RRB Group D Previous Year Paper (Held on: 30 Aug 2022 Shift 1)

Shortcut Trick

Surface Area = 4 × π × r²

r² = (Total Surface Area) ÷ (4 × π)

r² = (14872/7) × (1/4) × (7/22) = 14872 ÷ 88 = 169

r = √169 = 13 cm

∴ The correct answer is 13 cm.

Alternate Method

Given:

Surface Area (S) = $2124\frac{4}{7}$ cm² = (2124 × 7 + 4) ÷ 7 = 14872 ÷ 7 cm²

π = $\frac{22}{7}$

Formula Used:

Surface Area of Sphere = 4πr²

Calculations:

⇒ 4 × (22/7) × r² = 14872/7

⇒ 88/7 × r² = 14872/7

⇒ 88 × r² = 14872

⇒ r² = 14872 ÷ 88

⇒ r² = 169

⇒ r = √169

⇒ r = 13 cm

∴ The correct answer is 13 cm.

Additional Information

Volume of a Sphere

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

Hemisphere Properties

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

Ratio of Surface Area to Volume

For a sphere, the ratio of Surface Area (S) to Volume (V) is S/V = 3/r.

The correct answer is Rajasthan

Key Points

• Rajasthan was the first state in India to adopt the Panchayati Raj system on 2nd October 1959.
• The Panchayati Raj system was inaugurated by the then Prime Minister of India, Pt. Jawaharlal Nehru, at Nagaur in Rajasthan.
• The system aims to decentralize power and governance to the grassroots level, ensuring local self-governance.
• The adoption of the Panchayati Raj system marked a significant step towards democratic decentralization in India.

Additional Information

• The Panchayati Raj system is a three-tier structure consisting of the Gram Panchayat (village level), Panchayat Samiti (block level), and Zila Parishad (district level).
• The system was introduced based on the recommendations of the Balwant Rai Mehta Committee, which was set up in 1957.
• The 73rd Constitutional Amendment Act of 1992 provided constitutional status to the Panchayati Raj institutions, making them a mandatory feature of rural governance in India.
• The amendment also aimed to enhance the participation of women and marginalized sections of society in the decision-making process at the local level.

Shortcut Trick

Identify the highest common factor first to reduce numbers: 84, 105, 140 are all multiples of 7.

Numbers reduced: 12, 15, 20.

LCM of (12, 15, 20) is 60.

Final LCM = 60 × 7 = 420.

∴ The correct answer is 420.

Alternate Method

Given: Numbers are 84, 105, and 140.

Method: Prime Factorization Method

⇒ 84 = 2² × 3 × 7

⇒ 105 = 3 × 5 × 7

⇒ 140 = 2² × 5 × 7

⇒ LCM = 2² × 3 × 5 × 7

⇒ LCM = 4 × 3 × 5 × 7 = 420

∴ The correct answer is 420.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by each of the given numbers.

HCF and LCM Relation

For two numbers a and b, Product of numbers (a × b) = HCF(a, b) × LCM(a, b).

LCM of Fractions

LCM of fractions = (LCM of Numerators) ÷ (HCF of Denominators).

Given Statement: Recent marketing trends suggest that words like 'premium', ‘exquisite', 'priority' are considered prestigious by consumers of the middle income group and hence increase the chances of sale of any product advertised with these words.

Now, 

Assumptions:

1. The products advertised with the said 'prestigious' words definitely cost higher than those which are not advertised with such words - Not Implicit (The statement does not provide information regarding the cost of the products. It only talks about the perception of these words by the middle income group and their effect on sales.) 2. Such prestigious words have no impact on sales among the lower income group - Not Implicit (The statement only discusses the impact on the middle income group and does not provide information about the lower income group.)

Here, Neither assumption I nor II is implicit.

Hence, the correct answer is "Option 4".

The correct answer is 1

Key Points

• The valency of group 17 elements is 1.
• Group 17 elements are also known as halogens and include fluorine, chlorine, bromine, iodine, and astatine.
• These elements have seven electrons in their outermost shell and require one more electron to achieve a stable octet configuration.
• Due to this, the valency of halogens is typically 1, as they tend to gain one electron during chemical reactions.

Additional Information

• The halogens are highly reactive, especially with alkali metals and alkaline earth metals, forming salts.
• These elements are found in various states at room temperature: fluorine and chlorine are gases, bromine is a liquid, and iodine and astatine are solids.
• The reactivity of halogens decreases down the group, with fluorine being the most reactive and astatine the least.
• Halogens have significant applications in daily life, including disinfection, pharmaceuticals, and the production of various chemicals.

Shortcut Trick

Present Ratio (Father : Sum of Sons) = 1.5 : 1 → 3 : 2

After 6 years, let the age of the Father be F + 6 and Sum of Sons be S + 12 (since there are 2 sons).

Ratio after 6 years = 6 : 5

Using the present ratio 3x : 2x ⇒ (3x + 6) / (2x + 12) = 6 / 5

15x + 30 = 12x + 72 ⇒ 3x = 42

∴ The correct answer is 42 years.

Alternate Method

Given:

Present Age of Father = 1.5 × (Sum of Sons' ages)

Ratio after 6 years = 6 : 5

⇒ Let the present sum of ages of two sons be S.

⇒ Present age of Father (F) = 1.5S = (3/2)S ⇒ F/S = 3/2.

⇒ Let F = 3x and S = 2x.

⇒ After 6 years, Father's age = 3x + 6.

⇒ After 6 years, Sum of two sons' ages = S + 6 + 6 = 2x + 12.

⇒ According to the question: (3x + 6) / (2x + 12) = 6 / 5

⇒ 5(3x + 6) = 6(2x + 12)

⇒ 15x + 30 = 12x + 72

⇒ 3x = 42

⇒ Present age of Father = 3x = 42.

∴ The correct answer is 42 years.

Additional Information

Ages of Multiple Persons

When calculating the sum of ages after 'n' years for 'k' persons, the sum increases by (n × k) years.

Ratio Method for Ages

Always ensure that the variable (x) is applied to the present ratio to simplify the calculation of current age values directly.

Shortcut Trick

For a dishonest dealer, Gain% = (Error ÷ Actual Weight) × 100.

Let the actual weight be x gm. The written weight is 984 gm.

The shopkeeper makes a 23% gain by selling x gm while charging for 984 gm.

Using the multiplier: Charged Weight = Actual Weight × (100 + Gain%) ÷ 100.

984 = x × (123 ÷ 100) ⇒ x = (984 × 100) ÷ 123 = 8 × 100 = 800 gm.

∴ The correct answer is 800 gm.

Alternate Method

Given: Marked weight = 984 gm, Profit% = 23%.

Formula: Gain% = [(True Value − Weight Used) ÷ Weight Used] × 100

⇒ Let the actual measure used by the shopkeeper be x gm.

⇒ Profit = 984 − x.

⇒ Profit% = [(984 − x) ÷ x] × 100 = 23.

⇒ 100 × (984 − x) = 23x.

⇒ 98400 − 100x = 23x ⇒ 98400 = 123x.

⇒ x = 98400 ÷ 123 = 800 gm.

∴ The correct answer is 800 gm.

Additional Information

Dishonest Dealer Concept

A shopkeeper gains when he uses a smaller weight than the true weight. Gain% = [Error ÷ (True Value − Error)] × 100.

Effective Gain

If a shopkeeper cheats by x% while buying and y% while selling, net gain% = [((100+x)(100+y) ÷ 100) − 100]%.

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

Key Points

• The correct matching of Column I with Column II is as follows:
• a - iv: No digestion
• b - i: Villi absorb nutrients
• c - ii: Length depends on food the organism eats
• d - iii: Helps in emulsification of fats

Additional Information

• The human alimentary canal consists of various organs where digestion and absorption of nutrients take place.
• The small intestine is responsible for the absorption of nutrients through structures called villi.
• The length of the alimentary canal can vary depending on the diet of the organism.
• The liver produces bile which aids in the emulsification of fats, a process necessary for fat digestion.
• Some parts of the alimentary canal, such as the esophagus, do not participate in digestion but serve as passageways for food.
• The large intestine is primarily responsible for the absorption of water from the remaining indigestible food matter.

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

1. D sits to the immediate left of F.

2)Only six people sit between S and D.

CASE 1: 

CASE 2: 

3. K sits third to the right of F.

4. S sits at the extreme left end of the row.

CASE 1:

CASE 2:

 

As it is given that S sits at the extreme left end, so CASE 1 gets eliminated and we have the final arrangement in CASE 2

So, 12 persons are seated in a row.

Hence the correct answer is "Option 1".

Shortcut Trick

Total members in the family = 4 (Father, Mother, and 2 Children).

Total age of family = Average × Number of members = 26 × 4 = 104 years.

Sum of ages of Father and 2 Children = 62 years.

Mother's age = Total age − Sum of others = 104 − 62 = 42 years.

∴ The correct answer is 42 years.

Alternate Method

Given:

Average age of 4 members = 26 years

Sum of ages of (Father + 2 Children) = 62 years

Formula Used:

Total Sum = Average × Number of observations

Calculations:

⇒ Total age of (Father + Mother + 2 Children) = 4 × 26

⇒ Total age = 104 years

⇒ Age of (Father + 2 Children) + Mother = 104

⇒ 62 + Mother = 104

⇒ Mother = 104 − 62

⇒ Mother = 42 years

∴ The correct answer is 42 years.

Additional Information

Definition of Average

The average (Arithmetic Mean) is the ratio of the sum of all observations to the total number of observations.

Total Sum Formula

If the average and number of items are known, the total sum is calculated as: Sum = Average × Count.

Property of Sum

The sum of a larger group can be expressed as the addition of the sums of its constituent sub-groups.

Given: 

Starting from point A, Jagdish walks 98 m towards the west.

He takes a left turn and walks 54 m.

He takes a left turn again and walks 112 m.

Again, he takes a left turn and walks 54 m to reach point B.

So, point B is 14 m west of point A

Hence the correct answer is "Option 4".

The correct answer is Awadhi

Key Points

• Awadhi has not been mentioned in the 8th Schedule of the Indian Constitution.
• The 8th Schedule of the Indian Constitution lists the official languages recognized by the Constitution.
• Currently, there are 22 languages listed in the 8th Schedule.
• Languages such as Dogri, Odia, and Maithili are included in the 8th Schedule.
• The inclusion of a language in the 8th Schedule means the language is recognized by the Indian government for official purposes.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26th November 1949 and came into effect on 26th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The 8th Schedule of the Constitution initially had 14 languages, but it was expanded over time to include more languages.
• Amendments to the Schedule can be made through a process outlined in Article 368 of the Constitution.
• The recognition of languages in the 8th Schedule helps preserve and promote linguistic diversity in India.

The correct answer is Baking soda

Key Points

• Baking soda is effective in neutralizing the acidic venom injected by a bee sting.
• Applying a paste made of baking soda and water to the affected area can help reduce pain and swelling.
• It works by counteracting the acidity of the venom, providing relief from the discomfort caused by the sting.
• Other home remedies like vinegar (which is acidic) or common salt do not neutralize the venom as effectively as baking soda.

Additional Information

• Bee stings inject venom that can cause pain, swelling, and redness at the site of the sting.
• It's important to remove the stinger as quickly as possible to prevent more venom from entering the skin.
• Individuals who are allergic to bee stings should seek immediate medical attention as they may experience severe reactions such as anaphylaxis.
• Other treatments that can help alleviate symptoms include ice packs, antihistamines, and over-the-counter pain relievers.

Given:

(18 ÷ 9) × (-7 + 9) - 7 × 2 

Formula used:

Follow the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Calculation:

(18 ÷ 9) × (-7 + 9) - 7 × 2

⇒ 2 × (2) - 7 × 2

⇒ 4 - 14

⇒ -10

∴ The correct answer is option (4).

The correct answer is Gross domestic product (GDP)

Key Points

• Gross domestic product (GDP) is the most commonly used measure for the size of the economy.
• GDP represents the total monetary value of all finished goods and services produced within a country's borders in a specific time period, typically annually or quarterly.
• It includes all private and public consumption, government outlays, investments, and exports minus imports that occur within a defined territory.
• GDP is a comprehensive measure of a nation's overall economic activity and is often used to gauge the health of an economy.
• Higher GDP values typically indicate a prosperous economy, while lower GDP values may indicate economic struggles.

Additional Information

• Gross National Product (GNP) is another measure of economic activity, but it includes the value of all goods and services produced by a country's residents, regardless of the location of production.
• Net Domestic Product (NDP) is derived from GDP by subtracting depreciation on a country’s capital goods.
• Net National Product (NNP) is GNP minus depreciation.
• The GDP growth rate is an important indicator of economic performance, showing how fast an economy is growing or shrinking over time.
• GDP can be measured using three approaches: the production (or output) approach, the income approach, and the expenditure approach.
• GDP per capita is often used as an indicator of the standard of living in a country, dividing the GDP by the population size.

The correct answer is Friday

Key Points

• Friday is the day when Jumma Namaz is performed in the community mosque.
• Jumma Namaz is a congregational prayer that Muslims hold every Friday, just after noon instead of the Zuhr prayer.
• It is considered one of the most exalted Islamic rituals and one of its obligatory acts.
• The significance of Friday is highlighted in the Quran in Surah Al-Jumu'ah, verse 9, which calls for the faithful to leave off business and gather for the prayers.

Additional Information

• The term Jumma derives from the Arabic word for Friday, which is the sixth day of the Islamic week.
• Friday is considered a special day for Muslims, often referred to as the "weekly Eid".
• Many Muslims prepare for Jumma prayers by taking a special bath, wearing clean clothes, and applying perfume.
• The Friday prayer is led by an Imam, who usually delivers a sermon (Khutbah) before the prayer.
• Attending the Jumma prayer is considered mandatory for adult male Muslims, while women may attend but are not required to do so.

The correct answer is Both the statements are true

Key Points

• Both the statements are true. Sodium hydroxide is indeed prepared by the chlor-alkali process.
• The chlor-alkali process produces three products: chlorine gas, hydrogen gas, and sodium hydroxide.
• This process involves the electrolysis of sodium chloride solution (brine), leading to the production of these three substances.
• The chlor-alkali process is a crucial industrial method for producing these chemicals, which have a wide range of applications in various industries.

Additional Information

• Sodium hydroxide (NaOH), also known as caustic soda, is a strong base used in various applications like soap making, paper production, and water treatment.
• Chlorine gas (Cl₂) is used for disinfection, in the production of PVC, and other chemical syntheses.
• Hydrogen gas (H₂) is used as a fuel, in the production of ammonia for fertilizers, and in hydrogenation reactions in the food industry.
• The chlor-alkali process is vital for the chemical industry, providing essential chemicals for numerous processes and products.

The correct answer is Ions move in first by active transport, followed by water along the concentration gradient

Key Points

• Ions move in first by active transport, followed by water along the concentration gradient.
• Active transport is a process where ions are moved into the root cells against their concentration gradient using energy from ATP.
• Once the ions are inside, they create a concentration gradient that facilitates the passive movement of water into the root cells through osmosis.
• This process ensures efficient absorption of both water and nutrients essential for plant growth.

Additional Information

• Root hairs play a crucial role in increasing the surface area for absorption.
• Water and mineral ion absorption is critical for photosynthesis, growth, and overall plant health.
• Besides active transport and osmosis, plants also use other mechanisms like facilitated diffusion and endocytosis for nutrient uptake.
• Maintaining optimal soil conditions, such as pH and moisture levels, can enhance the efficiency of nutrient absorption.

The correct answer is i, iii and iv

• The advantages of building dams include storing water for irrigation, generating electricity, and transferring water to great distances via canals.
• Dams provide a controlled water supply, which is crucial for agricultural activities, particularly in areas with irregular rainfall.
• They also play a vital role in hydroelectric power generation, contributing to the energy needs of a region.
• Canals that originate from dams help in distributing water over large areas, supporting both irrigation and domestic water supply.

Additional Informatio

• Some Important Dams of India​

• "Dams are the temples of modern India" proclaimed by Jawaharlal Nehru.
• Oldest dam in India is the Kallanai dam in Tamil Nadu built on the Kaveri river.
• The largest dam in India is the Tehri dam.

The logic followed here is:

So, the missing term of the series is '42'

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (Digit Sum 1st number)² = 2nd number.

Now,

For, 25 : 49

⇒ (2 + 5)² = 7² = 49.

For, 42 : 36

⇒ (4 + 2)² = 6² = 36.

Similarly, for 74 ∶ ?

⇒ (7 + 4)² = 11² = 121.

Hence, the correct answer is "Option 1".

Given: (left) 248 382 415 127 335 (right)

The second digit of the largest number is: 1 (415)

And, 

The first digit of the second smallest number is: 2 (248)

So, the multiplication of the first digit of the second smallest number and the second digit of the largest number is:

→ 2 * 1 = 2.

The correct answer is "Option 4".

The correct answer is Between Beas and Ravi

Key Points

• Bari Doab is the region located between the Beas and Ravi rivers.
• The term "Doab" is derived from Persian, meaning "land between two rivers".
• In Punjab, India, the area between the Beas and Ravi is known as the Bari Doab, which is one of the major divisions of the region.
• This fertile area has historically been crucial for agriculture and settlements.

Additional Information

• The Punjab region is divided into several doabs, which are named based on the rivers that bound them.
• Other well-known doabs in Punjab include the Rechna Doab (between Chenab and Ravi) and the Chaj Doab (between Jhelum and Chenab).
• The concept of doabs is significant in understanding the geographical and cultural landscape of the Punjab region.

The correct answer is Mirzapur

Key Points

• The Standard Meridian of India passes through Mirzapur.
• The longitude of the Standard Meridian is 82.5° E, which is used as the reference for Indian Standard Time (IST).
• Mirzapur is located in the state of Uttar Pradesh.
• This meridian helps in maintaining a uniform time zone across the country.

Additional Information

• The Indian Standard Time (IST) is 5 hours and 30 minutes ahead of Greenwich Mean Time (GMT+5:30).
• Having a standard meridian helps in avoiding confusion and ensuring that the entire country follows the same time.
• The concept of a standard time zone is crucial for the synchronization of activities, especially in a country as vast as India.

The correct answer is -6 cm

Key Points

• The radius of curvature (R) of a concave mirror is given as 12 cm.
• According to the New Cartesian Sign Convention, the radius of curvature for a concave mirror is taken as negative.
• The relationship between the focal length (f) and the radius of curvature (R) of a concave mirror is given by the formula: $f=\frac{R}{2}$
• Substituting the given value: $f=\frac{-12}{2}=-6cm$
• Hence, the principal focus is located at x = -6 cm.

Additional Information

• In the New Cartesian Sign Convention, distances measured against the direction of the incident light are taken as negative, while those measured along the direction of the incident light are taken as positive.
• For concave mirrors, the focal point and the center of curvature lie on the same side as the reflecting surface, hence their distances are considered negative.
• This sign convention helps in deriving and applying the mirror formula and magnification formula correctly.

Given series: 5 6 2 6 5 8 5 3 5 0 2 6 3 8 2 5 6 9 3 7

According to the question such odd numbers are there each of which is immediately preceded by an even number and also immediately followed by an even number:

Required condition: Even number - Odd number - Even number

5 6 2 6 5 8 5 3 5 0 2 6 3 8 2 5 6 9 3 7

Thus, there are three such odd numbers which is immediately preceded by and also immediately followed by an even number.

Hence, "Option 1" is the correct answer.

The correct answer is Bengaluru

Key Points

• Bengaluru hosted the Khelo India University Games 2021.
• The Khelo India University Games is a national-level multi-sport event for university athletes in India, aimed at promoting sports and identifying talent at the university level.
• The event is part of the Khelo India initiative, which seeks to foster a strong sports culture in the country.
• Bengaluru, the capital city of Karnataka, has a rich history of hosting various national and international sporting events, making it an ideal location for the games.

Additional Information

• The Khelo India Programme was launched by the Ministry of Youth Affairs and Sports in 2018 to revive the sports culture in India at the grassroots level.
• It includes various components such as the Khelo India School Games, Khelo India Youth Games, and Khelo India University Games.
• The programme provides financial assistance for the development of sports infrastructure and the training of athletes.
• Khelo India University Games 2021 featured a wide range of sports, including athletics, basketball, football, badminton, swimming, and more.
• The event saw participation from numerous universities across India, showcasing the sporting talent of the country's youth.

The correct answer is 3, ketone

Key Points

• Propanone, also known as acetone, has 3 carbons and a ketone functional group.
• Its chemical formula is C3H6O.
• Propanone is the simplest and most important ketone.
• It is widely used as a solvent and an intermediate in organic synthesis.
• The ketone functional group is characterized by a carbonyl group (C=O) bonded to two carbon atoms.

Additional Information

• Ketones are a class of organic compounds characterized by the presence of a carbonyl group bonded to two hydrocarbon groups.
• Propanone is commonly used in nail polish removers and as a cleaning agent.
• In the body, acetone is produced during the metabolism of fats and is present in small amounts in the blood and urine.
• Propanone is a colorless, volatile, and flammable liquid with a characteristic odor.

Shortcut Trick

Find two factors of ab = 140 whose sum is a + b = 27.

The factors are 20 and 7 (since 20 × 7 = 140 and 20 + 7 = 27).

Substitute these values into the expression: a³ + b³ = 20³ + 7³

Calculation: 8000 + 343 = 8343.

∴ The correct answer is 8343.

Alternate Method

Given:

a + b = 27

ab = 140

Formula Used:

The algebraic identity for the sum of cubes is: a³ + b³ = (a + b)³ − 3ab(a + b)

Calculations:

⇒ a³ + b³ = (27)³ − 3 × 140 × (27)

⇒ a³ + b³ = 19683 − 420 × 27

⇒ a³ + b³ = 19683 − 11340

⇒ a³ + b³ = 8343

∴ The correct answer is 8343.

Additional Information

Sum of Cubes (Factored Form)

Another way to express the sum of cubes is a³ + b³ = (a + b)(a² − ab + b²).

Difference of Cubes

The identity for the difference of two cubes is a³ − b³ = (a − b)(a² + ab + b²).

Square of a Binomial

To find a² + b², use the identity (a + b)² = a² + b² + 2ab, which rearranges to a² + b² = (a + b)² − 2ab.

Shortcut Trick

Relative Speed in same direction = 36 − 18 = 18 km/h.

Convert speed to m/s: 18 × (5/18) = 5 m/s.

Total distance (2L) = Speed × Time = 5 × 8 = 40 m.

Length of each engine (L) = 40 ÷ 2 = 20 m.

∴ The correct answer is 20 m.

Alternate Method

Given:

Speed of faster engine (S₁) = 36 km/h

Speed of slower engine (S₂) = 18 km/h

Time taken to cross (t) = 8 sec

Length of each engine = L

Formula Used:

Relative Speed (Same direction) = S₁ − S₂

Distance = Speed × Time

Calculations:

⇒ Relative Speed = 36 − 18 = 18 km/h

⇒ Speed in m/s = 18 × (5/18) = 5 m/s

⇒ Total Distance = L + L = 2L

⇒ 2L = 5 × 8

⇒ 2L = 40

⇒ L = 20 m

∴ The correct answer is 20 m.

Additional Information

Relative Speed Rules

When two objects move in the same direction, relative speed is S₁ − S₂. When they move in opposite directions, it is S₁ + S₂.

Unit Conversion

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

Crossing Distance

When one train crosses another train or a long object, the total distance covered is the sum of the lengths of both objects.

Shortcut Trick

Total frequency N = 100 ⇒ N/2 = 50.

Calculate Cumulative Frequency (CF): 5, 23, 38, 60...

The first CF ≥ 50 is 60, so the median class is 60−70.

The cumulative frequency of the class preceding 60−70 is 38.

∴ The correct answer is 38.

Alternate Method

Given: Total number of farmers (N) = 100.

⇒ N/2 = 100 ÷ 2 = 50.

⇒ CF for 30−40 = 5

⇒ CF for 40−50 = 5 + 18 = 23

⇒ CF for 50−60 = 23 + 15 = 38

⇒ CF for 60−70 = 38 + 22 = 60

⇒ Since 60 is the first cumulative frequency greater than or equal to 50, the median class is 60−70.

⇒ The class preceding the median class is 50−60.

⇒ The cumulative frequency of the class 50−60 is 38.

∴ The correct answer is 38.

Additional Information

Median Class Identification

The median class is the class interval whose cumulative frequency is just greater than or equal to N/2.

Median Formula for Grouped Data

Median = l + [(N/2 − cf)/f] × h, where cf is the cumulative frequency of the class preceding the median class.

Cumulative Frequency (CF)

It is the sum of all previous frequencies up to the current point. It is essential for calculating positional averages like median, quartiles, and deciles.

The correct answer is CuSO4 (aq) + BaCl2 (aq) → BaSO4 (s) + CuCl2 (aq)

Key Points

• CuSO4 (aq) + BaCl2 (aq) → BaSO4 (s) + CuCl2 (aq) is a precipitation reaction.
• In a precipitation reaction, two aqueous solutions react to form an insoluble solid called a precipitate.
• Here, when copper(II) sulfate solution reacts with barium chloride solution, barium sulfate, which is insoluble in water, precipitates out.
• The other product, copper(II) chloride, remains in the aqueous phase.

Additional Information

• Precipitation reactions are a type of double displacement reaction where an insoluble salt is formed as a product.
• These reactions are commonly used in various chemical analyses and separations.
• The formation of a precipitate can be used to identify the presence of specific ions in a solution.
• Other examples of precipitation reactions include the reaction between silver nitrate and sodium chloride to form silver chloride precipitate.
• Precipitation reactions are important in fields such as analytical chemistry, environmental science, and materials science.

Shortcut Trick

Total simple interest for 2 years = ₹2,000.

Interest for 1 year = 2,000 ÷ 2 = ₹1,000.

Rate of interest (R) = (Interest for 1 year ÷ Principal) × 100

R = (1,000 ÷ 10,000) × 100 = 10%.

∴ The correct answer is 10%.

Alternate Method

Given:

Principal (P) = ₹10,000

Time (T) = 2 years

Simple Interest (SI) = ₹2,000

Formula Used:

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

Calculations:

⇒ 2,000 = (10,000 × R × 2) ÷ 100

⇒ 2,000 = 100 × R × 2

⇒ 2,000 = 200 × R

⇒ R = 2,000 ÷ 200

⇒ R = 10%

∴ The correct answer is 10%.

Additional Information

Simple Interest Property

In simple interest, the Principal remains constant throughout the loan period, meaning the interest earned each year is the same.

Amount Formula

The total Amount (A) repaid after the time period is the sum of the Principal and the Interest: A = P + SI.

Effective Rate of Interest

The total percentage interest paid over the whole period is R × T. In this case, 10% × 2 = 20% of the Principal.

Given series: 5P Q S D A B U E H I R I A A Y E J S B R X M F G U A B U E H I R

According to the question such vowels are there in the series each of which is immediately preceded by a consonant and also immediately followed by a consonant:

Required condition: Consonant - Vowel - Consonant

P Q S D A B U E H I R I A A Y E J S B R X M F G U A B U E H I R

Thus, there are four such vowels which are immediately preceded by and also immediately followed by a consonant.

Hence, "Option 4" is the correct answer.

The correct answer is Foods like chips and canned snacks are low in nutrition and should be avoided during adolescence/reproductive phase

Explanation:

• Foods like chips and canned snacks are low in nutrition and should be avoided during adolescence/reproductive phase - This is a factual statement and not a myth.
• Adolescence and the reproductive phase are crucial periods for growth and development, where balanced nutrition is essential.
• Chips and canned snacks are often high in unhealthy fats, sugars, and sodium, while being low in essential nutrients.
• Consuming these foods regularly can lead to poor health outcomes, including obesity, cardiovascular disease, and nutrient deficiencies.
• During menstruation, a girl should not be permitted to work in the kitchen - This is a myth.
• Menstruating does not affect a girl's ability to work in the kitchen or perform any day-to-day activities.
• Restricting her from normal activities is based on societal taboos and misconceptions rather than scientific evidence.
• If a girl looks at boys while menstruating, she becomes pregnant - This is clearly a myth.
• Pregnancy can only occur through fertilization of the egg by sperm. Looking at someone cannot result in pregnancy. This statement is based on misconceptions and lacks any scientific basis.
• The mother is ultimately accountable for her child's sexual orientation - This is a myth.
• A child's sexual orientation is not determined by the mother or any other parental influence. Sexual orientation is complex interplay of genetic, hormonal, and environmental factors. During reproduction, each parent contributes one of their two sex chromosomes to the offspring:
• The mother can only provide an X chromosome.
• The father can provide either an X or a Y chromosome.

The combination of these chromosomes determines the sex of the offspring:

• XX (female): If the offspring inherits an X chromosome from both parents.
• XY (male): If the offspring inherits an X chromosome from the mother and a Y chromosome from the father.

The correct answer is a and d

Key Points

• Lymph carries digested and absorbed fat from the intestine.
• Lymph drains excess fluid from the extracellular space back into the blood.
• Lymph does not carry CO2 to the lungs or RBCs to the lymph nodes.

Additional Information

• The lymphatic system is a network of tissues and organs that help rid the body of toxins, waste, and other unwanted materials.
• The primary function of the lymphatic system is to transport lymph, a fluid containing infection-fighting white blood cells, throughout the body.
• The lymphatic system includes lymphatic vessels, lymph nodes, and other lymphoid organs such as the spleen and thymus.
• Maintaining fluid balance in the body and filtering out harmful substances are critical roles of the lymphatic system.

Given:

The numerator is 1 less than the denominator.

If 6 is added to the numerator, the fraction becomes 5/4.

Formula used:

Let the denominator be x, then the numerator is x - 1.

When 6 is added to the numerator:

(x - 1 + 6)/x = 5/4

Calculation:

⇒ (x + 5)/x = 5/4

⇒ 4(x + 5) = 5x

⇒ 4x + 20 = 5x

⇒ 20 = 5x - 4x

⇒ x = 20

⇒ Numerator = x - 1 = 20 - 1 = 19

∴ The fraction is 19/20.

The correct answer is Only (a)

Key Points

• Option 3 is correct because an electric motor uses split rings for the commutator, which helps in reversing the direction of current in the coil every half rotation to ensure continuous rotation in the same direction.
• Statement (b) is incorrect because the direction of the force on the motor's coil is found using Fleming's left-hand rule, not the right-hand rule.
• Fleming's right-hand rule is used to find the direction of induced current in generators, not in motors.

Additional Information

• An electric motor converts electrical energy into mechanical energy.
• The split ring commutator ensures that the direction of current through the coil is reversed every half turn, which keeps the coil rotating in the same direction.
• Fleming's left-hand rule states that if the thumb, forefinger, and middle finger of the left hand are stretched mutually perpendicular to each other, with the forefinger in the direction of the magnetic field, the middle finger in the direction of the current, then the thumb points in the direction of the force or motion of the conductor.

Shortcut Trick

Total Distance = Train Length + Tunnel Length = 725 + 235 = 960 m.

Speed in m/s = 960 ÷ 48 = 20 m/s.

Convert to km/h: 20 × (18/5) = 72 km/h.

∴ The correct answer is 72 km/h.

Alternate Method

Given:

Length of train (L₁) = 725 m

Length of tunnel (L₂) = 235 m

Time taken (t) = 48 sec

Formula Used:

Speed = Total Distance ÷ Total Time

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

Calculations:

⇒ Total Distance = 725 + 235 = 960 m

⇒ Speed (m/s) = 960 ÷ 48

⇒ Speed (m/s) = 20 m/s

⇒ Speed (km/h) = 20 × (18/5)

⇒ Speed (km/h) = 4 × 18 = 72 km/h

∴ The correct answer is 72 km/h.

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.

Relative Speed

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

Train Crossing Objects

When a train crosses a pole or man, distance = length of train. When it crosses a platform or tunnel, distance = length of train + length of object.

Given: Seven boxes J, K, L, M, N, O and P are kept one over the other

1. Only five boxes are kept between K and J.

2. L is kept immediately above P.

3. M is kept immediately below N.

4. O is kept at one of the positions above J.

5. N is kept immediately below K. 

As O is kept above J and N is kept immediately below K, so is is not possible in CASE 2 so it gets eliminated.

So, 4 boxes are kept between N and J

Hence the correct answer is "Option 2".

The logic followed here is:

For, MON ∶ PLQ

For, KIT ∶ NFW  

Similarly for, PEN : SBQ

Hence the correct answer is "Option 1".

Shortcut Trick

Subtract the remainder 13 from each number: 3795, 4785, and 5115.

Find the HCF of (4785 − 3795 = 990) and (5115 − 4785 = 330).

HCF(990, 330) = 330. Since 3795 ÷ 330 leaves remainder 165 (not 0), the HCF of all three is 165.

Sum of digits of X = 165 is 1 + 6 + 5 = 12.

∴ The correct answer is 12.

Alternate Method

Given: Numbers are 3808, 4798, 5128 and remainder is 13.

Formula Used: X = HCF(Number₁ − Remainder, Number₂ − Remainder, Number₃ − Remainder)

⇒ First number = 3808 − 13 = 3795

⇒ Second number = 4798 − 13 = 4785

⇒ Third number = 5128 − 13 = 5115

⇒ X = HCF(3795, 4785, 5115)

⇒ 3795 = 5 × 3 × 11 × 23

⇒ 4785 = 5 × 3 × 11 × 29

⇒ 5115 = 5 × 3 × 11 × 31

⇒ Common factors are 5, 3, and 11. X = 5 × 3 × 11 = 165

⇒ Sum of digits = 1 + 6 + 5 = 12

∴ The correct answer is 12.

Additional Information

HCF with same remainder

To find the greatest number that divides a, b, c leaving the same remainder 'r', find HCF(a−r, b−r, c−r).

HCF with unknown same remainder

If the remainder is not given, the greatest number is HCF(|a−b|, |b−c|, |c−a|).

LCM Application

The smallest number divisible by a, b, c leaving remainder 'r' in each case is LCM(a, b, c) + r.

Given Statement: L = U > V > E < Z < Q

Now,

Conclusions:

Option 1: Q > V → False (V > E < Z < Q No definite relation can be possible between Q and V)

Option 2: L < V → False (L = U > V It gives L > V)

Option 3: E = L → False (L = U > V > E It gives E < L)

Option 4: U > E → True (U > V > E It gives U > E)

Hence, the correct answer is "Option 4".

The logic followed here is:

 For 'PUNCH' is coded as 'OWMEG'

For 'SHAWL' is coded as 'RJZYK'

Similarly 'KARMA' will be coded as 'JCQOZ'

Hence the correct answer is "Option 1".

The correct answer is Confederation of Indian Industry

Key Points

• The India Plastics Pact was launched in September 2021 as a joint initiative between the Confederation of Indian Industry (CII) and the World-Wide Fund for Nature-India (WWF India).
• The pact aims to bring together businesses, governments, and NGOs to work towards a circular economy for plastics, reducing the environmental impact of plastic waste.
• It focuses on four targets: eliminating unnecessary plastic packaging, ensuring all plastic packaging is reusable or recyclable, increasing the recycling of plastic packaging, and ensuring an average of 25% recycled content in plastic packaging.
• The India Plastics Pact is the first of its kind in Asia and is part of a global network of Plastics Pacts that are working towards a shared vision of a world where plastics never become waste.

Additional Information

• The Confederation of Indian Industry (CII) is a non-government, not-for-profit, industry-led, and industry-managed organization, playing a proactive role in India’s development process.
• World-Wide Fund for Nature-India (WWF India) is one of the largest conservation organizations in India, working to promote harmony between human beings and nature.
• The India Plastics Pact aligns with the principles of a circular economy, which is aimed at eliminating waste and the continual use of resources.
• By bringing together stakeholders across the value chain, the pact seeks to drive systemic change and create a sustainable approach to plastic use and waste management.

The correct answer is Shri Jagdeep Dhankhar

Key Points

• Shri Jagdeep Dhankhar is the current Chairman of Rajya Sabha as of August 12, 2022.
• The Chairman of Rajya Sabha is also the Vice President of India.
• The role of the Chairman includes presiding over the sessions of the Rajya Sabha, maintaining order, and ensuring the rules of the house are followed.
• The Chairman has the authority to decide on points of order and can also cast a deciding vote in case of a tie.

Additional Information

• The Rajya Sabha, also known as the Council of States, is the upper house of India's bicameral Parliament.
• The Rajya Sabha is a permanent body and is not subject to dissolution, but one-third of its members retire every two years.
• The Vice President of India is elected by an electoral college consisting of members of both houses of Parliament.
• The Vice President serves as the ex-officio Chairman of Rajya Sabha.
• The current Vice President and Chairman of Rajya Sabha, Shri Jagdeep Dhankhar, took office on August 11, 2022.

The correct answer is Urethra

Key Points

• The Urethra is part of the urinary system and not the female reproductive system.
• The female reproductive system includes structures such as the Uterus, Ovaries, and Fallopian tubes.
• The Uterus is where a fertilized egg implants and develops into a fetus.
• The Ovaries produce eggs and hormones like estrogen and progesterone.
• The Fallopian tubes transport the eggs from the ovaries to the uterus.

Additional Information

• The Urethra serves the role of expelling urine from the body.
• In females, the urethra is shorter and opens just above the vaginal opening.
• Understanding the distinction between the reproductive and urinary systems is crucial for comprehending human anatomy.

The correct answer is Chhotanagpur plateau

Key Points

• The Chhotanagpur plateau is the region with the maximum concentration of iron and steel industry in India.
• This area is rich in mineral resources, particularly iron ore, coal, and limestone, which are essential for iron and steel production.
• Major steel plants like Tata Steel in Jamshedpur, Bokaro Steel Plant, and others are located in this region.
• The presence of these resources and industries has made the Chhotanagpur plateau a hub for the iron and steel industry.

Additional Information

• The Chhotanagpur plateau spans across the states of Jharkhand, Odisha, West Bengal, and Chhattisgarh.
• The region's extensive coal deposits are crucial for the steel industry as they provide the necessary fuel for steel production.
• Besides iron and steel, the region also supports other industries such as aluminum and cement due to its rich mineral base.
• This industrial concentration has also led to the development of infrastructure and urbanization in the region.

The correct answer is chlorofluorocarbon

Key Points

• Chlorofluorocarbons (CFCs) are the primary chemical compounds that contribute to the depletion of the ozone layer.
• CFCs are used in various applications such as refrigerants, propellants in aerosol sprays, and solvents in the manufacturing industry.
• When CFCs are released into the atmosphere, they eventually reach the stratosphere where they are broken down by ultraviolet radiation, releasing chlorine atoms.
• Chlorine atoms react with ozone (O₃) molecules, causing the ozone molecules to break apart into oxygen molecules (O₂), thus depleting the ozone layer.
• The depletion of the ozone layer increases the amount of harmful ultraviolet (UV) radiation reaching the Earth's surface, which can lead to adverse environmental and health effects.

Additional Information

• The Montreal Protocol, adopted in 1987, is an international treaty designed to phase out the production and consumption of ozone-depleting substances, including CFCs.
• Since the implementation of the Montreal Protocol, there has been a significant reduction in the emission of CFCs, and the ozone layer is showing signs of recovery.
• Other chemicals that contribute to ozone depletion include halons, carbon tetrachloride, and methyl chloroform, but CFCs are the most well-known and widely used.
• It is crucial to continue monitoring and regulating these substances to ensure the continued recovery and protection of the ozone layer.

The correct answer is can cause wilting of plants

Key Points

• Can cause wilting of plants is a disadvantage of transpiration.
• Transpiration is the process of water movement through a plant and its evaporation from aerial parts, especially from the leaves.
• While transpiration has several advantages, such as providing water for photosynthesis, transporting mineral ions, and cooling the plant through evaporation, it can also lead to wilting if the water loss exceeds the water uptake.
• Wilting occurs when the plant loses more water through transpiration than it can absorb from the soil, leading to a loss of turgor pressure and causing the plant to droop.

Additional Information

• Transpiration plays a crucial role in the water cycle and helps in nutrient uptake from the soil.
• It also helps in maintaining the temperature of the plant by cooling it through the evaporation process.
• However, excessive transpiration can lead to water stress, especially in arid conditions or during periods of drought.
• Plants have evolved various mechanisms to minimize water loss, such as closing their stomata, developing thick cuticles, and having reduced leaf surface area.

The correct answer is Tamil Nadu

Key Points

• Tamil Nadu experiences winter rainfall due to the retreating monsoon.
• The retreating monsoon, also known as the northeast monsoon, occurs when the monsoon winds reverse direction and blow from the northeast to the southwest.
• This phenomenon typically happens during the months of October to December.
• During this period, Tamil Nadu and parts of Andhra Pradesh receive significant rainfall.
• This rainfall is crucial for the agricultural activities in these regions.

Additional Information

• The retreating monsoon is influenced by the shifting of the Intertropical Convergence Zone (ITCZ) towards the south.
• During the southwest monsoon, the ITCZ is positioned over the Indian subcontinent, bringing heavy rainfall to the region.
• As the ITCZ moves southwards, the southwest monsoon winds weaken, and the northeast monsoon winds begin to dominate.
• These winds pick up moisture from the Bay of Bengal and bring rainfall to the southeastern coast of India.
• The northeast monsoon is relatively less intense compared to the southwest monsoon but is vital for the water resources in Tamil Nadu.

Given: Six students - 1, 2, 3, 4, 5 and 6 - are sitting around a circular table facing the centre.

1. 4 is sitting to the immediate right of 5 and immediate left of 6.

2. 5 is sitting second to the right of 3.

3. 6 and 3 are the immediate neighbours of 1. 

So, '3' is sitting to the immediate left of '2'

Hence the correct answer is "Option 4".

The correct answer is When the fiscal deficit is equal to the interest payment

Key Points

• The primary deficit is defined as the fiscal deficit of the current year minus interest payments on previous borrowings.
• When the fiscal deficit is equal to the interest payment, the primary deficit is zero.
• This implies that the government is only borrowing to pay interest on existing debt and not for other expenditures.
• The concept of primary deficit helps in understanding the extent to which the government is borrowing to meet expenses other than interest payments.

Additional Information

• The fiscal deficit is the difference between the total revenue and total expenditure of the government.
• Interest payments are a major component of the fiscal deficit, particularly for countries with high levels of debt.
• Managing the primary deficit is crucial for maintaining fiscal sustainability and ensuring that debt levels do not become unmanageable.
• A zero primary deficit indicates that the government's current income is sufficient to cover its current expenditures, excluding interest payments.

The logic followed here is:

So, the missing term of the series is '306'

Hence the correct answer is "Option 1".

The correct answer is Bihu

Key Points

• Bihu is a set of three important Assamese festivals celebrated in the state of Assam: Rongali or Bohag Bihu, Kongali or Kati Bihu, and Bhogali or Magh Bihu.
• These festivals mark the Assamese New Year and are considered very significant in Assamese culture.
• Bihu is celebrated with traditional dance, music, and feasting, and is a time for joy and community bonding.
• Rongali Bihu, celebrated in April, is the most popular and marks the beginning of the Assamese New Year.
• Kongali Bihu, observed in October, is more solemn and marks the time of growing crops.
• Bhogali Bihu, celebrated in January, is a harvest festival and marks the end of the harvesting season.

Additional Information

• Onam is a festival celebrated in Kerala.
• Pongal is a festival celebrated in Tamil Nadu.
• Baisakhi is a festival celebrated in Punjab.

Given: To reach point Q from point S, a person has to walk 83 m towards the west.

He must then take a right turn and walk 240 m.

He must take another right turn and walk 147 m.

He must take another right turn and walk 240 m to reach the destination

So, point Q is 64m west from point S.

Hence the correct answer is "Option 1".

The correct answer is 10; 6

Key Points

• If carbon forms a C4- ion, it gains 4 additional electrons to its neutral state.
• Neutral carbon has 6 protons and 6 electrons.
• Therefore, a C4- ion will have 10 electrons (6 + 4) and 6 protons.
• Hence, the number of electrons and protons in the carbon ion will be 10 and 6 respectively.

Additional Information

• A neutral carbon atom has an atomic number of 6, which means it has 6 protons.
• In its ionized state as C4-, carbon has gained 4 extra electrons, leading to a total of 10 electrons.
• Protons remain unchanged during ionization, thus the number of protons in C4- is still 6.
• This ionization process impacts the electrical charge balance but not the number of protons in the nucleus.

The correct answer is PARAM Ganga

Key Points

• PARAM Ganga is the first 'Made in India' Petascale Supercomputer installed at IIT Roorkee under the National Supercomputing Mission (NSM) in 2022.
• The National Supercomputing Mission (NSM) is an initiative by the Government of India to empower national academic and R&D institutions by installing a vast network of supercomputers.
• PARAM Ganga enhances the research capabilities of IIT Roorkee in various fields including weather forecasting, drug discovery, and computational fluid dynamics.
• The supercomputer is built with indigenous technology and components, marking a significant step towards self-reliance in high-performance computing.
• PARAM Ganga's installation aligns with the vision of the Digital India program and aims to make India a global leader in supercomputing.

Additional Information

• The National Supercomputing Mission (NSM) was launched in 2015 with an aim to connect national academic and research institutions with a grid of supercomputing facilities.
• Under the NSM, India plans to build a network of over 70 high-performance computing facilities with a computing capacity of 450 Petaflops.
• PARAM Ganga is part of the larger PARAM series of supercomputers developed by the Centre for Development of Advanced Computing (C-DAC).
• The mission is jointly steered by the Ministry of Electronics and Information Technology (MeitY) and the Department of Science and Technology (DST).
• NSM also aims to develop a skilled workforce in supercomputing technologies through specialized training programs and collaborations with global leaders in the field.

The least possible Venn diagram for the above statement is as follows:

Conclusions:

I. All B's are S's - FALSE (Because all B are G and some G are S it implies some B are S but all is not definite)

II. Some A's are B's - FALSE (Because, no definite relation is given  between A and B, so it is possible only)

So, 'Neither conclusion I nor II follows'.

Hence, the correct answer is "Option 4".

The correct answer is Copper-based nanoparticle coated anti-viral face mask

Key Points

• A copper-based nanoparticle coated anti-viral face mask was being developed under the 'Nano mission project' to fight against the Covid-19 pandemic in February 2022.
• Copper nanoparticles are known for their strong anti-microbial properties, which can effectively neutralize viruses and bacteria.
• The development of such masks aimed to provide enhanced protection against the spread of Covid-19.
• The 'Nano mission project' focuses on harnessing the potential of nanotechnology to address critical health challenges.

Additional Information

• Nanotechnology involves manipulating matter at the nanoscale to create materials with unique properties and functions.
• The use of nanoparticles in face masks can enhance filtration efficiency and provide additional anti-viral protection.
• Face masks have been a crucial tool in mitigating the spread of Covid-19, and innovations in this area continue to evolve.
• The 'Nano mission project' is an initiative by the Government of India to promote and support research in nanoscience and nanotechnology.
• Such initiatives aim to leverage advanced technology to address public health crises and improve overall healthcare outcomes.

Given Statement: F = U ≥ P = M ≤ K < W < T

Now,

Conclusions:

Option 1: F ≥ P → True (F = U ≥ P It gives F ≥ P)

Option 2: M > F → False (F = U ≥ P = M It gives M ≤ F)

Option 3: P ≥ K → False (P = M ≤ K It gives P ≤ K)

Option 4: T < K → False (K < W < T It gives T > K)

Hence, the correct answer is "Option 1".

According to the given Venn diagram:

The shaded area shows the 'total number of female actors who are also models'

So, 'the total number of female actors who are models is 17'

Hence the correct answer is "Option 4".

Shortcut Trick

Sum of consecutive interior angles on the same side of a transversal is always 180°.

Given ratio = 2 : 3 ⇒ Total parts = 2 + 3 = 5 units.

5 units = 180° ⇒ 1 unit = 36°.

Greater angle = 3 units = 3 × 36° = 108°.

∴ The correct answer is 108°.

Alternate Method

Given: Ratio of two interior angles on the same side of a transversal = 2 : 3.

Formula Used: When two parallel lines are intersected by a transversal, the sum of consecutive interior angles is 180°.

Let the two angles be 2x and 3x.

⇒ 2x + 3x = 180°

⇒ 5x = 180°

⇒ x = 180° ÷ 5

⇒ x = 36°

⇒ Smaller angle = 2 × 36° = 72°

⇒ Greater angle = 3 × 36° = 108°

∴ The correct answer is 108°.

Additional Information

Alternate Interior Angles

Angles on opposite sides of the transversal and between the parallel lines are equal.

Shortcut Trick

An equation is reducible to a quadratic if, after clearing denominators or applying substitution, the highest power of the variable is 2.

In Option A, substituting (m + 1) = y gives y − 1/y = 65, which results in y² − 65y − 1 = 0 (a second-degree equation).

Options B and D involve x³ terms upon simplification, making them cubic equations.

Option C involves multiple variables and results in a higher-degree term (b³) when simplified.

∴ The correct answer is (m + 1) − 1/(m + 1) = 65.

Alternate Method

Given Equations:

A) (m + 1) − 1/(m + 1) = 65

B) x³ + 3x = 2x³ − 4x²

C) (a + b)² = 3/b

D) x + (3x − 2) = 1/x² − 6

Simplification and Analysis:

For Option A:

⇒ Let (m + 1) = y

⇒ y − 1/y = 65

⇒ (y² − 1) / y = 65

⇒ y² − 1 = 65y

⇒ y² − 65y − 1 = 0

Since the highest degree is 2, it is a quadratic equation.

For Option B:

⇒ x³ + 3x = 2x³ − 4x²

⇒ 2x³ − x³ − 4x² − 3x = 0

⇒ x³ − 4x² − 3x = 0 (Highest degree is 3, so it is Cubic).

For Option D:

⇒ 4x − 2 = 1/x² − 6

⇒ (4x − 2) × x² = 1 − 6x²

⇒ 4x³ − 2x² + 6x² − 1 = 0

⇒ 4x³ + 4x² − 1 = 0 (Highest degree is 3, so it is Cubic).

∴ The correct answer is (m + 1) − 1/(m + 1) = 65.

Additional Information

Standard Form of Quadratic Equation

A quadratic equation is expressed as ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Degree of an Equation

The degree is the highest exponent of the variable in the polynomial. Degree 1 is linear, degree 2 is quadratic, and degree 3 is cubic.

Reducible Equations

Equations that are not polynomials in their given form but can be converted to standard quadratic form through algebraic manipulation or substitution.

Discriminant Rule

For ax² + bx + c = 0, the discriminant D = b² − 4ac determines the nature of the roots (real or imaginary).

Shortcut Trick

Identify the highest power (degree) of the variable x after simplification.

Options (1) and (2) are linear because the x² terms cancel out upon expansion.

Option (3) is cubic because it contains an x³ term from (2x)−1)³.

Option (4) is quadratic because the x² term remains and the highest power is 2.

∴ The correct answer is √2x² + 3x − 4 − 2x + 5 = 0.

Alternate Method

Given: √2x² + 3x − 4 − 2x + 5 = 0

Method: A standard quadratic equation is of the form ax² + bx + c = 0, where a ≠ 0.

⇒ √2x² + (3x − 2x) + (−4 + 5) = 0

⇒ √2x² + 1x + 1 = 0

⇒ Here, a = √2, b = 1, and c = 1.

⇒ Since the coefficient of x² is not zero and the highest degree is 2, it is a quadratic equation.

∴ The correct answer is √2x² + 3x − 4 − 2x + 5 = 0.

Additional Information

Standard Form

Any equation that can be rearranged into the form ax² + bx + c = 0 is quadratic.

Discriminant

The nature of roots is determined by D = b² − 4ac.

Nature of Roots

If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

The correct answer is 44 Ω.

Key Points

• The toaster has a power rating of 1100 W and operates at a voltage of 220 V.
• Using the formula P = V² / R, we can calculate the resistance of the toaster coil.
• Rearranging the formula to solve for resistance: R = V² / P.
• Substituting the given values: R = 220² / 1100 = 48400 / 1100 = 44 Ω.

Additional Information

• Power (P): The rate at which energy is consumed or generated, measured in watts (W), calculated as P = V² / R for resistive loads.
• Voltage (V): The electrical potential difference that drives current through a circuit, measured in volts (V).
• Resistance (R): The opposition to the flow of electric current in a circuit, measured in ohms (Ω).
• Ohm's Law: It defines the relationship between voltage, current, and resistance as V = IR, where V is voltage, I is current, and R is resistance.
• Watt (W): The unit of power, calculated as the product of voltage and current, or in the case of resistive circuits, P = V² / R.

The logic followed here is:

Logic: (1st number × 3rd number) + 4 = 2nd number.

Now,

For, (12, 112, 9)

⇒ (12 × 9) + 4 = 108 + 4 = 112.

For, (6, 28, 4)

⇒ (6 × 4) + 4 = 24 + 4 = 28.

For, (18, 94, 5)

⇒ (18 × 5) + 4 = 90 + 4 = 94.

Hence, the correct answer is "Option 4".

Shortcut Trick

Side of rhombus (a) = 1/2 × √(d₁² + d₂²)

a = 1/2 × √(5² + 12²) = 1/2 × √(25 + 144) = 1/2 × 13 = 6.5 cm

Perimeter = 4 × side = 4 × 6.5 = 26 cm

∴ The correct answer is 26 cm.

Alternate Method

Given: Diagonal 1 (d₁) = 5 cm, Diagonal 2 (d₂) = 12 cm.

Formula Used: Diagonals of a rhombus bisect each other at 90°. Side² = (d₁/2)² + (d₂/2)².

⇒ In the right-angled triangle formed by the half-diagonals:

⇒ Side² = (5/2)² + (12/2)²

⇒ Side² = (2.5)² + (6)²

⇒ Side² = 6.25 + 36 = 42.25

⇒ Side = √42.25 = 6.5 cm

⇒ Perimeter = 4 × Side = 4 × 6.5 = 26 cm

∴ The correct answer is 26 cm.

Additional Information

Area of Rhombus

The area is calculated using the product of diagonals: Area = 1/2 × d₁ × d₂.

Properties of Rhombus

All four sides are equal, opposite angles are equal, and diagonals bisect each other at 90 degrees.

Relation between Side and Diagonals

The sum of squares of diagonals is equal to four times the square of the side: d₁² + d₂² = 4a².

The correct answer is Right to Privacy

Key Points

• Right to Privacy was declared a Fundamental Right by the Supreme Court of India in 2017.
• This landmark decision came from the case Justice K.S. Puttaswamy (Retd.) vs Union of India.
• The judgment held that the right to privacy is protected under Article 21 of the Indian Constitution, which guarantees the right to life and personal liberty.
• This ruling has significant implications for various aspects of individual privacy, including data protection and personal freedom.

Additional Information

• The Supreme Court of India plays a crucial role in interpreting and upholding the Constitution.
• The judgment on the right to privacy overturned previous rulings that did not recognize privacy as a fundamental right.
• This decision aligns India with other democracies that recognize the right to privacy as an essential human right.
• The ruling has paved the way for the development of comprehensive data protection laws in India.

Given:

125 ÷ 25 × 6 + [3 + (8 - 2)] ÷ 3

Formula used:

Order of operations (BODMAS/BIDMAS): Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication, Addition and Subtraction

Calculation:

125 ÷ 25 × 6 + [3 + (8 - 2)] ÷ 3

⇒ 125 ÷ 25 × 6 + [3 + 6] ÷ 3

⇒ 125 ÷ 25 × 6 + 9 ÷ 3

⇒ 5 × 6 + 3

⇒ 30 + 3

⇒ 33

∴ The correct answer is option (4).

Shortcut Trick

From the second condition, if 1 student moves from B to A they become equal, which means the difference between B and A is 2 (B − A = 2).

Test the correct answer 17 for A: If A = 17, then B = 19 (since B is 2 more than A).

Apply the first condition: Shift 5 students from A to B.

A becomes 17 − 5 = 12; B becomes 19 + 5 = 24.

Since 24 is twice 12, the condition is satisfied.

∴ The correct answer is 17.

Alternate Method

Let the number of students in Classroom A be x and in Classroom B be y.

Case 1: 5 students shifted from A to B.

⇒ New students in A = x − 5

⇒ New students in B = y + 5

⇒ y + 5 = 2 × (x − 5)

⇒ y + 5 = 2x − 10 ⇒ y − 2x = −15 ⇒ 2x − y = 15 --- (Equation 1)

Case 2: 1 student shifted from B to A.

⇒ New students in A = x + 1

⇒ New students in B = y − 1

⇒ x + 1 = y − 1 ⇒ y − x = 2 --- (Equation 2)

Solving the equations:

⇒ From Equation 2: y = x + 2

⇒ Substitute y in Equation 1: 2x − (x + 2) = 15

⇒ 2x − x − 2 = 15

⇒ x = 15 + 2

⇒ x = 17

∴ The correct answer is 17.

Additional Information

Framing Linear Equations

Linear equations are used to represent relationship constraints between two or more unknown quantities. Keywords like 'shifted', 'twice', and 'same' translate to arithmetic operations and equality.

Substitution Method

This involves expressing one variable in terms of the other from one equation (e.g., y = x + 2) and substituting it into the second equation to reduce it to a single-variable equation.

Checking Balance

When 1 item moves from B to A to make them equal, the initial difference is always 2. Generally, if moving 'n' items creates equality, the initial difference is 2n.

Given:

Angle for industry = 62^o

Angle for transportation = 55^o

Total amount spent on industry and transportation = $10 million

Total angle of the circle = 360^o

Formula used:

Total expenditure = (Amount spent on industry and transportation / (Angle of industry + Angle of transportation)) × Total angle

Calculation:

⇒ Total expenditure = (10 / (62 + 55)) × 360

⇒ Total expenditure = (10 / 117) × 360

⇒ Total expenditure ≈ 30.8 million

∴ The total approximate amount spent by the country on all sectors is $30.8 million.

Shortcut Trick

Net Selling Price (SP) = Marked Price (MP) × (100−d₁)% × (100−d₂)% × (100−d₃)%

42000 = 58000 × 0.95 × 0.90 × (1 − x/100)

42000 = 58000 × 0.855 × (1 − x/100) ⇒ 42000 = 49590 × (1 − x/100)

(1 − x/100) = 42000 ÷ 49590 ≈ 0.8469

x/100 = 1 − 0.8469 = 0.1531 ⇒ x ≈ 15.3

∴ The correct answer is 15.3.

Alternate Method

Given → Marked Price (MP) = Rs. 58,000, Final SP = Rs. 42,000, d₁ = 5%, d₂ = 10%, d₃ = x%. Formulas: SP = MP × (100 − d₁)/100 × (100 − d₂)/100 × (100 − d₃)/100

⇒ Price after first discount (5%) = 58000 − (5/100 × 58000) = 58000 − 2900 = Rs. 55,100. ⇒ Price after second discount (10%) = 55100 − (10/100 × 55100) = 55100 − 5510 = Rs. 49,590. ⇒ Discount amount required for third discount = 49590 − 42000 = Rs. 7,590. ⇒ x = (7590 ÷ 49590) × 100 ≈ 15.3055%.

∴ The correct answer is 15.3.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the base for the next discount is the value after the previous discount. Single equivalent discount for a and b is (a + b − ab/100)%.

Marked Price vs Selling Price

Marked Price is the list price, while Selling Price is the actual price after subtracting all discounts. Discount = MP − SP.

Given Table:

According to the given condition:

Given: $ # 9 4 @ 3

Here, 1st rule applies i.e. 1st element is a symbol and the last is a number.

$ → coded as L (as interchanged with code of 3)

# → coded as H

9 → coded as J

4 → coded as T

@ → coded as D

3 → coded as N (as interchanged with code of $)

So, $ # 9 4 @ 3 → Coded as L H J T D N

Hence, "Option 2" is the correct answer.

The correct answer is Rast Goftar

Key Points

• Rast Goftar was a journal published in 1851 for the purpose of social-religious reforms among the Parsis.
• The journal played a significant role in the reformist movement within the Parsi community, advocating for modernization and social change.
• It was part of the broader 19th-century reform movements in India that aimed at addressing social issues and promoting progressive values.
• The publication helped in spreading new ideas and encouraging debates on various social and religious topics among the Parsis.

Additional Information

• The Parsi community, originally from Persia (modern-day Iran), is a small yet influential minority in India, particularly in Mumbai.
• The 19th century saw a wave of social and religious reform movements across various communities in India, aiming at modernization and addressing social evils.
• Other significant journals of the time included Somaprakash, Bombay Herald, and Bombay Post, each catering to different audiences and purposes.
• The reformist movements often intersected with the broader Indian independence movement, with many reformers also being active in the struggle against British colonial rule.

The logic followed here is:

So, the missing term of the series is '34UW'

Hence, the correct answer is "Option 2".

Shortcut Trick

Using the complementary angle properties: if A + B = 90°, then sin A = cos B and tan A = cot B.

Here, 16° + 74° = 90° ⇒ sin 16°/cos 74° = 1.

Also, 14° + 76° = 90° ⇒ tan 14°/cot 76° = 1.

Sum = 1 + 1 = 2.

∴ The correct answer is 2.

Alternate Method

Given:

The expression is $\rm \frac{\sin 16°}{\cos 74°} + \frac{\tan14°}{\cot76°}$

Formula Used:

⇒ sin(90° − θ) = cos θ

⇒ tan(90° − θ) = cot θ

Calculations:

Convert the numerator terms using complementary angles:

⇒ sin 16° = sin(90° − 74°) = cos 74°

⇒ tan 14° = tan(90° − 76°) = cot 76°

Substitute these values back into the expression:

⇒ $\rm \frac{\cos 74°}{\cos 74°} + \frac{\cot 76°}{\cot 76°}$

⇒ 1 + 1 = 2

∴ The correct answer is 2.

Additional Information

Complementary Angle Trigonometric Identities

For any acute angle θ, sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, tan(90° − θ) = cot θ, and sec(90° − θ) = cosec θ.

Reciprocal Identities

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

The correct answer is V3 > V1 > V2

Key Points

• Option 2 is correct because the speed of light in a medium is inversely proportional to the refractive index of the medium.
• The refractive indices of mediums 1, 2, and 3 are 1.46, 1.65, and 1.31, respectively.
• Since the refractive index is inversely proportional to the speed of light, the medium with the highest refractive index will have the lowest speed of light.
• Thus, the correct relation is V3 > V1 > V2, corresponding to Option 2.

Additional Information

• Refractive Index is a measure of how much the speed of light is reduced inside a medium compared to the vacuum.
• The speed of light in vacuum is approximately 3 x 10^8 m/s.
• For a medium with refractive index n, the speed of light in that medium is given by V = c/n, where c is the speed of light in vacuum.
• Therefore, higher the refractive index, lower the speed of light in that medium.

The least possible Venn diagram for the given statement is as follows:

Conclusions:

(I) Some laptops are mobile phones - FALSE (Because there is no definite relation given between laptop and mobile phones it is a possible case only)

(II) Some telephones are laptops - FALSE (Because no definite relation is given between telephones and laptop it is a possible case only)

(III) All tablets are telephones - FALSE (Because, all mobile is laptop and some tablet is telephone is given in the statement and all mobile is telephone is a possibility but not definite)

So, 'None of the conclusions follows'

Hence, the correct answer is "Option 2".

Given: Eight clowns I, J, K, L, M, N, O and P were sitting around a square table, facing the centre. 

M is sitting at one of the corners

1. K was sitting to the immediate left of O.

2)  J was sitting to the immediate right of M.

3. P was sitting second to the right of L.

4. J was sitting fourth to the left of P.

5. N was sitting fourth to the left of K.

6. O was sitting to the immediate left of M.

So, M was sitting fourth to the left of I.

Hence, the correct answer is "Option 3".

The correct answer is Option 3: 1.16, towards

Key Points

• The refractive index of glass with respect to ice is calculated by dividing the refractive index of glass by that of ice, which gives a value of 1.16.
• As given in the question, the ray of light passes from ice to glass, and the refractive index of ice is less than that of glass.
• When light passes from a medium of lower refractive index to a higher refractive index, the ray bends towards the normal.
• In this case, since the refractive index of glass is higher than that of ice, the ray bends towards the normal in glass.
• This bending of light is governed by Snell’s law, which relates the angle of incidence and refraction to the refractive indices of the two media.

Additional Information

• Refractive Index: The refractive index (n) of a material is the ratio of the speed of light in a vacuum to the speed of light in the material. It indicates how much light is bent or refracted when entering the material from another medium.
• Snell's Law: Snell’s law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant and equals the ratio of the refractive indices of the two media.
• Light Behavior: When light moves from a less dense medium to a denser one (lower to higher refractive index), it bends towards the normal. Conversely, it bends away from the normal when it moves from a denser to a less dense medium.
• Applications of Refraction: Refraction plays a significant role in optics, such as in lenses, eyeglasses, microscopes, and other optical instruments.

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

1. K sits to the immediate left of G.

2)L sits to the immediate right of P.

3. P is fourth to the right of G.

4. L is fourth to the left of H.

So, total 11 persons are seated in the row

Hence, the correct answer is "Option 4".

Shortcut Trick

Let Initial Income = 100 units. Initial Expenditure = 72 units → Initial Savings (y) = 28 units.

New Income = 112 units. New Expenditure = 72 + 5% of 72 = 72 + 3.6 = 75.6 units.

New Savings (x) = 112 − 75.6 = 36.4 units.

Change in savings = 36.4 − 28 = 8.4 units.

Required percentage = (8.4 ÷ 28) × 100 = 30%.

∴ The correct answer is 30%.

Alternate Method

Given: Initial expenditure = 72% of income, Income increase = 12%, Expenditure increase = 5%.

Formula: Income = Expenditure + Savings

⇒ Let initial Income = 100.

⇒ y (Initial Savings) = 100 − 72 = 28.

⇒ New Income = 100 × (112/100) = 112.

⇒ New Expenditure = 72 × (105/100) = 75.6.

⇒ x (New Savings) = 112 − 75.6 = 36.4.

⇒ Required value = $\rm (\frac{x-y}{y}\times 100)\%$

⇒ Value = [(36.4 − 28) ÷ 28] × 100 = (8.4 ÷ 28) × 100 = 0.3 × 100 = 30%.

∴ The correct answer is 30%.

Additional Information

Income-Expenditure Alligation

You can use alligation between Expenditure % change and Savings % change to find the Income % change, where the ratio of parts is Expenditure : Savings.

Percentage Change Formula

Percentage Change = [(Final Value − Initial Value) ÷ Initial Value] × 100. This is used to find the growth or decline of a quantity relative to its base.

Shortcut Trick

Identify the expression as the Difference of Squares identity: (a² − b²) ÷ (a − b) = (a + b).

Here, a = 2.46 and b = 1.46.

Applying the trick: 2.46 + 1.46 = 3.92.

Converting the decimal to a fraction: 3.92 = 392/100.

∴ The correct answer is 392/100.

Alternate Method

Given:

Expression = (2.46 × 2.46 − 1.46 × 1.46) ÷ (2.46 − 1.46)

Formula Used:

Algebraic Identity: a² − b² = (a + b)(a − b)

Calculations:

⇒ Let a = 2.46 and b = 1.46

⇒ Expression = (a² − b²) ÷ (a − b)

⇒ Expression = [(a − b)(a + b)] ÷ (a − b)

⇒ Expression = (a + b)

⇒ Expression = 2.46 + 1.46

⇒ Result = 3.92

⇒ To express as a fraction: 3.92 = 392/100

∴ The correct answer is 392/100.

Additional Information

Algebraic Identities (Squares)

Standard square identities include (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Algebraic Identities (Cubes)

For cubic terms: a³ − b³ = (a − b)(a² + ab + b²) and a³ + b³ = (a + b)(a² − ab + b²).

Decimal to Fraction Conversion

To convert a decimal to a fraction, place the number over a power of 10 corresponding to the number of decimal places (e.g., 0.x = x/10, 0.xx = xx/100).