SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 2) (Previous Year Paper)

A + B - C ÷ D × E - F → A is sister of B, B is brother of C, C is wife of D, D is father of E, E is brother of F.

By using the symbols in the table given below, we can draw the following family tree:

1. C is the mother of F → True 2. E is the brother of B → False (E is son of D) 3. A is the sister of the wife of D → True 4. A is the sister of C → True

Hence, ‘E is the brother of B’ is the correct answer.

The logic followed here is:

Logic: First number - Second number = 61 and Third number - Second number = 109

• (85, 24, 133) → 85 - 24 = 61 and 133 - 24 = 109
• (97, 36, 145) → 97 - 36 = 61 and 145 - 36 = 109

Similarly,

• (79, 18, 127) → 79 - 18 = 61 and 127 - 18 = 109

Hence, '(79, 18, 127) ' is the correct answer.

The logic followed here is: Sum of the positional value of opposite letter of the give letters.

Similarly,

Hence, '43' is the correct answer.

1. - and +

625 ÷ 25 - 7 × 318 + 112 = 381

⇒ 25 - 7 × 318 + 112 = 381

⇒ 25 - 2226 + 112 = 381

⇒ 137 - 2226 = 381 

⇒ -2089 ≠ 381

2. ÷ and +

625 + 25 ÷ 7 × 318 - 112 = 381

⇒ 625 + 3.57 × 318 - 112 = 381

⇒ 625 + 1135.26 - 112 = 381

⇒ 1760.26 - 112 = 381

⇒ 1648.26 ≠ 381

3. ÷ and -

625 - 25 + 7 × 318 ÷ 112 = 381

⇒ 625 - 25 + 7 × 2.83 = 381

⇒ 625 - 25 + 19.81 = 381

⇒ 644.81 - 25 = 381

⇒ 619.81 ≠ 381

4. + and ×

625 ÷ 25 × 7 + 318 - 112 = 381

⇒ 25 × 7 + 318 - 112 = 381

⇒ 175 + 318 - 112 = 381

⇒ 493 - 112 = 381

⇒ 381 = 381

Hence, '+ and ×' is the correct answer.

The logic followed here is:

Hence, '488' is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. For '

' element → Increasing in each box subsequently.

2. For '

' element → No change.

Final series is

Hence, ‘option - (2)’ is the correct answer.

Logic : Next two Consecutive letters according to English alphabetic series are written.

So,

• BULL : CDVWMNMN

And,

• SHOT : TUIJPQUV

​Similarly,

• TENS : ?

​Hence, "UVFGOPTU" is the correct answer.

Given : C _ _ SRCNP _ _ _ N _ SRC _ PS _ _ 

By checking options :

1. PSNRCPNR → C P S SRCNP N R C N P SRC N PS R → (It doesn't Follows the pattern)
2. NPSRCPRN → C N P SRCNP S R C N P SRC R PS N → (It doesn't Follows the pattern)
3. NPSRPCRN → C N P SRCNP S R P N C SRC R PS N → (It doesn't Follows the pattern)
4. NPSRCPNR → C N P SRCNP S R C N P SRC N PS R → (It follows the pattern of : CNPSR - CNPSR - CNPSR - CNPSR)

⇒Option - (4) gives the pattern of "C N P S R - C N P S R - C N P S R - C N P S R"

Hence, "NPSRCPNR" is the correct answer.

The logic followed here is :- 

• First and second letter - Difference between the position value according to English alphabetic series is (5).
• First and third letter - Opposite letter pairs according to English alphabetic series.

​So,

• Option - (1) : HMS

​

• Option - (2) : AFZ

​

• Option - (3) : KQP

​

• Option - (4) : DIW

​

Thus, out of all the options 'KQP' is the odd one out as the difference between first and the second letter (6) respectively.

​Hence, "KQP" is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. For '

' element → Element is alternately darkened and shifting clockwise direction.

2. For '

' element → Decreasing in each box starting with 4 to none subsequently

3) 2) For '

' element → No change

Final series is

Hence, ‘option - (2)’ is the correct answer.

Logic : (1st number × 3rd number) = (2nd number ÷ 3)

Given :

• (2, 114, 19)

2 × 19 = 114 ÷ 3

38 = 38 (LHS = RHS)

And,

• (12, 216, 6)

12 × 6 = 216 ÷ 3

72 = 72 (LHS = RHS)

So,

• Option - (1) : (5, 20, 2)

5 × 2 = 20 ÷ 3

10 ≠ 6.67 (LHS ≠ RHS)

• Option - (2) : (6, 144, 8)

6 × 8 = 144 ÷ 3

48 = 48 (LHS = RHS)

• Option - (3) : (11, 176, 4)

11 × 4 = 176 ÷ 3

44 ≠ 58.67 (LHS ≠ RHS)

• Option - (4) : (4, 128, 7)

4 × 7 = 128 ÷ 3

28 ≠ 42.67 (LHS ≠ RHS)

Hence, "Option - (2)" is the correct answer.

According to the question,

Given that: 14 - 4 ÷ 133 + 7 × 17

After replacing the symbols with their meanings, we get :-

= 14 ×4 + 133 ÷ 7 - 17 

= 14 ×4 + 19 - 17

= 56 + 19 - 17

= 75 - 17

= 58

Hence, the correct answer is "58".

The correct mirror image of the given figure when mirror is placed at MN is as shown below:

Hence, the correct answer is "Option - (3)".

Logic : (1st number × 2nd number × 3) - 2 = (3rd number )

So,

• (6, 2, 34)

6 × 2 × 3 - 2 = 34 

36 - 2 = 34 (LHS = RHS)

And,

• (1, 5, 13)

1 × 5 × 3 - 2  = 13

13 = 13 (LHS = RHS)

Similarly,

• (9, 1, ?)

9 × 1 × 3 - 2 = ? 

27 - 2 = ?

25 = ?

Hence, "25" is the correct answer.

According to the sequence in the dictionary:

4. Salary
5. Salesman
6. Salinity
7. Salivate
8. Salmon
9. Salvage

Hence, the correct option is "4, 1, 3, 6, 5, 2".

Given:

 

• The image must not to be rotated

  

Hence, the correct answer is "Option - (4)".

Logic : Tool : Tool used for

• Thermometer : Temperature

⇒ Thermometer is a tool used to measure temperature.

So,

• Option - (1) : Taseometer : Acceleration → Incorrect

​⇒ Taseometer is a tool used to measure physical strain in a structure and acceleration is measured by tool called accelerator.

• Option - (2) : Micrometer : Speed → Incorrect

​⇒ Micrometer is a tool used to measure extremely small distances or thickness and speed is measured by tool called speedometer.

• Option - (3) : Voltmeter : Voltage → Correct

​⇒ Voltmeter is a tool used to measure voltage.

• Option - (4) : Galvanometer : Sound → Incorrect

​⇒ Galvanometer is a tool used to measure small electric currents and sound is measured by tool called decibel meter.

Hence, "Voltmeter : Voltage" is the correct answer

The correct mirror image of the given combination when mirror is placed at PQ is as shown below:

Detailed Explanation:

• The line PQ is the mirror
• The word "RUVSYN" the mirror image should be flipped horizontally instead of vertically ⇒ Option 1 is eliminated.
• The word "RUVSYN" the third letter is "V". So, the mirror image should be "V" ⇒ Option 3 is eliminated..
• The word "RUVSYN" the fifth letter is "Y". So, the mirror image should be "Y" ⇒ Option 4 is eliminated.

Hence, the correct answer is "Option - (2)".

The correct mirror image of the given figure when mirror is placed at AB is as shown below:

Hence, the correct answer is "Option - (2)".

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some books are clowns → Follow (As, all clowns are books. So, as whole clowns comes in books therefore it is definitely true.)

II. All books are heavy → Does not Follow (As, some books are heavy. So, it is possible but not definitely true.)

III. Some trucks are heavy → Follow (As, some heavy are trucks . So, as some part of heavy is common with trucks therefore it is definitely true.)

So, Only conclusions I and III follow.

Hence, the correct answer is "Only conclusions I and III follow".

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

Given:

(i) (4, 5, 83)

⇒ (4 + 5)² + 2 = 83

⇒ (9)² + 2 = 83

⇒ 81 + 2 = 83

⇒ 83 = 83 (LHS = RHS)

(ii) (5, 5, 102)

⇒ (5 + 5)² + 2 = 102

⇒ (10)² + 2 = 102

⇒ 100 + 2 = 102

⇒102 = 102 (LHS = RHS)

Option (1) :

​(8, 9, 330)

⇒ (8 + 9)² + 2 = 330

⇒ 289 + 2 = 330

⇒ 291 ≠ 330 (LHS ≠ RHS)

Option (2) :

(3, 3, 11)

⇒ (3 + 3)² + 2 = 11

⇒ (6)² + 2 = 11

⇒ 36 + 2 = 11

⇒ 38 ≠ 11 (LHS ≠ RHS)

Option (3) :

(7, 6, 170)

⇒ (7 + 6)² + 2 = 170

⇒ (13)² + 2 = 170

⇒ 169 + 2 = 170

⇒ 171 ≠ 170 (LHS ≠ RHS)

Option(4) :

​(8, 3, 123)

⇒ (8 + 3)² + 2 = 123

⇒11² + 2 = 123

⇒ 121 + 2 = 123

⇒ 123 = 123 (LHS = RHS)

Hence, "Option (4)" is the correct answer.

Logic : (9) is added to and (5) are subtracted from each number alternately.

So, the series is :

43 + 9 = 52

52 - 5 = 47

47 + 9 = 56

56 - 5 = 51

51 + 9 = 60

60 - 5 = 55

Hence, "56" is the correct answer.

Logic : Increasing number series is added to the position values according to English alphabetic series diagonally.

So,

• RJN : OLU

And,

• DHL : MJG

​Similarly,

• VKC : ?

​Hence, "DMY" is the correct answer.

Logic :

• Vowels → Position value according to English alphabetic series is written.
• Consonants → Position value according to English alphabetic series is multiplied by (2).

So,

• 'CHECK' is written as '6165622'

And,

• 'SURGE' is written as '382136145'

​Similarly,

• 'PRIEST' will be written as :

​Hence, "3236953840" is the correct answer.

Logic : (1) and (2) are alternately added to the position value according to English alphabetic series.

So,

​Hence, "QXOT" is the correct answer.

The correct answer is 7th edition.

Key Points

• Hon’ble President of India Droupadi Murmu to confer Digital India Awards 2022 on 7^th January 2023 at Vigyan Bhawan, New Delhi. Celebrating Exemplary Digital Initiatives of the country.
• In the category ‘Digital Initiatives for Ease of Doing Business’, NIC’s eAbkari and Invest Punjab received Gold and Silver Awards at Digital India Awards 2022.
• Developed by NIC, Ksheerasree Portal received Silver Awards at Digital India Awards 2022 in the category ‘Digital Initiatives at Grassroots Level’.
• Transport Mission Mode Project (eTransport MMP), driven by the Ministry of Road Transport and Highways and executed by NIC received Gold Award while Judgement Search Portal developed by NIC received Silver Award for the category – Digital Empowerment of Citizens.
• eShram and Duare Sarkar projects of NIC received Gold and Platinum awards for the category – Digital Empowerment of Citizens at Digital India Awards 2022.
• Developed by NIC, Bilaspur District Website and Kottayam District Website received Platinum and Gold awards for the category – Best Web & Mobile Initiatives Complying with GIGW & Accessibility Guidelines at Digital India Awards 2022.
• The ‘Uttar Pradesh Mine Mitra’ portal has been selected for the Digital India Award – 2022 (PLATINUM) in ‘Digital Initiatives for Ease of Doing Business’ category.

Additional InformationThe Digital India Awards:

• Organizer: The Digital India Awards are organized by the National Informatics Centre (NIC) under the Ministry of Electronics and Information Technology, Government of India.
• Purpose: The purpose of these awards is to recognize and promote innovation in e-governance and digital transformation of government service delivery mechanisms.
• Categories: The awards are given to government entities under various categories, including, but not limited to:
• Innovation in Pandemic.
• Excellence in Digital Governance - Central Ministries/Departments, State/UTs, and Districts.
• Open Data Champion.
• Exemplary Product (National and State).
• Eligibility: Central and State Government Ministries, Departments, District Administrations, Local Bodies, and Public Sector Units are eligible for the nomination.
• Judging Criteria: The judging criteria typically include the project's scope and quality, use of emerging technology, level/measure of innovation, and user experience.
• Award Frequency: These awards are scheduled on a regular basis, typically annually.

The correct answer is Smriti Mandhana.

Key Points

• Rachael Heyhoe Flint Trophy for ICC Women’s Cricketer of the Year has been given to Smriti Mandhana (India).
• ICC Men’s T20I Cricketer of the Year has been awarded to Mohammad Rizwan (Pakistan).
• ICC Women’s T20I Cricketer of the Year has been awarded to Tammy Beaumont (England).
• ICC Umpire of the Year has been awarded to Marais Erasmus.​

Additional Information

The correct answer is C3H₆.

Key Points

• Propene or propylene is a colorless gas with a slightly sweet smell. It belongs to the alkene group of hydrocarbons.
• Chemical Formula: C₃H₆
• Structural Formula: H₂C=CH-CH₃
• Molecular Geometry: Trigonal planar around the carbon-carbon double bond; Tetrahedral around the carbon atoms attached to three other atoms.
• Covalent bond: The chemical bond formed by sharing of two valence electron between the two atoms. There are 8 carbon-hydrogen covalent bonds and 2 carbon-carbon covalent bonds present in the propane molecule. So, the total number of covalent bonds present in propane is (8 + 2 = 10)
• A covalent bond is represented clearly by drawing an electron - dot structure.
• Hybridization: sp² hybridized around the carbon of the double bond; sp³ hybridized around the last carbon.
• Polarity: Non-polar because of its symmetric geometric structure and the similar electronegativity of Carbon and Hydrogen.
• In terms of reactions, propene is commonly involved in addition reactions due to the presence of the double bond:
• Combustion: Like all hydrocarbons, propene burns in oxygen to produce water and carbon dioxide.
• C₃H₆ + 4.5 O₂ -> 3 CO₂ + 3 H₂O
• Addition of Halogens: When reacted with halogens like Bromine (Br2), the bromine molecule adds across the double bond.
• C₃H₆ + Br₂ -> C₃H₆Br₂
• Hydrogenation: Propene can undergo hydrogenation to produce propane, in the presence of a metallic catalyst.
• C₃H₆ + H₂ -> C₃H₈
• Polymerization: Propene is particularly important in the industry as a monomer in the production of polypropylene, a versatile plastic.

Additional Information

Alkenes are hydrocarbons that contain a carbon-carbon double bond. Here are some common alkenes:

• Ethene (ethylene): This is the simplest alkene and is utilized broadly in the chemical industry. Its chemical formula is C2H4 and its structural formula is H2C=CH2.
• Butene: There are three isomers of butene; 1-butene, 2-butene (cis and trans). The chemical formula for Butene is C₄H8. The structural formulas are CH₂=CH-CH₂-CH₃ for 1-butene and CH₃-CH=CH-CH₃ for 2-butene.
• Pentene: There are three isomers of pentene; 1-Pentene, 2-Pentene (cis and trans). The chemical formula for Pentene is C5H10. The structural formulas are CH2=CH-(CH2)3-CH3 for 1-Pentene and CH3-CH=CH-(CH2)2-CH3 for 2-Pentene.
• These molecules are important in both natural processes (such as ripening of fruits) and industrial processes (such as polymer production, preparation of alcohols, etc.). The "cis" and "trans" prefixes refer to the geometry of the substituents around the double bond. In "cis" isomers, the larger substituents are on the same side of the double bond, while in "trans" isomers, they are on opposite sides.
• All alkenes have similar chemical properties due to the presence of the carbon-carbon double bond. They all can undergo addition reactions where a molecule can add across the double bond, and polymerization reactions where individual alkene molecules (monomers) combine to form long chains (polymers), such as polyethylene and polypropylene plastics.

The correct answer is Gaur.

Key Points

• The Gaur, also known as the Indian Bison, is the closest wild relative of domestic cattle.
• This species is protected and can be found in several national parks in India, including Nagarhole and Bandipur in Karnataka.
• Gaurs are the largest and most powerful of all wild cattle, and are distinguished by their deep, hollow bodies, tall stature, and prominent dorsal ridges.

Additional Information

The correct answer is Budget.

• Budget: An annual statement of the estimated receipts and expenditure of the government over the fiscal year (April - March in India). It outlines the intended revenue collection and spending.
• Plan Expenditure: Money the government spends on developmental activities.
• Non-Plan Expenditure: Money the government spends on obligatory services like defense, salaries, etc.
• Budget Surplus: It exists when the government's revenue exceeds its expenditures. This is the opposite of a deficit.
• Balanced Budget: A situation in financial planning or the budgeting process where total revenues are equal to or greater than total expenses.
• Revenue Receipts (RR): Total income earned by the government from its regular activities and non-debt sources.
• RR = Tax Revenue + Non-Tax Revenue
• Revenue Expenditure (RE): Regular expenses incurred by the government for its day-to-day functioning.
• RE = Interest Payments + Grants + Salaries + Pensions + Subsidies + Maintenance
• Capital Receipts (CR): Total funds raised by the government from its non-recurring sources like borrowings, disinvestment, and loans.
• CR = Borrowings + Disinvestment + Loans Recovered
• Capital Expenditure (CE): Expenditure incurred by the government on creating assets, like infrastructure, that have long-term benefits.
• CE = Investments + Loans and Advances
• Fiscal Deficit (FD): It is the excess of total expenditure over total receipts, excluding borrowings.
• FD = Total Expenditure - Total Receipts (excluding borrowings)
• Primary Deficit (PD): Fiscal deficit minus interest payments.
• PD = Fiscal Deficit - Interest Payments
• Revenue Deficit (RD): It is the excess of revenue expenditure over revenue receipts.
• RD = Revenue Expenditure - Revenue Receipts
• Gross Domestic Product (GDP): The total value of all goods and services produced within a country's borders in a specific time period.
• GDP = Consumption + Investment + Government Spending + (Exports - Imports)
• Direct Taxes: Taxes levied directly on the income or wealth of individuals and organizations. Examples: Income Tax, Corporate Tax.
• Indirect Taxes: Taxes collected indirectly from consumers through the sale of goods and services. Examples: Goods and Services Tax (GST), Excise Duty, Customs Duty
• Deficit Financing: The government borrows money to meet its expenses when revenue falls short.
• Deficit Financing = Total Expenditure - Total Receipts (excluding borrowings)
• Revenue Deficit as a Percentage of GDP: It measures the extent of reliance on borrowings for day-to-day expenses.
• Revenue Deficit % of GDP = (RD / GDP) * 100​
• The Acworth Committee's recommendations, Railways' finances were separated in 1924, leading to the distinct Railway Budget from the General Budget.
• In 2017, the NDA Government ended the practice initiated in 1924 by merging the Railway Budget with the Union Budget, marking a departure from British-era norms.

The correct answer is PM - DevINE.

Key Points

• Scheme Name: Prime Minister's Development Initiative for North East Region (PM-DevINE)
• Duration: Four years from 2022-23 to 2025-26 (remaining period of 15th Finance Commission)
• Implementing Ministry: Ministry of Development of North Eastern Region (DoNER)
• Funding: 100% Central funding.
• Total Outlay: Rs. 6,600 crore
• Objective:
• Fund infrastructure and social development projects
• Support livelihood activities for youth and women
• Address development gaps in various sectors
• Implementation Approach:
• Front-loading of sanctions in 2022-23 and 2023-24
• Focus on completing sanctioned projects by 2025-26
• Projects to be implemented on Engineering-procurement-Construction (EPC) basis for efficient execution
• Implementation Entities: North Eastern Council, Central Ministries/agencies
• Expenditure Focus: Completion of PM-DevINE projects by 2025-26
• Impact:
• Creation of infrastructure
• Support for industries and social development
• Generation of livelihood activities, employment for youth and women
• Integration and Focus:
• Aligned with PM Gati Shakti for infrastructure development
• Addresses development gaps in the North Eastern Region (NER)
• Provides larger end-to-end development solutions
• Non-Duplication: No overlap with other MDoNER or Central/State schemes
• Background: Addressing development gaps and Basic Minimum Services (BMS) shortfalls in NE States
• Status: Additionality to existing resources, not a substitute for other Central and State schemes
• Announcement: Included in Union Budget 2022-23, reflects government's emphasis on NE Region's development
• Monitoring: Parameters aligned with BER District Sustainable Development Goal (SDG) Index 2021-22 by NITI Aayog, UNDP, and MDoNER.

Additional Information

The correct answer is Yamini Krishnamurthy.

Key Points Yamini Krishnamurthy:

• ​Indian dancer Yamini Krishnamurthy specializes in Kuchipudi and Bharatanatyam.
• She holds the honor of being the Tirumala Tirupati Devasthanam's Asthana Nartaki (resident dancer).
• She was also referred to as the "torch bearer" of the Kuchipudi dancing style.

Additional InformationUma Sharma:

• Uma Sharma is a famous Indian Kathak dancer.
• In the city of Delhi, Uma Sharma was born in 1942.
• She was trained in dance by Guru Hiralalji and Girvar Dayal of the Jaipur Gharana in her early years.
• She afterward enrolled as Pandit Sunder Prasad's student in the Jaipur Gharana.
• In 1973, she became the youngest dancer to receive the Padma Shri award from the Government of India, and in 2001, she received the Padma Bhushan.
• She also received the Sangeet Natak Akademi Award and the Sahitya Kala Parishad Award.

Rukmini Devi:

• Rukmini Devi Arundale was an Indian classical dancer who led the renaissance of the ‘Bharatnatyam’ dance form and founded the Kalakshetra Foundation in Madras (now Chennai).
• She was also a theosophist who was greatly inspired by Annie Besant.
• She founded the Kalakshetra Foundation in Madras (now Chennai).

The correct answer is Devilal v. State of Madhya Pradesh.

Key Points

• In the case of Devilal v. State of Madhya Pradesh in February 2021, the Indian Supreme Court ruled that if an accused claims to be a juvenile (under 18 years of age) and above 16 years at the time of occurrence of the incident, then the matter must be examined by the Juvenile Justice Board, even if the claim arises after charges have been framed or during the course of a trial.
• Even if the accused does not assert his/her claim of juvenility, the court, on coming to know through any means that the offender was a juvenile at the time of commission of the offence, should forward the child to the jurisdictional Juvenile Justice Board for an inquiry into the age.
• This principle is in line with the child-centric approach of the Juvenile Justice (Care and Protection of Children) Act of 2015.

Additional Information

• Juvenile Justice (Care and Protection of Children) Act, 2015: This is the primary law concerning minors in conflict with the law. The Act provides that individuals under the age of 18 years are termed 'children,' and it outlines a child-friendly approach in the adjudication and disposition of matters.
• Provisions for Heinous Crimes: As per Section 15 of the Juvenile Justice (Care and Protection of Children) Act, 2015, if a child above the age of 16 years is found to be in conflict with law for committing a heinous offence (crime with a minimum sentence of 7 years), the Juvenile Justice Board can conduct a preliminary assessment about the mental and physical ability of the child to commit such offence, and the ability of the child to understand the consequences. The Board can then decide whether to try the child as an adult or to follow the regular procedure.
• Constitutional Provisions: Article 15(3) allows the state to make special provisions for children. Article 39(e) and (f) further mandate the state to ensure that the tender age of children is not abused and their childhood is protected from moral and material abandonment, and that they are given opportunities and facilities to develop in a healthy manner.
• Child-Friendly Procedures: The law stresses the need for processes to be child-friendly. Children are entitled to legal aid and the procedures are required to be conducted in a simple and non-intimidating atmosphere.
• Rights of the Child: The law also enumerates the general principles of care and protection of children, which include principles like presumption of innocence, dignity and worth, family responsibility, best interests of the child, and more.
• Rehabilitative Approach: The law emphasizes reformation and rehabilitation of children found to be in conflict with law and outlines various measures for their social integration.
• The case of Devilal v. State of Madhya Pradesh reinforces the principles of the Juvenile Justice Act, mandating the court to consider the age of the offender at the time of the offence, and not the age at the time of trial or conviction.

The correct answer is Part V.

Key Points

• The Union Executive of India's Constitution is covered in Part V.
• This part, ranging from article 52 to 151, lays out the roles and powers of the President, Vice-president, Council of Ministers, Attorney General of India, Comptroller and Auditor General, and other executive functions of the Central Government of India.
• Additionally, it details processes such as the appointment, terms of office, and the conditions of service of these posts.

Important Points

Additional Information

• President (Article 52-62): The President is the head of the Union Executive and also the first citizen of India. Articles describe the election, qualifications, term of office, Oath, conditions of the President's office, and the process in the event of impeachment.
• Vice-President (Article 63-71): The Constitution provides for a Vice-President and outlines the manner of their election, their role (especially as the ex-officio Chairman of Rajya Sabha), and the process for removal from office.
• Council of Ministers with the Prime Minister at the head (Article 74-75): Article 74 mandates a Council of Ministers with the Prime Minister as the head to aid and advise the President. Article 75 provides details on who appoints the Prime Minister and other ministers, their responsibilities, the oath of office, etc.
• Attorney General (Article 76): The Attorney General is the highest law officer in the country. Article 76 outlines the qualifications, appointment, duties and rights of the Attorney General.
• Comptroller and Auditor General (Article 148-151): The CAG audits all expenditures from the Consolidated Fund of India. Details about the office, appointment, removal, and duties of the CAG are provided here.

Points to ponder

• The President has the power to seek advice from the Supreme Court (Article 143).
• The Vice-President acts as President during any vacancies or when the President is unable to fulfill their duties.
• The Prime Minister has a pivotal role in the functioning of the Union Government. The President exercises his/her powers on the advice of the Prime Minister and the Council of Ministers.
• Article 77 lays down the procedure for the work of the Government of India - it should be done in the name of the President.
• The Attorney General, though not a member of the parliament, has the right to participate in its proceedings.
• The CAG reports to the President, who places these reports before both Houses of the Parliament.

The correct answer is China.

Key Points

• The People's Republic of China won 96 gold medals overall in the Tokyo 2020 Paralympics, followed by Great Britain and the United States of America.
• With 96 gold medals and 207 total medals, China took the top spot in the medal count for the fifth consecutive Paralympics.
• With 41 gold medals and 124 overall medals, Great Britain placed second for the eighth time.
• With 37 gold medals, the United States came in third place overall, which was their highest result since the 2008 Games.
• Most successful athlete: China's Zhou Jiamin was one of the most successful athletes at the Tokyo Paralympics, winning three gold medals and setting one world record in Shooting Para Sport.
• China's dominance in table tennis: Chinese athletes demonstrated their expertise in Table Tennis, securing numerous gold medals in different classes.
• Record-breaking games: The Tokyo 2020 Paralympics had 4,537 athletes from 163 National Paralympic Committees - the most in the history of the Games.
• New Sports: Badminton and Taekwondo were included for the first time in the Paralympic Games.

Additional Information

• Out of a total of 162 countries, India is ranked 24th in the overall medal tally in the Tokyo Paralympics 2020.
• Indian Flag Bearers: opening ceremony - Javelin thrower Tek Chand closing ceremony - Shooter Avani Lekhara.
• The Indian theme song of Paralympics 2020: “Kar de Kamaal tu” by Sanjeev Singh who composed and sang the song.
• India won 19 medals which includes five gold, eight silver, and six bronze.

The correct answer is South Korea.

Key Points

• Nine countries have hosted the Asian Games to date.
• Thailand has hosted the most editions (1966, 1970, 1978, 1998), with Bangkok as the venue for all four.
• South Korea hosted three times (1986, 2002, 2014).
• China also hosted three times (1990, 2010, 2023).
• India hosted twice: inaugural edition in 1951 and 1982.
• 20th Asian Games in 2026: Japan, Aichi-Nagoya
• 21st Asian Games in 2030: Qatar, Doha
• 22nd Asian Games in 2034: Saudi Arabia, Riyadh

Additional Information

• First Asian Games: The first Asian Games were held in New Delhi, India, in 1951.
• Organizer: The Olympic Council of Asia (OCA) organizes the Games.
• Frequency: The Asian Games are held every four years, similar to the Olympics.
• Participating Nations: There are 45 nations participating in the Games.
• Mascots: Mascots, which began to be used in the 1982 Asian Games, usually represent the culture of the host country.
• Top Performer: China has been the top-performing nation in the Games since 1982, as of data up until September 2021.
• Non-Olympic Sports: Some sports played in the Asian Games, such as Kabaddi and Sepaktakraw, are not part of the Olympic Games.
• The Asian Games also feature Paralympic events, known as the Asian Para Games, which take place shortly after the main Games.

The correct answer is Hector Munro.

Key PointsBattle of Buxar:

• The Battle of Buxar occurred on 22nd October, 1764 on the banks of the Ganges River near Buxar, a city in the state of Bihar in India.
• The forces of three regional powers — Mir Qasim, the dethroned Nawab of Bengal; Shuja-ud-Daula, the Nawab of Awadh; and Shah Alam II, the Mughal emperor — formed an alliance against the British East India Company.
• Major Hector Munro led the Company's forces.
• Despite having larger forces, the Indian allies were defeated.
• Major reasons for their defeat, included discord between leaders, lack of strong centralized control, and the superior military strategy of the British forces.
• The battle marked a significant turning point in the history of India, as it affirmed the military supremacy of the East India Company over the Indian powers and set the background for their political power over the region.
• After the battle, the Treaty of Allahabad was signed in 1765.
• As per the treaty's terms, the East India Company acquired the rights for revenue collection (Diwani rights) in the provinces of Bengal, Bihar, and Orissa.
• These rights marked the beginning of the Company's formal rule in India.
• The treaty also stipulated the stationing of Company troops in Awadh to lend military assistance to the Nawab if required, which weakened the sovereignty of the region.
• The 1765 Treaty of Allahabad also required Nawab Shuja-ud-Daulah to pay Rs. 50 lakh as war indemnity which significantly weakened Awadh financially.
• The victory at Buxar gave the East India Company an immense boost in confidence and marked the beginning of British imperialism in India.
• Finally, the Battle of Buxar was significant because it was the first time the British fought in India for territorial gains and political power, as opposed to previous battles which were primarily fought over trade disputes.

The correct answer is 44^th.

Key Points

• The Right to Property was removed as a Fundamental Right from the Indian Constitution by the 44th Amendment in 1978. It was changed into a legal right under Article 300A in Part XII of the Constitution.
• The Right to Property underwent numerous changes throughout history in the Indian Constitution before it was eventually downgraded to a legal right. It started as a Fundamental Right:
• Post-independence - The original Constitution of India, when it came into effect in 1950, recognized the Right to Property as a Fundamental Right under Articles 19(1)(f) and 31. Article 19(1)(f) allowed citizens to acquire, hold, and dispose of property, while Article 31 provided that "no person shall be deprived of his property save by authority of law."
• First Amendment, 1951 - In response to significant land reform initiatives and intended to prevent the judiciary from undermining those policies, the First Amendment was introduced, which placed restrictions on the Right to Property.
• Fourth Amendment, 1955 - This amendment further reduced the right to property in response to a series of court decisions that favored landowners' rights to fair compensation over the state's rights to carry out land and tenancy reforms.
• Over time, several other amendments were made affecting the Right to Property: the Seventeenth Amendment of 1964, the Twenty-Fifth Amendment of 1971, the Thirty-Ninth Amendment of 1975, among others.
• Forty-Fourth Amendment, 1978 - Eventually, the Right to Property was removed as a Fundamental Right. The 44^th Amendment, enacted by the Janata Party which came into power in 1977, downgraded the right to a constitutional/legal right. The amendment also introduced a new article, Article 300A, which provided: "No person shall be deprived of his property save by authority of law." This means that the government can deprive a citizen of private property, but it has to be as per a valid law.
• This change made it possible for the government to implement land reform and redistribution policies without fear of them being declared unconstitutional by the courts. The Right to Property is now protected under the Indian Constitution as a legal right, not as a Fundamental Right. This means that while an individual still has the right to property, it is not an absolute right and can be regulated by the government.

The correct answer is Nagaland.

Key PointsChangai Dance:

• The Changai dance is a folk dance associated with the Chang tribe of Nagaland, an Indian state in the northeastern region.
• Chang Tribe: The Chang tribe is a prominent Naga tribe known for its distinct cultural practices and traditions.
• Celebratory Occasions: The Changai dance is performed during various festive occasions and celebrations within the Chang community.
• Unity and Culture: The dance serves as a way to foster unity and a sense of community among the Chang tribe members, while also showcasing their cultural identity.
• Energetic and Lively: The Changai dance is characterized by its vibrant and energetic movements. Dancers move in synchronized steps to the rhythm of traditional musical instruments.
• Traditional Attire: Dancers adorn colorful traditional attire during the performance, enhancing the visual appeal of the dance.
• Musical Instruments: The dance is accompanied by traditional musical instruments such as drums, gongs, and bamboo instruments, adding to the rhythmic ambiance.
• Synchronized Patterns: Dancers form circles or rows and engage in coordinated patterns of movement, swaying, and hopping.
• Cultural Transmission: The Changai dance plays a vital role in passing down cultural traditions, stories, and values from one generation to the next.
• Social Significance: Beyond entertainment, the dance reinforces a sense of belonging and identity within the Chang tribe.
• Cultural Heritage: The dance is a reflection of the rich cultural heritage of the Chang tribe and showcases their history, beliefs, and way of life.
• Nagaland's Identity: Changai dance contributes to the cultural diversity of Nagaland, highlighting the state's unique cultural tapestry.
• Symbol of Joy: The dance symbolizes joy, celebration, and the spirit of togetherness, making it an integral part of Nagaland's cultural landscape.

Additional Information

The correct answer is Jackfruit.

Key Points

• The national fruit of Bangladesh is the jackfruit.
• Jackfruit is well-suited for Bangladesh's climate and is highly valued for its nutritional content.
• In Bangladesh, jackfruit is known for being delicious, sweet, and juicy. It is commonly used in curries and various dishes.
• Different products are made from jackfruit in Bangladesh, including canned fruit, dried fruit, and pulp.
• A typical jackfruit tree can produce about 150 fruits annually, while some exotic varieties can yield as many as 250 to 500 fruits.
• Jackfruit seeds are a significant source of nutrition, containing high levels of Vitamin B1 and Vitamin B2.
• The seeds are also rich in starch, although they are relatively low in iron and calcium.
• Each jackfruit can contain anywhere from 100 to 500 seeds, which have an oily texture.
• Jackfruit's versatility, low cost, and nutritional value make it the perfect choice as Bangladesh's national fruit.

Additional Information

The correct answer is Sulphites.

Key PointsSulphites:

• Sulphites are natural compounds found in foods like dried fruits, wine, and beer.
• They're also added as additives to prevent browning, discoloration, and spoilage in foods and drinks.
• Sulphites release sulphur dioxide (SO₂), an irritant gas, which can cause allergy-like symptoms in individuals with conditions like asthma.
• Around 13% of people with asthma also suffer from sulphite sensitivity.
• People with urticaria may also experience worsened symptoms after consuming sulphites.
• Due to health concerns, products containing sulphites are labeled, helping individuals make informed choices.

Additional Information

The correct answer is Arya Samaj.

Key PointsArya Samaj:

• In 1875, Swami Dayanand Sarswati founded the Arya Samaj.
• Its main aim was to propagate the true knowledge of the Vedas and discard all evils  that had crept into the Hindu society later in its name.
• He opposed to polytheism, avataravada and ritualism.
• Arya Samaj advocated social reform and worked to improve the condition of women. It fought untouchability and the rigidities of the hereditary caste system and promoted social equality.
• The Arya Samaj especially has contributed a lot towards it by their Shuddhi Movement, that is, a form of purification by which those Hindus who had converted to Islam or Christianity could come back to their own religion.
• His slogan was ‘go back to the Vedas’ whose authority he accepted.
• For the first time in the history of India, the Vedas were printed in India under his patronage.
• Personally, his most important work was Satyartha Prakasha (The Light of Truth).
• The use of Hindi language in which he wrote and preached made his ideas accessible to the people of Northern India.
• Arya Samaj also had a major role to play in the national movement as it inculcated a spirit of self respect and self reliance among the people.
• In 1883, Swami Dayanand left his body after an eventful life.
• His followers started a Dayanand Anglo-Vedic (DAV) School and College in Lahore (now in Pakistan) in 1886.
• “DAV Movement” founded in 1886 by Lala Laijpat Rai picked up momentum due to the arduous efforts of Mahatma Hans Raj, Pandit Gurudutt Vidyarthi and may other dedicated Arya Samaj activist.

Additional Information

The correct answer is Pt. Ram Narayan - Sarod.

Key Points

• Pandit Ram Narayan, an Indian musician, is renowned for his contribution to popularizing the sarangi as a solo concert instrument.
• He is a Hindustani classical musician known for his expertise in playing the sarangi, a bowed instrument with a skin-covered resonator.
• Born in 1927 in Amber village, Rajasthan, he played a pivotal role in elevating the sarangi's status as a solo classical instrument.
• Pandit Ram Narayan's efforts led to the recognition of the sarangi's potential for solo performances in the world of classical music.

Additional Information

The correct answer is Rapid industrialisation with focus on heavy industries.

Key PointsSecond Five-Year Plan (1956 - 61):

• Target Growth: 4.5%
• Actual Growth: 4.27%
• Growth Model: The plan used the simple aggregative Mahalanobis Model for overall projections.
• Resource Allocation Strategy: The strategy of allocating resources to different sectors, including agriculture and industry, was based on the two & four-sector Model developed by Prof. P.C. Mahalanobis. This plan is also known as the Mahalanobis Plan.
• Economic Atmosphere: The plan was formulated during a period of relative economic stability.
• Priority Shift: The plan marked a shift in priority, with agriculture being accorded lower importance.
• Focus on Industrialization: The plan focused on achieving rapid industrialization, particularly in heavy and basic industries.
• Public Sector Development: The plan recognized the importance of the public sector in driving industrial growth. Several public sector enterprises were established during this period, including the Hindustan Machine Tools (HMT), Steel Authority of India (SAIL).
• Infrastructure Development: The plan prioritized infrastructure development, including the expansion of transportation networks, power generation, and irrigation facilities. Projects like the Bhakra Nangal Dam and the creation of a national railway grid were undertaken to support agricultural and industrial growth.
• Import Strategy: The plan advocated substantial imports through foreign loans to support industrialization efforts.
• Industrial Policy 1956: The plan's industrial policy was based on the goal of establishing a socialistic pattern of society.
• Challenges and Limitations: An acute shortage of foreign exchange (forex) led to the scaling down of development targets.
• Price Rise: The plan witnessed a notable price rise of about 30%, which was in contrast to the decline in prices during the earlier plan.
• Moderate Success: Despite its goals, the Second Five-Year Plan achieved only moderate success due to the challenges faced and the limitations in achieving set targets.

Additional Information

The correct answer is Earthquakes.

Key Points

• Plate Tectonics:
• Seismographs can provide indirect evidence supporting the theory of plate tectonics.
• By recording earthquake patterns and magnitudes around the world, they help illustrate the world’s tectonic plate boundaries where earthquakes are common.
• Epicenter and Focus of Earthquakes:
• Seismographs play a crucial role in locating the epicenter (geographical location directly above the focus on the surface) and the focus (actual location within the earth where the earthquake originates) of an earthquake.
• Data collected from minimum three seismograph stations is used to triangulate the epicenter of an earthquake.
• Seismic Wave Speed Variations:
• P-waves (primary waves) and S-waves (secondary waves) recorded by seismographs travel at different speeds and through different parts of the Earth's interior.
• Based on their arrival times at seismograph stations, we can infer properties of the Earth's interior, such as the presence of a molten outer core (which S-waves cannot travel through).
• Seismicities:
• Analysis of seismographs can help identify areas known as seismicities - geographical zones with a high frequency of earthquakes.
• Historical data from seismographs can therefore be used to predict regions where future earthquakes may occur.
• Earth's Interior Structure:
• Seismograph readings help scientists understand the Earth's interior structure better.
• For instance, changes in seismic wave velocity indicate interfaces between different layers of the Earth's interior, such as the crust, mantle, and core.
• Human-Induced Seismic Activity:
• Seismographs not only capture natural seismic activity, but also man-made seismic events such as those resulting from mining, reservoir-induced seismicity, nuclear tests, and construction work.

Additional InformationEarthquake Waves:

• Earthquake waves are vibrations in the Earth's crust caused by seismic events like earthquakes or volcanic activity.
• Two main types: body waves and surface waves.

Body Waves:

• Generated at the earthquake's focus and travel in all directions through the Earth's interior.
• Interact with surface rocks, generating surface waves.
• Changes in velocity and direction due to material density differences.
• Two types: P-waves (primary waves) and S-waves (secondary waves).

P-Waves (Primary Waves): 

• Fastest seismic waves, reaching the surface first.
• Similar to sound waves, they travel through gaseous, liquid, and solid materials.
• Provide important information about the Earth's interior structure.

S-Waves (Secondary Waves):

• Arrive at the surface after P-waves.
• Can only travel through solid materials, not liquids or gases.
• Vital for understanding the Earth's interior composition and structure.

Surface Waves:

• ​Generated by interaction between body waves and surface rocks.
• Slowest seismic waves, causing significant damage.
• Displace rocks and contribute to structural collapses.

The correct answer is Easter.

The correct answer is Amylum.

Key Points

• "Amylum" is the Latin word for starch. Starch is a white, granular, organic chemical that is produced by all green plants. It serves as the plant's energy reserve, which is stored in chloroplasts in the form of glucose polymers.
• In human diet, starch is a primary source of energy. Many of the staple foods humans consume are high in starch, including potatoes, wheat, maize (corn), rice, and cassava. Commercially, starch is used in the manufacture of adhesives, paper, textiles, and as a food additive.
• Enzymes that break down starch into its constituent glucose units are known as amylases, a term derived from "amylum".
• Appearance: Starch is a white powder without taste or smell.
• Two Types: Straight Amylose and Branched Amylopectin.
• Amylose: This is a linear, long chain of glucose units. Because of its straight, unbranched structure, amylose can form a helix shape which is ideal for storing energy.
• Amylopectin: Unlike amylose, amylopectin has a branched chain structure.
• Its branches allow for more points of access for enzymes, facilitating quick energy release when required.
• Glycogen in animals is a more branched form of amylopectin.
• Conversion to Sugars: Starch can be turned into sugars for making drinks and fuels.
• Used in Foods: Processed starch is used in many foods. Some foods that are particularly high in starch include grains (such as wheat, rice, and corn), root vegetables (like potatoes and carrots), and legumes (such as beans and lentils).
• Thickening and Adhesive: Starch mixed with warm water becomes a paste used to thicken or stick things.
• Industrial Uses: Industries use starch to make paper and stiffen clothes before ironing. It is used in food processing as a thickener, stabilizer and sugar replacer. In non-food industries, it is used in the manufacture of bio-plastics, adhesives, paper, textiles, and even in oil drilling to reduce fluid loss.

Additional Information

The correct answer is Iqtadari.

Key PointsIqtadari System:

• The Iqtadari system was a significant administrative and revenue collection system employed by the Delhi Sultanate.
• Under this system, territories were divided into administrative units known as Iqta'at, and these units were granted to officials called Iqtadars.
• The Iqtadars were responsible for collecting taxes and revenue from their assigned territories and forwarding a portion of the collected revenue to the central authority.
• The Iqtadars held both administrative and fiscal authority in their assigned regions.

Influence on Bahmani Sultanate:

• The Bahmani Sultanate was established in the Deccan region as an independent kingdom after the disintegration of the Delhi Sultanate.
• The Iqtadari system's influence extended to the Bahmani Sultanate, as it adopted similar administrative practices to manage its territories.
• While not an exact replication, the Bahmani rulers implemented a system of revenue collection and administration that was reminiscent of the Iqtadari system.
• This helped them organize and manage their vast and diverse territories efficiently.

Influence on Vijayanagara Empire:

• The Vijayanagara Empire was another significant medieval South Indian kingdom that coexisted with the Bahmani Sultanate.
• While geographically separated from the Delhi Sultanate, the Iqtadari system indirectly influenced the Vijayanagara Empire's administrative and revenue collection practices.
• The Vijayanagara rulers, like their counterparts in the Deccan, implemented an administrative structure that involved the collection of revenue from various regions under their control.
• Although not a direct adoption, the idea of revenue collection and administrative divisions in the Iqtadari system influenced the governance model of the Vijayanagara Empire.

Additional Information

Important Points

The correct answer is CO₂ + H₂O + heat and light.

Key Points

• When ethanol (CH₃CH₂OH) undergoes complete combustion with oxygen (O₂), the products formed are carbon dioxide (CO₂), water (H₂O), heat and light.
• This reaction is an example of rapid oxidation, where a substance reacts with oxygen to release energy in the form of heat and light.
• The balanced chemical equation is:
• CH₃CH₂OH + 3O₂ $\rightarrow$ 2CO₂ + 3H₂O + heat and light
• Remember, sufficient oxygen should be present for complete combustion to occur.
• In a limited supply of oxygen, incomplete combustion will occur, leading to the formation of carbon monoxide (CO) and water.

The correct answer is Tax assessment.

Key PointsThe Samaharta:

• The Samaharta was one of the most important executive officials in the Mauryan administration.
• His primary responsibility was to oversee the collection of taxes from all types of sources.
• Most of the superintendents, or adhayakshas, who were responsible for running various economic departments, functioned under his orders.
• He played a crucial role in the revenue system of the Mauryan empire.

Additional Information

Shortcut Trick According to the triangle inequality theorem, the length of any side of a triangle must be strictly between the difference and the sum of the other two sides. Difference of given sides = 42 − 30 = 12 cm Sum of given sides = 42 + 30 = 72 cm Therefore, the range for the third side x is: 12 < x < 72. ∴ The correct answer is 12 < x < 72.

Alternate Method Given: The lengths of the three sides of the triangle are 30 cm, 42 cm, and x cm. Formula Used: For any triangle with sides a, b, and c, the triangle inequality theorem states that: |a − b| < c < a + b

Calculations: Let the three sides of the triangle be: a = 30 cm b = 42 cm c = x cm According to the theorem, the sum of any two sides must be strictly greater than the third side: ⇒ a + b > c ⇒ 30 + 42 > x ⇒ 72 > x     ---(1) Similarly, the sum of the other combinations must also be greater than the remaining side: ⇒ a + c > b ⇒ 30 + x > 42 ⇒ x > 12     ---(2) ⇒ b + c > a ⇒ 42 + x > 30 ⇒ x > −12     ---(3) (This is always true since side lengths must be positive) Combining inequalities (1) and (2), we get the valid range for x: ⇒ 12 < x < 72 Analysis of incorrect options: ⇒ Option (1) is incorrect because x cannot be equal to 12. If x = 12, the sum of the two smaller sides (30 + 12) equals the third side (42), which violates the strict inequality requirement. ⇒ Option (2) is mathematically impossible as a number cannot be simultaneously less than 12 and greater than 72. ⇒ Option (4) is incorrect because including the boundary values (12 and 72) results in a degenerate triangle (a straight line segment) rather than a proper triangle. ∴ The correct answer is 12 < x < 72.

Additional Information Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is always strictly greater than the length of the remaining side: a + b > c, b + c > a, and c + a > b. Difference of Sides Rule The absolute difference between the lengths of any two sides of a triangle is always strictly less than the length of the third side: |a − b| < c. Degenerate Triangle If the sum of two sides equals the third side (e.g., a + b = c), the three vertices become collinear, forming a straight line segment instead of a proper triangle.

Shortcut Trick

For a number to be divisible by 88, it must be exactly divisible by its co-prime factors, 8 and 11.

Check the given options for divisibility by 8 (last 3 digits) and 11 (difference of alternating sums).

Checking Option 4 (99968): 968 ÷ 8 = 121, so it is divisible by 8.

For 11: Sum of odd places = (9 + 9 + 8) = 26; Sum of even places = (9 + 6) = 15.

Difference = 26 − 15 = 11, which is divisible by 11.

∴ The correct answer is 99968.

Alternate Method

Given:

We need to find the largest 5-digit number exactly divisible by 88.

Method Used:

Divide the largest 5-digit number by 88 and subtract the remainder from it to get a completely divisible number.

Calculations:

⇒ The largest 5-digit number is 99999.

⇒ Let us divide 99999 by 88 to find the remainder.

⇒ 99999 = 88 × 1136 + 31

⇒ The remainder when 99999 is divided by 88 is 31.

⇒ To make it exactly divisible by 88, we subtract this remainder from the largest 5-digit number.

⇒ Required number = 99999 − 31

⇒ Required number = 99968

∴ The correct answer is 99968.

Additional Information

Divisibility Rule of 8

A number is divisible by 8 if the number formed by its last three digits is completely divisible by 8.

Divisibility Rule of 11

A number is divisible by 11 if the difference between the sum of digits at odd positions and the sum of digits at even positions is 0 or a multiple of 11.

Finding the Largest n-digit Divisible Number

Divide the highest n-digit number (e.g., 99999) by the given divisor. The required answer is the highest n-digit number minus the obtained remainder.

Calculation:

⇒ 100% = 2500

⇒ 1% = 25

Laptops sold by company A = 40% = 40 × 25 = 1000

Laptops sold by company C = 8% = 8 × 25 = 200

Difference between the sale of laptops of company A and C = 1000 - 200 = 800

∴ The correct answer is 800.

Shortcut Trick

If a + 1/a = k, then a⁵ + 1/a⁵ = (a² + 1/a²) × (a³ + 1/a³) − (a + 1/a).

Given k = 7.

Value of a² + 1/a² = k² − 2 = 7² − 2 = 47.

Value of a³ + 1/a³ = k³ − 3k = 7³ − 3(7) = 343 − 21 = 322.

Therefore, a⁵ + 1/a⁵ = (47 × 322) − 7 = 15134 − 7 = 15127.

∴ The correct answer is 15127.

Alternate Method

Given: a + 1/a = 7

Formula Used: (a + b)² = a² + b² + 2ab and (a + b)³ = a³ + b³ + 3ab(a + b)

Calculations:

⇒ (a + 1/a)² = 7²

⇒ a² + 1/a² + 2(a)(1/a) = 49

⇒ a² + 1/a² + 2 = 49

⇒ a² + 1/a² = 47

⇒ (a + 1/a)³ = 7³

⇒ a³ + 1/a³ + 3(a)(1/a)(a + 1/a) = 343

⇒ a³ + 1/a³ + 3(7) = 343

⇒ a³ + 1/a³ = 322

⇒ (a² + 1/a²) × (a³ + 1/a³) = 47 × 322

⇒ a⁵ + a²/a³ + a³/a² + 1/a⁵ = 15134

⇒ a⁵ + 1/a + a + 1/a⁵ = 15134

⇒ (a⁵ + 1/a⁵) + (a + 1/a) = 15134

⇒ a⁵ + 1/a⁵ + 7 = 15134

⇒ a⁵ + 1/a⁵ = 15134 − 7 = 15127

∴ The correct answer is 15127.

Additional Information

Algebraic Power Identities

For any variable a + 1/a = k, the Square relationship is a² + 1/a² = k² − 2.

Cubic Identity

The Cube relationship is given by a³ + 1/a³ = k³ − 3k.

Fourth and Sixth Power

Higher powers can be derived: a⁴ + 1/a⁴ = (k² − 2)² − 2 and a⁶ + 1/a⁶ = (k³ − 3k)² − 2.

Negative Sign Case

If a − 1/a = k, then a² + 1/a² = k² + 2 and a³ − 1/a³ = k³ + 3k.

Shortcut Trick

Convert obtuse angles to supplementary forms: 133° = 180° − 47° and 136° = 180° − 44°.

Using 2^nd quadrant rules: sec(180° − θ) = −sec θ and cosec(180° − θ) = cosec θ.

Expression = cos 47° × (−sec 47°) + sin 44° × cosec 44°.

Since cos θ × sec θ = 1 and sin θ × cosec θ = 1:

Result = −1 + 1 = 0.

∴ The correct answer is 0.

Alternate Method

Given:

Expression = cos 47° sec 133° + sin 44° cosec 136°

Formula Used:

sec(180° − θ) = −sec θ

cosec(180° − θ) = cosec θ

cos θ × sec θ = 1

sin θ × cosec θ = 1

Calculations:

⇒ Split the obtuse angles into (180° − θ) form to simplify.

⇒ sec 133° = sec(180° − 47°) = −sec 47°

⇒ cosec 136° = cosec(180° − 44°) = cosec 44°

⇒ Substitute these simplified values back into the given expression.

⇒ Expression = cos 47° × (−sec 47°) + sin 44° × cosec 44°

⇒ Expression = −(cos 47° × sec 47°) + (sin 44° × cosec 44°)

⇒ Since a trigonometric function multiplied by its reciprocal is exactly 1:

⇒ Expression = −1 + 1 = 0

∴ The correct answer is 0.

Additional Information

ASTC Rule

In the 2^nd quadrant (90° to 180°), only Sine (sin) and Cosecant (cosec) are positive. Cosine (cos), Secant (sec), Tangent (tan), and Cotangent (cot) are negative.

Reciprocal Identities

sin θ × cosec θ = 1 | cos θ × sec θ = 1 | tan θ × cot θ = 1.

Supplementary Angles

Angles that add up to 180° are supplementary. sin(180° − θ) = sin θ, while cos(180° − θ) = −cos θ.

Shortcut Trick

Time for A and B (same direction) to meet = Track length ÷ Relative speed = 1200 ÷ (4 − 2) = 600 s.

Time for A and C (opposite direction) to meet = Track length ÷ Relative speed = 1200 ÷ (2 + 6) = 150 s.

First meeting time of all three = LCM of (600 s, 150 s) = 600 s.

Convert to minutes: 600 ÷ 60 = 10 min.

∴ The correct answer is 10 min.

Alternate Method

Given: Length of circular track = 1200 m. Speeds: A = 2 m/s, B = 4 m/s (same direction) and C = 6 m/s (opposite direction).

To find when all three meet for the first time, we calculate the relative meeting times between pairs:

⇒ Relative speed of A and B = 4 − 2 = 2 m/s (Same direction).

⇒ Time for A and B to meet (T_AB) = 1200 ÷ 2 = 600 s.

⇒ Relative speed of A and C = 2 + 6 = 8 m/s (Opposite direction).

⇒ Time for A and C to meet (T_AC) = 1200 ÷ 8 = 150 s.

⇒ Relative speed of B and C = 4 + 6 = 10 m/s (Opposite direction).

⇒ Time for B and C to meet (T_BC) = 1200 ÷ 10 = 120 s.

⇒ Time for all three to meet = LCM (T_AB, T_AC, T_BC) = LCM (600, 150, 120).

⇒ Meeting Time = 600 seconds.

⇒ Time in minutes = 600 ÷ 60 = 10 min.

∴ The correct answer is 10 min.

Additional Information

Relative Speed on Circular Track

When moving in the same direction, relative speed = |v₁ − v₂|. When moving in the opposite direction, relative speed = v₁ + v₂.

Meeting at the Starting Point

To find the time when they meet specifically at the starting point, take the LCM of the individual times each person takes to complete one full lap (L/v₁, L/v₂, L/v₃).

Number of Distinct Meeting Points

For two runners with speeds in ratio x:y (simplest form), the number of distinct meeting points is |x − y| if in the same direction and x + y if in opposite directions.

Shortcut Trick

Interest for 4 years (11 − 7) = 18906 − 14522 = ₹4384

Interest for 1 year = 4384 ÷ 4 = ₹1096

Interest for 7 years = 1096 × 7 = ₹7672

Sum (Principal) = Amount_7yr − Interest_7yr = 14522 − 7672 = ₹6850

∴ The correct answer is ₹6850.

Alternate Method

Given:

Amount in 7 years (A₇) = ₹14,522

Amount in 11 years (A₁₁) = ₹18,906

Formula Used:

Amount (A) = Principal (P) + Simple Interest (SI)

SI = (P × R × T) ÷ 100

Calculations:

⇒ Interest for 4 years = A₁₁ − A₇

⇒ Interest for 4 years = 18906 − 14522 = ₹4384

⇒ Simple Interest for 1 year = 4384 ÷ 4 = ₹1096

⇒ Simple Interest for 7 years = 1096 × 7 = ₹7672

⇒ Principal (P) = Amount after 7 years − Interest for 7 years

⇒ P = 14522 − 7672

⇒ P = ₹6850

∴ The correct answer is ₹6850.

Additional Information

Simple Interest Nature

In Simple Interest, the interest remains constant for every year as it is always calculated on the original Principal.

Rate of Interest Formula

Rate (R) = (SI × 100) ÷ (P × T). In this case, R = (1096 × 100) ÷ (6850 × 1) = 16%.

Difference between CI and SI

For a period of 2 years, the difference is given by P(R ÷ 100)².

Shortcut Trick

Net percentage increase in area = x + x + (x × x)/100

Here, increase in side (x) = 34%

⇒ Area increase = 34 + 34 + (34 × 34)/100

⇒ Area increase = 68 + 1156/100 = 68 + 11.56 = 79.56%

∴ The correct answer is 79.56%.

Alternate Method

Given: Increase in side of equilateral triangle = 34%

Formula Used: Area of equilateral triangle = (√3/4) × a²

⇒ Let original side (a₁) = 100 units

⇒ New side (a₂) = 100 + 34% of 100 = 134 units

⇒ Ratio of areas = (a₁)² : (a₂)²

⇒ Ratio of areas = (100)² : (134)²

⇒ Ratio of areas = 10000 : 17956

⇒ Percentage increase in area = [(17956 − 10000) ÷ 10000] × 100

⇒ Percentage increase in area = [7956 ÷ 10000] × 100 = 79.56%

∴ The correct answer is 79.56%.

Additional Information

Equilateral Triangle Properties

All three sides are equal and each internal angle is 60°. Height = (√3/2) × a.

Successive Percentage Change

When a quantity depends on the product of two variables (like Area = k × x × y), the net change is given by x + y + xy/100.

Area Scaling

If the linear dimensions of a 2D shape are scaled by a factor k, the area scales by k².

Formula used:

Sum of geometric progression (S_n) = {a × (rⁿ - 1)}/(r - 1)

Where, a = first term ; r = common ratio ; n = number of term

Calculation:

3 +32 + 33 +...+ 38.

Here, a = 3 ; r = 3 ; n = 8

Sum of the series (S₈) = {a × (r8 - 1)}/(r - 1)

⇒ {3 × (3⁸ - 1)}/(3 - 1)

⇒ (3 × 6560)/2 = 3280 × 3 

⇒ 9840

∴ The correct answer is 9840.

Given:

A can do a piece of work = 30 days

B can do a piece of work = 40 days

C can do a piece of work = 50 days

Formula used:

Total work = efficiency × time

Calculation:

According to the question:

⇒ (20 + 15 + 12) = 47 units = 3 days

⇒ 47 × 12 = 564 units = 3 × 12 = 36 days

⇒ (564 + 20 + 15) = 599 units = 38 days

Total work = 600 units = 38 + (1/12) = 38$1\over12$ days.

∴ The correct answer is 38$1\over12$ days.

Shortcut Trick

Since Time is constant, Distance is directly proportional to Speed.

Ratio of speeds (Constable : Thief) = 8 : 6 = 4 : 3

Difference in ratio parts = 4 − 3 = 1 unit

1 unit → 200 m (initial gap)

Distance run by thief = 3 units → 3 × 200 m = 600 m

∴ The correct answer is 600 m.

Alternate Method

Given: Initial distance = 200 m, Speed of Constable = 8 km/h, Speed of Thief = 6 km/h.

Formula Used: Relative Speed = Speed₁ − Speed₂ (same direction); Time = Distance ÷ Relative Speed; Distance = Speed × Time.

⇒ Relative Speed = 8 − 6 = 2 km/h

⇒ Convert to m/s: 2 × (5/18) = 5/9 m/s

⇒ Time taken to catch the thief = Initial Distance ÷ Relative Speed

⇒ Time = 200 ÷ (5/9) = 200 × 9 ÷ 5 = 360 seconds

⇒ Distance run by thief = Speed of thief × Time

⇒ Speed of thief in m/s = 6 × (5/18) = 5/3 m/s

⇒ Distance = (5/3) × 360 = 5 × 120 = 600 m

∴ The correct answer is 600 m.

Additional Information

Relative Speed

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

Constant Time Concept

If two objects start and stop at the same time, the ratio of their distances is equal to the ratio of their speeds (D₁/D₂ = S₁/S₂).

Given:

Red pens : blue pens : green pens = 7 : 4 : 9

Total number of pens = 320

Calculation:

Red pens : blue pens : green pens = 7 : 4 : 9

⇒ 20 units = 320 pens

⇒ 1 unit = 16 pen

Red pen = 7 units = 16 × 7 = 112 pens

∴ The correct answer is 112 pens.

Given:

Ravi can do a piece of work = 40 days

Sudha can do the same work = 60 days

Formula used:

Total work = efficiency × time

Calculation:

According to the question:

⇒ (Sudha + Ravi) = 2 days

⇒ (2 + 3) = 5 units = 2 days

⇒ 5 × 24 = 120 units = 2 × 24 = 48 days.

∴ The correct answer is 48 days.

Given:

Length of an arc = 23.1 cm

Angle subtended on center by arc = 18°

Formula used:

Length of an arc = (2 × π × R × θ)/360

Area of circle = π × R²

Where, R = radius

Calculation:

Length of an arc = (2 × π × R × θ)/360

⇒ 23.1 = (2 × 22 × R × 18)/(360 × 7)

⇒ 23.1 = (22 × R)/(10 × 7)

⇒ R = (2.1 × 70)/2 = 73.5 cm

Area of circle = π × R2

⇒ (22/7) × 73.5 × 73.5

⇒ 22 × 10.5 × 73.5

⇒ 16978.50 cm2

∴ The correct answer is 16978.50 cm2.

Calculation:

Total selected from Delhi = 94 + 48 + 90 + 70 + 82 = 384

Total selected from Maharastra = 85 + 70 + 84 + 60 + 65 = 364

Required percentage = (364 × 100)/384 = 94.79%

∴ The correct answer is 94.79%.

Given:

tan $\frac{π }{6}$ + sec $\frac{π }{6}$ = x

Formula used:

Tan 30° = 1/√3

Sec 30° = 2/√3

Calculation:

tan π/6 + sec π/6 = x

⇒ tan 30° + sec 30° = x

⇒ 1/√3 + 2/√3 = x

⇒ x = 3/√3 = √3

∴ The correct answer is √3.

Given:

Radius of base (R) = 6 cm

Height of cone (H) = 8 cm

Formula used:

Total surface area = π × R (l + R)

Where, slant height (l) = √(H² + R²)

R = radius ; H = height

Calculation:

Slant height (l) = √(H2 + R2)

⇒ √(82 + 62) = √(64 + 36)

⇒ √100 = 10 cm

Total surface area = π × R (l + R)

⇒ (22/7) × 6 × (10 + 6)

⇒ (22/7) × 6 × 16

⇒ 2112/7 = 301.71 cm2

∴ The correct answer is 301.71 cm2.

Shortcut Trick

If Group A takes X days and Group B takes Y days to complete the same work.

Combined time for both groups working together = (X × Y) ÷ (X + Y)

Here, X = 25 days (for 15 men) and Y = 40 days (for 25 women).

Required days = (25 × 40) ÷ (25 + 40) = 1000 ÷ 65 = 200 ÷ 13 = 15 5/13 days.

∴ The correct answer is 15 5/13 days.

Alternate Method

Given:

Time taken by 15 men = 25 days

Time taken by 25 women = 40 days

Calculations:

⇒ Combined efficiency of (15 Men + 25 Women) = 8 + 5 = 13 units/day

⇒ Total Work = 200 units

⇒ Time taken = Total Work ÷ Combined Efficiency

⇒ Time taken = 200 ÷ 13

⇒ Time taken = 15 5/13 days

∴ The correct answer is 15 5/13 days.

Additional Information

Man-Day Concept

The total work is proportional to the number of persons and the number of days: W = M₁ × D₁ = M₂ × D₂.

Efficiency Relation

Efficiency is inversely proportional to time. If ratio of time is a:b, the ratio of efficiency is b:a.

Work and Wages

Wages are distributed in the ratio of efficiency or the ratio of work done by each individual/group.

Given:

Suhani tax rate = 30%

Suhani income = Rs.90000

Ritika tax rate = 40%

Calculation:

According to the question:

⇒ (90000 × 30%) + (y × 40%) = (90000 + y) × 37%

⇒ 27000 + y × 40% = 33,300 + y × 37%

⇒ y × 3% = (33300 - 27000)

⇒ y = (6300 × 100)/3

⇒ y = 210000

∴ The correct answer is 210000.

Given:

A working hours = 5 hours/day

A can complete a task = 8 days

B working hours = 6 hours/day

B can finish the same task = 10 days

Concept used:

M₁ × D₁ × H₁ = M₂ × D₂ × H₂

M = person ; D = days ; H = hours 

Calculation:

According to the question:

⇒ A × 5 × 8 = B × 6 × 10

⇒ A/B = 3/2

Total work = A × 5 × 8 = 3 × 40 = 120 units

Required time taken = 120/{(3 + 2) × 8}

⇒ 120/40 = 3 days

∴ The correct answer is 3 days.

Formula used:

(a - b)² = a² + b² - 2ab

(a² - b²) = (a + b) × (a - b)

(a + b)2 = a2 + b2 + 2ab

Calculation:

$\frac{x^4 - 2x^2 + 1}{x^2 - 2x + 1}$

⇒ {(x²)² + 1 - 2 × (x²) × 1}/(x - 1)²

⇒ (x² - 1)²/(x - 1)²

⇒ {(x + 1)²(x - 1)²}/(x - 1)²

⇒ (x + 1)2 = x2 + 2x + 1

∴ The correct option is 3.

Given:

x - (1/x) = √6

Formula used:

x⁸ - (1/x⁸) = {x⁴ + (1/x⁴)} × {x² + (1/x²)} × {x + (1/x)} × {x - (1/x)}

If x - (1/x) = a, then x + (1/x) = √(a2 + 4)

Calculation:

x - (1/x) = √6

x² + (1/x²) = (√6)² + 2 = 8

Square both sides:

x⁴ + (1/x⁴) = (8)² - 2 = 62

Using, If x - (1/x) = a, then x + (1/x) = √{(√a)2 + 4} .

x + (1/x) = √{(√6)² + 4} = √10

Substituting the values, we get

x8 - (1/x8) = {x4 + (1/x4)} × {x2 + (1/x2)} × {x + (1/x)} × {x - (1/x)}

⇒ 62 × 8 × √10 × √6 = 496 × 2 × √15 = 992√15

∴ The correct answer is 992√15.  

 Shortcut Trick

If a - 1/a = m,

• Then a² +1/a² = m² + 2

• Then a⁴ + 1/a⁴ = m⁴ + 4m² + 2

if a2 +1/a2 = m , then a +1/a = √(m+2) 

⇒ x - 1/x =√6

⇒ x²+1/x² = (√6)² +2 = 8

⇒ x +1/x = √10

⇒ x⁴+ 1/x⁴ = (√6)⁴+4(√6)² +2 = 36+24+2 = 62 

⇒ x8 - (1/x8) = {x4 + (1/x4)} × {x2 + (1/x2)} × {x + (1/x)} × {x - (1/x)}

⇒ 62 × 8 × √10 × √6 = 496 × 2 × √15

⇒ 992√15

Shortcut Trick

Convert percentages to multipliers: 12% off ⇒ 0.88, 20% off ⇒ 0.80, 25% off ⇒ 0.75.

Net multiplier = 0.88 × 0.80 × 0.75 = 0.88 × 0.6 = 0.528.

Single discount % = (1 − 0.528) × 100 = 0.472 × 100 = 47.2%.

Alternatively, using Ratio Method: (25:22) × (5:4) × (4:3) ⇒ 500:264.

Discount = (500 − 264) ÷ 500 × 100 = 236 ÷ 5 = 47.2%.

∴ The correct answer is 47.2%.

Alternate Method

Given → Discounts are 12%, 20%, and 25%. Formulas: Successive discount = a + b − (a × b ÷ 100) | SP = MP × (100 − D₁)% × (100 − D₂)% × (100 − D₃)%

⇒ First, apply formula to 12% and 20%: 12 + 20 − (12 × 20 ÷ 100) = 32 − 2.4 = 29.6%. ⇒ Now, apply formula to 29.6% and 25%: 29.6 + 25 − (29.6 × 25 ÷ 100). ⇒ 54.6 − (740 ÷ 100) = 54.6 − 7.4 = 47.2%. ⇒ Single equivalent discount = 47.2%.

∴ The correct answer is 47.2%.

Additional Information

Successive Discount Concept

A successive discount refers to the discount offered on the reduced price after a previous discount has been applied, rather than on the original marked price.

Marked Price & Selling Price

The Marked Price (MP) is the price printed on the label, and Selling Price (SP) = MP − Discount.

Given:

Sin θ = 4/5

Formula used:

tan θ = P/B ; cot θ = B/P

By Pythagorean theorem:

⇒ H2 = P2 + B2 

Where, P = perpendicular ; B = base ; H = hypotenuse

Calculation:

Sin θ = 4/5 = P/H

By Pythagorean theorem:

⇒ H² = P² + B²

⇒ 5² = 4² + B²

⇒ B2 = 52 - 42

⇒ B = √(25 - 16) = √9

⇒ B = 3

tan θ - Cot θ

⇒ (P/B) - (B/P) 

⇒ (4/3) - (3/4) = (16 - 9)/12

⇒ 7/12

∴ The correct answer is 7/12.

Given:

Ram sells a suitcase to Mohan at a profit = 20%

Mohan sells a suitcase to Shivam at a profit = 40%

Shivam pays to Mohan = Rs.1430

Concept used:

P% profit = C.P : S.P = 100 : (100 + P)

Where, C.P = cost price ; S.P = selling price

Calculation:

Let Ram buy the suitcase = 100x

Ram sells a suitcase to Mohan = 100x × (100 + 20)% = 120x

Mohan sells it to Shivam = 120x × (100 + 40)% = 168x

According to the question:

⇒ 168x = Rs.1430

⇒ x = 1430/168 = 715/84

⇒ 100x = (715 × 100)/84 = Rs.851.19

∴ The correct answer is 851.19.

Alternate MethodCalculation:

Now,

Ram : Shivam = 100 × 100 : 120 × 140

⇒ 25 : 42

⇒ 42 units = Rs.1430

⇒ 1 unit = 1430/42 = 715/21

⇒ 25 units = (715 × 25)/21 = Rs.851.19

∴ The correct answer is Rs.851.19.