RRB Technician Grade III Official Paper (Held On: 30 Dec, 2024 Shift 2) (Previous Year Paper)

Shortcut Trick

Factor out the constants: (50 × (1 + cot²A)) ÷ (25 × (1 + tan²A)).

Using identities: (50 × cosec²A) ÷ (25 × sec²A) = 2 × (cosec²A ÷ sec²A).

Since cosec²A ÷ sec²A = (1/sin²A) ÷ (1/cos²A) = cos²A/sin²A = cot²A.

Result = 2 × cot²A.

∴ The correct answer is 2 cot²A.

Alternate Method

Given: Expression = (50 + 50cot²A) / (25 + 25tan²A)

Formula Used: 1 + cot²A = cosec²A and 1 + tan²A = sec²A

⇒ Expression = [50(1 + cot²A)] / [25(1 + tan²A)]

⇒ Expression = [50 × cosec²A] / [25 × sec²A]

⇒ Expression = 2 × (1/sin²A) / (1/cos²A)

⇒ Expression = 2 × (cos²A / sin²A)

⇒ Expression = 2 cot²A

∴ The correct answer is 2 cot²A.

Additional Information

Trigonometric Identities

Fundamental identities include sin²A + cos²A = 1, 1 + tan²A = sec²A, and 1 + cot²A = cosec²A.

Reciprocal Relations

cosec A = 1/sin A, sec A = 1/cos A, and cot A = cos A / sin A = 1/tan A.

Value Substitution Method

For competitive exams, you can also substitute A = 45°. Numerator = 50+50(1)=100, Denominator = 25+25(1)=50. Result = 100/50 = 2. Option (1) gives 2(1) = 2.

Let us first decode the given symbols and then draw a family tree.

 

 

 

 

 

Given:

‘A + B - C × D ÷ E'

'A + B' means 'A is the daughter of B'

'B - C' means 'B is the wife of C',

'C × D' means 'C is the son of D' and

'D ÷ E' means 'D is the husband of E'.

Thus, A is Son's daughter of E.

Hence, the correct answer is "Option 3".

The Correct answer is 1, 2 and 3.

Key Points

• Raigad Fort is one of the 12 forts nominated under the title "Maratha Military Landscapes of India" for UNESCO World Heritage status for the year 2024-25. This reflects its historical and architectural significance.
• It was the capital of the Maratha Empire and the seat of Chhatrapati Shivaji Maharaj, the most illustrious Maratha sovereign. Shivaji Maharaj was formally coronated as the Chhatrapati at Raigad in 1674.
• The fort is geographically unique, being surrounded by valleys shaped by the Kal and Gandhari rivers. It is an isolated massif without any direct connection to neighboring hills, making it a natural fortress and strategically advantageous.
• Raigad Fort is located in the Sahyadri mountain range in the state of Maharashtra, India.
• The fort is also known for its remarkable features, including the Maha Darwaja (main gate), the Samadhi of Shivaji Maharaj, and the Jagadishwar Temple.
• Its location and structure demonstrate the military and architectural acumen of the Marathas.

 Additional Information

• UNESCO World Heritage Nomination
• The nomination of 12 forts, including Raigad, under the title "Maratha Military Landscapes of India", aims to recognize the historical and cultural importance of Maratha architecture and military strategies.
• Other forts in this nomination include Shivneri, Rajgad, Torna, and Sindhudurg, highlighting the Marathas' strategic planning and engineering skills.
• Chhatrapati Shivaji Maharaj
• Shivaji Maharaj was the founder of the Maratha Empire, which played a critical role in resisting Mughal dominance in India.
• He was known for his administrative reforms, the establishment of a strong navy, and strategic fortifications like Raigad.
• Geographical Importance of Raigad Fort
• Its location on an isolated hill, surrounded by deep valleys, made it a natural fortress.
• The fort's design ensured defense and surveillance, with steep pathways and narrow entrances that provided added security.

The Correct answer is Odisha.

Key Points

• Kishore Jena, an athlete from Odisha, has made history by becoming the first javelin thrower from the state to represent India in the finals of the World Athletics Championship.
• He achieved this milestone during the 2023 World Athletics Championships, held in Budapest, Hungary.
• Jena qualified for the finals with an impressive throw of 80.55 meters in the qualification round.
• His participation and success at the global level mark an important moment for Odisha’s sports ecosystem, which has seen significant growth in recent years.
• Odisha is known for its support of sports infrastructure, hosting events like the Hockey World Cup and training athletes in diverse disciplines.
• Jena’s achievement is a testimony to the state’s evolving sports culture and its contribution to India's athletics landscape.
• His performance also highlights the growing prominence of javelin throw as a sport in India, following the success of athletes like Neeraj Chopra.

 Additional Information

• Karnataka
• Karnataka is a state in southern India known for its rich history, diverse culture, and contributions to sports like cricket, hockey, and badminton.
• The state is home to athletes like Anil Kumble in cricket and Prakash Padukone in badminton.
• However, Karnataka is not traditionally associated with javelin throw or athletics at the global level.
• West Bengal
• West Bengal is primarily known for its passion for sports like football and cricket.
• It has produced renowned athletes in football, including Baichung Bhutia, but has limited representation in javelin throw.
• Rajasthan
• Rajasthan is known for its contributions to sports like wrestling, kabaddi, and shooting.
• The state has produced athletes like Apurvi Chandela in shooting but is not prominently linked with javelin throw.

The Correct answer is Chloroplast.

Key Points

• Chloroplasts are specialized organelles found in plant cells and some algae.
• They are the site of photosynthesis, a process by which plants convert light energy into chemical energy in the form of glucose.
• Chloroplasts contain a green pigment called chlorophyll, which absorbs light energy from the sun.
• The main components of chloroplasts include the thylakoid membranes (where the light-dependent reactions occur) and the stroma (where the Calvin cycle or light-independent reactions take place).
• Photosynthesis in chloroplasts is vital for the survival of most life forms on Earth because it produces oxygen and serves as the basis of the food chain.
• Chloroplasts are unique to plants and algae and are not present in animal cells.
• Like mitochondria, chloroplasts have their own DNA and ribosomes, allowing them to produce some of their own proteins and enzymes independently.

 Additional Information

• Mitochondria
• Mitochondria are often referred to as the powerhouses of the cell.
• They are responsible for producing ATP (adenosine triphosphate) through the process of cellular respiration.
• Unlike chloroplasts, mitochondria are present in both plant and animal cells.
• Nucleus
• The nucleus is the control center of the cell and contains the cell’s genetic material (DNA).
• It plays a critical role in cell division and gene expression.
• The nucleus is surrounded by a nuclear envelope and contains a dense region called the nucleolus, which is involved in ribosome production.
• Ribosome
• Ribosomes are molecular machines responsible for protein synthesis.
• They can be found floating freely in the cytoplasm or attached to the endoplasmic reticulum (forming rough ER).
• Ribosomes are present in both prokaryotic and eukaryotic cells.

Shortcut Trick

Co-prime numbers are pairs that have no common factor other than 1.

Check pairs: (52, 24) → both even, (455, 49) → both ÷ 7, (363, 77) → both ÷ 11.

Pair (81, 16): Factors of 81 are 3⁴ and Factors of 16 are 2⁴. No common factor.

∴ The correct answer is 81, 16.

Alternate Method

Given: Four pairs of numbers to check for co-primality.

Definition: HCF(a, b) = 1 for co-primes.

⇒ Case 1: 52 and 24. Both are even, so HCF ≥ 2. (Actual HCF = 4).

⇒ Case 2: 81 and 16. Factors of 81 = {1, 3, 9, 27, 81}. Factors of 16 = {1, 2, 4, 8, 16}. Only common factor is 1.

⇒ Case 3: 455 and 49. 49 = 7 × 7. 455 = 7 × 65. HCF = 7.

⇒ Case 4: 363 and 77. 77 = 7 × 11. 363 = 11 × 33. HCF = 11.

∴ The correct answer is 81, 16.

Additional Information

Co-prime Numbers

Two numbers are co-prime if their Highest Common Factor (HCF) is 1. They do not need to be prime numbers individually.

Consecutive Numbers

Any two consecutive integers (like 14, 15) are always co-prime to each other.

Prime Numbers Rule

Two different prime numbers are always co-prime (e.g., 7 and 13).

The Correct answer is 20 J.

Key Points

• Work done is calculated using the formula: W = F × d × cos θ, where:
• W is the work done.
• F is the force applied.
• d is the displacement of the body.
• θ is the angle between the direction of force and displacement.
• In this case, the force applied is 10 N, displacement is 2 m, and the force acts in the same direction as the displacement. Thus, cos θ = cos 0 = 1.
• Substituting the values into the formula:
• W = 10 × 2 × 1 = 20 J.
• Hence, the work done is 20 Joules.
• This calculation is based on the principle of mechanics and is relevant in physics to determine the energy transferred by a force.

The Correct answer is Repeated cell division at one specific site.

Key Points

• Hydra reproduces asexually by a process known as budding.
• The formation of a bud in Hydra occurs due to repeated cell division at one specific site, which leads to the outgrowth of a small structure (the bud).
• The bud develops as a result of mitotic cell division in the epidermal and gastrodermal cells at that localized site.
• This bud grows and eventually forms a miniature Hydra that is genetically identical to the parent organism.
• Once the bud reaches maturity, it detaches from the parent body and becomes an independent organism.
• This method of reproduction allows Hydra to reproduce quickly and efficiently in favorable conditions.
• The process of budding in Hydra is a classic example of asexual reproduction, which does not involve the fusion of gametes.
• This mechanism is advantageous for Hydra as it enables rapid population growth in a stable environment.

 Additional Information

• Cell cycle
• The cell cycle is the series of events that take place in a cell leading to its division and duplication.
• It is primarily involved in the growth and repair of tissues, but it is not directly responsible for the formation of a bud in Hydra.
• The cell cycle includes stages such as G1, S, G2, and mitosis.
• Mutation
• A mutation refers to a change in the genetic material of an organism, which can occur spontaneously or be induced by external factors.
• While mutations can lead to structural or functional changes, they are not the reason for bud formation in Hydra.
• Mutations are generally associated with genetic diversity, disorders, or evolution.
• Overgrowth of the whole body
• Overgrowth refers to an uncontrolled or abnormal increase in the size of the entire organism, which is not the process seen in Hydra budding.
• In Hydra, the growth is localized to a specific site, leading to the formation of a bud rather than the overgrowth of the entire body.

Given:

$\frac{3}{7} + \frac{2}{7} + \frac{1}{14} - 3 = ?$

Formula used:

To add or subtract fractions, find the LCM of the denominators.

Calculations:

? = 3/7 + 2/7 + 1/14 − 3

⇒ ? = (3 × 2 + 2 × 2 + 1 − 3 × 14) / 14

⇒ ? = (6 + 4 + 1 − 42) / 14

⇒ ? = (11 − 42) / 14

⇒ ? = −31/14

∴ The correct answer is option (3).

The Correct answer is Kerala.

Key Points

• The book "Maa-Mother" was authored by the Additional Secretary to the Governor of Kerala.
• It was launched by the Law and Justice Minister Arjun Ram Meghwal in November 2024.
• This book is a tribute to the author's mother, showcasing emotional and personal insights about maternal love and sacrifices.
• Kerala, known for its literary and cultural heritage, often produces notable works in the field of literature.
• The Governor’s Office in Kerala has played a significant role in promoting initiatives related to education and literature.
• Such books often aim to inspire readers and emphasize the value of familial bonds and the role of mothers in shaping lives.

 Additional Information

• Tamil Nadu
• Tamil Nadu is known for its rich literary tradition, with contributions to Tamil literature dating back thousands of years.
• The state is home to prominent writers and poets who have shaped the Dravidian literary culture.
• While Tamil Nadu is culturally significant, the book "Maa-Mother" was not authored by any official from this state.
• Rajasthan
• Rajasthan is known for its contributions to art, literature, and folk traditions.
• It has produced significant works in Rajasthani and Hindi literature, but the book "Maa-Mother" was not associated with this state.
• Maharashtra
• Maharashtra is recognized for its literary contributions, especially in Marathi literature.
• The state has had a notable history of authors and poets, including names like P.L. Deshpande and Kusumagraj.
• Despite its literary prominence, the book "Maa-Mother" was not authored by an official from Maharashtra.

The Correct answer is Chennai.

Key Points

• Chennai successfully hosted India’s first-ever night street race in August 2023.
• The event was part of the Indian Racing League (IRL), which aims to promote motorsports in India.
• The race took place on the Madras International Circuit, one of the oldest and most prominent racing tracks in India.
• This marked a significant milestone for motorsport enthusiasts in India, showcasing global standards of racing infrastructure and organization.
• The event featured participation from top-tier drivers and included advanced technologies in track lighting and safety measures.
• Chennai has long been considered the hub of motorsports in India, with a strong legacy of hosting motorsport events.
• The success of the night street race reflects the city’s capability to organize international-standard events and boosts tourism and global recognition.
• Night races are significant as they enhance the visual appeal for spectators, allowing better attendance and television viewership.

 Additional Information

• Bengaluru
• Bengaluru is often referred to as the Silicon Valley of India because of its role as the leading information technology hub.
• The city is known for its pleasant weather and vibrant startup ecosystem.
• Bengaluru hosts various motorsport events, but it did not host India’s first-ever night street race.
• Kolkata
• Kolkata is renowned for its colonial architecture, rich culture, and history.
• The city is not traditionally associated with motorsports but is known for hosting other sporting events such as football and cricket tournaments.
• Mumbai
• Mumbai is India’s financial capital and home to several corporate headquarters and entertainment hubs.
• While Mumbai has hosted car rallies and other automotive events, it did not host the night street race in 2023.

Given: 

D, E, F, G, L, M and N are sitting around a circular table facing the centre.

Only two people sit between F and L when counted from the left of L.

G sits second to the left of F. G sits to the immediate right of M

N sits third to the left of M.

E is not an immediate neighbour of N.

Thus, 'G' sits third to the right of D.

Hence, the correct answer is "Option 3".

The logic followed here is:

Option 1) TA-BK

Option 2) SW-FM

Option 3) ZG - HQ

Option 4) BI-JS

Thus, 'SW- FM' not follow the same logic.

Hence, the correct answer is "Option 2".

Given:

The number of plants planted on Friday = 12

The number of plants planted on Saturday = 10

Formula used:

Ratio = (Number of plants planted on Friday) / (Number of plants planted on Saturday)

Calculations:

Ratio = 12 / 10

⇒ 12 / 10 = 6 : 5

∴ The correct answer is the ratio is 6 : 5.

Given code language:

As L is common in both the code language, its code is 5.

Hence, the correct answer is "Option 4".

Formula used:

Modal class is the one with the highest frequency. The modal size is the shoe size corresponding to the maximum number of pairs demanded.

Calculations:

Shoe size 5: 44

Shoe size 6: 48

Shoe size 7: 58

Shoe size 8: 46

Shoe size 9: 39

Shoe size 10: 37

The highest demand is for shoe size 7, with 58 pairs demanded.

∴ The modal size of shoes demanded is 7.

Decoding the given information :

Given:

22 B 5 D 12 A 4 C 6 = ?

Now, replacing the sign from left to right and using BODMAS rule, we get :

22 × 5 - 12 ÷  4 + 6 = ?

→ 22 × 5 - 12 ÷  4 + 6

→ 22 × 5 - 3 + 6

→ 110 - 3 + 6

→ 113

Hence, the correct answer is "Option 4".

Shortcut Trick

Total Percentage Interest = Rate × Time

⇒ 4% × 5 = 20%

Simple Interest = 20% of ₹5,000

⇒ 0.20 × 5000 = ₹1000

∴ The correct answer is ₹1000.

Alternate Method

Given:

Principal (P) = ₹5,000

Rate (R) = 4% per annum

Time (T) = 5 years

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ SI = (5000 × 4 × 5) ÷ 100

⇒ SI = (5000 × 20) ÷ 100

⇒ SI = 100000 ÷ 100

⇒ SI = ₹1000

∴ The correct answer is ₹1000.

Additional Information

Total Amount Formula

The total amount (A) is the sum of Principal and Simple Interest: A = P + SI = P(1 + RT/100).

Simple Interest Characteristics

Simple interest remains constant every year because it is always calculated on the original Principal amount.

Rate and Time relationship

If the Rate is given per month, the Time must also be converted into months to use the standard formula correctly.

The Correct answer is Phototropism — movement towards water.

Key Points

• Phototropism refers to the movement or growth of plants in response to light.
• It is a directional movement where the plant grows towards the light source (positive phototropism) or away from it (negative phototropism).
• The hormone responsible for phototropism is auxin, which facilitates growth on the side of the plant away from the light.
• Phototropism ensures that plants optimize the absorption of light for photosynthesis.
• The statement “movement towards water” is incorrect because phototropism is specifically related to light stimuli, not water.
• Water stimuli lead to hydrotropism, which is another form of tropism.

 Additional Information

• Chemotropism — movement towards chemical
• Chemotropism refers to the growth or movement of plants in response to a chemical stimulus.
• Examples include the growth of pollen tubes towards ovules during fertilization in plants.
• This type of tropism helps plants in important processes such as reproduction.
• Hydrotropism — movement towards water
• Hydrotropism is the movement or growth of plant roots towards a water source.
• It ensures that plant roots can access adequate water for survival and growth.
• This type of tropism is crucial for plants thriving in dry or arid conditions.
• Geotropism — in response to the pull of earth or gravity
• Geotropism refers to the growth or movement of plants in response to gravity.
• Plant roots exhibit positive geotropism by growing downward into the soil.
• Plant shoots exhibit negative geotropism by growing upward away from the gravitational pull.
• This type of tropism helps plants maintain proper structural orientation.

The logic followed here is:

Thus, 'ORU' will be the next in the series.

Hence, the correct answer is "Option 2".

Decoding the given information :

 

Now check each option:

Option 1) 18 C 5 A 42 D 6 B 17

18 + 5 ÷ 42 - 6 × 17

→ 18 + 5 ÷ 42 - 6 × 17

→ 18 + 0.199 - 6 × 17

→ 18 + 0.199 - 102

→ -83.881 ≠ 80

Option 2) 18 A 5 B 42 C 6 D 17

18 ÷ 5 × 42 + 6 - 17

→ 18 ÷ 5 × 42 + 6 - 17

→ 3.6 × 42 + 6 - 17

→ 151.2 + 6 - 17

→ 140.2 ≠ 80

Option 3) 18 B 5 C 42 A 6 D 17

18 × 5 + 42 ÷ 6 - 17 

→18 × 5 + 42 ÷ 6 - 17 

→18 × 5 + 7 - 17 

→ 90 + 7 -17

→ 80 

Option 4) 18 D 5 A 42 B 6 C 17

18 - 5 ÷ 42 × 6 + 17

→ 18 - 5 ÷ 42 × 6 + 17

→ 18 - 0.119 × 6 + 17

→ 18 - 0.714 + 17

→ 34.286 ≠ 80.

Hence, the correct answer is "Option 3".

Shortcut Trick

Ratio of A : B : C = 5 : 7 : 15

Given: A’s share (5 units) = ₹1500

Total units = 5 + 7 + 15 = 27 units

Value per unit = 1500 ÷ 5 = ₹300

Total amount = 27 × 300 = ₹8100

∴ The correct answer is ₹8100.

Alternate Method

Given:

Ratio of distribution (A : B : C) = 5 : 7 : 15

A’s share = ₹1500

Formula Used:

Total Amount = (Sum of Ratios ÷ Specific Ratio Part) × Specific Share

Calculations:

⇒ Let the common multiplier be x.

⇒ A’s share = 5x, B’s share = 7x, C’s share = 15x

⇒ 5x = 1500

⇒ x = 1500 ÷ 5 = 300

⇒ Total Amount = 5x + 7x + 15x = 27x

⇒ Total Amount = 27 × 300

⇒ Total Amount = ₹8100

∴ The correct answer is ₹8100.

Additional Information

Ratio and Proportion

Ratio is a comparison of two or more quantities. If a sum S is divided in the ratio a:b:c, then part of A = S × [a ÷ (a+b+c)].

Unitary Method

This method involves finding the value of a single unit and then multiplying by the total required units to find the final result.

Compound Ratio

The compound ratio of a:b and c:d is (ac):(bd), used when multiple distribution criteria are given.

Shortcut Trick

Volume of a cylinder = Base Area × Height (h)

Base Area = 38.5 cm² ⇒ πr² = 38.5 ⇒ r = 3.5 cm

Curved Surface Area (CSA) = 2πrh = 616 ⇒ 2 × (38.5/r) × h = 616

⇒ h = (616 × 3.5) ÷ (2 × 38.5) = 28 cm

Volume = 38.5 × 28 = 1078 cm³

∴ The correct answer is 1078 cm³.

Alternate Method

Given:

Curved Surface Area (CSA) = 616 cm²

Base Area = 38.5 cm²

Formula Used:

⇒ Base Area = πr²

⇒ CSA = 2πrh

⇒ Volume = πr²h

Calculations:

⇒ πr² = 38.5

⇒ (22/7) × r² = 38.5

⇒ r² = (38.5 × 7) ÷ 22 = 1.75 × 7 = 12.25

⇒ r = √12.25 = 3.5 cm

⇒ 2 × (22/7) × 3.5 × h = 616

⇒ 2 × 22 × 0.5 × h = 616

⇒ 22 × h = 616

⇒ h = 28 cm

⇒ Volume = 38.5 × 28 = 1078 cm³

∴ The correct answer is 1078 cm³.

Additional Information

Total Surface Area (TSA) of Cylinder

It is the sum of CSA and the areas of the two circular bases: TSA = 2πrh + 2πr² = 2πr(h + r).

Hollow Cylinder Volume

For a hollow cylinder with external radius R and internal radius r, Volume = π(R² − r²)h.

Ratio of CSA to Volume

For any cylinder, the ratio of its Curved Surface Area to its Volume is 2/r.

Shortcut Trick

For a cube with side 's', the Volume is given by s³.

Side = 6xyz²

Volume = (6xyz²)³ = 6³ × x³ × y³ × (z²)³

Volume = 216 × x³ × y³ × z⁶

∴ The correct answer is 216 x³y³z⁶.

Alternate Method

Given:

Side of the cube (s) = 6xyz²

Formula Used:

Volume of a cube = (Side)³

Calculations:

⇒ Volume = (6xyz²)³

⇒ Volume = 6³ × x³ × y³ × (z²)³

⇒ Volume = 216 × x³ × y³ × z^(2×3)

⇒ Volume = 216x³y³z⁶

∴ The correct answer is 216 x³y³z⁶.

Additional Information

Surface Area of Cube

The Total Surface Area of a cube is 6 × s² and the Lateral Surface Area is 4 × s².

Diagonal of a Cube

The length of the longest diagonal of a cube with side 's' is s√3.

Laws of Exponents

For any variable 'a', (a^m)ⁿ = a^m×n and (ab)ⁿ = aⁿbⁿ.

The Correct answer is Heating.

Key Points

• Heating is not a method used for preventing rusting of iron.
• Rusting is a chemical process that occurs when iron reacts with oxygen and moisture in the environment, forming iron oxide.
• Heating does not create a protective barrier or alter the surface of iron to prevent it from reacting with oxygen or water.
• While heating may temporarily remove moisture from the surface of the metal, it does not prevent the reintroduction of moisture or oxygen, and thus, rusting can still occur.
• Effective rust prevention methods involve creating a physical or chemical shield between the iron and the external environment.

 Additional Information

• Chrome Plating
• Chrome plating involves coating the surface of iron or steel with a layer of chromium.
• The chromium layer provides a shiny appearance and prevents the surface from coming into contact with oxygen and moisture.
• It is widely used in industries for both decorative and protective purposes.
• Painting
• Painting is a common method for protecting iron from rusting by applying a layer of paint on the surface.
• The paint acts as a barrier, preventing moisture and oxygen from reaching the metal surface.
• It is cost-effective and widely used in construction, infrastructure, and automobile industries.
• Galvanising
• Galvanising is the process of coating iron or steel with a layer of zinc.
• The zinc layer acts as a sacrificial metal, corroding in place of the iron and thereby protecting it from rusting.
• It is commonly used in applications like roofing sheets, fencing, and pipelines.

Given code:

Thus, code for 'H' is 6.

Hence, the correct answer is "Option 1".

Shortcut Trick

Square root of one number is 3 → First number = 3² = 9.

Square of first number = 9² = 81.

Square of second number = 145 − 81 = 64.

Second number = √64 = 8.

∴ The correct answer is 8.

Alternate Method

Given: Sum of squares of two numbers = 145, Square root of one number = 3.

Formula Used: x² + y² = 145

Let the two positive numbers be x and y.

⇒ x² + y² = 145

⇒ √x = 3 (given)

⇒ x = 3² = 9

⇒ 9² + y² = 145

⇒ 81 + y² = 145

⇒ y² = 145 − 81

⇒ y² = 64

⇒ y = √64 = 8

∴ The correct answer is 8.

Additional Information

Perfect Squares

A number that is the square of an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Square Root Relationship

If √a = b, then a = b². In this problem, √x = 3 implies x = 9.

Pythagorean Triplets

Sets of three positive integers a, b, and c such that a² + b² = c². While 145 is not a perfect square, it is the sum of two squares: 8² + 9².

Shortcut Trick

To find a number divisible by all numbers from 1 to 10, calculate the LCM of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Identify the highest powers of primes: 2³ (8), 3² (9), 5¹ (5), and 7¹ (7).

LCM = 8 × 9 × 5 × 7 = 72 × 35 = 2520.

∴ The correct answer is 2520.

Alternate Method

Given: Divisibility by natural numbers from 1 to 10 inclusive.

Formula Used: Divisibility rules and Least Common Multiple (LCM).

⇒ Prime factors of 1 to 10 are:

⇒ 1 = 1 | 2 = 2 | 3 = 3 | 4 = 2² | 5 = 5 | 6 = 2 × 3 | 7 = 7 | 8 = 2³ | 9 = 3² | 10 = 2 × 5

⇒ LCM = 2³ × 3² × 5 × 7

⇒ LCM = 8 × 9 × 5 × 7 = 2520

⇒ Verify options: 608 (not by 3), 504 (not by 5/10), 1000 (not by 3/7/9).

∴ The correct answer is 2520.

Additional Information

LCM of First N Natural Numbers

The smallest number divisible by 1 to N is found by taking the product of the highest powers of all prime numbers less than or equal to N.

Divisibility Rules

A number is divisible by 9 if the sum of digits is divisible by 9, and by 5 if it ends in 0 or 5. 2520 satisfies all such rules for 1 through 10.

Shortcut Trick

Equate the quantity of mangoes to find the profit per unit cycle.

CP of 3 kg = Rs. 21 ⇒ CP of 15 kg = 21 × 5 = Rs. 105.

SP of 5 kg = Rs. 50 ⇒ SP of 15 kg = 50 × 3 = Rs. 150.

Profit on 15 kg = 150 − 105 = Rs. 45.

Quantity for Rs. 102 profit = (15 ÷ 45) × 102 = 34 kg.

∴ The correct answer is 34 kg.

Alternate Method

Given: CP rate = 3 kg for Rs. 21 | SP rate = 5 kg for Rs. 50 | Target Profit = Rs. 102.

Formulas: CP per kg = Total Price ÷ Total Quantity | Profit per kg = SP per kg − CP per kg | Required Quantity = Total Profit ÷ Profit per kg.

⇒ Cost Price (CP) per kg = 21 ÷ 3 = Rs. 7 per kg.

⇒ Selling Price (SP) per kg = 50 ÷ 5 = Rs. 10 per kg.

⇒ Profit per kg = SP − CP = 10 − 7 = Rs. 3 per kg.

⇒ Total quantity to be sold = Total Profit ÷ Profit per kg = 102 ÷ 3 = 34 kg.

∴ The correct answer is 34 kg.

Additional Information

Unitary Method in Profit and Loss

Calculating the price of a single unit helps in comparing buying and selling rates easily. Formula: Price per unit = Total Cost ÷ Total Units.

Profit Margin Calculation

Profit Percentage = (Profit ÷ CP) × 100. In this case: (3 ÷ 7) × 100 ≈ 42.85%.

The Correct answer is energy.

Key Points

• Work and energy are scalar quantities and both are measured in the same unit, which is the joule (J) in the SI system.
• The mathematical definition of work is the product of force and displacement in the direction of the force: Work = Force × Displacement × cos(θ), where θ is the angle between the force and displacement.
• Energy is the capacity to do work, and it can exist in various forms such as kinetic energy, potential energy, thermal energy, etc.
• The unit equivalence arises because energy is fundamentally defined in terms of work. For example, 1 joule of energy is the work done when a force of 1 newton displaces an object by 1 meter in the direction of the force.
• Both work and energy follow the principle of conservation, which states that energy cannot be created or destroyed, only transformed from one form to another.
• In practical applications, both work and energy are crucial concepts in areas like mechanics, thermodynamics, and electrical systems.

 Additional Information

• Momentum
• Momentum is defined as the product of an object's mass and velocity: Momentum = Mass × Velocity.
• The SI unit of momentum is kilogram meter per second (kg·m/s).
• Momentum is a vector quantity, meaning it has both magnitude and direction.
• It plays a key role in the study of collisions in physics, governed by the law of conservation of momentum.
• Force
• Force is defined as any interaction that causes an object to undergo a change in motion or shape.
• The SI unit of force is the newton (N), which is equivalent to kg·m/s².
• Force is a vector quantity and follows Newton’s laws of motion, particularly the second law: Force = Mass × Acceleration.
• Acceleration
• Acceleration refers to the rate of change of velocity of an object with respect to time.
• The SI unit of acceleration is meter per second squared (m/s²).
• It is also a vector quantity and is central to Newton's second law of motion.

The Correct answer is Ionic compounds in solid state conduct electricity.

Key Points

• Ionic compounds consist of ions bound by strong electrostatic forces of attraction known as ionic bonds.
• In the solid state, the ions in an ionic compound are held in a fixed position within a rigid lattice structure, meaning they are not free to move.
• Since the movement of ions is required for the conduction of electricity, ionic compounds do not conduct electricity in solid state.
• However, when dissolved in water or melted into a molten state, the rigid structure breaks down, allowing free ions to move and conduct electricity.
• This property makes ionic compounds electrolytes in their aqueous or molten forms.
• The statement that "ionic compounds in solid state conduct electricity" is therefore incorrect.

 Additional Information

• Ionic compounds are solids.
• Ionic compounds typically form crystalline solids due to the strong electrostatic forces between positive and negative ions.
• These solids exhibit properties such as hardness and brittleness and are commonly found in substances like sodium chloride (NaCl).
• Ionic compounds have a high melting point.
• The strong ionic bonds between the ions in an ionic compound require a significant amount of energy to break, resulting in a high melting point.
• For example, the melting point of sodium chloride is approximately 801°C.
• Ionic compounds are generally soluble in water.
• Due to the polar nature of water, it can interact with the ions in ionic compounds and help them dissolve by breaking the ionic bonds.
• This property is why substances like sodium chloride dissolve readily in water.

The least possible venn diagram is:

Conclusions:

(I) At least some rocks are planets → True (As, All planets are rocks, then at least some rocks are planets holds true).

(II) All planets are forests → True (As, All planets are rocks and All rocks are forests, then all planets are forests holds true).

Thus, Both conclusions I and II follow.

Hence, the correct answer is "Option 1".

Shortcut Trick

Given that 94% of the total population is 22,560.

To find 100% (Total Population): (22,560 ÷ 94) × 100

⇒ 240 × 100 = 24,000

∴ The correct answer is 24,000.

Alternate Method

Given:

Percentage value = 94%

Population corresponding to 94% = 22,560

Formula Used:

Total Population = (Given Value ÷ Percentage Value) × 100

Calculations:

Let the total population be x.

⇒ 94% of x = 22,560

⇒ (94 ÷ 100) × x = 22,560

⇒ x = (22,560 × 100) ÷ 94

⇒ x = 240 × 100

⇒ x = 24,000

∴ The correct answer is 24,000.

Additional Information

Percentage to Fraction Conversion

To convert a percentage to a fraction, divide the number by 100. For example, 94% = 94/100 = 47/50.

Base Change Property

If the value of x is given as p% of the total, then Total = (x ÷ p) × 100.

Successive Percentage Change

For two successive changes of a% and b%, the net percentage change is given by [a + b + (a × b)/100] %.

The Correct answer is All the appliances are connected in parallel.

Key Points

• In domestic circuits, all the appliances are connected in parallel configuration. This arrangement ensures that each appliance gets the same voltage, which is the voltage of the main supply.
• A parallel connection allows independent operation of devices. If one appliance fails or is turned off, others continue to function without interruption.
• The total resistance in a parallel circuit is always less than the resistance of any individual branch, which allows better current distribution across the circuit.
• Heavy appliances like air conditioners (ACs), geysers, refrigerators, and light appliances like bulbs, fans, and tube lights are all connected in parallel to ensure proper functioning and efficiency.
• A parallel circuit also provides the advantage of safe operation, as the current flowing through each appliance can be controlled by its own switch.
• This configuration is in compliance with standard electrical engineering practices used in residential and commercial installations worldwide.

 Additional Information

• Heavy appliances like AC, Geyser connected in series (Incorrect Option)
• Connecting heavy appliances like AC and geysers in series would result in voltage drop across each device, leading to malfunction or reduced efficiency.
• In a series circuit, if one device fails, the entire circuit is disrupted, which is impractical for domestic use.
• Light appliances like bulbs, tube lights connected in series (Incorrect Option)
• In a series connection, if one light appliance (e.g., bulb) fails, the circuit is broken, and all other appliances will stop working. This makes it unsuitable for household applications.
• All appliances connected in series (Incorrect Option)
• Connecting all appliances in series would cause cumulative voltage drops, resulting in poor performance.
• It is also unsafe and not energy efficient for household electrical systems.

Given:

A, B, E, F, P, Q and R are sitting around a circular table facing the centre.

A sits to the immediate left of E. Only three people sit between E and Q when counted from the right of E.

Only one person sits between B and P when counted from the right of B. F sits to the immediate right of B.

Thus, Four people sit between R and E when counted from the left of R.

Hence, the correct answer is "Option 4".

The Correct answer is 1 Ampere.

Key Points

• To calculate the current flowing through the resistors, we use Ohm’s Law: V = IR, where V is the voltage, I is the current, and R is the resistance.
• Here, two resistors of 2 Ω each are connected in series. In a series connection, the total resistance is the sum of individual resistances.
• Total resistance, R = 2 Ω + 2 Ω = 4 Ω.
• The voltage of the battery is given as 4 V. Using Ohm’s Law: I = V / R.
• Substitute the values: I = 4 V / 4 Ω = 1 Ampere.
• Hence, the current flowing through the resistors is 1 Ampere.
• This result demonstrates the direct relationship between voltage, current, and resistance in a circuit as described by Ohm's Law.

 Additional Information

• Ohm’s Law
• Ohm’s Law is a fundamental principle in electronics, expressing the relationship between voltage, current, and resistance in an electric circuit.
• It is mathematically represented as V = IR, where V is the potential difference, I is the current, and R is the resistance.
• It applies to linear and passive circuits where the resistance is constant.
• Series Connection of Resistors
• In a series connection, resistors are connected end-to-end, and the same current flows through all resistors.
• The total resistance in a series circuit is the sum of the individual resistances, i.e., R_total = R₁ + R₂ + ....
• Series circuits are used in applications where the current must pass through all components, such as in string lights.
• Practical Applications of Ohm’s Law
• Ohm’s Law is widely used in designing electric circuits and for troubleshooting electrical devices.
• It helps in calculating the required resistance, current, or voltage for specific components in circuits.
• This principle is essential for understanding the functionality of devices like resistors, capacitors, and inductors in electronics.

The Correct answer is Bhabha Atomic Research Centre (BARC).

Key Points

• Bhabha Atomic Research Centre (BARC) is India's premier nuclear research facility located in Trombay, Mumbai, Maharashtra.
• It was established in 1954 and named after the renowned Indian nuclear physicist Dr. Homi Jehangir Bhabha.
• BARC conducts research in the fields of nuclear science, engineering, and technology.
• The organisation is known for its work on nuclear reactors, isotope production, radiation technology, and nuclear medicine.
• The study conducted by BARC on background radiation levels in Kerala is significant as Kerala has regions with naturally high levels of radiation, particularly due to the presence of monazite sands containing thorium.
• BARC's expertise in radiation research helps ensure safety protocols and aids in the understanding of radiation effects on humans and the environment.
• BARC collaborates with various national and international organisations for advancements in nuclear technology.

 Additional Information

• Geological Survey of India (GSI)
• The Geological Survey of India (GSI), established in 1851, is one of India's oldest organisations.
• It is primarily involved in geological research and exploration of mineral resources.
• Its headquarters are located in Kolkata, West Bengal.
• GSI contributes to studies in earth sciences and provides geological data for various applications, but it does not specialise in radiation research.
• Indian Space Research Organisation (ISRO)
• ISRO, founded in 1969, is India's national space agency headquartered in Bangalore, Karnataka.
• ISRO focuses on space exploration, satellite development, and launching systems.
• Its areas of expertise include remote sensing, space applications, and satellite communication, but it does not engage in studies on radiation levels.
• Ministry of Environment
• The Ministry of Environment, Forest and Climate Change (MoEFCC) is a central government ministry in India.
• It is responsible for environmental protection, conservation of forests, and climate change mitigation.
• While it plays a role in formulating policies related to radiation effects on the environment, it does not conduct scientific studies directly like BARC does.

Shortcut Trick

Wages are distributed in the ratio of work done (which is efficiency × time).

Since A, B, and C worked for the same 3 days, wages are shared in the ratio of their individual efficiencies.

B's share = (B's efficiency ÷ Total efficiency) × Total Amount

B's share = (1/8 × 3 ÷ 1) × 3200 is not needed, simply: B's share = (3 ÷ 8) × 3200 = 3 × 400 = ₹1,200.

∴ The correct answer is ₹1,200.

Alternate Method

Given: Time taken by A = 6 days, B = 8 days, A+B+C = 3 days. Total Wage = ₹3,200.

Formula: Efficiency = Total Work ÷ Time; Wage of a person = (Work done by person ÷ Total work) × Total Wage.

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

⇒ Efficiency of C = 8 − (4 + 3) = 1

⇒ Ratio of work done by A : B : C in 3 days = (4×3) : (3×3) : (1×3) = 12 : 9 : 3 = 4 : 3 : 1

⇒ Total ratio parts = 4 + 3 + 1 = 8 units

⇒ 8 units = ₹3,200

⇒ 1 unit = ₹400

⇒ B's share (3 units) = 3 × ₹400 = ₹1,200

∴ The correct answer is ₹1,200.

Additional Information

Work and Wages Principle

Wages are always distributed in direct proportion to the work done by each individual, not necessarily their individual time taken.

Efficiency and Wage Relationship

If all persons work for the same duration, the ratio of their wages is equal to the ratio of their efficiencies.

Pipes and Cisterns

Similar logic applies where efficiency of an outlet pipe is taken as negative, while inlet pipes are positive.

The Correct answer is Only (b) is correct.

Key Points

• The pH range of the human body is approximately 7.0 to 7.8. This range is essential for maintaining proper biological functions, as the body operates optimally within this slightly alkaline range.
• The body's buffer systems, such as the bicarbonate buffer system, help maintain this pH range to support enzyme activity, oxygen transport, and metabolic processes.
• A deviation from this pH range can result in conditions like acidosis (too acidic) or alkalosis (too alkaline), which can disrupt essential bodily functions.
• This pH range is regulated by organs like the lungs and kidneys, which play a crucial role in maintaining acid-base balance in the body.

 Additional Information

• Tooth decay in humans: pH of mouth > 5.5
• This statement is incorrect because tooth decay occurs when the pH of the mouth falls below 5.5. At this pH level, the enamel, which is primarily composed of hydroxyapatite, begins to demineralize.
• Low pH in the mouth is often caused by the presence of acidic byproducts from bacterial activity during the breakdown of sugars.
• To prevent tooth decay, it is important to maintain good oral hygiene and limit the consumption of sugary foods and drinks.
• Acid rain: pH of rainwater > 8
• This statement is incorrect because acid rain has a pH less than 5.6, not greater than 8.
• Acid rain is caused by the presence of sulfur dioxide (SO₂) and nitrogen oxides (NOₓ) in the atmosphere, which react with water to form sulfuric acid and nitric acid.
• The impacts of acid rain include damage to forests, aquatic ecosystems, and buildings, as well as harm to soil quality.

The Correct answer is Magnesium (Mg).

Key Points

• Magnesium (Mg) is the least reactive among the given options due to its position in the reactivity series of metals.
• The reactivity of metals depends on their ability to lose electrons and form positive ions. Magnesium, being higher up in the periodic table's Group 2 (alkaline earth metals), is less reactive than alkali metals like sodium (Na) and potassium (K).
• Magnesium has a higher ionization energy compared to sodium (Na) and potassium (K), which means it requires more energy to remove its outer electrons.
• Unlike sodium and potassium, which react vigorously with water, magnesium reacts slowly with water and only at higher temperatures, forming magnesium hydroxide (Mg(OH)₂) and hydrogen gas.
• In air, magnesium forms a thin layer of magnesium oxide (MgO), which provides a protective barrier, reducing its reactivity compared to more reactive metals like sodium and potassium.
• Magnesium is widely used in applications such as alloys, fireworks, and flares due to its ability to burn with a bright white flame.

 Additional Information

• Sodium (Na)
• Sodium is a highly reactive alkali metal and reacts vigorously with water to form sodium hydroxide (NaOH) and hydrogen gas.
• It is stored in oil to prevent it from reacting with moisture and oxygen in the air.
• Sodium is widely used in industries for the production of compounds like caustic soda, sodium carbonate, and sodium cyanide.
• Potassium (K)
• Potassium is even more reactive than sodium and reacts explosively with water, producing potassium hydroxide (KOH) and hydrogen gas.
• It is also stored under oil to prevent reactions with air or water.
• Potassium is essential for biological systems and is a crucial component of fertilizers.
• Calcium (Ca)
• Calcium is an alkaline earth metal and is more reactive than magnesium but less reactive than sodium and potassium.
• It reacts with water to form calcium hydroxide (Ca(OH)₂) and hydrogen gas, though the reaction is not as vigorous as with sodium or potassium.
• Calcium is widely used in construction (e.g., in the form of lime and cement) and in biological systems (e.g., for strong bones and teeth).

Shortcut Trick

Selling Price (SP) = Marked Price (MP) × (100 − Discount%) ÷ 100

SP = 100 × (100 − 25) ÷ 100

SP = 100 × 75 ÷ 100 = 75

∴ The correct answer is Rs. 75.

Alternate Method

Given: Marked Price (MP) = Rs. 100, Discount% = 25%

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

⇒ Discount = (25 ÷ 100) × 100 = Rs. 25

⇒ Selling Price (SP) = 100 − 25 = Rs. 75

∴ The correct answer is Rs. 75.

Additional Information

Marked Price (MP)

The price printed on the article or the tag is called the Marked Price or List Price.

Discount

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

The logic followed here is:

Logic: 1^st number ÷ 3 = 2^nd number.

2^nd number ÷ 5 = 3^rd number.

For (105, 35, 7)

→ 105 ÷ 3 = 35 (equal to 2^nd number)

→ 35 ÷ 5 = 7 (equal to 3^rd number)

For (135, 45, 9)

→ 135 ÷ 3 = 45 (equal to 2^nd number)

→ 45 ÷ 5 = 9 (equal to 3^rd number)

Similarly, 

Option 1) (150, 50, 10)

→ 150 ÷ 3 = 50 (equal to 2^nd number)

→ 50 ÷ 5 = 10 (equal to 3^rd number)

Hence, the correct answer is "Option 1".

Shortcut Trick For a mean proportion x between two numbers a and b, the logic is x = √(a × b). ⇒ x = √(64 × 169) ⇒ x = 8 × 13 ⇒ x = 104 ∴ The correct answer is 104. Alternate Method Given: 64 : x :: x : 169 and x > 0 Formula Used: Product of means = Product of extremes

⇒ 64 / x = x / 169 ⇒ x2 = 64 × 169 ⇒ x = √(64 × 169) ⇒ x = 8 × 13 ⇒ x = 104 ∴ The correct answer is 104. Additional Information Mean Proportion If a, b, and c are in continued proportion such that a : b :: b : c, then b is the mean proportional to a and c, given by b = √(ac). Fourth Proportional In the proportion a : b :: c : d, the term d is called the fourth proportional, calculated as d = (b × c) ÷ a. Third Proportional If a : b :: b : c, then c is called the third proportional to a and b, calculated as c = b2 ÷ a.

The Correct answer is I = Q/t.

Key Points

• The relation I = Q/t is derived from the definition of electric current.
• Electric current is defined as the rate of flow of electric charge through a conductor.
• Here, I represents the current, Q is the total electric charge, and t is the time taken for the charge to flow.
• The formula indicates that the current is directly proportional to the amount of charge and inversely proportional to the time.
• The SI unit of current is the ampere (A), charge is measured in coulombs (C), and time in seconds (s).
• This fundamental equation is widely used in various applications of electricity and electronics.
• For example, it helps in calculating the current flowing through a circuit if the charge and time are known.
• The concept is crucial for understanding topics related to Ohm's law, circuits, and power calculations in electrical engineering.

The Correct answer is By changing the amount of water in them.

Key Points

• Plants like the Mimosa pudica (commonly known as the touch-me-not plant) exhibit a phenomenon called thigmonasty, where they respond to touch by moving their leaves.
• This movement is controlled by changes in the turgor pressure within specialized cells called pulvini, located at the base of the leaves.
• When stimulated, these cells rapidly lose water, causing a reduction in turgor pressure, which leads to the folding or drooping of the leaves.
• This water movement is facilitated by the opening and closing of ion channels in cell membranes, which regulate the flow of water and ions.
• The process is energy-efficient and does not involve permanent structural changes in the plant.
• Such movements are considered a form of rapid plant defense mechanism, potentially deterring herbivores or protecting the plant from damage.
• Unlike growth movements, thigmonastic movements are reversible and occur in response to external stimuli like touch, heat, or vibration.
• Other examples of thigmonastic movements can be observed in carnivorous plants like the Venus flytrap, which closes its leaves when prey touches its trigger hairs.

 Additional Information

• By changing the amount of nucleic acid in them
• Nucleic acids like DNA and RNA are involved in genetic information storage and protein synthesis, not mechanical movements like leaf folding.
• While nucleic acids play a vital role in plant growth and development, they are not directly involved in thigmonastic movements.
• By changing the amount of protein in them
• Proteins serve as enzymes and structural components in plants, but they do not directly control the rapid movement of leaves in response to touch.
• Ion channels, which are made up of proteins, are indirectly involved, but the movement itself is primarily driven by changes in water content.
• By changing the amount of lipid in them
• Lipids are essential for maintaining cell membrane integrity and energy storage but do not play a direct role in thigmonastic movements.
• Cell membranes facilitate water and ion movement but the folding action of leaves is not dependent on lipid concentration changes.

Shortcut Trick

Assume all 50 packets were biscuits (lower cost): Total = 50 × ₹5 = ₹250.

Extra amount spent = ₹273 − ₹250 = ₹23.

Cost difference per packet = ₹6 − ₹5 = ₹1.

Number of chips packets = 23 ÷ 1 = 23 packets.

Number of biscuit packets = 50 − 23 = 27 packets.

Difference = 27 − 23 = 4 packets.

∴ The correct answer is 4.

Alternate Method

Given: Total packets = 50, Total expenditure = ₹273, Cost of Chips = ₹6, Cost of Biscuits = ₹5.

Let the number of chips packets be x and biscuit packets be y.

⇒ x + y = 50 → (Eq 1)

⇒ 6x + 5y = 273 → (Eq 2)

⇒ Multiply Eq 1 by 5: 5x + 5y = 250

⇒ Subtracting from Eq 2: (6x − 5x) = 273 − 250

⇒ x = 23 (Chips packets)

⇒ y = 50 − 23 = 27 (Biscuit packets)

⇒ Required difference = y − x = 27 − 23 = 4

∴ The correct answer is 4.

Additional Information

Alligation Method

Average cost per packet = 273 ÷ 50 = ₹5.46. Alligation ratio (Chips:Biscuits) = (5.46 − 5) : (6 − 5.46) = 0.46 : 0.54 = 23 : 27.

Linear Equation in Two Variables

General form: ax + by = c. This method is effective when total quantity and total cost are both provided.

Substitution Method

Replace one variable in terms of another: y = (Total − x) and solve 6x + 5(50 − x) = 273.

The correct answer is Both Na+ (aq) and OH- (aq) ions.

Key Points

• Sodium hydroxide (NaOH) is a strong base and dissociates completely in water.
• When NaOH is dissolved in water, it separates into its constituent ions Na+ (aq) and OH- (aq).
• The dissociation process can be expressed by the equation: NaOH (s) → Na+ (aq) + OH- (aq).
• The presence of Na+ ions contributes to the overall ionic nature, while the OH- ions make the solution strongly basic.
• This reaction is an example of a strong electrolyte, as NaOH completely ionizes in water.
• The resulting solution is highly conductive due to the abundance of free ions.
• Such reactions are integral in many applications, such as in neutralization reactions, soap manufacturing, and pH regulation.

The logic followed here is:

BEST-SBET - TSEB

And,

ROLE - LROE - ELOR

Similarly,

DIVE - VDIE - EVID

Only option 2) follow same logic.

Hence, the correct answer is "Option 2".

The correct answer is Odisha.

Key Points

• Anil Pradhan, co-founder of the Young Tinker Foundation, has been recognized for his efforts in improving education in underserved areas.
• He was awarded the Rohini Nayyar Prize for Outstanding Contribution to Rural Development in 2024.
• Anil Pradhan hails from the state of Odisha, located in eastern India.
• The Young Tinker Foundation, co-founded by Pradhan, focuses on providing innovative educational solutions for rural and underprivileged communities, promoting hands-on learning and skill development.
• Odisha, the state of his origin, is known for its rich cultural heritage, including Odissi dance, ancient temples like the Konark Sun Temple, and its diverse tribal communities.
• The award highlights Anil's significant role in addressing rural educational challenges and creating positive social impact through his initiatives.

 Additional Information

• West Bengal
• West Bengal is a state in eastern India, known for its cultural landmarks such as the Victoria Memorial and its literary figures like Rabindranath Tagore.
• The state is also recognized for its contributions to education and social reform during the colonial era.
• Although West Bengal has a history of rural development initiatives, it is not the home state of Anil Pradhan.
• Assam
• Assam is situated in northeastern India and is famous for its tea plantations and the Kaziranga National Park, a UNESCO World Heritage Site.
• It has made significant strides in rural development but is not associated with the achievements of Anil Pradhan.
• Arunachal Pradesh
• Arunachal Pradesh, located in the northeastern region of India, is known for its pristine natural beauty and indigenous tribal cultures.
• Though rural development is a focus in this state, it is not linked to the work of Anil Pradhan or the Young Tinker Foundation.

Shortcut Trick

Check the unit digit of the given numbers. A perfect square never ends in 2, 3, 7, or 8.

Option 1 (222) ends in 2 → Not a perfect square.

Check known squares of numbers near 10 and 15: 10² = 100, 14² = 196, 15² = 225.

We see that 14 × 14 = 196.

∴ The correct answer is 196.

Alternate Method

Given: A list of numbers to identify a perfect square.

Formula: A number n is a perfect square if √n is an integer.

⇒ √222 ≈ 14.89 (Not an integer)

⇒ √124 ≈ 11.13 (Not an integer)

⇒ √141 ≈ 11.87 (Not an integer)

⇒ √196 = 14 (Integer)

Since 14² = 14 × 14 = 196, it is a perfect square.

∴ The correct answer is 196.

Additional Information

Unit Digit Rule

The last digit of a perfect square must be 0, 1, 4, 5, 6, or 9. It can never be 2, 3, 7, or 8.

Digital Sum Property

The digital sum (sum of digits until a single digit is reached) of a perfect square is always 1, 4, 7, or 9.

Common Squares

11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225.

Shortcut Trick

Total Cost = Production Cost × 1.10 (as transport is 10%)

Selling Price = Total Cost × 1.15 (as profit is 15%)

Selling Price = 2000 × 1.10 × 1.15 = 2000 × 1.265

Selling Price = 2530

∴ The correct answer is ₹2,530.

Alternate Method

Given: Production Cost = ₹2,000 | Transport = 10% of Production | Profit = 15% on Total Cost

⇒ Transportation Cost = 10% of ₹2,000 = (10/100) × 2000 = ₹200

⇒ Total Cost Incurred = Production Cost + Transportation Cost = ₹2,000 + ₹200 = ₹2,200

⇒ Markup/Profit = 15% of Total Cost = (15/100) × 2200 = ₹330

⇒ Selling Price = Total Cost + Profit = ₹2,200 + ₹330 = ₹2,530

∴ The correct answer is ₹2,530.

Additional Information

Total Cost Concept

Total cost includes the factory production cost plus all overhead expenses like transportation, taxes, and labor incurred before the sale.

Successive Percentage Increase

If a value is increased by x% and then by y%, the final value is Base × (1 + x/100) × (1 + y/100).

Markup Percentage

Markup % = (Selling Price − Cost Price) ÷ Cost Price × 100. In this case, the profit acts as the markup on the final cost.

The Correct answer is Karnala Fort.

Key Points

• Karnala Fort is not included in the list of India’s 12 forts nominated for UNESCO World Heritage under the title 'Maratha Military Landscapes of India' for the year 2024-25.
• This fort is located in the Raigad district of Maharashtra and is a popular trekking destination.
• Karnala Fort is known for its historical importance during the Maratha and Mughal era, but it is not part of the specific UNESCO nomination under the Maratha Military Landscape theme.
• The fort is situated within the Karnala Bird Sanctuary, which is a protected area and a hub for biodiversity.
• While it is significant regionally, it does not meet the specific criteria or thematic focus of the nominated forts under the Maratha Military Landscapes proposal.

 Additional Information

• Raigad Fort
• Raigad Fort is one of the most iconic forts of the Maratha Empire and was the capital of Chhatrapati Shivaji Maharaj.
• It is located in the Sahyadri mountain range in Maharashtra.
• Raigad Fort is included in the UNESCO nomination due to its historical significance, architectural marvels, and importance in Maratha history.
• Salher Fort
• Salher is one of the highest forts in Maharashtra, located in the Nashik district.
• It is significant for being the site of the Battle of Salher, one of the most famous battles fought by the Marathas against the Mughals.
• This fort is part of the UNESCO nomination due to its historical military importance.
• Rajgad Fort
• Rajgad was the first capital of the Maratha Empire under Chhatrapati Shivaji Maharaj.
• It is renowned for its strategic location, architectural brilliance, and its role in Maratha history.
• This fort is included in the UNESCO nomination for its historic and cultural value.

The Correct answer is ZnO.

Key Points

• In the given chemical reaction, ZnO + C → Zn + CO, the substance that undergoes reduction is ZnO.
• Reduction refers to the process where a substance gains electrons or its oxidation state decreases.
• In this reaction, the zinc oxide (ZnO) is reduced to metallic zinc (Zn).
• The oxygen in ZnO is removed and combines with carbon (C) to form carbon monoxide (CO), leaving behind pure zinc.
• ZnO acts as the oxidizing agent because it accepts electrons and facilitates the oxidation of carbon.
• This type of reaction is commonly observed in metal extraction processes, where oxides are reduced to obtain pure metals.
• The removal of oxygen from ZnO and its conversion to metallic zinc is a classic example of a reduction reaction.

 Additional Information

• CO
• CO (Carbon Monoxide) is formed as a byproduct in this reaction when carbon reacts with the oxygen from ZnO.
• It is an oxidized product, meaning it undergoes oxidation as the carbon gains oxygen to form CO.
• CO is a colorless, odorless gas that is widely used in industrial processes like the reduction of ores in metallurgy.
• Zn
• Zn (Zinc) is the reduced form of ZnO in this reaction.
• Pure zinc is a metallic element with various applications, including galvanization, alloying, and manufacturing of batteries.
• Zinc is a transition metal and an essential trace element for biological systems.
• C
• C (Carbon) in this reaction acts as the reducing agent, meaning it donates electrons by combining with oxygen from ZnO.
• Carbon is commonly used as a reducing agent in metallurgical processes due to its strong affinity for oxygen.
• Examples of carbon as a reducing agent include its use in the extraction of iron from iron ore and zinc from zinc oxide.

The correct answer is 273.15 K.

Key Points

• 273.15 K is the melting point of ice under standard atmospheric pressure (1 atm).
• This temperature corresponds to 0°C, which is the freezing point of water in the Celsius scale.
• The Kelvin scale is an absolute temperature scale used in scientific measurements, where 0 K is absolute zero, the point at which molecular motion stops.
• The conversion between Celsius and Kelvin is straightforward: Kelvin = Celsius + 273.15.
• The melting point of ice is a critical reference point in various scientific disciplines, including physics, chemistry, and meteorology.
• At this temperature, water exists in equilibrium between the solid (ice) and liquid (water) states.
• This property is often utilized in calibration of thermometers and other temperature-measuring instruments.

 Additional Information

• 300.15 K
• 300.15 K corresponds to 27°C, which is a typical room temperature and not related to the melting point of ice.
• This temperature is often used in scientific studies as the standard for "ambient conditions."
• 373.15 K
• 373.15 K is the boiling point of water under standard atmospheric pressure (1 atm).
• This temperature corresponds to 100°C on the Celsius scale.
• The boiling point is the temperature at which water transitions from the liquid phase to the gaseous phase (steam).
• 200.15 K
• 200.15 K corresponds to -73°C, which is significantly below the freezing point of water.
• This temperature is commonly observed in extremely cold environments, such as polar regions or outer space.

The logic followed here is:

Option 1) OSN 

Option 2) EID

Option 3) IMG

Option 4) MQL

Thus, 'IMG' not follow the same logic.

Hence, the correct answer is "Option 3".

The logic followed here is:

OLQN is related to URWT

And,

LINK is related to ROTQ

Similarly,

IFKH is related to

Thus, 'OLQN' is the correct answer.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: (1^st number ÷ 2) + 10 = 2^nd number.

X : 44 :: 72 : Y

For value of X.

X : 44

→ (X ÷ 2) + 10  = 44

→ (X ÷ 2) = 44 - 10

→ X = 34 × 2

→ X = 68 

Now for value of Y.

72 : Y

→ (72 ÷ 2) + 10

→ 36 + 10

→ 46.

Thus, value of X is 68 and value of Y is 46.

Hence, the correct answer is "Option 4".

Shortcut Trick

Assume Total Work = LCM(4, 20, 2) = 20 units.

Efficiency of A = 20 ÷ 4 = 5 units/day.

Efficiency of B = 20 ÷ 20 = 1 unit/day.

Combined Efficiency (A+B+C) = 20 ÷ 2 = 10 units/day.

Efficiency of C = 10 − (5 + 1) = 4 units/day.

Time taken by C = 20 ÷ 4 = 5 days.

∴ The correct answer is 5 days.

Alternate Method

Given: Time taken by A = 4 days, B = 20 days, and A+B+C = 2 days.

Formula Used: 1/T_total = 1/T_A + 1/T_B + 1/T_C

⇒ Total Efficiency of A + B + C = 10

⇒ Efficiency of A + Efficiency of B + Efficiency of C = 10

⇒ 5 + 1 + Efficiency of C = 10

⇒ Efficiency of C = 10 − 6 = 4 units/day

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

⇒ Time taken by C = 20 ÷ 4 = 5 days

∴ The correct answer is 5 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to time taken. If the ratio of time taken is x:y, the ratio of efficiency is y:x.

Work and Wages

Wages are distributed in the ratio of the work done or the ratio of efficiencies if the individuals work for the same duration.

LCM Method

To solve work problems quickly, assume the total work as the Least Common Multiple (LCM) of the individual time periods given.

The Correct answer is Urea.

Key Points

• Urea is a waste product formed in the liver during the breakdown of proteins and amino acids.
• It is transported to the kidneys via the bloodstream for excretion.
• Unlike substances such as glucose, amino acids, and salts, urea is not selectively reabsorbed by the nephron tubules as it serves no physiological purpose in the body.
• The primary function of the kidneys is to excrete urea along with other waste products through urine.
• The concentration of urea in the urine is significantly higher than in the blood because of the selective reabsorption of other useful substances.
• Urea plays a crucial role in maintaining the body's nitrogen balance by being efficiently removed from the bloodstream.

 Additional Information

• Glucose
• Glucose is a vital source of energy for the body and is selectively reabsorbed in the proximal tubule of the nephron.
• Under normal circumstances, all glucose is reabsorbed unless the blood glucose levels exceed the renal threshold, as in cases of diabetes mellitus.
• Amino Acids
• Amino acids are essential for protein synthesis and various metabolic processes.
• They are reabsorbed in the proximal tubule of the nephron to ensure they are not lost in the urine.
• Salts
• Salts, such as sodium and chloride ions, are selectively reabsorbed by the nephron to maintain proper electrolyte balance and osmotic pressure in the body.
• The reabsorption of salts is regulated by hormones such as aldosterone to adapt to the body's needs.

The Correct answer is both potential energy and kinetic energy.

Key Points

• Mechanical energy is the sum of a body's potential energy and kinetic energy.
• Potential energy refers to the energy stored in a body due to its position or configuration. For example, a raised object has gravitational potential energy.
• Kinetic energy is the energy a body possesses due to its motion. For example, a moving car has kinetic energy.
• The total mechanical energy of a body remains constant if only conservative forces (like gravitational forces) act on it.
• The law of conservation of energy ensures that mechanical energy is transformed between potential and kinetic forms without being lost.
• This concept is widely applicable in mechanics, engineering, and physics, helping to analyze motions, systems, and forces.

 Additional Information

• Potential energy only
• Potential energy is just one component of mechanical energy, related to a body's position or configuration.
• Examples include a stretched spring or water stored in a dam.
• It does not account for the energy associated with motion, which is an essential part of mechanical energy.
• Heat energy only
• Heat energy (or thermal energy) is associated with the motion of particles within a substance and is not a component of mechanical energy.
• It is generated due to processes like friction and is often considered a form of energy loss in mechanical systems.
• Heat energy cannot be classified as mechanical energy since it is not due to position or motion.
• Kinetic energy only
• Kinetic energy is only one component of mechanical energy, representing the energy of motion.
• For example, a rolling ball has kinetic energy, but if it is at a height, it will also have potential energy, making up the total mechanical energy.
• Mechanical energy is incomplete without considering both kinetic and potential energy.

The Correct answer is Power.

Key Points

• Power is defined as the rate at which work is done or energy is transferred.
• It is mathematically expressed as Power = Work Done / Time.
• The unit of power in the SI system is the watt (W), where 1 watt equals 1 joule per second.
• In the context of machines, power measures how quickly the machine performs work.
• A machine with a higher power rating can accomplish the same amount of work in less time compared to a machine with a lower power rating.
• The concept of power is critical in fields like engineering, physics, and energy management, where efficiency and performance are essential.
• Examples of power in machines include the horsepower rating of engines or the kilowatt rating of electrical devices.

 Additional Information

• Total energy consumed
• Total energy consumed refers to the overall amount of energy used by a machine or system during its operation.
• While total energy is an important concept, it does not measure how quickly the work is done, which is why it does not determine the rate of work performed.
• Rate of change of velocity
• The rate of change of velocity is known as acceleration.
• Although acceleration is a key concept in physics, it does not directly measure the rate of work performed by a machine.
• Acceleration is more relevant to the study of motion rather than energy transfer or work done.
• Total force exerted
• Total force exerted refers to the overall force applied by or on a machine.
• Force is a component of work, but it does not account for the time factor, which is crucial in determining the rate of work.
• For example, a large force applied over a long duration might result in less power than a smaller force applied quickly.

Given:

Charlie starts from point A and drives 5 km towards the South. He then takes two simultaneous right turns and drives 3 km and 2 km, respectively. He takes a final right turn and drives 3 km to reach point B.

Thus, Charlie has to drive 3 km North to reach Point A again.

Hence, the correct answer is "Option 4".

The correct answer is Differentiation.

Key Points

• Differentiation is the biological process through which cells or tissues undergo changes in their structure and function to become specialized.
• In plants, differentiation leads to the formation of permanent tissues, which are specialized tissues that no longer divide.
• Permanent tissues arise when meristematic tissues (actively dividing cells) lose their ability to divide and develop specific roles such as support, conduction, or photosynthesis.
• Examples of permanent tissues include parenchyma, collenchyma, and sclerenchyma.
• The process of differentiation is crucial for the growth, development, and functioning of plants.
• It helps in the formation of complex plant structures like vascular bundles and plays a key role in the adaptation of plants to various environmental conditions.

 Additional Information

• Vegetative Propagation
• Vegetative propagation is a method of asexual reproduction in plants where new plants grow from vegetative parts such as roots, stems, or leaves.
• It is commonly observed in plants like potato, ginger, and strawberry.
• This process does not involve differentiation but rather the regeneration of plant parts.
• Elongation
• Elongation refers to the increase in the length of plant cells or tissues.
• This process occurs during the growth phase and is driven by factors like water absorption, cell wall loosening, and hormonal activity such as auxins.
• Elongation is a precursor to differentiation but does not directly lead to the formation of permanent tissues.
• Germination
• Germination is the process by which a seed develops into a young plant or seedling under favorable conditions.
• It involves activities like water absorption, enzyme activation, and growth of the embryonic root and shoot.
• While germination initiates the development of plant tissues, it does not involve differentiation as permanent tissues arise later in development.

The Correct answer is Union Budget 2024-25.

Key Points

• The release of 109 high-yielding and climate-resilient varieties of 32 field and horticulture crops was announced under the Union Budget 2024-25.
• This initiative aims to address the challenges posed by climate change and ensure sustainable agricultural practices.
• The high-yielding varieties are designed to help farmers achieve higher productivity even under adverse climatic conditions.
• Such resilient varieties are expected to reduce crop losses due to droughts, floods, and pest infestations.
• It also supports the government’s agenda of promoting self-reliance (Atmanirbhar Bharat) in agriculture.
• These measures align with the broader goals of enhancing food security and ensuring the welfare of farmers.
• Additionally, it reflects the government's commitment to achieving sustainable development goals (SDGs), particularly those related to zero hunger and climate action.

Shortcut Trick

Speed in km/min = 90 ÷ 60 = 1.5 km/min.

Distance = 1.5 km/min × 10 min = 15 km.

∴ The correct answer is 15 km.

Alternate Method

Given:

Speed of the train (S) = 90 km/h

Time taken (T) = 10 minutes

Formula Used:

Distance = Speed × Time

Time in hours = Minutes ÷ 60

Calculations:

⇒ Convert time into hours: T = 10 ÷ 60 = 1/6 hours

⇒ Distance = 90 × (1/6)

⇒ Distance = 15 km

∴ The correct answer is 15 km.

Additional Information

Speed Unit Conversion

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

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal distances at speeds x and y, Average Speed = 2xy/(x+y).

Relative Speed

Same direction: Subtract speeds (S₁ − S₂). Opposite direction: Add speeds (S₁ + S₂).

Given: 

(Left) 5 4 6 3 4 1 7 9 5 4 8 1 5 2 3 1 7 1 7 4 3 9 6 9 4 5 1 4 7 (Right)

Condition: Even digits which are immediately preceded by a perfect square and immediately followed by an odd digit.

Perfect Square → Even digit → Odd digit

5 4 6 3 4 1 7 9 5 4 8 1 5 2 3 1 7 1 7 4 3 9 6 9 4 5 1 4 7

Thus, there 5 such pairs ( 4 6 3, 4 8 1, 9 6 9, 9 4 5, 1 4 7)

Hence, the correct answer is "Option 1".

The Correct answer is in front of; behind.

Key Points

• The centre of curvature of a mirror is the center of the sphere of which the mirror forms a part.
• For a concave mirror, the reflecting surface curves inward, and the center of curvature lies in front of the mirror.
• In the case of a convex mirror, the reflecting surface curves outward, and the center of curvature lies behind the mirror.
• This is because the center of curvature is always located on the side of the reflecting surface.
• In a concave mirror, the reflective side faces the center of the sphere, while in a convex mirror, the reflective side faces away from the center of the sphere.
• The location of the center of curvature is crucial in determining the behavior of light rays and image formation by mirrors.
• The center of curvature is a geometrical property and remains fixed for a given mirror.

The correct answer is 300 W.

Key Points

• The formula for calculating Power is given by:

Power = Work Done / Time.

• Work done is calculated using the formula:

Work Done = Force × Distance.

• Here, the force is equal to the weight of the boy, which is 600 N, and the distance climbed is 10 m.
• Substituting the values into the formula for work done:

Work Done = 600 N × 10 m = 6000 J (Joules).

• The time taken by the boy to climb is 20 seconds.
• Now, substitute the work done and time into the power formula:

Power = 6000 J / 20 s = 300 W (Watts).

• Therefore, the power expended by the boy is 300 W.

 Additional Information

• Power
• Power is the rate at which work is done or energy is transferred over time.
• The SI unit of power is the Watt, which is equivalent to one Joule per second.
• Power is a scalar quantity and is crucial for understanding the efficiency of machines and systems.
• Work Done
• Work Done is the energy transferred when a force is applied over a distance in the direction of the force.
• The SI unit of work is the Joule, and it is calculated as:

Work Done = Force × Distance × cos(θ), where θ is the angle between force and displacement.

• Force
• Force is an interaction that changes the motion of an object or causes it to deform.
• It is measured in Newtons (N), and 1 Newton is defined as the force required to accelerate a 1 kg mass by 1 m/s².

The Correct answer is Akashteer Command and Control System.

Key Points

• The Akashteer Command and Control System has been developed to enhance the defence capabilities of the Indian Army and improve technology absorption.
• This system is specifically designed for the Indian Army's Corps of Army Air Defence, which is responsible for protecting Indian airspace from aerial threats.
• It provides real-time situational awareness, enabling effective coordination and deployment of air defence resources.
• The system integrates advanced technology to streamline decision-making processes and improve operational efficiency.
• Akashteer ensures the seamless integration of various air defence weapon systems and sensors, enhancing the overall capability of the Corps.
• It is part of the broader effort to modernize India's defence infrastructure and ensure preparedness against evolving threats.
• The system also aligns with India’s vision of becoming self-reliant in defence technology through indigenous development.

 Additional Information

• Agni Command System
• The Agni Command System is not specifically related to air defence but may refer to systems associated with the Agni missile series, which are strategic missile systems developed by India.
• Agni missiles are part of India’s nuclear deterrence program under the Strategic Forces Command.
• Prithvi Command and Control System
• The Prithvi Command and Control System is linked to the Prithvi missile series, which are tactical surface-to-surface missiles developed for the Indian Armed Forces.
• While highly significant in India’s missile arsenal, this system does not specifically cater to the Corps of Army Air Defence.
• Varunastra Control Unit
• Varunastra is an advanced heavyweight torpedo developed by India for naval operations.
• It is not related to air defence systems but is highly effective for anti-submarine warfare.
• It reflects India's capability in indigenous defence manufacturing, specifically for maritime applications.

The Correct answer is Only a and b.

Key Points

• HIV (Human Immunodeficiency Virus) is a viral infection transmitted primarily through sexual contact, sharing needles, and from mother to child during childbirth or breastfeeding.
• HIV primarily affects the body's immune system by attacking CD4 cells (T-helper cells), making the individual vulnerable to opportunistic infections.
• Genital warts, caused by certain strains of the Human Papillomavirus (HPV), are also transmitted through sexual contact.
• HPV infections can cause warts on different parts of the body, including the genital area. Some strains of HPV can lead to cervical cancer.
• Both HIV and HPV are classified as sexually transmitted viral infections.

 Additional Information

• Gonorrhoea
• Gonorrhoea is caused by the bacterium Neisseria gonorrhoeae, not a virus.
• It is a sexually transmitted bacterial infection that affects mucous membranes, including those in the genital tract, rectum, and throat.
• Symptoms include pain during urination, discharge, and pelvic pain. It can also lead to complications like infertility if untreated.
• Syphilis
• Syphilis is caused by the bacterium Treponema pallidum.
• It is also a sexually transmitted bacterial infection, not a viral infection.
• Syphilis progresses through four stages: primary, secondary, latent, and tertiary. If untreated, it can cause severe complications, including damage to the brain and heart.

The Correct answer is Bleaching powder.

Key Points

• The reaction of dry chlorine gas with calcium hydroxide (Ca(OH)₂) leads to the formation of bleaching powder.
• The chemical formula of bleaching powder is Ca(OCl)₂ (Calcium Oxychloride).
• The reaction occurs as follows:

Cl₂ + Ca(OH)₂ → Ca(OCl)₂ + H₂O

• Bleaching powder is widely used as a disinfectant and a bleaching agent.
• It is particularly effective for water purification and as a fungicide in agriculture.
• Bleaching powder is also used in the textile industry for bleaching fabrics and in the paper industry for bleaching wood pulp.
• This compound is a good source of chlorine and releases chlorine when it comes into contact with water.

 Additional Information

• Hydrochloric Acid
• Hydrochloric acid (HCl) is a strong acid formed when hydrogen chloride is dissolved in water.
• It is mainly used in the chemical industry for large-scale production of organic compounds such as vinyl chloride and dichloroethane.
• It is also used in the food industry for processing food products and in cleaning applications.
• Hydrochloric acid is not formed during the reaction of dry chlorine with Ca(OH)₂.
• Calcium Chloride
• Calcium chloride (CaCl₂) is a highly soluble salt used for de-icing roads and as a desiccant in drying processes.
• It is also used in the food industry as a firming agent and in construction to accelerate the setting of concrete.
• Although calcium chloride can be formed in some chemical reactions involving chlorine, it is not the product of the reaction between dry chlorine and Ca(OH)₂.
• Calcium Oxide
• Calcium oxide (CaO), also known as quicklime, is a widely used chemical compound in the steel, paper, and chemical industries.
• It is obtained by heating limestone (CaCO₃) and does not result from the reaction of chlorine with Ca(OH)₂.
• Calcium oxide is known for its use in neutralizing acidic soils in agriculture.

Shortcut Trick

If a sum becomes x times in T years at compound interest, it becomes xⁿ times in nT years.

The sum becomes 2 times (x = 2) in 12 years (T = 12).

To become 8 times, we need it to become 2³ times (n = 3).

Total time to become 8 times = 12 × 3 = 36 years.

More years required = Total time − Time already elapsed = 36 − 12 = 24 years.

∴ The correct answer is 24 years.

Alternate Method

Given:

A sum doubles itself (becomes 2 times the principal) in 12 years at compound interest.

Formula Used:

A = P(1 + R/100)^T

P 2P 4P 8P

0 yrs 12 yrs 24 yrs 36 yrs

×2

×2

×2

More years = 36 − 12 = 24 years

Calculations:

⇒ 2P = P(1 + R/100)¹²

⇒ 2 = (1 + R/100)¹²         (Equation 1)

We need to find the total time T for the sum to become 8 times (8P):

⇒ 8P = P(1 + R/100)^T

⇒ 8 = (1 + R/100)^T

⇒ 2³ = (1 + R/100)^T

Substituting the value of 2 from Equation 1 into the above expression:

⇒ ((1 + R/100)¹²)³ = (1 + R/100)^T

⇒ (1 + R/100)³⁶ = (1 + R/100)^T

Comparing the powers on both sides:

⇒ T = 36 years

The total time required for the principal to become 8 times is 36 years.

The question asks for the additional years required after the sum has already doubled in the first 12 years.

⇒ More years = Total time − Initial time passed

⇒ More years = 36 − 12 = 24 years

∴ The correct answer is 24 years.

Additional Information

Continuous Multiplying Factor

In Compound Interest, a principal amount grows by a constant multiplying factor over equal time intervals. For example, if it triples in 5 years, it will become 9 times in 10 years, and 27 times in 15 years.

Difference between CI and SI

For 2 years, the difference between Compound Interest and Simple Interest on a certain sum is calculated using the formula: Difference = P(R/100)².

Half-Yearly Compounding

When compound interest is compounded half-yearly, the annual rate of interest is halved (R/2) and the given time period is doubled (2T) for the calculation.

The Correct answer is 90º.

Key Points

• The force experienced by a current-carrying conductor in a magnetic field is given by the formula: F = BIL sin θ, where:
• F is the force.
• B is the magnetic field strength.
• I is the current in the conductor.
• L is the length of the conductor in the magnetic field.
• θ is the angle between the current and the magnetic field.
• The sine function (sin θ) determines the magnitude of the force. The value of sin θ is maximum when θ = 90º, which makes the force maximum.
• When the angle between the current and the magnetic field is 90º, the conductor experiences the maximum force, as sin 90º = 1.
• This phenomenon is based on the principle of the motor effect, which explains how a force is exerted on a current-carrying conductor in a magnetic field.
• This principle is widely used in the functioning of electric motors, generators, and other electromagnetic devices.
• At other angles (such as 0º, 45º, or 60º), the value of sin θ is less than 1, resulting in a smaller force.

 Additional Information

• Angle 60º
• At an angle of 60º, the value of sin θ is approximately 0.866, which results in a force that is less than the maximum force.
• Angle 0º
• When the angle is 0º, the direction of the current is parallel to the magnetic field, and the value of sin θ is 0.
• This means that no force is exerted on the conductor at this angle.
• Angle 45º
• At an angle of 45º, the value of sin θ is approximately 0.707, which results in a force that is less than the force at 90º.

The Correct answer is Fungi.

Key Points

• Fungi are primarily multicellular organisms, with some exceptions like yeast, which are unicellular.
• The majority of fungi, such as molds and mushrooms, have a complex multicellular structure consisting of thread-like structures called hyphae.
• Fungi play a vital role in the ecosystem as decomposers, breaking down dead organic matter and recycling nutrients.
• They lack chlorophyll and are classified as heterotrophic organisms, meaning they obtain their nutrients from external sources.
• Fungi can exist in various forms, including saprophytes, parasites, or symbionts (e.g., mycorrhizal fungi that form mutualistic relationships with plants).
• Examples of multicellular fungi include Mushrooms (Agaricus), Molds (Rhizopus), and Puffballs.
• Unlike unicellular organisms, fungi have specialized cells and structures, making them distinct from organisms like bacteria and protozoa.

 Additional Information

• Bacteria
• Bacteria are unicellular prokaryotic organisms that lack a nucleus and membrane-bound organelles.
• They reproduce primarily by binary fission and are found in diverse environments, including soil, water, and the human body.
• They play a crucial role in nitrogen fixation, decomposition, and fermentation.
• Examples of bacteria include E. coli, Streptococcus, and Lactobacillus.
• Paramecium
• Paramecium is a unicellular eukaryotic organism belonging to the group of protozoa.
• It is covered with cilia, which aid in movement and feeding.
• Paramecium is commonly found in freshwater environments and feeds on microorganisms like bacteria and algae.
• Chlamydomonas
• Chlamydomonas is a unicellular green alga that contains chloroplasts and can perform photosynthesis.
• It is commonly found in freshwater and damp soil.
• Chlamydomonas reproduces both sexually and asexually and serves as a model organism in biological research.

The Correct answer is Concave Mirror.

Key Points

• A concave mirror has a negative focal length because its focal point lies on the same side as the reflecting surface, which is conventionally taken as negative in the Cartesian coordinate system for optics.
• In a concave mirror, light rays that are parallel to the principal axis converge to a point (focus) after reflecting off the mirror.
• The focal length of the mirror is measured from the pole (the center of the mirror) to the focal point, and for concave mirrors, this distance is considered negative.
• Concave mirrors are widely used in applications such as reflecting telescopes, shaving mirrors, and solar furnaces due to their ability to focus light.
• They are also used in car headlights to direct light into a beam and in ophthalmology for examining eyes.
• The mirror equation (1/f = 1/v - 1/u) confirms that the focal length of a concave mirror is negative, where f is the focal length.

 Additional Information

• Plane Mirror
• A plane mirror has an infinite focal length because it does not curve, and the reflected rays do not converge or diverge to form a focus.
• Plane mirrors are commonly used in household mirrors, optical instruments, and periscopes.
• Convex Mirror
• A convex mirror has a positive focal length because its focal point lies on the opposite side of the reflecting surface, which is conventionally taken as positive.
• Convex mirrors are used in applications such as rear-view mirrors in vehicles because they provide a wider field of view.
• Both Convex and Concave
• This option is incorrect because the focal length of a convex mirror is positive, whereas the focal length of a concave mirror is negative.

The Correct answer is The blue-green colour of copper (II) chloride.

Key Points

• When dilute hydrochloric acid (HCl) is added to copper oxide (CuO), a chemical reaction occurs where the copper oxide reacts with the acid to form copper (II) chloride (CuCl₂) and water (H₂O).
• The reaction is an example of an acid-base reaction or a neutralization reaction, where the base (CuO) reacts with the acid (HCl).
• Copper (II) chloride appears as a blue-green coloured solution due to the presence of hydrated copper ions.
• This reaction can be represented as:

CuO + 2HCl → CuCl₂ + H₂O.

• The colour change from the black solid of copper oxide to the blue-green solution of copper (II) chloride is visually distinctive and confirms the formation of the product.
• Copper oxide is a basic oxide, and its reaction with hydrochloric acid demonstrates its ability to neutralize acids.
• Copper (II) chloride is widely used in applications like dyeing, printing, and as a catalyst in organic synthesis.

The Correct answer is vas deferens.

Key Points

• The vas deferens, also known as the ductus deferens, is a part of the male reproductive system responsible for transporting sperm cells.
• This tube connects the epididymis, where sperm is stored and matures, to the ejaculatory duct in the prostate gland.
• The vas deferens is a muscular tube that uses peristaltic contractions to propel the sperm forward during ejaculation.
• It is an essential structure for the proper functioning of the male reproductive system, ensuring that sperm reaches the urethra for expulsion during ejaculation.
• During a surgical procedure called vasectomy, the vas deferens is cut or blocked to prevent the transport of sperm, thus serving as a method of male contraception.
• The vas deferens also plays a role in mixing sperm with fluids from the seminal vesicles and prostate gland to form semen.

 Additional Information

• Urethra
• The urethra is a tube that carries urine from the urinary bladder to the outside of the body in both males and females.
• In males, the urethra also serves as a passage for semen during ejaculation.
• It is not directly involved in the transport of sperm from the testes to the ejaculatory duct.
• Seminal Vesicle
• The seminal vesicles are glandular structures that produce a significant portion of the fluid that makes up semen.
• They secrete a fructose-rich fluid that provides energy for sperm movement.
• However, they do not play a role in transporting sperm directly from the testes.
• Urinary Bladder
• The urinary bladder is a hollow organ responsible for storing urine until it is excreted from the body.
• It is not part of the reproductive system and does not transport sperm.