Given:

The number is 257461398.

Arranging the digits of the number 257461398 in ascending order from left to right:

The new number formed is 123456789.

The second digit from the left is 2.

The third digit from the right is 7.

The sum of these two digits is 2 + 7 = 9.

Hence, the correct answer is "Option 3".

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

Only L sits to the left of S.

Only four people sit between L and N.

Only M sits between A and B, and A is not an immediate neighbour of N.

Thus, T sits at the extreme right of the line.

Hence, the correct answer is "Option 2".

The correct answer is Hiuen Tsang.

Key Points

• Hiuen Tsang (Xuanzang) was a Chinese Buddhist monk, scholar, and traveler who visited India during King Harsha's reign (606–647 CE).
• He arrived in India around 631 CE and spent over 15 years studying Indian culture, religion, and philosophy.
• Hiuen Tsang documented his travels in the renowned text "Si-Yu-Ki" (Records of the Western Regions), which offers valuable insights into Indian society during Harsha's era.
• He visited Harsha's court at Kannauj and was warmly received by the king, who organized debates and discussions on Buddhist philosophy.
• Hiuen Tsang's accounts provide detailed descriptions of cities, universities like Nalanda, political administration, and the socio-economic conditions in India during the 7^th century.

Additional Information

• Fa-Hien
• Fa-Hien was another Chinese traveler who visited India earlier (399–414 CE) during the Gupta period.
• He primarily focused on Buddhist texts and monastic practices and documented his travels in "A Record of Buddhist Kingdoms."
• I-Tsing
• I-Tsing was a Chinese Buddhist monk and traveler who visited India in the 7^th century, primarily to study Buddhism at Nalanda University.
• He wrote extensively about Buddhist practices and translated several Indian texts into Chinese.
• King Harsha
• Harsha was a ruler of northern India known for his patronage of Buddhism and other religions.
• Under his rule, Kannauj became a center of learning and culture.
• Nalanda University
• An ancient center of learning located in Bihar, India, which attracted scholars like Hiuen Tsang and I-Tsing.
• It was a hub for Buddhist studies, offering extensive libraries and accommodations for international students.

Shortcut Trick

Sum of exterior angles of any polygon is always 360°.

Sum of interior angles = 360° + 400% of 360° = 5 × 360° = 1800°.

For a regular polygon, the ratio of each interior angle to each exterior angle is the same as the ratio of their sums.

Ratio (Interior : Exterior) = 1800 : 360 = 5 : 1.

Since Interior + Exterior = 180°, then 6 units = 180° ⇒ 1 unit = 30°.

Each interior angle x = 5 × 30° = 150°.

∴ The correct answer is 150°.

Alternate Method

Given:

Sum of exterior angles = 360°

Sum of interior angles = 360° + (400/100) × 360° = 1800°

Formula Used:

Sum of interior angles = (n − 2) × 180°

Each interior angle of a regular polygon = (Sum of interior angles) ÷ n

A B C D x° 30° Interior Angle Exterior Angle

Given:

$\dfrac{1}{20}$ is what percentage of $\dfrac{1}{30}$?

Formula used:

Percentage = $\dfrac{\text{Part}}{\text{Whole}} \times 100$

Calculation:

⇒ Percentage = $\dfrac{\dfrac{1}{20}}{\dfrac{1}{30}} \times 100$

⇒ Percentage = $\dfrac{30}{20} \times 100$

⇒ Percentage = 150%

∴ The correct answer is option (4).

The pattern followed here is.

Thus, the missing term in the series is DH71.

Hence, the correct answer is "Option 2."

The correct answer is option 3,The Indian Air Force contingent in Exercise INIOCHOS-25 included Su-30 MKI fighters, IL-78 aerial refuelers, and C-17 transport aircraft.

Key Points

• Exercise INIOCHOS-25 is an annual multi-national air combat exercise hosted by Greece.
• The Indian Air Force participated in the exercise with a diverse contingent including Su-30 MKI fighters, IL-78 aerial refuelers, and C-17 transport aircraft.
• The Su-30 MKI is a twin-engine, multirole fighter aircraft designed for air superiority and ground attack missions.
• The IL-78 aerial refueler enhances the operational range of combat aircraft by enabling mid-air refueling.
• The C-17 Globemaster III is a heavy-lift transport aircraft capable of rapid strategic airlift of troops and cargo.

Additional Information

• Su-30 MKI Fighter Aircraft
• Developed by Russia's Sukhoi and customized by Hindustan Aeronautics Limited (HAL) for the Indian Air Force.
• Equipped with advanced avionics, long-range missiles, and precision-guided munitions.
• It is capable of air-to-air and air-to-ground combat missions.
• IL-78 Aerial Refueler
• The IL-78 is a Soviet-origin aerial refueling aircraft operated by the Indian Air Force.
• It significantly increases the operational reach of combat aircraft during missions.
• India has customized the IL-78 with refueling pods to meet its operational requirements.
• C-17 Globemaster III
• A strategic transport aircraft developed by Boeing, widely used for military logistics.
• It can carry heavy payloads, such as armored vehicles, troops, and humanitarian supplies.
• The Indian Air Force operates C-17s for rapid deployment and disaster relief missions.
• Exercise INIOCHOS
• Organized by the Hellenic Air Force, it is one of Europe’s premier air combat exercises.
• It involves participants from multiple countries, including NATO and non-NATO members.
• The exercise focuses on enhancing interoperability and combat readiness in realistic operational scenarios.

The correct answer is Zamindari.

Key Points

• The Zamindari system was introduced by the British East India Company in 1793 through the Permanent Settlement Act in parts of Bengal, Bihar, and Odisha.
• Under this system, Zamindars (landlords) were made the owners of the land and were tasked to collect a fixed revenue from the peasants.
• The Zamindars had to pay a fixed amount of revenue to the British government, irrespective of the actual agricultural output or crop yield.
• Failure to pay the fixed revenue would result in the confiscation of the Zamindar's land by the British authorities.
• This system was highly exploitative, as Zamindars often extracted exorbitant rents from the farmers, leading to widespread poverty and distress among the peasantry.

Additional Information

• Permanent Settlement Act (1793):
• Introduced by Lord Cornwallis, it aimed to create a loyal class of landlords who would support British rule.
• Zamindars were recognized as the hereditary owners of the land, with the right to collect rent from peasants.
• The land revenue was fixed permanently, meaning it would not be increased in the future.
• Ryotwari System:
• Introduced in Madras and Bombay Presidencies by Thomas Munro and Alexander Read.
• Under this system, peasants (ryots) were recognized as the landowners and were directly responsible for paying land revenue to the government.
• Mahalwari System:
• Implemented in parts of North-Western Provinces, Punjab, and Central India.
• Revenue settlement was made collectively with a village or group of villages (mahal).
• Exploitation Under Zamindari:
• The fixed revenue often exceeded the peasant's capacity to pay, especially during famines or crop failures.
• The system resulted in the marginalization of peasants and the enrichment of Zamindars.

Shortcut Trick

Ratio of number of boys = 14 : 4 = 7 : 2.

Assume base average = 38 kg.

Deviation of 14 boys = 40.25 − 38 = +2.25 kg.

Total deviation = 14 × 2.25 = 31.5 kg.

Average increase = 31.5 ÷ 18 = 1.75 kg.

Final Average = 38 + 1.75 = 39.75 kg.

∴ The correct answer is 39.75 kg.

Alternate Method

Given:

Average weight of first 14 boys = 40.25 kg

Average weight of remaining 4 boys = 38 kg

Formula Used:

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

Calculations:

⇒ Total weight of 14 boys = 14 × 40.25 = 563.5 kg

⇒ Total weight of 4 boys = 4 × 38 = 152 kg

⇒ Total number of boys = 14 + 4 = 18 boys

⇒ Total weight of class = 563.5 + 152 = 715.5 kg

⇒ Required Average weight = 715.5 ÷ 18

⇒ Average weight = 39.75 kg

∴ The correct answer is 39.75 kg.

Additional Information

Weighted Average Formula

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

Properties of Average

If every observation is increased by a constant k, the new average also increases by k. The average always lies between the minimum and maximum values of the data set.

Deviation Concept

Net deviation about the average is always zero. This principle is used to solve mixture and average problems faster by assuming a middle value as the mean.

Shortcut Trick

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

∴ ∠STR = (∠P + ∠Q) ÷ 2 ⇒ 8° = (∠P + ∠Q) ÷ 2 ⇒ ∠P + ∠Q = 16°

Given ratio of ∠P : ∠Q = 7 : 9. Sum of ratio parts = 7 + 9 = 16 units.

Since 16 units = 16°, then 1 unit = 1°.

Difference between ∠Q and ∠P = 9 − 7 = 2 units = 2°.

∴ The correct answer is 2°.

Alternate Method

Given:

In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at T.

∠STR = 8°

Ratio of ∠P : ∠Q = 7 : 9

Formula Used:

Sum of all interior angles of a quadrilateral = 360°

Sum of angles in a triangle = 180°

Calculations:

In ▵STR:

⇒ ∠STR + ∠TSR + ∠TRS = 180°

Since ST and RT are the bisectors of ∠S and ∠R respectively:

⇒ ∠TSR = ∠S ÷ 2

⇒ ∠TRS = ∠R ÷ 2

Substituting these values in the triangle angle sum equation:

⇒ 8° + (∠S ÷ 2) + (∠R ÷ 2) = 180°

⇒ (∠S + ∠R) ÷ 2 = 180° − 8°

⇒ (∠S + ∠R) ÷ 2 = 172°

⇒ ∠S + ∠R = 344°

In quadrilateral PQRS, the sum of all interior angles is 360°:

⇒ ∠P + ∠Q + ∠R + ∠S = 360°

⇒ ∠P + ∠Q + 344° = 360°

⇒ ∠P + ∠Q = 360° − 344°

⇒ ∠P + ∠Q = 16°

Given that the ratio of ∠P to ∠Q is 7 : 9, let ∠P = 7x and ∠Q = 9x:

⇒ 7x + 9x = 16°

⇒ 16x = 16°

⇒ x = 1°

Therefore, the measures of the angles are:

⇒ ∠P = 7 × 1° = 7°

⇒ ∠Q = 9 × 1° = 9°

The difference between the measures of ∠Q and ∠P is:

⇒ ∠Q − ∠P = 9° − 7° = 2°

Option Analysis:

• Option (1) 0.5°: Incorrect. If the difference were 0.5°, then 2x = 0.5° ⇒ x = 0.25°, which would mean ∠P + ∠Q = 16 × 0.25° = 4°, contradicting the given ∠STR = 8°.

• Option (2) 4°: Incorrect. If the difference were 4°, then 2x = 4° ⇒ x = 2°, which would mean ∠P + ∠Q = 16 × 2° = 32°, contradicting the given ∠STR = 8°.

• Option (3) 2°: Correct. This value perfectly satisfies the angle sum property and the given angle bisector relation.

• Option (4) 7°: Incorrect. If the difference were 7°, then 2x = 7° ⇒ x = 3.5°, which would mean ∠P + ∠Q = 16 × 3.5° = 56°, contradicting the given ∠STR = 8°.

∴ The correct answer is 2°.

Additional Information

Angle Bisector Theorem in Quadrilaterals

The angle formed by the bisectors of two adjacent angles of a quadrilateral is equal to half the sum of the remaining two angles: ∠STR = (∠P + ∠Q) ÷ 2.

Sum of Interior Angles of a Polygon

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

Opposite Angle Bisectors

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

The correct answer is 56 seats, JMM-led alliance INDIA.

Key Points

• The JMM-led alliance INDIA secured a total of 56 seats in the 2024 Jharkhand Assembly elections, ensuring a majority in the 81-member Assembly.
• The alliance was composed of the Jharkhand Mukti Morcha (JMM), Indian National Congress (INC), and Rashtriya Janata Dal (RJD), among others.
• The JMM, under the leadership of Chief Minister Hemant Soren, played a pivotal role in consolidating votes from tribal and rural regions of the state.
• The alliance's stronghold in areas with significant tribal populations and its welfare-focused initiatives contributed to its decisive victory.
• This election outcome reinforced the INDIA alliance's position as a significant opposition bloc in the context of Indian politics.

Additional Information

• Jharkhand Assembly Elections:
• The Jharkhand Legislative Assembly has 81 seats, and a party or coalition needs 41 seats to form a majority government.
• The state has a significant tribal population, which plays a crucial role in determining electoral outcomes.
• JMM-led INDIA Alliance:
• The INDIA alliance is a coalition of opposition parties at the national level, focusing on challenging the BJP-led NDA in various states.
• JMM's leadership in this alliance underscored its influence in Jharkhand politics.
• 2024 Political Landscape:
• The 2024 elections were seen as a litmus test for the INDIA alliance's strength against the BJP.
• Regional alliances like the one in Jharkhand demonstrated the importance of localized strategies in national politics.
• Voter Turnout:
• Jharkhand witnessed a voter turnout of over 70%, showcasing the citizens' active participation in the democratic process.
• Tribal and rural voters formed a significant portion of the electorate.

Given:

2 is added to each odd digit and 1 is subtracted from each even digit in the number 1374526.

The new number formed is 3593715.

The third digit from the left is 9.

The third digit from the right is 7.

The sum of these two digits is 9 + 7 = 16.

Hence, the correct answer is "Option 4".

Shortcut Trick

To find the value of (a − b) / (a + b)² based on the given options, we first find the squares.

(a − b)² = (a² + b²) − 2ab = 179 − 2(14) = 151 ⇒ (a − b) = √151.

(a + b)² = (a² + b²) + 2ab = 179 + 2(14) = 179 + 28 = 207.

Combining these to match the required format: (a − b) / 207 = √151 / 207.

∴ The correct answer is √151/207.

Alternate Method

Given:

a² + b² = 179

ab = 14

Formula Used:

(a − b)² = a² + b² − 2ab

(a + b)² = a² + b² + 2ab

Step-by-step Calculation:

⇒ (a − b)² = 179 − 2 × 14

⇒ (a − b)² = 179 − 28 = 151

⇒ a − b = √151

⇒ (a + b)² = 179 + 2 × 14

⇒ (a + b)² = 179 + 28 = 207

⇒ Using the numerator (a − b) and denominator (a + b)² to match the target value:

⇒ Result = √151 / 207

∴ The correct answer is √151/207.

Additional Information

Algebraic Identities

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

Relationship between Identities

The relationship between the sum and difference squares is given by (a + b)² − (a − b)² = 4ab.

Square Root Properties

For any positive number n, √n is the value which when multiplied by itself gives n. If n is not a perfect square, it is kept in surd form.

Shortcut Trick

A number is divisible by 12 if it is divisible by both 3 and 4.

Divisibility by 4: Last two digits must be divisible by 4 (Eliminates option 4).

Divisibility by 3: Sum of digits must be divisible by 3.

For 2184: 2 + 1 + 8 + 4 = 15 (Divisible by 3).

∴ The correct answer is 2184.

Alternate Method

Given: Numbers (1) 2184, (2) 2800, (3) 1264, (4) 2349.

Formula: Divisibility by 12 ⇒ Divisibility by co-prime factors 3 and 4.

⇒ Checking 2184: Last two digits are 84. 84 ÷ 4 = 21 (Divisible by 4).

⇒ Sum of digits of 2184 = 2 + 1 + 8 + 4 = 15. 15 ÷ 3 = 5 (Divisible by 3).

⇒ Checking 2800: Sum = 2 + 8 + 0 + 0 = 10 (Not divisible by 3).

⇒ Checking 1264: Sum = 1 + 2 + 6 + 4 = 13 (Not divisible by 3).

⇒ Checking 2349: Last digit is odd (Not divisible by 4).

∴ The correct answer is 2184.

Additional Information

Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is a multiple of 3.

Divisibility Rule of 4

A number is divisible by 4 if the last two digits are divisible by 4 or are double zeros (00).

Composite Divisibility

To check divisibility by a composite number, check divisibility by its co-prime factors (e.g., 6 = 2 × 3, 15 = 3 × 5).

Given:

4 6 ÷ % 8

Rule No. (1): This condition does not apply because the first element (4) and the last element (8) are numbers, not symbols.

Rule No. (2): This condition does not apply because the third element (÷) is a symbol, not a prime number.

Rule No. (3): This condition applies because the fifth element (8) is a multiple of 4. So, the fifth element will be coded as β.

Based on the applicable rule (3), the fifth element will be coded as β.

The code for 4 is V.

The code for 6 is H.

The code for ÷ is E.

The code for % is O.

The code for 8 is Z.

But, due to rule (3), 8 will be coded as β.

Thus, '4 6 ÷ % 8' is coded as → V H E O β.

Hence, the correct answer is "Option 4".$

Shortcut Trick

Speed of Car = 1032 ÷ 8 = 129 kmph.

Speed of Train = 2 × 129 = 258 kmph.

Speed of Bike = 1/3 × 258 = 86 kmph.

Distance by Bike = 86 × 17 = 1462 km.

∴ The correct answer is 1462 km.

Alternate Method

Given:

Car Distance = 1032 km, Car Time = 8 hours.

Formula Used:

Speed = Distance ÷ Time

Distance = Speed × Time

Calculations:

⇒ Speed of Car = 1032 ÷ 8 = 129 kmph

⇒ Speed of Train = 2 × 129 = 258 kmph

⇒ Speed of Bike = 258 ÷ 3 = 86 kmph

⇒ Distance covered by Bike in 17 hours = 86 × 17

⇒ Distance = 1462 km

∴ The correct answer is 1462 km.

Additional Information

Conversion of Speed Units

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

Average Speed

For two equal distances covered at speeds x and y, Average Speed = (2 × x × y) ÷ (x + y).

Relative Speed

In the same direction, subtract speeds (u − v). In the opposite direction, add speeds (u + v).

Given:

• Total students in the row = 37
• Vishesh's position = 13^th from the right end.
• Namrata's position = 10^th to the left of Vishesh.

Vishesh's position from the left end.

Using the formula: Rank from Left = Total students - Rank from Right + 1

Vishesh's position from the left = 37 - 13 + 1

= 24 + 1 = 25^th from the left.

Namrata is 10^th to the left of Vishesh, so her position from the left end will be 10 less than Vishesh's position from the left.

Namrata's position from the left = Vishesh's position from left - 10

= 25 - 10 = 15^th

Thus, Namrata's position from the left end is 15^th.

Hence, the correct answer is "Option 1".

The correct answer is Open the folder and right-click New Text Document.

Key Points

• The method to create a new text file in Windows involves navigating to the specific folder where the file is to be created.
• Once inside the folder, right-click on an empty space to open the context menu.
• From the context menu, hover over the "New" option, which displays a list of file types you can create.
• Select "Text Document" from the list, and a new text file will appear in the folder.
• You can then rename the text file and start editing it by opening it in a text editor (e.g., Notepad).

Additional Information

• Context Menu: The right-click menu in Windows, also known as the context menu, provides various options based on the location or item you right-click on.
• File Types in "New" Option: The "New" option in the context menu allows users to create different file types such as Word documents, Excel sheets, PowerPoint presentations, and more, depending on installed software.
• Text Editor: A text file (.txt) can be opened and edited using basic text editors like Notepad (default in Windows) or advanced ones like Notepad++, Sublime Text, or Visual Studio Code.
• Keyboard Shortcut (Optional): Some users prefer using the keyboard shortcut "Shift + F10" to open the context menu as an alternative to right-clicking.
• File Naming: After creating the text file, it is important to name it appropriately to ensure easy identification and organization of files within the folder.

The correct answer is option 1,

Key Points

• φ X174 phage is a bacteriophage with one of the smallest known DNA lengths, approximately 5,386 nucleotides.
• It is a single-stranded DNA virus belonging to the Microviridae family, primarily infecting Escherichia coli.
• The genome of φ X174 phage is circular and highly compact, encoding only 11 genes.
• Its small genome has made it a model organism for studying viral replication and genetics.
• The discovery of φ X174 phage contributed to advancements in molecular biology, including the first complete sequencing of a DNA genome by Frederick Sanger in 1977.

Additional Information

• Bacteriophage A: A larger bacteriophage compared to φ X174, with a genome size typically ranging between 40,000–50,000 base pairs.
• Human haploid cell: Contains approximately 3 billion base pairs (3,000,000,000 bp) of DNA, representing one set of chromosomes.
• Escherichia coli: A bacterial genome comprising approximately 4.6 million base pairs (4,600,000 bp), widely studied in genetics and microbiology.
• DNA length comparison: DNA length varies significantly across organisms, reflecting differences in genetic complexity and biological function.
• DNA sequencing: The study of genome sizes has been pivotal in understanding evolutionary relationships and gene functionality across different species.

Given:

 9 8 # @ 4

Rule No. (i): This condition does not apply because the last element (4) is an even number, not an odd number.

Rule No. (ii): This condition applies because the first element (9) is a perfect square and the last element (4) is also a perfect square. So, their codes will be interchanged.

Rule No. (iii): This condition does not apply because the first element (9) is a number, not a symbol.

Based on the applicable rule (ii), the 1^st and last elements' codes are interchanged.

The code for 9 is L.

The code for 8 is Y.

The code for # is F.

The code for @ is J.

The code for 4 is K.

So, 9 will be coded as K (the original code for 4).

And 4 will be coded as L (the original code for 9).

Thus, '9 8 # @ 4' is coded as → K Y F J L.

Hence, the correct answer is "Option 4".$

The logic followed here is,

For, BACK-ABCK - ВСКА

ΜΙΝΟ - ΙΜΝΟ - ΜΝΟΙ

Similarly, 

Option 2) TEAR - ETAR - TARE

Hence, the correct answer is "Option 2".

Shortcut Trick

Let V be Vashnavi age and S be Sooraj age.

From given: 5V − 7S = 18 and 5V − 8S = 17.

Subtracting the equations: (5V − 7S) − (5V − 8S) = 18 − 17 ⇒ S = 1.

Substitute S = 1 in 5V − 8S = 17 ⇒ 5V − 8 = 17 ⇒ 5V = 25 ⇒ V = 5.

Sum of ages = 5 + 1 = 6 years.

∴ The correct answer is 6 years.

Alternate Method

Given:

5 × Vashnavi age = 7 × Sooraj age + 18

8 × Sooraj age = 5 × Vashnavi age − 17

Calculations:

⇒ Let Vashnavi age be V and Sooraj age be S.

⇒ 5V = 7S + 18 --- (i)

⇒ 8S = 5V − 17 --- (ii)

⇒ Substitute 5V from (i) into (ii):

⇒ 8S = (7S + 18) − 17

⇒ 8S = 7S + 1

⇒ S = 1 year

⇒ Put S = 1 in (i): 5V = 7(1) + 18

⇒ 5V = 25 ⇒ V = 5 years

⇒ Sum = V + S = 5 + 1 = 6 years.

∴ The correct answer is 6 years.

Additional Information

Linear Equations in Two Variables

Problems involving ages of two people usually result in a system of two linear equations which can be solved by substitution or elimination.

Age Difference Property

The difference between the ages of two people remains constant regardless of the number of years passed or preceding.

Ratio Method

If the ratio of ages is given at different time intervals, the cross-multiplication method is the fastest way to find individual ages.

Shortcut Trick

Required number − 7 = LCM of 16, 20, 10, 27

LCM(16, 20, 10, 27) = 16 × 5 × 27 = 2160

Required number = 2160 + 7 = 2167

∴ The correct answer is 2167.

Alternate Method

Given: Divisors are 16, 20, 10, 27. The number is diminished by 7 to be divisible.

Formula Used: Required Number = LCM(Divisors) + Remainder/Diminished value

Step 1: Find prime factors of each number:

⇒ 16 = 2⁴

⇒ 20 = 2² × 5

⇒ 10 = 2 × 5

⇒ 27 = 3³

Step 2: Calculate LCM by taking highest powers of all prime factors:

⇒ LCM = 2⁴ × 3³ × 5

⇒ LCM = 16 × 27 × 5

⇒ LCM = 432 × 5 = 2160

Step 3: Add the diminished value to the LCM:

⇒ Required Number = 2160 + 7 = 2167

∴ The correct answer is 2167.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is perfectly divisible by a given set of numbers.

Diminished vs Increased Logic

If a number is diminished by 'x', add 'x' to the LCM. If it is increased by 'x', subtract 'x' from the LCM.

Divisibility by 27

A number is divisible by 27 if the sum of its digits (in a specific weighted manner) or the number itself is a multiple of 27.

Shortcut Trick

Let a = 0.54 and b = 0.46. Observe that a + b = 0.54 + 0.46 = 1.

Using the identity a³ + b³ = (a + b)(a² − ab + b²), where the sum factor is 1.

The value is simply (0.54² − 0.54 × 0.46 + 0.46²) = 0.2916 − 0.2484 + 0.2116.

This simplifies to 0.0432 + 0.2116 = 0.2548.

∴ The correct answer is 0.2548.

Alternate Method

Given: The expression to evaluate is (0.54)³ + (0.46)³.

Step 1: Calculate the cube of the first term.

⇒ 0.54 × 0.54 = 0.2916

⇒ 0.2916 × 0.54 = 0.157464

Step 2: Calculate the cube of the second term.

⇒ 0.46 × 0.46 = 0.2116

⇒ 0.2116 × 0.46 = 0.097336

Step 3: Find the sum of the two results.

⇒ Value = 0.157464 + 0.097336

⇒ Value = 0.2548

∴ The correct answer is 0.2548.

Additional Information

Algebraic Identity for Sum of Cubes

The formula is a³ + b³ = (a + b)(a² − ab + b²). This is very useful when a + b results in a simple integer like 1 or 10.

Algebraic Identity for Difference of Cubes

The formula is a³ − b³ = (a − b)(a² + ab + b²), which is the counterpart for subtraction of cubic terms.

BODMAS in Simplification

Always prioritize Exponents (Powers/Orders) before performing addition or subtraction in expressions like xⁿ + yⁿ.

The correct answer is 1606.

Key Points

• The Dutch East India Company (VOC) established its factory at Petapuli (modern-day Pulicat) on the North Coromandel Coast in the year 1606.
• Petapuli served as the first Dutch settlement in India and became the headquarters for their trade activities in the region.
• The Dutch East India Company was formed in 1602 and was one of the first multinational corporations involved in global trade.
• The factory at Petapuli was strategically located to facilitate trade in spices, textiles, and other goods from South India.
• This marked the beginning of Dutch dominance in the trade networks of the Coromandel Coast during the 17^th century.

Additional Information

• Coromandel Coast:
• The Coromandel Coast is a stretch of southeastern India along the Bay of Bengal.
• This region was historically significant for its thriving trade in spices, textiles, and other commodities.
• Dutch East India Company (VOC):
• Founded in 1602, the VOC was a chartered company established by the Dutch government.
• It monopolized Dutch trade in the Indian Ocean and played a dominant role in global commerce during the 17^th century.
• Trade in Pulicat:
• Pulicat became an important port for the Dutch, where they traded textiles, spices, and other goods.
• The Dutch built a fort, known as Fort Geldria, to strengthen their control over the region.
• Decline of Dutch Power in India:
• By the 18^th century, the Dutch influence in India declined due to competition from the British and French East India Companies.
• The British eventually dominated trade and established colonial rule over India.

The correct answer is Article 11.

Key Points

• Article 11 of the Indian Constitution empowers the Parliament to regulate the right of citizenship through legislation.
• It allows the Parliament to make laws concerning the acquisition, termination, and other matters related to citizenship.
• This article is part of Part II (Articles 5 to 11) of the Constitution, which deals with Citizenship.
• Using the powers under Article 11, the Parliament has enacted laws like the Citizenship Act of 1955 and its subsequent amendments.
• While Articles 5 to 10 determine the citizenship status of individuals at the commencement of the Constitution, Article 11 enables future legislative actions on citizenship matters.

Additional Information

• Part II of the Constitution: It deals with the provisions related to citizenship from Articles 5 to 11.
• Citizenship Act of 1955: This law, enacted under Article 11, specifies the methods for acquiring, losing, and determining Indian citizenship.
• Modes of Acquiring Citizenship: The Citizenship Act provides five modes: by birth, descent, registration, naturalization, and incorporation of territory.
• Amendments to Citizenship Act: Significant amendments include the Citizenship (Amendment) Act, 2019, which introduced provisions for granting citizenship to certain persecuted minorities from neighboring countries.
• Difference Between Articles 5-10 and Article 11: Articles 5-10 primarily address citizenship at the time of the Constitution's commencement, while Article 11 grants the Parliament the power to legislate on citizenship matters post-constitution.

BODMAS Rule:

According to the question, the letters are interchanged as follows:

Now, given the equation: 29 S 9 P 3 R 13 P 4 S 55 = ?

After interchanging the specified letters, the new equation is:

29 + 9 × 3 − 13 × 4 + 55 = ?

Perform operations according to BODMAS:

⇒ 29 + 9 × 3 − 13 × 4 + 55

⇒ 29 + 27 − 52 + 55

⇒ 56 − 52 + 55

⇒ 4 + 55 = 59

Hence, the correct answer is "Option 4".

Given:

The simplified value of 74 - 3 × (21 + 15) + 36

Calculation:

74 - 3 × (21 + 15) + 36

⇒ 74 - 3 × (36) + 36

⇒ 74 - 108 + 36

⇒ (74 + 36) - 108

⇒ 110 - 108

⇒ 2

∴ The correct answer is option (1).

The logic followed here is:

 

Thus, the missing term in the series is 86.

Hence, the correct answer is "Option 1";

The correct answer is Her retirement from international hockey.

Key Points

• Vandana Katariya, a renowned Indian women's hockey player, announced her retirement from international hockey in April 2025.
• She holds the record for the most international caps in Indian women’s hockey history, with over 250 appearances for the national team.
• Katariya is celebrated for her historic performance at the Tokyo 2020 Olympics, where she became the first Indian woman to score a hat-trick in Olympic hockey.
• Her decision to retire marks the end of a remarkable career spanning over a decade, during which she played a pivotal role in elevating Indian women's hockey on the global stage.
• She cited her desire to focus on mentoring young talent and contributing to the development of grassroots hockey in India as reasons for her decision.

Additional Information

• Vandana Katariya’s Legacy:
• She debuted for the Indian women’s hockey team in 2009 and became one of the most consistent performers.
• She was part of the squad that won the 2016 Asian Champions Trophy and qualified for back-to-back Olympic Games in 2016 and 2020.
• Her contributions were instrumental in India’s fourth-place finish at the Tokyo 2020 Olympics.
• Women's Hockey in India:
• The Indian women’s hockey team has shown significant progress in recent years, achieving historic milestones like reaching the semi-finals in the Tokyo Olympics.
• The rise of players like Vandana Katariya has inspired a new generation of athletes to pursue hockey professionally.
• Grassroots Development:
• Vandana has expressed her intention to focus on grassroots hockey development by training young players in her home state of Uttarakhand.
• Such initiatives aim to strengthen the talent pipeline for Indian women’s hockey.
• Achievements and Awards:
• Vandana was awarded the Arjuna Award in 2016 for her contributions to Indian hockey.
• She remains a role model for aspiring athletes, particularly young women from rural backgrounds.

The correct answer is option 1,Key Points:

• The Ganga Basin is the most populous river basin in India, supporting a significant portion of the country's population.
• The basin covers approximately 1 million square kilometers and spans across 11 states, including Uttar Pradesh, Bihar, West Bengal, and Uttarakhand.
• It is home to major cities such as Delhi, Kanpur, Lucknow, Allahabad, Varanasi, Patna, and Kolkata.
• The fertile alluvial plains of the Ganga Basin make it an agricultural hub, contributing to high population density.
• The Ganga River provides water for irrigation, drinking, and industrial purposes, further boosting population concentration in the region.

Additional Information:

• River Basin: A geographical area drained by a river and its tributaries, forming a crucial unit for water management and planning.
• Alluvial Plains: Fertile flatlands formed by the deposition of sediment from rivers, ideal for agriculture and human settlement.
• Population Density: The number of people living per unit area; the Ganga Basin has one of the highest population densities in the world.
• Urbanization: The Ganga Basin hosts several metropolitan cities, contributing to economic activities and increasing population concentration.
• Environmental Challenges: The Ganga Basin faces issues such as pollution, deforestation, and over-extraction of resources due to the high population and industrial activities.

Shortcut Trick

Convert the given equation to tan A: √2 ÷ sin A = 2 ÷ cos A

⇒ cos A ÷ sin A = 2 ÷ √2

⇒ cot A = √2 ⇒ tan A = 1/√2

Using sec²A = 1 + tan²A ⇒ sec A = √(1 + 1/2) = √(3/2)

⇒ tan A × sec A = (1/√2) × (√3/√2) = √3/2

∴ The correct answer is √3/2.

Alternate Method

Given: √2 cosec A = 2 sec A

Formula: cosec A = 1/sin A, sec A = 1/cos A, tan A = sin A/cos A

⇒ √2 / sin A = 2 / cos A

⇒ sin A / cos A = √2 / 2

⇒ tan A = 1 / √2

⇒ Let Perpendicular (P) = 1 and Base (B) = √2

⇒ Hypotenuse (H) = √(P² + B²) = √(1² + (√2)²) = √3

⇒ sec A = H / B = √3 / √2

⇒ tan A × sec A = (1 / √2) × (√3 / √2)

⇒ tan A × sec A = √3 / 2

∴ The correct answer is √3/2.

Additional Information

Trigonometric Identities

Fundamental relations: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Ratio Definitions

tan θ = P/B, sec θ = H/B, and cosec θ = H/P where P, B, H are parts of a right-angled triangle.

The given three-digit numbers are: 441, 317, 999, 155, 444.

Now,

The highest number is 999. Its third digit is 9.

The lowest number is 155. Its first digit is 1.

Perform the subtraction.

Subtract the third digit of the highest number 9 from the first digit of the lowest number 1.

1 - 9 = -8.

Hence, the correct answer is "Option 4".

The correct answer is option 4,

Key Points

• Print Preview in MS Excel 365 allows users to check how the spreadsheet will appear when printed, ensuring the layout, formatting, and page breaks are correctly aligned.
• Users can adjust settings such as margins, orientation, and scaling before finalizing the print.
• It helps in identifying issues like text cutoff, misaligned columns, or large blank spaces in the document.
• Print Preview is accessible through the File menu or by pressing Ctrl + F2 in most versions of Excel.
• The feature saves time and resources by preventing unnecessary printing errors or wastage.

Additional Information

• Page Layout Options:
• Users can adjust page margins, headers/footers, and scaling in the Page Layout tab.
• Orientation settings (portrait or landscape) can be managed for better presentation.
• Print Area:
• Excel allows users to define a specific print area, ensuring only selected cells are printed.
• This is useful when printing large datasets or reports.
• Page Break Preview:
• This feature shows where page breaks occur, enabling users to drag and adjust them as needed.
• It is accessible via the View tab.
• Scaling Options:
• Users can scale content to fit on one page or a set number of pages.
• It prevents columns or rows from spilling onto additional pages unnecessarily.
• Printer Settings:
• Excel provides printer-specific settings, such as paper size selection and print quality adjustments.
• Users can choose to print in color or grayscale depending on their printer’s capabilities.

The correct answer is Bhimbetka Caves.

Key Points

• The Bhimbetka Caves are a UNESCO World Heritage Site located in the Raisen district of Madhya Pradesh, India.
• The rock shelters of Bhimbetka contain paintings that date back to the Stone Age, specifically the Mesolithic period (c. 10,000 BCE).
• These paintings depict scenes from everyday life, including hunting, dancing, and communal activities, providing insights into the lives of early humans.
• The art includes representations of animals such as bison, tigers, and elephants, as well as human figures engaged in activities.
• The Bhimbetka Cave complex is one of the earliest examples of human interaction with the environment, showcasing continuity in artistic expression over thousands of years.

Additional Information

• Rock Art Terminology:
• Rock art refers to human-made markings placed on natural stone, typically in caves or open-air shelters.
• It includes petroglyphs (carvings) and pictographs (paintings).
• UNESCO World Heritage Status:
• Bhimbetka was declared a UNESCO World Heritage Site in 2003 due to its archaeological and cultural significance.
• The site is noted for its unique record of human settlement and evolution over different historical periods.
• Mesolithic Period:
• The Mesolithic period, also known as the Middle Stone Age, is characterized by the transition from hunting and gathering to agriculture.
• Rock art from this period is significant for its depiction of social and cultural development.
• Discovery of Bhimbetka:
• The caves were first discovered by Indian archaeologist V.S. Wakankar in 1957 while surveying the Narmada Valley.
• Over 750 rock shelters have been identified, with around 500 containing paintings.
• Comparative Sites:
• Other significant rock art sites in India include the Adamgarh Hills (Madhya Pradesh) and the Kupgal petroglyphs (Karnataka).
• Globally, comparable sites include the Lascaux Caves in France and the Altamira Cave in Spain.

The given three-digit numbers are: 941, 915, 741, 807, 776.

Now,

The highest number is 941. Its third digit is 1.

The lowest number is 741. Its first digit is 7.

Perform the addition.

Add the third digit of the highest number 1 to the first digit of the lowest number 7.

1 + 7 = 8.

Hence, the correct answer is "Option 2".

Given: F, G, H, J, K and L live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

1. Only three people live between K and G, where K lives below G.

• Case 1: G is on Floor 5, and K is on Floor 1.
• Case 2: G is on Floor 6, and K is on Floor 2.

2. H lives on an odd numbered floor and immediately above K.

In Case 1, K is on Floor 1, so H lives on Floor 2. Floor 2 is not an odd-numbered floor. So, Case 1 is eliminated.

In Case 2, K is on Floor 2, so H lives on Floor 3. Floor 3 is an odd-numbered floor. This case is valid.

So, the arrangement is:

3. J lives on one of the floors below F and on one of the floors above L.

From the final arrangement, the person who lives on floor numbered 4 is J.

Hence, the correct answer is "Option 4".

Shortcut Trick

Speed Ratio (Normal : New) = 4 : 1

Time Ratio (Normal : New) = 1 : 4 (Since Time ∝ 1/Speed for constant distance)

Difference in time units = 4 − 1 = 3 units

Given difference = 39 minutes ⇒ 1 unit = 39 ÷ 3 = 13 minutes

Normal Time (1 unit) = 13 minutes

∴ The correct answer is 13 minutes.

Alternate Method

Given:

Normal speed = S, New speed = S/4

Time difference (Δt) = 39 minutes

Formula Used:

Time = Distance ÷ Speed

Calculations:

⇒ Let normal time be T. Then new time = T + 39

⇒ Since Distance is constant, S₁ × T₁ = S₂ × T₂

⇒ S × T = (S/4) × (T + 39)

⇒ 4T = T + 39

⇒ 3T = 39

⇒ T = 13 minutes

∴ The correct answer is 13 minutes.

Additional Information

Inverse Proportion of Speed and Time

When the distance is constant, the time taken is inversely proportional to the speed (T ∝ 1/S). If speed becomes 1/n times, time becomes n times.

Late/Early Concept Formula

Distance = [ (S₁ × S₂) / |S₁ − S₂| ] × Difference in time. This is useful for finding the actual distance between two points.

Shortcut Trick

Assume a base temperature of 30°C.

Find the deviations from 30: (28−30), (30−30), (32−30), (31−30), (29−30) → −2, 0, +2, +1, −1.

Net deviation = (−2) + 0 + (+2) + (+1) + (−1) = 0.

Average = Base + (Net Deviation ÷ Total Days) = 30 + (0 ÷ 5) = 30°C.

∴ The correct answer is 30°C.

Alternate Method

Given: Recorded temperatures for 5 consecutive days are 28°C, 30°C, 32°C, 31°C, and 29°C.

Formula Used: Average = (Sum of all observations) ÷ (Number of observations)

⇒ Sum of temperatures = 28 + 30 + 32 + 31 + 29

⇒ Sum = 150°C

⇒ Number of days = 5

⇒ Average = 150 ÷ 5

⇒ Average = 30°C

∴ The correct answer is 30°C.

Additional Information

Arithmetic Mean Property

The algebraic sum of the deviations of a set of values from their arithmetic mean is always zero.

Effect of Change in Origin

If a constant value 'k' is added to or subtracted from every observation, the new average will also be increased or decreased by 'k'.

Weighted Average

When observations have different levels of importance, the average is calculated as Σwx ÷ Σw, where 'w' is the weight assigned to each value 'x'.

The correct answer is option 3,

Key Points

• The Nagaland Forest Management Project focuses on sustainable forest management practices, biodiversity conservation, and enhancing the livelihood of communities dependent on forests.
• The project is funded by the Japan International Cooperation Agency (JICA), emphasizing international collaboration in environmental conservation.
• It aims to restore degraded forests, improve forest productivity, and ensure equitable benefits for local communities.
• Key components include afforestation, promotion of agroforestry, and capacity building to support sustainable forest management.
• The project has demonstrated significant progress in forest management, earning it the prestigious SKOCH Award for excellence in December 2024.

Additional Information

• Forest Management: Forest management refers to practices aimed at maintaining and improving the health and sustainability of forest ecosystems.
• Biodiversity Conservation: Efforts to preserve the variety of life forms within ecosystems, including flora, fauna, and microorganisms.
• Agroforestry: A land management system that integrates trees and shrubs into agricultural landscapes for environmental and economic benefits.
• SKOCH Award: The SKOCH Award is a prestigious recognition given to projects and initiatives demonstrating excellence in governance, technology, and social impact.
• Japan International Cooperation Agency (JICA): JICA is a governmental agency that provides financial and technical assistance to support development projects worldwide, including environmental conservation initiatives.

The correct answer is option 1,"

The correct answer is Sudipta Sengupta.

Key Points

• Sudipta Sengupta is a renowned Indian geologist and author known for her pioneering contributions in the field of earth sciences.
• 'Breaking Rocks and Barrier' is a biographical account of Sudipta Sengupta's experiences and challenges as a woman geologist.
• The book highlights her journey of overcoming gender stereotypes in a male-dominated field.
• Sudipta Sengupta is also recognized for her work in structural geology and tectonics, having conducted extensive research in the Himalayas.
• Her contributions have paved the way for greater inclusion and recognition of women in the field of geology and academia.

Additional Information

• Structural Geology:
• Structural geology studies the three-dimensional distribution of rock units and their deformation.
• This field is crucial for understanding tectonic processes and the formation of mountain ranges.
• Sudipta Sengupta has contributed significantly to the study of Himalayan tectonics.
• Women in Geology:
• Sudipta Sengupta's achievements have inspired many women to pursue careers in geology and earth sciences.
• Gender inclusion in STEM fields remains a global challenge, with initiatives aimed at reducing the gender gap.
• Himalayan Tectonics:
• The Himalayas are a prime region for studying tectonic activity due to their dynamic geological evolution.
• Research in this area helps understand seismic risks and resource exploration.
• Indian Contributions to Earth Sciences:
• India has a rich history of geological research, including contributions to mineral exploration and tectonics.
• Pioneers like Sudipta Sengupta have strengthened India's position in global earth sciences.

"

Shortcut Trick

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

In this question, k = 9.

∴ x² + 1/x² = 9² − 2

⇒ 81 − 2 = 79

∴ The correct answer is 79.

Alternate Method

Given:

The value of x + 1/x = 9.

Formula Used:

We use the algebraic identity: (a + b)² = a² + b² + 2ab

Calculations:

Squaring both sides of the given equation:

⇒ (x + 1/x)² = 9²

⇒ x² + (1/x)² + 2 × x × (1/x) = 81

⇒ x² + 1/x² + 2 = 81

⇒ x² + 1/x² = 81 − 2

⇒ x² + 1/x² = 79

∴ The correct answer is 79.

Additional Information

Algebraic Identity for Cubes

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

Subtraction Identity

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

Higher Power (Power of 4)

To find x⁴ + 1/x⁴, take the result of x² + 1/x² (say m), then calculate m² − 2.

Shortcut Trick

Equate the percentages and fractions directly: 22% × First Number = 4/9 × Second Number.

22/100 × A = 4/9 × B ⇒ 11/50 × A = 4/9 × B.

Ratio A : B = (4 × 50) : (11 × 9) = 200 : 99.

∴ The correct answer is 200:99.

Alternate Method

Given: 22% of First Number (x) = 4/9 of Second Number (y).

Formula Used: Ratio x : y = (Value attached to y) : (Value attached to x) when equating products.

⇒ 22% × x = (4/9) × y

⇒ (22/100) × x = (4/9) × y

⇒ (11/50) × x = (4/9) × y

⇒ x/y = (4/9) ÷ (11/50)

⇒ x/y = (4/9) × (50/11)

⇒ x/y = 200/99

∴ The correct answer is 200:99.

Additional Information

Percentage to Fraction Conversion

To convert x% to a fraction, divide by 100. Example: 22% = 22/100 = 11/50.

Ratio and Proportion Property

If Ax = By, then the ratio x : y is B : A. This is used to solve equated quantities efficiently.

The correct answer is option 4,

Key Points

• INS Imphal visited Port Louis, Mauritius, in March 2025 to participate in the 57^th National Day celebrations of Mauritius.
• The visit of INS Imphal underlines the strong bilateral relations between India and Mauritius, particularly in the maritime domain.
• The ship's deployment was part of India's commitment to promoting maritime security and cooperation in the Indian Ocean Region.
• INS Imphal is an indigenously built stealth destroyer of the Indian Navy, equipped with advanced weaponry and sensors.
• Such visits enhance diplomatic ties and foster collaboration in defense, culture, and trade between both nations.

Additional Information

• INS Imphal:
• It is a Project 15B class stealth guided-missile destroyer commissioned by the Indian Navy.
• The ship is equipped with state-of-the-art sensors and weapons, including BrahMos missiles and indigenous systems.
• It is designed to operate in multi-threat environments and is capable of undertaking a variety of missions.
• India-Mauritius Relations:
• India and Mauritius share strong cultural, economic, and strategic ties, with Mauritius being a key partner in the Indian Ocean Region.
• India has been actively involved in supporting Mauritius in various sectors, including defense, infrastructure, and health.
• Bilateral naval exercises like the "SAMUDRA SHAKTI" enhance maritime cooperation between the two nations.
• Indian Ocean Region (IOR):
• The IOR is a strategically important region with significant trade routes and geopolitical influence.
• India plays a pivotal role in ensuring maritime security and stability in the region through collaborations and naval deployments.
• National Day Celebrations in Mauritius:
• The National Day of Mauritius is celebrated on March 12^th every year to mark its independence from British rule in 1968.
• The event is significant for showcasing the nation's achievements and fostering international partnerships.

Shortcut Trick Ratio of Selling Price (SP) of 35 books to Cost Price (CP) of 28 books is given as equal. 35 × SP = 28 × CP ⇒ SP ÷ CP = 28 ÷ 35 = 4 ÷ 5. Since SP < CP, there is a loss. Loss percentage = (CP − SP) ÷ CP × 100 = (5 − 4) ÷ 5 × 100 = 1 ÷ 5 × 100 = 20%. ∴ The correct answer is 20% loss.

Alternate Method Given: Selling Price of 35 books = Cost Price of 28 books. Formulas: Loss = CP − SP | Loss% = (Loss ÷ CP) × 100

⇒ Let the Cost Price (CP) of 1 book be 1 unit. ⇒ CP of 28 books = 28 units and CP of 35 books = 35 units. ⇒ According to the question, Selling Price (SP) of 35 books = 28 units. ⇒ Loss = CP of 35 books − SP of 35 books = 35 − 28 = 7 units. ⇒ Loss% = (7 ÷ 35) × 100 = (1 ÷ 5) × 100 = 20%. ∴ The correct answer is 20% loss.

Additional Information Loss and Gain Basic Concepts When SP > CP, it is a Gain. Gain% = (Gain ÷ CP) × 100. When CP > SP, it is a Loss. Inverse Relation of Articles If CP of 'x' articles = SP of 'y' articles, Profit/Loss% = ((x − y) ÷ y) × 100. Positive result means Profit, negative means Loss.

Shortcut Trick

Total surface area to be painted (Inside + Outside) = 2 × 2πr² = 4πr².

Radius (r) = 3.5 cm = 7/2 cm.

Total Area = 4 × (22/7) × (7/2) × (7/2) = 154 cm².

Cost = (154 ÷ 10) × 17 = 15.4 × 17 = ₹261.8.

∴ The correct answer is ₹261.8.

Alternate Method

Given:

Radius (r) = 3.5 cm

Rate of painting = ₹17 per 10 cm²

Formula Used:

Curved Surface Area (CSA) of hemisphere = 2πr²

Total painting area = Inside CSA + Outside CSA = 2πr² + 2πr² = 4πr²

Calculations:

⇒ Total Area = 4 × (22/7) × 3.5 × 3.5

⇒ Total Area = 4 × (22/7) × 12.25

⇒ Total Area = 154 cm²

⇒ Cost of painting 10 cm² = ₹17

⇒ Cost of painting 1 cm² = ₹1.7

⇒ Total Cost = 154 × 1.7

⇒ Total Cost = ₹261.8

∴ The correct answer is ₹261.8.

Additional Information

Surface Area of Sphere

Total surface area of a full sphere is 4πr².

Total Surface Area of Hemisphere

For a solid hemisphere, TSA = CSA + Area of base = 2πr² + πr² = 3πr².

Volume of Hemisphere

The volume of a hemisphere is (2/3)πr³.

The correct answer is Bal Gangadhar Tilak.

Key Points

• Bal Gangadhar Tilak, a prominent Indian freedom fighter, was imprisoned in Mandalay Jail, Burma, from 1908 to 1914.
• He was arrested on charges of sedition for his writings in the newspaper "Kesari", where he criticized British colonial policies.
• During his imprisonment, Tilak wrote his famous work, "Gita Rahasya", a commentary on the Bhagavad Gita.
• Mandalay Jail, located in present-day Myanmar, was used by the British to imprison Indian freedom fighters due to its isolation and harsh conditions.
• Tilak's imprisonment further galvanized the Indian independence movement, earning him the title "Lokmanya" (accepted by the people).

Additional Information

• Sedition under British Rule:
• Section 124A of the Indian Penal Code, introduced by the British in 1870, was used to suppress freedom fighters and curb dissent.
• Freedom fighters like Tilak, Mahatma Gandhi, and Bhagat Singh were charged with sedition for their anti-colonial activities.
• Kesari Newspaper:
• Founded by Tilak in 1881, "Kesari" was a Marathi newspaper advocating self-rule (Swaraj).
• Tilak's articles in Kesari were instrumental in spreading nationalist ideas among the masses.
• Gita Rahasya:
• While imprisoned in Mandalay Jail, Tilak penned "Gita Rahasya", emphasizing selfless action (Karma Yoga) as a path to liberation.
• The book remains a significant contribution to Indian philosophy and nationalist thought.
• Other Contributions of Tilak:
• Tilak was one of the first leaders to call for Swaraj (self-rule) as a birthright of Indians.
• He played a key role in popularizing Ganesh Chaturthi and Shivaji Jayanti as public festivals to unite people against colonial rule.

The correct answer is Kanvas.

Key Points

• The Kanvas replaced the Shunga Dynasty in Magadha around 73 BCE after the assassination of the last Shunga ruler, Devabhuti, by his minister Vasudeva Kanva.
• Vasudeva Kanva established the Kanva Dynasty, marking the end of Shunga rule and initiating a short-lived Kanva rule in Magadha.
• The Kanva Dynasty ruled for approximately 45 years, with four rulers: Vasudeva, Bhumimitra, Narayana, and Susharman.
• The Kanvas were eventually overthrown by the Satavahanas, who expanded their influence in the Deccan and northern India.
• The Kanva Dynasty is considered a transitional period in Indian history, marked by political instability and regional fragmentation.

Additional Information

• Shunga Dynasty:
• The Shungas ruled Magadha from approximately 185 BCE to 73 BCE, succeeding the Mauryan Empire.
• They were known for their patronage of art, including the construction of the Bharhut and Sanchi Stupas.
• The dynasty was marked by internal rebellions and external threats, leading to its eventual decline.
• Satavahana Dynasty:
• The Satavahanas succeeded the Kanva Dynasty and ruled large parts of central and southern India.
• They were known for their contributions to trade, art, and architecture, including the Amaravati Stupa.
• Their rule marked the beginning of significant cultural and economic exchanges in the Deccan region.
• Magadha:
• Magadha was one of the most powerful Mahajanapadas in ancient India, located in present-day Bihar.
• It was a center of political, cultural, and spiritual activity, home to the rise of Jainism and Buddhism.
• Several major dynasties, including the Mauryas, Shungas, Kanvas, and Guptas, ruled Magadha over time.
• Political Instability During Kanva Rule:
• The Kanva Dynasty faced challenges in maintaining control over Magadha due to its brief rule and external invasions.
• Their decline created a power vacuum, eventually filled by the expanding Satavahanas.

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

Only five people sit between M and L.

F sits to the immediate left of L.

Only one person sits between F and E.

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

Thus, N sits third from the left end of the row.

Hence, the correct answer is "Option 2".

The given three-digit numbers are: 107, 788, 634, 346, 488.

Now,

The highest number is 788. Its first digit is 7.

The lowest number is 107. Its third digit is 7.

Perform the addition.

Add the first digit of the highest number 7 to the third digit of the lowest number 7.

7 + 7 = 14.

Hence, the correct answer is "Option 3".

The correct answer is Bhumji.

Key Points

• The Chuar Rebellion (1767–1809) was a tribal uprising in the Jungle Mahals region of present-day West Bengal and Jharkhand.
• The rebellion was primarily led by the Bhumji tribal community, along with other tribal groups like the Santhals and Kurmis.
• The British East India Company’s exploitative revenue policies and increased taxes on forest produce triggered the rebellion.
• The Bhumji chiefs, particularly the leaders of the Midnapore and Manbhum regions, played a significant role in organizing the resistance.
• The rebellion was also marked by the participation of local zamindars and peasants who were discontented with colonial economic policies.

Additional Information

• Chuar Rebellion Context:
• The term 'Chuar' was used by the British to describe the tribal insurgents and forest dwellers of the region.
• The rebellion was fueled by colonial interference in traditional tribal ways of life and exploitation of natural resources.
• Key Leaders:
• Prominent leaders of the rebellion included Raghunath Mahato and Durjan Singh.
• They mobilized tribal warriors and peasants against British forces.
• Impact:
• The rebellion was suppressed by the British, but it highlighted the widespread resistance to colonial policies in tribal regions.
• It paved the way for subsequent tribal uprisings like the Santhal Rebellion (1855–56).
• Jungle Mahals:
• The Jungle Mahals region included parts of present-day Purulia, Bankura, and Midnapore districts in West Bengal.
• The area was rich in forests and inhabited by several tribal communities.

Given: 

Mr. C starts from Point D and drives 3 km towards the west.

He then takes a left turn, drives 11 km, turns left, and drives 9 km.

He then takes a right turn and drives 5 km, turns left drives 7 km.

He then takes a left turn, drives 16 km.

He takes a final left turn, drives 9 km, and stops at Point E.

He should drive 4 km towards the West in order to reach Point D again.

Hence, the correct answer is "Option 4".

The correct answer is Betla National Park.

Key Points

• Betla National Park is located in the Latehar district of Jharkhand, India, and is part of the Palamu Tiger Reserve (PTR).
• The park is known for its rich biodiversity, including tigers, elephants, and various other species of flora and fauna.
• TRAFFIC, a wildlife trade monitoring network, collaborates globally to curb illegal wildlife trade and protect endangered species.
• Sniffer dogs are trained to detect wildlife contraband such as tiger bones, skins, and other illegal animal products, aiding in anti-poaching efforts.
• Betla National Park is strategically significant due to its proximity to areas prone to wildlife trafficking, making the deployment of sniffer dogs crucial.

Additional Information

• Palamu Tiger Reserve (PTR)
• PTR is one of India's first tiger reserves, established under Project Tiger in 1973.
• It spans across the Latehar and Garhwa districts in Jharkhand and covers an area of over 1,129 square kilometers.
• The reserve is home to multiple species, including Bengal tigers, leopards, elephants, and sloth bears.
• Efforts for wildlife conservation in PTR include anti-poaching measures and habitat restoration.
• TRAFFIC
• TRAFFIC is a global wildlife trade monitoring organization founded in 1976.
• It is a joint program of the World Wildlife Fund (WWF) and the International Union for Conservation of Nature (IUCN).
• TRAFFIC works to ensure that wildlife trade does not threaten the conservation of nature.
• Its initiatives include training sniffer dogs, raising awareness, and collaborating with law enforcement agencies.
• Role of Sniffer Dogs in Conservation
• Sniffer dogs are trained to detect wildlife products such as ivory, rhino horns, and tiger skins.
• They play a crucial role in curbing illegal wildlife trade and poaching activities.
• Such dogs are deployed at key locations like airports, border checkpoints, and wildlife reserves.
• Training programs for sniffer dogs are conducted by organizations like TRAFFIC and government agencies.
• Biodiversity of Betla National Park
• The park hosts diverse ecosystems, including tropical dry deciduous forests and grasslands.
• It is home to several endangered species like Indian bison (gaur) and giant squirrels.
• Betla National Park also features historical sites, including ancient forts and caves.
• Ecotourism initiatives in the park aim to combine conservation with sustainable tourism.

The correct answer is Tungsten.

Key Points

• Tungsten is the most suitable material for making electric bulb filaments due to its high melting point of approximately 3422°C, which allows it to operate at high temperatures without melting.
• It has a very low rate of evaporation at high temperatures, ensuring a longer lifespan of the filament.
• Tungsten has excellent tensile strength, which prevents it from breaking easily when subjected to thermal expansion and contraction.
• Its high resistivity enables it to convert electrical energy into heat efficiently, producing bright light.
• When used in an inert gas-filled bulb, tungsten's performance is further enhanced by reducing filament evaporation and improving efficiency.

Additional Information

• Properties of Tungsten:
• The high melting point of tungsten makes it suitable for applications requiring heat resistance.
• Its density is around 19.3 g/cm³, making it one of the heaviest metals.
• Tungsten's low vapor pressure at high temperatures ensures minimal material loss.
• Why Other Materials Are Not Suitable:
• Copper: Low melting point (~1085°C) makes it unsuitable for high-temperature applications like filaments.
• Aluminium: Melts at approximately 660°C and lacks the durability required for filaments.
• Iron: Melting point (~1538°C) is higher than copper or aluminium but still insufficient compared to tungsten.
• Inert Gas in Bulbs: Modern electric bulbs are filled with inert gases like argon or a mixture of argon and nitrogen to prevent the oxidation of the tungsten filament and reduce evaporation.
• Historical Background: The use of tungsten in filaments was pioneered in the early 20^th century, replacing earlier materials like carbon due to its superior properties.
• Applications Beyond Bulbs: Tungsten is also used in x-ray tubes, welding electrodes, and aerospace due to its heat-resistant properties.

Given:

Mr. GHI starts from Point A and drives 16 km towards the east.

He then takes a right turn, drives 18 km, turns right, and drives 26 km.

He then takes a right turn and drives 26 km.

He takes a final right turn, drives 10 km, and stops at Point P.

He should drive 8 km to the south in order to reach Point A again.

Hence, the correct answer is "Option 2".

Shortcut Trick For the equation 5x2 − 11x + 2 = 0, find two numbers whose product is 10 (5 × 2) and sum is −11. The required numbers are −10 and −1. To find the roots directly, divide these factors by the coefficient of x2 (which is 5) and reverse the signs. Roots = −(−10 ÷ 5) = 2 and −(−1 ÷ 5) = 1/5. ∴ The correct answer is 1/5, 2.

Alternate Method Given Equation: 5x2 − 11x + 2 = 0 In the factorisation method, we split the middle term (−11x) into two terms such that their sum is −11x and their product is (5x2) × 2 = 10x2. ⇒ 5x2 − 10x − x + 2 = 0 ⇒ 5x(x − 2) − 1(x − 2) = 0 ⇒ (5x − 1)(x − 2) = 0 Now, set each factor to zero to find the roots: ⇒ 5x − 1 = 0 ⇒ 5x = 1 ⇒ x = 1/5 And, ⇒ x − 2 = 0 ⇒ x = 2 ∴ The correct answer is 1/5, 2.

Additional Information Discriminant (D) The term D = b2 − 4ac determines the nature of roots. If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary. Quadratic Formula Roots can also be found using x = (−b ± √D) ÷ 2a. Sum and Product of Roots For ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

The correct answer is Gram Panchayat.

Key Points

• The Gram Panchayat is the grassroots-level body in the three-tier Panchayati Raj system in India.
• It is directly elected by the people of the village, forming the first tier of the Panchayati Raj system.
• The Gram Panchayat is responsible for local governance and development activities in villages.
• Its members are elected for a term of five years by the eligible voters in the village.
• The head of the Gram Panchayat is called the Sarpanch, who is also elected by the villagers.

Additional Information

• Panchayati Raj System in India:
• The Panchayati Raj system is a decentralized form of governance in which gram panchayats are the basic units of administration.
• It was constitutionalized through the 73^rd Constitutional Amendment Act, 1992.
• The system has three levels: Gram Panchayat (village level), Panchayat Samiti (block level), and Zila Parishad (district level).
• Roles and Responsibilities of Gram Panchayat:
• Implementation of development programs such as rural housing, sanitation, and drinking water supply.
• Maintenance of public assets like roads, schools, and community centers.
• Promotion of literacy, health, and awareness programs in rural areas.
• Funding of Gram Panchayats:
• Funds are provided through grants from the central and state governments, revenue generated locally, and other sources.
• The Finance Commission recommends financial allocations to Panchayati Raj institutions.
• Importance of Grassroots Governance:
• It ensures that governance is inclusive and caters to the specific needs of rural populations.
• It encourages local participation in decision-making and promotes accountability.

The correct answer is Chimamanda Ngozi Adichie.

Key Points

• Chimamanda Ngozi Adichie is a renowned Nigerian author known for her impactful storytelling and exploration of themes such as identity, feminism, and post-colonialism.
• Her notable works include "Half of a Yellow Sun", which won the Orange Prize for Fiction, and "Americanah", which received global acclaim.
• Adichie is celebrated for her TED Talk titled "We Should All Be Feminists," which has had a profound cultural influence and was adapted into a book.
• The 2025 novel "Dream Count" is set to be one of her latest contributions to contemporary literature, showcasing her ability to merge storytelling with critical societal themes.
• She has been featured on several prestigious global platforms, emphasizing the importance of African narratives in global literature.

Additional Information

• Post-Colonial Literature:
• Post-colonial literature examines the effects of colonialism on cultures and societies.
• Chimamanda Adichie's works often address the lasting impacts of colonial rule in Nigeria and explore themes of cultural identity and heritage.
• Feminism in Literature:
• Adichie is a prominent voice in contemporary feminist literature.
• Her works often challenge gender norms and advocate for gender equality, making her a global feminist icon.
• Representation of Africa in Global Literature:
• Adichie emphasizes the importance of authentic African stories being told by African writers.
• She challenges stereotypes and promotes a nuanced understanding of African societies and cultures.
• Awards and Recognition:
• Adichie has received numerous accolades, including the MacArthur Genius Grant and the PEN Pinter Prize.
• Her works have been translated into multiple languages, showcasing their universal appeal and significance.

The correct answer is 5^th.

Key Points

• The 5^th Edition of the European Political Community (EPC) Summit is scheduled to take place in November 2024.
• The EPC Summit is a platform for fostering political dialogue and cooperation among European countries, including both EU and non-EU members.
• It was first launched in 2022, with the inaugural summit held in Prague, Czech Republic.
• The primary objective of the summit is to address pressing geopolitical challenges, enhance security, and strengthen economic ties across Europe.
• The EPC Summit involves leaders from 44 European nations, focusing on shared concerns such as energy security, migration, and infrastructure development.

Additional Information

• European Political Community (EPC):
• The EPC is a political forum aimed at fostering cooperation between European countries beyond the framework of the EU.
• It was proposed by French President Emmanuel Macron in May 2022 to address shared challenges across the continent.
• Key Themes of the EPC Summit:
• Security and defense cooperation to counter geopolitical threats.
• Collaborative efforts on energy security and the transition to renewable energy sources.
• Addressing migration challenges and enhancing infrastructure connectivity.
• Inaugural EPC Summit:
• The first summit was held on October 6, 2022, in Prague, Czech Republic.
• The event brought together leaders from 44 European countries, including non-EU states like the UK and Turkey.
• Significance of EPC:
• Acts as a unifying platform for European nations amidst rising geopolitical tensions and global challenges.
• Promotes multilateralism and strengthens Europe’s global standing.

The correct answer is Ministry of Commerce and Industry.

Key Points

• The Ministry of Commerce and Industry leads the implementation of the Start-up India initiative under the Department for Promotion of Industry and Internal Trade (DPIIT).
• The Start-up India initiative was launched by Prime Minister Narendra Modi on January 16, 2016, to boost entrepreneurship in India.
• The program aims to nurture innovation, simplify regulatory frameworks, and offer financial support to start-ups through government schemes.
• Key support under the initiative includes tax exemptions, easier patent filing, and access to funding through funds such as the Fund of Funds for Start-ups (FFS).
• As of 2023, over 90,000 start-ups have been recognized under the Start-up India initiative, making India the third-largest start-up ecosystem in the world.

Additional Information

• Department for Promotion of Industry and Internal Trade (DPIIT):
• DPIIT is a department under the Ministry of Commerce and Industry responsible for formulating and implementing policies for industrial growth and promotion.
• It plays a crucial role in facilitating ease of doing business and fostering the growth of start-ups in India.
• Fund of Funds for Start-ups (FFS):
• FFS was established under the Start-up India initiative with a corpus of Rs. 10,000 crores to provide funding support to start-ups.
• It is managed by the Small Industries Development Bank of India (SIDBI) and supports alternate investment funds (AIFs) that invest in start-ups.
• Tax Exemptions for Start-ups:
• Eligible start-ups can avail of a 100% tax exemption on profits for three consecutive years within their first ten years of incorporation.
• The initiative also provides exemptions from angel tax under certain conditions to encourage investments in start-ups.
• Start-up India Seed Fund Scheme (SISFS):
• Launched in 2021, SISFS aims to provide financial assistance to start-ups at the ideation and product development stages.
• Funds are disbursed through incubators, ensuring start-ups receive early-stage support to grow and scale.
• Ease of Doing Business Initiatives:
• Start-ups benefit from simplified compliance requirements and reduced regulatory burdens under the initiative.
• Self-certification and single-window clearance systems have been introduced to streamline processes.

The correct answer is Jawaharlal Nehru.

Key Points

• Jawaharlal Nehru was the first chairman of the Planning Commission of India, as the position of chairman was traditionally held by the Prime Minister of India.
• The Planning Commission was established on 15 March 1950, with the aim of formulating and overseeing India’s Five-Year Plans.
• The first Five-Year Plan (1951-1956), under Nehru’s leadership, focused on agricultural development and infrastructure building to address food shortages and boost economic growth.
• The Planning Commission was later replaced by the NITI Aayog (National Institution for Transforming India) in 2015 under Prime Minister Narendra Modi.
• As the first Prime Minister of independent India, Nehru played a pivotal role in shaping the country’s economic policies through the Planning Commission.

Additional Information

• Planning Commission:
• It was a non-constitutional and non-statutory body tasked with assessing resources and formulating development plans for India.
• The commission was headquartered in New Delhi and worked under the direct supervision of the Prime Minister.
• It operated through the formulation of Five-Year Plans to address sectors like agriculture, industry, education, and health.
• Five-Year Plans:
• The First Five-Year Plan (1951-1956) focused on agriculture, irrigation, and energy to rebuild India's economy post-independence.
• The Second Five-Year Plan (1956-1961), also known as the Mahalanobis Plan, emphasized rapid industrialization.
• These plans aimed to achieve self-sufficiency, equitable distribution of resources, and sustainable growth.
• NITI Aayog:
• It replaced the Planning Commission on 1 January 2015 to promote cooperative federalism and align with India’s changing economic needs.
• NITI Aayog focuses on policy think-tanks, innovation, and partnerships with states for development.
• Jawaharlal Nehru’s Vision:
• Nehru’s vision for India emphasized industrialization, scientific development, and modern economic strategies to uplift the nation.
• He viewed planning as a means to achieve social justice, reduce inequality, and accelerate progress.

The correct answer is diskpart.

Key Points

• Diskpart is a command-line utility in Windows operating systems that enables users to manage storage devices, such as disks, partitions, and volumes.
• Introduced in Windows 2000, it is available in all subsequent Windows versions, including Windows 11.
• Diskpart allows users to perform advanced storage tasks like creating, deleting, and resizing partitions, marking partitions as active, and assigning drive letters.
• This tool is particularly useful for troubleshooting disk-related issues and configuring storage on servers or virtual environments.
• Diskpart is accessed via the Command Prompt (cmd.exe) or Windows PowerShell, and requires administrative privileges to execute commands.

Additional Information

• MSConfig: A system configuration tool used to troubleshoot the Windows startup process, manage startup programs, and enable/disable services.
• Regedit: A registry editor tool in Windows that allows users to view, edit, and manage the Windows Registry, a hierarchical database storing system settings.
• Gpedit.msc: The Group Policy Editor, used to configure system and user settings in a Windows environment, mainly for administrative purposes.
• Virtual Hard Disk (VHD): A file format that represents a virtual disk drive. Diskpart can manage VHDs, enabling users to attach, detach, or create virtual disks.
• Administrative Privileges: Diskpart commands require administrative rights to execute, ensuring only authorized users can make critical changes to the storage system.

The correct answer is To suggest various pre-designed templates and layouts based on the content on the current slide.

Key Points

• The 'Design Ideas' feature in MS PowerPoint is part of the Design tab and provides layout suggestions to enhance slide aesthetics based on existing content.
• It uses AI-based algorithms to analyze the text, images, and other elements on the slide to propose visually appealing designs.
• This feature helps users save time by eliminating the need for manual formatting, offering professionally designed templates instantly.
• The 'Design Ideas' feature is available in Microsoft 365 and other supported versions of PowerPoint, providing a user-friendly way to create visually impactful presentations.
• Users can activate the feature by clicking the 'Design Ideas' button in the Design tab or it may appear automatically when adding content to a slide.

Additional Information

• Artificial Intelligence in PowerPoint
• MS PowerPoint integrates AI to enhance user productivity and design capabilities through features like 'Design Ideas' and 'Presenter Coach.'
• AI identifies patterns in user content to deliver personalized suggestions for slide layouts, images, and graphics.
• Other Design Tools in PowerPoint
• In addition to 'Design Ideas,' PowerPoint also offers features like themes, transitions, and animations to customize presentations.
• Users can access additional design elements through PowerPoint's integration with online libraries such as Office 365's image and icon repository.
• Version Compatibility
• The 'Design Ideas' feature is available in PowerPoint for Microsoft 365, PowerPoint 2019, and later versions.
• Some features may require an active internet connection to fetch AI-based suggestions.
• How to Enable 'Design Ideas'
• To enable the feature, users can navigate to File > Options > General and ensure the 'Show Design Ideas automatically' option is selected.
• It can also be manually triggered from the 'Design' tab during slide editing.

The pattern followed here is.

Thus, the missing term in the series is DGC 121.

Hence, the correct answer is "Option 2."

Shortcut Trick

Combined efficiency of A + B + C = 1/20

Efficiency of A = 1/50, Efficiency of B = 1/60

Efficiency of C = 1/20 − (1/50 + 1/60) = 3/60 − (1.2/60 + 1/60) = (15 − 6 − 5)/300 = 4/300 = 1/75

∴ The correct answer is 75 minutes.

Alternate Method

⇒ Efficiency of A + B + C = 15 units/min

⇒ Efficiency of A = 6 units/min

⇒ Efficiency of B = 5 units/min

⇒ Efficiency of C = (A + B + C) − A − B

⇒ Efficiency of C = 15 − 6 − 5 = 4 units/min

⇒ Time taken by C = Total Work ÷ Efficiency of C

⇒ Time taken by C = 300 ÷ 4 = 75 minutes

∴ The correct answer is 75 minutes.

Additional Information

Pipes and Cisterns Logic

If an inlet pipe fills a tank in x hours and an outlet pipe empties it in y hours, the net part filled in 1 hour = (1/x − 1/y).

Negative Efficiency

In pipe systems, an outlet pipe (drain pipe) is always assigned a negative efficiency because it removes work/water from the system.

Given Statements:

All grapes are apples.

All apples are kiwis.

Some kiwis are bananas.

The least possible Venn diagram for the given statements is:

Conclusions:

I. All apples are bananas - False (Because there is no definite relation given between apples and bananas. Only a part of kiwis is bananas, and apples are a part of kiwis, but there is no direct connection established between apples and bananas.)

II. Some kiwis are grapes - True (Because 'All grapes are apples' and 'All apples are kiwis.' This means that all grapes are a part of kiwis, which logically implies that some kiwis are grapes.)

So, Only conclusion II follows.

Hence, the correct answer is "Option 3".

The correct answer is Tea.

Key Points

• Tea is one of the major crops associated with plantation agriculture in India, primarily cultivated in states like Assam, West Bengal, Tamil Nadu, and Kerala.
• Plantation agriculture involves large-scale cultivation of crops on estates for commercial purposes, and tea is a prime example.
• Tea plantations are highly labor-intensive and provide employment to millions of workers, especially in northeastern and southern India.
• India is the second-largest producer and consumer of tea globally, contributing significantly to the export market.
• Climate conditions such as high rainfall, moderate temperature, and humid environments in hilly regions favor the growth of tea plantations.

Additional Information

• Plantation Agriculture
• Plantation agriculture is a type of commercial farming where crops like tea, coffee, rubber, and sugarcane are grown on large estates.
• This form of agriculture often requires substantial capital investment and skilled labor.
• It is practiced in tropical and subtropical regions with favorable climatic conditions.
• India's plantation crops contribute significantly to the economy through export earnings.
• Tea Cultivation in India
• Tea cultivation dates back to the British era when it was introduced in Assam.
• India has major tea-growing regions such as Darjeeling, Nilgiri Hills, and Assam.
• The tea industry is regulated by the Tea Board of India, which oversees production, marketing, and export.
• India's tea is famous for its varieties, including Assam Tea, Darjeeling Tea, and Nilgiri Tea.
• Key Factors for Tea Growth
• Tea requires acidic soil with high organic content and good drainage.
• The plant thrives in a humid climate with temperatures between 20°C to 30°C.
• Heavy rainfall (150-250 cm annually) and shade are crucial for optimal growth.
• Global Significance
• India is one of the world's largest tea exporters, with countries like Russia, the USA, and the UK being major importers.
• Tea is a culturally significant beverage in India, consumed daily by millions.
• The tea industry supports rural development and provides substantial employment opportunities.

Shortcut Trick

Successive percentage formula: Net Change = a + b + (a × b) ÷ 100.

Here, Markup (a) = 60%, Discount (b) = −X%, and Net Profit = 52%.

52 = 60 − X + (60 × −X) ÷ 100

52 − 60 = −X − 0.6X ⇒ −8 = −1.6X

X = 8 ÷ 1.6 = 5.

∴ The correct answer is 5.

Alternate Method

Let Cost Price (CP) = 100. Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = CP × (100 + Profit%) ÷ 100 | Discount% = (MP − SP) ÷ MP × 100.

⇒ Given Markup = 60%, so Marked Price (MP) = 100 + 60 = 160. ⇒ Given Profit = 52%, so Selling Price (SP) = 100 + 52 = 152. ⇒ Discount Amount = MP − SP = 160 − 152 = 8. ⇒ Discount% (X) = (8 ÷ 160) × 100. ⇒ X = (1 ÷ 20) × 100 = 5%.

∴ The correct answer is 5.

Additional Information

Marked Price and Discount

The price printed on an item is the Marked Price (MP). Discount is always calculated on the MP to reach the Selling Price (SP).

Markup Percentage

The extra price added to the Cost Price (CP) to set the MP is the markup. Markup% = [(MP − CP) ÷ CP] × 100.

The correct answer is Western Ghats and Arabian Sea.

Key Points

• The Western Coastal Plains of India are situated between the Western Ghats and the Arabian Sea.
• They are narrower compared to the Eastern Coastal Plains, with an average width ranging from 50 to 100 km.
• The plains extend from Gujarat in the north to Kerala in the south, covering the states of Maharashtra, Goa, and Karnataka in between.
• These plains are divided into three distinct sections: the Konkan Coast (Maharashtra and Goa), the Kanara Coast (Karnataka), and the Malabar Coast (Kerala).
• The region is known for its fertile soil, lagoons, backwaters, and estuaries, which support agriculture, fishing, and tourism.

Additional Information

• Western Ghats:
• A UNESCO World Heritage Site and one of the eight "hottest hotspots" of biological diversity globally.
• It is a continuous mountain range running parallel to the western coast of India.
• The Western Ghats play a crucial role in influencing the monsoon climate in India.
• Arabian Sea:
• Part of the northern Indian Ocean, bounded by India to the east, Pakistan and Iran to the north, and the Arabian Peninsula to the west.
• It is a major route for maritime trade and has significant economic importance.
• Backwaters of Kerala:
• A network of interconnected lakes, rivers, and canals along the Malabar Coast.
• Famous for houseboat tourism and traditional fishing practices.
• Economic Significance:
• The Western Coastal Plains are important for agriculture, with crops like rice and coconut grown extensively.
• Fishing is a major occupation along the coast due to the proximity to the Arabian Sea.
• The region also supports industries like shipbuilding and tourism.

Shortcut Trick

Net efficiency = Filling rate − Emptying rate.

Let Total capacity (LCM of 8 and 16) = 16 units.

Filling pipe efficiency = 16 ÷ 8 = 2; Emptying pipe efficiency = 16 ÷ 16 = 1.

Combined efficiency = 2 − 1 = 1 unit/hour.

Time for 3/4 filled = (3/4 × 16) ÷ 1 = 12 hours.

∴ The correct answer is 12 hours.

Alternate Method

Given: Filling time = 8 hours, Emptying time = 16 hours.

Formula Used: Work = Efficiency × Time; Net Efficiency = (1/Filling time) − (1/Emptying time).

⇒ Combined efficiency of both pipes = 2 − 1 = 1 unit/hour.

⇒ Target volume to be filled = 3/4 × Total Capacity

⇒ Target volume = 3/4 × 16 = 12 units.

⇒ Time taken = Target volume ÷ Combined efficiency

⇒ Time taken = 12 ÷ 1 = 12 hours.

∴ The correct answer is 12 hours.

Additional Information

Pipes and Cisterns Concept

Filling pipes (inlets) have positive efficiency, while emptying pipes (outlets) have negative efficiency.

Net Work Formula

If pipe A fills in 'x' hours and pipe B empties in 'y' hours, net work in 1 hour = (1/x − 1/y). If x < y, the tank will eventually fill.

Fractional Filling

To find time for a specific fraction of the tank, multiply the total fill time by that fractional value.

Given Expression: S + D - F × G ÷ H

S + D: S is the son of D.

D - F: D is the brother of F.

F × G: F is the wife of G.

G ÷ H: G is the father of H.

According to the given information Family Tree Representation:

S is Mother's brother's son to H

Hence, the correct answer is "Option 4"

Shortcut Trick

If A is r% more than B, then B is less than A by [r / (100 + r)] × 100%.

Required percentage = [51 / (100 + 51)] × 100

⇒ 5100 ÷ 151 ≈ 33.77%

∴ The correct answer is 33.77%.

Alternate Method

Given:

Let B's salary = 100

A's salary is 51% more than B.

⇒ A's salary = 100 + 51% of 100 = 100 + 51 = 151

Calculations:

Difference between A and B = 151 − 100 = 51

Percentage by which B is less than A = (Difference / A's salary) × 100

⇒ Required % = (51 / 151) × 100

⇒ Required % = 5100 / 151

⇒ Required % = 33.7748...

Rounding to two decimal places, we get 33.77%.

∴ The correct answer is 33.77%.

Additional Information

Percentage Change Comparison

When comparing two quantities, if A is x% more than B, then B is [x / (100 + x)] × 100% less than A.

Base Change Rule

Percentage is always calculated relative to the base value. When finding 'less than A', A's value becomes the denominator.

Inverse Case

If A is x% less than B, then B is [x / (100 − x)] × 100% more than A.

Shortcut Trick

Arrange the 11 observations in ascending order:

20, 20, 35, 43, 56, 62, 68, 72, 79, 85, 90

Since the number of terms (N = 11) is odd, the median is the middle term:

Median = ((N + 1) ÷ 2)^th term = 6^th term = 62

∴ The correct answer is 62.

Alternate Method

Given:

Observations: 85, 62, 20, 72, 20, 43, 35, 90, 68, 56, 79

Total number of observations (N) = 11

Formula Used:

When N is odd, Median = ((N + 1) ÷ 2)^th observation after arranging in ascending order.

Calculations:

Arrange the given observations in ascending order:

⇒ 20, 20, 35, 43, 56, 62, 68, 72, 79, 85, 90

Count the total number of observations:

⇒ N = 11

Since N is an odd number, the median is calculated as:

⇒ Median = ((11 + 1) ÷ 2)^th term

⇒ Median = (12 ÷ 2)^th term

⇒ Median = 6^th term

Looking at the arranged sequence, the 6^th term is 62.

Let us verify why the other options are incorrect:

⇒ Option (1) 68 is the 7^th term, which is not the middle term.

⇒ Option (3) 56 is the 5^th term, which is not the middle term.

⇒ Option (4) 72 is the 8^th term, which is not the middle term.

∴ The correct answer is 62.

Additional Information

Median for Even Number of Terms

If N is even, the median is the average of the (N ÷ 2)^th term and the ((N ÷ 2) + 1)^th term. Formula: Median = [ (N/2)^th term + (N/2 + 1)^th term ] ÷ 2.

Mean (Arithmetic Average)

The sum of all observations divided by the total number of observations. Formula: Mean = (Sum of all observations) ÷ N.

Mode

The observation that appears most frequently in the data set. For the given data, 20 appears twice, so the mode is 20.

Empirical Relationship

The relationship between Mean, Median, and Mode for moderately skewed distributions is: Mode = 3 × Median − 2 × Mean.

Shortcut Trick

Loss of 31% means selling at (100 − 31) = 69% of CP.

Profit of 34% means selling at (100 + 34) = 134% of CP.

Ratio-unitary method: If 69 units = 483, then 1 unit = 483 ÷ 69 = 7.

Target Selling Price = 134 units = 134 × 7 = 938.

∴ The correct answer is ₹938/m.

Alternate Method

Given: Selling Price 1 (SP₁) = ₹483, Loss% = 31%, Target Profit% = 34%.

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

⇒ Cost Price (CP) = (483 × 100) ÷ (100 − 31) = (483 × 100) ÷ 69 = 7 × 100 = ₹700.

⇒ Required Selling Price (SP₂) = [700 × (100 + 34)] ÷ 100 = 700 × 1.34 = 938.

∴ The correct answer is ₹938/m.

Additional Information

Cost Price & Selling Price Relationship

When the cost price is constant, the ratio of two selling prices is directly proportional to the percentage values: SP₁/SP₂ = (100 ± P/L₁)/(100 ± P/L₂).

Profit and Loss Basics

Profit is earned when SP > CP, and Loss occurs when CP > SP. All percentages are calculated on the Cost Price unless specified otherwise.