SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 1) (Previous Year Paper)

Here, we use the figure (1) and (2) to find opposite faces, From the common number (1) written faces number in the clockwise direction.

Here, the opposite of face showing 6 is face showing 4.

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

Given:

18, 23, ?, 41, 54, 71

The logic followed in the given series is:

Here, the missing term is '30'.

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

The embedded part of this image is:

 

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

Here, we use the table given below:

Logic: Opposite alphabet is written.

RAT : IZG →

YUM : BNF →

Similarly, for 'SIP : ?' →

Here, 'SIP : HRK' is the correct pair.

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

Here, we use the table given below:

Logic: Code = [(Addition of all letter's position value) × (Number of letters)]

'BARBIE' is written as '222' →

'ELSA' is written as '148' →

Similarly, 'ARIEL' will be written as:

Here, the code for 'ARIEL' is '225'.

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

Mistake PointsAthletics is a Game, Athlete is a person, so solve it accordingly.

Given:

Cricket, Athlete, Sport

The Venn diagram for the given classes is:

Cricket is a type of sport and an athlete is a person who plays sport.

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

Here, we use the BODMAS table given below:

Given:

⇒ 173 ÷ 169 + 13 × 5 - 13 = 225

(1) + and -

⇒ 173 ÷ 169 + 13 × 5 - 13 = 225

After interchanging the signs:

⇒ 173 ÷ 169 - 13 × 5 + 13 = 225

Apply BODMAS rule:

⇒ 1.02 - 13 × 5 + 13

⇒ 1.02 - 65 + 13

⇒ 14.02 - 65 = (-50.97)

Here, the equation is not satisfied.

(2) ÷ and -

⇒ 173 ÷ 169 + 13 × 5 - 13 = 225

After interchanging the signs:

⇒ 173 - 169 + 13 × 5 ÷ 13 = 225

Apply BODMAS rule:

⇒ 173 - 169 + 13 × 0.384

⇒ 173 - 169 + 5

⇒ 178 - 169 = 9

Here, the equation is not satisfied.

(3) ÷ and +

⇒ 173 ÷ 169 + 13 × 5 - 13 = 225

After interchanging the signs:

⇒ 173 + 169 ÷ 13 × 5 - 13 = 225

Apply BODMAS rule:

⇒ 173 + 13 × 5 - 13

⇒ 173 + 65 - 13

⇒ 238 - 13 = 225

⇒ '173 + 169 ÷ 13 × 5 - 13 = 225'

Here, the equation is satisfied.

(4) - and ×

⇒ 173 ÷ 169 + 13 × 5 - 13 = 225

After interchanging the signs:

⇒ 173 ÷ 169 + 13 - 5 × 13 = 225

Apply BODMAS rule:

⇒ 1.02 + 13 - 5 × 13

⇒ 1.02 + 13 - 65

⇒ 14.02 - 65 = (-50.97)

Here, the equation is not satisfied.

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

Logic: First no. = [(Second no.)² - 2]

Checking all the given options:

(1) 80 : 9 →

⇒ [(9)² - 1]

⇒ (81 - 1) = 80

(2) 142 : 12 →

⇒ [(12)2 - 2]

⇒ (144 - 2) = 142

(3) 23 : 5 →

⇒ [(5)2 - 2]

⇒ (25 - 2) = 23

(4) 7 : 3 →

⇒ [(3)2 - 2]

⇒ (9 - 2) = 7

Here, in '80 : 9' different logic is followed.

Hence, the correct answer is "Option (1)".

Here, we use the table given below:

Given:

DELIGHT : UJJMQKK :: PLIGHT : UJJMQV :: CREATE : ?

The logic followed in the given pairs:

DELIGHT : UJJMQKK →

PLIGHT : UJJMQV →

Similarly, for 'CREATE : ?' →

Here, 'CREATE : FVDIWI' is the correct pair.

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

The logic followed in the given figure series is:

From Figure (1) to (2):

The symbols move as shown below.

From Figure (2) to (3):

The symbols move as shown below.

From Figure (3) to (4):

The symbols move as shown below.

From Figure (4) to Answer Figure (5):

The symbols move as shown below.

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

Logic: The figure repeats alternatively.

From Figure (1) to (3):

Similarly,

From Figure (2) to (4):

Hence, the correct answer is "Option (1)".

The correct order of words as they would appear in the English dictionary is:

5. Displace
6. Display
7. Dispute
8. Dissolve
9. Distance
10. Disturb

The correct order is '5, 2, 6, 1, 3, 4'.

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

Preparing the family tree diagram by using the following symbols:

As per the given data:

 

 

 

 

 

Given expression: 'A + P - Q × R - S'

A is the son of P, P is the wife of Q, Q is the father of R and R is the wife of S.

Here, A is the son of S.

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

Given:

(12, 4, 64)

(8, 6, 14)

Logic: Third number = [{(First no.)² - (Second no.)²} ÷ 2]

(12, 4, 64) →

⇒ [{(12)² - (4)²} ÷ 2]

⇒ [(144 - 16) ÷ 2]

⇒ (128 ÷ 2) = 64

(8, 6, 14) →

⇒ [{(8)2 - (6)2} ÷ 2]

⇒ [(64 - 36) ÷ 2]

⇒ (28 ÷ 2) = 14

Checking all the given options:

1. (7, 3, 28) →

⇒ [{(7)2 - (3)2} ÷ 2]

⇒ [(49 - 9) ÷ 2]

⇒ (40 ÷ 2) = 20

2. (10, 6, 42) →

⇒ [{(10)2 - (6)2} ÷ 2]

⇒ [(100 - 36) ÷ 2]

⇒ (64 ÷ 2) = 32

3. (11, 9, 15) →

⇒ [{(11)2 - (9)2} ÷ 2]

⇒ [(121 - 81) ÷ 2]

⇒ (40 ÷ 2) = 20

4. (9, 5, 28) →

⇒ [{(9)2 - (5)2} ÷ 2]

⇒ [(81 - 25) ÷ 2]

⇒ (56 ÷ 2) = 28

Here, (9, 5, 28) shows a similar relation to the given set of numbers.

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

Given:

(14, 10, 296)

(8, 17, 353)

Logic: Third no. = [(First no.)² + (Second no.)²]

(14, 10, 296) →

⇒ [(14)² + (10)²]

⇒ (196 + 100) = 296

(8, 17, 353) →

⇒ [(8)2 + (17)2]

⇒ (64 + 289) = 353

Checking all the given options:

1. (29, 7, 690) →

⇒ [(29)2 + (7)2]

⇒ (841 + 49) = 890

2. (18, 6, 576) →

⇒ [(18)2 + (6)2]

⇒ (324 + 36) = 360

3. (5, 13, 194) →

⇒ [(5)2 + (13)2]

⇒ (25 + 169) = 194

4. (12, 3, 135) →

⇒ [(12)2 + (3)2]

⇒ (144 + 9) = 153

Here, (5, 13, 194) shows a similar relation to the given set of numbers.

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

Here, we use the table given below:

Given:

SAME : WDOF :: LIFE : PLHF :: GOAL : ? 

Logic: (4), (3), (2) and (1) are added to the position value of the first, second, third and fourth alphabet.

SAME : WDOF →

LIFE : PLHF →

Similarly, for 'GOAL : ?' →

Here, 'GOAL : KRCM' is the correct pair.

Hence, the correct answer is "Option (1)".

Here, we use the table given below:

Given:

LCAZ, NECX, PGEV, ?, TKIR

Logic: (2) is added to the position value of the first three alphabets and (2) is subtracted from the position value of the last alphabet.

Here, 'RIGT' is the missing term.

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

Here, we use the BODMAS table given below:

Given:

⇒ 11 * 13 * 238 * 17 * 34 = 123

(1) + × - ÷

⇒ 11 * 13 * 238 * 17 * 34 = 123

After Putting the signs:

⇒ 11 + 13 × 238 - 17 ÷ 34 = 123

Apply BODMAS rule:

⇒ 11 + 13 × 238 - 0.5

⇒ 11 + 3094 - 0.5

⇒ 3105 - 0.5 = 3104.5

Here, the equation is not satisfied.

(2) × + ÷ -

⇒ 11 * 13 * 238 * 17 * 34 = 123

After Putting the signs:

⇒ 11 × 13 + 238 ÷ 17 - 34 = 123

Apply BODMAS rule:

⇒ 11 × 13 + 14 - 34

⇒ 143 + 14 - 34

⇒ 157 - 34 = 123

Here, the equation is satisfied.

(3) + ÷ × -

⇒ 11 * 13 * 238 * 17 * 34 = 123

After Putting the signs:

⇒ 11 + 13 ÷ 238 × 17 - 34 = 123

Apply BODMAS rule:

⇒ 11 + 0.054 × 17 - 34

⇒ 11 + 0.928 - 34

⇒ 11.928 - 34 = (-22.07)

Here, the equation is not satisfied.

(4) ÷ - + ×

⇒ 11 * 13 * 238 * 17 * 34 = 123

After Putting the signs:

⇒ 11 ÷ 13 - 238 + 17 × 34 = 123

Apply BODMAS rule:

⇒ 0.846 - 238 + 17 × 34

⇒ 0.846 - 238 + 578

⇒ 578.846 - 238 = 340.84

Here, the equation is not satisfied.

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

Given:

MAL_VY_MALIV_OM_LIVYO_A_I_YO

Checking all the given options:

1. IOYALVM

MALIVYO / MALIVYO / MALIVYO / LAVIMYO

2. IYOMALV

MALIVYY / MALIVOO / MMLIVYO / AALIVYO

3. IOYAMLV

MALIVYO / MALIVYO / MALIVYO / MALIVYO

Here, the series is completed.

4. IYOMAVL

MALIVYY / MALIVOO / MALIVYO / AAVILYO

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

Here, we use the table given below:

Logic: (3) is added to the position value of the alphabet to make the code.

'FILM' is written as '9121516' →

'EAST' is written as '842223' →

Similarly, 'HOME' will be coded as:

Here, the code for 'HOME' is '1118168'.

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

The mirror image of the given figure is :

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

The mirror image of the given figure is :

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

Given:

(14, 60, 16)

(12, 40, 8)

Logic: Second no. = [(First no. + Third no.) × 2]

(14, 60, 16) →

⇒ [(14 + 16) × 2]

⇒ (30 × 2) = 60

(12, 40, 8) →

⇒ [(12 + 8) × 2]

⇒ (20 × 2) = 40

Checking all the given options:

1. (19, 80, 21) →

⇒ [(19 + 21) × 2]

⇒ (40 × 2) = 80

2. (15, 45, 30) →

⇒ [(15 + 30) × 2]

⇒ (45 × 2) = 90

3. (25, 120, 15) →

⇒ [(25 + 15) × 2]

⇒ (40 × 2) = 80

4. (20, 30, 40) →

⇒ [(20 + 40) × 2]

⇒ (60 × 2) = 120

Here, (19, 80, 21) shows a similar relation to the given set of numbers.

Hence, the correct answer is "Option (1)".

Given:

Football fans, Cricket fans, Doctors

The Venn diagram for the given classes is:

A football fan can be a doctor and a cricket fan too.

Hence, the correct answer is "Option (1)".

Given:

First row: 15, 3, 252

Second row: 11, 5, 246

Third row: 9, 6, ?

Logic: 'Row wise'

First row → Third no. = [(First no.)² + (Second no.)³]

The first row (15, 3, 252) →

⇒ [(15)² + (3)³]

⇒ (225 + 27) = 252

The second row (11, 5, 246) →

⇒ [(11)2 + (5)3]

⇒ (121 + 125) = 246

Similarly, for the third row (9, 6, ?) →

⇒ [(9)2 + (6)3]

⇒ (81 + 216) = 297

Here, the question mark is replaced by '297'.

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

The correct answer is Margashirsa-Pausa.

Key Points

• Hemanta season:-
• ​It falls in the months of Margashirsa-Pausa according to the Indian calendar.
• Hemanta is one of the six seasons mentioned in the Indian calendar, which is based on the position of the sun
• Hemanta season is also known as the pre-winter season and is characterized by cool and dry weather.
• The months of Margashirsa-Pausa fall between November-December and December-January respectively.

Additional Information

• Sravana-Bhadra:-
• Itis a combination of two months in the Indian calendar and falls during the monsoon season (July-August/ August-September).
• Chaitra-Vaisakha:-
• It is the period between March-April and April-May and marks the beginning of the spring season.
• Jyaistha-Asadha:-
• It is the period between May-June and June-July and marks the beginning of the summer season.

The correct answer is Alkynes.

Key Points

• Alkynes:-
• ​These have the highest boiling point among the given options due to their strong intermolecular forces of attraction.
• Alkynes have triple bonds between carbon atoms, which results in a linear shape and close packing of molecules, leading to strong van der Waals forces.
• Alkanes have weaker intermolecular forces due to their single bonds and branched structures, resulting in lower boiling points.
• Alkenes have double bonds, which create a kink in the molecule and reduce the surface area available for intermolecular interactions, leading to lower boiling points.
• Free carbon dioxide is a gas at room temperature and pressure, and hence, it has the lowest boiling point among the given options.

Additional Information

• Alkanes:
• These are hydrocarbons with single bonds between carbon atoms, and their boiling points increase with increasing chain length and molecular weight.
• Alkenes:
• ​These are hydrocarbons with double bonds between carbon atoms, and their boiling points are lower than those of corresponding alkanes due to their lower intermolecular forces.
• Free carbon dioxide:
• It is a gas at room temperature and pressure and is formed during respiration, combustion, and other processes.
• It has a boiling point of -78.5^oC at standard temperature and pressure.

The correct answer is 2013.

Key Points

• National Urban Health Mission (NUHM):-
• It was launched by the Government of India in 2013 to improve the health status of the urban population, especially the poor and vulnerable sections.
• The National Urban Health Mission (NUHM) as a sub-mission of National Health Mission (NHM) has been approved by the Cabinet on 1^st May 2013.
• NUHM aims to provide equitable and quality primary healthcare services to urban communities, focusing on maternal and child health, communicable and non-communicable diseases, and urban health infrastructure development.
• The mission is implemented in 779 cities and towns with a population of more than 50,000, and it covers around 7.75 crore people across the country.
• NUHM is a sub-mission under the National Health Mission (NHM), which was launched in 2013 by merging the National Rural Health Mission (NRHM) and the National Urban Health Mission (NUHM).

Additional Information

• List of some prominent health schemes in India:
• Ayushman Bharat - Pradhan Mantri Jan Arogya Yojana (PMJAY): 2018
• National Health Mission (NHM): 2013
• Rashtriya Swasthya Bima Yojana (RSBY): 2008
• National Urban Health Mission (NUHM): 2013
• Pradhan Mantri Surakshit Matritva Abhiyan (PMSMA): 2016
• Mission Indradhanush: 2014
• National Rural Health Mission (NRHM): 2005
• Janani Suraksha Yojana (JSY): 2005
• Pradhan Mantri Matru Vandana Yojana (PMMVY): 2017
• National Tuberculosis Elimination Program (NTEP): 2020 (renamed from RNTCP)
• Revised National Tuberculosis Control Program (RNTCP): 1997
• Swachh Bharat Abhiyan (Clean India Campaign): 2014
• National AIDS Control Programme (NACP): 1992
• National Vector Borne Disease Control Programme (NVBDCP): 2003 (merged program)
• National Cancer Control Programme (NCCP): 1975
• National Mental Health Programme (NMHP): 1982

The correct answer is Uttar Pradesh and Maharashtra.

Key Points

• Uttar Pradesh:-
• It alone has a population of over 199 million people, making it the most populous state in India.
• Maharashtra:-
• With a population of over 112 million, It is the second most populous state in India.
• Uttar Pradesh and Maharashtra have the highest population among all Indian states according to the Census of India 2011.
• These two states together account for more than 25% of the total population of India.

Additional Information

• Arunachal Pradesh and Manipur are among the least populous states in India and have a combined population of less than 3 million people.
• Similarly, Bihar, has a population of around 104 million, which is lower than that of both Uttar Pradesh and Maharashtra.
• Uttar Pradesh and Bihar, is incorrect as it does not include Maharashtra, which has a higher population than Bihar.

The correct answer is Julia.

Key Points

• Cyclones:-
• These​ are natural disasters that can cause severe damage to property, infrastructure, and loss of lives.
• Julia:-
• It did not hit India during the years 2021-2022.

Additional Information

• Cyclone Yaas hit the eastern coast of India in May 2021, causing significant damage and displacement of people.
• Cyclone Tauktae hit the western coast of India in May 2021, causing severe damage to infrastructure and loss of lives.
• Cyclone Gulab hit the eastern coast of India in September 2021, causing heavy rainfall and flooding in some regions.

The correct answer is Breaking down emulsified fats.

Key Points

• Lipase is an enzyme that plays a crucial role in the digestion of fats in the body.
• The breakdown of fats is essential for the absorption and utilization of essential fatty acids and fat-soluble vitamins.
• Lipase breaks down emulsified fats:
• The process of digestion starts in the mouth where the food is chewed and mixed with saliva.
• Saliva contains an enzyme called salivary lipase that starts breaking down fats.
• However, the majority of fat digestion happens in the small intestine where the emulsified fats are acted upon by pancreatic lipase.
• This enzyme breaks down the emulsified fats into fatty acids and glycerol, which can be absorbed by the body.
• Lipase works with bile:
• Bile is a digestive fluid produced by the liver and stored in the gallbladder.
• Bile contains bile salts that help in the emulsification of fats, making them easier for lipase to break down.
• Lipase and bile work together to digest fats and ensure their absorption in the body.
• Lipase deficiency can lead to malabsorption:
• In some cases, people may have a deficiency of lipase, which can result in malabsorption of fats.
• This can lead to symptoms like bloating, gas, diarrhea, and weight loss.
• People with conditions like cystic fibrosis, pancreatitis, and celiac disease may have a deficiency of lipase.

Additional Information

• Breaking down roughage: This is the function of enzymes like cellulase, which break down the fiber in plant foods.
• Lipase does not play a role in breaking down roughage.
• Secreting intestinal fluids: This is the function of the intestinal glands, which secrete fluids that help in the digestion and absorption of nutrients.
• Lipase is not involved in this process.
• Digesting proteins: This is the function of enzymes like pepsin and trypsin, which break down proteins into amino acids.
• Lipase does not play a role in digesting proteins.
• Hence, the correct option is 2) Breaking down emulsified fats.

The correct answer is Kumudini Lakhia.

Key Points

• Kumudini Lakhia: She is a well-known Kathak dancer and choreographer.
• She founded the KADAMB Centre for Dance in 1964 with the aim of promoting and preserving the traditional Indian dance forms.
• She has been awarded the Padma Shri and Padma Bhushan for her contributions to the field of dance.
• Kathak:-
• It is a classical dance form of India, originating from northern India.
• It is known for its intricate footwork, graceful movements, and storytelling through dance.
• The dance form has evolved over time and has been influenced by various cultures and regions.

Additional Information

• Shovana Narayan: She is a well-known Kathak dancer and has been awarded the Padma Shri and Padma Bhushan for her contributions to the field of dance.
• However, she did not found the KADAMB Centre for Dance.
• Sitara Devi: She was a legendary Kathak dancer and was known as the Empress of Kathak.
• She received numerous awards and honours for her contributions to the field of dance.
• However, she did not found the KADAMB Centre for Dance.
• Rohini Bhate: She was a renowned Kathak dancer and choreographer.
• She founded the Nrityabharati Kathak Dance Academy in Pune, Maharashtra.
• However, she did not found the KADAMB Centre for Dance.

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

Key Points

• Alzheimer's disease:-
• It affects the brain, Diphtheria affects the nose and throat, Gonorrhoea affects the reproductive tract, and Mumps affects the salivary glands.
• Alzheimer's disease is a progressive brain disorder that affects memory, thinking, and behavior.
• It is the most common cause of dementia among older adults.
• Diphtheria:-
• It is a bacterial infection that affects the nose, throat, and sometimes the skin.
• ​It can cause breathing problems, heart failure, and paralysis.
• Gonorrhoea:-
• It is a sexually transmitted infection that can affect the genitals, rectum, and throat.
• It can cause painful urination, discharge, and infertility.
• Mumps:-
• It is a viral infection that affects the salivary glands.
• It can cause swelling, fever, and headache.

The correct answer is Pradhan Mantri Jan Dhan Yojana.

Key Points

• Pradhan Mantri Jan Dhan Yojana:-
• ​It is a government initiative to provide access to financial services like banking, insurance, and pension to the underprivileged sections of society.
• Pradhan Mantri Jan Dhan Yojana is NOT an initiative by the government for the development of the microfinance sector in India.

Additional Information

• E-Shakti Initiative:-
• It is a program that aims to empower women by digitizing SHGs.
• The initiative provides a platform for SHGs to connect with banks, access credit, and avail of other financial services.
• The program also provides training to women on digital literacy and financial management.
• Pradhan Mantri Mudra Yojana:-
• It is a scheme that provides loans to micro and small enterprises.
• The scheme aims to promote entrepreneurship and support the growth of small businesses.
• The loans are provided under three categories- Shishu, Kishor, and Tarun, based on the stage of business development.
• India Micro Finance Equity Fund:-
• It is a government-sponsored fund that invests in microfinance institutions to support the growth of the microfinance sector.
• The fund aims to provide equity support to microfinance institutions and promote financial inclusion.

The correct answer is 42.195 km.

Key Points

• The maximum distance covered in a marathon is 42.195 km.
• This is the standard distance for a marathon according to the International Association of Athletics Federations (IAAF).
• The distance was set in 1921 for the Olympic Games held in London and has since become the standard distance for marathons worldwide.

Additional Information

• A marathon is a long-distance race with a distance of 42.195 kilometers or 26.2 miles.
• The race is named after the Greek soldier Pheidippides who ran from the city of Marathon to Athens to deliver the news of victory against the Persians in 490 BCE.
• 40 km is the distance for some ultramarathons, but not for a standard marathon.
• 42.5 km is the distance for the Comrades Marathon held in South Africa, which is an ultramarathon.
• 41.5 km is the distance for the Jungfrau Marathon held in Switzerland, which is a mountain marathon.

The correct answer is Bombay.

Key Points

• Elphinstone:-
• It was a British statesman, diplomat, and colonial administrator who served as the Governor of Bombay from 1819 to 1827.
• During his tenure, Elphinstone introduced several reforms in Bombay, including the establishment of the Bombay University.
• Elphinstone was also known for his efforts to promote education and improve the condition of the poor in Bombay.
• Bombay:-
• Bombay was a province of British India that covered the western part of the Indian subcontinent.
• It included the present-day states of Maharashtra, Gujarat, and parts of Karnataka.

Additional Information

• North West Frontier Province: This province was created in 1901 and it was located in the north-western region of British India.
• It is now part of Pakistan.
• Madras: Madras was a province of British India that covered the southern part of the Indian subcontinent.
• It was created in 1801 and it was renamed as Tamil Nadu after India's independence.
• Bengal: Bengal was a province of British India that covered the eastern part of the Indian subcontinent.
• It was divided into East Bengal and West Bengal after India's independence.

The correct answer is 2022.

Key Points

• Thomas Cup:-
• ​It is a prestigious international badminton tournament held every two years.
• India won its first-ever Thomas Cup title or Badminton World Men's Team Championship for the first time in 73 years on May 15, 2022, beating Indonesia 3-0 in the final in Bangkok.
• In the edition of the Thomas Cup held in 2018, China emerged as the champions.

Additional Information

• No Thomas Cup as was held in 2019, and 2021 years due to the COVID-19 pandemic.

The correct answer is Dadabhai Naoroji.

Key Points

• Dadabhai Naoroji:-
• He was a prominent Indian nationalist leader, a member of the Indian National Congress, and the first Indian to be elected to the British Parliament.
• The president of the second session of the Indian National Congress was Dadabhai Naoroji.
• Naoroji was a prominent economist and is known for his theories on the economic exploitation of India by the British colonial administration.
• He highlighted the concept of the "Drain of Wealth," which referred to the economic resources being drained from India to Britain due to colonial policies.
• One of Naoroji's most famous works is the book titled "Poverty and Un-British Rule in India," published in 1901.

Additional Information

• Womesh Chandra Bonnerjee:-
• He was the first president of the Indian National Congress and served in that position twice, in 1885 and 1892.
• Pherozeshah Mehta:-
• He​ was a lawyer, social reformer, and political leader who played a prominent role in the Indian National Congress and the Indian independence movement.
• George Yule:-
• ​He was a British businessman who served as the president of the Indian National Congress in 1888**.**

The correct answer is Rukmini Devi Arundale.

Key Points

• Rukmini Devi Arundale:-
• She​ was a legendary Bharatanatyam exponent, theosophist, and founder of the Kalakshetra Dance School, which is located in Chennai, Tamil Nadu.
• She was awarded the Padma Bhushan award in 1956 for her contributions to dance and education.
• Arundale was also a prominent animal welfare activist and was instrumental in the establishment of the Animal Welfare Board of India.
• She was a disciple of Annie Besant and was deeply influenced by theosophy, which played a significant role in shaping her worldview and approach to dance.

Additional Information

• Sonal Mansingh:-
• She is a renowned Indian classical dancer and choreographer who has been awarded the Padma Vibhushan, the second-highest civilian award in India.
• She is known for her expertise in several dance forms, including Bharatanatyam, Odissi, and Kuchipudi.
• Saroja Vaidyanathan:-
• She is a well-known Bharatanatyam dancer and guru who has been honored with several awards, including the Padma Shri and the Sangeet Natak Akademi Award.
• She is the founder of Ganesa Natyalaya, a dance school in Delhi.
• Mallika Sarabhai:-
• She is a contemporary dancer and choreographer who has also acted in films and television shows.
• She is the daughter of renowned classical dancer Mrinalini Sarabhai and the famous physicist Vikram Sarabhai.
• She has been awarded the Padma Shri for her contributions to the field of performing arts.

The correct answer is Carnatic music.

Key Points

• MS Subbulakshmi:-
• She​ was a renowned Carnatic vocalist and musician who popularized the genre of Carnatic music not only in India but around the world.
• She was the first musician to be awarded the Bharat Ratna, India's highest civilian award, for her contribution to music.
• MS Subbulakshmi's music was deeply rooted in the tradition of Carnatic music, which has its origins in South India.
• She was known for her renditions of devotional songs and bhajans in the Carnatic style, which were widely appreciated by audiences of all backgrounds.

Additional Information 

• Ghazal music:-
• It is a form of poetic expression set to music that originated in the Middle East and South Asia.
• It is characterized by its use of rhyming couplets and a melancholic tone.
• Sufi devotional music:-
• It is a form of Islamic devotional music that is popular in South Asia and the Middle East.
• It is characterized by its use of poetry and music to express devotion to God.
• Hindustani music:-
• It is a classical music tradition that originated in North India.
• It is characterized by its use of ragas, which are melodic frameworks for improvisation.
• Carnatic music:-
• It is a classical music tradition that originated in South India.
• It is characterized by its use of ragas and talas, which are rhythmic cycles.

The correct answer is (i), (ii) and (iii).

Key Points

• Green Revolution:-
• It​ was a significant development in India's agricultural sector that aimed to increase agricultural productivity and reduce food insecurity.
• However, it also had some negative effects.
• Depletion of groundwater table:-
• The Green Revolution promoted the use of high-yielding crop varieties, which required more water for irrigation.
• As a result, farmers started extracting groundwater at an unsustainable rate, leading to a decline in the groundwater table.
• This, in turn, led to water scarcity and affected the livelihoods of farmers who depended on groundwater for irrigation.
• Deterioration in the quality of soil:-
• The use of chemical fertilizers and pesticides was a key feature of the Green Revolution.
• Over time, this led to soil degradation, loss of soil fertility, and reduced crop yields.
• Soil erosion, salinization, and acidification were some of the other negative impacts on soil quality.
• Increased input cost:-
• The adoption of new technologies and practices under the Green Revolution required farmers to invest in expensive inputs like seeds, fertilizers, and machinery.
• This increased the cost of cultivation, making it difficult for small and marginal farmers to afford these inputs.
• As a result, they had to borrow money from moneylenders at high-interest rates, leading to a cycle of debt and poverty.

Additional Information

• Green Revolution: It refers to the period of rapid agricultural development in the 1960s and 1970s, which aimed to increase food production through the use of high-yielding crop varieties, chemical fertilizers, and pesticides.
• Positive Effects: The Green Revolution led to a significant increase in food production, reduced food prices, and improved food security in India.
• It also created new job opportunities and increased rural income.
• Sustainable Agriculture: It refers to an agricultural system that is environmentally friendly, socially just, and economically viable.
• It promotes the use of organic farming practices, crop diversification, and conservation of natural resources.

The correct answer is three.

Key Points

• Rail Kaushal Vikas Yojana:-
• It was launched in September 2021 by the Government of India to provide training to candidates for employment in the railway sector.
• The program aims to train 50,000 candidates over a period of three years.
• The training will cover various skills such as welding, electrical work, carpentry, and other technical skills required for railway jobs.
• The program will also provide soft skills training to improve the overall employability of the candidates.

Additional Information

• Indian Railways:
• The largest rail network in Asia and the world's fourth-largest, covering vast distances across India.
• Operates a wide range of passenger and freight services, contributing significantly to India's transportation and economy.
• Established during British colonial rule, it plays a crucial role in connecting diverse regions and people within the country.

The correct answer is Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).

Key Points

• Assertion (A) is true because a rough surface provides more contact points between the object and the surface, increasing the frictional force and reducing slipping.
• Reason (R) is also true because frictional force increases with roughness as the irregularities in the surface create more resistance.
• Both Assertion (A) and Reason (R) are related and true, and Reason (R) provides a correct explanation for Assertion (A).

Additional Information

• Frictional force:-
• It is a force that opposes motion between two surfaces in contact.
• It is dependent on the nature of the surfaces in contact, the normal force, and the coefficient of friction.

The correct answer is Supplementary Nutrition Programme; National Nutrition Mission.

Key Points

• The Supplementary Nutrition Programme (SNP):-
• It​ is a government initiative aimed at improving the nutritional status of pregnant and lactating mothers, infants, and children under the age of 6 years.
• The program provides free food to the beneficiaries and aims to reduce malnutrition and stunting.
• National Nutrition Mission (NNM):-
• It is a flagship program of the government launched in 2018 with the aim of reducing malnutrition among children and women.
• The program provides a comprehensive approach to address malnutrition through various interventions such as the promotion of breastfeeding, dietary diversification, and the use of fortified foods.
• Finance Minister Nirmala Sitharaman announced the merger of two programs under the umbrella of Mission POSHAN 2.0. The two programs are the Supplementary Nutrition Programme and the National Nutrition Mission.

Additional Information

• Mission POSHAN 2.0:-
• It is a continuation and expansion of the Government of India's efforts to address malnutrition and improve the nutritional status of women, children, and adolescents.
• It focuses on ensuring a more comprehensive and multi-sectoral approach to combat malnutrition. Some key points about Mission POSHAN 2.0:
• It utilizes technology for real-time monitoring, data collection, and assessment of nutritional interventions, aiding in better planning and implementation.
• The mission focuses on behavior change communication, aiming to promote better nutritional practices and habits at the community level.
• Adequate budget allocation is crucial for the successful implementation of the mission's strategies and interventions.

The correct answer is Justice Rituraj Awasthi.

Key Points

• Justice Rituraj Awasthi:-
• He​ was appointed as the chairperson of the 22^nd Law Commission in 2022.
• He succeeded Justice BS Chauhan who completed his term in August 2021.
• Justice Awasthi was a judge of the Allahabad High Court before his appointment as the chairperson of the Law Commission.
• Law Commission:-
• It is a non-statutory body constituted by the government of India to provide expert advice on legal reform.

Additional Information

• Justice UU Lalit:-
• He is a judge of the Supreme Court of India.
• He was appointed as a judge of the apex court in August 2014.
• Justice VV Raman:-
• He is a retired judge of the Madras High Court.
• He served as a judge of the high court from 2006 to 2018.
• Justice KT Shankaran:-
• He is a retired judge of the Kerala High Court.
• He served as a judge of the high court from 1999 to 2011.

The correct answer is Article 15.

Key Points

• Article 15:-
• It prohibits discrimination on the grounds of religion, race, caste, sex, or place of birth.
• In this scenario, A asking her maid to leave the cinema hall based on her occupation is a form of discrimination on the grounds of social status, which is covered under Article 15.

Additional Information

• Article 16:-
• It deals with equality of opportunity in matters of public employment.
• Article 18:-
• ​It deals with abolition of titles.
• Article 17:-
• It​ deals with the abolition of untouchability.

The correct answer is Sukumar Sen.

Key Points

• Sukumar Sen:-
• He​ was appointed as the first Chief Election Commissioner of India in 1950, when the Election Commission of India was established.
• Election Commission of India:-
• ​It is an autonomous constitutional body responsible for conducting free and fair elections in India.
• It was established on 25^th January 1950, and Sukumar Sen was appointed as the first Chief Election Commissioner of India.

Additional Informations

• Dr. Nagendra Singh:-
• He was a former Chief Justice of India and served as the judge of the International Court of Justice.
• He was not the first Chief Election Commissioner of India.
• SP Sen Verma:-
• He was a former Deputy Speaker of the Lok Sabha and a member of the Constituent Assembly.
• He was also not the first Chief Election Commissioner of India.
• KVK Sundaram:-
• He was a former Chief Secretary of the state of Uttar Pradesh and served as the Chief Election Commissioner of India from 1986 to 1990.
• He was not the first Chief Election Commissioner of India.

The correct answer is Losar festival.

Key Points

• Losar festival:-
• It​ is a Tibetan festival that marks the Tibetan New Year and is celebrated in Ladakh at the end of the harvesting season.
• It is a three-day festival that is celebrated with great enthusiasm by the Tibetan and Ladakhi communities.
• The festival is marked by various rituals, including the burning of incense, offerings to the deities, and traditional dance performances.

Additional Information

• Matho Nagrang:-
• It​ is a festival celebrated in the Matho Monastery of Ladakh, and it involves the performance of masked dances.
• Yuru Kabgyat:-
• It is another festival celebrated in Ladakh, which involves the worship of the Buddhist deity Vajrakilaya and the performance of traditional dances.
• Dosmoche:-
• It​ is a festival celebrated in Leh, Ladakh, to mark the end of winter and the beginning of the sowing season.
• It involves the performance of masked dances and the burning of effigies.

The correct answer is Chola.

Key Points

• Sabha:-
• It​ was an assembly of elders who made decisions for the village, while Ur was an assembly of common people who discussed and debated various issues.
• Chola dynasty:-
• It was known for its administrative and political prowess, and the existence of these assemblies is a testament to their commitment to democratic principles.
• Sabha and Ur were two types of village assemblies that were referred to during the Chola dynasty.

Additional Information

• Rashtrakuta dynasty:-
• It​ was known for its military conquests and architectural achievements, and there is no mention of village assemblies in their history.
• Gurjara Pratihara dynasty:-
• It​ was a powerful kingdom in North India, but there is no evidence of village assemblies being referred to during their reign.
• Chalukya dynasty:-
• It was known for its art and architecture, but there is no mention of village assemblies in their history either.

The correct answer is Seleucus Nicator.

Key Points

• Mauryan emperor Chandragupta Maurya:-
• He was the founder of the Mauryan Empire in ancient India.
• He defeated a number of rulers and warlords to establish his empire, including the Nanda dynasty that ruled Magadha before him.
• Seleucus Nicator:-
• He​ was a Greek general who served under Alexander the Great and later became the founder of the Seleucid Empire in Persia.
• According to ancient sources, the two rulers fought a war in which Seleucus was defeated and forced to cede territory to Chandragupta.

Additional Information

• Cassander:-
• He​ was a Macedonian general who became king of Macedonia after Alexander's death.
• He did not have any direct involvement with India or the Mauryan Empire.
• Antigones:- 
• He was another Macedonian general who fought for control of Alexander's empire.
• Like Cassander, he did not have any direct involvement with India or the Mauryan Empire.
• Ptolemy :-
• He was a Macedonian general who founded the Ptolemaic dynasty in Egypt after Alexander's death.
• He also did not have any direct involvement with India or the Mauryan Empire.

Given:-  

A shopkeeper sold a pair of headphones for Rs. 5,520 at a gain of 20%.

Formula used:-

Gain percent= [(Selling Price−Cost Price) ​ ×100]/Cost price   

Loss percent= [(Cost Price - Selling Price) ​ ×100]/Cost price 

Calculation:-

 SP = CP + Gain 5520 

⇒ 5520 = CP + (20 × CP)/100 

⇒ (120/100 CP) =  5520 ​   

⇒ CP = 4600 

 Loss percent = [( 4600− 4370 )/4600] × 100 

⇒ ( 230/4600) × 100 = 5%  

∴ If the headphones were sold for Rs. 4,370, there would be a loss of 5%.

Given:-

Males (M)+ female(F) = 18000  

(105% of M) + (107% of F) = 19200.

Calculation:- 

⇒ M + F = 18000  ...(1)

⇒ (105/100) M + (107/100)F = 19200 ...(2)

Put the value of M from equation (1) We get,

⇒ 105(18000 -  F ) + 107F = 1920000  

⇒ 2F = 30,000 

⇒ F = 15,000

So,

⇒ M = 18000 - 15000 = 3000

The ratio of the populations of males and females = M / F

⇒ Ratio = 3000 /15000

⇒ Ratio = 1/5 

∴ The required answer is 1/5.

Shortcut Trick

Total Capacity (LCM of 120 and 54) = 1080 units.

Efficiency of 1 inlet pipe = 1080 ÷ 120 = +9 units/hr.

Efficiency of 1 outlet pipe = 1080 ÷ (−54) = −20 units/hr.

Net efficiency of (8 inlets + 3 outlets) = (8 × 9) + (3 × −20) = 72 − 60 = +12 units/hr.

Time required to fill tank = 1080 ÷ 12 = 90 hours.

∴ The correct answer is 90 hours.

Alternate Method

Given:

⇒ Time taken by 1 inlet pipe to fill the tank = 120 hours

⇒ Time taken by 1 outlet pipe to empty the tank = 54 hours

⇒ Number of inlet pipes opened = 8

⇒ Number of outlet pipes opened = 3

Formula Used:

⇒ Efficiency = Total Work ÷ Time

⇒ Total Time = Total Work ÷ Net Combined Efficiency

Calculations:

⇒ Efficiency of 8 inlet pipes = 8 × (+9) = +72 units/hour

⇒ Efficiency of 3 outlet pipes = 3 × (−20) = −60 units/hour

⇒ Net combined efficiency when both types are opened together = +72 − 60 = +12 units/hour

⇒ The positive sign indicates that the tank is being filled.

⇒ Total time required to completely fill the tank = 1080 ÷ 12

⇒ Total time = 90 hours

∴ The correct answer is 90 hours.

Additional Information

Pipes and Cisterns Basics

If an inlet pipe fills a tank in x hours and an outlet pipe empties it in y hours, the net part of the tank filled in 1 hour is given by (1/x − 1/y).

Efficiency Approach (LCM Method)

Treat inlet pipes as positive work providers (filling) and outlet pipes as negative work providers (draining). The total capacity of the tank is considered as the Least Common Multiple (LCM) of their individual completion times.

Multiple Similar Pipes

When multiple pipes of the same capacity operate simultaneously, simply multiply the individual pipe's efficiency by the total number of identical pipes before evaluating the net overall flow.

Given:-

sin x = (3/10)

Formula used:- 

1 + tan²x = sec²x 

secx = 1/cosx 

tan x = sin x/cos x

Calculation:- 

⇒ tanx + cotx

⇒ tanx + 1/tanx  

⇒ (1 + tan2x )/tanx 

⇒ sec2x /tanx  

⇒ 1/sinx cosx  [cosx = (√100 - 9)/10]

⇒ 1/(3/10)(√91/10) = 100/3√91 

∴ The required answer is 100/3√ 91.

Given:

The marked price of a frock is Rs. 4,500. It is to be sold at Rs. 2,400 at two successive discounts

Calculation:

MP of the article = Rs. 4500

SP of the article after getting 20% discount = 4500 × (80/100) = 3600

Second SP of the article = Rs. 2400

Second discount = 3600 – 2400 = 1200

∴ Discount percentage = 1200/3600 × 100 = 100/3%

∴ The correct option is 4

Shortcut Trick

Apply the divisibility rule of 11: The difference between the sum of digits at odd positions and the sum of digits at even positions must be 0 or a multiple of 11.

For 97174: Sum of odd positions (9+1+4) = 14; Sum of even positions (7+7) = 14.

Difference = 14 − 14 = 0.

Since the difference is 0, the number is divisible by 11.

∴ The correct answer is 97174.

Alternate Method

Given: Four numbers to check for divisibility by 11.

Formula Used: Divisibility by 11 ⇒ (Sum of digits at odd places) − (Sum of digits at even places) = 0, 11, 22, ...

Checking Option (1) 97174:

⇒ Sum of digits at 1^st, 3^rd, and 5^th places = 9 + 1 + 4 = 14

⇒ Sum of digits at 2^nd and 4^th places = 7 + 7 = 14

⇒ Difference = 14 − 14 = 0 (Divisible by 11)

Checking Option (2) 56923:

⇒ Sum of odd places = 5 + 9 + 3 = 17; Sum of even places = 6 + 2 = 8

⇒ Difference = 17 − 8 = 9 (Not divisible by 11)

Checking Option (3) 63962:

⇒ Sum of odd places = 6 + 9 + 2 = 17; Sum of even places = 3 + 6 = 9

⇒ Difference = 17 − 9 = 8 (Not divisible by 11)

Checking Option (4) 17295:

⇒ Sum of odd places = 1 + 2 + 5 = 8; Sum of even places = 7 + 9 = 16

⇒ Difference = |8 − 16| = 8 (Not divisible by 11)

∴ The correct answer is 97174.

Additional Information

Divisibility by 3 and 9

A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9 respectively.

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 divisible by 7.

Divisibility by 8

A number is divisible by 8 if the last three digits of the number are divisible by 8.

Shortcut Trick

Total distance to cross = Sum of train lengths = 130 + 120 = 250 m.

Relative speed in same direction = 50 − 40 = 10 km/h.

Convert speed to m/s = 10 × (5/18) = 25/9 m/s.

Time taken = Distance ÷ Speed = 250 × (9/25) = 90 sec.

∴ The correct answer is 90 sec.

Alternate Method

Train 1 (130 m)

40 km/h

Train 2 (120 m)

50 km/h

Total Dist = 250 m | Rel Speed = 10 km/h

Given:

Length of first train (L₁) = 130 m

Length of second train (L₂) = 120 m

Speed of first train (S₁) = 40 km/h

Speed of second train (S₂) = 50 km/h

Formula Used:

Time taken to cross = (Total Distance) ÷ (Relative Speed)

Total Distance = L₁ + L₂

Relative Speed (Same direction) = S₂ − S₁

Speed in m/s = Speed in km/h × (5/18)

Calculations:

⇒ Total Distance = 130 + 120 = 250 m

⇒ Relative Speed = 50 − 40 = 10 km/h

⇒ Relative Speed in m/s = 10 × (5/18) = 50/18 = 25/9 m/s

⇒ Time taken = 250 ÷ (25/9)

⇒ Time taken = (250 × 9) ÷ 25

⇒ Time taken = 10 × 9 = 90 sec

∴ The correct answer is 90 sec.

Additional Information

Trains Running in Opposite Directions

When two objects move towards each other, their relative speed is the sum of their individual speeds (S₁ + S₂).

Crossing a Stationary Point

When a train crosses a vertical pole, a standing man or a signal post, the total distance covered is exactly equal to the length of the train itself.

Unit Conversion Trick

To rapidly convert km/h to m/s, simply multiply the value by 5/18. Conversely, to change m/s back to km/h, multiply by 18/5.

Shortcut Trick

Sum of numbers (a + b) = √784 = 28

Difference (a − b) = √[(a + b)² − 4ab] = √[784 − 4 × 192] = √16 = 4

Difference between squares = (a + b)(a − b) = 28 × 4 = 112

∴ The correct answer is 112.

Alternate Method

Given:

Square of the sum: (a + b)² = 784

Product of numbers: ab = 192

Formula Used:

1. a² − b² = (a + b)(a − b)
2. (a − b)² = (a + b)² − 4ab

Calculations:

⇒ a + b = √784 = 28

⇒ (a − b)² = 784 − 4(192)

⇒ (a − b)² = 784 − 768 = 16

⇒ a − b = √16 = 4

⇒ a² − b² = (a + b) × (a − b)

⇒ a² − b² = 28 × 4 = 112

∴ The correct answer is 112.

Additional Information

Algebraic Identities

(a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab are fundamental identities used to relate sums, products, and squares.

Difference of Squares

The expression a² − b² is always equal to the product of the sum and the difference of the two numbers.

Natural Numbers

Since the numbers are specified as natural numbers, both a and b must be positive integers {1, 2, 3, ...}.

Calculation:

$\frac{\sec ^2\left(90^{\circ}-θ\right)-\cot ^2 θ}{2\left(\sin ^2 35^{\circ}+\sin ^2 55^{\circ}\right)}$

⇒ (cosec² θ - cot²θ) / 2( (sin²35° + cos²35°)

⇒ 1 /2 = 0.5

∴ The correct option is 0.5

Calculation:

Factors of 484: 1, 2, 4, 11, 22, 44, 121, 242, 484

Now,

Among all the factors of 484, only 1, 4, 121, and 484 are the perfect square.

Thus, the Sum of the factors that are perfect square

⇒ 1 + 4 + 121 + 484

⇒ 610

Hence, the correct answer is 610.

Calculation:

Percentage increase in the sale of earphones from 2017 to 2020 is,

⇒ (84 - 49.70)/ 49.7 × 100 = 69%

∴ The correct option is 1

Given:

C1 and C2 are two concentric circles such that the radius of C2 is less than the radius of C1.

AB is the chord of C1 of length 12 cm

Concept :

• The radius at the point of contact is perpendicular to the tangent.
• A line perpendicular to the chord, passing through the center of the circle bisects the chord.

 

Calculation:

The length of the AP will be half of AB

So the length of AP is 12 / 2 = 6cm

∴ The correct option is 4

Formula used:

Area of an arc = θ/360 × πr² .

 θ = arc / radius

1 radian = 180°/π

Calculation:

Here the arc = 3r

So,  θ = 3r / r 

⇒ 3^c 

We know, 

π^c = 180°

3^c = (180/π × 3) = 540/π  degree

So, angle in degree (θ) = (540/π) degree

The area of the sector OAB is,

⇒ (540/π)/360  × πr²

⇒ 540/360 × r² = 3/2 r² = 1.5 r²

∴ The area of the sector OAB is 1.5 r².

Given:

The average age of a group of friends is 27 years.

If 4 new friends whose average age is 25 years join them, the average age of the entire group becomes 26 years.

Calculation:-

Let's denote the initial number of friends in the group as "N".

The sum of the ages of the initial N friends = 27N.

After 4 new friends join the group, the average age becomes 26 years.

Now, the total sum of ages of the entire group after the 4 new friends join,    

⇒ 26 (N + 4).

According to this question,

⇒  27N + 4 ×  25 = 26N + 104 

⇒ 27N + 100 = 26N + 104

⇒ N + 100 = 104

Subtract 100 from both sides: N = 4

∴ Initially, there were 4 friends in the group.

Calculation:

$\frac{1^2-m^2}{(1+m)^2}$

⇒ (1+m)(1-m) / (1+m)² 

⇒ $\frac{1-m}{1+m}$

∴ The correct option is 2

Calculation:

cosec 2910° + sec 4260° + tan 2565° + cot 1755°

⇒ cosec (2970 - 60)° + sec (4230 + 30)° + tan (2610 - 45)° + (cot 1800 - 45)° 

⇒ cosec (33 × 90 - 60)° + sec (47 × 90 + 30)° + tan (29 × 90 - 45)° + (cot 20 × 90 - 45)°

⇒ sec60° + cosec30° + cot45° - cot45°

⇒ 2 + 2 + 1 - 1 = 4

∴ The correct option is 3

 

Alternate Method

cosec 2910° + sec 4260° + tan 2565° + cot 1755°

⇒ cosec (360 × 8 + 30)° + sec(360 × 12 - 60)° + tan(360 × 7 + 45)° + cot(360 × 5 - 45)°

⇒ cosec30° + sec60° + tan45° - cot45°

⇒ 2 + 2 + 1 - 1 = 4

∴ The correct option is 3.

Given:

(a3 + b3 + c3 - 3abc) = 405, and (a + b + c) = 15

Concept used:

(a3 + b3 + c3 - 3abc) = 1/2 (a + b + c) [(a - b)2 + (b - c)2+(c - a)2]

Calculation:

(a3 + b3 + c3 - 3abc) = 1/2 (a + b + c) [(a - b)2 + (b - c)2+(c - a)2]

⇒ 405 = 1/2 × 15  (a - b)2 + (b - c)2+(c - a)2. 

⇒  (a - b)2 + (b - c)2+(c - a)2. = 810 / 15

⇒  (a - b)2 + (b - c)2+(c - a)2 = 54

∴ The correct option is 2

Given:

Radhika owns 2 dogs, 3 rabbits and 4 parrots as pets.

Calculation:

Total number of pets is, 2 + 3 + 4 = 9

The required ratio is,  3: 9 = 1 : 3

∴ The correct option is 2

Given:

PT is tangent to a circle whose center is O, and where T is a point on the circle.

PT = 12 cm and PO = 13 cm

Concept used:

The radius = √(PO² - PT²)

Calculation: 

The radius (r) = √(PO2 - PT2)

⇒ r = √(132 - 122) 

⇒ r = √(169 - 144) 

⇒ r = √25 = 5 cm

∴ The correct option is 4

Given: 

A and B can individually complete a piece of work in 18 days and 30 days, respectively.

A and B started working together, but A left $16\frac{2}{3}$ days before the work is completed

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day 

Calculation:

Let, after x days work completed

Let the total work is the 90 units (LCM of 30 and 18)

Efficiency of A is 90 / 18 = 5 units

Efficiency of B is 90 / 30 = 3 units

As per the question,

5 × (x - 50/3) + 3x = 90

⇒ 8x  = 90 + 250 /3

⇒ 8x = 520/3

⇒ x = 65/3

A work for 65 /3 - 50/3 = 5 days

∴ The correct option is 2

Shortcut Trick

Divide first case by 20: 3/D + 2/U = 0.625

Divide second case by 21: 4/D + 3/U = 0.90

Eliminate 1/D: 3 × (4/D + 3/U) − 4 × (3/D + 2/U) = 3(0.9) − 4(0.625)

1/U = 2.7 − 2.5 = 0.2 ⇒ Upstream speed (U) = 5 km/h

3/D + 2(0.2) = 0.625 ⇒ 3/D = 0.225 ⇒ Downstream speed (D) = 13.33 km/h

Boat speed = (13.33 + 5) ÷ 2 = 9.165 ≈ 9 km/h

∴ The correct option is C.

Alternate Method

Given:

Case 1: Distance downstream = 60 km, Distance upstream = 40 km, Time = 12.5 hours

Case 2: Distance downstream = 84 km, Distance upstream = 63 km, Time = 18.9 hours (as 54/60 = 0.9)

Formula:

Time = Distance ÷ Speed | Speed of boat in still water (x) = (D + U) ÷ 2

Boat Speed (x) = (D + U) ÷ 2

Downstream: x + y (Speed D)

Upstream: x − y (Speed U)

⇒ Let 1/D = a and 1/U = b

⇒ 60a + 40b = 12.5 --- (i)

⇒ 84a + 63b = 18.9 --- (ii)

⇒ Multiply (i) by 1.4: 84a + 56b = 17.5

⇒ Subtracting from (ii): (84a + 63b) − (84a + 56b) = 18.9 − 17.5

⇒ 7b = 1.4 ⇒ b = 0.2

⇒ U = 1/b = 1/0.2 = 5 km/h

⇒ 60a + 40(0.2) = 12.5 ⇒ 60a + 8 = 12.5

⇒ 60a = 4.5 ⇒ a = 0.075

⇒ D = 1/a = 1/0.075 = 13.33 km/h

⇒ Speed of boat (x) = (13.33 + 5) ÷ 2 = 18.33 ÷ 2 = 9.165 km/h

⇒ Nearest integer = 9 km/h

∴ The correct option is C.

Additional Information

Downstream and Upstream Speeds

If speed of boat is x and stream is y, then Downstream (D) = x + y and Upstream (U) = x − y.

Calculating Still Water and Stream Speed

Boat speed in still water x = (D + U) ÷ 2; Speed of stream y = (D − U) ÷ 2.

Time Conversion

To convert minutes to hours, divide by 60. Example: 54 minutes = 54/60 = 0.9 hours.

Calculation:

The percentage of candidates that qualified from Goa over those that appeared from Goa in 2012

⇒ (810/7800) × 100 = 10.38

The percentage of candidates that qualified from Goa over those that appeared from Goa in 2013

⇒ (800/7500) × 100 = 10.66

The percentage of candidates that qualified from Goa over those that appeared from Goa in 2014

⇒ (920/8800) × 100 = 10.45

The percentage of candidates that qualified from Goa over those that appeared from Goa in 2015

⇒ (850/7200) × 100 = 11.80

∴ The correct option is 4

Given:

A sum of money becomes $\frac{8}{7}$ of itself in 2 years at a certain rate of simple interest

Formula used:

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

Calculation:

Let,R =rate of interest 

Let principal is = P 

As per the formula,

 P/7 = P× R × 2 / 100

⇒ R = 50/7

= $7 \frac{1}{7} \%$

∴ The correct option is 3

Shortcut Trick

Ratio of sides of three cubes = 3 : 4 : 5.

Diagonal of new cube = 18√3 cm ⇒ Side of new cube = 18 cm.

Sum of volume units = 3³ + 4³ + 5³ = 27 + 64 + 125 = 216 units.

Let common ratio be x: 216x³ = 18³ ⇒ 216x³ = 5832.

x³ = 5832 ÷ 216 = 27 ⇒ x = 3.

Sides = 3 × 3, 4 × 3, 5 × 3 = 9 cm, 12 cm, 15 cm.

∴ The correct answer is 9 cm, 12 cm and 15 cm.

Alternate Method

Given: Ratio of sides = 3 : 4 : 5; Diagonal of the resulting cube = 18√3 cm.

Formula Used: Volume of cube = (side)³; Diagonal of cube = (side)√3.

⇒ Let the sides of the three cubes be 3x, 4x, and 5x respectively.

⇒ Diagonal of the new cube = a√3 = 18√3 cm.

⇒ Side of the new cube (a) = 18 cm.

⇒ Volume of new cube = a³ = 18³ = 5832 cm³.

⇒ Total volume of three small cubes = (3x)³ + (4x)³ + (5x)³.

⇒ 27x³ + 64x³ + 125x³ = 5832.

⇒ 216x³ = 5832.

⇒ x³ = 5832 ÷ 216 = 27.

⇒ x = √³27 = 3 cm.

⇒ Side 1 = 3 × 3 = 9 cm.

⇒ Side 2 = 4 × 3 = 12 cm.

⇒ Side 3 = 5 × 3 = 15 cm.

∴ The correct answer is 9 cm, 12 cm and 15 cm.

Additional Information

Volume and Surface Area of Cube

For a cube with side 's', Volume = s³ and Total Surface Area = 6s².

Diagonal of a Cube

The longest rod that can be placed in a cube is its diagonal, given by s√3.

Melting and Recasting

When objects are melted to form a new shape, the sum of the volumes of the original objects remains equal to the volume of the new object.

Given:

M or 2W or, 3B can finish a work = 121 days 

Concept used:

(M1 × T1)/W1 = (M2 × T2)/W2

Where, 

M → Men 

T → Time 

W → Work 

Calculations:

M = 2W 

⇒ W = M/2

M = 3B  

⇒ B = M/3 

M + W + B 

⇒ M + (M/3) + (M/2)

⇒ 11M/6

(M1 × T1)/W1 = (M2 × T2)/W2

⇒ (1 × 121)/1 = ((11M/6) × T2)/1 

⇒ T2 = 66 days

∴ Time taken by one man, one woman and one boys together to finish the work is 66 days

The correct answer is "Convalescence."

 Key Points

• "Convalescence" means the process or period of resting in order to get better after an illness or operation. (स्‍वास्‍थ्‍य-लाभ)
• Example: She was in a state of convalescence.
• ​Therefore, gradual recovery of health and strength is "Convalescence."
• The correct answer is Option 1.

 Additional Information

• Potency means the power or strength of something. (शक्ति, प्रभाव)
• Benefaction means a charitable act or gift. (एक धर्मार्थ कार्य या उपहार)
• Rejuvenation means the process of making something look or feel younger, fresher, or more lively. (पुनर्यौवन)

The correct answer is "pious."

 Key Points

• The word 'nefarious' means wicked or criminal. (पापी, दुष्ट, अपराधी, अधर्मी, जघन्य)
• Example: That was a nefarious activity.
• "Pious" means devout or righteous. (धर्म में गहरा विश्‍वास करने या प्रदर्शित करने वाला; भक्त, धर्मपरायण)
• Example: She is a pious follower of the faith, never missing her prayers.
• In this context, the teacher did not stop the person from entering the hall because they could tell that their intentions were not wicked or criminal.
• The antonym of 'nefarious' is 'pious.'
• The correct answer is Option 1.
• The sentence could be rewritten as "The teacher could tell that his intentions were not nefarious, so he was allowed to enter the hall."

Additional Information

• "Traitorous" means disloyal or treacherous. (विश्वासघाती)
• 'Envious" means jealous or covetous. (दूसरे के पास जो वस्‍तु है उसका इच्‍छुक)
• "Perfidious" means deceitful or untrustworthy. (धोखेबाज या अविश्वसनीय)

The correct answer is: Option 3 i.e. 'Aggreement'.

Key Points

• The word "Aggreement" is incorrectly spelt. The correct spelling is "Agreement". (सहमति)
• Example: They finally reached an agreement after hours of negotiation.
• "Agreement" refers to a mutual arrangement, contract, or understanding between parties. (सहमति)
• Example: The two companies signed an agreement to cooperate on the new project.

Therefore, the correct answer is: Aggreement.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Arbitrary (मनमाना): Based on random choice or personal whim, rather than any reason or system.
• Example: The decision seemed arbitrary and was not based on any logical rationale.
• Favourite (पसंदीदा): Preferred to all others of the same kind.
• Example: Chocolate ice cream is my favourite dessert.
• Conviction (दोषसिद्धि): A firmly held belief or firmness of opinion.
• Example: His speech was delivered with great conviction and passion.

The correct answer is "Doing a job in a quick and competent manner."

 Key Points

• "On the ball" means being alert, attentive, and efficient. (सतर्क, चौकस और कुशल होना)
• Example: Our new employee is really on the ball - she's already finished all her tasks for the day.
• This idiom is often used in professional or work-related contexts.
• Therefore, the idiom "On the ball" means "Doing a job in a quick and competent manner."
• The correct answer is option 2.

Here, the erroneous part is "had expect."

 Key Points

• The error is in the verb tense agreement.
• The past perfect is made from the verb "had" and the past participle of a verb.
• Structure: Subject + had + V3
• Example: I had finished the work.
• The correct verb form to use after "had" is "expected", not "expect".
• The correct answer is Option 1.

Correct sentence: My students had expected guidance from my end.

The correct answer is "Ductile."

 Key Points

• "Ductile" means capable of being stretched or bent into different shapes without breaking. (बिना टूटे विभिन्न आकारों में खींचने या मोड़ने में सक्षम)
• Example: Gold is a ductile metal that can be drawn into thin wires.
• ​Thus, capable of being bent or pulled into different shapes means "ductile."
• The correct answer is Option 3.

Additional Information

• Lithe: means thin, supple, and graceful. ((व्यक्ति या उनके शरीर के लिए प्रयुक्त) लचीला तथा सुरुचिपुर्ण ढंग से मुड़नेवाला, लचकदार और नम्य)
• Willowy: means slender and graceful like a willow tree. (विलो पेड़ की तरह पतला और सुंदर)
• Lissome: means thin, supple, and graceful. ((मनुष्य के शरीर के लिए प्रयुक्त) पतला एवं लचीला)