RRB Group D Previous Year Paper (Held on: 17 Sept 2022 Shift 3)

The correct answer is 36 Ω.

Key Points

Given:

Electric lamp resistance is 30 Ω and conductor resistance is 6 Ω which are connected in series to  6 V battery.

Formula:

For, resistors in series we have:

 $Rs=R1+R2+....+Rn$

Calculations:

$R1=30 Ω$

$R2=6 Ω$

$Rs=R1+R2=30+6=36Ω$

Therefore, total resistance of the circuit is 36 Ω.

Shortcut Trick

If a + b + c = 0, then a³ + b³ + c³ = 3abc.

Check: 23 + (−11) + (−12) = 23 − 23 = 0.

Result = 3 × 23 × (−11) × (−12) = 3 × 23 × 132 = 69 × 132.

69 × 132 = 9108.

∴ The correct answer is 9108.

Alternate Method

Given: a = 23, b = −11, c = −12.

Formula Used: a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca).

Calculations:

⇒ a + b + c = 23 + (−11) + (−12) = 0.

⇒ Since (a + b + c) = 0, the equation becomes a³ + b³ + c³ = 3abc.

⇒ 23³ + (−11)³ + (−12)³ = 3 × 23 × (−11) × (−12).

⇒ 69 × (−11 × −12) = 69 × 132.

⇒ 69 × 132 = 9108.

∴ The correct answer is 9108.

Additional Information

Algebraic Identity

The expression a³ + b³ + c³ − 3abc is zero whenever a + b + c = 0 or a = b = c.

Product of Three Numbers

Multiplying three numbers x, y, z where two are negative results in a positive value: (+) × (−) × (−) = (+).

The correct answer is Interest received on loans.

Key Points

• Interest received on loans is not a capital receipt.
• Capital receipts are inflows of funds that result in an increase in the net worth of a business or organization.
• Revenue receipts are inflows of funds that result in an increase in the income of a business or organization.

Additional Information

• Examples of capital receipts include the sale of fixed assets, the sale of equity or debt securities, the receipt of loans or other forms of financing, and the recovery of loans that were previously made.
• Capital receipts are typically used to finance long-term investments or to fund other capital expenditures, such as the expansion of a business or the acquisition of new assets.
• Revenue receipts, on the other hand, are typically generated from the ongoing operations of a business and are used to fund the day-to-day expenses of the business, such as salaries, rent, and utilities. Examples of revenue receipts include sales of goods or services, rent or lease payments, and interest income.

Given:

Calculation:

Total number of girls in the year 2016 in both colleges

= 60 + 210

= 270

Total number of girls in the year 2019 in both colleges

= 70 + 150

= 220

Ratio of girls in the year 2016 and 2019 in both colleges

= 270 : 220

= 27 : 22

Thus, the required ratio is 27 : 22.

Hence, the correct answer is option 1).

The correct answer is Bluish green.

Key Points:

• Red cabbage
• A purple solution known as a red cabbage indicator determines if the product is acidic or basic.
• A solution that serves as pH indicator can be made using red cabbage, which is frequently available in homes.
• Flavin, often known as anthocyanin, is a pigment molecule found in cabbage that reacts with acidity to change the color.
• The purple solution typically changes colour when it reacts with an acid, turning red, and when it reacts with the base, changing colour to bluish-green.
• The material is mainly neutral if it does not alter the colour.

Additional Information:

• To determine how acidic or basic the solution is, use pH scale.
• It ranges from 0 to 14, with 7 serving as the neutral.
• Anything with a pH below 7 is considered an acid, whereas anything with pH over 7 is considered a base.
• A material with pH of 2 is 10 times more acidic than one with pH of 3.
• The pH scale is a logarithmic scale.
• As the pH of the solution drops, the amount of hydrogen ions in the solution rises.

The correct answer is Karnataka.

Key Points:

• There are 1.10 million tonnes of Jet Black granite in the Kollegal region of Karnataka, which is split across Chamarajanagar, Mysore, and Mandya districts.
• Jet Black granite is used for flooring, decorative stones, and landscaping and is highly sought-after in the US, European, and Chinese markets.
• Karnataka was the leading exporter of granite before 1992, with a share of more than 50% of all exports.
• However, from 1993 to 1994, quarrying was prohibited in the Kollegal region due to the operations of the forest brigand Veerappan.

Additional Information:

• Granite is in high demand on the international market in the forms of rough-cuts, bush-hammered and charred slabs, paving tiles, wall panelling, stair treads and bathroom/kitchen unit tops.
• The state's granite potential has mainly gone untapped.
• The demand for granite ornaments is increasing internationally.
• Some of the strongest and most resilient stones in the world may be found in the charmokites of Tamil Nadu, Karnataka, and Andhra Pradesh.

The correct answer is 2.

Key Points:

• Between 1952 and 2020, two seats in the Lok Sabha, the lower house of the Indian Parliament, were reserved for Anglo-Indians.
• These two nominees were put forth by the Indian President at the government's suggestion.
• The President of India may propose no more than two members of the Anglo-Indian community if, in his/her judgement, that community is not sufficiently represented in the House.

Confusion Points

• The Anglo-Indian reserved seats in the Indian Parliament and State Legislatures disappeared in January 2020 thanks to the 126th Constitutional Amendment Bill of 2019, which was signed into law as the 104th Constitutional Amendment Act, 2019.
• At the time of the Indian Constitution's ratification, Article 331 provided the Anglo-Indian community a reserve; however, this reservation would end ten years after the Constitution's inception.

Additional Information:

• The Anglo-Indian community was the only one in India to nominate candidates for the Lok Sabha, or lower chamber, of the Indian Parliament.
• Jawaharlal Nehru granted this authority to Frank Anthony, the All India Anglo-Indian Association's first and longest-serving president.
• The representatives of the community were two people.
• This was carried out since the town lacked a native state of its own.
• Each of the 14 Indian states (Andhra Pradesh, Bihar, Chhattisgarh, Gujarat, Jharkhand, Karnataka, Kerala, Madhya Pradesh, Maharashtra, Telangana, Tamil Nadu, Uttar Pradesh, Uttarakhand, and West Bengal) also had a nominated representative in their respective State Legislative Assemblies.

The correct answer is "The Karve Committee".

 Key Points

• The Karve Committee
• In 1955, a small-scale industrial committee was established.
• Another name for it was a Karve committee.
• It was given the name Dattatreya Gopal Karve in honor of the professor and economist from India who made significant contributions to public policy, cooperative movements, and economics.
• The Karve Committee was established in 1955 to promote the development of small-scale companies.

Additional Information

• Kothari Commission
• The Government of India established the National Education Commission, also known as the Kothari Commission, as an ad hoc commission with the mandate to review all facets of the Indian educational system, create a general framework for education, and suggest rules and policies for the advancement of education in the country.
• Abid Hussain Committee
• On small-scale industries and Exim policy, the Abid Hussain Committee was appointed.
• The Nayak Committee
• The Reserve Bank of India established a Committee on December 9 under Deputy Governor Shri P.R. Nayank to investigate the challenges that small-scale industries (SSI) face while trying to secure financing.

Development Authority is NOT correct.

• Development Authority is not a part of the Local Government in India.
• Development Authority means a person or body appointed as a Development Authority as contemplated by and in accordance with the Municipal Government Act.
• It was envisaged that the development authorities would help in planning, implementing and coordinating development activities in a structured manner.
• The actual implementation of urban projects and master plans has started after the formation of the Urban Development Authorities.

Key Points 

• Local government in India refers to the government jurisdiction below the state level.
• A uniform three-tier structure of
• panchayats at village (Gram Panchayat - GP),
• intermediate or block (Panchayat Samiti - PS) and
• district (Zilla Parishad - ZP) levels.
• All the seats in the Panchayat at each level are to be filled by election from the respective regional constituencies.

Additional Information

• India is a federal republic with three regions of government: central, state and local.
• The 73rd and 74th Constitutional Amendments provide recognition and protection to local governments and in addition, each state has its own local government legislation.
• Since 1992, local government in India takes place in two different forms.
• Urban areas covered by the 74th Amendment to the Constitution have municipalities, but they derive their powers from individual state governments, while the powers of rural areas have been formalized under the Panchayati Raj system under the 73rd Amendment to the Constitution.

The correct answer is virus.

Key Points:

• Warts
• Small bumps called warts frequently appear on the skin of the hands and the feet.
• Warts can seem different and might grow singly or in groups.
• Some have a higher propensity to affect certain body parts.
• Though warts are not malignant, they can resemble several types of cancer.
• The human papillomavirus infection is what causes warts (HPV).
• The virus makes the top layer of the skin that generates an excessive quantity of keratin, a tough protein (epidermis).
• The additional keratin gives the wart its rough, hard texture.

Additional Information:

• Warts are transferred by intimate skin-to-skin contact even though they aren't regarded to be very contagious.
• The virus can also spread indirectly through contaminated surfaces or items, such as the area around a swimming pool.
• Your risk of infection increases if your skin is damaged or wet.
• After contracting the infection, a wart or verruca may not appear for several weeks or even months.

According to given information,

The third element from the right end of the given series is 9

(Left) 6 % 7 & 9 4 3 @ 2 8 * 3 # 9 & 2 (Right)

And,

The fourth element from the left end of the given series is &

(Left) 6 % 7 & 9 4 3 @ 2 8 * 3 # 9 & 2 (Right)

There are total 3 symbols between the third element from the right end and the fourth element from the left end of the given series i.e. @ ,  * , #

(Left) 6 % 7 & 9 4 3 @ 2 8 * 3 # 9 & 2 (Right)

Hence, "Option 1" is the correct answer.

The correct answer is "DigiSaksham". 

Key Points

• This digital skills program was started with the intention of promoting youth employability by enhancing their digital abilities, which have become crucial in today's increasingly technologically advanced world.
• Microsoft India and the Ministry of Labor and Employment collaborated on Digi Saksham.
• It is a continuation of the government's continuous initiatives to assist young people in rural and semi-urban areas.
• "Aga Khan Rural Support Programme India (AKRSP-I)" is the organization that will carry out the program on the ground.​

Additional Information

• ​​More than 3 lakh youth will receive free training in digital skills, including fundamentals and advanced computers, as part of the DigiSaksham program in the first year.
• The National Career Service (NCS) Portal is the place where you can access this training program.
• The campaign prioritizes hiring semi-urban job seekers from underserved communities who have lost their jobs due to the ongoing COVID-19 pandemic.

Given:

Calculation:

Number of Air coolers sold by the store Q on Thursday

= 27

Number of Air coolers sold by the store T on Saturday 

= 15

Number of Air coolers sold by store S on Tuesday

= 60

Average of above three 

= $\frac{(27 + 15 + 60)}{3}$

= $\frac{102}{3}$

= 34

Thus, the required value is 34.

Hence, the correct answer is option 1).

Shortcut Trick

Ratio of ages 5 years ago = 7 : 1 (Gap = 6 units)

Ratio of ages 5 years hence = 3 : 1 (Gap = 2 units)

Equating gaps: 5 years ago = 7 : 1 | 5 years hence = 9 : 3

Difference (9 − 7) = 2 units → 10 years (5 ago to 5 hence)

1 unit = 5 years ⇒ Ramesh 5 years ago = 7 × 5 = 35 years

∴ The correct answer is 40 years.

Alternate Method

Let the present age of Ramesh be R and his son be S.

Given:

Case 1 (5 years hence): R + 5 = 3 × (S + 5)

Case 2 (5 years ago): R − 5 = 7 × (S − 5)

Calculations:

⇒ From Case 1: R − 3S = 10 ... (i)

⇒ From Case 2: R − 7S = −30 ... (ii)

⇒ Subtracting (ii) from (i): 4S = 40

⇒ S = 10 years

⇒ Substitute S in (i): R − 3(10) = 10

⇒ R − 30 = 10

⇒ R = 40 years

∴ The correct answer is 40 years.

Additional Information

Ratio Difference Method

When the time gap between two ratios is constant, we multiply ratios by the difference of the other ratio to equalize the units of age change.

Age Problems Logic

The difference between the ages of two people remains constant throughout their lives, regardless of the number of years passed.

Equation Balancing

Always ensure to add or subtract years from both parties when moving forward or backward in time (e.g., n years hence = Age + n).

According to the given information,

• Adya is heavier than Dilipa
• Adya is lighter than fiya

​Fiya  > Adya > Dilipa

• Bidan is heavier than Fiya
• Charu is heavier than Bidan
• Charu is lighter than Esha

Esha > Charu > Bidan > Fiya  > Adya > Dilipa

• Only one student is heavier than Esha.
• Only two students are lighter than Dilipa

A > Esha > Charu > Bidan > Fiya  > Adya > Dilipa > B > C

There are 9 total students in the group.

Hence, "Option 1" is the correct answer.

Concept used:

BODMAS

Preference will be given on the basis of the letters coming first in the word Bodmas.

Calculation:

23.96 + 24.96 + 23.16 - 18.89 × 3.04 + 36.13 ÷ 6.1

Taking appro×imation: 24 + 25 + 23 - 19 × 3 + 36 ÷ 6

= 24 + 25 + 23 - 57 + 6 = 21

Thus, the required closest value is 21.

Hence, the correct answer is option 3).

Shortcut Trick

Original Speed = 100% = 84 km/h

Reduced Speed = 100% − 12% = 88%

New Speed = 84 × 0.88

New Speed = 73.92 km/h

∴ The correct answer is 73.92 km/h.

Alternate Method

Given:

Initial Speed of the bus = 84 km/h

Percentage Reduction in speed = 12%

Calculations:

⇒ Reduction in speed = 12% of 84

⇒ Reduction = (12 ÷ 100) × 84

⇒ Reduction = 0.12 × 84 = 10.08 km/h

⇒ New Speed = Initial Speed − Reduction

⇒ New Speed = 84 − 10.08

⇒ New Speed = 73.92 km/h

∴ The correct answer is 73.92 km/h.

Additional Information

Percentage Change Formula

New Value = Original Value × (100 ± Change%) ÷ 100. Use ± for increase or decrease.

Speed Conversion

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

Successive Percentage

If speed changes by a% and then b%, effective change = [a + b + (a × b)/100]%.

The correct answer is "Rajasthan".

Key Points

• Summer, which lasts from April through June in Rajasthan, is the hottest of all seasons.
• Rajasthan experiences extremely hot summers with temperatures averaging between 32 and 46 degrees Celsius.
• The environment is typically 38 degrees Celsius.
• Mt Abu is the only location in the state with a lower temperature this time of year.
• During the day, scorching winds from the west are known as "Loo" winds.

Additional Information

• Assam:
• The northeastern Indian state of Assam is renowned for its biodiversity, historical landmarks, and tea plantations.
• The largest city in Assam, Guwahati, is located in the west and is home to the hilltop Kamakhya Temple and silk bazaars.
• Maharashtra:
• Maharashtra is a state in western India's peninsula that takes up a sizable chunk of the Deccan Plateau.
• Maharashtra is the second-most populous country subdivision in the world as well as the second-most populous state in India.
• Telangana:
• A state in southern India is called Telangana.
• The Charminar, a 16th-century mosque in Hyderabad's capital, has four arches that support four enormous minarets.
• The monument offers a view of the city's venerable Laad Bazaar.

Shortcut Trick

Net percentage increase for two successive decades of 10% each = 10 + 10 + (10 × 10)/100 = 21%.

Population in 2000 = 2,25,000 × 121%.

Population in 2000 = 2,250 × 121 = 2,72,250.

∴ The correct answer is 2,72,250.

Alternate Method

Given:

Initial Population (P) in 1980 = 2,25,000

Rate of increase (R) = 10% per decade

Time period (n) = 1980 to 2000 = 2 decades

Formula Used:

Final Population = P × (1 + R/100)ⁿ

⇒ Population in 1990 = 2,25,000 × (110/100) = 2,47,500

⇒ Population in 2000 = 2,47,500 × (110/100)

⇒ Population in 2000 = 2,475 × 110

⇒ Population in 2000 = 2,72,250

∴ The correct answer is 2,72,250.

Additional Information

Successive Percentage Change

If a value is increased by x% and then by y%, the net percentage change is given by [x + y + (xy/100)]%.

Population Depreciation

If the population decreases at a rate R, the final population is calculated as P × (1 − R/100)ⁿ.

Multiplying Factor

For a 10% increase, the multiplying factor is 1.1. For two such increases, it is 1.1 × 1.1 = 1.21.

Given Table : 

According to Given series + 5 ^ 9 # 2 Condition 1 will be used 

If the first element is a symbol and the last, is a number, the codes for these two (the first and the last elements) are to be interchanged.

So, Code will be 

Thus, PFDZKN is the required code.

Hence, "Option 4" is the correct answer.

Given series: (Left) Q A Y S R E Z I L X B O P A R D I H O U K (Right)

Required pattern: Vowel → Consonant → Vowel

So, There are 3 consonants are there, each of which is immediately preceded by a vowel and also immediately followed by a vowel.

Hence, "Option 3" is the correct answer.

Shortcut Trick

Radius (r) = Diameter ÷ 2 = 12 ÷ 2 = 6 cm.

Volume = (4/3) × (22/7) × 6³ = (4/3) × (22/7) × 216.

⇒ 4 × (22/7) × 72 = 6336 ÷ 7 = 905 (1/7) cm³.

∴ The correct answer is 905 1/7 cm³.

Alternate Method

Given:

Diameter (d) of the sphere = 12 cm

π = 22/7

Formula Used:

Radius (r) = d/2

Volume (V) = (4/3)πr³

Calculations:

⇒ Radius (r) = 12 ÷ 2 = 6 cm

⇒ Volume = (4/3) × (22/7) × (6)³

⇒ Volume = (4/3) × (22/7) × 216

⇒ Volume = 4 × (22/7) × 72

⇒ Volume = 6336 ÷ 7

⇒ Volume = 905 (1/7) cm³

∴ The correct answer is 905 1/7 cm³.

Additional Information

Surface Area of Sphere

The total surface area of a sphere is given by the formula 4πr².

Volume of Hemisphere

The volume of a hemisphere is exactly half of a sphere: (2/3)πr³.

Total Surface Area of Hemisphere

For a solid hemisphere, the total surface area is 3πr² (curved surface + base area).

Given statement: Q < A < B ≤ C > D > E ≥ F

I. F < C → True  (as F ≤  E < D < C)

II. D < A → False ( as A < B ≤ C > D not possible)

Only conclusion I is true.

Hence, "Option 3" is the correct answer.

Given number: 56137428

After arranging in ascending order from left to right the number will be: 12345678

The digits which are second from the left is 2 : 12345678 

And second from the right is 7 : 12345678

The sum of  the digits which are second from the left and second from the right in the new number is 2 + 7 = 9

Hence, "Option 1" is the correct answer.

Shortcut Trick

Convert to standard quadratic equation form: x² − 7x + 10 = 0.

Identify the Sum of roots (−b/a) = 7 and Product of roots (c/a) = 10.

Check the options to find two numbers that satisfy both conditions.

For 5 and 2: Sum = 5 + 2 = 7 and Product = 5 × 2 = 10.

∴ The correct answer is 5, 2.

Alternate Method

Given: The equation is x + 10/x = 7.

Method: Standard algebraic factorization.

⇒ x + 10/x = 7

⇒ (x² + 10) / x = 7

⇒ x² + 10 = 7x

⇒ x² − 7x + 10 = 0

⇒ x² − 5x − 2x + 10 = 0

⇒ x(x − 5) − 2(x − 5) = 0

⇒ (x − 5)(x − 2) = 0

⇒ x − 5 = 0 or x − 2 = 0

⇒ x = 5 or x = 2

∴ The correct answer is 5, 2.

Additional Information

Quadratic Formula

For any equation ax² + bx + c = 0, the roots can be found using x = (−b ± √(b² − 4ac)) / 2a.

Nature of Roots

The discriminant D = b² − 4ac determines the type of roots: if D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Relationship between Roots and Coefficients

The Sum of roots (α + β) is always −b/a and the Product of roots (αβ) is always c/a.

The logic followed here is:

The difference between the odd terms is +6 & the difference between the even terms is +6.

Hence, the correct answer is Option 2.

Given:

4515 ÷ 12.9 = 350

Calculation:

4515 ÷ 12.9 = 350

⇒ $\frac{4515}{12.9}$ = 350

⇒ $\frac{(4.515 × 1000)}{(12.9)}$ = 350

⇒ $\frac{4.515}{12.9} = \frac{350}{1000}$

⇒ $\frac{4.515}{12.9}$ = 0.35

Thus, the required value is 0.35.

Hence, the correct answer is option 4).

Logic: First number × Second number - 6 = Third number

(12, 8, 90) → 12 × 8 - 6 ⇒ 96 - 6 = 90

and,

(8, 8, 58) → 8 × 8 - 6 ⇒ 64  - 6 = 58

Similarly,

(13, 7, 85) → 13 × 7 - 6 ⇒ 91  - 6 = 85

Hence, "Option 2" is the correct answer.

The correct answer is "10th".

Key Points

• A population that identifies as Sikh as well as a select group of initiated Sikhs are both referred to as Khalsa.
• The Tenth Guru of Sikhism, Guru Gobind Singh, founded the Khalsa tradition in 1699.
• Its founding was a significant occasion in Sikhism's history.
• Sikhs commemorate the foundation of Khalsa during the Vaisakhi holiday.

Additional Information

• Among the Dogras, Vaisakhi is also pronounced as Baisakhi.
• It is customarily observed every year on the first day of the month of Vaisakh, marking both the beginning of the month of Vaisakh and the new year of the Dogra calendar.
• In Northern India specifically, it is seen as a celebration of the spring harvest.
• Beyond its significance as the harvest festival, when Sikhs hold kirtans, visit nearby Gurdwaras, participate in community fairs, hold nagar kirtan processions, hoist the Nishan Sahib flag, and come together to socialize and share festive foods.
• Baisakhi commemorates significant historical occurrences in Sikhism and the Indian subcontinent that took place in the Punjab region.
• The Khalsa order was founded on April 13, 1699, by Guru Gobind Singh, the tenth Guru of Sikhism, and is commemorated by the major Sikh festival of Vaisakhi.

The correct answer is "Sand dune".

Key Points

• Wind that primarily blows in one direction creates the crescent-shaped sand dune known as Barchan, often spelt Barkhan.
• It can be found in sandy deserts all over the world.
• It is one of the most prevalent types of dunes.

Additional Information

• These sand dunes feature a very uneven cross-section, with a much sharper slope known as the slip face facing the wind and a much softer slope facing the opposite direction.
• The barchans' crescent-shaped horns, which are convex and point into the wind to show how the sand is moving horizontally.
• At its bottoms, Barchans can have heights of 9 to 30 metres (30 to 100 feet) and widths of 30 to 370 metres (1,214 to 1,214 feet).

Shortcut Trick

Use the direct relationship formula: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Ratio MP : CP = (100 + 10) : (100 − 10) = 110 : 90 = 11 : 9.

Marked-up value = 11 − 9 = 2 units.

Markup percentage = (2 ÷ 9) × 100 = 22.22%.

∴ The correct answer is 22.22%.

Alternate Method

Given: Discount = 10%, Profit = 10%.

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

⇒ Let Cost Price (CP) = 100.

⇒ Since Profit is 10%, Selling Price (SP) = 100 + 10 = 110.

⇒ This SP is obtained after a 10% discount on Marked Price (MP). So, 0.90 × MP = 110.

⇒ MP = 110 ÷ 0.90 = 1100 ÷ 9 = 122.22.

⇒ Markup Percentage = ((122.22 − 100) ÷ 100) × 100 = 22.22%.

∴ The correct answer is 22.22%.

Additional Information

Relation between MP and CP

The ratio of Marked Price to Cost Price can always be expressed as (100 + Profit%) / (100 − Discount%).

Marked Price vs Selling Price

Marked Price is the price printed on the label, while Selling Price is the final amount paid after deducting the Discount.

We have drawn the figure according to the information given in the question,

Distance between office and car parking area = 20 + 15 = 35 meters.

And Shiv is in the West direction where he parked his car from the office.

Hence, "Option 3 " is the correct answer.

The correct answer is "Indira Gandhi canal".

Key Points

• An important irrigation canal in India is the Indira Gandhi Canal.
• It begins in Punjab's Firozpur and ends with irrigation systems in Rajasthan's Thar Desert.
• Seven districts in Rajasthan are traversed by the canal: Barmer, Bikaner, Churu, Hanumangarh, Jaisalmer, Jodhpur, and Sriganganagar. Thus, Rajasthan now has more greenery.

Additional Information

• Indira Gandhi canal
• The project formerly known as the Indira Gandhi canal was given a new name in her honour.
• The Indira Gandhi Canal project was started in 1983 and finished in 2010 when Manmohan Singh was the prime minister of India.
• The Indira Gandhi Canal, which has a length of 445 km, was constructed to start agricultural operations in Rajasthan's fields.
• The Indira Gandhi Canal connects Punjab and Rajasthan over its length and was constructed using the Sutlej and Beas rivers.

Given word:  FRANTIC

Each vowel in the word FRANTIC is changed to the letter following it in the English alphabetical order So, the vowels in the word are 2 i.e.  A, and I.

After changing, the word will be: FRBNTJC

And each consonant in the word FRANTIC is changed to the letter preceding it in the English alphabetical order. So, consonants in the word are 5 i.e. F, R, N, T, C

After changing, the word will be: EQBMSJB.

B letter will appear twice in the group of letters thus formed.

Hence, "Option 1" is the correct answer.

Calculation:

According to the question,

[(ka)b-c × (kb)c-a × (kc)a-b] × (x0 - 1)

= [(ka)b-c × (kb)c-a × (kc)a-b] × (1 - 1)

= [(ka)b-c × (kb)c-a × (kc)a-b] × 0

= 0

Thus, the required value is 0.

Hence, the correct answer is option 3).

Shortcut Trick

Sum of ages 4 years ago = 20 − (4 × 2) = 12 years.

Ratio of Brijesh : William (4 years ago) = 1 : 2.

Total ratio units = 1 + 2 = 3 units.

3 units = 12 years ⇒ 1 unit = 4 years.

William's age 4 years ago = 2 units = 8 years.

William's present age = 8 + 4 = 12 years.

∴ The correct answer is 12 years.

Alternate Method

Given:

Sum of present ages of William (W) and Brijesh (B) = 20 years.

Condition: 4 years ago, Brijesh's age was half of William's age.

Formula used:

Sum of ages = Age₁ + Age₂

Age 'n' years ago = Present Age − n

Calculations:

⇒ W + B = 20 ⇒ B = 20 − W

⇒ 4 years ago: B − 4 = (W − 4) ÷ 2

⇒ 2 × (B − 4) = W − 4

⇒ 2 × (20 − W − 4) = W − 4

⇒ 2 × (16 − W) = W − 4

⇒ 32 − 2W = W − 4

⇒ 32 + 4 = W + 2W

⇒ 36 = 3W

⇒ W = 36 ÷ 3 = 12

∴ The correct answer is 12 years.

Additional Information

Constant Age Difference

The difference between the ages of two people always remains constant, regardless of how many years pass or go by.

Age Ratio Property

If the ratio of ages of A and B is x : y, then their ages can be assumed as xk and yk, where k is a common constant.

Sum of Ages Change

If there are 'n' people, the sum of their ages increases or decreases by n × t after or before 't' years.

The Venn Diagram is given below : 

The highlighted portion represents philanthropists who are NEITHER men NOR doctors.

3 philanthropists are NEITHER men NOR doctors.

Hence, "Option 2" is the correct answer.

The correct answer is 10000.

Key Points:

• The "Scheme for Protection and Preservation of Endangered Languages of India" was started by the Indian government (SPPEL).
• The Central Institute of Indian Languages (CIIL), Mysore, works on the conservation, recording, and preservation of all Indian mother tongues and endangered languages that are spoken by fewer than 10,000 people nationwide.
• 117 endangered languages and mother tongues from all over India have been selected for study and recording in the scheme's initial phase on the basis of priority.
• The University Grants Commission (UGC) has also launched two programs for the protection of endangered languages, namely "Establishment of Centres for Endangered Languages in Central Universities" and "Funding Support to the State Universities for Study and Research in Indigenous and Endangered languages in India."
• A total of Rs. 45.89 crores were made available by the UGC and CIIL between 2015–16 and 2019–20 under their programs for the preservation of endangered Indian languages.

Additional Information:

• As a means of communication and self-expression, language is a crucial component of any culture.
• Future generations lose a critical component of the culture that is required to fully comprehend it when a language is lost to extinction.
• Due to this, language is now a particularly vulnerable piece of cultural heritage, making its preservation even more crucial.
• According to statistics from the United Nations Educational, Scientific, and Cultural Organization ("Atlas of Languages in Danger of Disappearing"), there are an estimated 7,000 languages spoken worldwide today, with the eight most frequent languages being spoken by half of the world's population.

The correct answer is option 4)660W

Given:

$R1=10Ω,R2=20Ω,R3=30Ω$ are in parallel with a battery of 60 V connected with it

Formula:

For resistors in parallel: ${1 \over Rp}={1\over R1}+{1\over R2}+{1\over R3}$

and Power is $P={V^2\over R}$

Calculations:

${1 \over Rp}={1\over R1}+{1\over R2}+{1\over R3}$

${1 \over Rp}={1\over 10}+{1\over 20}+{1\over 30}$

${1 \over Rp}={6+3+2\over 60}={11\over 60}$

Therefore, $Rp={60\over 11}$.

Now, $P={V^2\over R}$

$P={60^2\over {60\over 11}}$

\(P={360011\over 60}=6011=660W\)

Therefore, the net power consumed is 660W.

The logic followed here is:

The difference between the odd terms is +2 & the difference between even terms is -2. 

Hence, the correct answer is Option 3.

Shortcut Trick

Multiply each marks obtained by its frequency (no. of students) and sum them up.

Total Marks = (25 × 5) + (30 × 6) + (35 × 3) + (40 × 1) = 125 + 180 + 105 + 40 = 450.

Total Students = 5 + 6 + 3 + 1 = 15.

Mean = 450 ÷ 15 = 30.

∴ The correct answer is 30 marks.

Alternate Method

Given:

Marks (x): 25, 30, 35, 40

Frequency (f): 5, 6, 3, 1

Formula Used:

Mean (x̄) = Σf_ix_i ÷ Σf_i

Calculations:

⇒ Total Students (Σf) = 5 + 6 + 3 + 1 = 15

⇒ Total Marks (Σfx) = (25 × 5) + (30 × 6) + (35 × 3) + (40 × 1)

⇒ Σfx = 125 + 180 + 105 + 40 = 450

⇒ Mean = 450 ÷ 15

⇒ Mean = 30

∴ The correct answer is 30 marks.

Additional Information

Arithmetic Mean

The Arithmetic Mean is the average of a set of numerical values, calculated by dividing the sum of values by the count of values.

Assumed Mean Method

Used for larger data sets: Mean = A + (Σfd ÷ Σf), where A is the assumed mean and d = x − A is the deviation.

Properties of Mean

If every value in the data set is increased or decreased by a constant, the mean also increases or decreases by that same constant.

Six persons, Aditya, Binod, Chaya, Dilshan, Estar and Fatima

Months : January, March, May, July, September and November.

• ​None of them travelled after Binod it means Binod travels in November.
• Binod travelled immediately after Chaya.

• Only three people travelled before Estar.
• Aditya travelled immediately after Fatima.
• Dilshan did not travel in the month of May.

Aditya travelled in the month of May.

Hence, "Option 3" is the correct answer.

Six persons, A, B, C, D, E and F

Months : January, March, May, July, September and November.

• None of them travelled after B it means B travels in the november
• B Travels just after C

• Only three people travelled before E.
• A travelled just after F.
• D did not travel in the month of May.

A travelled in month of May.

Hence, "Option 2" is the correct answer.

The correct answer is 14 u.

Key Points:

• homologous series
• A homologous series is made up of substances with the same functional group and similar chemical properties.
• A homologous series' members are referred to as homologs.
• A -CH₂ group distinguishes the following members of a homologous series from one another.
• A -CH₂ group has a molecular mass of 14 amu.
• As a result, the mass of each succeeding homologue in a homologous series varies by 14 amu.

Additional Information:

• Methane (CH₄) is followed by ethane (C₂H₆), propane (C₃H₈), butane (C₄H₁₀), and pentane (C5H12) in the homologous series of straight-chained alkanes.
• In that series, each new methylene bridge (-CH₂- unit) introduced in the chain causes the subsequent members to differ in mass.
• As a result, each member's molecular mass varies by 14 atomic mass units.
• "Adjacent homologues" are members of such a series that are close to one another, such as methane and ethane.
• Numerous physical characteristics in that series, such as the boiling point, gradually alter with increasing mass.
• Ethane (C₂H₆), for instance, has a higher boiling point than methane (CH₄).

The correct answer is the small intestine.

Key Points:

• Small intestine
• The small intestine entirely digests proteins, lipids, and carbohydrates.
• It receives the liver and pancreatic fluids for this purpose.
• The three parts of the small intestine are the duodenum, jejunum, and ileum.
• The substance that enters the duodenum through the pyloric end of the stomach is known as chyme (acidic).
• The small intestine is where ingested macromolecules are fully digested.
• The contents of the stomach are absorbed by the small intestine before entering the bloodstream.

Additional Information:

• The stomach:
• ​Pepsin from the stomach and trypsin and chymotrypsin from the pancreas are the three main enzymes that break down dietary proteins into polypeptides in the stomach and duodenum.
• Different exopeptidases and endopeptidases subsequently break these polypeptides down into amino acids.
• The rectum:
• The rectum's duties include collecting stool from the colon, alerting you to the presence of stool, and holding the stool until evacuation occurs.
• The large intestine:
• ​The large intestine's function is to absorb water and salt from food that hasn't been completely digested as well as to expel any leftover trash.
• By the time food and digestive juices hit your big intestine, the majority of digestion and absorption have already taken place.

The correct answer is Sonali Bank Ltd.

Key Points:

• There are 1230 branches total for Sonali Bank.
• The Dinajpur Board Branch branch is the most recent to begin operations.
• 67 of them are in urban areas, 746 are in rural areas, and two are abroad.
• For the purpose of facilitating remittances in foreign currencies, it also runs the Sonali Exchange Company Inc. in the USA, Sonali Exchange in Dubai (UAE), Sonali Bank (UK) Ltd. in the United Kingdom, Hong Kong (HAR), and Singapore.
• Including Dhaka, Chittagong, Sylhet, Moulvibazar, Beanibazar, Balaganj, Biswanath, Jagannathpur, Sunamganj, Gopalganj, Nabiganj Upazila, Hobigonj, Kulaura, Tajpur, Sonali Bank UK sends money directly to up to 25 locations in Bangladesh.
• The Reserve Bank of India claims that Sonali Bank is a foreign bank operating in India.

Additional Information:

• By combining and nationalizing the National Bank of Pakistan, Bank of Bahawalpur, and Premier Bank branches that had been located in East Pakistan before the 1971 Bangladesh Liberation War, Sonali Bank was founded in 1972 under the Bangladesh Banks (Nationalisation) Order.
• Sonali Bank had a paid-up capital of 30 million taka when it was founded.
• Dr. Atiur Rahman was a director of Sonali Bank from 1996 to 1999.
• In 2001, it had a paid-up capital of Tk 3.272 billion and an authorized capital of Tk 10 billion.
• Its authorized and paid-up capital are currently 10 and 9 billion Bangladeshi taka, respectively.
• On June 30, 2000, the bank's reserve funds were Tk 2.050 billion, up from Tk 60 million on June 30, 1979.

Given:

3 + 3 × [{11 - 2} ÷ 3] - 2 × 3

Concept used:

BODMAS

Preference will be given on the basis of Letters coming first in the word Bodmas.

Calculation:

3 + 3 × [{11 - 2} ÷ 3] - 2 × 3 

= 3 + 3 × [{9} ÷ 3] - 2 × 3

= 3 + 3 × [3] - 6

= 3 + 9 - 6

= 12 - 6

= 6

Thus, the required value is 6.

Hence, the correct answer is option 2).

The correct answer is option 2)+3

Given:

$f=-18cm$

$u=-12cm$

Formula:

Mirror formula: ${1\over f}={1\over u}+{1\over v}$

Magnification: $m={-v\over u}$

Calculations:

${1\over f}={1\over u}+{1\over v}$

${1\over -18}={1\over -12}+{1\over v}$

${1\over v}={1\over 12}-{1\over 18}$

${1\over v}={18-12\over 12*18}={6\over216}$

$v={216\over6}=36cm$

Therefore, we have $m={-v\over u}$

$m={-(36)\over -12}=+3$

Thus, the magnification produced by the mirror is +3.

The correct answer is Only A.

Key Points:

• The output and equilibrium price will both shift in the same direction in response to changes in demand.
• A fall in demand will result in a decrease in a good's equilibrium price and quantity.
• At the original price, there is an excess supply due to the decline in demand.
• Price will drop due to the oversupply, and as a result, producers will be ready to create less of the good, reducing output.
• A rise in demand will result in an increase in a good's equilibrium price and output.
• Excess demand arises at the starting price as a result of the growth in demand.
• The price will increase (inflationary gap) due to excessive demand, and as the price increases, manufacturers will be more inclined to sell, boosting output.

Additional Information:

• Equilibrium price and output will move in opposite directions as a result of a change in supply.
• A decrease in the equilibrium price and a rise in the equilibrium quantity of an item will result from an increase in supply.
• At the starting price, the increase in supply results in an excess supply.
• A surplus of supply lowers the price and raises the quantity sought.
• An increase in equilibrium price and a drop in the equilibrium quantity of a good will result from a decrease in supply.
• At the starting price, there is an excess demand due to the decrease in supply.
• The price rises and the quantity requested declines as a result of excessive demand.

Circle = Hockey

Square = Golf players

Triangle = Badminton players

Persons who play golf, hockey, and Badminton are 3 + 7 = 10

And persons who play both golf and hockey but NOT badminton are 10 - 3 = 7

Hence, "Option 2" is the correct answer.

The Correct Answer is Cannot be composted.

Key Points

• ​Biodegradable plastics can decompose naturally in the environment, giving an end product that is less harmful and can also be easily recycled through an organic process.
• ​Biodegradable plastics consume less energy during their manufacture, even though their production requires more investment. Hence, reduction of environmental pollution.
• Biodegradable plastics break down easily and can be absorbed by the soil or converted into compost. Even if a complete breakdown does not occur, it helps in achieving a reduction in the amount of space required to dispose of plastic waste.
• Biodegradable plastics lessen the amount of greenhouse gas emissions. Their decomposition does not release harmful products.

Additional Information

• There is a risk of contamination as the crops are typically sprayed with pesticides and can easily be transferred or included in the end product.
• There is a need for costly equipment, industrial processors, and composters.
• Some biodegradable plastics may produce methane when decomposing in landfills, it can accelerate climate change.
• Biodegradable Plastics need to be disposed of in very particular methods and require water to decompose properly, to ensure proper and timely decomposition.

Shortcut Trick

Area of rectangle = Length × Breadth = 1400 m².

Difference between Length and Breadth = 22 m.

Test options for Breadth (b): If b = 28, then Length (l) = 28 + 22 = 50.

Product: 50 × 28 = 1400. This matches the given area.

∴ The correct answer is 28 m.

Alternate Method

Given: Area = 1400 m², Length (l) = Breadth (b) + 22.

Formula Used: Area = l × b

⇒ b × (b + 22) = 1400

⇒ b² + 22b − 1400 = 0

⇒ b² + 50b − 28b − 1400 = 0

⇒ b(b + 50) − 28(b + 50) = 0

⇒ (b − 28)(b + 50) = 0

⇒ b = 28 or b = −50 (Breadth cannot be negative)

∴ The correct answer is 28 m.

Additional Information

Perimeter of Rectangle

The distance around the boundary of a rectangle is given by 2 × (Length + Breadth).

Diagonal of Rectangle

The straight line connecting opposite corners is calculated using √(Length² + Breadth²).

Quadratic Roots Property

For a quadratic equation ax² + bx + c = 0, the sum of roots is −b/a and the product is c/a.

Shortcut Trick

The parts are related as A/2 = B/3 = C/5 = k.

Ratio of A : B : C = 2 : 3 : 5.

Total units = 2 + 3 + 5 = 10 units.

Given total amount = ₹2,000.

10 units = 2,000 ⇒ 1 unit = 200.

A's part (2 units) = 2 × 200 = 400.

∴ The correct answer is ₹400.

Alternate Method

Given → Total Amount = ₹2,000 | Condition: (1/2)A = (1/3)B = (1/5)C. Formulas: Total = A + B + C | Ratio x : y : z ⇒ Share of x = [x ÷ (x+y+z)] × Total.

⇒ Let (1/2)A = (1/3)B = (1/5)C = k. ⇒ A = 2k, B = 3k, C = 5k. ⇒ 2k + 3k + 5k = 2,000. ⇒ 10k = 2,000 ⇒ k = 200. ⇒ A's part = 2 × 200 = 400.

∴ The correct answer is ₹400.

Additional Information

Ratio and Proportion

If aA = bB = cC, then the ratio A : B : C is 1/a : 1/b : 1/c.

Division of Amount

To divide a sum S in ratio a:b:c, the parts are [a/(a+b+c)]S, [b/(a+b+c)]S, and [c/(a+b+c)]S.

The correct answer is Fe(s).

Key Points:

• The given reaction is:
• 4Fe(s) + 3O2(g) → 2Fe2O3(s).
• Oxidizing agents are substances that have the ability to add oxygen, a non-metallic chemical, and remove hydrogen, or a metallic element.
• Iron oxide is created when iron and air interact (rust).
• Iron is oxidized in this reaction by the addition of oxygen.
• Here, the oxidizing agent is oxygen.

Additional Information:

• Oxidation-reduction
• An oxidation-reduction (redox) reaction is a chemical process in which two compounds exchange electrons.
• Any chemical reaction in which the oxidation number of a molecule, atom or ion changes by acquiring or losing an electron is referred to as an oxidation-reduction reaction.
• Many fundamental processes of life, such as photosynthesis, respiration, combustion, and corrosion or rusting, depend on redox reactions.
• Energy changes in form of heat, light, electricity, etc. accompany these reactions.
• The addition of oxygen or hydrogen to various compounds is another step in the oxidation and reduction reactions.

The Correct Answer is IIT-Bombay.

Key Points

• ​"NanoSniffer" was introduced on April 9, 2021, by Union Education Minister Ramesh Pokhriyal, or "Nishank."
• India used a NanoSniffer micro-electromechanical system (MEMS) to create the first micro-sensor-based explosive trace detector (ETD) in the world.
• The IIT Bombay startup NanoSniff Technologies created Nanosniffer, while Vehant Technologies, a spin-off of the IIT Delhi startup Kritikal Solutions, is responsible for marketing it.
• It accurately identifies a variety of military, commercial, and homemade explosives threats and offers visible and auditory alerts with a sunlight-readable colour display. NanoSniffer offers trace detection of the nano-gram level of explosives in less than 10 seconds.

Additional Information

• NanoSniffer
• ​High Energy Materials Research Laboratory (HEMRL) testing conducted by the DRDO in Pune found Nanosniffer to be successful.
• The nation's top counterterrorism unit, the National Security Guard, has also tested Nanosniffer (NSG).
• The development of NanoSniffer is a step towards Atmanirbhar Bharat, Prime Minister Narendra Modi's goal for an independent India.

Given:

\(\left[(12 \div 4) \times\left{\frac{12}{3}+\frac{5}{3} \times(7-4)\right}\right] \)

Concept used:

BODMAS

Preference will be given on the basis of the letter coming first in the word Bodmas.

Calculation:

\(\left[(12 \div 4) \times\left{\frac{12}{3}+\frac{5}{3} \times(7-4)\right}\right] \)

= \(\left[(12 \div 4) \times\left{\frac{12}{3}+\frac{5}{3} \times(3)\right}\right] \)

= \(\left[(12 \div 4) \times\left{4+5\right}\right] \)

= [(12 ÷ 4) × $9$]

= 3 × $9$

= 27

Thus, the required value is 27.

Hence, the correct answer is option 4.

Given number: 2079816

After arranging numbers in increasing order from left to right it becomes ,

0126789

And the middle digit will be 6.

Hence, "Option 2" is the correct answer.

Given:

$\frac{0.068 \times 3.5 \times 12}{3.6 \times 0.17 \times 7}$

Calculation:

$\frac{0.068 \times 3.5 \times 12}{3.6 \times 0.17 \times 7}$

= $\frac{68 \times 3.5 \times 12}{36 \times 17 \times 7}$

= $\frac{2856}{4284}$

= $\frac{2}{3}$

Hence, the required value is $\frac{2}{3}$

According to the given information directions are represented as,

Mohit is in the East direction with respect to Kamal.

Hence, "Option 3" is the correct answer.

According to english alphabet series 

The pattern followed here is :

ULJ - POO - KLT

and,

LMF - GNK - BMP

Similarly,

PIO - KRT - FIY

Hence, "Option 1" is the correct answer.

Shortcut Trick

Ratio of Cost Price (CP) to Marked Price (MP) is given by (100 − D%) : (100 + P%).

CP : MP = (100 − 20) : (100 + 25) = 80 : 125.

Simplifying the ratio: 16 : 25.

According to the question, 25 units = ₹150.

1 unit = 150 ÷ 25 = ₹6.

16 units = 16 × 6 = ₹96.

∴ The correct answer is ₹96.

Alternate Method

Given: Marked Price (MP) = ₹150, Discount = 20%, Profit = 25%. Formulas: Selling Price (SP) = MP × (100 − D%) ÷ 100 | Cost Price (CP) = SP × 100 ÷ (100 + P%).

⇒ SP = 150 × (100 − 20) ÷ 100 = 150 × 0.8 = ₹120. ⇒ CP = 120 × 100 ÷ (100 + 25) = 120 × 100 ÷ 125. ⇒ CP = 120 × 4 ÷ 5 = 24 × 4 = ₹96.

∴ The correct answer is ₹96.

Additional Information

Relationship between CP and MP

The direct formula CP/MP = (100 − Discount%) / (100 + Profit%) is derived by equating the two expressions for Selling Price (SP).

Marked Price and Discount

Discount is always calculated on the Marked Price (MP), while Profit or Loss is calculated on the Cost Price (CP).

The correct answer is less deep than it actually is.

Key Points:

• When viewed directly above, swimming pools appear shallower than they actually are due to light reflection at the water's surface.
• The reason for this is that the light rays emanating from the submerged item do not strike us directly.
• As long as the light is in the water, it goes straight; however, if the light exits the water obliquely into the air, it is bent downward toward the surface.
• Refraction is the term for this bending, which happens whenever light travels through one transparent medium and then into another that has a different density.
• Our eyes do not account for refraction; instead, they determine the object's position as though the light had come from a straight line.
• Light accelerates once again as it leaves a liquid or piece of glass and enters the air.
• It will refract away from the normal if it encounters the glass-air interface at any angle other than 0°.
• This is accurate for small angles, however as the angles increase, something else occurs.
• Because of this, swimming pools seem to get shallower as you approach the end that is farthest from you.

Additional Information:

• Refraction in physics is the redirection of a wave as it travels through one medium and then another.
• A change in the medium or a change in the wave's speed might both result in a redirection.
• Although refraction of light waves is the most frequently seen phenomenon, refraction can also occur with sound waves and water waves.
• The wave speed change and the initial wave propagation direction in relation to the wave speed change both affect how much a wave is refracted.

Shortcut Trick

Total Salary = 100%

Rent = 20% | Remaining = 100% − 20% = 80%

Sum of non-rent values = 600 (Conveyance) + 3500 (Grocery) + 500 (Savings) = ₹4,600

80% of Salary = 4,600

100% of Salary = (4,600 ÷ 80) × 100 = 57.5 × 100 = ₹5,750

∴ The correct answer is ₹5,750.

Alternate Method

Given:

House Rent = 20% of Salary

Conveyance = ₹600

Grocery = ₹3,500

Savings = ₹500

Formula Used:

Total Salary = Rent + Conveyance + Grocery + Savings

Monthly Salary Distribution (100%)

Rent 20% Conveyance + Grocery + Savings 80% = ₹4,600

Total Salary (x) = ?

Calculations:

⇒ Let the total monthly salary be x.

⇒ Expenditure on Rent = 20% of x = 0.20x

⇒ Sum of Conveyance, Grocery, and Savings = 600 + 3,500 + 500 = ₹4,600

⇒ Total Salary − Rent = Conveyance + Grocery + Savings

⇒ x − 0.20x = 4,600

⇒ 0.80x = 4,600

⇒ x = 4,600 ÷ 0.80

⇒ x = 46,000 ÷ 8

⇒ x = 5,750

∴ The correct answer is ₹5,750.

Additional Information

Basic Income-Expenditure Relation

Income = Total Expenditure + Savings. This is the fundamental equation for all salary-based problems.

Percentage Expenditure

If p% is spent on one item, then the remaining percentage is (100 − p)%. The absolute value of the remaining amount can be equated to this remaining percentage.

Successive Percentage Method

If a man spends x% of salary and then y% of the remaining salary, the final savings = Total × (100 − x)/100 × (100 − y)/100.

The correct answer is The** rituals of the Yagna.**

Key Points

• The Yajur Veda contains the rituals of the Yagna.
• The Yajur Veda is an ancient collection of Sanskrit verses and mantras, used in Hindu rituals and worship.
• It is one of the four primary scriptures of Hinduism known as the Vedas - Rig Veda, Yajur Veda, Atharva Veda and Sama Veda.**
• The name is derived from the Sanskrit roots - yajus, meaning "sacrifice" or "worship" and veda, meaning "knowledge", Yajur Veda can be translated as "Knowledge of the Sacrifice".
• The Yajur Veda is divided into two parts - the "pure" or white Yajur Veda known as Shukla, and the "dark" or black Yajur Veda known as Krishna. The Shukla deals with prayers and specific instructions for devotional sacrifices, whereas the Krishna deals with sacrificial rituals.

Additional Information

• The Sama Veda deals with melodies. 
• ​It is a collection of melodies and chants, and is also called the "Book of Song", "Veda of Chants" or "Yoga of Song."
• It should not be read or recited, but sung.
• The Atharva Veda contains magic spells. 
• ​It is a collection of 20 books containing chants, hymns, spells and prayers; and involves issues such as healing of illnesses, black magic, prolonging life, and rituals for removing maladies and anxieties.
• The Rig Veda is the Veda of mantra.
• It is organized into 10 books, called mandalas.
• It is the oldest of the Vedas, and one of the oldest extant texts in any Indo-European language.

Shortcut Trick Convert the equation to standard form: x2 + 18x + 56 = 0. Check the Sum of roots (−b/a = −18) and Product of roots (c/a = 56). Since the product is positive and the sum is negative, both roots must be negative. Calculate Discriminant D = 182 − 4(56) = 100, which is a perfect square. A perfect square discriminant implies that the roots are rational. ∴ The correct answer is both the roots are negative and rational.

Alternate Method Given Equation: (x + 12) (x + 6) = 42 Step 1: Expand the left side of the quadratic equation. ⇒ x(x + 6) + 12(x + 6) = 16 ⇒ x2 + 6x + 12x + 72 = 16 Step 2: Bring all terms to one side to form the standard quadratic equation ax2 + bx + c = 0. ⇒ x2 + 18x + 72 − 16 = 0 ⇒ x2 + 18x + 56 = 0 Step 3: Solve for x by factorization (splitting the middle term). ⇒ x2 + 14x + 4x + 56 = 0 ⇒ x(x + 14) + 4(x + 14) = 0 ⇒ (x + 14)(x + 4) = 0 Step 4: Find the roots of the equation. ⇒ x + 14 = 0 or x + 4 = 0 ⇒ x = −14, −4 Conclusion: Both −14 and −4 are negative integers, and all integers are rational numbers. ∴ The correct answer is both the roots are negative and rational.

Additional Information Discriminant and Nature of Roots The nature of roots is determined by D = b2 − 4ac. If D > 0 and is a perfect square, roots are real, distinct, and rational. If D > 0 and not a perfect square, roots are irrational. Signs of Roots For the equation ax2 + bx + c = 0, if a, b, and c have the same sign, both roots are negative. If c/a is positive and −b/a is negative, both roots are negative. Rational Numbers A number is rational if it can be expressed as p/q where p and q are integers and q ≠ 0. All integers (like −14 and −4) are rational because they can be written as −14/1 and −4/1.

Shortcut Trick

The standard congruence criteria for triangles are SSS, SAS, ASA, AAS, and RHS.

The condition SSA (Two sides and a non-included angle) is not a valid criterion for congruence.

In the SSA case, it is possible to construct two different triangles using the same measurements, known as the ambiguous case.

Unless the angle is specifically the included angle (forming the SAS rule), the triangles are not necessarily congruent.

∴ The correct answer is If two sides and an angle of one triangle are equal to two sides and an angle of the other triangle, then the two triangles are congruent.

Alternate Method

Given: Various criteria for triangle congruence.

Properties Used: SAS (Side-Angle-Side) axiom and the Ambiguous Case of triangles.

⇒ For congruence, the SAS rule state that the angle must be the included angle between the two equal sides.

⇒ If the angle is not included (SSA), we can have a situation as shown in the diagram.

⇒ Consider ΔABC and ΔABD. They both share side AB (c), side BC = BD (a), and ∠A (35°).

⇒ Even though they have two sides and one angle equal, ΔABC is clearly not congruent to ΔABD.

⇒ This proves that two sides and an angle (non-included) do not guarantee congruence.

∴ The correct answer is If two sides and an angle of one triangle are equal to two sides and an angle of the other triangle, then the two triangles are congruent.

Additional Information

SAS Congruence Criterion

Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

ASA and AAS Rules

Two triangles are congruent if two angles and any side (included or non-included) are equal, as the third angle is automatically equal by the angle sum property.

RHS Congruence Criterion

For right-angled triangles, if the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of another, they are congruent (this is a special case of SSA).

The SSA Ambiguous Case

SSA does not guarantee congruence because, depending on the side lengths, zero, one, or two distinct triangles can be formed with the same given parts.

Shortcut Trick

The volume of a sphere is proportional to the cube of its radius (V ∝ r³).

Since the larger sphere is melted and cast into 1000 identical small spheres, the volume of each small sphere is 1 ÷ 1000 of the larger sphere.

Scale factor of radius = ³√(1 ÷ 1000) = 1 ÷ 10

Radius of small sphere = 10 cm × (1 ÷ 10) = 1 cm

Diameter of small sphere = 2 × 1 cm = 2 cm

∴ The correct answer is 2 cm.

Alternate Method

Given:

Radius of the larger sphere (R) = 10 cm

Number of identical small spheres (n) = 1000

The total volume of the small spheres is equal to the volume of the larger sphere.

Formula Used:

Volume of a sphere = (4 ÷ 3) × π × r³

Calculations:

Let the radius of each small sphere be r.

Since the total volume of 1000 small spheres equals the volume of the larger sphere:

⇒ 1000 × (4 ÷ 3) × π × r³ = (4 ÷ 3) × π × R³

Dividing both sides by (4 ÷ 3) × π:

⇒ 1000 × r³ = R³

Substitute the value of R = 10 cm:

⇒ 1000 × r³ = 10³

⇒ 1000 × r³ = 1000

⇒ r³ = 1

⇒ r = 1 cm

The diameter (d) of each of the small spheres is:

⇒ d = 2 × r

⇒ d = 2 × 1 cm = 2 cm

∴ The correct answer is 2 cm.

Additional Information

Volume and Surface Area of a Sphere

For any sphere of radius r, its volume is V = (4 ÷ 3) × π × r³ and its total surface area is A = 4 × π × r².

Volume Conservation in Recasting

When a solid object is melted and recast into another set of solid shapes, the total volume remains constant: V_initial = V_final.

Scaling of Spheres Property

If a larger sphere of radius R is recast into n identical small spheres of radius r, the relation is given by r = R ÷ n^1/3.

The correct answer is ₹3,000.

Key Points:

• On March 5, 2019, Prime Minister Narendra Modi unveiled the Pradhan Mantri Shram Yogi Maan-dhan pension programme.
• With the help of this massive pension plan, unorganised workers with monthly incomes of no more than Rs 15,000 are protected from financial hardship as they age.
• Any unorganised worker between the ages of 18 and 40 whose employment is temporary in nature, including home-based workers, street vendors, head loaders, brick kiln workers, cobblers, rag pickers, domestic workers, washermen, rickshaw pullers, rural landless labourers, agricultural workers, construction workers, beedi workers, handloom weavers, leather workers, etc.
• The employee should not be enrolled in any mandatory social security programmes, such as the National Pension System (NPS), the Employees' State Insurance Corporation programme, or the Employees' Provident Fund Organization programme.
• If an unorganised worker joins the programme and has made regular contributions up until the age of 60, he would receive a pension that is at least Rs. 3000 per month.
• A monthly family pension equal to 50% of the pension will be paid to the surviving spouse after his or her passing.

Additional Information:

• There is no minimum level of education required to join the Scheme.
• The subscriber just needs to pay the set contribution amount that was established at the time of joining the Scheme.
• For unorganised workers who are older than 40, there is no exception available for them to join the scheme.
• When the family pension is informed of a death and a death certificate is produced, the spouse, if still alive, will automatically be the beneficiary.
• Following the demise of the subscriber and his or her spouse, the dependents will not be eligible for pension payments.

The correct answer is Antim Panghal.

Key Points:

• Antim Panghal was significantly better than her competitors in the 53 kg weight class.
• She defeated Amory Andrich of Germany, the U20 European champion, in the first round before pinning Ayaka Kimura (Japan).
• She out-technical Nataliia Klivchutska of Ukraine to win the semifinal match.
• In the crucial match, Antim defeated Alytn Shagayeva of Kazakhstan.
• After scoring two more points with one more takedown, she secured the deal.

Additional Information:

• Mulayam Yadav 
• ​Indian socialist leader Mulayam Singh Yadav created the Samajwadi Party.
• He held the positions of Minister of Defence and Chief Minister of Uttar Pradesh for three terms each during the course of his more than a six-decade political career in India.
• Sushil Kumar
• Sushil Kumar Solanki is an Indian wrestler.
• He carried the Indian flag during the opening ceremony of the 2012 London Olympics.
• Since 1952 Olympian Khashaba Dadasaheb Jadhav's bronze medal, his 2008 Olympic medal was India's first wrestling medal.

Five friends: Sandya, Rinku, Prachi, Thiru and Madavi (all are facing north)

Sandya is to the immediate left of Rinku

Sandya is to the immediate right of Prachi.

Thiru is an immediate neighbour of both Rinku and Madavi.

Madavi is somewhere to the right of Rinku.

Madavi is sitting at the rightmost end.

Hence, "Option 4" is the correct answer.

The correct answer is 35 Years.

Key Points:

• The position of the president was established on January 26, 1950, when India became a republic after obtaining independence on August 15, 1947, when its constitution took effect.
• The legislative assemblies of each of India's states and territories, as well as both chambers of the Indian Parliament, which were all chosen directly by the people, are used to elect the president in an indirect manner.
• Although all of the executive functions granted to the president are actually exercised by the prime minister on the advice of Cabinet Ministers, Article 53 of the Indian Constitution stipulates that the president may exercise these powers personally or through subordinate authority.
• The legal minimum age to run in the Indian presidential election is 35.

Additional Information:

• According to Article 60, the president's main responsibility is to uphold, defend, and preserve the Indian constitution and the law.
• On the chief justice's recommendation, the president selects the Chief Justice of India and other judges.
• A judge may be fired by the President with the support of two-thirds of the two Houses of the parliament.
• According to Article 76(1) of the Indian Constitution, the president of India appoints the Attorney General of India, who serves at the president's leisure as the government of India's top legal advisor.
• The president may also request the advisory opinion of the supreme court under Article 143 if they believe a legal issue or a matter of public interest has emerged.
• According to Article 88, the president may request that the attorney general attend the parliamentary proceedings and, if any, notify him of any illegal activity.

Six students P, Q, R, S, T, and U (All of them are facing north)

• T stands at the extreme right end of the row

• T is to the immediate right of U.

• Q stands third to the left of U.

• Q stands to the immediate left of S.

• Q stands second from one of the ends

• Q stands immediately to the right of P.

• Only two persons stand between P and R.

• R stands second to the left of the T.

• The number of persons standing to the left of T is the same as to the right of P.

Two persons stand between Q and U

Hence, "Option 3" is the correct answer.

Shortcut Trick

Check options for given conditions: Sum of digits = 9 and Tens digit = 2 × Units digit.

Option 1: 54 → 5+4=9, but 5 is not 2×4.

Option 2: 45 → 4+5=9, but 4 is not 2×5.

Option 3: 36 → 3+6=9, but 3 is not 2×6.

Option 4: 63 → 6+3=9 and 6 = 2 × 3. Condition satisfied.

∴ The correct answer is 63.

Alternate Method

Given: Sum of digits = 9, Tens digit = 2 × Units digit.

Formula Used: Number = 10x + y, where x is tens digit and y is units digit.

⇒ Let the units digit be y.

⇒ The tens digit is 2y.

⇒ Sum of digits: 2y + y = 9

⇒ 3y = 9

⇒ y = 3

⇒ Tens digit (x) = 2 × 3 = 6

⇒ Number = 10(6) + 3 = 63

∴ The correct answer is 63.

Additional Information

Interchanging Digits

If digits are reversed, the new number is 10y + x. The difference between original and reversed number is always 9 × (x − y).

Divisibility by 9

A number is divisible by 9 if the sum of its digits is a multiple of 9.

Place Value vs Face Value

Face value is the digit itself, while place value depends on its position (e.g., in 63, place value of 6 is 60).

The correct answer is 220 V, 50 Hz.

Key Points:

• The government of India chooses the home power supply based on the environment in which we live and the supply cables that we employ.
• This configuration applies to any electrical appliance we use in our nation.
• The main voltage in India is 220V, and it alternates at a rate of 50 cycles per second.
• It is comparable to several of the nations in Europe.
• Another reason for the widespread adoption of 220V is that it has a smaller distribution footprint and costs less to distribute.
• We utilize high-resistance lines to distribute this voltage, hence the power will be quite large because power is calculated as the square of voltage times resistance.

Additional Information:

• If we compare the plug points between the USA and India, we will see that India has a 50Hz mains frequency whereas the USA has 60Hz.
• We must be aware that the frequency of the AC mains has a significant impact on a circuit's impedance.
• Therefore, the mains frequency must not change.
• All electrical goods created for the Indian market are set up to operate best at 50Hz.