RRB Group D Previous Year Paper (Held on: 6 Sept 2022 Shift 1)

According to the given diagram:

There are 8 married girls are graduates but NOT working.

Hence, the correct answer is "Option 2".

The correct answer is ZnO is oxidised to Zn

Key Points

• ZnO acts as an oxidising agent:
• An oxidising agent is a substance that gets reduced and, in the process, causes another substance to be oxidized.
• Since ZnO is reduced to Zn in this reaction, it acts as an oxidizing agent.
• C acts as a reducing agent:
• A reducing agent is a substance that gets oxidized while causing another substance to be reduced.
• Since C is oxidized to CO, it acts as a reducing agent.
• Carbon is oxidised from an oxidation state of 0 in elemental form to +2 in CO.
• ZnO is reduced to Zn as its oxidation state decreases from +2 (in ZnO) to 0 (in elemental Zn).
• Therefore the statement ZnO is oxidised to Zn is incorrect

Additional Information​

• Oxidation Reaction​​An oxidation reaction is a chemical process where a substance loses electrons, leading to an increase in its oxidation state. This process is often accompanied by the gain of oxygen or the loss of hydrogen in a chemical reaction.

The logic followed here is:

Logic: 1^st number + 9 = 2^nd number.

Now,

For, 17 : 26

⇒ 17 + 9 = 26

For, 5 : 14

⇒ 5 + 9 = 14

Similarly, for 22 ∶ ?

⇒ 22 + 9 = 31.

Hence, the correct answer is "Option 3".

Given: > 3 ^ 1 3 & > 9 3 8 4 ! ^ 3 5 4 1 * 2 9 8 > * # 9 ! 9 6

• Numbers are there that are immediately preceded by a symbol and immediately followed by a symbol​:
• So, Needed pattern is: Symbol - Number - Symbol .

> 3 ^ 1 3 & > 9 3 8 4 ! ^ 3 5 4 1 * 2 9 8 > * # 9 ! 9 6

Clearly, there is only 'two' pairs numbers are there that are immediately preceded by a symbol and immediately followed by a symbol​.

Hence, the correct answer is "2".

Given word: 'BACKFIRE'

After arranged in reverse alphabetical order:

 

Now,

there is no alphabet that will remain unchanged if each of the letters in the word 'BACKFIRE' is arranged in reverse alphabetical order.

Hence, the correct answer is "Option 1".

The correct answer is Br2 (g)

Key Points

• The given reaction is
• 2AgBr(s) $\rm\xrightarrow{sumlight}$ 2Ag(s) + ?
• When silver bromide (AgBr) is exposed to light, it undergoes photodissociation.
• The light energy causes AgBr to break down into silver (Ag) and bromine gas (Br _22​).
• Thus the complete reaction is 
• 2AgBr(s) $\rm\xrightarrow{sumlight}$ 2Ag(s) + br₂ (g)
• Silver bromide is an ionic compound made up of silver ions (Ag +) and bromide ions (Br −).
• It is a light-sensitive material, commonly used in photographic films.

Additional Information

• Here is the full form of the Options
• Cl ​ (g) - Chlorine gas
• Br ​ (g) - Bromine gas
• H  (g) - Hydrogen gas
• CO  (g) - Carbon dioxide gas

Shortcut Trick

Direct formula for meeting distance: D = [S₁ × S₂ × Time Difference] ÷ (S₂ − S₁)

Here, S₁ = 75 km/h, S₂ = 90 km/h, and Time Difference = 16:30 − 14:30 = 2 hours.

D = [75 × 90 × 2] ÷ (90 − 75)

D = 13500 ÷ 15

D = 900 km

∴ The correct answer is 900 km.

Alternate Method

Given:

Speed of Sampark Kranti Express = 75 km/h

Departure time of Sampark Kranti = 14:30 hours

Speed of Rajdhani Express = 90 km/h

Departure time of Rajdhani = 16:30 hours

Formula Used:

Distance = Speed × Time

Relative Speed (same direction) = S₁ − S₂

Calculations:

⇒ Time difference between the departures = 16:30 − 14:30 = 2 hours.

⇒ Distance covered by Sampark Kranti Express in these 2 hours = 75 × 2 = 150 km.

⇒ This 150 km is the head start distance between the two trains.

⇒ Relative speed of Rajdhani Express with respect to Sampark Kranti = 90 − 75 = 15 km/h.

⇒ Time taken by Rajdhani Express to catch up = Distance ÷ Relative speed.

⇒ Catch up time = 150 ÷ 15 = 10 hours.

⇒ The meeting distance from Delhi = Speed of Rajdhani × Time taken.

⇒ Distance = 90 × 10 = 900 km.

∴ The correct answer is 900 km.

Additional Information

Relative Speed

When two objects move in the same direction, their relative speed is the difference of their individual speeds (S₁ − S₂). When they move in opposite directions, it is the sum of their speeds (S₁ + S₂).

Catch-up Time Formula

Time to meet = Head start distance ÷ Relative speed. This determines the duration required for the faster object to overtake the slower one.

Average Speed

When a journey covers two equal halves at different speeds S₁ and S₂, Average Speed = (2 × S₁ × S₂) ÷ (S₁ + S₂).

The logic followed here is:

Hence, the correct answer is "Option 3".

Shortcut Trick

Assume total goods = 12 units (common multiple of 3 and 4).

66(2/3)% of 12 = 8 units at +26% profit.

Remaining = 4 units. 25% of 4 = 1 unit at +20% profit.

Balance = 3 units at −40% loss.

Net Profit % = [(8 × 26) + (1 × 20) + (3 × −40)] ÷ 12 = [208 + 20 − 120] ÷ 12 = 108 ÷ 12 = 9%.

∴ The correct answer is 9.

Alternate Method

Given:

Part 1: 66(2/3)% = 2/3 of total goods sold at 26% profit.

Remaining = 1 − 2/3 = 1/3.

Part 2: 25% of remaining = 1/4 × 1/3 = 1/12 of total goods sold at 20% profit.

Part 3: Still remaining = 1/3 − 1/12 = 3/12 = 1/4 of total goods sold at 40% loss.

Calculations:

⇒ x = (2/3 × 26) + (1/12 × 20) + (1/4 × −40)

⇒ x = 52/3 + 5/3 − 10

⇒ x = (52 + 5)/3 − 10

⇒ x = 57/3 − 10

⇒ x = 19 − 10

⇒ x = 9

∴ The correct answer is 9.

Additional Information

Weighted Average Method

When parts of a whole are sold at different profit/loss percentages, the overall profit/loss is the weighted average: Overall % = (n₁p₁ + n₂p₂ + ...) / (n₁ + n₂ + ...).

Successive Discounts vs Partial Sales

Partial sales involve dividing the quantity, whereas successive discounts involve reducing the price repeatedly. Do not confuse weighted average with the formula a + b + ab/100.

Percentage to Fraction Conversion

Always use 66(2/3)% = 2/3 and 25% = 1/4 to simplify ratio-based calculations in profit and loss problems.

The correct answer is Mysore(Mysuru)

Key Points

• The Central Institute of Indian Languages (CIIL) is an Indian research and teaching institute based in Mysuru, part of the Language Bureau of the Ministry of Education.
• It was founded on 17 July 1969.
• The institution advises and Assists Central as well as State Governments in the matters of language.
• It contributes to the development of all Indian Languages by creating content and corpus.
• It protects and Documents Minor, Minority and Tribal Languages and Promotes Linguistic harmony by teaching 20 Indian languages to non-native learner

Additional Information

Shortcut Trick

Since Distance is constant, Speed is inversely proportional to Time (S ∝ 1/T).

Ratio of Time = 8 : 6 = 4 : 3

∴ Ratio of Speed = 3 : 4

Given, 3 units = 75 km/h → 1 unit = 25 km/h

New speed = 4 units = 4 × 25 = 100 km/h

∴ The correct answer is 100 km/h.

Alternate Method

Given: Initial speed (S₁) = 75 km/h, Initial time (T₁) = 8 hours, New time (T₂) = 6 hours.

Formula Used: Distance = Speed × Time

⇒ Distance = 75 × 8

⇒ Distance = 600 km

⇒ New Speed = Distance ÷ New Time

⇒ New Speed = 600 ÷ 6

⇒ New Speed = 100 km/h

∴ The correct answer is 100 km/h.

Additional Information

Speed-Time Inverse Relation

When distance is constant, the product of speed and time remains the same (S₁T₁ = S₂T₂). This is useful for solving comparison problems without finding distance.

Average Speed

For two equal distances covered at speeds a and b, the average speed is given by (2ab) ÷ (a + b).

Relative Speed

If two objects move in the same direction, relative speed is |S₁ − S₂|. In opposite directions, it is (S₁ + S₂).

The correct answer is the Ministry of Home Affairs

Key Points

• The Criminal Procedure (Identification) Bill 2022 was introduced in Lok Sabha on March 28, 2022 by Shri Ajay Kumar, , in the Ministry of Home Affairs.
• It was introduced in the Indian Parliament to address certain deficiencies in the existing laws related to the identification of individuals involved in criminal activities.
• The bill expands the methods of identification beyond traditional fingerprinting. It allows the collection of biometric data, including:
• Fingerprints
• Photographs
• Iris scans
• Other biological samples or measurements
• The bill seeks to amend the Identification of Prisoners Act, of 1920, which primarily dealt with the identification of convicted individuals.
• The Ministry of Home Affairs is responsible for implementing this bill, coordinating with state and union territory governments to ensure that the necessary infrastructure is in place for the collection and management of biometric data.

The correct answer is i-b, ii-a,iii-c

Key Points

• Lemon:
• Contains citric acid.
• Nettle sting:
• Contains methanoic acid (also known as formic acid), which is responsible for the stinging sensation.
• Tomato:
• Contains oxalic acid in smaller amounts.
• So the correct matching is

• Thus, the correct matches are:  i - b, ii - a, iii - c

The correct answer is b.

Key Points

• The part labeled 'b' in the phloem tissue is known as the sieve tube element.
• Sieve tube elements are characterized by their perforated walls, known as sieve plates, which facilitate the transport of nutrients.
• The main function of sieve tube elements is to transport organic substances, such as sugars, throughout the plant.
• Sieve plates are crucial for maintaining the flow of phloem sap between adjacent sieve tube elements.

Additional Information

• Phloem Tissue:
• Phloem is one of the two types of vascular tissue in plants, the other being xylem.
• It is responsible for the transport of organic nutrients, particularly sucrose, from the leaves to other parts of the plant.
• Sieve Tube Elements:
• Sieve tube elements are specialized cells that form long tubes for the transportation of phloem sap.
• They lack a nucleus and have fewer organelles to facilitate the easy flow of sap.
• Sieve Plates:
• Sieve plates are the end walls of sieve tube elements that are perforated to allow the flow of sap between cells.
• They play a critical role in maintaining the continuity of the phloem transport system.
• Companion Cells:
• Companion cells are closely associated with sieve tube elements and aid in their function.
• They provide metabolic support and help in the loading and unloading of sugars into the sieve tubes.

The correct answer is 10

Key Points

• The 42^nd Amendment Act of 1976 added 10 Fundamental Duties to the Indian Constitution.
• The duties were added to promote a sense of patriotism and responsibility among citizens
• They are listed in Article 51A of Part IV-A of the Constitution
• They are non-justiciable, meaning they cannot be enforced by law.
• The amendment was brought in during the emergency period and was a response to the perceived breakdown of civic sense and morality in the country.
• The Fundamental Duties are a set of moral obligations that are expected of every citizen of India, and they were added to the Constitution to promote national unity and a sense of responsibility among citizens.

The correct answer is that They may intersect each other.

Key Points

• The statement "They may intersect each other" is not true about indifference curves between two goods.
• Indifference curves cannot intersect each other because it would break down the indifference curve analysis
• Indifference curves graphically represent the different levels of consumer satisfaction at each commodity bundle.
• The slope of Indifference curves is downward sloping.
• Higher indifference curves (IC) mean higher satisfaction levels.

Shortcut Trick

Volume ratio of Original to Smaller sphere is 27 ∶ 1.

Radius ratio R ∶ r = √³27 ∶ √³1 = 3 ∶ 1.

Surface Area ratio of Original to 6 Smaller spheres = R² ∶ 6 × r².

Ratio = 3² ∶ 6 × 1² = 9 ∶ 6 = 3 ∶ 2.

∴ The correct answer is 3 ∶ 2.

Alternate Method

Given:

Radius of original sphere (R) = 12 cm

Number of identical smaller spheres (n) = 27

Formula Used:

Volume of sphere = (4/3) × π × radius³

Surface Area of sphere = 4 × π × radius²

Calculations:

⇒ Volume of Original Sphere = 27 × Volume of Smaller Sphere

⇒ (4/3) × π × (12)³ = 27 × (4/3) × π × r³

⇒ 1728 = 27 × r³

⇒ r³ = 1728 ÷ 27 = 64

⇒ r = 4 cm

⇒ Surface Area of Original Sphere (S₁) = 4 × π × (12)² = 576π

⇒ Surface Area of 6 Smaller Spheres (S₂) = 6 × (4 × π × 4²) = 6 × 64π = 384π

⇒ Required Ratio = S₁ ∶ S₂ = 576π ∶ 384π

⇒ Ratio = 576 ∶ 384 = 3 ∶ 2

∴ The correct answer is 3 ∶ 2.

Additional Information

Volume and Surface Area Relationship

When a solid is melted and recast, the Total Volume remains constant. Volume = (4/3)πr³.

Radius and Area Ratio Rule

If the ratio of radii of two spheres is a ∶ b, then the ratio of their surface areas is a² ∶ b².

Hemisphere Properties

For a hemisphere of radius r, Curved Surface Area = 2πr² and Total Surface Area = 3πr².

Given numbers: 224, 637, 816, 471, 303

If we add 5 to each of the following numbers, we get

229, 642, 821, 476, 308

Then write the digits in each number in reverse order:

922, 246, 128, 674, 803

Then arrange the numbers in ascending order:

128, 246, 674, 803, 922

The position of One numbers will NOT change that number is 246.

Hence, 'One' is the correct answer.

Shortcut Trick

Put A = 45° in the given expression.

(sin 45° + cosec 45°)² + (cos 45° + sec 45°)² = (1/√2 + √2)² + (1/√2 + √2)²

⇒ (3/√2)² + (3/√2)² = 9/2 + 9/2 = 9.

Check options at A = 45°: Option (3) is 5 + cosec² 45° + sec² 45° = 5 + 2 + 2 = 9.

∴ The correct answer is 5 + cosec² A + sec² A.

Alternate Method

Given: (sin A + cosec A)² + (cos A + sec A)²

Formula Used: (a + b)² = a² + b² + 2ab; sin A × cosec A = 1; cos A × sec A = 1; sin² A + cos² A = 1

⇒ (sin² A + cosec² A + 2 sin A cosec A) + (cos² A + sec² A + 2 cos A sec A)

⇒ sin² A + cosec² A + 2(1) + cos² A + sec² A + 2(1)

⇒ (sin² A + cos² A) + cosec² A + sec² A + 2 + 2

⇒ 1 + cosec² A + sec² A + 4

⇒ 5 + cosec² A + sec² A

∴ The correct answer is 5 + cosec² A + sec² A.

Additional Information

Trigonometric Identities

Fundamental identities: sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Reciprocal Relations

Reciprocal products: sin θ × cosec θ = 1, cos θ × sec θ = 1, and tan θ × cot θ = 1.

The correct answer is Suktas

Key Points 

• Rigveda
• It is an ancient Indian collection of Vedic Sanskrit hymns.
• It is the oldest known Vedic Sanskrit text.
• It is one of the four sacred canonical texts of Hinduism.
• It contains 1028 hymns which are arranged in 10 mandalas.
• The sum of the hymns in Rigveda is in the form of Dialogue.
• Hymns of the Rigveda are known as Sukta.

Additional Information

• Janas: Refers to early Vedic tribes or communities in ancient India, led by kings or chieftains (rajas), which formed the basis of Vedic social organization.
• Rudras: A group of deities in Vedic tradition, often associated with storms, wind, and destruction. Rudra, a fierce aspect of Shiva, is the leader of these deities.
• Rituals: In Vedic culture, rituals were central to religious practices, involving sacrifices (yajnas) performed to honor gods, maintain cosmic order, and seek blessings for prosperity and success.

The correct answer is v1 > v2 > v3

Key Points

• The refractive index (n) of a medium is related to the speed of light (v) in that medium by the formula:
• n = c / v
• where c is the speed of light in a vacuum
• Therefore, we can write the following equations for the given mediums:
• 1.31 = c / v1
• 1.36 = c / v2
• 1.44 = c / v3
• From these equations, we can deduce that:
• v1 > v2 > v3
• This means that the speed of light is greatest in medium 1 and smallest in medium 3.
• So, the correct relation between the speeds of light in the three mediums is:v1 > v2 > v3

The correct answer is Kerala

Key Points

• The Painkuni Festival is celebrated in Kerala, India
• The festival takes place at the Sree Padmanabha Swamy Temple in Thiruvananthapuram, Kerala
• The festival is celebrated in March or April
• The festival is a 10-day celebration
• The festival is closely associated with the Royal Family of Travancore

Additional InformationSome festivals of given options 

Shortcut Trick

Factorize all polynomials: x⁴ − 8x = x(x − 2)(x² + 2x + 4) and 2x² + 5x − 3 = (2x − 1)(x + 3).

Substitute and cancel common terms: P = [x(x−2)(x²+2x+4) / (2x−1)(x+3)] × [(2x−1) / (x²+2x+4)] × [(x+3)(x−3) / x(x−2)].

After cancellation of all common factors, the simplified value is P = x − 3.

Calculate the final expression: P² − 1 = (x − 3)² − 1 = x² − 6x + 9 − 1 = x² − 6x + 8.

∴ The correct answer is x² − 6x + 8.

Alternate Method

Given:

P = [ (x⁴ − 8x) / (2x² + 5x − 3) ] × [ (2x − 1) / (x² + 2x + 4) ] × [ (x² − 9) / (x² − 2x) ]

Formula Used:

1. a³ − b³ = (a − b)(a² + ab + b²)
2. a² − b² = (a − b)(a + b)
3. (a − b)² = a² − 2ab + b²

Calculations:

⇒ Factorizing Term 1: x⁴ − 8x = x(x³ − 8) = x(x − 2)(x² + 2x + 4)

⇒ Factorizing Denominator of Term 1: 2x² + 5x − 3 = 2x² + 6x − x − 3 = 2x(x + 3) − 1(x + 3) = (2x − 1)(x + 3)

⇒ Factorizing Term 3: x² − 9 = (x − 3)(x + 3) and x² − 2x = x(x − 2)

⇒ P = [ x(x − 2)(x² + 2x + 4) / ((2x − 1)(x + 3)) ] × [ (2x − 1) / (x² + 2x + 4) ] × [ (x − 3)(x + 3) / (x(x − 2)) ]

⇒ Cancelling common factors: P = x − 3

⇒ P² − 1 = (x − 3)² − 1

⇒ P² − 1 = (x² − 6x + 9) − 1

⇒ P² − 1 = x² − 6x + 8

∴ The correct answer is x² − 6x + 8.

Additional Information

Cubic Identity Factorization

The identity a³ − b³ = (a − b)(a² + ab + b²) is frequently used to simplify rational expressions involving higher-degree polynomials.

Quadratic Polynomial Simplification

A quadratic expression ax² + bx + c can be factored into two linear factors by finding two numbers whose sum is b and whose product is ac.

Difference of Squares

The property a² − b² = (a − b)(a + b) is a fundamental tool for reducing the complexity of algebraic fractions before multiplication or division.

The correct answer is a is the reproductive part, whereas b is the vegetative part.

Key Points

• a represents the sporangium, which is the reproductive structure in Rhizopus.
• The sporangium contains spores, which are released for reproduction.
• b represents the hyphae, which are the vegetative parts of Rhizopus.
• Hyphae are responsible for nutrient absorption and growth of the fungus.

Additional Information

• Rhizopus
• Rhizopus is a genus of common fungi that grows on organic substances like bread, fruits, and vegetables.
• They are known for their fast-growing nature and are often referred to as bread molds.
• Rhizopus species play a significant role in decomposition and nutrient cycling in ecosystems.
• Sporangium
• The sporangium is a structure found in fungi, algae, and some plants, which produces and contains spores.
• In Rhizopus, the sporangium is the reproductive organ that releases spores to propagate the fungus.
• Hyphae
• Hyphae are the long, thread-like structures that make up the body of a fungus.
• They form a network called mycelium, which is involved in nutrient absorption and growth.
• Spores
• Spores are reproductive units in fungi, capable of developing into a new individual without sexual fusion.
• They are usually resistant to adverse environmental conditions and can remain dormant until conditions are favorable for growth.

The correct answer is Iron ore.

Key Points

• The Ballary-Chitradurga-Chikmagalur-Tumkur belt located in Karnataka is renowned for its vast reserves of iron ore.
• It is considered one of the major iron ore belts in India, contributing significantly to the country's iron and steel industry.
• The Kudremukh mines, located in the Western Ghats of Karnataka, are entirely focused on exports.
• A pipeline carries the ore in a slurry form to a port close to Mangalore.
• One of the three main iron ore belts is the one that runs through Odisha and Jharkhand.
• The other two are the Bellary-Chitradurga-Chikmagalur-Tumkur belt and the Durg-Bastar Chandrapur belt.
• The Odisha-Jharkhand belt's Badampahar mines produce high-grade hematite ore.

Additional Information

• Manganese ore can be found in the districts of Balaghat, Chhindwara, and Jhabua in Madhya Pradesh, in Nagpur and Bhandara in Maharashtra and Sundargarh, Koraput, and Ganjam in Odisha.
• The major copper mines are the Khetri copper belt in Rajasthan, Singhbhum copper belt in Jharkhand and Malanjkhand copper belt in Madhya Pradesh which are mined by HCL.
• Singhbhum belt is mined by M/s Indian Copper Complex.
• Titanium Sponge Plant of India is located at Kerala Minerals and Metals Ltd (KMML), Chavara, Kollam district of Kerala.

The correct answer is 5 cm

Key Points

• When a ray of light is incident on a concave mirror parallel to its principal axis, after reflection it passes through the focus of the mirror.
• For a concave mirror, the relationship between focal length (f) and radius of curvature (R) is:
• f = R/2
• Here, R = 10 cm is given.
• Therefore, f = 10 cm / 2 = 5 cm
• Hence, the reflected ray will pass through a point on the axis at a distance of 5 cm from the mirror.

The correct answer is Maintenance costs is very high

Key Points

• The disadvantage of watershed management among the given options is Maintenance cost is very high.
• While watershed management offers numerous benefits, such as mitigating droughts and floods, increasing the life of downstream dams and reservoirs,
• and Increasing the income of the watershed community, it also involves significant maintenance costs.
• These costs can arise from activities like:
• Infrastructure maintenance: Repairing and maintaining dams, canals, and other structures within the watershed.
• Reforestation and afforestation: Planting trees to improve soil erosion control and water retention.
• Monitoring and evaluation: Tracking the effectiveness of watershed management practices and making necessary adjustments.
• These maintenance costs can be substantial, especially in large or complex watersheds.
• Therefore, while watershed management is a valuable approach to sustainable resource management,
• it is important to consider the associated costs and ensure adequate funding is available for long-term maintenance.

Given: A certain number of people are sitting in a row, facing north.

S is seventh to the right of L.

K is third to the right of J.

L is third to the right of K.

If no other person is sitting in the row.

There are 14 total number of persons seated.

Hence, the correct answer is "Option 4".

The correct answer is Social Justice and Empowerment

Key Points

• The National Backward Classes Finance & Development Corporation (NBCFDC) is a Government of India undertaking under the aegis of the Ministry of Social Justice and Empowerment
• The Ministry is responsible for promoting the welfare and empowerment of socially disadvantaged groups, including backward classes, Scheduled Castes, and Scheduled Tribes.
• This  Ministry implements various schemes and programs to address the socio-economic challenges faced by these communities, such as education, employment, and housing.

Additional Information

• Ministry of Micro, Small and Medium Enterprises
• The Ministry is responsible for promoting the growth and development of micro, small, and medium enterprises (MSMEs) in India.
• The Ministry provides financial assistance, technology support, and market access to MSMEs, thereby contributing to job creation and economic growth.
• Ministry of Tribal Affairs
• The Ministry is responsible for the welfare and development of tribal communities in India.
• The Ministry implements various schemes and programs to address the unique challenges faced by tribal communities, such as education, healthcare, and infrastructure development.
• Ministry of Rural Development
• The Ministry is responsible for promoting the development of rural areas in India.
• The Ministry implements various schemes and programs to improve rural infrastructure, agriculture, and livelihoods, thereby reducing poverty and inequality.

The correct answer is Bardoli

Key Points

• Bardoli is the taluka in Gujarat where Vallabhbhai Patel led the peasant movement against the enhancement of land revenue in 1928.
• Th is movement, known as the Bardoli Satyagraha, was a significant milestone in India's struggle for independence.
• Due to the flood, ignoring the plight of the farmers, the Bombay Presidency increased the tax rates by 22%, resulting in the Bardoli Satyagraha.
• In January 1928, farmers in Bardoli invited Vallabhai Patel to launch a protest movement, in which they all took a pledge not to pay taxes.
• A large number of women took an active part in the movement.
• It was these women who gave Patel the nickname Sardar.
• The movement focused on the conditions of the rich and middle-class farmers and largely neglected the poor farmers.

Additional Information

• Vallabhbhai Patel
• Vallabhbhai Patel, known as the "Iron Man of India," was a prominent Indian statesman and freedom fighter.
• He played a crucial role in uniting India after independence.
• He negotiated with hundreds of princely states, persuading most of them to join the Indian Union.
• He was a dedicated follower of Mahatma Gandhi and participated in several civil disobedience movements against British rule.
• His leadership in the Kheda and Bardoli satyagrahas demonstrated his courage and commitment to the Indian independence struggle.

Given:

Grams = 25 g

Formula used:

Kilograms = Grams / 1000

Calculations:

Kilograms = 25 g / 1000

⇒ Kilograms = 25 / 1000

⇒ Kilograms = 1 / 40

∴ 25 grams = 1/40 kilograms

The correct answer is 24 March.

Key Points 

• World TB Day is celebrated every year on 24 March annually to commemorate the date when Dr. Robert Koch announced his discovery of Mycobacterium tuberculosis, the bacillus that causes TB in 1882.
• This Day is observed to educate people about TB, its impact around the world.
• The theme of World TB Day 2022 - 'Invest to End TB. Save Lives.'

Additional Information 

• List of Important Days/Events in March:​

Given: (Left) S 3 & H P W 8 # J * M 2 F A 2 Y 1 V (Right)

Now, 

Symbols, which are immediately preceded by a letter and also immediately followed by a number

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

(Left) S $ 3 & H P W 8 # J * M 2 F A 2 $ Y 1 V (Right)

There are 1 Symbols which are preceded by a letter and also immediately followed by a number.

Hence, the correct answer is 'Option 3'.

Shortcut Trick

For a mixed recurring decimal like 4.56767..., keep the integer 4 aside.

Fraction part = (Entire non-repeating and repeating digits − Non-repeating digits) ÷ (9 for each repeating digit followed by 0 for each non-repeating decimal digit).

Fraction = (567 − 5) ÷ 990 = 562 ÷ 990.

Simplify 562 ÷ 990 by dividing by 2 → 281 ÷ 495.

∴ The correct answer is 4(281/495).

Alternate Method

Given: x = 4.5676767...

Method: Multiply by powers of 10 to isolate the period and subtract.

⇒ 1000x − 10x = 4567.6767... − 45.6767...

⇒ 990x = 4522

⇒ x = 4522 ÷ 990

⇒ x = 2261 ÷ 495

⇒ Converting to mixed fraction: 4522 ÷ 990 = 4 + 562/990

⇒ x = 4(281/495)

∴ The correct answer is 4(281/495).

Additional Information

Pure Recurring Decimal

A decimal in which all the figures after the decimal point are repeated. Example: 0.666... = 6/9 = 2/3.

Mixed Recurring Decimal

A decimal in which at least one figure after the decimal point is not repeated and some figures are repeated. Example: 0.1666... = (16−1)/90 = 15/90 = 1/6.

Rational Number Property

Every terminating or recurring decimal can be expressed in the form p/q and is therefore a rational number.

The logic followed here is:

Hence, the correct answer is "Option 2".

The logic followed here is:

UPR : YTV

LZB : PDF

Similarly,

MKN : QOR

Hence, the correct answer is "Option 4".

The correct answer is it damages the cilia in the upper respiratory tract

Key Points

• Cigarette smoke contains harmful chemicals that damage the cilia, tiny hair-like structures in the upper respiratory tract.
• These cilia help to clear mucus and debris from the lungs.
• When damaged, the cilia become less effective, leading to increased mucus buildup and potential respiratory infections.
• The harmful effects of cigarette smoking on the cilia in the upper respiratory tract:
• Cilia impairment: The chemicals in cigarette smoke, such as tar and nicotine, can damage or paralyze the cilia.
• Mucus buildup: With impaired cilia, mucus can accumulate in the lungs, creating a breeding ground for bacteria and other harmful microorganisms.
• Increased risk of infections: The buildup of mucus can lead to respiratory infections like bronchitis and pneumonia.
• Chronic obstructive pulmonary disease (COPD): Long-term damage to the cilia and lungs can contribute to COPD, a serious lung disease characterized by difficulty breathing.

Shortcut Trick

Subtract the remainders from the numbers: 7072 − 22 = 7050, 8505 − 45 = 8460, 9925 − 55 = 9870.

Find the HCF of 7050, 8460, and 9870.

The differences between the numbers are 1410 and 1410.

The HCF x = 1410.

Sum of digits of 1410 = 1 + 4 + 1 + 0 = 6.

∴ The correct answer is 6.

Alternate Method

Given: Numbers are 7072, 8505, 9925 and remainders are 22, 45, 55.

Formula: Greatest number x = HCF of (N₁−R₁, N₂−R₂, N₃−R₃)

⇒ Required numbers: (7072 − 22) = 7050; (8505 − 45) = 8460; (9925 − 55) = 9870

⇒ Finding differences between consecutive numbers: (8460 − 7050) = 1410 and (9870 − 8460) = 1410

⇒ Since 1410 divides all three numbers, HCF (x) = 1410

⇒ Sum of digits of x = 1 + 4 + 1 + 0 = 6

∴ The correct answer is 6.

Additional Information

HCF of Numbers with Remainders

To find the greatest number that divides several numbers leaving specific remainders, always subtract each remainder from its respective number first, then calculate the HCF.

HCF by Difference Method

The HCF of two or more numbers is either the difference between the numbers or a factor of that difference.

Common Remainder Property

If the remainder is the same in each case (but unknown), the greatest number is the HCF of the differences (N₂−N₁), (N₃−N₂), and (N₃−N₁).

The correct answer is Mango

Key Points 

• Vegetative propagation:
• This is a type of asexual reproduction where new plants grow from the vegetative parts (like stem, root, leaf) of a plant.
• Mango, grape, sugarcane, and rose:
• ​ All these plants can reproduce through vegetative propagation.
• For example, mango can be propagated by grafting, grape by cuttings, sugarcane by stem cuttings, and rose by cuttings.
• Mango:
• ​ Mango is primarily grown from seeds. Although mango trees can be propagated by grafting, it's not a widely used method.
• Therefore, out of the given options, mango is the plant that does not primarily reproduce through vegetative propagation.

Additional Information

• Grape: Grapes can be easily propagated by cutting a vine and planting it.
• Sugarcane: Sugarcane stem cuttings can be planted to grow new plants.
• Rose: Rose cuttings can be planted in soil to produce new plants.

Shortcut Trick For Scheme (A), Net Discount = 12 + 15 − (12 × 15) ÷ 100 = 25.2%. For Scheme (B), Net Discount = 15 + 10 + 2 − (150 + 20 + 30) ÷ 100 + (15 × 10 × 2) ÷ 10000 = 25.03%. For Scheme (C), total discount on 10 toys = (40% × 3 + 15% × 7) ÷ 10 = (120 + 105) ÷ 10 = 22.5%. For Scheme (D), Net Discount = (Free items ÷ Total items) × 100 = (2 ÷ 12) × 100 = 16.67%. Comparing all values: 25.2% > 25.03% > 22.5% > 16.67%. ∴ The correct answer is (A).

Alternate Method Given → Marked Price (MP) of 1 toy = 100 | Total toys to buy = 10. Formulas: Successive Discount = a + b − (ab ÷ 100) | Net Discount% = (Total Discount ÷ Total MP) × 100.

⇒ Scheme A: 12 + 15 − (12 × 15 ÷ 100) = 27 − 1.8 = 25.2%. ⇒ Scheme B: 15 + 10 − 1.5 = 23.5%; then 23.5 + 2 − (23.5 × 2 ÷ 100) = 25.5 − 0.47 = 25.03%. ⇒ Scheme C: (3 × 40 + 7 × 15) = 120 + 105 = 225 total units. Discount % = 225 ÷ (10 × 100) × 100 = 22.5%. ⇒ Scheme D: Buy 10 get 2 free means 12 toys for price of 10. Discount % = (2 ÷ 12) × 100 = 16.67%. ⇒ Scheme (A) provides the maximum discount. ∴ The correct answer is (A).

Additional Information Successive Discounts When multiple discounts are applied, the final price is lower than the sum of individual percentages. Formula: 100 − [100 × (1 − d1/100) × (1 − d2/100) ...] Free Item Calculation Discount % = [Free Articles ÷ Total Articles (Paid + Free)] × 100.

Shortcut Trick

Change in Consumption = MPC × Change in Income.

Given MPC = 0.5 and ΔIncome = ₹500.

ΔConsumption = 0.5 × 500 = 250.

∴ The correct answer is ₹250.

Alternate Method

Given → Marginal Propensity to Consume (MPC) = 0.5, Increase in Income (ΔY) = ₹500. Formulas: MPC = ΔC ÷ ΔY | ΔC = MPC × ΔY

Steps: ⇒ We know that MPC represents the ratio of change in consumption to the change in income. ⇒ ΔC = MPC × ΔY ⇒ ΔC = 0.5 × 500 ⇒ ΔC = 250

∴ The correct answer is ₹250.

Additional Information

Marginal Propensity to Consume (MPC)

It measures the proportion of an aggregate raise in pay that a consumer spends on the consumption of goods and services. Formula: MPC = ΔC / ΔY.

Marginal Propensity to Save (MPS)

It is the fraction of an increase in income that is not spent and instead used for saving. MPC + MPS = 1.

The correct answer is Lord Ripon

Key Points

• Lord Ripon is known in India as the father of local self-government.
• He is known as the father of local self-government because he passed a resolution of local self-government which laid the democratic forms of municipal governance in India in 1882.
• The Municipal Institutions that had grown up in the country since the British Crown occupied India developed his local self-government scheme.
• He was the viceroy and Governor-General of India.

Additional Information

• Lord Warren Hastings (1773-1785):
• First Governor-General of Bengal, overseeing the early consolidation of British rule in India.
• He Reformed the judicial system by setting up civil and criminal courts (diwani and faujdari courts).
• Faced impeachment in Britain for alleged corruption but was acquitted after a long trial.
• Lord Canning (1856-1862):
• The last Governor-General and the first Viceroy of India after the Government of India Act, 1858.
• He Managed the aftermath of the Revolt of 1857, known for his policy of clemency toward rebels.
• He Introduced significant reforms, including the Indian Penal Code and the foundation of modern civil service.
• Lord Cornwallis (1786-1793):
• He Introduced the Permanent Settlement of Bengal in 1793, fixing land revenue and granting landlords hereditary rights.
• He is Reformed the administration and judiciary, introducing the Cornwallis Code, which professionalized civil services.
• He Played a significant role in the Third Anglo-Mysore War against Tipu Sultan, leading to British victories in southern India.

Shortcut Trick

Area of Rectangle = Area of Circle

77 × 50 = (22/7) × r²

r² = (77 × 50 × 7) / 22 = (7 × 50 × 7) / 2 = 7 × 25 × 7 ⇒ r = 7 × 5 = 35 m

Perimeter (Circumference) = 2 × (22/7) × 35 = 2 × 22 × 5 = 220 m

∴ The correct answer is 220 m.

Alternate Method

Given: Length (l) = 77 m, Breadth (b) = 50 m

Formula Used: Area of rectangle = l × b; Area of circle = πr²; Circumference = 2πr

⇒ Area of Rectangle = 77 × 50 = 3850 m²

⇒ Area of Circle = πr² = 3850

⇒ (22/7) × r² = 3850

⇒ r² = (3850 × 7) ÷ 22

⇒ r² = 175 × 7 = 1225

⇒ r = √1225 = 35 m

⇒ Perimeter of Circle = 2 × (22/7) × 35

⇒ Perimeter = 2 × 22 × 5 = 220 m

∴ The correct answer is 220 m.

Additional Information

Area and Perimeter of a Rectangle

The Area is l × b and the Perimeter is 2(l + b). The diagonal is √(l² + b²).

Circle Properties

For a circle with radius r, Area = πr² and Circumference = 2πr. Diameter (d) = 2r.

Standard Ratios for Circle

If r = 7, then Circumference = 44 and Area = 154. Scaling the radius by k scales Area by k² and Circumference by k.

The correct answer is an increase in their atomic masses

Key Points

• Dobereiner arranged elements in triads based on the observation that the atomic mass of the middle element in a triad was approximately
• the average of the atomic masses of the other two elements.
• This arrangement implies that the elements within a triad were arranged in order of increasing atomic masses.
• He called these groups of three elements "triads."
• Examples of Dobereiner's Triads:
• Chlorine (35.5), Bromine (79.9), Iodine (126.9): The atomic mass of bromine (79.9) is approximately the average of chlorine (35.5) and iodine (126.9).
• Lithium (6.9), Sodium (23), Potassium (39.1): The atomic mass of sodium (23) is approximately the average of lithium (6.9) and potassium (39.1).

The Correct answer is erect, 1.0 cm.

Key Points

• The problem involves a convex mirror, where the focal length (f) is given as 8 cm, and the object distance (u) is -24 cm (negative as it is placed in front of the mirror).
• The mirror formula is used to determine the image distance (v): $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
• Substituting the values: $\frac{1}{8} = \frac{1}{v} + \frac{1}{-24}$
• Solving for v: v = 6 cm
• The image distance is positive, indicating that the image is formed on the same side as the reflecting surface, characteristic of a convex mirror.
• The magnification (m) is calculated using the formula: m = v/u
• Substituting the values: $m = \frac{6}{-24} = -\frac{1}{4}$
• The negative sign of magnification indicates that the image is erect.
• The height of the image is determined using the magnification: $Image \space height = Magnification \times Object\space height$
• Substituting the values: $Image \space height = \frac{1}{4} × 4.0 \space cm = 1.0 \space cm$
• Hence, the image formed is erect and has a height of 1.0 cm.

Additional Information

• Convex mirrors
• Convex mirrors always form virtual, erect, and diminished images, irrespective of the object’s position.
• They are commonly used in vehicle rearview mirrors as they provide a wider field of view.
• Mirror formula
• The mirror formula is applicable for all spherical mirrors and is expressed as: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$, where:
• f is the focal length,
• v is the image distance, and
• u is the object distance.
• Magnification
• Magnification (m) is the ratio of the image height to the object height and is also related to the object and image distances as:$m=\frac{v}{u}$
• A positive magnification indicates an erect image, while a negative magnification indicates an inverted image.

The correct answer is 2022

Key Points

• The 15^th edition of the Indian Premier League (IPL) was played in the year 2022.
• It featured eight teams competing for the title.
• Gujarat Titans emerged as the champions for the first time, defeating Rajasthan Royals in the final.

Additional Information

• The Indian Premier League (IPL) is a professional Twenty20 cricket league in India.
• It was founded in 2008 and is considered one of the most popular and valuable sports leagues in the world.
• The IPL is a franchise-based league, meaning that teams are owned by private companies.
• This model has contributed to the league's commercial success.
• Players are selected for teams through an auction system.

The correct answer is 3

Key Points

• The number of field lines drawn inside a solenoid is proportional to the magnetic field strength within it.
• The magnetic field strength of a solenoid is directly proportional to the product of its number of turns and the current flowing through it.
• Given that the current in both solenoids is the same, the magnetic field strength is directly proportional to the number of turns.
• Since the number of field lines drawn inside solenoid P is thrice that drawn inside solenoid Q,
• the magnetic field strength in P is also thrice that in Q.
• Therefore, the number of turns in solenoid P is 3 times the number of turns in solenoid Q.

Shortcut Trick

Simple Interest (SI) = Amount − Principal = 9,250 − 7,500 = ₹1,750

SI per year = 1,750 ÷ 7 = ₹250

Rate % = (SI per year ÷ Principal) × 100

Rate % = (250 ÷ 7,500) × 100 = 250 ÷ 75 = 10/3 = 3(1/3)%

∴ The correct answer is 3(1/3)%.

Alternate Method

Given:

Principal (P) = ₹7,500

Amount (A) = ₹9,250

Time (T) = 7 years

Formula Used:

SI = (P × R × T) / 100

Amount = P + SI

Calculations:

⇒ SI = Amount − Principal

⇒ SI = 9,250 − 7,500 = 1,750

⇒ 1,750 = (7,500 × R × 7) / 100

⇒ 1,750 = 75 × R × 7

⇒ 1,750 = 525 × R

⇒ R = 1,750 / 525

⇒ R = 70 / 21 (Dividing by 25)

⇒ R = 10 / 3 (Dividing by 7)

⇒ R = 3(1/3)%

∴ The correct answer is 3(1/3)%.

Additional Information

Simple Interest Formula

SI is calculated only on the Principal amount: SI = (P × R × T) / 100, where P is Principal, R is Rate, and T is Time.

Relationship between Amount and SI

The total Amount (A) received at the end of the period is the sum of Principal and Interest: A = P × [1 + (RT/100)].

Principal Formula

To find the Principal when Amount, Rate, and Time are given: P = (100 × A) / (100 + RT).

The correct answer is Decomposers

Key Points

• Decomposers are the group of organisms that break down dead and decaying organisms
• Decomposers break down dead organisms into simpler substances, releasing nutrients and carbon into the soil.
• These nutrients are then used by primary producers and plants.
• Bacteria and fungi are examples of decomposers
• Decomposers play a vital role in the flow of energy through an ecosystem.
• They make up the largest population in the food chain.

Additional Information

• Consumers:
• Organisms that cannot produce their own food and rely on other organisms for nutrition.
• Examples: Herbivores (eat plants), carnivores (eat animals), omnivores (eat both plants and animals).
• Producers:
• Organisms that can produce their own food through photosynthesis or chemosynthesis.
• Examples: Plants, algae, bacteria.
• Scavengers:
• Organisms that consume dead or decaying organic matter.
• Examples: Vultures, hyenas, crows.

Shortcut Trick

For two numbers a and b, the third proportional is given by b² ÷ a.

Given: a = 18 and b = 72.

Calculation: (72 × 72) ÷ 18 ⇒ 4 × 72 = 288.

∴ The correct answer is 288.

Alternate Method

Given: First number (a) = 18, Second number (b) = 72.

Formula Used: If x is the third proportional to a and b, then a : b :: b : x.

⇒ 18 / 72 = 72 / x

⇒ 1 / 4 = 72 / x

⇒ x = 72 × 4

⇒ x = 288

∴ The correct answer is 288.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Fourth Proportional

If a, b, and c are three numbers, the fourth proportional x is such that a : b = c : x, meaning x = (b × c) ÷ a.

Continued Proportion

Three numbers a, b, and c are in continued proportion if a/b = b/c, which implies b² = ac.

The correct answer is ₹1 lakh to ₹2 lakh

Key Points

• As of March 2022, Pradhan Mantri Jan Dhan Account holders were entitled to an accidental insurance cover ranging from ₹1 lakh to ₹2 lakh .
• The PMJDY scheme provides free accidental insurance coverage to all account holders.
• This cover is designed to provide financial support to the family of the account holder in the event of an accidental death or permanent total disability.
• The accidental insurance coverage is linked to the RuPay debit card issued to PMJDY account holders.
• The card must be used for at least one transaction (financial or non-financial) in the preceding 90 days to be eligible for the insurance.
• The coverage amount varies depending on the type of PMJDY account and the premium paid.
• While the basic coverage was ₹1 lakh, some account holders may have been eligible for higher coverage amounts.

Shortcut Trick

Speed in m/s = 36 × (5/18) = 10 m/s.

Length of train = Speed × Time = 10 × 80 = 800 m.

∴ The correct answer is 800 metres.

Alternate Method

Given:

Time taken to cross the pole = 80 seconds

Speed of the train = 36 km/h

Formula Used:

Distance = Speed × Time

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

Calculations:

⇒ Speed = 36 × (5/18) m/s

⇒ Speed = 2 × 5 = 10 m/s

⇒ Distance (Length of train) = Speed × Time

⇒ Length = 10 m/s × 80 s

⇒ Length = 800 metres

∴ The correct answer is 800 metres.

Additional Information

Unit Conversion

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

Train Crossing Stationary Object

When a train crosses a point object (pole, man, tree), the distance covered is equal to the length of the train.

Train Crossing Platform

When a train crosses a platform or bridge, the total distance covered = Length of train + Length of platform.

Shortcut Trick

A straight angle is an angle that forms a straight line. By definition, the measure of a straight angle is exactly 180º. It is equivalent to two right angles (90º + 90º).

∴ The correct answer is 180º.

Alternate Method

Given: Angle type = Straight Angle.

Definition: A straight angle is an angle whose measure is exactly 180 degrees. It represents a half-rotation around a point.

⇒ Measure of a right angle = 90º

⇒ Measure of a straight angle = 2 × right angle

⇒ Straight angle = 2 × 90º = 180º

∴ The correct answer is 180º.

Additional Information

Types of Angles

Acute Angle: Measures between 0º and 90º. Obtuse Angle: Measures between 90º and 180º.

Reflex and Complete Angles

Reflex Angle: Measures between 180º and 360º. Complete Angle: Measures exactly 360º.

The logic followed here is:

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

Now,

For, 11 : 132

⇒ (11 + 1) × 11 = 12 × 11 = 132.

For, 12 : 156

⇒ (12 + 1) × 12 = 13 × 12 = 156.

Similarly, for 13 : ?

⇒ (13 + 1) × 13 = 14 × 13 = 182.

Hence, the correct answer is "Option 1".

Shortcut Trick

Apply Cross-Multiplication Method on Income and Expenditure ratios.

Income (7 : 5) and Expenditure (17 : 12) with savings (12000, 9000).

(7 × 12) − (5 × 17) units = (17 × 9000) − (12 × 12000)

|84 − 85| units = |153000 − 144000| ⇒ 1 unit = ₹9,000

Income of Seema = 7 × 9000 = ₹63,000; Darshan = 5 × 9000 = ₹45,000

Total Expenditure = (63000 − 12000) + (45000 − 9000) = 51000 + 36000 = ₹87,000

∴ The correct answer is ₹87,000.

Alternate Method

Given: Ratio of Income = 7 : 5, Savings = ₹12,000 and ₹9,000, Ratio of Expenditure = 17 : 12.

Formula Used: Income − Savings = Expenditure

⇒ Let the incomes be 7x and 5x.

⇒ (7x − 12000) / (5x − 9000) = 17 / 12

⇒ 12(7x − 12000) = 17(5x − 9000)

⇒ 84x − 144000 = 85x − 153000

⇒ x = 153000 − 144000 = 9000

⇒ Seema Expenditure = 7(9000) − 12000 = 51000

⇒ Darshan Expenditure = 5(9000) − 9000 = 36000

⇒ Total Expenditure = 51000 + 36000 = 87000

∴ The correct answer is ₹87,000.

Additional Information

Income-Expenditure Relationship

The fundamental relation is Income = Expenditure + Savings. Ratio problems can be solved by assuming a variable for either income or expenditure.

Cross-Multiplication Technique

Used when two ratios and the absolute changes (savings/additions) are given: (a:b) → (c:d) with changes m and n, then 1 unit = |dm − bn| / |ad − bc|.

Ratio Balancing

If savings were equal, the difference between ratio parts of income and expenditure could be equated by multiplying the ratios by the difference of the other ratio.

The correct answer is Anthracite - Lowest grade of hard coal

Key Points

• Anthracite - Lowest grade of hard coal
• ​Anthracite is actually the highest grade of hard coal, not the lowest.
• It has the highest carbon content and the lowest amount of volatile matter, making it the most efficient coal for burning.
• It is primarily used for heating and cooking due to its high heat output and clean burning properties.

Additional Information

• Bituminous coal is the most popular coal in commercial use due to its versatility and high energy content.
• Metallurgical coal is used for smelting iron in blast furnaces because it has a high carbon content and low sulfur content, which are essential for the iron-making process.
• Lignite is a low-grade brown coal with a high moisture content and low heat content.

Given: A, B, C, D, E, F, G and H.

1. D is sitting at one of the corners.

2. H was sitting to the immediate left of D.

3) Only A was sitting between G and D.

4) B was sitting second to the right of G.

5) C was sitting fourth to the left of G.

6) Only E was sitting between B and C.

Final arrangement:

So, F was sitting third to the right of D.

Hence, the correct answer is "Option 4".

The correct answer is Only(b)

Key Points

• The angle of refraction at surface AB is the same for different colours of white light.
• This statement is incorrect.
• When white light passes through a refracting surface like AB of a prism,
• the different colours (wavelengths) of light bend by different amounts due to their different refractive indices in the glass.
• This is the phenomenon of dispersion.
• Since the refractive index depends on the wavelength, each colour will have a different angle of refraction.
• The angle of refraction at the surface AC is different for different colours.
• This statement is correct.
• As light exits through surface AC, the different colours of light will refract at different angles
• because they travel through the prism at different speeds (due to different refractive indices for different wavelengths).
• This results in different angles of refraction for each colour, which is why a spectrum of colours emerges from the prism.

The correct answer is Goalkeeper

Key Points

• Sreejesh P.R. played a crucial role as the Goalkeeper for the Indian men's hockey team during the Tokyo Olympics in 2021.
• His remarkable saves, especially in the bronze medal match against Germany, were instrumental in securing India's first Olympic hockey medal in 41 years.
• The goalkeeper is the last line of defence in hockey.
• Their primary responsibility is to prevent the opposing team from scoring by blocking shots directed at the goal.
• Unlike other players, the goalkeeper is allowed to use any part of their body, including hands, feet, and stick, to stop the ball within the shooting circle.

Additional Information

• Defender:
• Defenders primarily focus on preventing the opposing team from scoring.
• They play in the backline, protecting the goal and trying to intercept or block attacks.
• They also help in building up play from the back by passing the ball to midfielders or forwards.
• Tackling, positioning, marking opponents, and clearing the ball from dangerous areas.
• Forward:
• Forwards are the main attackers who are responsible for scoring goals.
• They play near the opponent's goal and work on creating scoring opportunities by dribbling, passing, and shooting the ball.
• Speed, dribbling, positioning, finishing (shooting), and quick decision-making.
• Midfielder:
• Midfielders play a versatile role, linking both the defense and the attack.
• They are involved in both defending and creating opportunities for forwards.
• Midfielders need to control the game, distribute the ball, and support both offensive and defensive plays.
• Passing, ball control, stamina, positioning, and vision to make key plays.

Given Equation: [{(19 × 12) - (2 ÷ 4)} + (2 - 3)] ÷ 2

BODMAS Rule:

Decoding the given information:

 

Now replacing the symbols from left to right using BODMAS Rule, we get:

⇒ [{(19 - 12)} + (2 × 4)] ÷ (2 + 3)] × 2

⇒ [{(7)} + (8)] ÷ (2 + 3)] × 2

⇒ [7 + 8] ÷ 5 × 2

⇒ 15 ÷ 5 × 2

⇒ 3 × 2 = 6.

Hence, the correct option is "Option 1".

Shortcut Trick

Average age of 6 children = 42 ÷ 6 = 7 years.

Since the ages are in Arithmetic Progression with a common difference of 2, the average lies exactly between the 3^rd and 4^th child.

Age of 3^rd child = 7 − 1 = 6 years | Age of 4^th child = 7 + 1 = 8 years.

Age of 6^th (eldest) child = 8 + (2 × 2) = 12 years.

∴ The correct answer is 12 years.

Alternate Method

Given: Sum of 6 children = 42, Interval = 2 years.

Let the age of the youngest child be x.

⇒ Ages are: x, (x + 2), (x + 4), (x + 6), (x + 8), (x + 10).

⇒ Sum = x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) = 42

⇒ 6x + 30 = 42

⇒ 6x = 42 − 30

⇒ 6x = 12

⇒ x = 2 years

⇒ Eldest child age = x + 10 = 2 + 10 = 12 years.

∴ The correct answer is 12 years.

Additional Information

Arithmetic Progression (AP) in Ages

When values are at equal intervals, the sum is given by S_n = n/2 × [2a + (n−1)d]. Here n=6, d=2, and S_n=42.

Middle Term Concept

For an even number of terms in AP, the average is the mean of the two middle terms. Average = Total Sum ÷ Number of terms.

Given statements:

All paintings are arts

Some walls are doors

Some paintings are windows

The least possible diagram:

Conclusions:

(I) Some arts are walls - False (Because, there is no relation between arts and walls, so it can be possible only)

(II) Some arts are windows - True (Because, All paintings are arts and Some paintings are windows implies that Some arts are windows)

(III) Some paintings are doors - False (Because, there is no relation between paintings and doors, so it can be possible only)

So, Only conclusion II follows.

Hence, the correct answer is "Option 3".

Given: Seven people, A, B, C, D, E, F and G.

Only three people sit between G and F.

Only two people sit to the left of G.

B is not an immediate neighbour of F.

B sits second to the right of D.

C sits to the immediate right of E.

Thus, A sits at the extreme left end of the row.

Hence, the correct answer is "Option 1".

The correct answer is i - c, ii - b, iii - a

Key Points

• The correct matches are:

• | Functional Group | Compound Type | | --- | --- | | i)-COOH | Carboxylic c)acid | | ii)R-CO-R | b)Ketone | | iii)-COOR | a)Ester |

• Carboxylic acid:

• This functional group consists of a carbonyl group (C=O) attached to a hydroxyl group (-OH).

• Carboxylic acids are organic compounds that often have acidic properties.

• Ketone:

• ​ This functional group also contains a carbonyl group (C=O), but it is located within a carbon chain, not at the end.

• Ketones are often used as solvents or flavoring agents.

• Ester:

• ​ This functional group is formed by the reaction between a carboxylic acid and an alcohol.

• Esters are often found in natural oils and fats, and they are used as flavorings and fragrances.

The logic followed here is:

Given Sequence: S L _ _ G S _ _ N G _ _ A N G

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) L A N A L S → S L L A G / S N A N G / L S A N G

Option 2) A N L A S L → S L A N G / S L A N G / S L A N G

Here, 'S L A N G' followed a pattern.

Option 3) A L N A S L → S L A L G / S N A N G / S L A N G

Option 4) A L A N L S → S L A L G / S A N N G / L S A N G

Hence, the correct answer is "Option 2".

The correct answer is dry and hot winds

Key Points

• The Loo is a strong, dry, and hot wind that blows over the plains of North India, especially during the summer months (April to June).
• It typically occurs during the afternoon and can cause severe heat waves, with temperatures often exceeding 45°C.
• The Loo is dangerous as it can cause heatstroke and dehydration if one is exposed to it for long periods.

Additional Information

• Types of Winds:
• Primary Winds (or Planetary Winds):
• Trade Winds:
• These winds blow from the subtropical high-pressure areas towards the equatorial low-pressure belt.
• In both hemispheres, they move from east to west between 30° latitude and the equator.
• Westerlies:
• These winds blow from the subtropical high-pressure areas towards the subpolar low-pressure areas, generally from the west.
• They dominate the middle latitudes between 30° and 60°.
• Polar Easterlies: These are cold winds that blow from the polar high-pressure areas towards the subpolar low-pressure areas, moving from east to west.
• Secondary Winds (or Periodic Winds):
• Monsoons:
• Monsoons are seasonal winds, characterized by the reversal of wind direction.
• In India, the Southwest Monsoon brings heavy rainfall during the summer, while the Northeast Monsoon brings dry weather in the winter.
• Land and Sea Breezes:
• These are diurnal (day-night) winds.
• Land breezes blow from the land to the sea at night, and sea breezes blow from the sea to the land during the day due to differences in heating between land and water.
• Tertiary Winds (or Local Winds):
• Loo: As mentioned above, the Loo is a hot, dry wind blowing across northern India.
• Chinook: A warm, dry wind that blows down the eastern slopes of the Rockies in North America, causing rapid temperature increases.
• Mistral: A cold, dry wind blowing from the northwest towards the Mediterranean in southern France.
• Föhn: A warm wind blowing down the northern slopes of the Alps.

The correct answer is 1 - c, 2 - a, 3 - b

Key Points

• The correct matches are:

• | Category | Number of Elements | | --- | --- | | Total number of elements found | 118 | | Naturally available elements | 94 | | Elements found through laboratory processes | 24 |

• Total number of elements found: As of October 2024, there are 118 elements recognized by the International Union of Pure and Applied Chemistry (IUPAC).

• Naturally available elements: Out of the 118 elements, 94 are found naturally on Earth or in astronomical spectra.

• Elements found through laboratory processes: The remaining 24 elements are heavier and not found naturally. These elements have been synthesized in laboratories or nuclear reactors.

Shortcut Trick

Check the common difference for divisors 24 and 32: 24 − 11 = 13 and 32 − 19 = 13.

Find LCM of (24, 32) = 96. General form: 96k − 13.

Also, the number must satisfy (N − 2) is divisible by 15 and N is divisible by 31.

Testing k = 25 ⇒ N = 96 × 25 − 13 = 2400 − 13 = 2387.

Check: 2387 ÷ 31 = 77 (Rem = 0) and 2387 ÷ 15 (Rem = 2). Both satisfy.

∴ The correct answer is 2380 and 2390.

Alternate Method

Given:

Divisors: 15, 24, 32, 31

Remainders: 2, 11, 19, 0

Calculations:

⇒ Let the number be N.

⇒ N = 24a + 11 ⇒ N = 24(a + 1) − 13

⇒ N = 32b + 19 ⇒ N = 32(b + 1) − 13

⇒ Common Difference = Divisor − Remainder = 24 − 11 = 13 and 32 − 19 = 13.

⇒ N must be of form: LCM(24, 32) × k − 13 = 96k − 13.

⇒ Condition 1: (96k − 13) ÷ 31 ⇒ Remainder = (3k − 13) ÷ 31. For Rem = 0, 3k − 13 = 0, 31, 62...

⇒ 3k = 13 + 62 = 75 ⇒ k = 25.

⇒ Condition 2: (96k − 13) ÷ 15 ⇒ Remainder = (6k − 13) ÷ 15. For k = 25:

⇒ (6 × 25 − 13) = 150 − 13 = 137. 137 ÷ 15 gives Remainder = 2. (Condition satisfied).

⇒ N = 96 × 25 − 13 = 2400 − 13 = 2387.

∴ The correct answer is 2380 and 2390.

Additional Information

LCM and Remainder Theorem

When a number leaves the same negative remainder (Divisor − Remainder = constant d), the number is LCM(divisors) × k − d.

Divisibility Rules

A number N is divisible by 31 if the result of subtracting three times the last digit from the rest is divisible by 31.

Common Remainder Property

If N = a×q₁ + r and N = b×q₂ + r, then N = LCM(a, b) × k + r.

Shortcut Trick

Value of a = 50 and b = 20.

Directly calculate the cubes of given numbers.

a³ = 50³ = 1,25,000

b³ = 20³ = 8,000

a³ + b³ = 1,25,000 + 8,000 = 1,33,000.

∴ The correct answer is 1,33,000.

Alternate Method

Given:

⇒ a = 50

⇒ b = 20

Formula Used:

⇒ a³ + b³ = (a + b)(a² − ab + b²)

Calculations:

⇒ a + b = 50 + 20 = 70

⇒ a² = 50 × 50 = 2,500

⇒ b² = 20 × 20 = 400

⇒ ab = 50 × 20 = 1,000

⇒ (a² − ab + b²) = 2,500 − 1,000 + 400 = 1,900

⇒ a³ + b³ = 70 × 1,900

⇒ a³ + b³ = 1,33,000

∴ The correct answer is 1,33,000.

Additional Information

Sum of Cubes Formula

a³ + b³ = (a + b)(a² − ab + b²). This is a basic algebraic identity used for factorisation.

Difference of Cubes Formula

a³ − b³ = (a − b)(a² + ab + b²). Note the change in signs of b and the product ab.

Whole Cube Expansion

(a + b)³ = a³ + b³ + 3ab(a + b). This can be rearranged to find the sum of individual cubes.

Given:

[89 - ($\frac{{336}}{{301}}$) × {68 - (50 ÷ 3 + $\frac{7}{6}$)} + 67]

Calculation:

[89 - ($\frac{{336}}{{301}}$) × {68 - (50 ÷ 3 + $\frac{7}{6}$)} + 67]

⇒  [89 - ($\frac{{336}}{{301}}$) × {68 - ($\frac{50}{3}$ + $\frac{7}{6}$)} + 67]

⇒  [89 - ($\frac{{336}}{{301}}$) × {68 - ($\frac{100}{6}$ + $\frac{7}{6}$)} + 67]

⇒  [89 - ($\frac{{336}}{{301}}$) × {68 - ($\frac{107}{6}$)} + 67]

⇒  [89 - ($\frac{{336}}{{301}}$) × {$\frac{408}{6}$ - $\frac{107}{6}$} + 67]

⇒  [89 - ($\frac{{336}}{{301}}$) × {$\frac{301}{6}$} + 67]

⇒ 89 - 56 + 67

⇒ 156 - 56 = 100

∴ The correct answer is 100.

The correct answer is ($\frac{9}{4}$) R

Key Points

• The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.
• We can use the formula:  
• ​$R = ρL/A$
• where:
• R is the resistance
• ρ is the resistivity of the material
• L is the length of the wire
• A is the cross-sectional area of the wire
• Therefore, the new resistance is:
• $R' = ρ(1.5L) / (2/3A) = (9/4)ρL/A = (9/4)R$
• If the length of the wire increases by 50%, the new length becomes 1.5L.
• Since the volume of the wire remains constant, the cross-sectional area must decrease by a factor of 2/3 to maintain the same volume.
• Therefore, the new resistance is:
• $R' = ρ(1.5L) / (2/3A) = (9/4)ρL/A = (9/4)R$
• So, the resistance of the new wire is (9/4) times the resistance of the original wire.

Given:

Fund spent on security = 70 crores

Fund spent on education = 30 crores

Fund spent on health = 60 crores

Calculation:

Difference between the funds spent on security and education = 70 - 30

⇒ 40 crores

The sum of the ‘difference between the funds spent on security and education and the funds spent on health,

⇒  40 + 60 = 100 crores

∴ The correct answer is 100 crores.

According to the given information:

1. C lives on floor number 5.

2. B lives on an odd numbered floor but not an floor number 3.

3. Neither D nor E lives on the lowermost floor.

4. A lives on an odd numbered floor and is immediately above D.

 

So, E lives on floor number 2.

Hence, the correct answer is "Option 3".

The correct answer is Uniform

Key Points

• A solenoid produces a uniform magnetic field inside it.
• This means that the magnetic field strength is the same at all points within the solenoid, regardless of the distance from the centre.
• This uniformity is due to the way the magnetic field lines are arranged within the solenoid.
• The field lines are parallel to each other and run the length of the solenoid.
• This creates a consistent magnetic field throughout the interior space.

Additional Information

• The magnetic field inside a long solenoid is uniform for several reasons related to the structure and operation of the solenoid:
• Even Distribution of Turns: In a solenoid, the wire is wound evenly around a cylindrical form, creating a series of loops or turns that are distributed along the length of the solenoid. This even distribution of turns ensures that, at every point inside the solenoid (except near the ends), there is an equal contribution to the magnetic field from each coil of wire.
• Parallel Magnetic Field Lines: Due to the shape and arrangement of the coils, the magnetic field lines inside the solenoid are nearly parallel to each other and to the longitudinal axis of the solenoid. This parallelism results from the superposition of the magnetic fields produced by each turn of the solenoid, with the directional components perpendicular to the axis canceling out and only the components along the axis adding up. This creates a uniform direction and magnitude of the magnetic field in the central region of the solenoid.
• Negligible Edge Effects: In a long solenoid, the effects that disrupt uniformity, such as the fringing of the magnetic field, are significant only near the ends of the solenoid. In the central region, these effects are negligible, contributing to the uniformity of the magnetic field.

Shortcut Trick

Assume Base Average = 20

Net Deviation = [31 × (26 − 20)] + [41 × (56 − 20)]

⇒ Net Deviation = (31 × 6) + (41 × 36) = 186 + 1476 = 1662

Total Students = 25 + 31 + 41 = 97

Actual Average = 20 + (1662 ÷ 97) ≈ 20 + 17.13 = 37.13

∴ The correct answer is 37.13.

Alternate Method

Given:

Number of students (n₁, n₂, n₃) = 25, 31, 41

Average marks (A₁, A₂, A₃) = 20, 26, 56

Formula Used:

Combined Average = (n₁A₁ + n₂A₂ + n₃A₃) ÷ (n₁ + n₂ + n₃)

Calculations:

⇒ Total Marks = (25 × 20) + (31 × 26) + (41 × 56)

⇒ Total Marks = 500 + 806 + 2296

⇒ Total Marks = 3602

⇒ Total Students = 25 + 31 + 41 = 97

⇒ Average = 3602 ÷ 97

⇒ Average ≈ 37.134...

∴ The correct answer is 37.13.

Additional Information

Weighted Average Formula

Weighted Average = (∑ w_ix_i) ÷ (∑ w_i), where w_i represents weights (number of students) and x_i represents values (marks).

Deviation Method for Averages

Actual Average = Assumed Average + (Net Deviation ÷ Total Count). This simplifies large multiplications by focusing on differences from a central value.

Rounding Off Rule

If the third decimal digit is 5 or more, round up the second digit; if less than 5, keep it as is. Here, 37.134 rounds down to 37.13.

The correct answer is Potential difference across each resistor is equal.

Key Points

• In a parallel circuit, the potential difference (V) across each resistor is the same, regardless of their resistance values.
• This is due to the nature of parallel connections, where each component is directly connected across the power source.
• Therefore, the correct statement is that the potential difference across each resistor (3 Ω, 2 Ω, and 6 Ω) is equal.
• The formula for voltage in parallel circuits is V = IR, where I is current and R is resistance, but here, the key is that V remains constant across all resistors.