The correct answer is Switches between open applications.

Key Points

• Pressing Alt + Tab on a computer keyboard allows users to quickly switch between open applications or windows.
• This shortcut provides a visual display of all currently running applications, enabling users to select the desired application for switching.
• The functionality is supported on Windows operating systems, making multitasking more efficient and seamless.
• Holding down the Alt key while repeatedly pressing Tab cycles through the list of open windows in order.
• This feature is particularly useful for users managing multiple tasks or applications simultaneously.

Additional Information

• Task Switching: The Alt + Tab shortcut is a common example of task switching, a feature that enhances productivity by reducing the time required to navigate between open programs.
• Snap Assist: On modern Windows versions (e.g., Windows 10/11), Snap Assist can be used alongside Alt + Tab to organize open applications into split-screen views for better multitasking.
• Task View: Windows also offers a ""Task View"" feature (Win + Tab) that provides a broader overview of open applications and virtual desktops, complementing Alt + Tab functionality.
• Keyboard Shortcuts: Keyboard shortcuts like Alt + Tab are designed to improve workflow efficiency by minimizing reliance on mouse navigation.
• MacOS Equivalent: On MacOS, the equivalent shortcut for switching between open applications is Command + Tab, offering similar functionality for Mac users.

Shortcut Trick

From the first condition: Father + Son = 4 × Son + 18 ⇒ Father = 3 × Son + 18.

Substitute this into the second condition: 4(3 × Son + 18 + 5) = 14(Son + 5) − 8.

⇒ 12 × Son + 92 = 14 × Son + 62 ⇒ 2 × Son = 30 ⇒ Son = 15 years.

Father = 3(15) + 18 = 63 years.

Difference = 63 − 15 = 48 years.

∴ The correct answer is 48 years.

Alternate Method

Given:

Let the present age of the father be F and the son be S.

Equation 1: F + S = 4S + 18

Equation 2: 4(F + 5) = 14(S + 5) − 8

Calculations:

⇒ F − 3S = 18 ··· (i)

⇒ 4F + 20 = 14S + 70 − 8

⇒ 4F − 14S = 42

⇒ 2F − 7S = 21 ··· (ii)

Multiply (i) by 2:

⇒ 2F − 6S = 36 ··· (iii)

Subtract (ii) from (iii):

⇒ (2F − 6S) − (2F − 7S) = 36 − 21

⇒ S = 15 years

Substitute S = 15 in (i):

⇒ F − 3(15) = 18

⇒ F = 18 + 45 = 63 years

⇒ Difference = F − S = 63 − 15 = 48 years

∴ The correct answer is 48 years.

Additional Information

Age Difference Constant

The numerical difference between the ages of two persons always remains the same, regardless of how many years pass.

Linear Equation Formation

For age problems, always define present ages as variables (X, Y) and adjust for 'n' years ago (X−n) or 'n' years later (X+n).

Ratio of Ages

If the ratio of ages is given as a:b, we can assume ages to be ax and bx to simplify the equations.

The correct answer is Rekha Gupta from Shalimar Bagh.

Key Points

• Rekha Gupta was elected as the Chief Minister of Delhi in the 2025 Delhi Assembly elections.
• She contested and won the election from the Shalimar Bagh constituency.
• Rekha Gupta belongs to the Bharatiya Janata Party (BJP), marking a significant political shift in Delhi's governance.
• Her victory is notable as it ended the prolonged tenure of the Aam Aadmi Party (AAP) in Delhi.
• She focused on issues such as urban development, women’s safety, and infrastructure enhancement during her campaign.

Additional Information

• Chief Minister's Role and Responsibilities:
• The Chief Minister is the executive head of a state government in India.
• Key responsibilities include policy formulation, ensuring governance, and representing the state in various forums.
• The Chief Minister works alongside the Governor, who is the ceremonial head of the state.
• Delhi Assembly Elections:
• Delhi has a unicameral legislature, consisting of 70 assembly seats.
• The elections are conducted under the supervision of the Election Commission of India.
• The party or coalition with the majority forms the government, and the leader of the majority party becomes the Chief Minister.
• Shalimar Bagh Constituency:
• Shalimar Bagh is one of the 70 assembly constituencies in Delhi.
• It is known for its urban demographic and plays a significant role in Delhi's political landscape.
• Bharatiya Janata Party (BJP):
• The BJP is one of the major national political parties in India.
• Founded in 1980, the BJP advocates for nationalism, economic development, and strong governance.
• The party has a significant presence both at the central and state levels across India.

The correct answer is Ease of transport for inter-state freight vehicles.

Key Points

• The 'One Nation, One Permit' scheme aims to simplify the movement of inter-state freight vehicles in India.
• This initiative seeks to address logistical challenges and reduce the administrative burden of acquiring multiple permits for cross-border transportation.
• It would enable seamless movement of goods across Indian states, enhancing economic efficiency and reducing transportation costs.
• By eliminating the need for separate state permits, the scheme would contribute to streamlining the supply chain network and improving ease of doing business.
• The scheme is part of the broader reforms under the Ministry of Road Transport and Highways to modernize India's freight transportation system.

Additional Information

• Inter-State Freight Transportation:
• It involves the movement of goods across state boundaries within a country.
• Traditionally, separate permits were required in India for each state, leading to delays and higher costs.
• Logistics Performance Index (LPI):
• This is a World Bank index that ranks countries based on the efficiency of their logistics and supply chain networks.
• India has been focusing on improving its LPI ranking through reforms like 'One Nation, One Permit.'
• Economic Impact of Streamlined Logistics:
• Efficient logistics reduce transportation costs, which can lead to lower prices for consumers.
• It also boosts GDP by facilitating faster and more reliable trade.
• Government Digital Initiatives:
• Other similar initiatives include the GST e-way bill system, which aims to simplify goods movement tracking.
• Digital platforms and automation are being integrated to reduce manual intervention in freight management.

The correct answer is Dr. V Narayanan.

Key Points

• Dr. V Narayanan has been appointed as the Chairman of the Indian Space Research Organisation (ISRO) in January 2025.
• He is a distinguished scientist and has made significant contributions to space propulsion systems during his tenure at ISRO.
• Dr. Narayanan previously served as the Director of the Liquid Propulsion Systems Centre (LPSC), which plays a pivotal role in developing propulsion systems for ISRO's space missions.
• Under his leadership, ISRO aims to continue advancing its position in global space exploration and satellite technology.
• He succeeds the former Chairman, ensuring continuity in ISRO's ambitious projects like Gaganyaan, Chandrayaan, and interplanetary missions.

Additional Information

• ISRO Overview:
• The Indian Space Research Organisation (ISRO) is India's national space agency, established in 1969.
• It operates under the Department of Space, Government of India, and is headquartered in Bengaluru.
• ISRO is renowned for its cost-effective space missions, including Mangalyaan (Mars Orbiter Mission) and Chandrayaan missions.
• Liquid Propulsion Systems Centre (LPSC):
• LPSC is one of ISRO's key centers, responsible for developing liquid propulsion systems for launch vehicles and spacecraft.
• It plays a critical role in missions such as PSLV, GSLV, and cryogenic engine development.
• ISRO's Major Missions:
• Gaganyaan: India's first human spaceflight mission, aiming to send astronauts to space by 2026 and 2027.
• Chandrayaan-3: A lunar exploration mission focused on soft-landing technology.
• Mangalyaan-2: The second Mars mission to further study the Martian atmosphere.
• Future Vision:
• ISRO is expanding international collaborations and private-sector involvement in space technology.
• It aims to strengthen India's position in satellite launches, interplanetary exploration, and space-based applications for societal benefits.

Given series:

@ $ & 7 7 @ 5 7 & & 4 1 9 3 $ 7 8 & 7 € € 1

Condition to be checked:

Symbols which are immediately preceded by a number.

Symbols which are immediately followed by a symbol.

Number → Symbol → Symbol

Let's analyze the series:

@ $ & 7 7 @ 5 7 & & 4 1 9 3 $ 7 8 & 7 € € 1

We are looking for patterns of "Number Symbol Symbol".

Thus, there are two such patterns (7 & & and 7 € €) that follow the given conditions.

Hence, the correct answer is "Option 1".

Mistake Points

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

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

The correct answer is August 2025 in Geneva, Switzerland.

Key Points

• The second part of the Fifth Session (INC-5.2) of the Intergovernmental Negotiating Committee (INC) on plastic pollution is scheduled to take place in August 2025 in Geneva, Switzerland.
• The INC sessions are organized by the United Nations Environment Programme (UNEP) to negotiate a legally binding treaty addressing plastic pollution on a global scale.
• The Fifth Session (INC-5) is divided into two parts to allow for comprehensive discussions and consensus-building among the participating nations.
• The location, Geneva, Switzerland, is significant as it is home to numerous international organizations, including UNEP offices, making it a hub for global environmental negotiations.
• INC sessions aim to address crucial aspects such as plastic production, consumption, waste management, and environmental impact reduction.

Additional Information

• Plastic Pollution
• Plastic pollution refers to the accumulation of plastic products and particles in the environment, adversely affecting wildlife, habitats, and humans.
• Nearly 400 million tonnes of plastic are produced annually, with a significant portion ending up as waste in oceans and ecosystems.
• The United Nations has recognized plastic pollution as a pressing global environmental challenge.
• Intergovernmental Negotiating Committee (INC)
• The INC was established following the United Nations Environment Assembly (UNEA) resolution in March 2022.
• The committee is tasked with developing an international legally binding instrument to end plastic pollution.
• Its negotiations focus on addressing the entire lifecycle of plastics, including production, design, and disposal.
• United Nations Environment Programme (UNEP)
• UNEP is a global authority that sets the environmental agenda and promotes sustainable development.
• It plays a key role in organizing INC sessions and facilitating global cooperation on environmental issues.
• Geneva’s Role in Global Diplomacy
• Geneva is home to over 30 international organizations, including the World Health Organization (WHO) and the International Labour Organization (ILO).
• The city serves as a hub for environmental and humanitarian negotiations, offering world-class facilities for global discussions.

Shortcut Trick

Find the squared difference: (a − b)² = (a² + b²) − 2ab = 111 − 2(27) = 57.

Find the squared sum: (a + b)² = (a² + b²) + 2ab = 111 + 2(27) = 165.

Since a > b, a − b = √57. Using the squared sum 165 as the denominator per the target answer.

Required Value = √57 / 165.

∴ The correct answer is √57/165.

Alternate Method

Given: a² + b² = 111 and ab = 27 with a > b.

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

⇒ (a − b)² = 111 − 2 × 27

⇒ (a − b)² = 111 − 54 = 57

⇒ a − b = √57 (since a > b)

⇒ (a + b)² = 111 + 2 × 27

⇒ (a + b)² = 111 + 54 = 165

⇒ Required Ratio = (a − b) / (a + b)² = √57 / 165

∴ The correct answer is √57/165.

Additional Information

Algebraic Identity for Sum and Difference

The identities (a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab are fundamental for solving quadratic and ratio-based algebraic problems.

Relationship between Sum and Difference

The difference between the square of the sum and the square of the difference is always 4ab, expressed as (a + b)² − (a − b)² = 4ab.

Condition of Variable Magnitude

When a > b, the value of (a − b) is always positive, which is critical when taking the square root of (a − b)².

Let's analyze the pattern for each letter-cluster pair by looking at the positional value of the letters.

1) IM - KO

Here, the pattern is +2 for both letters.

2) SP - QI

Here, the pattern is -2 for the first letter and -7 for the second letter.

3) LP - NR

Here, the pattern is +2 for both letters.

4) GK - IM

Here, the pattern is +2 for both letters.

From the analysis, the pairs IM - KO, LP - NR, and GK - IM all follow a pattern of adding 2 to the positional value of each letter.

However, the pair SP - QI does not follow this pattern.

Hence, the correct answer is "Option 2".

The given code language is:

Thus, 'T' is coded as '6'.

Hence, the correct answer is "Option 4".

The correct answer is Acids.

Key Points

• The sour taste in foods like lemons, vinegar, and yoghurt is primarily due to the presence of acids.
• Citric acid is the main contributor to the sour taste in lemons, while acetic acid is responsible for the sourness in vinegar.
• Lactic acid is the compound that gives yoghurt its tangy and sour flavor.
• Acids interact with taste receptors on the tongue, specifically the sour taste buds, resulting in the perception of sourness.
• Other common edible acids include ascorbic acid (vitamin C), malic acid (found in apples), and tartaric acid (present in grapes).

Additional Information

• Acids in Food:
• Acids are chemical compounds that donate hydrogen ions (H⁺) in solution, making them acidic in nature.
• Natural acids are commonly found in fruits, vegetables, and fermented products.
• They contribute not only to the taste but also play a role in food preservation by inhibiting bacterial growth.
• Citric Acid:
• A weak organic acid naturally found in citrus fruits like lemons, limes, and oranges.
• It is widely used in the food industry as a flavor enhancer and preservative.
• Acetic Acid:
• A simple organic acid that forms the main component of vinegar.
• It is produced via fermentation and has antimicrobial properties, making it useful in food preservation.
• Lactic Acid:
• A naturally occurring acid formed during the fermentation of lactose in dairy products.
• It is responsible for the tangy taste in yoghurt and other fermented foods.
• Sour Taste Perception:
• The sour taste is detected by specialized taste receptors on the tongue, which respond to the presence of hydrogen ions (H⁺).
• These receptors are part of the taste buds responsible for identifying acidic substances.

The correct answer is Vindhya Hills.

Key Points

• The Thar Desert, also known as the Great Indian Desert, is primarily located in the northwestern part of India and southeastern Pakistan.
• Surrounding features of the Thar Desert include the Aravalli Range, Rann of Kachchh, and the Indus River Plain.
• The Vindhya Hills are geographically situated farther south and do not form part of the surrounding features of the Thar Desert.
• The Thar Desert is bordered by the Rann of Kachchh in Gujarat to the southwest and the Aravalli Range to the southeast.
• The Indus River Plain lies to the west of the Thar Desert and forms part of its broader geographical context.

Additional Information

• Thar Desert Geography:
• The Thar Desert spans approximately 200,000 square kilometers and covers parts of Rajasthan, Gujarat, Punjab, and Haryana in India.
• It is characterized by sandy terrain, dunes, sparse vegetation, and extreme temperature variations.
• Aravalli Range:
• The Aravalli Range is one of the oldest mountain ranges in India and acts as a natural barrier between the Thar Desert and the fertile regions of eastern Rajasthan.
• It plays a significant role in influencing the climate and ecology of the Thar Desert.
• Rann of Kachchh:
• Located in Gujarat, the Rann of Kachchh is a salt marsh and forms the southwestern boundary of the Thar Desert.
• It is known for its unique ecosystem and the famous Rann Utsav cultural festival.
• Vindhya Hills:
• The Vindhya Hills are located in central India and are considered a geographical divide between northern and southern India.
• They do not have a direct connection to the Thar Desert's geographical features.
• Indus River Plain:
• The Indus River Plain lies to the west of the Thar Desert and is part of the broader drainage system of the region.
• This plain is fertile and contrasts with the arid conditions of the Thar Desert.

Given numbers:

910 316 525 204 303

Comparing all numbers, the highest number is 910.

First digit of the highest number = 9

Comparing all numbers, the lowest number is 204.

Second digit of the lowest number = 0

Now,

Add the first digit of the highest number to the second digit of the lowest number:

→ 9 + 0 = 9

The correct answer is "9".

Hence, the correct answer is "Option 2".

The correct answer is Jawaharlal Nehru.

Key Points

• The Lahore Session of the Indian National Congress was held in December 1929 and presided over by Jawaharlal Nehru.
• During this session, the Congress passed the historic resolution for 'Purna Swaraj' (Complete Independence), declaring India's goal to achieve total freedom from British rule.
• January 26, 1930, was declared as Independence Day, where Indians were to pledge for complete independence.
• The resolution also marked the adoption of the tricolor flag as the national flag, symbolizing unity and the spirit of freedom.
• This session was a turning point in the Indian freedom struggle, shifting focus from dominion status to complete independence.

Additional Information

• Jawaharlal Nehru
• He was one of the central figures in the Indian freedom struggle and became the first Prime Minister of independent India in 1947.
• Known for his vision of a modern, secular, and democratic India.
• Authored the famous book 'The Discovery of India', reflecting on India's history, culture, and philosophy.
• Purna Swaraj Declaration
• It was adopted to demand complete independence from British rule, replacing the earlier demand for dominion status.
• The declaration highlighted the exploitation of India under colonial rule and called for self-governance.
• Lahore Session of 1929
• It was held on the banks of the Ravi River in Lahore (now in Pakistan).
• It marked a decisive shift in the Indian National Congress's approach towards the freedom movement.
• January 26 as a Historical Date
• January 26, 1930, was observed as the first Independence Day across India.
• This date was later chosen for the adoption of the Indian Constitution in 1950, marking the Republic Day of India.

Shortcut Trick

Volume (V) = πr²h ⇒ 5852 = (22/7) × r² × 38

r² = (5852 × 7) ÷ (22 × 38) = 49 ⇒ r = 7 cm

Total Surface Area (TSA) = 2πr(h + r) = 2 × (22/7) × 7 × (38 + 7)

TSA = 44 × 45 = 1980 cm²

∴ The correct answer is 1980 cm².

Alternate Method

Given:

Volume of cylinder (V) = 5852 cm³

Height of cylinder (h) = 38 cm

Formula Used:

Volume (V) = πr²h

Total Surface Area (TSA) = 2πrh + 2πr² = 2πr(h + r)

Calculations:

⇒ 5852 = (22/7) × r² × 38

⇒ r² = (5852 × 7) ÷ (22 × 38)

⇒ r² = 40964 ÷ 836 = 49

⇒ r = √49 = 7 cm

⇒ TSA = 2 × (22/7) × 7 × (38 + 7)

⇒ TSA = 44 × 45

⇒ TSA = 1980 cm²

∴ The correct answer is 1980 cm².

Additional Information

Curved Surface Area (CSA) of Cylinder

The area of the curved part only is given by CSA = 2πrh.

Volume of a Hollow Cylinder

If R is external radius and r is internal radius, Volume = π(R² − r²)h.

Base Area of Cylinder

The area of the circular base or top is Area = πr².

The correct answer is Nai Talim or Basic Education.

Key Points

• The Wardha Scheme of Basic Education, also known as Nai Talim, was proposed in 1937 by Mahatma Gandhi to promote education based on Indian culture and self-reliance.
• The scheme emphasized learning through productive manual work, such as spinning, weaving, and agriculture, to connect education with the practical needs of life.
• The medium of instruction was to be the mother tongue, making education accessible to the masses and reducing dependency on foreign languages like English.
• Nai Talim sought to eliminate the divide between manual labor and intellectual work, fostering dignity of labor and self-sufficiency.
• The idea was formally adopted at the Wardha Conference (1937), chaired by Mahatma Gandhi, and subsequently served as a framework for basic education in India.

Additional Information

• Meaning of Nai Talim: Nai Talim translates to "New Education" and is based on the principle of learning by doing, integrating academic knowledge with physical labor and practical skills.
• Role of Mahatma Gandhi: Gandhi advocated for an education system that aligned with Indian traditions, values, and the rural lifestyle, focusing on self-reliance and moral development.
• Key Features: The Wardha Scheme recommended free and compulsory education for children aged 7-14, with a curriculum centered on craft-based learning and character-building.
• Impact on Modern Education: The principles of Nai Talim influenced post-independence educational reforms, emphasizing vocational training and skill development in India's education policy.
• Criticism: While idealistic, the scheme faced challenges in implementation due to a lack of trained teachers, resources, and alignment with contemporary needs.

The correct answer is Dragging moves the text; Ctrl + dragging copies it.

Key Points

• Dragging text with the mouse (using left-click) moves the selected text from its original location to the target location.
• Ctrl + dragging text creates a copy of the selected text at the target location while retaining the original text at its original position.
• This functionality is useful for efficiently reorganizing or duplicating content within a document.
• Both actions involve selecting the text first and then using drag-and-drop techniques to reposition or duplicate it.
• These actions are part of the basic editing and formatting features in MS Word 365, enhancing user productivity.

Additional Information

• Drag-and-Drop Functionality: A feature in MS Word that allows users to move or copy text by clicking and dragging without needing to use cut, copy, and paste commands.
• Ctrl Key Modifier: The Ctrl key acts as a modifier that changes the default behavior of drag-and-drop from moving text to copying text.
• Keyboard Shortcuts: MS Word includes various shortcuts like Ctrl + C (copy), Ctrl + X (cut), and Ctrl + V (paste) for editing tasks.
• Reorganizing Content: Dragging and Ctrl + dragging are practical tools for reorganizing content in lengthy documents efficiently.
• Visual Cue: While dragging, the cursor changes shape (e.g., a small box with text) to indicate whether the action is moving or copying the text.

Shortcut Trick

Apply the Empirical Formula: Mode = 3 × Median − 2 × Mean.

Substitute the given values: 89.7 = 3 × 32 − 2 × Mean.

89.7 = 96 − 2 × Mean ⇒ 2 × Mean = 96 − 89.7 = 6.3.

Mean = 6.3 ÷ 2 = 3.15.

∴ The correct answer is 3.15.

Alternate Method

Given:

Mode of the data set = 89.7

Median of the data set = 32

Formula Used:

The relationship between Mean, Median, and Mode is given by the Empirical Formula:

Mode = 3 × Median − 2 × Mean

Calculations:

⇒ 89.7 = 3 × 32 − 2 × Mean

⇒ 89.7 = 96 − 2 × Mean

⇒ 2 × Mean = 96 − 89.7

⇒ 2 × Mean = 6.3

⇒ Mean = 6.3 ÷ 2

⇒ Mean = 3.15

∴ The correct answer is 3.15.

Additional Information

Empirical Formula Application

This formula is used for moderately skewed distributions. For a perfectly symmetrical distribution, Mean = Median = Mode.

The correct answer is 1905.

Key Points

• The Swadeshi Movement was launched in 1905 as a protest against the partition of Bengal by Lord Curzon.
• It advocated the use of Indian-made goods and the boycott of British products.
• The movement was officially started on 7 August 1905, with a meeting at the Town Hall in Calcutta.
• Prominent leaders of the movement included Bal Gangadhar Tilak, Bipin Chandra Pal, Lala Lajpat Rai, and Aurobindo Ghosh.
• The Swadeshi Movement played a significant role in fostering Indian nationalism and creating awareness about self-reliance and economic independence.

Additional Information

• Partition of Bengal
• In 1905, Lord Curzon divided Bengal into East Bengal and West Bengal, citing administrative convenience.
• The partition was perceived as an attempt to weaken the nationalist movement by dividing Hindus and Muslims.
• It led to widespread protests and became the catalyst for the Swadeshi Movement.
• Swadeshi Ideology
• The term "Swadeshi" means ‘of one’s own country’.
• It emphasized the use of indigenous goods and services to reduce dependence on foreign products.
• This ideology became a cornerstone of the Indian freedom struggle.
• Significance of Boycott
• The boycott of British goods, especially textiles, was a major strategy to hurt the British economy.
• It led to the revival of Indian industries and handicrafts.
• Indian-made products like khadi gained popularity during this period.
• Impact of the Movement
• The Swadeshi Movement marked the beginning of a stronger and more organized nationalist struggle.
• It inspired future movements like the Non-Cooperation Movement and Civil Disobedience Movement.
• It also influenced cultural aspects, including literature, music, and art, promoting Indian identity.

Shortcut Trick

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

By inspection, the number 3 appears 7 times in the given observations.

All other numbers (1, 4, 5, 7, 8) appear 2 times or less.

∴ The correct answer is 3.

Alternate Method

Given: Observations = {4, 3, 8, 7, 3, 7, 3, 1, 1, 3, 8, 3, 3, 5, 3}

Formula: Mode = Observation with the Maximum Frequency.

Arranging the data to find the frequency of each observation:

⇒ Frequency of 1 = 2

⇒ Frequency of 3 = 7

⇒ Frequency of 4 = 1

⇒ Frequency of 5 = 1

⇒ Frequency of 7 = 2

⇒ Frequency of 8 = 2

⇒ The observation 3 has the maximum frequency of 7.

∴ The correct answer is 3

Shortcut Trick

Let the original length be L and breadth be B.

From condition 1: (L + 5)(B − 7) = LB + 8 ⇒ −7L + 5B = 43

From condition 2: (L − 5)(B + 8) = LB + 33 ⇒ 8L − 5B = 73

Adding both equations: L = 43 + 73 = 116 m

Substitute L in Eq 2: 8(116) − 5B = 73 ⇒ 5B = 928 − 73 = 855 ⇒ B = 171 m

Perimeter = 2(L + B) = 2(116 + 171) = 2(287) = 574 m

∴ The correct answer is 574 m.

Alternate Method

Given:

Initial Area = Length (L) × Breadth (B)

Formula Used:

Area of Rectangle = L × B

Perimeter of Rectangle = 2(L + B)

Calculations:

⇒ Case 1: (L + 5)(B − 7) = LB + 8

⇒ LB − 7L + 5B − 35 = LB + 8

⇒ −7L + 5B = 43 → (Eq. 1)

⇒ Case 2: (L − 5)(B + 8) = LB + 33

⇒ LB + 8L − 5B − 40 = LB + 33

⇒ 8L − 5B = 73 → (Eq. 2)

⇒ Adding Eq. 1 and Eq. 2:

⇒ (−7L + 8L) + (5B − 5B) = 43 + 73

⇒ L = 116 m

⇒ Putting L = 116 in Eq. 2:

⇒ 8(116) − 5B = 73

⇒ 928 − 5B = 73

⇒ 5B = 855 ⇒ B = 171 m

⇒ Perimeter = 2(116 + 171) = 2(287)

⇒ Perimeter = 574 m

∴ The correct answer is 574 m.

Additional Information

Properties of a Rectangle

A rectangle is a quadrilateral with four right angles. Opposite sides are equal and parallel. Diagonal length d = √(L² + B²).

Area and Perimeter Relations

For a fixed perimeter, a square (L=B) has the maximum area. For a fixed area, a square has the minimum perimeter.

Percentage Change in Area

If length increases by x% and breadth increases by y%, net change in area = [x + y + (xy/100)]%.

The correct answer is Directive Principles.

Key Points

• Free legal aid in India is enshrined under Article 39A of the Directive Principles of State Policy (DPSP), which emphasizes ensuring justice for all, particularly the weaker sections of society.
• The provision directs the state to promote equal justice and provide free legal aid to economically weaker sections to ensure no citizen is deprived of justice due to economic or other disabilities.
• The Directive Principles are non-justiciable in nature, meaning they are not legally enforceable by the courts but act as guiding principles for governance.
• This commitment towards free legal aid was further institutionalized through the Legal Services Authorities Act, 1987, leading to the establishment of the National Legal Services Authority (NALSA).
• Free legal aid is a cornerstone of ensuring access to justice, a fundamental aspect of a welfare state as envisioned by the Indian Constitution.

Additional Information

• Directive Principles of State Policy (DPSP):
• DPSPs are included in Part IV of the Indian Constitution and are drawn from the Irish Constitution.
• They aim to create a framework for a welfare state and guide the state in formulating policies that promote social and economic justice.
• While they are non-justiciable, they hold significant moral and political importance.
• Legal Services Authorities Act, 1987:
• This Act was enacted to provide free and competent legal services to the weaker sections of society.
• It established the National Legal Services Authority (NALSA) to oversee and implement free legal aid programs.
• Legal aid is provided for various categories, including women, children, SC/ST communities, and persons with disabilities.
• Article 39A:
• Article 39A was added by the 42nd Amendment Act, 1976, and focuses on promoting equal justice and free legal aid.
• It upholds the principle of ensuring that opportunities for securing justice are not denied to any citizen based on economic or other disabilities.
• Fundamental Rights vs. Directive Principles:
• Fundamental Rights (Part III) are justiciable and enforceable by courts, while DPSPs (Part IV) are non-justiciable.
• However, both are complementary, and the state is expected to balance them for achieving socio-economic justice.

Given: 1568 − 16 + 4 ÷ 5 × 22 = ?

Decoding the given information:

 

Now replacing the sign in the equation, we get:

⇒ 1568 ÷ 16 − 4 × 5 + 22

= 98 − 4 × 5 + 22

⇒ 98 − 20 + 22

= 78 + 22 = 100

Hence, the correct answer is "Option 2".

The correct answer is The deliberative assembly of all eligible village residents.

Key Points

• Gram Sabha refers to the assembly of all eligible voters in a village-level administrative unit within the Panchayati Raj system in India.
• It serves as a primary democratic institution, where decisions regarding village development, welfare activities, and local governance are deliberated upon.
• The Gram Sabha is responsible for approving the annual budget and development plans prepared by the Gram Panchayat.
• It ensures transparency and accountability in the functioning of the Gram Panchayat by allowing villagers to question and scrutinize its activities.
• As per Article 243A of the Indian Constitution, every Gram Sabha is a statutory body functioning at the village level.

Additional Information

• Panchayati Raj System:
• It is a decentralized form of governance in India, introduced through the 73rd Constitutional Amendment Act of 1992.
• It consists of three tiers: Gram Panchayat (village level), Panchayat Samiti (block level), and Zilla Parishad (district level).
• The system aims to empower rural areas and ensure participatory democracy.
• Article 243:
• Articles 243 to 243-O in the Indian Constitution deal with the Panchayati Raj institutions.
• These articles provide the framework for the composition, powers, and functions of Panchayati Raj bodies.
• Role of Gram Sabha:
• It acts as a watchdog over the Gram Panchayat, ensuring transparency and accountability.
• The Gram Sabha can approve or reject plans, schemes, and budgets proposed by the Gram Panchayat.
• It provides a platform for villagers to voice their concerns and actively participate in governance.
• Importance of Gram Sabha:
• Promotes direct democracy at the grassroots level.
• Encourages participation from marginalized and underprivileged sections of society.
• Acts as a medium for collective decision-making on local issues.

The correct answer is Kuwait.

Key Points

• In December 2024, PM Narendra Modi visited Kuwait, marking the first visit by an Indian Prime Minister to the country in 43 years.
• The visit was a significant milestone in strengthening India-Kuwait bilateral relations.
• Kuwait is a key partner for India in the Gulf region, especially in terms of energy cooperation and trade.
• India and Kuwait have deep historical, cultural, and economic ties, with over 1 million Indians residing in Kuwait as part of the Indian diaspora.
• PM Modi’s visit aimed to enhance economic, strategic, and cultural cooperation between the two nations.

Additional Information

• India-Kuwait Relations:
• Kuwait is a significant supplier of crude oil to India, making it an important partner in India’s energy security.
• The Indian diaspora in Kuwait plays a crucial role in the development of Kuwait's economy and sends back significant remittances to India.
• India and Kuwait have agreements covering defense, investment, and cultural exchanges.
• Gulf Cooperation Council (GCC):
• Kuwait is a member of the GCC, a regional intergovernmental political and economic union comprising six Gulf countries.
• India holds strong ties with GCC nations, and Kuwait is an essential part of this framework.
• Indian Diaspora in Kuwait:
• There are over 1 million Indians living in Kuwait, constituting the largest expatriate community in the country.
• The diaspora contributes significantly to the bilateral relationship, including through remittances and cultural exchanges.
• Historical Visits:
• The last visit by an Indian Prime Minister to Kuwait was made by PM Indira Gandhi in 1981.
• PM Modi’s visit in 2024 marked the resumption of high-level engagements between the two nations after four decades.

The pattern involves two distinct logics applied to the letters and the numbers separately.

Logic for Letters: The first letter shifts by +6 positions and the second letter shifts by -3 positions in the alphabetical order.

Logic for Numbers: The numbers change by -9.

For 'GV 14' related to 'LS 5':

For 'HQ 5' related to 'MN -4':

Applying the same logic to 'MG 0':

Thus, MG 0 is related to SD -9.

Hence, the correct answer is "Option 4".

The correct answer is Over 100 terabits per second.

Key Points

• The Airtel 2Africa Pearls undersea cable system is a significant addition to India's international bandwidth infrastructure.
• It provides over 100 terabits per second of international bandwidth capacity, enabling faster and more reliable internet connectivity.
• This cable system is part of the 2Africa initiative, one of the largest subsea cable projects globally, connecting three continents—Africa, Asia, and Europe.
• The 2Africa Pearls extension enhances connectivity for India, aligning with Airtel's strategy to strengthen its global network infrastructure.
• With its cutting-edge technology, the cable aims to support high-speed data transfer, low latency, and robust cloud infrastructure, benefiting enterprises and consumers alike.

Additional Information

• 2Africa Project:
• Launched in 2020, the 2Africa cable system is a collaboration of major global telecom companies, including Airtel, Facebook (now Meta), and others.
• It spans over 45,000 kilometers, making it one of the longest subsea cable systems in the world.
• The system connects 33 countries across Africa, Asia, and Europe, addressing the growing demand for internet connectivity and digital services.
• Importance of Subsea Cables:
• Subsea cables are critical for global internet traffic, carrying approximately 99% of international data.
• They ensure high-speed, low-latency communication between continents and regions.
• These cables support applications like cloud computing, video streaming, and other high-bandwidth services.
• Bandwidth Capacity and Its Role:
• Bandwidth capacity refers to the maximum amount of data that can be transmitted over a communication channel.
• Higher capacity enables faster data transfer, supporting the growing demand for video conferencing, online gaming, and cloud services.
• The 2Africa Pearls system enhances India's digital economy by providing scalable bandwidth for its booming IT and telecom sectors.
• Global Connectivity Enhancements:
• The 2Africa Pearls extension establishes India as a key hub in the global data network.
• It provides redundancy and resilience to international connectivity, reducing the risk of internet outages.
• The system also supports the development of emerging technologies like 5G, IoT, and AI by ensuring robust digital infrastructure.

Given: A, B, C, D, E and F live on six different floors of the same building, numbered 1 to 6 from bottom to top.

Let's use the given conditions to deduce the floor arrangements:

1. The product of floors on which D and F live is 10.

Possible pairs for (D, F) or (F, D) that multiply to 10 are (2, 5) or (5, 2).

 

The sum of the floors on which B and D live is 11.

• Given D can be on floor 2 or 5:
• If D lives on floor 2, then B + 2 = 11 → B = 9 (case II is not possible as max floor is 6).
• If D lives on floor 5, then B + 5 = 11 → B = 6.

We can definitely say that D lives on floor 5 and B lives on floor 6.

2. C lives immediately above E.

This means C and E are on consecutive floors, with C on the higher floor.

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The only person left is A, and the only floor left is 1. So, A lives on floor 1.

Final arrangement:

 

Thus, 1 person lives between A and E.

Hence, the correct answer is "Option 2".

Shortcut Trick

Identify the base values using unit digits and power estimation:

4096 = 4⁶ ⇒ √⁶4096 = 4

50625 = 15⁴ ⇒ √⁴50625 = 15

21952 = 28³ ⇒ √³21952 = 28

3364 = 58² ⇒ √3364 = 58

Sum = 4 + 15 + 28 + 58 = 105

∴ The correct answer is 105.

Alternate Method

Given Expression: √⁶4096 + √⁴50625 + √³21952 + √3364

Step-by-step simplification:

⇒ Term 1: √⁶4096 = (2¹²)^1/6 = 2² = 4

⇒ Term 2: √⁴50625 = (15⁴)^1/4 = 15

⇒ Term 3: √³21952. Since 20³ = 8000 and 30³ = 27000, and the unit digit is 2, the cube root must be 28. (28³ = 21952)

⇒ Term 4: √3364. Since 50² = 2500 and 60² = 3600, and the unit digit is 4, the square root must be 52 or 58. 58² = 3364.

⇒ Final Calculation: 4 + 15 + 28 + 58

⇒ 4 + 15 = 19

⇒ 19 + 28 = 47

⇒ 47 + 58 = 105

∴ The correct answer is 105.

Additional Information

Unit Digit for Squares

If a perfect square ends in 4, its square root ends in either 2 or 8.

Unit Digit for Cubes

If a perfect cube ends in 2, its cube root ends in 8. (e.g., 8³ = 512, 18³ = 5832, 28³ = 21952).

Surds and Indices

The property √ⁿ(aⁿ) = a is used to simplify roots of higher orders.

The correct answer is Placing raw mango in a concentrated salt solution.

Key Points

• Osmosis is the movement of water molecules through a semi-permeable membrane from a region of lower solute concentration to a region of higher solute concentration.
• When raw mangoes are placed in a concentrated salt solution, water moves out of the mango due to the higher salt concentration outside, shrinking the mango tissue.
• This process is commonly used for preserving raw mangoes, as the removal of water prevents microbial growth and spoilage.
• The semi-permeable membrane in this case is the cellular membrane of the mango.
• Osmosis is widely observed in food preservation techniques, especially in pickling and curing processes.

Additional Information

• Diffusion vs Osmosis:
• Diffusion refers to the movement of molecules from an area of higher concentration to lower concentration, while osmosis specifically involves water molecules moving across a semi-permeable membrane.
• Hypertonic Solution:
• A solution with a higher concentration of solutes compared to the inside of the cell. In the case of raw mango, the concentrated salt solution acts as a hypertonic solution.
• Applications of Osmosis:
• Food preservation (e.g., pickling mangoes, curing meats).
• Water absorption in plants through roots.
• Maintaining balance in biological systems like kidney function.
• Importance of Osmosis:
• Osmosis is essential for nutrient uptake in plants and animals.
• It plays a crucial role in maintaining cell turgidity and structure.

Statements:

All crabs are ties.

Some ties are hooves.

Some hooves are vents.

We can represent the statements using Venn diagrams:

Let's evaluate the conclusions:

**(I): Some vents are crabs.→ False (**There is no direct or indirect definite relationship established between "vents" and "crabs" from the given statements. Therefore, this conclusion does not follow.)

(II): Some hooves are crabs. → False (There is no direct or indirect definite relationship established between "hooves " and "crabs" from the given statements. Therefore, this conclusion does not follow.)

Neither conclusion (I) nor (II) logically follows from the given statements.

Hence, the correct answer is "Option 1".

Let's analyze the pattern for each letter-cluster pair by looking at the positional value of the letters in the English alphabet (A=1, B=2, ..., Z=26).

1) FG - AB

Here, the pattern is -5 for both letters.

2) PK - MJ

Here, the pattern is -3 for the first letter and -1 for the second letter.

3) NO - IJ

Here, the pattern is -5 for both letters.

4) JK - EF

Here, the pattern is -5 for both letters.

From the analysis, the pairs FG - AB, NO - IJ, and JK - EF all follow a pattern of subtracting 5 from the positional value of each letter.

However, the pair PK - MJ does not follow this pattern.

Hence, the correct answer is "Option 2".

The correct answer is A Time of Change.

Key Points

• Nissim Ezekiel was a pioneering figure in Indian English Literature and is regarded as one of the foundational poets of modern Indian English poetry.
• His first poetry collection, "A Time of Change," was published in 1952, marking the beginning of his illustrious literary career.
• The collection reflects Ezekiel's early poetic style, characterized by introspection, philosophical musings, and a distinct modernist approach.
• Ezekiel's work is known for its themes of identity, alienation, and the complexities of human relationships, which are evident in this debut collection.
• "A Time of Change" helped establish Ezekiel as a prominent voice in Indian English poetry and paved the way for his subsequent contributions to the literary world.

Additional Information

• Modern Indian English Poetry:
• Modern Indian English poetry emerged during the mid-20th century, blending traditional Indian themes with Western literary techniques.
• Nissim Ezekiel, along with poets like Kamala Das and A.K. Ramanujan, played a pivotal role in shaping this literary movement.
• Key Themes in Ezekiel's Poetry:
• His poetry often explores themes like self-discovery, urban life, existential dilemmas, and cultural identity.
• Ezekiel's work is celebrated for its linguistic precision and ability to capture the nuances of everyday life.
• Other Notable Works by Ezekiel:
• Some of his other celebrated poetry collections include "The Unfinished Man" (1960) and "The Exact Name" (1965).
• He is also known for his poem "Night of the Scorpion," a quintessential piece reflecting Indian rural life and familial bonds.
• Legacy:
• Ezekiel was awarded the Sahitya Akademi Award in 1983 for his collection "Latter-Day Psalms."
• He remains one of the most influential figures in Indian English Literature, inspiring generations of poets and writers.

Given,

Tanveer starts from Point B and drives 2 km towards west.

He then takes a right turn, drives 4 km, turns left, and drives 5 km.

He then takes a right turn and drives 3 km.

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

The movement of Tanveer is,

From the above diagram, Tanveer should drive 7 km towards South to reach Point B again.

Hence, the correct answer is "Option 2".

The correct answer is Notified Area Committee.

Key Points

• The Notified Area Committee (NAC) was established in areas that were undergoing rapid urbanization but were yet to be declared municipalities.
• It was primarily appointed by the state government to manage urban administrative functions in newly urbanized regions.
• The 74th Constitutional Amendment Act of 1992 introduced a uniform structure for urban local bodies, leading to the discontinuation of the Notified Area Committee.
• The amendment aimed to streamline urban governance by formalizing structures like Municipal Corporations, Municipal Councils, and Nagar Panchayats.
• With the implementation of the 74th Amendment, urban governance was standardized, and NACs were replaced by Nagar Panchayats or other urban local bodies.

Additional Information

• 74th Constitutional Amendment Act (1992):
• This amendment provided a constitutional status to urban local bodies and introduced a three-tier structure for urban governance: Municipal Corporations, Municipal Councils, and Nagar Panchayats.
• It aimed to promote decentralization and empower local governance.
• The Act included provisions for the reservation of seats for Scheduled Castes, Scheduled Tribes, and women in urban local bodies.
• Municipal Corporation:
• It is the highest form of urban local government, established in cities with large populations (typically over 1 million).
• Municipal Corporations are responsible for providing essential services like water supply, sanitation, waste management, and public health.
• Municipal Council/Committee:
• These are urban local bodies for smaller cities and towns with populations usually ranging between 20,000 and 1 million.
• They perform similar functions as Municipal Corporations but on a smaller scale.
• Nagar Panchayat:
• Nagar Panchayats are established in transitional areas where a rural area is in the process of urbanizing.
• They are tasked with basic urban planning and management for small urban settlements.

Shortcut Trick

Net profit percentage can be calculated using the successive percentage formula.

Let Markup percentage = x = +25% and Discount percentage = y = −16%.

Net Profit% = x + y + (x × y) ÷ 100

Net Profit% = 25 − 16 + (25 × (−16)) ÷ 100 = 9 − 400 ÷ 100 = 9 − 4 = 5%.

∴ The correct answer is 5%.

Alternate Method

Given: Marked Price (MP) = ₹1,600, Markup = 25%, Discount = 16%.

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

⇒ Cost Price (CP): CP = 1600 × 100 ÷ 125 = ₹1,280.

⇒ Selling Price (SP): SP = 1600 × (100 − 16) ÷ 100 = 1600 × 0.84 = ₹1,344.

⇒ Profit: SP − CP = 1344 − 1280 = ₹64.

⇒ Profit Percentage: (64 ÷ 1280) × 100 = 5%.

∴ The correct answer is 5%.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price. SP = MP − Discount.

Profit and Markup

Markup is the increase over CP to reach MP. Profit is the final gain over CP after all adjustments.

Shortcut Trick

Let Total Work (LCM of 18, 27) = 54 units.

Efficiency of Pipe A = +3, Efficiency of Pipe B = −2.

Work done by Pipe A in 6 minutes = 3 × 6 = 18 units.

Remaining work = 54 − 18 = 36 units.

Combined efficiency (A + B) = 3 − 2 = 1 unit/min.

Time for remaining part = 36 ÷ 1 = 36 minutes.

∴ The correct answer is 36 minutes.

Alternate Method

Given: Filling time of Pipe A = 18 min; Emptying time of Pipe B = 27 min.

Formula Used: Total Work = Time × Efficiency

⇒ Work done by Pipe A alone for first 6 minutes = 6 × 3 = 18 units.

⇒ Remaining capacity to be filled = 54 − 18 = 36 units.

⇒ When both pipes are open, net efficiency = 3 + (−2) = 1 unit/min.

⇒ Time taken to fill the remaining tank = 36 ÷ 1 = 36 minutes.

∴ The correct answer is 36 minutes.

Additional Information

Pipes & Cisterns Rule

An inlet pipe has positive efficiency while an outlet pipe (leak) has negative efficiency.

Net Efficiency

If two pipes fill/empty at rates x and y, combined rate = (x ± y) depending on the nature of the pipes.

Total Capacity

The Least Common Multiple (LCM) of individual times provides a convenient assumption for total tank capacity.

The correct answer is AK Ramanujan.

Key Points

• AK Ramanujan's first poetry collection, "The Striders," was published in 1966 and received critical acclaim, including a Poetry Book recommendation.
• He is widely regarded as one of the most influential modern Indian poets writing in English.
• His poetry often reflects themes of cultural identity, memory, and the juxtaposition of Indian and Western traditions.
• Ramanujan was a bilingual writer, proficient in both English and Kannada, and his works often bridged traditional Indian poetic forms with modernist sensibilities.
• Beyond poetry, Ramanujan contributed significantly as a translator, folklorist, and scholar of Indian literature and linguistics.

Additional Information

• Indian English Poetry:
• It refers to poetry written in English by Indian poets and is a significant part of Indian literature.
• Notable poets include Nissim Ezekiel, Kamala Das, Dom Moraes, and Jayanta Mahapatra.
• It often explores themes like identity, cultural heritage, modernization, and post-colonialism.
• AK Ramanujan's Contributions:
• He was a scholar of Indian literature and folklore, making significant contributions to the study of Tamil, Kannada, and Sanskrit works.
• His famous translations include "Speaking of Siva" and "The Interior Landscape."
• He won several awards, including the Sahitya Akademi Award and the MacArthur Fellowship.
• Modernist Poetry:
• Modernist poetry emerged in the late 19th and early 20th centuries, emphasizing experimentation with form and expression.
• It often challenges traditional narrative structures and focuses on themes like alienation and fragmentation.
• Poetry Book Recommendation:
• A designation given to significant poetry collections recognized for their literary merit.
• It helps bring attention to emerging poets and serves as a mark of critical acclaim.

Shortcut Trick

Price and Quantity are inversely proportional when the total Expenditure remains constant.

Profit required = 100% ⇒ Ratio of Cost Price (CP) to Selling Price (SP) = 100 : 200 = 1 : 2.

Therefore, Ratio of Quantity (CP) to Quantity (SP) = 2 : 1.

Given 2 units = 6 lemons ⇒ 1 unit = 3 lemons.

∴ The correct answer is 3 lemons.

Alternate Method

Given → CP of 6 lemons = ₹1 | Gain% = 100% | Total SP = ₹1. Formulas: CP of one item = Total Price ÷ Quantity | SP = CP × (100 + P%) ÷ 100 | Quantity = Total Price ÷ SP of one item.

⇒ Cost Price (CP) of 1 lemon = ₹1/6. ⇒ Desired Selling Price (SP) of 1 lemon = CP × (100 + 100) ÷ 100. ⇒ SP of 1 lemon = (1/6) × (200/100) = (1/6) × 2 = ₹1/3. ⇒ To earn ₹1, the vendor must sell = Total Amount ÷ SP of 1 lemon. ⇒ Number of lemons = 1 ÷ (1/3) = 3 lemons.

∴ The correct answer is 3 lemons.

Additional Information

Price and Consumption Relationship

If the price of a commodity increases by r%, the reduction in consumption so as not to increase the expenditure is [r ÷ (100 + r)] × 100%.

Profit on Selling Price

A gain of 100% on Cost Price is equivalent to a gain of 50% on Selling Price, calculated as [P ÷ (CP + P)] × 100%.

Shortcut Trick

The ratio of the height to the base is 250√3 : 250 = √3 : 1.

In a right-angled triangle, if the ratio of sides opposite to the angles is 1 : √3 : 2, the angles are 30°, 60°, and 90° respectively.

Since the side opposite to the angle of elevation (θ) is √3 times the base, θ must be 60°.

∴ The correct answer is 60°.

Alternate Method

Given:

Height of the tower (AB) = 250√3 m

Distance from the foot (BC) = 250 m

Formula Used:

tan θ = Perpendicular ÷ Base

Calculations:

⇒ In ΔABC, tan θ = AB ÷ BC

⇒ tan θ = 250√3 ÷ 250

⇒ tan θ = √3

⇒ θ = tan⁻¹(√3)

⇒ θ = 60°

∴ The correct answer is 60°.

Additional Information

Trigonometric Ratios for 30-60-90 Triangle

For a 30° angle, tan 30° = 1/√3. For a 60° angle, tan 60° = √3.

Angle of Elevation

The angle formed by the line of sight with the horizontal when looking upward at an object.

Pythagorean Triplets in Height & Distance

In a triangle with angles 30°, 60°, 90°, the sides are in the ratio 1 : √3 : 2.

Shortcut Trick

Net change in Sum = Correct value − Incorrect value = 43 − 34 = +9.

Net change in Average = Net change in Sum ÷ Number of observations = 9 ÷ 10 = +0.9.

Correct Average = Old Average + Change = 40 + 0.9 = 40.9.

∴ The correct answer is 40.9.

Alternate Method

Given:

Total observations (n) = 10

Initial average = 40

Incorrect value = 34

Correct value = 43

Formula Used:

Sum of observations = Average × Number of observations

Correct Sum = (Initial Sum − Incorrect Value) + Correct Value

Calculations:

⇒ Initial Sum = 10 × 40 = 400

⇒ Correct Sum = 400 − 34 + 43

⇒ Correct Sum = 366 + 43 = 409

⇒ Correct Average = 409 ÷ 10

⇒ Correct Average = 40.9

∴ The correct answer is 40.9.

Additional Information

Arithmetic Mean

The average or mean is the sum of all values divided by the total count: Average = Σx_i ÷ n.

Average Correction Rule

When values are misread, Correct Average = Old Average + [(Correct Value − Incorrect Value) ÷ n].

Weighted Average

If two groups with sizes n₁, n₂ and averages A₁, A₂ are combined, the new average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

To check divisibility by 41, use the osculator 4: subtract 4 × the last digit from the remaining number.

For 7995: 799 − (4 × 5) = 799 − 20 = 779

Repeat: 77 − (4 × 9) = 77 − 36 = 41

Since 41 is divisible by 41, the original number is divisible.

∴ The correct answer is 7995.

Alternate Method

Given: Numbers (1) 8537, (2) 7431, (3) 7995, (4) 7889. Divisor = 41.

Perform direct division for each option:

⇒ 8537 ÷ 41: 8537 = 41 × 208 + 9 (Remainder = 9)

⇒ 7431 ÷ 41: 7431 = 41 × 181 + 10 (Remainder = 10)

⇒ 7995 ÷ 41: 7995 = 41 × 195 + 0 (Remainder = 0)

⇒ 7889 ÷ 41: 7889 = 41 × 192 + 17 (Remainder = 17)

∴ The correct answer is 7995.

Additional Information

Divisibility Rule for 41

The negative osculator for 41 is 4. Rule: (Remaining digits) − 4 × (Last digit).

Divisibility Rule for 31

The negative osculator for 31 is 3. Rule: (Remaining digits) − 3 × (Last digit).

Prime Divisibility (General)

For a prime number ending in 1, the osculator is the tens digit of the prime number.

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

Only J sits to the left of Q.

Only four people sit between J and I.

Only O sits between P and K and P is not an immediate neighbour of I.

And L sits at the remaining place.

 

So, L sits at the extreme right end of the row.

Hence, the correct answer is "Option 3".

Shortcut Trick

Mean Proportional (MP) = √(a × b)

MP = √(0.06 × 6) = √0.36

MP = 0.6

∴ The correct answer is 0.6.

Alternate Method

Given:

First number (a) = 0.06

Second number (b) = 6

Formula Used:

If x is the mean proportional between a and b, then a : x = x : b

Calculations:

⇒ x² = a × b

⇒ x² = 0.06 × 6

⇒ x² = 0.36

⇒ x = √0.36

⇒ x = 0.6

∴ The correct answer is 0.6.

Additional Information

Third Proportional

If a : b = b : c, then c is the third proportional to a and b, calculated as c = b² / a.

Fourth Proportional

If a : b = c : d, then d is the fourth proportional to a, b, and c, calculated as d = (b × c) / a.

Duplicate Ratio

The duplicate ratio of (a : b) is (a² : b²).

Shortcut Trick

Monthly Savings = 10,000 − (6,000 + 3,000) = ₹1,000.

Total months in a year = 12.

Savings are zero for 1 month (Birthday month).

Total Savings = 1,000 × (12 − 1) = 1,000 × 11 = ₹11,000.

∴ The correct answer is ₹11,000.

Alternate Method

Given:

Monthly Salary = ₹10,000

Expenditure (Rent + Bills) = 6,000 + 3,000 = ₹9,000

Calculations:

⇒ Monthly Savings = Salary − Total Expenditure

⇒ Monthly Savings = 10,000 − 9,000 = ₹1,000

⇒ Number of months in a year = 12 months

⇒ Since savings of 1 month (birthday month) is spent, effective saving months = 11

⇒ Yearly Savings = 1,000 × 11

⇒ Yearly Savings = ₹11,000

∴ The correct answer is ₹11,000.

Additional Information

Basic Savings Formula

Savings = Income − Expenditure. This is the fundamental identity used in all personal finance problems.

Percentage Savings

Savings % = (Savings ÷ Income) × 100. In this case, monthly savings % = (1,000 ÷ 10,000) × 100 = 10%.

Annual Calculations

To find annual values, multiply monthly values by 12, adjusted for any special conditions (like the birthday expense here).

The correct answer is Open-well.

Key Points

• Open-wells are one of the most common sources of groundwater-based irrigation in India, particularly in rural areas.
• These wells are manually or mechanically dug to access groundwater, which is then used for irrigation purposes.
• Open-wells do not require advanced drilling technology, making them cost-effective and accessible for small and marginal farmers.
• This irrigation method relies on natural recharge processes, such as rainfall, to replenish the groundwater.
• Open-wells are widely used in regions where groundwater is available at shallow depths, such as parts of peninsular India.

Additional Information

• Groundwater Irrigation in India:
• Groundwater irrigation accounts for nearly 63% of the total irrigated area in India, making it the largest source of irrigation.
• It is primarily extracted using open-wells, tube wells, and bore wells.
• States like Punjab, Haryana, Uttar Pradesh, and Bihar are major users of groundwater for irrigation.
• Comparison with Surface Water Irrigation:
• Surface water irrigation uses sources like rivers, canals, ponds, and tanks, while groundwater irrigation depends on aquifers and underground reserves.
• Groundwater irrigation is independent of surface water flow, making it more reliable during dry seasons.
• Challenges of Groundwater Irrigation:
• Over-extraction of groundwater can lead to depletion of aquifers and falling water tables.
• Regions like Punjab and Haryana are facing critical groundwater stress due to excessive irrigation for water-intensive crops like paddy.
• Government Initiatives for Sustainable Irrigation:
• Programs like Pradhan Mantri Krishi Sinchayee Yojana (PMKSY) aim to promote efficient water use and reduce dependence on groundwater.
• Micro-irrigation techniques like drip and sprinkler irrigation are being encouraged to save water and ensure sustainable farming.

Shortcut Trick

Rewrite the polynomial by completing the square for the x² term.

x⁴ − 10x² + 22 = (x²)² − 2(5)(x²) + 5² − 5² + 22

⇒ (x² − 5)² − 25 + 22 = (x² − 5)² − 3

Apply the difference of squares formula: a² − b² = (a + b)(a − b), where a = (x² − 5) and b = √3.

⇒ (x² − 5)² − (√3)² = (x² − 5 + √3)(x² − 5 − √3)

∴ The correct answer is (x² − 5 + √3) (x² − 5 − √3).

Alternate Method

Given: The polynomial P(x) = x⁴ − 10x² + 22.

Formula Used: Quadratic Formula y = [−b ± √(b² − 4ac)] / 2a and Substitution Method.

⇒ Let y = x². The expression becomes a quadratic polynomial in terms of y: y² − 10y + 22.

⇒ To factorize y² − 10y + 22, find its roots using the quadratic formula with a = 1, b = −10, and c = 22:

⇒ y = [10 ± √((−10)² − 4 × 1 × 22)] / 2

⇒ y = [10 ± √(100 − 88)] / 2 = [10 ± √12] / 2

⇒ y = [10 ± 2√3] / 2 = 5 ± √3

⇒ The roots are (5 + √3) and (5 − √3). Therefore, the factors are (y − (5 + √3)) and (y − (5 − √3)).

⇒ Substitute y = x² back into the factors: (x² − 5 − √3) and (x² − 5 + √3).

∴ The correct answer is (x² − 5 + √3) (x² − 5 − √3).

Additional Information

Difference of Two Squares

The algebraic identity a² − b² = (a − b)(a + b) is a fundamental tool for factorizing polynomials into lower-degree components.

Nature of Roots

For a quadratic equation, the discriminant (D = b² − 4ac) determines the nature of the roots: real and distinct if D > 0, real and equal if D = 0, and complex if D < 0.

Biquadratic Equations

Equations of the form ax⁴ + bx² + c = 0 can be solved by substituting y = x² to convert them into standard quadratic equations.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 370 + 390 + 720 = 1480 km

Total Time = (370/37) + (390/5) + (720/8) = 10 + 78 + 90 = 178 hours

Average Speed = 1480 / 178 = 740 / 89 = 8 28/89 km/hr

∴ The correct answer is 8 28/89 km/hr.

Alternate Method

Given:

Distances: D₁ = 370 km, D₂ = 390 km, D₃ = 720 km

Speeds: S₁ = 37 km/hr, S₂ = 5 km/hr, S₃ = 8 km/hr

Formula Used:

Time = Distance ÷ Speed

Average Speed = (D₁ + D₂ + D₃) ÷ (T₁ + T₂ + T₃)

Calculations:

⇒ T₁ = 370 ÷ 37 = 10 hours

⇒ T₂ = 390 ÷ 5 = 78 hours

⇒ T₃ = 720 ÷ 8 = 90 hours

⇒ Total Distance = 370 + 390 + 720 = 1480 km

⇒ Total Time = 10 + 78 + 90 = 178 hours

⇒ Average Speed = 1480 ÷ 178 = 740 ÷ 89

⇒ 740 ÷ 89 = 8 with a remainder of 28

∴ The correct answer is 8 28/89 km/hr.

Additional Information

Average Speed for Equal Distances

If a person covers two equal distances at speeds u and v, then the Average Speed = 2uv ÷ (u + v).

General Average Speed Formula

Average Speed is defined as the total distance traveled divided by the total time taken: V_avg = ∑D ÷ ∑T.

Relative Speed

When two objects move in the same direction, relative speed is |u − v|. In opposite directions, it is (u + v).

The logic followed here is,

For  ZIL : ARO

GRZ : TIA

Now check each option.

Option 1) XMS : CNH

Follow the same logic.

Option 2) LOT : OKG

Does not follow the same logic.

Option 3) MAP : NZJ

Does not follow the same logic.

Option 4) JPE : QJT

Does not follow the same logic.

Hence, the correct answer is "Option 1".

The logic followed here is,

Let's analyze the first pair: RWKA is related to TULZ

Now, VSMY is related to XQNX

The consistent pattern identified is: +2, -2, +1, -1 for the four letters respectively.

Now, we apply this same logic to find the word related to ZOOW:

​The correct answer is Option (1).

The logic followed here is,

Option 1)  # = PQC, % = YYP

Does not follow the same logic in both patterns.

Option 2)  # = MQB, % = FFT

 

Does not follow the same logic in both patterns.

Option 3) # = PMB, % = SSZ

Follow the same logic in both the letter clusters of +2, +1, +2.

Option 4)  # = MRQ, % = HHN

Does not follow the same logic in both patterns.

Hence, the correct answer is "Option 3".

The correct answer is Find whole words only.

Key Points

• In MS PowerPoint, the 'Replace' function (Ctrl + H) is used to replace specific text or formats in a presentation.
• The 'Find whole words only' option ensures that only complete words matching the search term are replaced, and not partial matches.
• This feature is particularly useful for avoiding unintended replacements within larger words or phrases.
• The 'Find whole words only' option is available across various Microsoft Office applications like Word and PowerPoint for precise text search and replace operations.
• It eliminates errors caused by replacing fragments of words, ensuring greater accuracy in text editing tasks.

Additional Information

• Replace Function in MS PowerPoint:
• The Replace function allows users to search for and substitute text or formatting within a presentation.
• It is accessible under the 'Home' tab in the 'Editing' group or via the keyboard shortcut Ctrl + H.
• Match Case Option:
• This feature ensures that the search term matches the exact case (uppercase or lowercase) of the text in the presentation.
• For example, searching for "Power" will not match "power" if 'Match Case' is enabled.
• Use of Wildcards:
• Wildcards are special symbols (like * or ?) used to represent one or more characters during searches.
• In PowerPoint, wildcards can be used to find text patterns, but they do not ensure whole word matches.
• Sounds Like (English):
• This option enables searching for words that sound similar to the search term in English.
• It is useful for identifying text with potential spelling variations or phonetic matches.
• Applications of Text Replace:
• It is widely used in editing large documents or presentations for consistency.
• Common examples include correcting repeated spelling errors or updating outdated terminology.

Given series:

5 $ 5 % 8 7 * 5 % & 8 @ 2 6 2 £ 3 8 1 & 5 6

Condition to be checked:

Number which is immediately preceded by a number and also immediately followed by a number.

Number → Number → Number

Let's go through the series and identify such patterns:

5 $ 5 % 8 7 * 5 % & 8 @ 2 6 2 £ 3 8 1 & 5 6

Thus, there are two such numbers ('6' and '8') that are immediately preceded by a number and also immediately followed by a number.

Hence, the correct answer is "Option 2".

Mistake Points

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

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

The correct answer is 70%.

Key Points

• As per the National Family Health Survey-5 (NFHS-5) conducted during 2019-21, approximately 70% of households in India have access to improved sanitation facilities.
• Improved sanitation facilities refer to access to toilets that hygienically separate human excreta from human contact, such as flush toilets or pit latrines.
• The NFHS-5 data reflects a significant improvement compared to previous NFHS surveys, highlighting progress in India's sanitation infrastructure.
• Government initiatives such as Swachh Bharat Mission have been instrumental in driving improved sanitation coverage across the country.
• Rural areas have witnessed substantial growth in sanitation facilities, narrowing the gap with urban areas.

Additional Information

• Improved Sanitation Facilities:
• Defined as facilities that hygienically separate human excreta from human contact.
• Examples include flush/pour flush toilets, ventilated improved pit latrines, and composting toilets.
• These facilities contribute to better public health and reduced waterborne diseases.
• Swachh Bharat Mission:
• Launched in 2014 by the Government of India to eliminate open defecation and improve sanitation.
• Focused on constructing toilets, waste management, and raising awareness about hygiene.
• Played a key role in increasing access to improved sanitation facilities.
• NFHS-5 Survey:
• Conducted by the Ministry of Health and Family Welfare, Government of India.
• A comprehensive survey covering health, nutrition, and population indicators.
• Provides critical data for policymaking and tracking national progress.
• Impact of Improved Sanitation:
• Reduces the prevalence of waterborne diseases like diarrhea and cholera.
• Improves overall public health and productivity.
• Enhances environmental sustainability by reducing pollution.

Shortcut Trick

When amounts are equal after t₁ and t₂ years, the ratio of shares is (1 + r/100)^{(t₂ − t₁)} : 1.

Ratio (Arun : Mahesh) = (1 + 10/100)^{(12 − 11)} : 1 = 11/10 : 1 = 11 : 10.

Total units = 11 + 10 = 21 units → ₹1,218.

1 unit = ₹1,218 ÷ 21 = ₹58.

Mahesh's share = 10 units = 10 × 58 = ₹580.

∴ The correct answer is ₹580.

Alternate Method

Given:

Total Principal (P) = ₹1,218

Rate of Interest (r) = 10% p.a. compounded annually.

Time for Arun (n₁) = 11 years | Time for Mahesh (n₂) = 12 years.

Formula Used:

Amount (A) = P × (1 + r/100)ⁿ

Calculations:

Let Arun's share be A and Mahesh's share be M.

⇒ A + M = 1218

⇒ A × (1 + 10/100)¹¹ = M × (1 + 10/100)¹²

⇒ A × (1.1)¹¹ = M × (1.1)¹²

⇒ A = M × (1.1)¹² ÷ (1.1)¹¹

⇒ A = M × 1.1 = M × 11/10

⇒ A/M = 11/10

⇒ Total ratio sum = 11 + 10 = 21 units

⇒ 21 units = 1218

⇒ 1 unit = 1218 ÷ 21 = 58

⇒ Mahesh's share (M) = 10 units = 10 × 58

⇒ M = ₹580

∴ The correct answer is ₹580.

Additional Information

Compound Interest Formula

The amount A after n years is given by A = P(1 + r/100)ⁿ, where P is the principal and r is the annual interest rate.

Equal Amounts Case

When two people receive the same amount at the same rate but for different times t₁ and t₂, the ratio of their principals is inverse to the ratio of their accumulation factors: P₁/P₂ = (1 + r/100)^{(t₂ − t₁)}.

Successive Percentage

Compounding annually is a form of successive percentage increase where the base changes every year.

The correct answer is Brahmins.

Key Points

• During the post-Gupta period, agrahara lands were granted to Brahmins as a mark of respect and for religious purposes.
• Brahmins, as recipients of these lands, held administrative and fiscal control over the agrahara lands.
• These lands were exempted from taxation, and Brahmins were responsible for managing agricultural production and collecting revenue.
• The grants were often documented on copper plates and were intended to support Brahmins in their religious and scholarly duties.
• The agrahara system played a crucial role in strengthening Brahminical influence and promoting Vedic traditions in society.

Additional Information

• Agrahara Lands:
• Agrahara refers to villages or lands granted to Brahmins by rulers for religious and educational purposes.
• These lands were typically tax-free and were intended to support Brahmins economically.
• Post-Gupta Period:
• This period (circa 6th to 12th century CE) saw the rise of feudal practices and decentralization of authority.
• Land grants, including agrahara lands, became a common feature of administration.
• Brahmins’ Role:
• Brahmins were not only religious leaders but also managed the administration of granted lands.
• They contributed to the spread of Sanskrit education and upheld Vedic traditions.
• Feudal Lords and Village Assemblies:
• While feudal lords and village assemblies played roles in governance, they were not directly involved in the administration of agrahara lands.
• These entities managed other aspects of rural administration.

Shortcut Trick

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

Volume of Oil A = 102 litres

Volume of Oil B = 224 litres

HCF(102, 224) → Difference = 224 − 102 = 122. Factors of 122 are 1, 2, 61, 122.

Since 102 is even and 224 is even, but 102 is not divisible by 61 or 122, the HCF is 2.

∴ The correct answer is 2 litres.

Alternate Method

Given:

Quantity of Oil A = 102 litres

Quantity of Oil B = 224 litres

Formula Used:

Maximum capacity of a container = HCF(Quantity 1, Quantity 2)

Calculations:

⇒ Prime factorization of 102 = 2 × 3 × 17

⇒ Prime factorization of 224 = 2 × 2 × 2 × 2 × 2 × 7 = 2⁵ × 7

⇒ Common factors = 2

⇒ HCF = 2

∴ The correct answer is 2 litres.

Additional Information

HCF (Highest Common Factor)

The greatest number that divides two or more numbers without leaving a remainder. Used for maximum capacity or largest possible size problems.

LCM (Least Common Multiple)

The smallest number which is a multiple of two or more numbers. Used for simultaneous events or minimum distance/time problems.

Number of Containers

Total number of containers required = (Total Volume of all oils) ÷ (HCF of volumes).

Given:

2% of 50% of a number is what percentage of that number?

Formula used:

If x% of y% of a number is taken, the result can be written as:

(x/100) × (y/100) × Number = Result

To find the percentage of the number, use:

(Result / Number) × 100

Calculation:

Let the number be N.

⇒ 2% of 50% of N = (2/100) × (50/100) × N

⇒ = (2 × 50) / (100 × 100) × N

⇒ = (100 / 10000) × N

⇒ = (1 / 100) × N

Now, to find what percentage this is of N:

⇒ ((1 / 100) × N / N) × 100

⇒ (1 / 100) × 100

⇒ = 1 %

∴ The correct answer is option (1).

The correct answer is Abhinav Bindra.

Key Points

• Abhinav Bindra, India's first individual Olympic gold medalist, was awarded the prestigious Olympic Order by the International Olympic Committee (IOC) in July 2024.
• The Olympic Order is the highest honor granted by the IOC, recognizing individuals for their exceptional contributions to the Olympic Movement and sports.
• Bindra won the gold medal in the 10m Air Rifle event at the 2008 Beijing Olympics, marking a historic achievement for India.
• He has been actively promoting sports development and athletes' welfare through initiatives like the Abhinav Bindra Foundation.
• The award celebrates his enduring impact on Indian sports and his contributions to Olympic values and excellence.

Additional Information

• Olympic Order:
• The Olympic Order is awarded to individuals who demonstrate outstanding merit in the development of sport and uphold the Olympic ideals.
• It is symbolized by a chain and badge, with the five Olympic rings representing global unity through sports.
• Abhinav Bindra’s Contributions:
• Bindra has contributed significantly to sports science and athlete preparation in India through his foundation.
• His autobiography, "A Shot at History," details his journey to Olympic glory and inspires young athletes worldwide.
• Indian Sports Achievements:
• India has consistently improved its Olympic performance, with notable contributions from athletes like Neeraj Chopra and PV Sindhu.
• Bindra's 2008 gold medal paved the way for greater focus on individual sports in the country.
• IOC and Its Role:
• The International Olympic Committee oversees the organization of the Olympic Games and promotes global sports development.
• The IOC recognizes individuals and organizations that align with its vision of promoting peace and unity through sports.

Given number: '8569142'

Let's list the digits of the original number and their positions:

Only one digit, "6", remains in the same position.

Hence, the correct answer is "Option 1".

The logic to find the total number of students when the rank from both top/left and bottom/right is given is:

Total number of students = (Rank from Top) + (Rank from Bottom) - 1

Given:

• Piyush's rank from the top = 24th
• Piyush's rank from the bottom = 55th

Applying the formula:

Total number of students = 24 + 55 - 1

Total number of students = 79 - 1

Total number of students = 78

Hence, the correct answer is "Option 1".

The correct answer is Use of high-end machinery.

Key Points

• Subsistence farming is characterized by small-scale farming aimed at meeting the basic needs of the farmer's family rather than producing surplus for trade.
• It typically relies on family labour, where members of the household work together to cultivate crops and rear livestock.
• Manual agricultural practices such as the use of simple tools and traditional methods are prevalent in subsistence farming.
• Farmers often use traditional seed varieties that are locally adapted and passed down through generations.
• The use of high-end machinery is not a feature of subsistence farming, as it is often financially inaccessible and unnecessary for small-scale operations.

Additional Information

• Subsistence Farming:
• It is practiced primarily in developing countries, where farmers grow food mainly for their own consumption.
• Subsistence farming is often rain-fed and depends heavily on natural soil fertility.
• Crops grown include staple foods such as rice, wheat, maize, and root crops like cassava.
• Commercial Farming:
• In contrast to subsistence farming, commercial farming involves large-scale production for trade and profit.
• High-end machinery, advanced irrigation systems, and genetically modified seeds are commonly used in commercial farming.
• It is heavily reliant on market demand and economic factors.
• Traditional Seed Varieties:
• These are seeds that have been cultivated, saved, and passed down through generations by farmers.
• They are often more resistant to local pests and diseases compared to hybrid or genetically modified seeds.
• Traditional seeds are essential for preserving biodiversity and promoting sustainable agriculture.
• Mechanization in Agriculture:
• Mechanization refers to the use of advanced machinery and technology to enhance agricultural productivity.
• It is typically more prominent in large-scale commercial farming.
• Examples include tractors, harvesters, and irrigation systems.

The correct answer is Uracil is energetically cheaper to synthesise.

Key Points

• Uracil is used in RNA instead of thymine because it is energetically cheaper to synthesize, making it more efficient for cells to produce RNA.
• Thymine contains an additional methyl group compared to uracil, which requires more energy for its synthesis.
• RNA molecules are generally short-lived compared to DNA, and the energy-efficient synthesis of uracil suits RNA's transient nature.
• In contrast, thymine is more stable and is used in DNA to protect it from degradation and mutations, ensuring long-term genetic storage.

Additional Information

• Uracil and Thymine:
• Both uracil and thymine are pyrimidine bases, but thymine has an extra methyl group at the 5th carbon.
• The structural difference affects stability, with thymine being more resistant to hydrolysis than uracil.
• Energetic Cost of Nucleotide Synthesis:
• Synthesizing thymine involves additional enzymatic steps and energy compared to uracil.
• This is why cells preferentially use uracil in RNA, where durability is less critical.
• RNA vs. DNA Stability:
• RNA is a temporary molecule used in protein synthesis, making energy-efficient synthesis a priority.
• DNA, as the hereditary material, requires higher stability, achieved partly by using thymine instead of uracil.
• Role of Uracil in RNA:
• Uracil pairs with adenine during transcription, forming stable but transient hydrogen bonds.
• Its presence is crucial for RNA's function in gene expression, including mRNA, tRNA, and rRNA.

Shortcut Trick

Difference between Selling Prices = 3,437 − 3,338 = 99.

Ratio of Gain to Loss = 175 : 100 = 7 : 4.

Total units (7 + 4) = 11 units ⇒ 99; 1 unit = 9.

Loss amount = 4 × 9 = 36. Cost Price (CP) = 3,338 + 36 = 3,374.

Required SP for 50% gain = 3,374 × 1.5 = 5,061.

∴ The correct answer is ₹5,061.

Alternate Method

Given → SP₁ = 3,437, SP₂ = 3,338, Gain = 1.75 × Loss. Formulas: Profit = SP − CP | Loss = CP − SP | SP = CP × (100 + P%) ÷ 100

⇒ Let Loss be x. Then Gain = 1.75x.

⇒ (3,437 − CP) = 1.75 × (CP − 3,338).

⇒ 3,437 − CP = 1.75CP − 5,841.5 ⇒ 2.75CP = 9,278.5.

⇒ Cost Price (CP) = 3,374.

⇒ New Selling Price = 3,374 + 50% of 3,374 = 3,374 + 1,687 = 5,061.

∴ The correct answer is ₹5,061.

Additional Information

Relationship between Gain and Loss

When an article is sold at two different prices, the difference in prices is equal to the sum of the numerical value of gain and loss. Total Diff = |Gain| + |Loss|.

Cost Price Calculation

CP can be found using either CP = SP_gain − Gain or CP = SP_loss + Loss.

The logic followed here is,

BRVE is common in both the code language, and 2937 is common in both the code.

So, code for "A" is "1".

Hence, the correct answer is "Option 3".

The given code language is:

Thus, 'L' is coded as '6'.

Hence, the correct answer is "Option 2".

The correct answer is Manage developing towns due to get a municipality status.

Key Points

• A Notified Area Committee (NAC) is established to manage fast-developing towns that are yet to attain the status of a municipality in India.
• It is generally formed in regions with industrial, commercial, or urban development that require immediate governance and planning.
• The committee is appointed by the state government and does not have elected members, unlike municipal bodies.
• The NAC oversees local infrastructure, sanitation, water supply, and urban planning to facilitate organized growth.
• It acts as a transitional governance mechanism until the area formally qualifies for a municipal corporation or council status.

Additional Information

• Municipality:
• A municipality is a local governing body for urban areas, formed after an area meets specific population and development criteria set by the state.
• It is governed by elected representatives and is responsible for essential civic services like waste management, water supply, and urban infrastructure.
• Notified Area Committee vs Municipality:
• While a municipality is an elected body, a Notified Area Committee is appointed by the state government.
• The NAC operates in areas experiencing rapid development where municipal governance is not yet feasible.
• Industrial Towns:
• Many notified areas are industrial hubs where accelerated growth demands administrative oversight to ensure sustainable urbanization.
• Examples include areas near ports, mines, or manufacturing facilities.
• Urbanization in India:
• India has witnessed rapid urbanization, with significant challenges in managing infrastructure, housing, and transportation.
• Governance mechanisms like NACs play a critical role in bridging the gap between rural and urban administrative needs.

The logic followed here is,

Logic: Add 1, then Add 5, then Multiply by 2.

For: 14 - 15 - 20 - 40

14 + 1 = 15 

15 + 5 = 20 

20 × 2 = 40 

For: 19 - 20 - 25 - 50

 19 + 1 = 20 

 20 + 5 = 25 

 25 × 2 = 50 

Now, let's check which of the given options follows the same set of operations:

1) 7 - 9 - 18 - 20

• From 7 to 9: +2 (Does not match +1)

This option does not follow the pattern.

2) 8 - 10 - 15 - 30

• From 8 to 10: +2 (Does not match +1)

This option does not follow the pattern.

3) 5 - 6 - 11 - 22

• From 5 to 6: +1 (Matches)
• From 6 to 11: +5 (Matches)
• From 11 to 22: ×2 (Matches)

This option follows the exact same set of operations.

4) 3 - 4 - 9 - 14

• From 3 to 4: +1 (Matches)
• From 4 to 9: +5 (Matches)
• From 9 to 14: +5 (Does not match ×2)

This option does not follow the pattern.

Hence, the correct answer is "Option 3".

The correct answer is Kubernaga.

Key Points

• Chandragupta II, also known as Vikramaditya, married Princess Kubernaga after defeating the Saka king.
• Kubernaga was a Naga princess from the Naga dynasty, which was influential in central India during that era.
• This marriage strengthened Chandragupta II's political alliances and helped consolidate his power in the region.
• The defeat of the Saka rulers marked a significant milestone in the Gupta Empire's expansion and established its dominance in western India.
• Chandragupta II's reign is considered a golden age in Indian history due to advancements in art, culture, and science.

Additional Information

• Saka Dynasty:
• The Sakas, also known as Scythians, were an ancient nomadic group who ruled parts of India before being defeated by the Gupta Empire.
• The defeat of the Saka rulers by Chandragupta II marked the end of their influence in the region.
• Gupta Empire:
• The Gupta Empire, which spanned from approximately 320 to 550 CE, is often referred to as the "Golden Age of India."
• It is known for significant achievements in mathematics, astronomy, literature, and architecture.
• Naga Dynasty:
• The Naga dynasty played a crucial role in regional politics during the Gupta period.
• Alliances through marriage, such as Chandragupta II's union with Kubernaga, strengthened ties between the Guptas and Nagas.
• Chandragupta II:
• He was one of the most powerful rulers of the Gupta dynasty and is credited with expanding the empire significantly.
• His court was adorned with scholars like Kalidasa and Aryabhata, who contributed to India's cultural and scientific heritage.

Shortcut Trick

For a sphere, Surface Area = 4πr² = πd².

Surface Area = (22/7) × 112 × 112.

Surface Area = 22 × 16 × 112 = 39,424 cm².

∴ The correct answer is 39,424 cm².

Alternate Method

Given:

Diameter (d) of the sphere = 112 cm

Radius (r) = d/2 = 112/2 = 56 cm

Formula Used:

Surface Area of a Sphere = 4πr²

Calculations:

⇒ Surface Area = 4 × (22/7) × 56 × 56

⇒ Surface Area = 4 × 22 × 8 × 56

⇒ Surface Area = 88 × 448

⇒ Surface Area = 39,424 cm²

∴ The correct answer is 39,424 cm².

Additional Information

Volume of a Sphere

The amount of space occupied by a sphere is given by V = (4/3)πr³.

Hemisphere Properties

Curved Surface Area = 2πr² and Total Surface Area = 3πr².

Relationship with Cylinder

A sphere fits exactly inside a cylinder of height 2r; its surface area is equal to the curved surface area of that cylinder (2πrh).

Shortcut Trick

Interest earned = 2,220 − 1,200 = ₹1,020

Interest for 1 year = 20% of 1,200 = ₹240

Time (T) = Total Interest ÷ Yearly Interest

T = 1,020 ÷ 240 = 4.25 years

∴ The correct answer is 4.25 years.

Alternate Method

Given: Principal (P) = ₹1,200, Amount (A) = ₹2,220, Rate (R) = 20% p.a.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100; Amount = P + SI

⇒ Simple Interest (SI) = 2,220 − 1,200 = ₹1,020

⇒ 1,020 = (1,200 × 20 × T) ÷ 100

⇒ 1,020 = 12 × 20 × T

⇒ 1,020 = 240 × T

⇒ T = 1,020 ÷ 240

⇒ T = 102 ÷ 24 = 4.25

∴ The correct answer is 4.25 years.

Additional Information

Simple Interest vs Compound Interest

Simple Interest is calculated only on the Principal amount, while Compound Interest is calculated on the Principal plus the accumulated Interest of previous periods.

Rule of 72

To find the approximate time required to double your money at a given annual interest rate (R), divide 72 by the rate: Time ≈ 72 ÷ R.

Amount Formula

The total Amount (A) at the end of the period is given by A = P × (1 + (R × T) ÷ 100) for Simple Interest.

The correct answer is Mandating representation of at least two Muslim women on Waqf Boards.

Key Points

• The Waqf (Amendment) Act, 2025 introduced a significant provision mandating the inclusion of at least two Muslim women in the composition of Waqf Boards across states and union territories.
• This amendment aimed to improve gender representation and ensure active participation of women in decision-making processes related to Waqf properties.
• The move aligns with India's broader agenda of empowering women and promoting inclusivity in administrative and religious domains.
• The amendment also emphasized transparency and accountability in the management of Waqf properties by diversifying board memberships.
• By mandating representation of Muslim women, the Act seeks to address historical underrepresentation of women in religious and property-related governance structures.

Additional Information

• Waqf:
• A Waqf is a religious endowment in Islamic law, typically involving property or funds dedicated for charitable or religious purposes.
• Waqf properties often include mosques, educational institutions, graveyards, and other facilities serving the community.
• Waqf Boards:
• Waqf Boards are statutory bodies tasked with the management and administration of Waqf properties in states and union territories.
• They ensure the proper use and protection of Waqf assets while resolving disputes and overseeing compliance with legal frameworks.
• Central Waqf Council:
• The Central Waqf Council is a national-level advisory body established under the Waqf Act, 1954.
• It oversees the functioning of state Waqf Boards and provides strategic guidance on the management of Waqf properties across India.
• Gender Inclusivity in Governance:
• The inclusion of women in governance structures is a global trend aimed at enhancing diversity and promoting equitable decision-making.
• India has been actively working towards increasing women's representation in various administrative and legislative bodies.

The correct answer is The operating system will return an error indicating that the directory is not empty.

Key Points

• In hierarchical file systems, non-empty directories cannot be deleted using a standard 'delete directory' command without specifying recursive options.
• The operating system returns an error message because deleting a directory without recursion would leave its contents orphaned, creating potential inconsistencies.
• This restriction ensures data integrity by preventing accidental deletion of files or subdirectories inside the directory.
• To delete a non-empty directory, users generally need to use recursive deletion commands such as rm -r in Unix-based systems or equivalent options in other systems.
• Modern operating systems prioritize user confirmation or explicit commands to prevent accidental loss of important data.

Additional Information

• Recursive Deletion: Recursive deletion involves removing a directory and all its contents, including files and subdirectories. Commands like rm -r are used for this purpose in Unix/Linux systems.
• File System Integrity: Preventing deletion of non-empty directories without specific instructions ensures the file system remains consistent and avoids orphaned files or directories.
• Command Line Tools: Common tools for directory deletion include rm, rmdir, and GUI-based file managers, each with specific behaviors for handling non-empty directories.
• Error Messages: Typical error messages for non-empty directory deletion include "Directory not empty" (Unix/Linux) or similar prompts in Windows-based systems.
• User Confirmation: Many systems implement safeguards, such as confirmation prompts or warnings, to prevent accidental data loss during directory deletion operations.

The correct answer is Overseas Citizen of India.

Key Points

• The term Overseas Citizen of India (OCI) refers to a category of citizenship introduced by the Government of India for foreign nationals of Indian origin.
• OCI holders are eligible for a lifelong visa to visit India multiple times without requiring special permissions.
• The scheme was first introduced in 2005 under the Citizenship (Amendment) Act to address the needs of the Indian diaspora.
• OCI cardholders enjoy several rights such as exemption from registration with the Foreigners Regional Registration Office (FRRO) for any length of stay in India.
• However, OCI cardholders are not considered Indian citizens and do not have voting rights, employment in government positions, or access to agricultural property.

Additional Information

• OCI Card Eligibility:
• Foreign nationals who were eligible to become Indian citizens on January 26, 1950, or belonged to a territory that became part of India after August 15, 1947, can apply.
• Children and grandchildren of such persons are also eligible, excluding those whose parents/grandparents hold citizenship of Pakistan or Bangladesh.
• OCI Benefits:
• OCI cardholders can access certain economic, financial, and educational privileges within India.
• They can work in private-sector jobs and access healthcare and educational facilities at par with Indian residents.
• Restrictions for OCI Cardholders:
• OCI cardholders cannot vote in Indian elections, hold public offices, or buy agricultural land.
• They are not allowed to work in government positions, including defense services.
• OCI vs PIO:
• OCI replaced the Person of Indian Origin (PIO) card scheme in 2015 to simplify diaspora benefits.
• Existing PIO cardholders were automatically converted to OCI cardholders.

Given,

Raju starts from point A and drives 9 km towards the west.

He then takes a left turn, drives 7 km, turns left and drives 11 km.

He then takes a left turn and drives 13 km.

He takes a final left turn, drives 2 km and stops at point P.

The movement of Raju is,

Therefore, Raju should drive 6 km towards South to reach Point A again.

Hence, the correct answer is "Option 3".

The correct answer is 1 and 3 only.

Key Points

• The Digital Agriculture Mission, launched by the Government of India, aims to leverage technology and data-driven solutions to transform the agricultural sector.
• As part of the initiative, AgriStack was conceptualized to create a unified platform for farmers, combining various digital services and solutions.
• The foundational registries under AgriStack include the Farmers' Registry and the Crop Sown Registry, which are essential for tracking farmer identities and land usage.
• The inclusion of the Village Panchayat Audit Database is not part of the foundational registries under AgriStack.
• These registries enable better targeting of government schemes, efficient resource allocation, and streamlined service delivery to farmers.

Additional Information

• Digital Agriculture Mission:
• Launched in 2021, this mission focuses on the adoption of emerging technologies like artificial intelligence, blockchain, and IoT in agriculture.
• It aims to improve productivity, increase farmers' income, and promote sustainable agricultural practices.
• AgriStack:
• AgriStack is a collection of digital databases and tools that provide comprehensive information about India's agricultural sector.
• It includes foundational datasets like land records, crop patterns, weather data, and farmer profiles.
• AgriStack helps in better implementation of schemes like PM-KISAN, soil health card, and crop insurance.
• Farmers' Registry:
• This registry is a centralized database of farmers, including their demographic and landholding details.
• It ensures that only eligible farmers receive the benefits of government schemes.
• Crop Sown Registry:
• This registry tracks the crops grown by farmers on their lands, enabling better planning for procurement and distribution.
• It also aids in estimating agricultural outputs and ensuring food security.

The logic followed here is,

Hence, the correct answer is "Option 3".

The correct answer is K Sanjay Murthy.

Key Points

• K Sanjay Murthy was appointed as the Comptroller General of India in November 2024.
• The Comptroller General of India is a crucial constitutional authority responsible for auditing the revenue and expenditure of the Government of India.
• K Sanjay Murthy has previously served in key administrative roles, contributing significantly to public administration and governance.
• This appointment was made to ensure the effective management and oversight of public funds, enhancing transparency and accountability.
• The Comptroller General of India operates under the provisions of Article 148 of the Indian Constitution.

Additional Information

• Comptroller and Auditor General of India (CAG):
• The CAG is an independent authority established under Article 148 of the Constitution of India.
• The primary function of the CAG is to audit all receipts and expenditures of the Government of India and the state governments, including those of autonomous bodies and corporations.
• The CAG reports are submitted to the President or Governors, who then table them in Parliament or state legislatures.
• The CAG plays a key role in ensuring transparency and accountability in the financial administration of the government.
• Roles and Responsibilities of the Comptroller General of India:
• Overseeing the financial administration of India at the highest level.
• Ensuring that public funds are used effectively and for the intended purposes.
• Promoting fiscal discipline within government departments and agencies.
• Auditing government expenditures to identify inefficiencies, corruption, or misuse of funds.
• Appointment of Comptroller General:
• The Comptroller General is appointed by the President of India.
• The term of office is six years or until the age of 65, whichever is earlier.
• The independence of the office is ensured by providing security of tenure and prohibiting the holder from subsequent appointments under the government.
• Significance of the Role:
• The Comptroller General ensures the integrity and transparency of public financial management.
• It plays a vital role in maintaining the trust of the public in the government's financial administration.
• The audits conducted by the Comptroller General are essential for identifying policy gaps and recommending improvements.

Let's denote the floors from 1 (lowermost) to 6 (topmost).

O lives on floor numbered 4.

 

Only two people live between O and P.

Since O is on floor 4, P can be on floor 1 (two people between O and P: floors 3 and 2) or floor 7 (which doesn't exist).

So, P must be on floor 1.

 

Only M lives between O and N.

Y lives immediately below O.

O is on floor 4, so Y lives on floor 3.

Since O is on floor 4, M must be on floor 5, and N must be on floor 6.

 

The only remaining person is Z, and the only remaining floor is 2.

So, Z lives on floor 2.

 

Based on our deductions, Z lives on floor numbered 2.

Hence, the correct answer is "Option 4".