SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 3) (Previous Year Paper)

The logic followed in the given figure series is :

From Figure (1) to (2):

The symbols move as shown in the figure and the symbol V changes.

From Figure (2) to (3):

The symbols move as shown in the figure and the symbol Z changes.

From Figure (3) to (4):

The symbols move as shown in the figure and the symbol rectangle changes.

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

The symbols move as shown in the figure and the symbol P changes.

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

The mirror image of the given figure is:

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

Here, we use the table given below:

Logic: (2), (4) and (6) are added to the position value of the first, second and third alphabet.

Checking all the given options:

1. HJNT

2. PRVB

3. SUXZ

4. MOSY

Here, in 'SUXZ' different logic is followed.

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

Preparing the family tree diagram by using the following symbols:

As per the given data:

 

 

 

 

 

Given expression: 'D @ N @ H & Y @ F % V'

D is the daughter of N, N is the daughter of H, H is the husband of Y, Y is the daughter of F and F is the wife of V.

Here, V is the wife's father of H.

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

Here, we use the BODMAS table given below:

Given:

⇒ 24 - (9 ÷ 12) + (84 × 4) + 28 = 23

(1) 24 and 28, - and ÷

⇒ 24 - (9 ÷ 12) + (84 × 4) + 28 = 23

After interchanging the sign and numbers:

⇒ 28 ÷ (9 - 12) + (84 × 4) + 24 = 23

Apply BODMAS rule:

⇒ 28 ÷ (-3) + 336 + 24

⇒ (-9.33) + 336 + 24

⇒ 360 - 9.33 = 350.67

Here, the equation is not satisfied.

(2) 24 and 28, × and ÷

⇒ 24 - (9 ÷ 12) + (84 × 4) + 28 = 23

After interchanging the sign and numbers:

⇒ 28 - (9 × 12) + (84 ÷ 4) + 24 = 23

Apply BODMAS rule:

⇒ 28 - 108 + 21 + 24

⇒ 73 - 108 = (-35)

Here, the equation is not satisfied.

(3) 9 and 4, ÷ and ×

⇒ 24 - (9 ÷ 12) + (84 × 4) + 28 = 23

After interchanging the sign and numbers:

⇒ 24 - (4 × 12) + (84 ÷ 9) + 28 = 23

Apply BODMAS rule:

⇒ 24 - 48 + 9.33 + 28

⇒ 61.33 - 48 = 13.33

Here, the equation is not satisfied.

(4) 12 and 4, ÷ and ×

⇒ 24 - (9 ÷ 12) + (84 × 4) + 28 = 23

After interchanging the sign and numbers:

⇒ 24 - (9 × 4) + (84 ÷ 12) + 28 = 23

Apply BODMAS rule:

⇒ 24 - 36 + 7 + 28

⇒ 59 - 36 = 23

⇒ '24 - (9 × 4) + (84 ÷ 12) + 28 = 23'

Here, the equation is satisfied.

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

Preparing the family tree diagram by using the following symbols:

As per the given data:

 

 

 

 

 

Given expression: 'H % I $J$ K * L'

H is the daughter of I, I is the son of J, J is the son of K and K is the sister of L.

Here, H is the son's daughter of J.

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

Given:

(5, 7, 140)

(6, 4, 96)

Logic: Third no. = [(First no.) × (Second no.) × 4]

(5, 7, 140) →

⇒ [5 × 7 × 4]

⇒ (35 × 4) = 140

(6, 4, 96) →

⇒ [6 × 4 × 4]

⇒ (24 × 4) = 96

Checking all the given options:

1. (7, 3, 63) →

⇒ [7 × 3 × 4]

⇒ (21 × 4) = 84

2. (5, 14, 210) →

⇒ [5 × 14 × 4]

⇒ (70 × 4) = 280

3. (9, 2, 72) →

⇒ [9 × 2 × 4]

⇒ (18 × 4) = 72

4. (6, 7, 126) →

⇒ [6 × 7 × 4]

⇒ (42 × 4) = 168

Here, (9, 2, 72) shows a similar relation to the given set of numbers.

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

Given:

(15, 45, 90)

(8, 24, 48)

Logic: Third no. = [(First no. × 3) + (Second no.)]

(15, 45, 90) →

⇒ [(15 × 3) + 45]

⇒ (45 + 45) = 90

(8, 24, 48) →

⇒ [(8 × 3) + 24]

⇒ (24 + 24) = 48

Checking all the given options:

1. (9, 27, 45) →

⇒ [(9 × 3) + 27]

⇒ (27 + 27) = 54

2. (7, 21, 24) →

⇒ [(7 × 3) + 21]

⇒ (21 + 21) = 42

3. (6, 18, 36) →

⇒ [(6 × 3) + 18]

⇒ (18 + 18) = 36

4. (12, 36, 68) →

⇒ [(12 × 3) + 36]

⇒ (36 + 36) = 72

Here, (9, 2, 72) shows a similar relation to the given set of numbers.

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

Given:

2, 6, ?, 54, 162, 486

The logic followed in the given series:

Here, '18' is the missing number.

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

Here, we use the table given below:

Given:

WUS, QOM, KIG, ?

Logic: (6) is subtracted from the position value of each alphabet.

Here, 'ECA' is the next term.

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

The logic followed in the given figure series is :

From Figure (1) to (2):

The shape rotates 90º in the anticlockwise direction.

From Figure (2) to (3):

The shape rotates 90º in the anticlockwise direction.

From Figure (3) to Answer Figure (4):

The shape rotates 90º in the anticlockwise direction.

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

The embedded part of this image is:

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

Given:

6 ∶ 22 ∶∶ 17 : 66 ∶∶ 4 ∶ ?

Logic: Second no. = [(First no. × 4) - 2]

6 : 22 →

⇒ [(6 × 4) - 2]

⇒ (24 - 2) = 22

17 : 66 →

⇒ [(17 × 4) - 2]

⇒ (68 - 2) = 66

Similarly, for '4 : ?' →

⇒ [(4 × 4) - 2]

⇒ (16 - 2) = 14

Here, '4 : 14' is the correct pair.

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

Given:

A S D F_ A _ _ F G _ U D _ G A _ _ F G

Checking all the given options:

1. G T D A F V D

ASDFG / ATDFG / AUDFG / AVDFG

 

Here, the series is completed.

2. F T E A F W D

ASDFF / ATEFG / AUDFG / AWDFG

3. F T D A F V D

ASDFF / ATDFG / AUDFG / AVDFG

4. G T E A G X E

ASDFG / ATEFG / AUDGG / AXEFG

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

Here, we use the table given below:

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

'ABOVE' is written as '9' →

'SHINE' is written as '11' →

Similarly, 'PARTY" will be written as:

Here, 'PARTY' is written as '16'.

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

Statements:

Some laptops are phones.

Some phones are capsules.

Some capsules are pens.

The Venn diagram as per the given statements:

Conclusions:

I. Some laptops are capsules. → not follow (Because there is no direct relation given between laptops and capsules, so it can be possible but not definitely true)

II. Some phones are pens. → not follow (Because there is no direct relation given between phones and pens, so it can be possible but not definitely true)

III. Some pens are capsules. → Follow (Some capsules are pens, which means some pens are capsules too)

IV. Some pens are phones. → not follow (Because there is no direct relation given between pens and phones, so it can be possible but not definitely true)

Hence, the correct answer is "Only conclusion III follows".

Checking all the given options:

Logic: The first and the second number is the multiple of 4 and 3.

1. (64, 48) →

⇒ 16 × 4 = 64

⇒ 16 × 3 = 48

2. (72, 27) →

⇒ 18 × 4 = 72

⇒ 18 × 3 = 54 (not 27)

3. (96, 72) →

⇒ 24 × 4 = 96

⇒ 24 × 3 = 72

4. (108, 81) →

⇒ 27 × 4 = 108

⇒ 27 × 3 = 81

Here, (72, 27) is different from the others.

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

Logic: (Number of letters)³

'RAT' is coded as '27' → (3)³ = 27

'ZEBRA' is coded as '125' → (5)³ = 125

Similarly,

'RABBIT' is coded as → (6)³ = 216

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

Statements:

All blocks are toys.

All toys are books.

All books are stories.

The Venn diagram as per the given statements:

Conclusions:

I. Some toys are blocks. → Follows (All blocks are toys, which means some toys are blocks is definitely true)

II. Some blocks are books. → Follows (All blocks are toys, and all toys are books, which means some blocks are books  is definitely trues)

III. Some stories are toys. → Follows (All toys are books, and all books are stories, which means some stories are toys  is definitely true)

Hence, the correct answer is "All the conclusions follow".

Given:

Today = Friday

As we know that, on the 72^th day, the day will repeat itself.

After 72 days = [(7 × 10) + 2] = 10 weeks + 2 days

Here, we have 2 days left.

After 1 day → Saturday

After 2 days → Sunday

Here, after 72 days will be 'Sunday'.

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

Given:

4 : 33 :: ? : 109 :: 8 : 257

Logic: Second number = [{(First no.)³ + 2} ÷ 2]

4 : 33 →

⇒ [{(4)³ + 2} ÷ 2]

⇒ [(64 + 2) ÷ 2]

⇒ (66 ÷ 2) = 33

8 : 257 →

⇒ [{(8)3 + 2} ÷ 2]

⇒ [(512 + 2) ÷ 2]

⇒ (514 ÷ 2) = 257

Similarly, for '? : 109' →

⇒ [{(Y)3 + 2} ÷ 2] = 109

⇒ [{(Y)3 + 2}] = (109 × 2)

⇒ (Y)³ = 218 - 2

⇒ (Y)3 = 216

⇒ Y = 6

Here, '6 : 109' is the correct pair.

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

The mirror image of the given figure is:

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

Mistake PointsThe question is asking to find the number which is NOT Related, it means we need to find the wrong option.

Given:

(4, 11, 137)

(3, 12, 153)

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

(4, 11, 137) →

⇒ [(4)² + (11)²]

⇒ (16 + 121) = 137

(3, 12, 153) →

⇒ [(3)2 + (12)2]

⇒ (9 + 144) = 153

Checking all the given options:

1. (7, 8, 113) →

⇒ [(7)2 + (8)2]

⇒ (49 + 64) = 113

2. (13, 14, 365) →

⇒ [(13)2 + (14)2]

⇒ (169 + 196) = 365

3. (9, 11, 202) →

⇒ [(9)2 + (11)2]

⇒ (81 + 121) = 202

4. (4, 3, 61) →

⇒ [(4)2 + (3)2]

⇒ (16 + 9) = 25

Here, in (4, 3, 61) different logic is followed.

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

The mirror image of the given figure is:

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

Statements:

All plates are bowls.

No bowl is a glass.

Some glasses are vessels.

The Venn diagram as per the given statements:

Conclusions:

I. Some glasses are plates. → not follow (All plates are bowls, and No bowl is a glass, which means no plates are glasses is not possible)

II. Some bowls are plates. → Follow (All plates are bowls, which means some bowls are plates is definitely true)

III. Some vessels are bowls. → not follow (Because there is no definite relation given between vessels and bowls, so it can be possible only but not definitely true)

Hence, the correct answer is "Only conclusion II follows".

The correct answer is 1896.

Key Points

• The International Olympic Committee (IOC) was founded in 1894, and it was decided that the first modern Olympic Games would be held two years later in Athens, Greece.
• The first modern Olympic Games were held from April 6 to April 15, 1896, and featured 14 nations and 241 athletes competing in 43 events.
• The Games were a huge success and helped to revive the ancient tradition of Olympic competition, which had been dormant for more than 1,500 years.
• The modern Olympic Games have been held every four years since 1896, with the exception of 1916, 1940, and 1944 due to World War I and II.

Additional Information 

• The Olympic flag has a white background, with five interlaced rings in the centre: blue, yellow, black, green, and red.
• Each colour corresponds to a particular continent: blue for Europe, yellow for Asia, black for Africa, green for Australia and Oceania, and red for the Americas.
• The Olympic motto “Citius, Altius, Fortius” (“Faster, Higher, Stronger”) was coined by Father Henri Didon.
• Only three modern Olympic Games have been cancelled.
• The games were cancelled due to World War I (1914) and World War II (1940, 1944).
• The youngest Olympian is Greek gymnast Dimitrios Loundras, who competed in the 1896 Athens Olympics at the age of 10.

The correct answer is Ninth.

Key Points

• The correct answer is option 1, i.e., the ninth month of the Islamic calendar is Ramadan.
• Ramadan is considered one of the holiest months in the Islamic calendar, during which Muslims fast from dawn to dusk and engage in spiritual reflection and acts of charity.
• Ramadan is a time of spiritual growth and self-discipline for Muslims worldwide, and it is believed to be a time when the gates of heaven are open, and the gates of hell are closed.
• During Ramadan, Muslims are required to abstain from food, drink, and other physical needs during daylight hours, and they are encouraged to engage in acts of charity, prayer, and good deeds.

Additional Information

• 1^st Month- Muharram
• 2^nd Month- Safar
• 3^rd Month- Rabi' al-Awwal
• 4^th Month- Rabi' al-Thani
• 5^th Month- Jumada al-Awwal
• 6^th Month- Jumada al-Thani
• 7^th Month- Rajab
• 8^th Month- Sha'ban
• 9^th Month- Ramadan
• 10^th Month- Shawwal
• 11^th Month- Dhu al-Qi'dah
• 12^th Month- Dhu al-Hijjah

The correct answer is Chhattisgarh.

 Key Points

• The correct answer is option 2, Chhattisgarh.
• Panthi dance is a traditional folk dance of the Santnami community of Chhattisgarh.
• This dance form is performed on the occasion of Guru Ghasidas Jayanti, which is celebrated in honor of the founder of the Satnami sect.
• The dance is characterized by its rhythmic movements and foot-tapping beats, accompanied by the melodious sound of the 'manjiras' and 'dholak'.
• The dance is performed by both men and women and is a popular form of entertainment in rural areas of Chhattisgarh.

Additional Information

• Bihar - Bihar has its own traditional folk dances like Jat-Jatin, Jhijhia, and Jumari.
• Madhya Pradesh - Madhya Pradesh has its own traditional folk dances like Gond, Bhilala, and Baiga.
• Odisha - Odisha has its own traditional folk dances like Ghumura, Sambalpuri, and Dalkhai.

The correct answer is Manipuri.

Key Points

• The correct answer to the question is option 4, Manipuri.
• Darshana Jhaveri is a renowned Manipuri dancer from India who has been awarded the Padma Shri in 2007 for her contribution to the field of dance.
• Manipuri is a classical dance form that originated in the northeastern state of Manipur in India and is known for its graceful movements, delicate footwork, and storytelling through dance.
• Bharatanatyam is another popular classical dance form from South India that is characterized by intricate footwork, hand gestures, and facial expressions. It is known for its dynamic and rhythmic movements.
• Kathak is a North Indian classical dance form that emphasizes fast spins, footwork, and storytelling through dance. It is known for its intricate rhythmic patterns and graceful movements.
• Kathakali is a traditional dance-drama form from the southern state of Kerala that combines dance, music, and acting. It is known for its elaborate costumes, makeup, and facial expressions that are used to convey emotions and tell stories.
• Hence, the statement "Padma Shri awardee, Darshana Jhaveri is a Manipuri dancer of India" is correct.

The correct answer is SAFTA.

Key Points

• SAFTA stands for South Asian Free Trade Area and is a trade agreement among the member states of the South Asian Association for Regional Cooperation (SAARC).
• SAFTA was signed in 2004 and came into effect in 2006 with the aim to promote and enhance trade and economic cooperation among the SAARC countries.
• SAFTA aims to reduce and eliminate tariffs and non-tariff barriers on goods traded within the region, and to address other issues related to trade in services and investment.
• SAFTA also includes provisions for safeguard measures to protect domestic industries from sudden surges in imports from other member countries.
• APTA (Asia-Pacific Trade Agreement) is a trade agreement among six countries in the Asia-Pacific region, while NAFTA (North American Free Trade Agreement) is a trade agreement between the United States, Canada, and Mexico, and LAIA (Latin American Integration Association) is a regional trade bloc in Latin America.
• Hence, the correct answer is option 2, SAFTA.

The correct answer is Article 51 (A).

Key Points

• Article 51 (A) of the Indian Constitution enshrines the duty of every citizen to value and preserve the rich heritage of our composite culture.
• This Article is a part of the Fundamental Duties of citizens, which were added to the Constitution by the 42^nd Amendment Act, of 1976.
• The main keyword mentioned in the question is "composite culture," which refers to the diverse cultural traditions and practices of the various communities that make up India.
• Article 43 (A) of the Constitution deals with the participation of workers in the management of industries, Article 48 (A) provides for the protection and improvement of the environment and safeguarding of forests and wildlife, and Article 124 (A) deals with the establishment and constitution of the National Judicial Appointments Commission.
• Hence, the correct answer to the question is option 1, i.e., Article 51 (A).

Additional Information

• Part IV A of the Indian constitution constitutes fundamental duties for citizens under A 51A.
• The 11 fundamental duties are as follows-

It shall be the duty of every citizen of India—

• to abide by the Constitution and respect its ideals and institutions, the National Flag and the National Anthem;
• to cherish and follow the noble ideals which inspired our national struggle for freedom;
• to uphold and protect the sovereignty, unity and integrity of India;
• to defend the country and render national service when called upon to do so;
• to promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic and regional or sectional diversities; to renounce practices derogatory to the dignity of women;
• to value and preserve the rich heritage of our composite culture;
• to protect and improve the natural environment including forests, lakes, rivers and wildlife, and to have compassion for living creatures;
• to develop the scientific temper, humanism, and the spirit of inquiry and reform;
• to safeguard public property and to abjure violence;
• to strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavour and achievement;
• who is a parent or guardian to provide opportunities for education to his child or, as the case may be, ward between the age of six and fourteen years.

The correct answer is Vishnugupta.

Key Points

• Chandragupta Maurya overthrew the Nanda Dynasty of Magadha with the help of Vishnugupta, who is also known as Chanakya.
• Chanakya was a wise and learned scholar who played a crucial role in the rise of the Mauryan Empire.
• He was the chief advisor to Chandragupta Maurya and helped him in his conquests and administrative policies.
• It is believed that Chanakya wrote the famous book Arthashastra, which deals with economics, politics, and governance.
• With the help of Chanakya, Chandragupta Maurya was able to defeat the powerful Nanda Dynasty and establish the Mauryan Empire, which became one of the greatest empires in ancient India.

Additional Information 

• Skandagupta was a Gupta Emperor who ruled from 455 to 467 CE.
• He was known for his military campaigns against the Huns.
• Chandragupta II, also known as Vikramaditya, was a Gupta Emperor who ruled from 380 to 415 CE. He was known for his patronage of art and literature.
• Samudragupta was a Gupta Emperor who ruled from 335 to 375 CE.
• He was known for his military campaigns and conquests.

The correct answer is Kidambi Srikanth.

Key Points

• The correct answer is option 2, Kidambi Srikanth.
• Srikanth reached the final of the BWF World Championship Final in December 2021, becoming the first-ever Indian male shuttler to do so.
• Srikanth lost to his opponent, Victor Axelsen of Denmark, in the final.
• Srikanth has previously won the BWF Super Series and BWF Grand Prix Gold titles in his career.
• B Sai Praneeth, Chirag Shetty, and V Diju are all accomplished Indian badminton players, but none of them have reached the final of the BWF World Championship Final.

Additional Information

• B Sai Praneeth is an Indian badminton player who has won the bronze medal at the BWF World Championships in 2019.
• Chirag Shetty is an Indian doubles badminton player who has won numerous international titles with his partner Satwiksairaj Rankireddy.
• V Diju is a former Indian badminton player who has won numerous international titles in doubles events.
• He is currently a coach and commentator.

The correct answer is 1-b, 2-a, 3-d, 4-c

Key Points

• The given table shows the number of females per 1000 males in different states and union territories of India as per the 2011 census.
• According to the table, Kerala has the highest number of females per 1000 males with a ratio of 1084.
• Puducherry has the second-highest ratio with 1037 females per 1000 males.
• Haryana has a ratio of 879 females per 1000 males, and Delhi has the lowest ratio with 868 females per 1000 males.
• The sex ratio is an important indicator of the status of women in society and is used to measure gender imbalance.

The correct answer is Subhash Chandra Bose.

Key Points

• The correct answer is option 4, Subhash Chandra Bose, who founded the All India Forward Bloc in 1939 after resigning from the Congress Presidentship.
• Subhash Chandra Bose was a prominent leader of the Indian independence movement and a strong advocate of complete independence from British rule.
• Bal Gangadhar Tilak was a nationalist leader and social reformer who played a key role in the Indian independence movement, but he died in 1920 before the formation of the All India Forward Bloc.
• Mahatma Gandhi was the leader of the Indian independence movement and the Congress party, but he did not resign from the Congress Presidentship to form the All India Forward Bloc.
• Jawaharlal Nehru was a prominent leader of the Indian independence movement and the first Prime Minister of independent India, but he did not resign from the Congress Presidentship to form the All India Forward Bloc.

The correct answer is 8 years.

Key Points

• Pradhan Mantri Jan Dhan Yojana (PMJDY) is a financial inclusion program launched by the Indian government in August 2014.
• The objective of PMJDY is to provide access to financial services such as banking and insurance to the underprivileged sections of the society.
• The scheme also provides overdraft facilities, mobile banking, and RuPay debit cards to the account holders.
• The scheme has been successful in bringing a large number of people into the formal banking system.

The correct answer is RBI.

Key Points

• The correct answer is option 3, RBI, which is also known as the 'lender of the last resort'.
• The lender of the last resort is a term used to describe an institution that provides emergency funds to other financial institutions when they are facing a shortage of liquidity.
• This is usually done to prevent a financial crisis or a bank run.
• In India, the Reserve Bank of India (RBI) is the lender of the last resort.
• It has the authority to lend money to banks and other financial institutions in case of a crisis.
• The RBI also acts as the regulator of the banking system in India. It sets policies and guidelines for banks to follow, and monitors their performance to ensure that they are operating in a safe and sound manner.

Additional Information 

• SEBI(Securities Exchange Board of India) is the regulator of the securities market in India. It does not have the authority to lend money to financial institutions.
• RRBs (Regional Rural Banks) are a type of bank that focuses on providing banking services to the rural population. They do not have the authority to act as the lender of the last resort.
• SBI (State Bank of India) is a public sector bank in India. While it is one of the largest banks in the country, it does not have the authority to act as the lender of the last resort.

The correct answer is Group-16.

 Key Points

• Chalcogens are a group of non-metal elements that have similar chemical properties.
• The word chalcogen comes from the Greek word "chalcos" which means copper.
• Group-2 elements are called alkaline earth metals.
• Group-17 elements are called halogens.
• Group-18 elements are called noble gases.

Additional Information 

• Chalcogens are located in Group-16 of the periodic table.
• They include oxygen, sulfur, selenium, tellurium, and polonium.
• Chalcogens are known for their ability to form compounds with metals and nonmetals.
• They are important elements in biological systems and have numerous industrial applications.

The correct answer is Oleic acid.

Key Points

• The correct answer is option 2, which is Oleic acid.
• Oleic acid is a monounsaturated omega-9 fatty acid that is found in high quantities in olive oil.
• This acid has a high smoke point, which makes it a good choice for most cooking methods, including frying and baking.
• It is also known for its health benefits, such as reducing inflammation and improving heart health.
• Lauric acid (option 1) is a saturated fatty acid found in coconut oil and palm kernel oil and is known for its antimicrobial properties.
• Arachidic acid (option 3) is a saturated fatty acid found in peanut oil and other vegetable oils.
• Stearic acid (option 4) is a saturated fatty acid that is found in animal fats and some vegetable oils.
• Therefore, the correct answer to the question is option 2, Oleic acid, which makes up 55-80% of olive oil and is a good choice for most cooking methods.

The correct answer is Doppler weather radar.

Key Points

• The correct instrument is the Doppler weather radar, which is used for the detection of rainfall and precipitation types.
• Doppler weather radar uses pulses of electromagnetic energy to detect precipitation in the atmosphere.
• It can determine the speed and intensity of rainfall, and identify different types of precipitation such as rain, snow, or hail.
• Doppler weather radar is a critical tool for weather forecasting and warning systems, as it provides real-time data on precipitation patterns and can help predict severe weather events.

Additional Information

• Barometer is a tool used to measure atmospheric pressure and is not used to detect precipitation.
• A spectral pyranometer is used to measure solar radiation and is not used for detecting precipitation.
• A 2D sonic anemometer is used to measure wind speed and direction and is not used for detecting precipitation.

The correct answer is A only.

Key Points 

• Parliamentary Committees are formed to assist the Parliament in its work.
• There are three types of Parliamentary Committees - Standing Committees, Select Committees, and Joint Committees.
• The members of these Committees are elected or nominated by the Parliament or its Speaker.
• Statement A is correct.
• According to the rules, a minister cannot be a member of the Public Accounts Committee (PAC) as it is an oversight committee that examines the government's expenditures.
• Statement B is incorrect.
• ​ The members of the Estimates Committee are not nominated by the Speaker of the Lok Sabha. They are elected by the Lok Sabha from among its members.
• Statement C is incorrect.
• ​A minister cannot be a member of the Estimates Committee even if he is nominated by the Speaker.
• Statement D is incorrect.
• ​ The tenure of a member of the Committee on Public Undertakings is one year.

 

Additional Information

• The Public Accounts Committee (PAC) is the oldest and most important Parliamentary Committee.
• The Estimates Committee examines the estimates of expenditure of various ministries.
• The Committee on Public Undertakings examines the working of government-owned companies.

The correct answer is Mahmud Ghaznavi.

Key Points

• Mahmud Ghaznavi was a ruler of the Ghaznavid Empire, which was located in present-day Afghanistan and Pakistan.
• He invaded India multiple times between 1000 and 1027 A.D. and is known for his raids on Hindu and Buddhist temples in northern India.
• Al Biruni was a scholar and polymath who lived in the 11^th century A.D. in Central Asia. He was invited to India by Mahmud Ghaznavi, who was impressed by his knowledge and expertise in various fields.
• Al Biruni spent several years in India, where he studied Indian culture, religion, and science.
• He wrote several books on these topics, including "The Book of India," which is considered one of the most important works on Indian culture and history.
• Al Biruni's work had a significant impact on both Indian and Islamic scholarship, and his legacy continues to this day. He is remembered as one of the greatest scholars of the Islamic Golden Age.

Additional Information

• Abdullah Shah Ghazi was a Sufi saint who lived in the 8^th century A.D. and is revered by Muslims in Pakistan. He is not related to Al Biruni or his work.
• Al-Walid I was an Umayyad caliph who ruled from 705 to 715 A.D. He is known for his military campaigns in North Africa and Spain but had no direct connection to Al Biruni or India.
• Muhammad Bin Qasim was an Arab general who led the Umayyad conquest of Sindh in 711 A.D. He is known for his military exploits but had no direct connection to Al Biruni or his work.

The correct answer is At its Lahore Session in 1929.

Key Points

• The All India Congress formalized the demand for 'Purna Swaraj' or full independence for India at its Lahore Session in 1929.
• This demand was made on January 26, 1930, which was celebrated as Independence Day or 'Purna Swaraj Day'.
• The Lahore Session was presided over by Jawaharlal Nehru, who delivered the famous 'Tryst with Destiny' speech on the eve of India's independence in 1947.
• The Lahore Session also adopted the 'Poorna Swaraj Resolution' which declared that the goal of the Congress was complete independence for India.
• The Karachi Session of the All India Congress was held in 1931, but it did not formalize the demand for 'Purna Swaraj'.
• The Guwahati Session of the All India Congress was held in 1926, but it did not formalize the demand for 'Purna Swaraj'.
• The Madras Session of the All India Congress was held in 1927, but it did not formalize the demand for 'Purna Swaraj'..
• Hence, the correct answer is option 2.

Additional Information 

• The Indian National Congress (INC) was formed by Allan Octavian Hume in 1885.
• The first session of INC was held in Bombay from 28–31 December 1885 under the chairmanship of W.C. Bannerjee.
• Sessions of Indian National Congress

The correct answer is the Bombay Plan.

Key Points

• The correct answer is option 4, i.e., Bombay Plan.
• Bombay Plan was a set of proposals for the economic development of India, presented by a group of leading industrialists and economists in 1944.
• It was named after the city where it was drafted, i.e., Bombay (now Mumbai).
• The plan aimed to create a mixed economy in India, with a balance between the public and private sectors.
• It called for an increase in public investment in key sectors such as agriculture, industry, and infrastructure, while also promoting entrepreneurship and free enterprise.
• The Bombay Plan was seen as a response to the challenge of post-war reconstruction and development in India, as well as a critique of the laissez-faire policies of the colonial government.
• It was also influenced by socialist and Fabian ideas, as well as the experience of planned economies in other countries.
• The Bombay Plan received both praise and criticism from different quarters. Some saw it as a visionary blueprint for India's future, while others criticized it as elitist, impractical, or insufficiently radical. However, it remains an important landmark in the history of economic thought and policy in India.
• The other options mentioned in the question are not correct because they do not refer to any actual plan of economic development for India. Delhi, Gujarat, and Surat are all cities or states in India, but they do not have any such plans named after them. Therefore, option 4, i.e., Bombay Plan, is the correct answer.

The correct answer is Chiranjeevi.

Key Points

• Chiranjeevi won the Indian Film Personality Award in 2022, as awarded by IFFI.
• Chiranjeevi is a renowned actor and politician from Andhra Pradesh, India, who has acted in over 150 films in Telugu, Tamil, and Hindi languages.
• Prakash Raj is another well-known Indian actor who has won several awards, including five National Film Awards. However, he did not win the Indian Film Personality Award in 2022.
• Mahesh Babu is a popular Telugu actor who has won several awards, including four Filmfare Awards. He also did not win the Indian Film Personality Award in 2022.
• Rajnikant is a legendary actor from Tamil Nadu, India, who has acted in over 150 films in Tamil, Telugu, and Hindi languages. He is also a cultural icon in India and has a massive fan following. However, he did not win the Indian Film Personality Award in 2022.
• Hence, the correct answer is option 1, Chiranjeevi.

The correct answer is Raag Tarangini.

Key Points

• The correct answer is option 4, "Raag Tarangini".
• "Raag Tarangini" is a musical treatise written by Lochan Kavi in the 15^th century.
• It is considered as one of the earliest and most comprehensive works on Indian classical music.
• The text is divided into two parts, with the first part focusing on the theoretical aspects of music and the second part discussing the practical aspects of singing and playing instruments.
• "Hridayprakash" is a text on Ayurvedic medicine, written by Madhava Upadhyaya. It is not related to music.
• "Sangeet Darpan" is a text on Indian classical music, written by Damodar Gupt. It is not ascribed to Lochan Kavi.
• "Anup Vilas" is a text on Indian classical dance, written by Raghunatha Shiromani. It is not related to music.
• Hence, the statement "In the 15^th century, a text called Raag Tarangini is ascribed popularly to Lochan Kavi" is correct.

The correct answer is It is situated in the upper part of the abdomen on the left side.

Key Points

• The liver is situated in the upper part of the abdomen on the right side, not the left side. Hence, statement 1 is incorrect.
• The liver secretes bile juice that is stored in the gallbladder and helps in the digestion of fats. This is mentioned in statement 2, which is correct.
• The liver is the largest gland in the body and performs several vital functions such as detoxification, protein synthesis, and storage of vitamins and minerals. This is mentioned in statement 3, which is correct.
• The liver is reddish-brown in color due to the presence of blood vessels and hepatocytes (liver cells). This is mentioned in statement 4, which is correct.
• There is no option 5 mentioned in the question.

Additional Information

• The liver weighs around 1.5 kg in adults and is divided into four lobes.
• The liver receives blood from the hepatic artery and the portal vein, which carries nutrients from the intestines.
• The liver plays a crucial role in maintaining the body's metabolic balance by regulating glucose, cholesterol, and lipid levels.
• Liver diseases such as hepatitis, cirrhosis, and liver cancer can affect the liver's structure and function and can be life-threatening if left untreated.

The correct answer is 11-30 October.

Key Points

• The correct answer is option 1, i.e., the FIFA U-17 Women's World Cup was held from 11^th to 30^th October 2022.
• The FIFA U-17 Women's World Cup is a biennial international football tournament for female players under the age of 17, organized by the FIFA.
• 4-11 April, is not a possible period for the FIFA U-17 Women's World Cup in 2022 as it is too early in the year and clashes with other major football events.
• 8-21 June, is also not a possible period for the FIFA U-17 Women's World Cup in 2022 as it is too close to the FIFA Women's World Cup, which is scheduled to be held from 20 July to 20^th August.
• 11-19 December, is too late in the year for the FIFA U-17 Women's World Cup in 2022 and also clashes with other major football events.
• Hence, the statement "The correct answer is option 1" is correct.

The correct answer is Agnes Pockels.

Key Points

• Surface tension is the cohesive force that holds together the molecules on the surface of a liquid.
• Agnes Pockels was a German physicist who conducted experiments on surface tension in the late 19^th century.
• Pockels developed a method to measure surface tension using a balance and a thin film of liquid on a wire loop.
• The correct answer is option 4, Agnes Pockels.
• Her research on surface tension was fundamental in establishing the modern discipline known as surface tension, which describes the properties of liquid and solid surfaces and interfaces.
• Pockels developed a method to measure surface tension using a balance and a thin film of liquid on a wire loop, which laid the foundation for the modern understanding of surface tension and its applications in fields such as chemistry and materials science.

Additional Information

• Gerty Cori was a biochemist who won the Nobel Prize in Physiology or Medicine in 1947 for her work on carbohydrate metabolism.
• Nettie Stevens was a geneticist who discovered the XY sex-determination system in animals.
• Lise Meitner was a physicist who worked on nuclear fission and was part of the team that discovered nuclear fission.

The correct answer is Amarkantak Ranges.

Key Points

• The Amarkantak Ranges are located in Madhya Pradesh and are the source of the Narmada river. Hence, option 4 is the correct answer.
• The Narmada River rises from the Amarkantak Ranges, which are located in Madhya Pradesh.
• The Amarkantak Ranges are a part of the Satpura mountain range, which is spread across central India.
• The Narmada River flows through the states of Madhya Pradesh, Maharashtra, and Gujarat before emptying into the Arabian Sea.
• The Narmada River is the fifth largest river in India and is considered sacred by Hindus.
• Western Ghats is a mountain range that runs parallel to the west coast of India and is home to several important rivers. However, the Narmada River does not rise from the Western Ghats.
• The Gawilgarh Hills are a range of hills located in the state of Maharashtra. However, the Narmada river does not rise from the Gawilgarh Hills.
• The Satpura Ranges are a mountain range that spans several states in central India. The Narmada river rises from the Amarkantak Ranges, which are a part of the Satpura Ranges.

Additional Information

• The Narmada River is known for its marble rocks, which are a popular tourist attraction in the state of Madhya Pradesh.
• The Narmada River is also home to several species of fish, including the mahseer, which is a popular game fish.
• The Narmada River is considered to be one of the seven holy rivers in India and is worshipped by Hindus.
• The Narmada River is also an important source of irrigation water and is used for agriculture in the states through which it flows.

Formula used:

(X + Y) × (X - Y) = X² - Y²

Calculation:

[(1 + p)(1 + p2)(1 + p4)(1 + p8)(1 + p16)(1 - p) - 1]

[(1 - p²)(1 + p2)(1 + p4)(1 + p8)(1 + p16) - 1]

[(1 - p⁴)(1 + p4)(1 + p8)(1 + p16) - 1]

[(1 - p⁸)(1 + p8)(1 + p16) - 1]

[(1 - p¹⁶)(1 + p16) - 1]

[(1 - p³²) - 1] = - p32

∴ The correct option is 1

Shortcut Trick

Relative Speed approach: First, make the starting times the same.

In 1 hour (from 4:00 pm to 5:00 pm), Train 1 covers 65 km.

Remaining distance at 5:00 pm = 195 − 65 = 130 km.

Relative speed (opposite direction) = 65 + 35 = 100 km/h.

Time to meet after 5:00 pm = 130 ÷ 100 = 1.3 hours = 1 hour 18 minutes.

Meeting time = 5:00 pm + 1 hour 18 minutes = 6:18 pm.

∴ The correct answer is 6:18 p.m.

Alternate Method

Given: Distance = 195 km, Speed S₁ = 65 km/h (at 4 pm), Speed S₂ = 35 km/h (at 5 pm).

Formula Used: Time = Distance ÷ Relative Speed

⇒ Distance covered by first train in 1 hour (4 pm to 5 pm) = 65 × 1 = 65 km.

⇒ Remaining distance = 195 − 65 = 130 km.

⇒ Relative speed = 65 + 35 = 100 km/h.

⇒ Time taken to meet = 130 ÷ 100 = 1.3 hours.

⇒ 0.3 hours = 0.3 × 60 = 18 minutes.

⇒ Meeting time = 5:00 pm + 1 hour 18 minutes = 6:18 pm.

∴ The correct answer is 6:18 p.m.

Additional Information

Relative Speed in Opposite Direction

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

Relative Speed in Same Direction

When two objects move in the same direction, their relative speed is the difference of their individual speeds (S₁ − S₂).

Meeting Time Concept

To calculate meeting time using relative speed, ensure the distance used is the separation between the objects at the same instant of time.

Calculation: 

As per the question,

PB = AB - AP

⇒ 20 - 12 = 8cm

As we know

PA × PB = PD ×  PC

⇒ 12 × 8 = PD × 16

⇒ PD = 6

Then CD = PD + PC 

⇒ 16 + 6 = 22 cm

∴ The correct option is 1

Shortcut Trick

Weight of the leaving student = Old Average + (Remaining Students × Decrease in Average)

Decrease in average weight = 40 − 39.5 = 0.5 kg

Number of remaining students = 15 − 1 = 14

Weight = 40 + (14 × 0.5) = 40 + 7 = 47 kg

∴ The correct answer is 47 kg.

Alternate Method

Given:

Initial number of students = 15

Initial average weight = 40 kg

Number of students after one leaves = 14

New average weight = 39.5 kg

Formula Used:

Total Weight = Average × Number of Students

Weight of leaving student = (Initial Total Weight) − (Final Total Weight)

Calculations:

⇒ Total weight of 15 students = 15 × 40 = 600 kg

⇒ Total weight of 14 students = 14 × 39.5 = 553 kg

⇒ Weight of the student who left = 600 − 553 = 47 kg

∴ The correct answer is 47 kg.

Additional Information

Basic Average Formula

Average = (Sum of all observations) ÷ (Total number of observations).

Case of Replacement

Weight of new person = Weight of removed person + (Total number of people × Increase in average).

Weighted Average

Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂), where n represents the quantity and A represents the average of each group.

Formula used:

cos X cos Z + sin X sin Z = (cos Z - X)

Calculation:

Given that, Y = 90° and

sin X = 1/2 or X = 30° 

We know that 

X + Y + Z = 180° 

30° + 90° + Z = 180°

Z = 60° 

Therefore,

(cos Z - X) = cos (60° - 30°)

cos 30° = √3/2

∴ The correct option is 1

Given: 

Rekha alone can complete a work in 16 days, and Bina alone can complete the same work in 12 days.

Starting with Rekha, they work on alternate days.

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day 

Calculation:

Let the total work is the 48 units (LCM of 16 and 12)

The efficiency of Rekha is 48 / 16 = 3 units

The efficiency of Bina is  48 / 12 = 4 units

In 2 days they do 3 + 4 = 7 units

They do 42 units of work in 6 × 2 = 12 days

Then Rekha does 3 units in 1 day 

Then Bina does 3 units in 3/4 day 

Total number of days will be 12 + 1 + 3/4 = 13$\frac{3}{4}$ days

∴ The correct option is 4

Given:

A certain amount is lent at x% p.a. simple interest for 3 years.

Instead, if the amount was lent at 3x% p.a. simple interest for 'y' more years, then the simple interest would have been seven times the earlier interest

Formula used:

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

Calculation:

Let, P = principal. Time = T

As per the question,

⇒ 7 × P × 3 × x = P × (3 + Y) × 3x

⇒ 21Px = 9Px + 3PxY

⇒ 12 Px = 3PxY

⇒ 3Y = 12

⇒ Y =4

∴ The correct option is 2

Concept used:

Calculattion:

(16 + 14) ÷ 2 - 12 + 16 × 4 - 28 + 13 × (-16 + 13)

⇒ 15 - 12 + 64 - 28 + 13 × (-3)

⇒ 15 - 12 + 64 - 28 - 39

⇒ 3 - 3 = 0

Calculation:

Average of students enrolled from college D is

(710 + 750 + 680 + 720 + 740) / 5

= 3600 / 5

Average of students who passed from college D over all the years is

(650 + 710 + 640 + 690 + 710) / 5

= 3400/5

The ratio will be, 3600 / 5 : 3400/5 = 18 : 17

∴ The correct answer is 2

Given:

x - y = 5 and xy = 150

Calculation:

So from the equation we can assume the possible values of x and y

So x = 15 and y = 10

So X + Y = 25

∴ The correct answer is 2

Calculation:

$\frac{3}{2}÷\frac{1}{7}× \left[\left(\frac{1}{2}-\frac{1}{3}\right)÷ \frac{1}{42}\right]=?$

⇒ 3/2 ÷ 1/7 × [ 1/6 × 42]

⇒ 3/2 × 7 × 7

⇒ 147 / 2 = 73$\frac{1}{2}$

∴ The correct answer is 2

Given:

In a circular race of 1600 m, A and B start from the same point and at the same time with speeds of 27 km/h and 45 km/h, respectively.

Concept used:

Distance = speed × time

Calculation:

Relative speed is (45 - 27) × 5/18 = 5 m/s

Time will be, 1600/ 5 = 320 seconds

∴ The correct option is 2

Shortcut Trick

A does total work in 4 × 5 = 20 days

B does total work in 10 × 3 = 30 days

As per question,

 

Efficiency of B + C = 2 + 2.5 = 4.5

75% of work = 60 × (3/4) = 45

Time taken by B and C to complete the 75% work = 45/4.5 = 10 days.

∴ The correct answer is 10 days.

Given: 

A can do 20% of a work in 4 days, and B can do 33$\frac{1}{3}$% of the same work in 10 days.

They worked together for 9 days and then C completed the remaining work in 6 days.

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day 

Calculation:

A does total work in 4 × 5 = 20 days

B does total work in 10 × 3 = 30 days

Let total work is 60 units ( Lcm of 20 and 30)

The efficiency of A is

⇒ 60 / 20 = 3 unit

The efficiency of B is

⇒ 60 / 30 = 2 unit

They does together in 9 days 

9 × (3+2) = 45 units

The remaining 60 - 45 = 15 unit done by C in 6 days

Total work done by C in 6 × 4 = 24 days

Efficiency of C is 60 /24 = 2.5 unit

75% of the total work is 60 × 3/4 = 45 units

Combined efficiency of B and C = 4.5

The number of days required is 45 / 4.5 = 10 days

∴ The correct option is 4

Shortcut Trick

For successive discounts of a% and b%, the equivalent discount is given by the formula: (a + b − (a × b) / 100)%.

Here, a = 9 and b = 17.

Equivalent Discount = (9 + 17 − (9 × 17) / 100)%

⇒ 26 − (153 / 100) = 26 − 1.53 = 24.47%

∴ The correct answer is 24.47 %.

Alternate Method

Given:

First discount (d₁) = 9%

Second discount (d₂) = 17%

Formula Used:

Selling Price (SP) = Marked Price (MP) × (1 − d₁/100) × (1 − d₂/100)

Total Discount % = [(MP − SP) / MP] × 100

Calculations:

Let the Marked Price (MP) be 100.

⇒ Price after 1^st discount = 100 − 9% of 100 = 100 − 9 = 91

⇒ Price after 2^nd discount (SP) = 91 − 17% of 91

⇒ SP = 91 − (17 × 91) / 100

⇒ SP = 91 − 15.47 = 75.53

⇒ Total Discount = MP − SP = 100 − 75.53 = 24.47

⇒ Equivalent Discount Percentage = (24.47 / 100) × 100 = 24.47%

∴ The correct answer is 24.47 %.

Additional Information

Successive Discounts for Three Rates

For three successive discounts a%, b%, and c%, the net discount is calculated by first finding the equivalent of a and b, then using that result with c.

Relationship between MP and CP

MP/CP = (100 + Profit%)/(100 − Discount%). This is useful when both profit and discount percentages are given.

Fraction Method

Discounts can be converted to fractions (e.g., 20% = 1/5) and multiplied as (1 − 1/n) factors to find the final Selling Price relative to the Marked Price.

Given:

$\frac{cos,α}{sin,β}$ = 10 , $\frac{cos,α}{cos,β}$ = 11

Calculation:

10 sinβ = 11 cosβ

⇒ tanβ = 11/10

cos²β = 100/221

The correct option 2

Shortcut Trick

When multiple solid spheres are melted to form a single new sphere, the total volume remains constant.

New Radius (R) = (r₁³ + r₂³ + r₃³)^1/3

R = (1³ + 6³ + 8³)^1/3 = (1 + 216 + 512)^1/3

R = (729)^1/3 = 9 cm

∴ The correct answer is 9.0 cm.

Alternate Method

Given:

Radii of three spheres: r₁ = 1 cm, r₂ = 6 cm, r₃ = 8 cm

Formula Used:

Volume of a sphere = (4/3) × π × r³

Calculations:

⇒ Volume of new sphere = Volume of sphere 1 + Volume of sphere 2 + Volume of sphere 3

⇒ (4/3) × π × R³ = (4/3) × π × (r₁³ + r₂³ + r₃³)

⇒ R³ = 1³ + 6³ + 8³

⇒ R³ = 1 + 216 + 512

⇒ R³ = 729

⇒ R = (729)^1/3

⇒ R = 9 cm

∴ The correct answer is 9.0 cm.

Additional Information

Total Surface Area of a Sphere

The total surface area (A) of a solid sphere is given by the formula A = 4 × π × r².

Volume of a Hemisphere

A hemisphere is exactly half of a sphere; its volume is given by V = (2/3) × π × r³.

Recasting Concept

When a solid object is melted and recast into another shape, the Volume remains constant, but the Surface Area usually changes.

Cube Root of common numbers

Memorizing 7³ = 343, 8³ = 512, 9³ = 729, and 10³ = 1000 helps in fast calculations for mensuration.

Calculation:

$\frac{sinθ-2sin^3θ}{2cos^3θ-cosθ}$

Sinθ(1 - 2sin²θ) / Cosθ(2cos²θ - 1)

⇒ Sinθ × cos2θ / Cosθ cos2θ 

⇒ Sinθ / Cosθ = tanθ

∴ The correct option is 1

Calculation:

They together do in 1 hour,

 1/8 + 1/12 + 1/24

⇒ $3+2+1\over24$ = 1/4 part

So total work will be done in 4 hrs

Calculation:

The number of illiterate people in Goa is , 2/5 × 315000 × 12/100 =15120

The number of illiterate people in MP is , 4/5 × 315000 × 20/100  =50400

Total is 50400 + 15120 = 65520

∴ The correct option is 1

Shortcut Trick

Area of Sector = (1/2) × Radius × Arc length

112 = (1/2) × 28 × l

112 = 14 × l

l = 112 / 14 = 8 cm

∴ The correct option is B.

Alternate Method

Given:

Radius (r) = 28 cm

Area of sector (A) = 112 cm²

Formula Used:

Area of sector = (Arc length × Radius) / 2

r = 28 cm Area = 112 cm² Arc length (l) = ? Sector of a Circle

Calculations:

⇒ 112 = (l × 28) / 2

⇒ 112 = l × 14

⇒ l = 112 / 14

⇒ l = 8 cm

∴ The correct option is B.

Additional Information

Arc Length Formula

The length of an arc (l) with central angle θ is given by l = (θ/360) × 2πr.

Sector Area Formula

The area of a sector (A) with central angle θ is given by A = (θ/360) × πr².

Perimeter of a Sector

The total perimeter of a sector is the sum of the arc length and the two radii: P = l + 2r.

Relationship between Area and Arc Length

Area of sector = (1/2) × r × l, where r is the radius and l is the arc length.

Shortcut Trick

Difference in Percentage = 35% − 20% = 15%

Difference in Marks = 20 − (−10) = 30 marks

15% → 30 marks ∴ 1% → 2 marks

John needs 10 more marks to pass → 10 ÷ 2 = 5% extra

Passing Percentage = 20% + 5% = 25%

∴ The correct answer is 25.

Alternate Method

Given:

John: 20% marks, Failed by 10 marks.

Jack: 35% marks, 20 marks more than pass.

Formula Used:

Passing Marks = (Total Marks × Pass %) / 100

20% (John)

Pass %

35% (Jack)

+10 marks

−20 marks

Total Gap = 30 Marks = 15%

Let the total marks be x.

⇒ Passing marks = (20/100) × x + 10

⇒ Passing marks = (35/100) × x − 20

⇒ 0.20x + 10 = 0.35x − 20

⇒ 10 + 20 = 0.35x − 0.20x

⇒ 30 = 0.15x

⇒ x = 30 / 0.15

⇒ x = 200 marks

⇒ Passing marks = (20/100) × 200 + 10 = 40 + 10 = 50 marks

⇒ Passing percentage = (50 / 200) × 100

⇒ Passing percentage = 25%

∴ The correct answer is 25.

Additional Information

Percentage Change

To find the percentage change, use the formula: % Change = (Difference / Original Value) × 100.

Total Marks Calculation

Total Marks = (Sum of marks deficiency and excess) / (Difference in percentage) × 100.

Passing Marks Relation

Passing Marks = Passed Marks − Excess Marks OR Failed Marks + Marks Deficiency.

Shortcut Trick

The ratio of the first two numbers is 8 : 12 = 2 : 3.

For them to be in proportion, the third and fourth numbers must share the exact same ratio.

Let the fourth proportional be x, so 14 : x = 2 : 3.

x = (14 × 3) ÷ 2 = 21.

∴ The correct answer is 21.

Alternate Method

Given:

The given numbers are 8, 12, and 14.

Formula Used:

If four numbers a, b, c, and d are in proportion, then a : b :: c : d.

In any proportion, the Product of Extremes equals the Product of Means (a × d = b × c).

Calculations:

Let the fourth proportional be x.

⇒ 8 : 12 :: 14 : x

⇒ 8 ÷ 12 = 14 ÷ x

⇒ 8 × x = 12 × 14

⇒ 8x = 168

⇒ x = 168 ÷ 8

⇒ x = 21

∴ The correct answer is 21.

Additional Information

Third Proportional

If a and b are two numbers, their third proportional c satisfies a : b = b : c, which gives the formula c = b² ÷ a.

Mean Proportional

The mean proportional between any two given numbers a and b is calculated using the formula √(a × b).

Componendo and Dividendo Rule

If four numbers are in proportion such that a : b = c : d, then by this rule, (a + b) ÷ (a − b) = (c + d) ÷ (c − d).

Given:

A shopkeeper marks his goods in such a way that after allowing a discount of 22% he gains 20%. If the cost price of the article is ₹650

Formula used:

If a shopkeeper wants a profit of R% after allowing a discount of r%

Then cost price = Market price × $\frac{100-r}{100+R}$

Calculation:

As per the question,

650 = marked price × (100 - 22) / (100 + 20)

⇒  marked price = 650 × 120 / 78

⇒ Rs 1000

So the marked price of the article is Rs 1000

Given:

(x2 - $\frac{1}{x^2}$) = 4$√6$ = (x + $\frac{1}{x}$)(x - $\frac{1}{x}$)               ...(1)

squaring both sides

⇒ (x² - $\frac{1}{x^2}$)² = 16 × 6

⇒ x4 + $\frac{1}{x^4}$ - 2 = 96

⇒ x4 + $\frac{1}{x^4}$ = 98

⇒ x4 + $\frac{1}{x^4}$ + 2 = 98 + 2

⇒ (x2 + $\frac{1}{x^2}$)² = 100

⇒ x2 + $\frac{1}{x^2}$ = 10

⇒ x2 + $\frac{1}{x^2}$ + 2 = 10 + 2

⇒ (x + $\frac{1}{x}$)² = 12

⇒ x + $\frac{1}{x}$ = √12 = 2√3                                  ...(2)

so

⇒ x - $\frac{1}{x}$ = 2√2                 [after dividing equation (1) by (2)]

and

(x - $\frac{1}{x}$)3 = (x3 - $\frac{1}{x^3}$) - 3 (x - $\frac{1}{x}$)

⇒ (2√2)³ = x3 - $\frac{1}{x^3}$ - 3(2√2)

⇒ 16√2 + 6√2 =  x3 - $\frac{1}{x^3}$ 

⇒ x3 - $\frac{1}{x^3}$ = 22√2

Given:

The volume of one brick = 0.0014 m³

Length of wall = 14 m ; Breadth of wall = 0.125 m

and height of wall = 5 m

Formula used:

Volume of wall = L × B × H

Number of bricks = Volume of wall/volume of a brick

Where, L = length ; B = breadth ; H = height

Calculation:

Volume of wall = 14 × 0.125 × 5 = 8.75 m3

Number of bricks = 8.75/0.0014

⇒ 6250

∴ The correct answer is 6250.

The correct answer is "Let the wheels be taken by you."

Key Points 

• To convert an active sentence to passive, the object of the active sentence becomes the subject of the passive sentence, and the verb is changed to a passive form (usually "be" + past participle).
• In this case, "wheels" is the object of the active sentence "Take the wheels." Therefore, it becomes the subject of the passive sentence.
• "Be taken" is the passive form of "take."
• "By you" is added to indicate who is doing the action (in this case, taking the wheels).
• Thus, the given sentence in passive form will be:
• Let the wheels be taken by you.

Hence, the correct answer is option 3.

Additional Information

• Option 1, "Let the wheels take you," is in active voice and does not match the given sentence in passive voice.
• Option 2, "Let you take the wheels," is in active voice and has the subject and object reversed from the original sentence.
• Option 4, "Let wheels you take," is not grammatically correct.

The correct answer is "trapped inside".

Key Points 

• The original sentence uses the phrase "trapped beside", which does not accurately convey the intended meaning.
• The use of "beside" implies that the greenhouse gases are located next to the atmosphere, which is not possible.
• The correct preposition to use in this context is "inside", as the greenhouse gases are trapped within the Earth's atmosphere.
• Therefore, option 1 is the most appropriate substitution.

Hence, the correct answer is option 1.

Additional Information

• Option 3, "trapped outside", is incorrect as the greenhouse gases are not located outside of the Earth's atmosphere.
• Option 4, "trapped beyond", is incorrect as it implies that the greenhouse gases are located farther away from the Earth's atmosphere than they actually are.

The correct answer is Option 4)

Key Points

• In the given question, among the given options, the word "remmission" is used incorrectly.
• The correct spelling is "Remission".
• The incorrect spelling has an extra "m" in it.
• The word "remission" means a temporary or permanent decrease or subsiding of something. (किसी चीज़ का अस्थायी या स्थायी रूप से कम होना या कम होना)
• Example: The president allowed the remission of his punishment.

Hence, the correct answer is option 4.

Additional Information

• Option 1, "Arrangement" (व्यवस्था), is spelled correctly and means the act of organizing or arranging something.
• Option 2, "Jeopardize" (ख़तरे में डालना), is spelled correctly and means to put something or someone in danger.
• Option 3, "Corruption" (भ्रष्टाचार), is spelled correctly and means dishonest or fraudulent conduct by those in power.

The correct answer is "brakes."

Key Points

• In the given sentence, the word "breaks" is used incorrectly.
• The word "breaks" means a place in the surface of something where it has cracked from damage. 
• Example: Her words break my heart.
• The correct word to use in place of "breaks" is the word 'brakes' which refers to the mechanism used to slow down or stop a vehicle.
• Example: The brakes of the vehicle failed at that time.

Hence, the correct answer is option 2.

Additional Information

• The incorrect options are:
• Option 1 (brave) means showing courage or fearlessness. Example: She was brave enough to face her fears.
• Option 3 (bricks) are rectangular blocks used for building walls or other structures. Example: The house was made of red bricks.
• Option 4 (braces) are orthodontic devices used to align teeth. Example: She had to wear braces for a year.

The correct answer is "Slang."

Key Points

• Let us understand the meaning of the given and the marked words:
• Jargon means specialized language that is used by a particular group or profession.(शब्दजाल)
• Example: The computer programmer used a lot of jargon.
• Slang also refers to informal language used by a specific group or community.(बोलचाल की भाषा)
• Example: People addressed each other using their first names and used slang.
• Both words have a similar meaning and can be used interchangeably in certain contexts.

Hence, the correct answer is option 1.

Additional Information

• Option 2 (Verboseness) means using too many words or being excessively wordy.(शब्दाडंबरपूर्णता)
• Option 3 (Formality) means the level of seriousness or adherence to rules and regulations.(औपचारिकता)
• Option 4 (Eloquence) means the ability to speak or write in a persuasive and articulate manner.(सुवक्ता )

The correct answer is "If things were not going to be normal."

Key Points

• In the given sentence, the error lies in the part," If things were not going to be normal."
• The verb tense in this part of the sentence is incorrect.
• "Were" is in the past tense, while "will" is in the future tense.
• The sentence is referring to a situation in future.
• Thus, to maintain proper tense agreement, the correct version of this sentence would be:
• "If things are not going to be normal after the pandemic, mankind will have to accept the New Normal."

Thus, the correct answer is option 3.