SSC CHSL Tier-1 2023: Official Paper (Held On: 02 Aug 2023 Shift 1) (Previous Year Paper)

The logic followed here is:

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

Now,

For, (21, 66)

⇒ (21 × 3) + 3

⇒ 63 + 3 = 66.

For, (32, 99)

⇒ (32 × 3) + 3

⇒ 96 + 3 = 99.

Similarly, for (45, 138)

⇒ (45 × 3) + 3

⇒ 135 + 3 = 138.

Hence, the correct answer is "Option 3".

The logic followed here is:

For, DHJ is related to AEG

For, ZML is related to WJI

Similarly, for EKQ

So, 'EKQ' will be related to 'BHN'.

Hence, the correct answer is "Option 3".

The logic followed here is:

So, '321' will complete the series.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: (1^st number × 2^nd number) + 5 = 3^rd number.

Now,

For, (12, 11, 137)

⇒ (12 × 11) + 5

⇒ 132 + 5 = 137.

For, (17, 21, 362)

⇒ (17 × 21) + 5

⇒ 357 + 5 = 362.

Similarly, for (21, 25, 530)

⇒ (21 × 25) + 5

⇒ 525 + 5 = 530.

Hence, the correct answer is "Option 3".

Family Chart:

Decoding the Symbols:

 

Given: G ÷ H × I -J + K

It means: G is the Mother of H, H is the Brother of I, I is the Wife of J, J is the Father of K.

So, G is the 'Mother's mother' of K.

Hence, the correct answer is "Option 1".

The logic followed here is:

So, 'ER 84' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

Given equation: 114 C 85 A 5 B 4 D 33 = ?

Decoding the given information :

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

New equation : 114 + 85 ÷ 5 × 4 - 33 = ?

Calculation :

⇒ 114 + 85 ÷ 5 × 4 - 33 = ?

⇒ 114 + 17 × 4 - 33 = ?

⇒ 114 + 68 - 33 = ?

⇒ 182 - 33 = 149.

Hence, the correct answer is "Option 2".

Given word: AMPLIFY 

Now, arranging in alphabetical order:

we get, 

 

Here, the letter 'A', 'L', and 'Y' will remain unchanged after arranged in alphabetical order.

Hence, the correct answer is "Three".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 1".

Given equation: 75 ÷ 15 × 8 + 14 - 5 = 67

BODMAS Table: 

Let's check each option one by one.

Option 1) ÷ and × 

Given: 75 ÷ 15 × 8 + 14 - 5 = 67

After interchanging the signs we get;

⇒ 75 × 15 ÷ 8 + 14 - 5 = 67

⇒ 75 × 1.875 + 14 - 5 = 67

⇒ 140.625 + 14 - 5 = 67

⇒ 154.625 - 5 = 67

⇒ 149.625 ≠ 67

⇒ LHS ≠ RHS

Option 2) - and ÷

Given: 75 ÷ 15 × 8 + 14 - 5 = 67

After interchanging the signs we get;

⇒ 75 - 15 × 8 + 14 ÷ 5 = 67

⇒ 75 - 15 × 8 + 2.8 = 67

⇒ 75 - 120 + 2.8 = 67

⇒ 77.8 - 120 = 67

⇒ -42.2 ≠ 67

⇒ LHS ≠ RHS

Option 3) - and ×

Given: 75 ÷ 15 × 8 + 14 - 5 = 67

After interchanging the signs we get;

⇒ 75 ÷ 15 - 8 + 14 × 5 = 67

⇒ 5 - 8 + 14 × 5 = 67

⇒ 5 - 8 + 70= 67

⇒ 75 - 8 = 67

⇒ 67 = 67

⇒ LHS = RHS

Option 4) + and -

Given: 75 ÷ 15 × 8 + 14 - 5 = 67

After interchanging the signs we get;

⇒ 75 ÷ 15 × 8 - 14 + 5 = 67

⇒ 5 × 8 - 14 + 5 = 67

⇒ 40 - 14 + 5 = 67

⇒ 45 - 14 = 67

⇒ 31 ≠ 67

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 3".

Given Statements:

All elephants are tigers.

All tigers are horses.

No horse is a camel.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some horses are elephants - True (All Elephants are the part of Horse, it also gives some horses are elephants).

II. Some camels are tigers - False (Because, All the tigers are Horse and No horse are Camel, it gives no Camel are tigers).

So, Only conclusion I follows.

Hence, the correct answer is "Option 1".

The logic followed here is:

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

Now, checking the options:

Option 1) 46 - 41 - 12 → (46 - 41) × 3 → 5 × 3 = 15 ≠ 12.

Option 2) 16 - 9 - 21 → (16 - 9) × 3 → 7 × 3 = 21.

Option 3) 23 - 18 - 15 → (23 - 18) × 3 → 5 × 3 = 15.

Option 4) 34 - 28 - 18 → (34 - 28) × 3 → 6 × 3 = 18.

So, '46 - 41 - 12' odd among the given options.

Hence, the correct answer is "Option 1".

The triangles are:

So, there are '10' triangles in the given figure.

Hence, the correct answer is "10".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

The logic followed here is:

So, 'GX 18' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

The logic followed here is:

'RESENT' is written as 'TGUCLR',

‘PEOPLE' is written as 'RGQNJC’

Similarly, for 'PERSON'

So, 'PERSON' will be coded as 'RGTQML'.

Hence, the correct answer is "Option 1".

The logic followed here is:

So, 'YTA' will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

Given:

'will come back' is written as 'mp rq pl',

'back to school' is written as 'jn st mp'.

Here, 'back' will be coded as 'mp'.

Hence, the correct answer is "Option 4".

Given: 17 April 1992 is Friday.

then, 17 April 1993 will be Friday + 1 = Saturday.

So, the number of days between 17 April 1993 to 10 October 1993

= 13(April) + 31(May) + 30(June) + 31(July) + 31(August) + 30(September) + 10(October)

= 176 days → 176/7 = 25 week and 1 odd day.

So, 10 October 1993 = Saturday + 1 = Sunday.

Hence, the correct answer is "Option 1".

Mistake Points Yes, 1992 was a leap year but we have counted from 17^th April that's why it is treated as normal year because 29^th February is not counted in this year.

The logic followed here is:

So, '354' will complete the series.

Hence, the correct answer is "Option 3".

The logic followed here is:

Option 1) TVR

Option 2) DFB

Option 3) WYU

Option 4) MZK

Here, 'MZK' is odd among the given options.

Hence, the correct answer is "Option 4".

The logic followed here is:

So, 'XIWSP' will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

Family Chart:

Given: 

L is the sister of G, G is the son of M, M is married to D.

D is the sister of E, E is the son of C, C is married to S, S is the sister of P.

So, L is 'Sister's daughter' of E.

Hence, the correct answer is "Option 3".

The logic followed here is:

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

Now, checking the options:

Option 1) 46 - 141 → (46 × 3) + 3 → 138 + 3 = 141.

Option 2) 55 - 168 → (55 × 3) + 3 → 165 + 3 = 168.

Option 3) 35 - 108 → (35 × 3) + 3 → 105 + 3 = 108.

Option 4) 29 - 88 → (29 × 3) + 3 → 87 + 3 = 90 ≠ 88.

So, '29 - 88' odd among the given options.

Hence, the correct answer is "Option 4".

The logic followed here is:

1^st to 2^nd image:

2^nd to 3^rd image:

3^rd to 4^th image:

4^th to 5^th image:

So, the complete series will be:

Hence, the correct answer is "Option 1".

The correct answer is Guglielmo Marconi.

Key Points

• Guglielmo Marconi was awarded the Nobel Prize in Physics in 1909 along with Karl Ferdinand Braun for the development of practical wireless telegraphy.
• Marconi is widely recognized as the father of modern wireless communication.
• He conducted extensive experiments and research on radio waves and developed a practical system of wireless telegraphy that revolutionized communication.

Additional Information

• Heinrich Rudolf Hertz was a German physicist.
• He discovered the existence of electromagnetic waves, which laid the foundation for the development of wireless communication.
• John Michell was an English physicist and geologist.
• He made significant contributions to the field of astronomy and gravitation.
• Wilhelm Rontgen was a German physicist.
• He discovered X-rays, which revolutionized medical diagnosis.

The correct answer is Santoor.

Key Points

• Pandit Shivkumar Sharma is remembered for his mastery in playing the Santoor, a musical instrument that originated in the Kashmir Valley.
• The Santoor is a type of hammered dulcimer that is played by striking the strings with a pair of wooden mallets.
• Pandit Shivkumar Sharma is credited with popularizing the Santoor as a solo instrument in Indian classical music.
• He has also collaborated with other musicians from different genres and countries, including the Grateful Dead and the Kronos Quartet.

Additional Information

• Tabla:
• The word "tabla" comes from the Arabic word "tabl," which denotes a drum or flat-surfaced instrument that faces upward.
• It serves as both a solo performance instrument and a crucial rhythmic accompaniment for solo and instrumental music ensembles.
• Sarod:
• The sarod is a plucked bowl-lute chordophone that is native to Pakistan and northern India.
• There is a small additional bridge next to the upper nut of the sarod type with eight main strings and two chikari strings.
• Four drone strings rest upon this bridge.
• Sitar:
• Hindustani classical music uses the sitar, a plucked stringed instrument from the Indian subcontinent.
• The sitar, which is typically four feet long and has a deep pear-shaped gourd body, features twenty arched movable frets, a long, wide, hollow wooden neck, and front and side tuning pegs.

The correct answer is Bank Sakhi.

Key Points

• "Bank Sakhi" is a term used for women Self-Help Group (SHG) members who are appointed as banking agents.
• These women act as a bridge between the bank and the rural population, especially women, who may not be familiar with banking procedures.
• They provide banking services like account opening, deposit, withdrawal, and other financial services to the community they serve.

Additional Information

• Self-help groups are committees that act as financial intermediaries and are typically made up of 12 to 25 local women who are between the ages of 18 and 50.
• A minimum of three members, any two of whom may work together to manage their account, should be authorized by the SHG.
• The resolution may be submitted to the bank branch together with the properly completed application form that the promoter duly introduced.
• "Bank Mitra" is a term used for business correspondents who act as agents of banks and provide basic banking services to the unbanked population.

The correct answer is Potassium bitartrate.

Key Points

• Potassium bitartrate is the by-product of the fermentation of grape juice or other fruit juices during the alcohol-making process.
• It is also known as cream of tartar.
• It is a white crystalline powder that is commonly used in baking as a leavening agent and to stabilize egg whites.

Additional Information

• Potassium citrate is a salt that is commonly used as a food additive and in medical treatments to prevent kidney stones.
• If you suffer from chronic kidney failure, you should avoid using potassium citrate.
• Potassium nitrate, also known as saltpeter, is a chemical compound that is used in fertilizers, fireworks, and as a food preservative.
• It exists as the mineral niter in nature.
• It is a source of nitrogen, which bears niter's name.
• Potassium hydrogen adipate is a salt that is used in the manufacture of synthetic fibers and plastics.
• It's a chemical substance found in a variety of powders used to make fruit-flavored or jelly-like desserts and drinks.

The correct answer is the Jharkhand.

• Mundari dance is associated with the tribal community of Jharkhand, India.
• It is a traditional dance form performed by the Mundari tribe during various occasions like weddings, festivals, and harvest seasons.
• The dance is performed in a group, with both men and women participating in it.
• The dance is characterized by rhythmic footwork, clapping, and synchronized movements of the dancers.
• The Mundari dance is an integral part of the cultural heritage of Jharkhand and is recognized as an important folk dance of the state.
• Mizoram is a northeastern state of India that has a rich cultural heritage.
• The state is known for its traditional dance forms like Cheraw, Khuallam, and Chheihlam.
• Arunachal Pradesh is a northeastern state of India that is known for its tribal culture.
• The state has various traditional dance forms like Aji Lamu, Chalo, and Ponung.
• Jharkhand is a state located in eastern India that is known for its rich tribal culture.
• The state has various traditional dance forms like Karma, Jhumar, and Chhau, apart from Mundari dance.

The correct answer is Kolkata.

Key Points

• Bandhan Financial Services is headquartered in Kolkata.
• Bandhan Financial Services was granted in-principal approval by RBI to start a universal bank in 2014, which means that they were given permission to set up a new bank, subject to fulfilling certain conditions laid down by the RBI.
• Bandhan Bank, the universal bank started by Bandhan Financial Services, began operations in August 2015 and has since expanded to become one of India's largest banks.

Additional Information

• Bandhan Financial Services was founded in 2001 by Chandra Shekhar Ghosh, a former field officer with BRAC, the Bangladesh-based microfinance organization.
• The organization provides microfinance services to women in rural and semi-urban areas of India, helping them start and grow small businesses.
• Mumbai is the financial capital of India and home to the Reserve Bank of India.
• Pune is a major center for IT and manufacturing industries.
• Lucknow is the capital city of the northern state of Uttar Pradesh.

The correct answer is 36 feet.

Key Points

• Standard tennis court dimensions are defined by the International Tennis Federation (ITF).
• For doubles matches, the full court width is utilized, extending to the outer doubles sidelines.
• This width measures 36 feet (10.97 meters).
• Singles matches use a narrower section within the doubles court, marked by the inner singles sidelines.

Additional Information

• Tennis is a racquet sport that can be played by two teams of two players each, or it can be played individually against one opponent.
• A hollow rubber ball covered in felt is struck by each player using a tennis racket that is strung with cord over or around a net and into the court of their opponent.
• Major Walter Wingfield of Her Majesty's Body Guard created the game, which he first played in 1874 under the name "Spharistike."
• Denbighshire, England hosted the first-ever game, and the first-ever public competition happened in 1875.

Basic Rules

• Scoring System: The match consists of points, games, and sets. A player wins a point when the opponent fails to return the ball within the prescribed dimensions of the court. Games are won by the first player to win at least four points in total and at least two points more than the opponent. A set consists of a sequence of games, with players alternating serves. Matches are generally best of three or five sets.
• Serving: Matches start with a coin toss to decide which player will serve first. The server must hit the ball over the net to the diagonally opposite service box. If the serve fails, the server gets a second attempt. A serve that lands in but is not returned by the opponent scores a point.
• Faults and Lets: A serve that fails to land in the opponent's service box is called a fault. If this happens twice in a row, the opponent wins the point. A let is when the serve hits the net but still lands in the service box, or a serve is disrupted by an outside influence – the serve is retaken with no penalty.

Equipment:

• Racket: Frame with tightly pulled strings.
• Ball: Felt-covered rubber.
• Apparel: Sportswear and tennis shoes.

Key Terminology:

• Ace: Unreturned serve.
• Break: Winning a game when opponent serves.
• Deuce: Score of 40-40; requires two consecutive points to win from this position.
• Love: Zero score.
• Advantage: Point after deuce; winning next point wins the game, losing returns to deuce.
• Rally: Exchange of ball between players.
• Volley: Hitting the ball before it bounces.
• Groundstroke: Forehand or backhand shot after the ball bounces.

Governing Bodies and Tournaments:

• Organizations: International Tennis Federation (ITF), Women's Tennis Association (WTA), Association of Tennis Professionals (ATP).
• Grand Slam Tournaments: Australian Open, French Open, Wimbledon, US Open.

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

Key Points

• Champakkulam boat race is a popular boat race held in Kerala.
• Somnath fair is an important fair held in Gujarat which attracts a large number of tourists.
• Surajkund fair is a cultural fair held in Haryana showcasing the rich cultural heritage of the state.
• Baneshwar fair is a religious fair held in Rajasthan dedicated to Lord Shiva.

Additional Information

• Kerala is known as "God's Own Country",
• ​It is famous for its backwaters, beaches, and traditional boat races.
• Gujarat is known for its vibrant culture, rich history, and scenic beauty.
• It is home to many important historical and cultural sites like the Somnath temple, Sabarmati Ashram, and Gir National Park.
• Haryana is a state located in northern India and is known for its agricultural and industrial development.
• It is also home to many important historical and cultural sites like the Surajkund Lake and the Kurukshetra War Memorial.
• Rajasthan is known as the "Land of Kings" and is famous for its rich history, culture, and architecture.
• It is home to many important historical and cultural sites like the Amer Fort, Jaisalmer Fort, and the Thar Desert.

The correct answer is 60°.

Key Points

• Mid-latitude deserts (BWK) are found between 35^o and 60^oN and S.
• These deserts are located poleward of subtropical high-pressure areas.
• BWK deserts are characterized by low precipitation and high evaporation rates.
• Examples of BWK deserts include the Mojave Desert in the United States and the Gobi Desert in Asia.

Additional Information

• In the southwestern United States, the Mojave Desert is a desert that receives rain shadows from the Transverse Ranges and the southern Sierra Nevada mountains.
• The sixth largest desert in the world, the Gobi Desert is a vast, icy area of grassland and desert located in southern Mongolia and northern China.

The correct answer is Bauxite.

Key Points

• Panchpatmali deposits in Koraput district are known for their abundant reserves of bauxite, which is the primary ore used to produce aluminum.
• Bauxite is a sedimentary rock that typically contains high levels of aluminum hydroxide minerals, as well as other impurities like iron oxides and silica.
• Panchpatmali deposits in Koraput district is located in Orissa.
• Bauxite deposits are created when rocks containing a lot of aluminum silicates break down.
• Panchpatmali deposits is the largest bauxite mines in Asia.​

Additional Information

• Iron ore is another mineral commonly found in India and is used primarily in the production of steel.
• Copper is a metal that is used in a variety of applications, from electrical wiring to plumbing.
• Manganese is a metal that is used primarily in the production of steel and other alloys.
• Bauxite is the primary source of gallium and aluminum in the world.

The correct answer is Third.

Key Points

• The Anglo-Maratha War that resulted in merging the Peshwas' territories with the Bombay Presidency was the Third Anglo-Maratha War.
• This war took place between 1817 and 1819 and was fought between the British East India Company and the Maratha Empire.
• The British won the war and as a result, the Peshwas' territories, which included Pune, were annexed by the British and merged with the Bombay Presidency.
• This war was significant in the history of India as it marked the end of the Maratha Empire's power and paved the way for British dominance in India.

Additional Information

• The First Anglo-Maratha War took place between 1775 and 1782 and was fought between the British East India Company and the Maratha Empire.
• The British were unable to defeat the Marathas and the war ended with the Treaty of Salbai.
• The Second Anglo-Maratha War took place between 1803 and 1805 and was fought between the British East India Company and the Maratha Empire.
• The British won the war and as a result, the Marathas lost a significant amount of territory.
• The third Anglo-Maratha War took place between 1817 and 1819 and was fought between the British East India Company and the Maratha Empire.
• The British were successful in defeating the Marathas and the war ended with the Treaty of Mandsaur.

The correct answer is It is not processed further by a producer.

Key Points

• A final good is a product that is purchased by the end-user for consumption, rather than for further processing or resale.
• The key term "final good" is used to distinguish between goods that are used by the end-user and goods that are used as inputs in the production of other goods.
• A final good, sometimes referred to as consumer goods, is a class of commodity that is used by the user to fulfill their immediate needs instead of being produced in order to create other goods.
• Only newly produced goods are included in the term "final goods" when referring to national income and output.

Additional Information

• Intermediate goods are goods that are used as inputs in the production of other goods. For example, steel used in the production of a car is an intermediate good.
• Products, such as partially finished goods, that are utilized as inputs in the production of other goods, including final goods, are referred to as intermediate goods, producer goods, or semi-finished products.
• A consumer durable is a final good that is expected to last for a long time and is used repeatedly. Examples include cars, refrigerators, and televisions.
• A class of consumer goods known as consumer durables are ones that last for a long period and don't need to be replaced regularly.
• A non-durable good is a final good that is consumed in a short period of time. Examples include food, toiletries, and cleaning supplies.

The correct answer is gopuram.

Key Points

• Gopuram refers to the ornate and towering gateways that mark the entrance to the temple grounds in South India and Sri Lanka.
• Gopurams are typically made of stone and feature intricate carvings and sculptures of gods, goddesses, and other mythological figures.
• The gopuram's roots are in the early Pallava kings' constructions, which are related to North India's central shikhara towers.
• There are 21 gopurams (tower gateways) at the Ranganathaswamy Temple in Srirangam, Tamil Nadu, which is the tallest temple tower in Asia, the Rajagopuram (shrine of the main gateway), is a striking 239.5 feet (73.0 m) high.

Additional Information

• Mandap:
• It refers to a pillared outdoor hall or pavilion used for public gatherings or religious ceremonies.
• The mandapa, an elaborate gateway that leads to the temple through the gopuram, is a porch-like structure in Hindu temples.
• It is a part of the main temple compound and is used for religious dancing and music.
• Ardhmandap:
• It refers to a smaller, semi-open hall or chamber typically found near the entrance of a temple.
• Typically, Ardhamandapa is an open, four-pillared structure that stands in front of the temple's mandapa entrance door, allowing for natural light and ventilation.
• Vimana:
• In Hindu temples in South India and Odisha, East India, the structure over the garbhagriha, or inner sanctum, is known as the vimana.
• Vimana refers to the towering, pyramid-shaped roof structure that sits atop the sanctum sanctorum (innermost shrine) of a South Indian temple.

The correct answer is Bt Cotton.

Key Points

• Bt Cotton is the only GM crop approved for commercial cultivation in India.
• It was first approved in 2002 for cultivation in six Indian states.
• Bt Cotton has been genetically modified to produce a toxin that kills bollworm, a major pest that affects cotton crops.
• The adoption of Bt Cotton in India has been controversial, with some arguing that it has led to increased farmer debt and decreased yields.

Additional Information

• A crop used in agriculture that has had its DNA altered through genetic engineering is known as a genetically modified crop (GM crop).
• In GM crop, Agrobacterium can be used to transfer sequences hosted in T-DNA binary vectors, or one can physically modify plant genomes.
• The goal is to give the plant a new characteristic that is not found in the species naturally.
• Mustard is currently awaiting approval for commercial cultivation in India.
• It has been genetically modified to improve yields and reduce the country's dependence on imported edible oil.
• Bt Brinjal was approved for commercial cultivation in India in 2009, but the approval was later revoked in 2010 due to concerns about its safety and impact on human health and the environment.

The correct answer is Shubman Gill.

Key Points 

• Shubham Gill won the orange cap in IPL - 2023.
• Shubman Gill is a cricket player from India.
• In addition to playing for Punjab in domestic cricket and the Gujarat Titans in the Indian Premier League, he is an international representative of the Indian cricket team.
• Gill was named Player of the Tournament during the 2018 Under-19 Cricket World Cup.
• The Orange Cap is awarded to the player who scores the most runs in an IPL season. It is a prestigious award in the tournament.

 Additional Information

• Ten franchise teams from cities around India compete in the men's Twenty20 (T20) cricket league known as the Indian Premier League (IPL).
• In 2007, the BCCI established the league.
• The Indian Premier League was the first sports event to be streamed live on YouTube in 2010.
• Every year, the competition is typically held in the summer, between March and May.
• Yashasvi Jaiswal is a young Indian batsman who made his IPL debut in 2020 for Rajasthan Royals.
• Faf du Plessis is a South African cricketer who has played for Chennai Super Kings in IPL.
• Devon Conway was hired by the Chennai franchise for Rs. 1.00 Cr. during the IPL 2023 Auction.

The correct answer is Gonds.

Key Points

• Gonds have been recognized as a Schedule Tribe in some parts of Uttar Pradesh through the Constitution (Scheduled Castes and Scheduled Tribes) Orders (Second Amendment) Bill, 2022.
• The Gonds are an ethnolinguistic group in India who call themselves "Koitur".
• Gondi, their mother tongue, is a member of the Dravidian language family.
• The Gondi community has been featured in two major films: S.S. Rajamouli's 2022 blockbuster RRR and the 2017 Amit V. Masurkar film Newton.
• Gonds are one of the largest tribal communities in India, primarily found in central India, including the states of Madhya Pradesh, Chhattisgarh, Maharashtra, and parts of Uttar Pradesh, Andhra Pradesh, and Telangana.

 Additional Information

• Erukala:
• It is a community in Andhra Pradesh.
• Although Yerukala is their mother tongue, the majority now speak Telugu.
• Bhils:
• These are a large tribal community primarily found in western India, including the states of Rajasthan, Gujarat, Maharashtra, and Madhya Pradesh.
• A subgroup of the Western Zone of the Indo-Aryan languages, they speak the Bhil languages.
• Chenchus:
• These are another tribal community primarily found in Andhra Pradesh, Telangana, and parts of Karnataka.
• The Dravidian language family includes the Chenchu language, which is spoken by the Chenchu people.

The correct answer is Most people will expect the interest rate to rise in the future.

Key Points

• When the general interest rate reaches a very low level, most people will expect the interest rate to rise in the future because they anticipate that the central bank will try to stimulate the economy by increasing interest rates.
• As a result, most people will prefer to hold cash or short-term securities rather than long-term bonds because the latter are more sensitive to changes in interest rates and may lose value if rates rise.
• Some investors may speculate that the interest rate will decline further, but this is less likely because interest rates cannot fall below zero and there are limits to how much the central bank can ease monetary policy.
• Any increase in the money supply may cause inflation and inflation expectations to rise, which would put upward pressure on interest rates, not downward pressure.

Additional Information

• Most people will prefer to hold bonds:
• It is unlikely to be true when interest rates are very low because bonds become less attractive as their yields decline and their prices rise.
• However, it is possible that some investors may still prefer to hold bonds because they need income or because they believe that interest rates will remain low for a long time.
• Most people will speculate a further decline in the rate of interest: 
• May be true in some cases, especially if investors believe that the central bank will continue to ease monetary policy or that the economy will remain weak.
• However, this is not a universal expectation and may depend on the specific circumstances.
• Any increase in the money supply will cause the interest rate to fall further: 
• It is incorrect because the relationship between the money supply and interest rates is not straightforward and depends on many factors, such as the demand for money, the velocity of circulation, and the role of banks in creating credit.
• In general, an increase in the money supply may lead to higher inflation expectations and higher interest rates, not lower ones.

The correct answer is Pradhan Mantri Kaushal Vikas Yojana.

Key Points

• Pradhan Mantri Kaushal Vikas Yojana (PMKVY) is a government scheme that provides skill development training to youth in India.
• The scheme aims to provide vocational training to youth across the country and help them acquire new skills for better employability.
• The training is provided through various training partners and centres, and the candidates can choose from a wide range of courses as per their interest and eligibility.
• The scheme also provides financial assistance to candidates who successfully complete the training and are placed in a job or start their own business.

Additional Information

• Pradhan Mantri Jan Dhan Yojana (PMJDY):
• It is a financial inclusion scheme that aims to provide banking services to the unbanked population of the country.
• The Indian Prime Minister, Narendra Modi, started this campaign for financial inclusion on August 28, 2014.
• Deendayal Antyodaya Yojana (DAY):
• It is a poverty alleviation scheme that aims to uplift the poor and vulnerable sections of the society.
• Swarnajayanti Gram Swarozgar Yojana (SGSY) was the original scheme introduced in 1999.
• In 2011, it changed its name to the National Rural Livelihood Mission.
• They eventually combined to form DDU-AY.
• Pradhan Mantri Garib Kalyan Anna Yojana (PMGKAY):
• It is a food security scheme that aims to provide food grains to the poor and needy during the COVID-19 pandemic.
• During India's COVID-19 pandemic on March 26, 2020, the government of India announced the food security welfare program.

The correct answer is Mahadev Govind Ranade.

Key Points

• Widow Remarriage Association was founded in 1861 in Bombay (now Mumbai), India.
• The Association was established to promote the remarriage of widows, which was considered taboo in Indian society at that time.
• The founder of the Association, Mahadev Govind Ranade, was a prominent social reformer and a member of the Bombay Presidency Association, which was formed in 1885 to work for social and political reforms in India.
• He was also a member of the Indian National Congress and the Bombay Presidency Association.
• He worked for social and political reforms in India and was a strong advocate for women's rights.​

Additional Information

• Dr. Atma Ram Pandurang:
• He was a social reformer and a member of the Prarthana Samaj, which was founded in Bombay in 1867.
• He worked for the upliftment of women and advocated for the education of girls.
• RG Bhandarkar:
• He was a historian and a member of the Indian National Congress.
• He supported social and political reforms in India.
• Dwarkanath Tagore:
• He was a prominent businessman and a member of the Brahmo Samaj, which was founded in Calcutta in 1828.
• He supported social and religious reforms.

The correct answer is Odisha.

Key Points

• Odissa has the highest number of aluminium smelting plants in India.
• Some of the major players in the aluminium industry in Odisha include National Aluminium Company Limited (NALCO), Vedanta Aluminium Limited, Hindalco Industries Limited, and Jindal Aluminium Limited.
• The method by which alumina is melted to create pure aluminum metal is known as primary production.
• The process of recycling aluminum scrap into reused aluminum is known as secondary production.

Additional Information

• Tamil Nadu, which is the second-largest producer of aluminium in India after Odisha, has a few aluminium smelting plants as well, including Madras Aluminium Company Limited (MALCO), which is a subsidiary of Vedanta Limited.
• Maharashtra, which is the third-largest producer of aluminium in India, has a few aluminium smelting plants, including Hindalco Industries Limited's plant in Belgaum, Karnataka, which is operated by its subsidiary Novelis.
• Uttar Pradesh have a few downstream aluminium units, including Bharat Heavy Electricals Limited's (BHEL) plant in Varanasi, which produces aluminium conductors and other equipment.

The correct answer is Four.

Key Points

• Aditi Ashok is an Indian professional golfer who started playing golf at the age of five.
• She turned professional in 2016 and joined the Ladies European Tour (LET) in the same year.
• Aditi Ashok has also played on the LPGA Tour and has represented India in the Olympics.
• As of February 2023, Aditi Ashok has overall won the LET four times.

Additional Information

• Founded in 1978, the Ladies European Tour is a professional golf tour for women.
• It is situated in England at the Buckinghamshire Golf Club, close to London.
• Members of the tour made the decision to establish the Women Professional Golfers' European Tour Limited as a separate company in 1988.

The correct answer is Article 23.

Key Points

• Article 23 of the Indian Constitution prohibits forced labour and any form of human trafficking.
• This includes trafficking of children and women for forced labour, prostitution, or any other form of exploitation.
• The article also prohibits the employment of children below the age of 14 in any hazardous occupation or process.
• Any contravention of this article is a punishable offence under the law.
• The article also provides for the rehabilitation of victims of forced labour and trafficking.

Additional Information

• Article 20:
• It deals with protection against double jeopardy and self-incrimination.
• No one may face charges or punishment for the same offense more than once.
• Article 19:
• It is related to right to freedom of speech and expression, assembly, association, movement, and residence.
• The ability to organize into cooperative societies, unions, or associations.
• Article 25:
• It deals with the right to freedom of religion.
• This fundamental right ensures that every individual has the freedom to profess, practice and propagate any religion of their choice without being discriminated against on any grounds.

The correct answer is Padma Bhushan.

Key Points

• Rukmini Devi Arundale received the Padma Bhushan award in 1956 for her contribution to the field of Bharatanatyam dance.
• She was a pioneer in the revival and popularization of Bharatanatyam, which had been looked down upon as a low-class art form.
• Rukmini Devi Arundale was also a social activist and worked towards the betterment of women's rights and animal welfare.
• She founded the Kalakshetra Foundation, an institute for the promotion of Indian art and culture, which continues to thrive today.

Additional Information

• Jnanpith Award:
• It is given for excellence in literature.
• The oldest and most prestigious literary award in India, the Jnanpith Award is given out every year.
• Saraswati Samman:
• It is given for outstanding literary work.
• It is an annual literary prize given for exceptional prose or poetry in any of the 22 Indian languages included in Schedule VIII of the Indian Constitution.
• Kabir Puraskar:
• This award is given for promoting communal harmony.
• In 1990, the Indian government launched the "Kabir Puraskar Scheme,"

The correct answer is 1865.

Key Points

• John Alexander Newlands propounded the concept of the "Law of Octaves" in the year 1865.
• The Law of Octaves proposed that the chemical elements exhibit similar properties after every eighth element when arranged in order of increasing atomic weight.
• This concept was later refined by Dmitri Mendeleev, who developed the modern periodic table of elements.

Additional Information

• The law of octaves by Newland was an early attempt to categorize elements into groups according to their characteristics.
• Based on their atomic masses, He put them in ascending order and saw that every eighth element had characteristics in common.
• Newlands compared the similarity between the elements to the octaves of music, where every eighth note is compared to the first.

The correct answer is To organise village panchayat.

Key Points

• Gandhian principle of Directive Principles of State Policy refers to the principles advocated by Mahatma Gandhi, the father of the nation, which were incorporated in the Constitution of India as a guiding framework for the government.
• One of the key Gandhian principles is to organize village panchayats, which are local self-governance institutions that promote community participation and decision-making at the grassroots level.
• The Indian Constitution contains several articles like Article 40, Article 43, Article 43 B, Article 46, Article 47, and Article 48.

Additional Information

• To Separate judiciary from executive:
• This principle aims to ensure the independence and impartiality of the judiciary, which is already enshrined in the Constitution of India as a fundamental right.
• The principle of separation of powers, which is a key feature of the Indian Constitution, already mandates a clear separation between the three branches of government - legislature, executive, and judiciary.
• To secure uniform civil code:
• This principle is aimed at promoting gender equality and social justice, but it remains a highly contentious issue in India due to opposition from some religious communities.
• The government has not yet been able to implement a uniform civil code due to opposition from various quarters.
• To provide equal pay for equal work:
• This principle is aimed at promoting gender equality in the workplace, but it remains a major challenge in India where women continue to face discrimination and unequal pay.
• The government has taken several measures to address this issue, including enacting laws and policies to ensure equal pay for equal work, but the implementation remains a challenge.

Calculation:

Total visitors = Male visitors + Female visitors

= 2000 + 1500

= 3500

The total visitors in the age group 25 - 35 is = 27% of 3500 = 945

so

The number of male visitors in the age group 25 - 35 is = 60% of 945 = 567

Similarly,

The total visitors in the age group 45 - 60 is = 29% of 3500 = 1015

so

The number of female visitors in the age group 45 - 60 is = 20% of 1015 = 203

The expected ratio will be,

567 : 203

⇒ 81: 29

∴ The correct option is 4

Given:

The marked price = 80% above its cost price.

Discount = 48%

Concept used:

SP = CP + profit

Profit is calculated on the cost price and discount on the market price.

Calculation:

Let the CP is = 100

The market price is = 180

The selling price will be,

⇒ 180 × 52/100 = 93.60

The loss percentage will be,

⇒ 100 - 93.60 

⇒ 6$\frac{2}{5}$ %

∴ The correct option is 3

Shortcut Trick

For any triangle with sides a, b, and c, the third side c must lie in the range:

|a − b| < c < a + b

Difference of sides < S < Sum of sides

⇒ |24 − 9| < S < 24 + 9

⇒ 15 < S < 33

∴ The correct answer is 15 < S < 33.

Alternate Method

Given:

Side 1 (a) = 9 units

Side 2 (b) = 24 units

Side 3 (c) = S units

Formula Used:

Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.

According to the theorem, for sides 9, 24, and S:

⇒ Case 1: 9 + 24 > S

⇒ 33 > S or S < 33

⇒ Case 2: 9 + S > 24

⇒ S > 24 − 9

⇒ S > 15

⇒ Case 3: 24 + S > 9 (Always true for any positive S)

Combining the conditions from Case 1 and Case 2:

⇒ 15 < S < 33

∴ The correct answer is 15 < S < 33.

Additional Information

Triangle Inequality Theorem

This theorem states that the sum of any two sides of a triangle is greater than the third side, which prevents the triangle from collapsing into a straight line.

Range of the Third Side

If two sides are x and y, the third side z must satisfy: (Difference of x,y) < z < (Sum of x,y).

Degenerate Triangle

A triangle where the sum of two sides equals the third side (a + b = c) is called a degenerate triangle, where the three vertices are collinear.

Shortcut Trick

Given 2x + 2/x = 5 ⇒ x + 1/x = 5/2 = k.

Using algebraic shortcut: x³ + 1/x³ = k³ − 3k.

x³ + 1/x³ = (5/2)³ − 3(5/2) = 125/8 − 15/2 = 65/8.

Required value = (x³ + 1/x³) + 2 = 65/8 + 2 = (65 + 16)/8 = 81/8.

∴ The correct answer is 81/8.

Alternate Method

Given:

2x + 2/x = 5

Formula Used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculations:

⇒ 2(x + 1/x) = 5

⇒ x + 1/x = 5/2

Now, perform cubing on both sides:

⇒ (x + 1/x)³ = (5/2)³

⇒ x³ + (1/x)³ + 3 × x × (1/x) × (x + 1/x) = 125/8

⇒ x³ + 1/x³ + 3(5/2) = 125/8

⇒ x³ + 1/x³ + 15/2 = 125/8

⇒ x³ + 1/x³ = 125/8 − 15/2

⇒ x³ + 1/x³ = (125 − 60)/8 = 65/8

According to the question, we need the value of (x³ + 1/x³ + 2):

⇒ 65/8 + 2

⇒ (65 + 16)/8 = 81/8

∴ The correct answer is 81/8.

Additional Information

Sum of Cubes Identity

The expression x³ + 1/x³ can always be derived from x + 1/x using the formula: (x + 1/x)³ − 3(x + 1/x).

Square Relationship

The square of the sum of a variable and its reciprocal is given by: x² + 1/x² = (x + 1/x)² − 2.

Difference of Cubes

Similarly, for subtraction: x³ − 1/x³ = (x − 1/x)³ + 3(x − 1/x), which is useful in reciprocal algebra problems.

Given:

Income = Rs 45000 , Expenditure = Rs 33000

Income is increased by 22% and expenditure is increased by 11%,

Concept used:

Income = expenditure + savings

Calculation: 

After increasing the income will be,

⇒ 45,000 × 122/100 = Rs 54900

After increasing the expenditure will be,

⇒ 33,000 × 111 /100 = Rs 36630

Increased savings is 54900 - 36630 = Rs 18270

∴ The correct option is 1

Given:

x + $\frac{1}{x}$ = 7

Formula used:

(A + B)2 = A2 + 2AB + B2 

Calculation:

​x + $\frac{1}{x}$ = 7​

⇒ (x + $\frac{1}{x}$) = 7

⇒ (x + $\frac{1}{x}$)2 = 49

⇒ x2 + $\frac{1}{x^2}$ = 49 - 2

⇒ 47

∴ The correct option is 3

Given:

The radius of the circles are 12cm and 13 cm 

Concept used:

Using Pythagoras theorem 

Formula used:

Hypotaneus² = Height² + Base² 

Calculation: 

 The length of the AP is

⇒ √(13² - 12²) 

⇒ √25 = 5 cm

The length of the chord(AB) of the larger circle which touches the smaller circle is,

⇒ 5 × 2 = 10 cm

∴ The correct option is 3

Given:

sinA + sin2A = 1

Concept used:

 sin2A + cos² A = 1

Calculation: 

sinA + sin2A = 1

⇒ sinA  = 1 -  sin2A

⇒ sinA  = cos2 A

Now,

(cos2 A + cos4A)

⇒ [cos2 A + (cos² A)²]

⇒ [cos2 A + (sin A)2]

⇒ cos2 A + sin ²A = 1

∴ The correct option is 1

Given:

The average age of 6 members = 25 years.

The youngest member is 4 years old.

Concept used:

Sum = average × total number

Calculation: 

The total age of the family is,

⇒ 25 × 6 = 150 years

The total age of the family just before the birth of the youngest member is,

⇒  150 - (4 × 6) = 126 years

The average age of the family just before the birth of the youngest member is,

⇒ 126 / 5 = 25.2 years

∴ The correct option is 4

Given:

cotθ = $\frac{9}{17}$

Concept used:

Cosec²θ -  cot²θ = 1

Calculation: 

As we know,

Cosec2θ -  cot2θ = 1

Putting the value of cotθ = 9/17 we get

​⇒ Cosec2θ -  (9/17)2= 1

​⇒ Cosec2θ = 1 +  (9/17)2

⇒  Cosec2θ = $1\frac{81}{289}$

∴ The correct option is 4

Given:

Rate of interest =  6%

The principal will be  increased its value by 40%

Formula used:

Simple interest = P × R × T / 100 [ P = principal, R = rate of interest, T = time]

Calculation:

Let,T = time and principal (P) = 100 

The simple interest got by the person is 40

As per the formula,

40 = 100 × 6 × T / 100

⇒ T = 40 /6

⇒ 20/3years = $6\frac{2}{3}$ years

∴ The correct option is 1

Given:

The radius = 6 cm , OB = 10 cm

Concept used:

OA is perpendicular on AB

Pythagoras theorem

Calculation: 

As per the question,

OB² - AO² = AB²

⇒ 10² - 6² = AB2

⇒ AB = √64

⇒ AB = 8 cm

∴ The correct option is 4

Given:

Height of Suhas' eyesight = 1.8 m

Height of tree = 3.15 m

Height of building = 11.25 m

Distance between building and tree = 45 m

Calculation:

From the figure,

TU = BE = 45 m

AS = DT = 1.8 m

⇒ BD = BT - DT = 3.15 - 1.8 = 1.35 m

BT = EU = 3.15 m

⇒ CE = CU - EU = 11.25 - 3.15 = 8.1 m

According to the question, the eyes of Suhas, the top of the tree, and the top of the building fall in one line

⇒ ∠BAD = ∠CBE                 ----(1)

Also, ∠BDA = ∠CEB = 90°   ----(2)

From (1) and (2), ΔABD and ΔBCE are similar triangles

⇒ AD/BD = BE/CE

⇒ AD/1.35 = 45/8.1

⇒ AD = (45/8.1) × 1.35

⇒ AD = 7.5 m

Now, AD = ST = 7.5

∴ The tree is located at a distance of 7.5 meters from Suhas.

Shortcut Trick

To find the third proportional (c) of two numbers 'a' and 'b', use the formula: c = b² ÷ a.

Here, a = 25 and b = 45.

Third proportional = (45 × 45) ÷ 25

Third proportional = 2025 ÷ 25 = 81.

∴ The correct answer is 81.

Alternate Method

Given:

First number (a) = 25

Second number (b) = 45

Formula Used:

If a, b, and c are in continued proportion, then a : b = b : c.

Calculations:

⇒ 25 : 45 = 45 : c

⇒ 25 ÷ 45 = 45 ÷ c

⇒ c = (45 × 45) ÷ 25

⇒ c = 2025 ÷ 25

⇒ c = 81

∴ The correct answer is 81.

Additional Information

Mean Proportional

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

Fourth Proportional

For three numbers a, b, and c, the fourth proportional 'd' satisfies a : b = c : d, meaning d = (b × c) ÷ a.

Continued Proportion

Three numbers are in continued proportion if the ratio of the first to the second is equal to the ratio of the second to the third.

Calculation:

Total number of students in commerce in college A is = 520

Total number of students in commerce in college B is = 550

Total number of students in commerce in college C is = 515

Total number of students in commerce in college D is = 690

Among these values, the minimum number of students in Commerce is in College C with 515 students.

Calculation :

The sale of wheat is 10 and the sale of rice is 20

The sale of onion is 5 and the sale of Sugar is also 5

The ratio between the sale of wheat and rice is,

⇒ 10 : 20 = 1 : 2

The ratio between the sale of sugar and onions is

⇒ 5 : 5 = 1 : 1

 ∴ The correct option is 1

Shortcut Trick

The radius (r) is calculated from the circumference: 2πr = 42π ⇒ r = 21 cm.

Using the volume formula for a cone: V = (1/3) × π × r² × h.

Substitute values: V = (1/3) × (22/7) × 21 × 21 × 24.

V = 22 × 21 × 24 = 11088 cm³.

∴ The correct answer is 11088 cm³.

Alternate Method

Given:

Height (h) of the cone = 24 cm

Circumference of the base = 42π cm

Formula Used:

Circumference of circle = 2πr

Volume of a cone = (1/3)πr²h

Calculations:

⇒ 2 × π × r = 42π

⇒ 2r = 42

⇒ r = 21 cm

⇒ Volume = (1/3) × (22/7) × 21 × 21 × 24

⇒ Volume = (1/3) × 22 × 3 × 21 × 24

⇒ Volume = 22 × 21 × 24

⇒ Volume = 462 × 24

⇒ Volume = 11088 cm³

∴ The correct answer is 11088 cm³.

Additional Information

Slant Height of a Cone

The slant height (l) is the distance from the apex to any point on the base circumference: l = √(r² + h²).

Curved Surface Area (CSA)

The area of the curved surface of a cone is given by the formula: CSA = πrl.

Total Surface Area (TSA)

The total surface area includes the base area and the curved area: TSA = πr(l + r).

Relation with Cylinder

The volume of a cone is exactly one-third the volume of a cylinder with the same radius and height.

Given:

A dishonest shopkeeper uses a weight of 920 gm for 1 kg weight.

Concept used:

Gain percentage = (Error value  / False weight) × 100

Calculation: 

So the gain percentage will be,

⇒ (1000 - 920 / 920) × 100

⇒ (80 /920) × 100 

⇒  8.70 %

∴ The correct option is 2

Shortcut Trick

Total work = LCM of 15 and 25 = 75 units.

Efficiency of A = 75 ÷ 15 = 5, Efficiency of B = 75 ÷ 25 = 3.

Work done by A and B in 5 days = 5 × (5 + 3) = 40 units.

Remaining work = 75 − 40 = 35 units.

Combined efficiency of A and C = 35 ÷ 4 = 8.75 units/day.

Efficiency of C = 8.75 − 5 = 3.75. Time taken by C = 75 ÷ 3.75 = 20 days.

∴ The correct answer is 20 days.

Alternate Method

Given:

Time taken by A to complete the work = 15 days

Time taken by B to complete the work = 25 days

A and B work together for 5 days.

Remaining work is completed by A and C in 4 days.

Calculations:

⇒ Work completed by A and B in 5 days = 5 × (5 + 3) = 40 units

⇒ Remaining work = Total work − Completed work = 75 − 40 = 35 units

⇒ A and C complete this remaining work in 4 days.

⇒ Combined efficiency of A and C = Remaining work ÷ Time = 35 ÷ 4 = 35/4 units/day

⇒ Efficiency of C = Combined efficiency of (A + C) − Efficiency of A

⇒ Efficiency of C = 35/4 − 5 = (35 − 20) / 4 = 15/4 units/day

⇒ Time taken by C alone = Total work ÷ Efficiency of C = 75 ÷ (15/4) = 75 × (4/15) = 20 days

∴ The correct answer is 20 days.

Additional Information

Total Work Concept

Total Work is typically taken as the Lowest Common Multiple (LCM) of the given individual time periods. Efficiency = Total Work ÷ Time taken.

Efficiency and Time Relationship

The efficiency of a person is inversely proportional to the time taken by them to complete a piece of work. If the ratio of time taken is a:b, their efficiency ratio will be b:a.

Chain Rule (Group Work)

If M₁ men can do W₁ work in D₁ days working H₁ hours per day, and M₂ men can do W₂ work in D₂ days working H₂ hours per day, then (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂.

Given:

The total race was 1.2 km.

The speed of Zeenat is 18 km/h and The speed of Nasreen is  27 km/h.

Concept used:

Distance = Speed × time 

Relative speed in the same direction is the difference of their speed.

Calculation:  

Relative speed will be (27 - 18) km/h = 9 km/h

The relative distance is 1.2 km 

So the time will be,

⇒ (1.2 / 9) × 60 

⇒ 0.4 × 20 = 8 minutes

∴ The correct option is 4

Shortcut Trick

A number is divisible by 11 if the difference between the sum of alternate digits is 0 or a multiple of 11.

For 752563, the alternate digit sums are (7 + 2 + 6) and (5 + 5 + 3).

Sum 1 = 15, Sum 2 = 13.

Difference = 15 − 13 = 2.

Since 2 is not 0 or a multiple of 11, the number is not divisible.

∴ The correct answer is 752563.

Alternate Method

Given: Numbers (1) 1735624, (2) 752563, (3) 1661308, (4) 1904529.

Formula Used: Sum of digits at odd positions − Sum of digits at even positions = 0, 11, 22...

Checking each option for divisibility by 11:

⇒ Option 1: 1735624 → (1+3+6+4) − (7+5+2) = 14 − 14 = 0 (Divisible)

⇒ Option 2: 752563 → (7+2+6) − (5+5+3) = 15 − 13 = 2 (Not Divisible)

⇒ Option 3: 1661308 → (1+6+3+8) − (6+1+0) = 18 − 7 = 11 (Divisible)

⇒ Option 4: 1904529 → (1+0+5+9) − (9+4+2) = 15 − 15 = 0 (Divisible)

∴ The correct answer is 752563.

Additional Information

Divisibility by 3 and 9

A number is divisible by 3 (or 9) if the sum of all its digits is divisible by 3 (or 9).

Divisibility by 7

Double the last digit and subtract it from the remaining number. If the result is divisible by 7, the original number is also divisible by 7.

Divisibility by 4 and 8

A number is divisible by 4 if its last two digits are divisible by 4. It is divisible by 8 if its last three digits are divisible by 8.

Given:

The discount  = 10 % and Profit = 20%

Concept used:

The discount is calculated on market price while profit is calculated on cost price.

Formula used:

Selling price = cost price + profit 

Calculation: 

Let the cost price is 100, 

Profit = 20% , so the selling price is 100 + 20 = 120

The market price is,

⇒ 120 × 100 /90 = 400 /3

The ratio between the market price and cost price is ,  

400 /3 : 100 ⇒ 4 : 3

∴ The correct option is  2

Shortcut Trick

Use the algebraic identity: (a − b)² = (a + b)² − 4ab.

Let a = 5x and b = 3y, then 4ab = 60xy.

Substitute the given values: (5x − 3y)² = (15)² − 30(2xy) = 225 − 30(6).

(5x − 3y)² = 225 − 180 = 45.

5x − 3y = √45 = 3√5.

∴ The correct answer is 3√5.

Alternate Method

Given:

5x + 3y = 15

2xy = 6

Formula Used:

(a − b)² = (a + b)² − 4ab

Calculations:

⇒ Here, a = 5x and b = 3y

⇒ 4ab = 4 × 5x × 3y = 60xy

⇒ From the given equation, 2xy = 6, so 60xy = 30 × (2xy) = 30 × 6 = 180

⇒ (5x − 3y)² = (5x + 3y)² − 60xy

⇒ (5x − 3y)² = (15)² − 180

⇒ (5x − 3y)² = 225 − 180

⇒ (5x − 3y)² = 45

⇒ 5x − 3y = √45

⇒ 5x − 3y = √(9 × 5) = 3√5

∴ The correct answer is 3√5.

Additional Information

Fundamental Algebraic Identities

(a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab. These are used to solve variables by squaring terms.

Relationship between Sum and Difference

(a + b)² − (a − b)² = 4ab. This identity is crucial when the sum and product are known and the difference is required.

Difference of Squares

a² − b² = (a − b)(a + b). This is used for factoring expressions or simplifying complex products.

Shortcut Trick

Let θ = 45°.

Substitute θ = 45° in the given expression:

cos 45° ÷ (sec 45° − 1) + cos 45° ÷ (sec 45° + 1)

⇒ (1/√2) ÷ (√2 − 1) + (1/√2) ÷ (√2 + 1) = (1/√2) × [(√2 + 1 + √2 − 1) ÷ (2 − 1)] = (1/√2) × 2√2 = 2.

Now, test θ = 45° in the options: 2 × cot²(45°) = 2 × 1² = 2.

∴ The correct answer is 2cot²θ.

Alternate Method

Given:

The trigonometric expression is: [cos θ ÷ (sec θ − 1)] + [cos θ ÷ (sec θ + 1)]

Formula Used:

⇒ sec²θ − 1 = tan²θ

⇒ cos θ × sec θ = 1

⇒ 1 ÷ tan²θ = cot²θ

Calculations:

Taking cos θ common from the terms:

⇒ cos θ × [1 ÷ (sec θ − 1) + 1 ÷ (sec θ + 1)]

Find the common denominator and simplify:

⇒ cos θ × [((sec θ + 1) + (sec θ − 1)) ÷ ((sec θ − 1)(sec θ + 1))]

⇒ cos θ × [2sec θ ÷ (sec²θ − 1)]

Substitute sec²θ − 1 = tan²θ into the denominator:

⇒ cos θ × [2sec θ ÷ tan²θ]

Since cos θ × sec θ = 1:

⇒ 2 ÷ tan²θ

⇒ 2cot²θ

∴ The correct answer is 2cot²θ.

Additional Information

Reciprocal Identities

Trigonometric reciprocal functions are defined as: cosec θ = 1 ÷ sin θ, sec θ = 1 ÷ cos θ, and cot θ = 1 ÷ tan θ.

Pythagorean Identities

The three primary Pythagorean relations are: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Quotient Identities

Quotient relations define tangent and cotangent in terms of sine and cosine: tan θ = sin θ ÷ cos θ and cot θ = cos θ ÷ sin θ.

Shortcut Trick

Rate for the first year = 10%.

Rate for the remaining 9 months (3/4 year) = 10% × 3/4 = 7.5%.

Effective CI Rate = 10 + 7.5 + (10 × 7.5) ÷ 100 = 18.25%.

Given CI = ₹1,460 → 18.25% of Principal = 1,460.

Principal (100%) = (1,460 ÷ 18.25) × 100 = ₹8,000.

∴ The correct answer is ₹8,000.

Alternate Method

Given:

Time (T) = 1 year 9 months = 1 (9/12) years = 1.75 years.

Rate (R) = 10% per annum.

Compound Interest (CI) = ₹1,460.

Formula Used:

For fractional years (n + a/b), Amount (A) = P(1 + R/100)ⁿ × [1 + (R × a/b)/100]

CI = A − P

Calculations:

⇒ Amount (A) = P × (1 + 10/100)¹ × [1 + (10 × 9/12)/100]

⇒ A = P × (11/10) × [1 + (10 × 3/4)/100]

⇒ A = P × (1.1) × (1 + 7.5/100)

⇒ A = P × 1.1 × 1.075

⇒ A = 1.1825P

⇒ CI = A − P = 1.1825P − P = 0.1825P

⇒ 0.1825P = 1460

⇒ P = 1460 ÷ 0.1825

⇒ P = (1460 × 10000) ÷ 1825

⇒ P = 8000

∴ The correct answer is ₹8,000.

Additional Information

Successive Percentage Change

For two successive rates r₁% and r₂%, the effective rate is given by [r₁ + r₂ + (r₁ × r₂) ÷ 100]%.

Effective Rate for Fractional Time

When time is in the form T = n + f (where f is a fraction), the rate for the fractional part of the year is R × f.

Amount Formula

Standard CI Amount: A = P(1 + r/100)^t. For annual compounding, interest is added to the principal at the end of each year.

The correct answer is: added insult to injury

Key Points

• The original phrase, "created insult to injury," is a misinterpretation of the idiom.
• The correct idiom is "added insult to injury."
• The idiom "added insult to injury" means to make a bad situation worse. (बुरी स्थिति को और भी बदतर बनाने)
• Example: After the car accident, the reckless driver not only caused damage to my vehicle but also insulted me, adding insult to injury.
• It fits the context of the sentence where Srujan already felt sad due to the harsh words of the boss, and his colleague's words worsened the situation.
• Corrected sentence: With the harsh words of the boss, Srujan felt sad, but his colleague’s words added insult to injury.

Therefore, the correct answer is option 4.

The correct answer is: The poem will be recited by the child.

Key Points

• The original sentence is in the active voice.
• The passive construction of the sentence involves switching the positions of the subject and the object and adjusting the verb accordingly.
• Structure (Active Voice): Subject (The child) + Will recite + Object (the poem)
• Structure (Passive Voice): Object (The poem) + Will be recited by + Subject (the child)
• When transforming this into the passive voice, the object of the active sentence becomes the subject of the passive sentence, and the subject becomes the agent preceded by the preposition "by."
• In this case, "will recite" in the active voice corresponds to "will be recited" in the passive voice.
• The use of "by" in the passive construction indicates the agent (the child) carrying out the action.

Therefore, the correct answer is option 2.

The erroneous part of the sentence is: itinary

Key Points

• The word 'Itinary' is misspelt in the given context.
• The correct spelling is 'Itinerary'.
• Itinerary refers to a detailed plan or schedule of a journey, including destinations, routes, and timing. (यात्रा कार्यक्रम)
• Example: Let me check the itinerary to see what's planned for today's excursion.
• Corrected sentence: You need to acknowledge the itinerary and accommodation details of your journey as per the given calendar.

Therefore, the correct answer is option 4.

Additional Information

• Calendar: A schedule or system of organizing time, typically into days, weeks, and months. (पंचांग)
• Accommodation: Lodging or living space, typically temporary, provided for individuals or groups. (आवास)
• Acknowledge: To recognize, accept, or admit the existence or truth of something. (प्राप्ति-स्वीकार)

The correct answer is: A speech delivered without prior preparation or rehearsal

Key Points

• Extempore: A speech delivered without prior preparation or rehearsal. (बिना तैयारी के)
• Example: The speaker delivered an impressive extempore speech on a topic suggested by the audience.
• In the context of the sentence, the speaker is referring to winning the first prize in an 'extempore' competition during their time in Class 5.
• This indicates that the competition involved speaking or performing without prior preparation, suggesting an impromptu or spontaneous nature.

Therefore, the correct answer is option 3.

The correct answer is: DCBA

Key Points

• Part D: This phrase sets the tone and prepares the reader for an emotional or surprising moment. It introduces the narrator's emotional response.
• Part C: This transition indicates a shift in the narrative, creating anticipation for what happened next. It signals the timing of the event.
• Part B: This part introduces the key element or object of the scene, which is the carcass of an animal. It provides the visual component to the narrative.
• Part A: This phrase concludes the sentence by describing the action or event related to the carcass. It completes the thought and gives closure to the sentence.
• The correct order of DCBA creates a coherent and meaningful sentence that follows a logical sequence of events, effectively conveying the narrator's experience.

Therefore, the correct answer is option 4.

The correct answer is: DBAC

Key Points

• Part D: This statement sets the stage by providing information on the significant investment of time and money required in the pharmaceutical industry.
• Part B: Following the introduction of the development process, this sentence adds a critical piece of information about the high failure rate in discovering new drugs, emphasizing the challenges involved.
• Part A: This question logically follows the information on the challenges in the pharmaceutical industry. It introduces the idea of seeking alternative approaches, specifically referencing Silicon Valley entrepreneurs and their potential interest in ancient wisdom.
• Part C: The concluding sentence provides context and explanation for why Silicon Valley entrepreneurs might be interested in decoding ancient wisdom. It connects the challenges in the pharmaceutical industry with the idea of looking for unconventional solutions and highlights the endangered status of ancient cultures.

Thus, option 3 is the correct answer.

The correct answer is: Anger

Key Points

• Resentment means a lingering feeling of bitterness or displeasure resulting from a perceived unfairness or offence. (क्रोध)
• Example: She felt resentment towards her colleague who took credit for her idea.
• Marked option Anger means an intense emotional response often triggered by perceived injustice, frustration, or provocation. (गुस्सा)
• Example: His face turned red with anger as he learned about the betrayal.
• So, the most appropriate synonym for 'resentment' is 'anger'.

Therefore, the correct answer is option 3.

Additional Information

• Calmness: A state of tranquillity and peace, free from disturbance or agitation. (धीरज)
• Happiness: A positive emotional state characterized by feelings of joy, contentment, and satisfaction. (ख़ुशी)
• Relaxation: The state of being free from tension or stress, often achieved through rest or leisure activities. (विश्राम)