WOA 20.

Explanation

The pattern followed in both pairs is a constant forward shift of +5 to the alphabetical position of each letter:

G (7) + 5 = L (12), C (3) + 5 = H (8), and H (8) + 5 = M (13), transforming GCH into LHM.

O (15) + 5 = T (20), K (11) + 5 = P (16), and P (16) + 5 = U (21), transforming OKP into TPU.

Explanation

In a proportion a : b :: c : d, the product of extremes equals the product of means (a × d = b × c).

7.5 × x = 19.5 × 16

x = (19.5 × 16) / 7.5 x = 312 / 7.5 x = 41.6

Explanation

According to the Economic Survey, India's Gross Expenditure on Research and Development (GERD) stands at 0.64% of its Gross Domestic Product (GDP). Public sector funding accounts for the majority of this spending, led primarily by central and state government organizations, while private sector contribution remains relatively low compared to other major global economies.

Explanation

Numbering the seven positions from left to right as 1 to 7:

Since only two people sit to the left of R, R is at position 3. P sits to the immediate right of R and immediate left of S, placing P at position 4 and S at position 5.

Q sits to the immediate left of O, so they form the adjacent pair (Q, O). Q cannot sit at an extreme end (position 1), so Q and O must occupy positions 6 and 7 respectively.

T sits at an extreme end, which must be position 1 since position 7 is occupied by O. The remaining person, N, takes position 2.

The complete arrangement from left to right is T, N, R, P, S, Q, O. Between N (position 2) and O (position 7) sit R, P, S, and Q, making a total of four people.

Explanation

Interchanging '+' with '−' and '×' with '÷' in the equation gives:

1125 ÷ 45 × 39 + 17 − 19

According to the BODMAS rule, perform division first: 1125 ÷ 45 = 25

Next, perform multiplication: 25 × 39 = 975

Then, perform addition: 975 + 17 = 992

Finally, perform subtraction: 992 − 19 = 973

Explanation

The given set of numbers is 614, 457, 249, 625, and 150.

The highest number is 625, and its second digit is 2. The lowest number is 150, and its second digit is 5.

Subtracting the second digit of the highest number from the second digit of the lowest number gives: 5 - 2 = 3

Explanation

Condition 1 does not apply because the first element (7) is a number, not a symbol. Condition 2 does not apply because the last element (5) is an odd number, not an even number. Condition 3 does not apply because the second element (2) is not a perfect square.

Since none of the conditions are met, each element is coded directly according to the table: 7 is coded as P, 2 as T, 4 as B, @ as F, and 5 as J, yielding PTBFJ.

Explanation

Since the product of A and E's floor numbers is 3 and A lives on a prime floor, A must live on floor 3 and E on floor 1.

With exactly two people living above B, B lives on floor 4.

F lives immediately below C, which places C on floor 6 and F on floor 5 as those are the only two adjacent vacant floors remaining.

This leaves D on floor 2.

Between D on floor 2 and F on floor 5, there are 2 people (A on floor 3 and B on floor 4).

Explanation

The given set of three-digit numbers is 401, 418, 733, 283, and 902.

The highest number in the set is 902, whose second digit is 0. The lowest number in the set is 283, whose third digit is 3.

Adding the second digit of the highest number to the third digit of the lowest number gives 0 + 3 = 3.

Explanation

The Climate Change Performance Index (CCPI) 2025 evaluated 63 countries along with the European Union, which collectively account for over 90% of global greenhouse gas emissions. Published annually since 2005 by Germanwatch, NewClimate Institute, and Climate Action Network International, the CCPI assesses national climate mitigation performance across four key categories: Greenhouse Gas Emissions (40%), Renewable Energy (20%), Energy Use (20%), and Climate Policy (20%).

Explanation

Taking point A as the origin (0, 0): 13 km West: (-13, 0) Left turn (South) 7 km: (-13, -7) Right turn (West) 6 km: (-19, -7) Left turn (South) 8 km: (-19, -15) Left turn (East) 19 km to P: (-19 + 19, -15) = (0, -15)

Point P is located at (0, -15). To move from point P (0, -15) back to point A (0, 0), Fardeen needs to travel a distance of 15 km directly North.

Explanation

Using the order of operations (BODMAS):

First, simplify the expression inside the brackets: 17 + 6 = 23

Next, perform the multiplication: 7 × 23 = 161

Finally, perform the addition and subtraction from left to right: 127 - 161 + 93 = (127 + 93) - 161 = 220 - 161 = 59

Explanation

Let the capacity of the tank be 180 units (LCM of 18 and 20).

Filling rate of pipe A = 180 / 18 = +10 units per minute Emptying rate of pipe B = 180 / 20 = -9 units per minute

In the first 6 minutes, pipe A alone fills 6 × 10 = 60 units. Remaining capacity of the tank = 180 - 60 = 120 units.

When pipe B is also opened, the net filling rate of both pipes combined = 10 - 9 = +1 unit per minute.

Time required to fill the remaining tank = 120 / 1 = 120 minutes.

Explanation

As of April 2025, negotiators from India and the United Kingdom confirmed that 90% of the Free Trade Agreement (FTA) terms had been successfully finalised. Major contentious areas such as professional mobility and worker visas were largely resolved, leaving only a few key sectors including tariffs on Scotch whisky, automobiles, and pharmaceuticals to be settled prior to concluding the agreement.

Explanation

Expanding each term in the expression:

(2x - 5y)² = 4x² - 20xy + 25y² (5x + 2y)² = 25x² + 20xy + 4y² (2x + 5y)(2x - 5y) = 4x² - 25y²

Summing the three expanded expressions gives:

(4x² + 25x² + 4x²) + (-20xy + 20xy) + (25y² + 4y² - 25y²) = 33x² + 4y²

Explanation

India assumed the Chairmanship of the Bay of Bengal Programme Inter-Governmental Organisation (BOBP-IGO) in 2025. The BOBP-IGO is a regional fisheries management body comprising Bangladesh, India, Maldives, and Sri Lanka that promotes sustainable fisheries management in the Bay of Bengal.

Explanation

Article 32 of the Constitution of India guarantees the right to move the Supreme Court for the enforcement of Fundamental Rights conferred under Part III of the Constitution. Under Article 32(2), the Supreme Court is empowered to issue directions, orders, or writs—including habeas corpus, mandamus, prohibition, quo warranto, and certiorari—specifically and exclusively for the protection and enforcement of these Fundamental Rights.

Explanation

Under Article 131 of the Constitution, the Supreme Court possesses exclusive original jurisdiction to decide federal disputes between the Centre and States or between two or more States, meaning no other court has the power to entertain such matters. In contrast, writ jurisdiction for the enforcement of Fundamental Rights under Article 32 is concurrent with the High Courts under Article 226, allowing an aggrieved party to approach either the Supreme Court or a High Court directly.

Explanation

The given series is an arithmetic sequence where each term decreases by 8 from the preceding term:

105 - 8 = 97 97 - 8 = 89 89 - 8 = 81 81 - 8 = 73 73 - 8 = 65

Explanation

tan θ = opposite / adjacent = height of top of ladder from ground / distance of foot of ladder from wall

Given tan θ = 15/8 and height = 30 m:

15/8 = 30 / distance

distance = (30 × 8) / 15 = 16 m

Explanation

Arranging the 7 people facing the centre in counter-clockwise order, where moving counter-clockwise corresponds to moving to the right of a person:

S sits to the immediate right of Q, placing S at 1 position to the right of Q. Three people sit between Q and V when counted from the right of Q, placing V at 4 positions to the right of Q. Two people sit between T and S when counted from the right of T, placing T at 2 positions to the left of Q (or 5 positions to the right of Q). U sits to the immediate right of R, which forces R and U to occupy the two adjacent vacant seats at 2 and 3 positions to the right of Q, respectively. P occupies the remaining seat at 6 positions to the right of Q.

Moving right from Q, the sequence of people is S, R, U, V, T, P. Counting from the right of Q up to U, the people sitting in between are S and R, which gives a total of 2 people.

Explanation

Remaining distance = (1 - 2/3) × 519 = 1/3 × 519 = 173 km

Remaining time = (1 - 5/7) × 7 = 2/7 × 7 = 2 hours

Required speed = Remaining distance / Remaining time = 173 / 2 = 86.5 km/hr

Explanation

Decoding the expression M + N × O ÷ P - Q step by step:

M + N means M is the mother of N. N × O means N is the wife of O. O ÷ P means O is the father of P. P - Q means P is the brother of Q.

Since P is the brother of Q, P and Q are siblings. O is the father of P, which means O is also the father of Q. N is the wife of O, so N is the mother of Q. Since M is the mother of N, M is the mother of Q's mother (mother's mother).

Explanation

Each term in the series is formed by moving the positional values of the corresponding letters backward by 3 in alphabetical order:

First letters: X (24) - 3 = U (21), U (21) - 3 = R (18), R (18) - 3 = O (15), O (15) - 3 = L (12)

Second letters: B (28) - 3 = Y (25), Y (25) - 3 = V (22), V (22) - 3 = S (19), S (19) - 3 = P (16)

Third letters: F (6) - 3 = C (3), C (3) - 3 = Z (26), Z (26) - 3 = W (23), W (23) - 3 = T (20)

Combining the resulting letters L, P, and T gives LPT.

Explanation

Civil courts possess jurisdiction to adjudicate matters of a non-criminal nature that concern private rights, legal entitlements, and civil remedies under the Code of Civil Procedure, 1908. Their primary function is to settle disputes between individuals or organizations, including claims over property title and ownership, recovery of debts, breach of contractual agreements, specific performance, and tortious liability.

Explanation

The pattern follows a constant shift of -3 positions for each letter in the English alphabet:

FARM: F(-3)=C, A(-3)=X, R(-3)=O, M(-3)=J FRESH: F(-3)=C, R(-3)=O, E(-3)=B, S(-3)=P, H(-3)=E

Applying the same -3 shift to RICH: R (18) - 3 = 15 (O) I (9) - 3 = 6 (F) C (3) - 3 = 26 (Z) H (8) - 3 = 5 (E)

Explanation

Slide Master is the top slide in a hierarchy of slides that stores information about the presentation theme, including layout, background, color, fonts, and placeholders. Any design change made to the Slide Master automatically applies to all slides linked to it, ensuring visual consistency across the entire presentation and eliminating the need to format individual slides manually.

Explanation

To find the median, first arrange the 11 observations in ascending order:

11, 18, 27, 30, 34, 35, 52, 76, 81, 83, 84

Since the number of observations n = 11 is odd, the median is given by the ((n + 1) / 2)th term, which is the (12 / 2)th = 6th term.

The 6th observation in the sorted list is 35.

Explanation

The empirical relationship between mean, median, and mode is given by:

Mode = 3 × Median - 2 × Mean

Rearranging the formula to solve for Mean:

Mean = (3 × Median - Mode) / 2

Substituting the given values (Median = 88 and Mode = 28.4):

Mean = (3 × 88 - 28.4) / 2 Mean = (264 - 28.4) / 2 Mean = 235.6 / 2 Mean = 117.8

Explanation

Let the Cost Price (CP) be 100%.

Since the marked price is 30% above the cost price, Marked Price (MP) = 130%. Since the profit percentage is 2%, Selling Price (SP) = 102%.

Discount = MP - SP = 130% - 102% = 28%.

Discount Percentage = (Discount / MP) × 100 = (28 / 130) × 100 = 280 / 13 = 21.538...% ≈ 21.54%

Explanation

The logic followed here is adding 7 to the first number to obtain the second number:

67 + 7 = 74 13 + 7 = 20

Applying the same logic to 52:

52 + 7 = 59

Explanation

None of the conditional rules apply to the group 7 2 @ 1 3 | : Condition (i) fails because the first element is a number and the last is a symbol. Condition (ii) fails because the last element is a symbol, not an even number. Condition (iii) fails because the second element, 2, is not a perfect square.

Since no condition is met, each character is coded directly using the given table: 7 corresponds to W, 2 to A, @ to Z, 1 to R, 3 to T, and | to M. Joining these codes in order gives WAZRTM.

Explanation

Raja Ram Mohan Roy was a pioneer of socio-religious reform in 19th-century India and the founder of the Brahmo Samaj in 1828. He actively campaigned against social evils, rigid caste hierarchies, and religious dogmas, promoting progressive reforms and human equality. Through his efforts, he advocated for legal and social recognition of rights that challenged traditional barriers, laying the groundwork for reformist legislation that facilitated inter-caste and inter-religious social integration.

Explanation

At the World Para Athletics Grand Prix 2025 held at Jawaharlal Nehru Stadium in New Delhi, host nation India topped the overall medal standings with a total of 134 medals. The medal tally comprised 45 gold, 40 silver, and 49 bronze medals.

Explanation

The net profit percentage depends only on the markup percentage and discount percentage, making the actual marked price redundant.

Net Profit % = Markup % - Discount % - (Markup % × Discount %) / 100

Substituting the given values: Net Profit % = 25 - 4 - (25 × 4) / 100 = 21 - 1 = 20%

Explanation

Distance between the two consecutive cabs = Speed of cab × Departure interval = 74 × (28/60) km.

Since the man is coming in the opposite direction, the relative speed between the cab and the man is (74 + S) km/hr, where S is the speed of the man.

The man covers this distance between the cabs at relative speed in 10 minutes: Distance = Relative Speed × Time 74 × (28/60) = (74 + S) × (10/60) 74 × 28 = (74 + S) × 10 2072 = 740 + 10S 10S = 1332 S = 133.2 km/hr

Explanation

The given series follows an alternating pattern of adding 18 and 11 to consecutive terms:

37 + 18 = 55 55 + 11 = 66 66 + 18 = 84 84 + 11 = 95 95 + 18 = 113

Following this sequence, the next term is obtained by adding 11:

113 + 11 = 124

Explanation

Comparing the two words 'GIVE' and 'VOLT', the letter common to both is 'V'. Similarly, comparing their respective numerical codes '4628' and '3567', the digit common to both is '6'. Therefore, the code for 'V' is 6.

Explanation

The Central Processing Unit (CPU) functions as the primary control unit and processing engine of a computer system. It fetches program instructions from memory, decodes them, and executes the necessary arithmetic, logical, and control operations, thereby processing raw data into useful information.

Explanation

Maharaja Bhupinder Singh of Patiala (ruled 1900–1938) was a prominent Sikh ruler who played a central role in patronising Sikh religious, educational, and cultural institutions. He contributed extensively to the funding and expansion of Khalsa College in Amritsar, provided major financial support for the monumental Sikh encyclopaedia Mahan Kosh compiled by Bhai Kahn Singh Nabha, and sponsored the restoration and upkeep of historic gurdwaras.

Explanation

The Mahanadi river originates near Sihawa in the Dhamtari district of Chhattisgarh and flows eastward through Odisha before discharging its water into the Bay of Bengal. It has a total length of 851 km, with a major drainage basin spanning over 1.42 lakh square kilometres across Chhattisgarh, Odisha, Madhya Pradesh, Jharkhand, and Maharashtra.

Explanation

Atul's regular monthly expenditure = ₹6,000 + ₹2,500 = ₹8,500. His regular monthly savings = ₹10,000 - ₹8,500 = ₹1,500.

Since he spends all his monthly savings in his birthday month, he saves money during 11 months of the year.

Total yearly savings = 11 × ₹1,500 = ₹16,500.

Explanation

The transformation rule for both letter-cluster pairs is a positional shift of +4, -4, and +4 applied to the first, second, and third letters respectively.

In the first pair, applying this rule to BPJ yields FLN: B (+4) = F P (-4) = L J (+4) = N

In the second pair, applying the same rule to TXB yields XTF: T (+4) = X X (-4) = T B (+4) = F

Explanation

In the governing pattern, each cluster consists of consecutive letters with an alphabetical position difference of +1, and shifting both letters backward by 5 positions forms the second cluster. In HK - LP, the letters in the first cluster H (8) and K (11) have a difference of +3, while the letters in the second cluster L (12) and P (16) have a difference of +4, failing to follow both the consecutive letter rule and the 5-position backward shift.

Explanation

Net rate of filling per minute = 1/10 − 1/20 = 1/20 of the tank.

Time taken to fill the tank completely = 1 / (1/20) = 20 minutes.

Explanation

Substituting the given mathematical operators into the expression: 1 + 45 ÷ 2 × 2 − 4

Applying the BODMAS rule: First, perform division: 45 ÷ 2 = 22.5 Next, perform multiplication: 22.5 × 2 = 45 Then, perform addition: 1 + 45 = 46 Finally, perform subtraction: 46 − 4 = 42

Explanation

According to the Sample Registration System (SRS) Statistical Report 2019 published by the Office of the Registrar General of India, the national Infant Mortality Rate (IMR) was 30 deaths per 1000 live births. This represented a decline from 32 per 1000 live births recorded in 2018. Within this national average, the rural IMR stood at 34 per 1000 live births, whereas the urban IMR was recorded at 20 per 1000 live births.

Explanation

Arranging the 7 people facing the centre in counter-clockwise order:

Assigning position 1 to P: Since Q sits third to the right of P, Q is at position 4. Q sits to the immediate right of U, placing U at position 3. U sits third to the left of V, placing V at position 6.

The remaining empty positions are 2, 5, and 7 for R, S, and T. Counting from the left of T, R sits two places away. Placing T at position 2 puts R at position 7 and S at position 5. In this setup, S is at position 5 and U is at position 3, satisfying the condition that S is not an immediate neighbour of U.

The complete counter-clockwise arrangement is P, T, U, Q, S, V, R.

Counting to the right of S (counter-clockwise) towards T, the individuals sitting between them are V, R, and P, making a total of 3 people.

Explanation

To find the combined ratio x : y : z, scale the individual ratios to make the y-term equal in both: x : y = 2 : 5 = 8 : 20 y : z = 4 : 7 = 20 : 35 Thus, x : y : z = 8 : 20 : 35.

Sum of ratio parts = 8 + 20 + 35 = 63. Value of 1 ratio unit = 15,120 ÷ 63 = 240.

Calculating the share of each person: x = 8 × 240 = 1,920 y = 20 × 240 = 4,800 z = 35 × 240 = 8,400

Explanation

Savings Percentage = 100% - 40% = 60%

Total Income = (Savings / Savings Percentage) × 100

Total Income = (18,000 / 60) × 100 = 30,000

Explanation

Applying the operations to each digit of the number 6154932:

6 (even) becomes 6 + 2 = 8 1 (odd) becomes 1 - 1 = 0 5 (odd) becomes 5 - 1 = 4 4 (even) becomes 4 + 2 = 6 9 (odd) becomes 9 - 1 = 8 3 (odd) becomes 3 - 1 = 2 2 (even) becomes 2 + 2 = 4

The new number formed is 8046824.

In this new number, the digit 8 appears twice and the digit 4 appears twice. Thus, exactly two digits appear more than once.

Explanation

The relationship between the letter-clusters is defined by shifting the positional values of the letters by +4, +2, and -2 respectively.

For the left pair HNT : LPR: H (8) + 4 = L (12) N (14) + 2 = P (16) T (20) - 2 = R (18)

Applying the exact same rule to PSV: P (16) + 4 = T (20) S (19) + 2 = U (21) V (22) - 2 = T (20)

This gives the second cluster % as TUT.

Explanation

The letter-cluster transformation follows the rule where positional values of the letters are shifted by +3, -3, and +2 respectively.

Applying this to XQB: X (24) + 3 = 27 ≡ A Q (17) - 3 = 14 = N B (2) + 2 = 4 = D This yields the cluster AND.

Applying the same rule to RWX: R (18) + 3 = 21 = U W (23) - 3 = 20 = T X (24) + 2 = 26 = Z This yields the cluster UTZ.

Explanation

Under Article 9 of the Constitution of India and Section 9 of the Citizenship Act, 1955, India strictly adheres to the principle of single citizenship. Any Indian citizen who voluntarily acquires the citizenship of another country automatically ceases to be a citizen of India by operation of law.

Explanation

Let the distance covered be d and the remaining distance be r.

Given d + r = 37 km and d = (4/3) × r. Substituting d into the total distance gives (4/3) × r + r = 37, which simplifies to (7/3) × r = 37. Thus, r = 111/7 km, and the distance covered is d = (4/3) × (111/7) = 148/7 km.

Time spent cycling = 1 hour 5 minutes = 1 + 5/60 = 13/12 hours.

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

Explanation

In a proportion a : b :: c : d, the product of the extremes equals the product of the means (a × d = b × c).

3.5 × x = 17.4 × 14

x = (17.4 × 14) / 3.5

Since 14 / 3.5 = 4:

x = 17.4 × 4 = 69.6

Explanation

Sum of all 12 marks = Average × Total students = 64 × 12 = 768.

Sum of the given 10 marks = 28 + 35 + 56 + 78 + 63 + 65 + 81 + 79 + 83 + 80 = 648.

Since x and y are the remaining two marks, x + y = 768 - 648 = 120.

The range of the marks is defined as y - x = 70.

Adding the two equations: (x + y) + (y - x) = 120 + 70 2y = 190 y = 95

Substituting y = 95: x = 120 - 95 = 25

This yields the ordered pair (x, y) = (25, 95).

Explanation

Each term in the triad consists of two letters that follow a fixed numerical positional shift:

First letter advances by +2 at each step: 5 (E) → 7 (G) → 9 (I) 7 (G) → 9 (I) → 11 (K)

Second letter advances by +2, then decreases by 3: 12 (L) → 14 (N) → 11 (K) 14 (N) → 16 (P) → 13 (M)

Applying this same rule starting with IP: First letters: 9 (I) + 2 = 11 (K) + 2 = 13 (M) Second letters: 16 (P) + 2 = 18 (R) - 3 = 15 (O)

Combining these position steps yields IP-KR-MO.

Explanation

For the first pen: Initial selling price = 630 × (1 + 0.70) = 630 × 1.70 = ₹1071 Final selling price after 9% discount = 1071 × (1 - 0.09) = 1071 × 0.91 = ₹974.61 Profit on first pen = 974.61 - 630 = ₹344.61

For the second pen: Profit on second pen = 722 × 0.71 = ₹512.62

Total profit = 344.61 + 512.62 = ₹857.23

Explanation

West Bengal launched a comprehensive healthcare initiative aimed at the triple elimination of mother-to-child transmission of HIV, syphilis, and Hepatitis B by 2026. This initiative focuses on early screening, timely intervention, and institutional delivery across the state.

Explanation

Using the difference of squares identity, a² - b² = (a + b)(a - b), where a = 2x + 3 and b = x + 1:

(2x + 3)² - (x + 1)² = [(2x + 3) + (x + 1)] [(2x + 3) - (x + 1)] = (3x + 4)(x + 2) = 3x² + 6x + 4x + 8 = 3x² + 10x + 8

Explanation

Discovered by Alexander Fleming in 1928, penicillin was the world's first effective antibiotic. Its development revolutionized medicine by allowing doctors to successfully treat previously fatal bacterial infections such as pneumonia, syphilis, and staphylococcal diseases, saving millions of lives and ushering in the modern era of antimicrobial therapy.

Explanation

Applying the given rules where vowels are replaced by their next letter and consonants by their preceding letter:

ACT becomes BBS (A → B, C → B, T → S), which contains no vowels.

BUS becomes AVR (B → A, U → V, S → R), which contains the vowel A.

CAR becomes BBQ (C → B, A → B, R → Q), which contains no vowels.

DAD becomes CBC (D → C, A → B, D → C), which contains no vowels.

Three of the formed letter clusters (BBS, BBQ, and CBC) contain no vowels.

Explanation

The two-day Chintan Shivir organized by the Ministry of Youth Affairs and Sports to prepare a roadmap for the 2028 and 2036 Olympic Games was held in Hyderabad on March 7-8, 2025.

Explanation

Taking Point A as the origin (0, 0) on a Cartesian plane where North is +y, South is -y, East is +x, and West is -x:

Driving 3 km South reaches (0, -3). Turning right (West) and driving 2 km reaches (-2, -3). Turning left (South) and driving 5 km reaches (-2, -8). Turning right (West) and driving 3 km reaches (-5, -8). Turning right (North) and driving 8 km reaches (-5, 0), which is Point P.

To return from Point P (-5, 0) to Point A (0, 0), Uday must travel along the x-axis from x = -5 to x = 0. The shortest distance is |0 - (-5)| = 5 km, and the required direction is East.

Explanation

Interchanging '+' with '-' and '×' with '÷', the given equation becomes:

63 × 12 + 98 ÷ 7 - 35 = ?

Applying the BODMAS rule:

First, perform division: 98 ÷ 7 = 14

Next, perform multiplication: 63 × 12 = 756

Now, substitute these back into the equation: 756 + 14 - 35 = 770 - 35 = 735

Explanation

Using the order of operations (BODMAS/PEMDAS), simplify the division first:

72 ÷ 6 = 12

Now, perform the addition and subtraction from left to right:

70 + 12 + 29 - 30 = 82 + 29 - 30 = 111 - 30 = 81

Explanation

Launched on 15 August 2019, the Jal Jeevan Mission aims to provide a Functional Household Tap Connection to every rural household by 2024, achieving 100% coverage across all villages in India. The mission ensures a service delivery level of 55 liters per capita per day of prescribed quality potable water to rural households on a regular and long-term basis.

Explanation

The radius of the base r = 100 / 2 = 50 cm.

The curved surface area of a right circular cone is given by CSA = π × r × l, where l is the slant height.

6500π = π × 50 × l l = 6500 / 50 = 130 cm

Using the relation between height h, radius r, and slant height l: h = √(l² - r²) h = √(130² - 50²) h = √(16900 - 2500) = √14400 = 120 cm

Explanation

The rate at which Pipe A fills the tank is 3700/9 litres per hour, and for Pipe B it is 3700/6 litres per hour.

When both pipes are opened together, their combined filling rate is: Rate = 3700 × (1/9 + 1/6) = 3700 × (5/18) = 18500/18 litres per hour

To fill a tank of 6400 litres, the required time is: Time = 6400 / (18500/18) = (6400 × 18) / 18500 = (64 × 18) / 185 = 1152/185 hours

Explanation

The difference between compound interest and simple interest for 2 years is given by the formula D = P × (R / 100)², where P is the principal and R is the rate of interest.

Substituting the given values P = 47,100 and R = 9:

D = 47,100 × (9 / 100)² D = 47,100 × (81 / 10,000) D = (471 × 81) / 100 D = 38,151 / 100 = 381.51

Explanation

The Tana Bhagat Movement was initiated in 1914 by Jatra Bhagat among the Oraon tribe of Chota Nagpur. It was a socio-religious and non-violent reform movement against British colonial policies, local landlords, and moneylenders. Because this movement emerged in the early twentieth century, the Tana Bhagats were not associated with the Santhal Rebellion, which took place much earlier in 1855–1856.

Explanation

The new arithmetic mean equals the original mean plus the average increase across all 25 numbers.

Total increase in sum = (10 × 12.5) + (10 × 15) + (5 × 0) = 125 + 150 = 275

Increase in arithmetic mean = 275 / 25 = 11

New arithmetic mean = 110 + 11 = 121

Explanation

Dmitri Mendeleev formulated the Periodic Law in 1869, stating that the physical and chemical properties of elements are a periodic function of their atomic masses. He arranged the known elements in increasing order of their atomic mass in horizontal rows (periods) and vertical columns (groups) so that elements with similar chemical properties fell into the same group.

Explanation

To fill identical containers completely with only one type of oil per container without mixing, the capacity of each container must be a common factor of 156 and 256. The maximum possible volume of each container is given by the Highest Common Factor (HCF) of 156 and 256.

Using prime factorisation: 156 = 2² × 3 × 13 256 = 2⁸

HCF(156, 256) = 2² = 4 litres

Explanation

Shifting agriculture, locally known as Jhum cultivation, is a traditional slash-and-burn farming system widely practiced by tribal communities in Northeast India. In this method, patches of forest land are cleared by burning vegetation to cultivate crops for a few seasons. Once the soil loses its natural fertility, farmers abandon the plot to clear a new patch. The removal of natural plant cover, combined with steep hill slopes and intense rainfall, leaves the topsoil exposed to rainwash, resulting in severe soil erosion, loss of organic nutrients, and deforestation across the region.

Explanation

Percentage Change = [(BE 2024-25 - RE 2023-24) / RE 2023-24] × 100

In the Union Budget 2024-25, the allocation for the Smart Cities Mission was reduced as major projects under the mission were nearing completion.

Given values: Revised Estimate (RE) 2023-24 = ₹8,000 crore Budget Estimate (BE) 2024-25 = ₹2,400 crore

Substituting the values into the formula: Percentage Change = [(2,400 - 8,000) / 8,000] × 100 Percentage Change = (-5,600 / 8,000) × 100 = -70%

Explanation

For Conclusion (I), cars are a subset of buses, and ships overlap with buses. The intersecting portion between ships and buses does not necessarily overlap with cars, so it cannot be definitively concluded that some ships are cars.

For Conclusion (II), combining "All cars are buses" and "All buses are trucks" yields "All cars are trucks". Its converse, "All trucks are cars", does not logically follow from the given premises.

Explanation

Using Cartesian coordinates with Point A at the origin (0, 0):

Driving 11 km south leads to (0, -11). Turning left (east) for 3 km leads to (3, -11). Turning left (north) for 4 km leads to (3, -7). Turning left (west) for 12 km leads to (-9, -7). Turning right (north) for 7 km leads to (-9, 0), which is Point P.

Point P lies 9 km west of Point A. Therefore, to return to Point A from Point P, Sunil needs to drive 9 km towards the east.

Explanation

Jat-Jatin is a popular folk dance of the Mithila and Kosi regions of Bihar, performed primarily during the monsoon season. It portrays the delicate emotions, romance, sweet disagreements, and affectionate quarrels between a married couple, Jat and Jatin, capturing the true essence of marital life through expressive storytelling and rhythmic music.

Explanation

Each letter cluster in the series follows a pattern where each positional letter decreases by 4 in the English alphabetical order:

First letters: V (22) - 4 = R (18); R (18) - 4 = N (14); N (14) - 4 = J (10); J (10) - 4 = F (6)

Second letters: C (3) - 4 = Y (25); Y (25) - 4 = U (21); U (21) - 4 = Q (17); Q (17) - 4 = M (13)

Third letters: J (10) - 4 = F (6); F (6) - 4 = B (2); B (2) - 4 = X (24); X (24) - 4 = T (20)

Combining the resulting letters yields FMT.

Explanation

Arranging the schedule from Monday to Sunday:

Since two people have the exam before T, T is scheduled on Wednesday (3rd day).

Only one person has the exam after D, placing D on Saturday (6th day).

There are three people between T (Wednesday) and F, which places F on Sunday (7th day).

U has the exam immediately before E. Placing U on Monday (1st day) and E on Tuesday (2nd day) leaves one person (T on Wednesday) between E and C, placing C on Thursday (4th day).

The remaining person, S, takes the remaining vacant slot on Friday (5th day).

Explanation

Holozoic nutrition is a mode of heterotrophic nutrition in which organisms take complex organic matter into their body in solid or liquid form. Ingestion is the initial process of taking food into the digestive tract through an intake organ, such as the mouth. It serves as the primary and indispensable first step, enabling the complex food material to subsequently undergo mechanical and chemical breakdown during digestion.

Explanation

Using the BODMAS rule for order of operations, evaluate the expression step by step:

First, simplify the innermost parentheses: 1 - 6 + 5 = 0.

Next, multiply inside the square brackets: 6 × 0 = 0.

Then, perform the division: 0 ÷ 12 = 0.

Finally, perform the addition: 194 + 0 = 194.

Explanation

An operating system serves as the core system software that manages a computer's physical hardware components—such as the central processing unit, memory, storage, and input/output devices—and coordinates all software execution. It acts as an intermediary between user applications and the physical computer architecture, allocating system resources, scheduling tasks, handling file management, and ensuring overall system security and stability.

Explanation

Union Minister for Women and Child Development, Annpurna Devi, led the Indian delegation at the 69th Session of the United Nations Commission on the Status of Women (UNCSW), held at the UN Headquarters in New York in March 2025. She delivered India's national statement at the Ministerial Forum, highlighting India's progress on gender equality, women-led development, and the implementation of flagship schemes for the health, nutrition, education, and economic empowerment of women and girls.

Explanation

Dry land farming is practiced in arid and semi-arid regions characterized by low, erratic, and uncertain annual rainfall, typically receiving less than 750 mm per year. Because these areas lack assured irrigation facilities, crop growth relies entirely on natural rainfall stored in the soil profile. Consequently, acute water scarcity and poor soil moisture availability serve as the primary limiting factor for agricultural productivity in dryland regions.

Explanation

In April 2025, Chief Justice of India Sanjiv Khanna officially recommended Justice Bhushan Ramkrishna (B. R.) Gavai as his successor. Following this recommendation, Justice B. R. Gavai took oath as the 52nd Chief Justice of India on 14 May 2025. Justice Gavai became the second CJI belonging to the Scheduled Caste community and the first from the Buddhist faith to head the Supreme Court of India.

Explanation

Breaking down the expression step by step from Q: P × Q means P is the wife of Q. O ÷ P means O is the father of P, so O is the father of Q's wife. N - O means N is the brother of O, and M + N means M is the mother of N, which means M is also the mother of O. Since M is the mother of O, M is the mother of Q's wife's father, which makes M the wife's father's mother of Q.

Explanation

Saura painting is a traditional wall mural art form practiced by the Saura tribe, an ancient particularly vulnerable tribal group inhabiting the state of Odisha. Locally known as Ikons, these ritualistic paintings are dedicated to the tribal deity Idital and are drawn on the red ochre mud walls of village homes during special occasions such as harvests and marriages. Created using natural pigments like rice paste, plant dyes, and ash, the art form features basic geometric patterns depicting human figures, flora, fauna, and daily tribal life.

Explanation

By comparing the two statements, the word queen is the only common word between pizza base queen and pig queen wave. Similarly, su is the only common code between du su qw and ic fv su. Therefore, queen is coded as su.

Explanation

The curved surface area (CSA) of a right circular cone is given by the formula CSA = π r l, where r is the radius of the base and l is the slant height.

Given the base diameter is 144 cm, the radius r = 144 ÷ 2 = 72 cm.

Substituting the radius and CSA into the formula: π × 72 × l = 5400π l = 5400 ÷ 72 = 75 cm

The height h of the cone is related to slant height and radius by h = √(l² - r²): h = √(75² - 72²) h = √((75 - 72)(75 + 72)) h = √(3 × 147) h = √441 = 21 cm

Explanation

The mode of grouped data is calculated using the formula Mode = L + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h.

For the modal class 140-145: Lower limit L = 140 Class interval width h = 5 Frequency of modal class f₁ = x Frequency of preceding class f₀ = 33 Frequency of succeeding class f₂ = 31

Substituting the values into the mode formula: 140 = 140 + [(x - 33) / (2x - 33 - 31)] × 5 0 = (x - 33) / (2x - 64) x - 33 = 0 x = 33

Explanation

Cache memory is a high-speed volatile memory situated between the Central Processing Unit (CPU) and main memory (RAM). Its primary purpose is to temporarily store frequently accessed data, program instructions, and execution results, enabling the CPU to retrieve them significantly faster than fetching from RAM and thereby improving overall system processing speed.

Explanation

Let x be the number of sarees and y be the number of suits.

Given the total item count and expenditure equations: x + y = 8 ... (1) 1500x + 1000y = 10000

Dividing the cost equation by 500 gives: 3x + 2y = 20 ... (2)

Multiplying equation (1) by 2: 2x + 2y = 16 ... (3)

Subtracting equation (3) from equation (2): (3x + 2y) - (2x + 2y) = 20 - 16 x = 4

Substituting x = 4 into equation (1): 4 + y = 8 y = 4

Explanation

By the Inscribed Angle Theorem, the angle subtended by an arc or chord at the centre of a circle is twice the angle subtended by the same arc or chord at any point on the remaining circumference.

Angle at centre = 2 × Angle at circumference

Therefore, the ratio of the angle at the centre to the angle at the circumference is 2:1.

Explanation

By converting all terms to the base 29/4, the left side simplifies to (29/4)^(3 - 2 + 11) = (29/4)¹², while the right side is (29/4)^(-(9m + 7)). Equating the exponents gives 12 = -9m - 7, which yields m = -19/9.

Explanation

Direct passenger flight services between India and China were suspended in March 2020 due to the outbreak of the COVID-19 pandemic. The suspension persisted following the escalation of border tensions along the Line of Actual Control (LAC) in eastern Ladakh in mid-2020. Both nations subsequently initiated discussions to restore direct air connectivity to facilitate trade, travel, and the gradual normalization of bilateral ties.

Explanation

The kernel is the foundational core component of an operating system. It operates with low-level system privileges to manage physical resources such as the CPU, memory, storage, and peripheral devices. By providing a bridge and abstraction layer between application software and the underlying system hardware, the kernel handles essential operations including process scheduling, memory allocation, and hardware device communication through system calls.

Explanation

The highest number among the given set (956, 521, 251, 156, 335) is 956, whose second digit is 5.

The lowest number among the set is 156, whose first digit is 1.

Adding the second digit of the highest number to the first digit of the lowest number yields 5 + 1 = 6.

Explanation

Applying the given rules (vowels +1, consonants -1) to each word:

DIE transforms to CJF (D becomes C, I becomes J, E becomes F), which contains no vowels.

CUP transforms to BVO (C becomes B, U becomes V, P becomes O), which contains the vowel O.

BOX transforms to APW (B becomes A, O becomes P, X becomes W), which contains the vowel A.

ASK transforms to BRJ (A becomes B, S becomes R, K becomes J), which contains no vowels.

Thus, exactly two letter clusters (CJF and BRJ) contain no vowels.

Explanation

Anne Michaels is a renowned Canadian poet and novelist who authored the novel 'Held', published in 2023. The book presents a poetic and fragmentary narrative spanning four generations across a century, exploring profound themes of memory, love, history, and human connection. 'Held' received critical acclaim and was selected for the six-book shortlist of the 2024 Booker Prize.

Explanation

For a quadratic equation ax² + bx + c = 0, the discriminant is given by D = b² - 4ac. For the given equation x² - 2x + 13 = 0, a = 1, b = -2, and c = 13.

D = (-2)² - 4(1)(13) = 4 - 52 = -48

Since the discriminant is negative (D < 0), the quadratic equation has no real roots.

Explanation

The Indian People's Theatre Association (IPTA) was established in 1943 as a progressive cultural movement to raise socio-political consciousness among the masses during the anti-colonial struggle. It used folk theatre, music, dance, and drama as powerful tools of social critique to oppose British imperialism, highlight economic exploitation, expose the horrors of the 1943 Bengal Famine, and articulate anti-fascist and anti-feudal dissent through creative art.

Explanation

The percentage of children in the group is 100% - (20% + 50%) = 30%.

Using the weighted average formula: Average weight = (Percentage of men × Average weight of men + Percentage of women × Average weight of women + Percentage of children × Average weight of children) / 100

Average weight = (20 × 45 + 50 × 60 + 30 × 20) / 100 = (900 + 3000 + 600) / 100 = 4500 / 100 = 45 kg.

Explanation

Since (26 + x), (40 + x), (22 + x), and (34 + x) are in proportion: (26 + x) / (40 + x) = (22 + x) / (34 + x)

Using the relation x = (ad - bc) / ((b + c) - (a + d)): x = (26 × 34 - 40 × 22) / ((40 + 22) - (26 + 34)) x = (884 - 880) / (62 - 60) x = 4 / 2 = 2

Now, for 4x : y :: y : (7x - 6): y² = 4x × (7x - 6)

Substituting x = 2: y² = 4(2) × (7(2) - 6) y² = 8 × (14 - 6) y² = 8 × 8 = 64

Since y > 0, y = √64 = 8.

Explanation

In February 2025, ISRO's Satish Dhawan Space Centre (SDSC SHAR), in collaboration with the Central Manufacturing Technology Institute (CMTI), Bengaluru, developed a 10-tonne vertical planetary mixer—the largest globally for processing solid propellants. Solid rocket motor manufacturing requires precise, high-capacity mixing of highly sensitive and hazardous chemical ingredients like fuels, oxidizers, and binders. Equipped with hydrostatic agitators and PLC-SCADA remote-control systems, this machine eliminates direct human exposure during the hazardous mixing phase while significantly improving batch capacity, quality consistency, throughput, and operational safety in heavy solid motor production.

Explanation

The 13th Governing Council Meeting of the Bay of Bengal Programme Inter-Governmental Organisation (BOBP-IGO) was held in Male, Maldives, from February 20 to 22, 2025. During this meeting, India assumed the chairmanship of the organisation from Bangladesh in the presence of senior representatives from member countries. The meeting was held alongside a high-level conference on policy guidance for mainstreaming the ecosystem approach to fisheries management in small-scale fisheries, hosted by the Ministry of Fisheries and Ocean Resources of the Maldives in collaboration with BOBP-IGO.

Explanation

In each given set, the sequence of mathematical operations applied to obtain successive numbers is + 2, × 2, and + 2:

3 + 2 = 5, 5 × 2 = 10, 10 + 2 = 12 8 + 2 = 10, 10 × 2 = 20, 20 + 2 = 22

Applying the same operation pattern starting with 18 yields: 18 + 2 = 20 20 × 2 = 40 40 + 2 = 42

Explanation

In the right-angled triangle formed by the tower, the ground, and the line of sight, tan θ = height / distance.

Given θ = 30° and distance = 48 m: tan 30° = height / 48 1 / √3 = height / 48 height = 48 / √3 = 16√3 m

Explanation

Under Paragraph 4 of the Sixth Schedule of the Indian Constitution, Autonomous District Councils and Regional Councils in the specified tribal areas of Assam, Meghalaya, Tripura, and Mizoram are empowered to constitute village councils or courts for the trial of suits and cases between tribal parties. These councils can appoint presiding officers and define the jurisdiction and powers of these local courts to administer justice according to tribal customary law.

Explanation

In the Linux GNOME desktop environment, the keyboard shortcut Alt + F2 opens the Run Command prompt window. This floating input box allows users to directly launch software applications, execute custom shell commands, or perform quick system management tasks—such as typing 'r' to restart the GNOME Shell—without needing to open a full terminal interface.

Explanation

The Mahanadi is a major east-flowing peninsular river that originates in the highlands of Chhattisgarh, in the Sihawa range of Dhamtari district. It flows eastward through Chhattisgarh and Odisha, forming a large delta before discharging directly into the Bay of Bengal near False Point. It forms an independent river system and is not part of the Ganga basin.

Explanation

The given series follows a pattern where consecutive even numbers are subtracted in increasing order:

802 - 2 = 800 800 - 4 = 796 796 - 6 = 790 790 - 8 = 782

Subtracting the next even number, 10, gives: 782 - 10 = 772

Explanation

The letter-clusters in the group follow a pattern where the second letter is obtained by subtracting 4 from the alphabetical position of the first letter, and the third letter is obtained by subtracting 2 from the position of the second letter. In DAX, the letter positions are D = 4, A = 1, and X = 24, which instead follows a pattern of subtracting 3 at each step (4 - 3 = 1, and 1 - 3 = 24).

Explanation

According to official data from the Ministry of Youth Affairs and Sports regarding Nehru Yuva Kendra Sangathan initiatives, a total of 28,275 youth received training in various vocational skills.

Explanation

Humayun lost the Mughal throne to Sher Shah Suri following his defeats at the Battle of Chausa (1539) and the Battle of Kannauj (1540), which led to the establishment of the Sur Empire (Second Afghan Empire). After spending fifteen years in exile in Persia under the protection of the Safavid ruler Shah Tahmasp, Humayun capitalized on the internal conflicts among Sher Shah's successors after the death of Islam Shah Suri. Led by his commander Bairam Khan, Humayun defeated Sikandar Shah Suri at the Battle of Machhiwara and the Battle of Sirhind in 1555, allowing him to re-occupy Delhi and Agra and re-establish Mughal rule.

Explanation

Mapping the days from 1 to 7 (Monday to Sunday):

X has an exam on the third day, so X is on Wednesday (Day 3). Since exactly three people have exams between X and T, T must be on Sunday (Day 7). The days between them are Thursday, Friday, and Saturday. Z is immediately after V, and Y is immediately after Z, forming a consecutive block of three days (V, Z, Y). The only remaining block of three consecutive empty days is Thursday (Day 4), Friday (Day 5), and Saturday (Day 6). Therefore, V is on Thursday, Z is on Friday, and Y is on Saturday. With Monday and Tuesday remaining for U and W, W takes Tuesday (since W cannot be on Monday) and U takes Monday.

Thus, V has an exam on Thursday.

Explanation

The International Cooperative Alliance (ICA) Global Cooperative Conference was held at Bharat Mandapam in New Delhi, India, from November 25 to 30, 2024, hosted by the Indian Farmers Fertiliser Cooperative (IFFCO) along with Indian member organizations. The theme of the conference was "Cooperatives Build Prosperity for All", highlighting the role of cooperative enterprises in fostering inclusive economic growth, equitable development, and sustainable livelihoods. The event also marked the global launch of the United Nations International Year of Cooperatives 2025.

Explanation

Article 243ZT of the Constitution of India, inserted by the 97th Constitutional Amendment Act, 2011, provides a transitional provision for existing state laws relating to co-operative societies. Under this article, any provision of any state law on co-operative societies in force immediately before the commencement of the amendment that is inconsistent with Part IXB continues to be in force until amended or repealed by a competent legislature, or until the expiration of 1 year from such commencement, whichever is earlier.