SSC CHSL Tier-1 2023: Official Paper (Held On: 10 Aug, 2023 Shift 4) (Previous Year Paper)

Logic : No specific pattern is followed here, random codes are assigned to each letter.

So,

• 'LAMP' is coded as '6413'
• 'MALE' is coded as '1246'

As some letters are common, so the codes will be :

​Therefore,

• 'P' will be coded as:

'P' is coded as '3'.

​Hence, "3" is the correct answer.

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

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

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

​​So,

• 15 is related to 29

​**(15 × 2)** - 1 = 29

30 - 1 = 29

29 = 29 (LHS = RHS)

​And,

• 22 is related to 43

​**(22 × 2)** - 1 = 43

44 - 1 = 43

43 = 43 (LHS = RHS)

​Similarly,

• 35 is related to ?

​**(35 × 2)** - 1 = ? 

70 - 1 = ?

69 = ?

Hence, "69" is the correct answer.

The number of triangles in the given figure is shown below :

   

   

Thus, there are 7 triangles in the given figure.

Hence, "7" is the correct answer.

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

Given : 

• 15 - 14 - 13

(15 + 13) ÷ 2 = 14

28 ÷ 2 = 14

14 = 14 (LHS = RHS)

And,

• 17 - 21 - 25

(17 + 25) ÷ 2 = 21

42 ÷ 2 = 21

21 = 21 (LHS = RHS)

So, 

• Option - (1) : 19 - 22 - 25

(19 + 25) ÷ 2 = 22

44 ÷ 2 = 22

22 = 22 (LHS = RHS)

• Option - (2) : 34 - 12 - 28

(34 + 28) ÷ 2 = 12

62 ÷ 2 = 12

31 ≠ 12 (LHS ≠ RHS)

• Option - (3) : 38 - 28 - 10

(38 + 10) ÷ 2 = 28

48 ÷ 2 = 28

24 ≠ 28 (LHS ≠ RHS)

• Option - (4) : 23 - 42 - 46

(23 + 46) ÷ 2 = 42

42 ÷ 2 = 42

21 ≠ 42 (LHS ≠ RHS)

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

According to the question,

Given that: 3 B 26 C 15 D 36 A 3 = ?

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

3 × 26 + 15 - 36 ÷ 3 = ? 

3 × 26 + 15 - 12 = ?

78 + 15 - 12 = ?

93 - 12 = ?

81 = ?

Hence, the correct answer is "81".

Logic: (3) is subtracted from the position value according to English alphabetic series.

​​So,

• HFIJ is related to ECFG

​ 

​And,

• WUXY is related to TRUV

​ 

​Similarly,

• NLOP is related to ?

​ 

Hence, "KILM" is the correct answer.

Logic:- (10) is added to the position value according to English alphabetic series.

Given:

• DAC : NKM

• PNM : ZXW

​So,

• Option - (1): HIJ : EFG

​

• Option - (2): GJM : QTW​​

• Option - (3) : POQ : STU

​

• Option - (4) : KHG : ADE

​

Thus, out of all options only 'GJM : QTW' follows the same logic as given.

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

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

Given:

• 12 : 65

(12 × 5) + 5 = 65

60 + 5 = 65 

65 = 65 (LHS = RHS)

• 13 : 70

(13 × 5) + 5 = 70

65 + 5 = 70 

70 = 70 (LHS = RHS)

So, 

• Option - (1): 14 : 65

(14 × 5) + 5 = 65

70 + 5 = 65 

75 ≠ 65 (LHS ≠ RHS)

• Option - (2) : 15 : 80

(15 × 5) + 5 = 80

75 + 5 = 80 

80 = 80 (LHS = RHS)

• Option - (3): 16 : 75

(16 × 5) + 5 = 75

80 + 5 =75 

85 ≠ 75 (LHS ≠ RHS)

• Option - (4): 18 : 85

(18 × 5) + 5 = 85

90 + 5 = 85 

95 ≠ 85 (LHS ≠ RHS)

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

Logic : Each number is multiplied by whole number series along with the addition of consecutive multiples of (2).

Hence, "306" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some kiwis are mangoes → Follow (As some mangoes are oranges and all oranges are kiwis. So, as whole oranges comes in kiwis and have some common part with mangoes. Therefore, it is definitely true)

II. Some guavas are oranges → Does not follow (As all oranges are kiwis and some kiwis are guavas. So, it is possible but not definitely true)

∴ Here, Only conclusion I follows.

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

Logic: (1^st number - 4) × 1^st number = 2^nd number

So,

• Option - (1) : 6 : 12

(6 - 4) × 6 = 12

2 × 6 = 12

12 = 12 (LHS = RHS)

• Option - (2) : 10 : 60

(10 - 4) × 10 = 60

6 × 10 = 60

60 = 60 (LHS = RHS)

• Option - (3) : 8 : 40

(8 - 4) × 8 = 40

4 × 8 = 40

32 ≠ 40 (LHS ≠ RHS)

• Option - (4) : 7 : 21

(7 - 4) × 7 = 21

3 × 7 = 21

21 = 21 (LHS = RHS)

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

Given : 11 October 1965 was Monday

Explanation :

The number of odd days from 11 October 1965 to 15 July 1973 :

∴ The number of odd days from 11 October 1965 to 15 July 1973 ⇒ 6

⇒So, One odd day get added to Saturday because day asked in future.

∴ Sunday was the day of the week on the 15 July 1973.

Hence, "Sunday" is the correct answer.

Additional Information

• Number of odd days for the days of week.

• Number of odd days for the days of months.

• Number of odd days for the years.

Logic: Product : Made from​

• Cheese is made with pasteurized or raw milk.

So,

• Option - (1) : Ketchup : Sauce

Ketchup fall under the category of sauce.

• Option - (2) : Wine : Grape

Wine is made from grapes.

• Option - (3) : Tomato : Chilli

Tomato and Chilli are types of vegetables.

• Option - (4) : Cake : Bake

Cake is a food item created by method named as baking.

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

Logic:- 

• Difference between the first and second letter position value according to English alphabetic series is (2).
• Difference between the second and third letter position value according to English alphabetic series is (4).

​So,

• Option - (1) : TVZ

​

• Option - (2) : KMQ

• Option - (3) : EGJ

​

• Option - (4) : BDH

​

Thus, out of all options only 'EGJ' doesn't follows the same logic as others.

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

Given:

Statement given: D × E - F + G ÷ H

So,

• D × E → D is the father of E.

• E - F → E is the husband of F.

• F + G → F is the mother of G.

• G ÷ H → G is the sister of H.

​

Thus, according to the final family tree D is the maternal grandfather i.e father's father of H.

Hence, "Father's father" is the correct answer.

Given :

Statement given : L / C + D × P

So,

• L / C → L is the wife of C.

• C + D → C is the father of D.

• D × P → D is the husband of P.

​

Thus, according to the final family tree D is the son of L.

Hence, "Son" is the correct answer.

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

Detailed Explanation:

• The line MN is the mirror
• The word "kh5F3ge" the fourth letter is "F". So, the mirror image should be "

" ⇒ Option 1 is eliminated.

• The word "kh5F3ge" the third digit is "5". So, the mirror image should be "

" ⇒ Option 3 is eliminated..

• The word "kh5F3ge" the first letter is "k". So, the mirror image should be "

" ⇒ Option 4 is eliminated.

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

Given: FLG_K_JMPH_RUFP_

By checking options:

1. GHMX ⇒ FLGGKHJMPHMRUFPX → (It doesn't Follows the pattern)

2) OWMO ⇒ FLGOKWJMPHMRUFPO →  (It doesn't Follows the pattern)

3) HJMW  ⇒ FLGHKJJMPHMRUFPW → (It follows the pattern of : 

) 

4) ABDG ⇒ FLGAKBJMPHDRUFPG → (It doesn't Follows the pattern)

Here, Option (3) Gives a pattern.

Hence, the correct answer is "HJMW".

Given : 12 January 2004 was Monday

Explanation :

The number of odd days from 12 January 2004 to 26 February 2011 :

∴ The number of odd days from 12 January 2004 to 26 February 2011 ⇒ 5

⇒So, One odd day get added to Saturday because day asked in future.

∴ Saturday was the day of the week on the 26 February 2011.

Hence, "Saturday" is the correct answer.

Additional Information  

• Number of odd days for the days of week.

 

• Number of odd days for the days of months.

 

• Number of odd days for the years.

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

1. For '1' element → Consecutive whole number series is followed here starting with '1'.

2. For '2' element → → Consecutive whole number series is followed here starting with '2'.

3. For '3' element → Consecutive odd number series is followed here starting with '3'.

Final series is

Hence, ‘option - (3)’ is the correct answer.

Logic : Alternately (9) and (4) are added to the position value according to English alphabetic series.

​​So,

• 'ZEPHYR' is coded as 'IIYLHV'

​ 

​And,

• 'SCHIZY' is coded as 'BGQMIC'

​ 

​Similarly,

• 'ZINCKY' is coded as :

​ 

Hence, "IMWGTC" is the correct answer.

Logic : Decreasing odd number series is subtracted subsequently.

Hence, "15" is the correct answer.

Given : 13 ÷ 145 × 29 - 79 + 17 = ?

According to the question, after replacing the signs :

• ‘+’ and ‘-’ are interchanged
• ‘×’ and ‘÷’ are interchanged

So,​​

13 × 145 ÷ 29 + 79 - 17 = ?

13 × 5 + 79 - 17 = ?

65 + 79 - 17 = ?

144 - 17 = ?

127 = ?

Hence, "127" is the correct answer.

Given : G_KMI_MGK_GIM_IK

By checking options :

1. IIKK → GIKMIIMGKKGIMKIK → (It doesn't Follows the pattern)
2. MGIK → GMKMIGMGKIGIMKIK → (It doesn't Follows the pattern)
3. GGMI → GGKMIGMGKMGIMIIK → (It doesn't Follows the pattern)
4. IKMG → GIKMIKMGKMGIMGIK → (It follows the pattern of : Shifting in the forward direction subsequently. 

)

⇒Option - (4) gives the pattern of "GIKM - IKMG - KMGI - MGIK"

Hence, "IKMG" is the correct answer.

The correct answer is Only Articles 20 and 21 can be suspended during emergency.

 Key Points

• Articles 20 and 21 are not the only fundamental rights that can be suspended during an emergency.
• Other fundamental rights can also be suspended in certain circumstances.
• Fundamental rights can be restricted by the state if it is necessary for the protection of public order, morality, health, or the rights of others.
• The Indian Constitution guarantees six fundamental rights to its citizens:
• right to equality, right to freedom, right against exploitation, right to freedom of religion, cultural and educational rights, and right to constitutional remedies.

Additional Information

• Fundamental rights are justiciable, which means that individuals can approach the courts if their fundamental rights are violated.
• Some fundamental rights are negative, which means that they impose a duty on the state to refrain from interfering with certain activities of individuals.
• For example, the right to freedom of speech and expression is a negative right.
• Fundamental rights can be suspended during an emergency, but not all of them.
• Fundamental rights such as the right to freedom of movement, assembly, and speech can also be suspended in certain circumstances.

The correct answer is Delhi-Kolkata-Mumbai-Chennai.

Key Points

• The Golden Quadrilateral connects the cities of Delhi, Kolkata, Mumbai, and Chennai.
• This highway network is approximately 5,846 km long and was completed in 2012.
• The project was initiated by the government of India in 2001 with the aim of improving connectivity and facilitating trade and commerce across the country.
• The Golden Quadrilateral is one of the largest highway projects in the world and has helped to boost economic growth in India.

Additional Information

• These mega roads, which essentially encircle India, are primarily designed to shorten travel times between its major cities.
• Other projects include the East-West corridor connecting Silchar (Assam) and Porbandar (Gujarat) and the North-South corridor connecting Srinagar (Jammu & Kashmir) and Kanyakumari (Tamil Nadu).
• The National Highway Authority of India is in charge of carrying out these road developments.
• With a length of 5,846 kilometers, it is the longest highway project in the world and the largest in India.
• At a cost of ₹600 billion, it is the first phase of the National Highways Development Project (NHDP) and consists of two, four, and six-lane expressways.
• The project began in 2001, was planned in 1999, and was finished in July of 2013.

The correct answer is Pradhan Mantri Garib Kalyan Anna Yojana.

 Key Points

• Pradhan Mantri Garib Kalyan Anna Yojana is a government scheme launched in 2020.
• Its aim was to provide subsidized food grains to poor households in India.
• The scheme aims to provide food security to the poor during the COVID-19 pandemic by providing 5 kg of wheat or rice and 1 kg of pulses per month for free for three months.

Additional Information

• Pradhan Mantri Kaushal Vikas Yojana is a government scheme launched in 2015.
• It aimed to provide skill training to youth for employability.
• Pradhan Mantri Jan Arogya Yojana is a government scheme launched in 2018.
• Its aim was to provide health insurance coverage to poor households in India.
• Atal Pension Yojana is a government scheme launched in 2015.
• Its aim was to provide a defined pension to workers in the unorganised sector.

The correct answer is Nitu Ghanghas.

Key Points

• Nitu Ghanghas won the women's lightweight gold medal at the 2022 Commonwealth Games in Birmingham and received the BBC Emerging Player of the Year Award.
• Nikhat Zareen is an Indian female boxer who won a gold medal at the 2011 Asian Youth Boxing Championship and a bronze medal at the 2019 AIBA Women's World Boxing Championships.
• Lovlina Borgohain is also an Indian female boxer who won a bronze medal at the 2020 Tokyo Olympics in the women's welterweight category.
• Saweety Boora is an Indian female boxer who won a silver medal at the 2014 Commonwealth Games in Glasgow and a bronze medal at the 2018 AIBA Women's World Boxing Championships.

Additional Information

• Women's lightweight boxing category has a weight limit of 60 kg (132 lbs).
• The 2022 Commonwealth Games were held in Birmingham, England from 28 July to 8 August 2022.
• BBC Emerging Player of the Year Award is given to a young athlete who shows exceptional performance and potential for the future.
• Nitu Ghanghas was awarded this in recognition of her achievements in the Commonwealth Games.

The correct answer is Uday Shankar.

Key Points

• Uday Shankar is considered the father of the modern Indian dance as he introduced a new form of dance that blended Indian classical dance with Western ballet.
• He founded the first Indian dance company, which toured extensively in Europe and the US.
• He also collaborated with famous artists like Pablo Picasso and Igor Stravinsky.

Additional Information

• Ambui Singh is a renowned Indian classical dancer, known for her performances in Kathak and Bharatanatyam styles.
• In 1956, he became the first recipient of the Sangeet Natak Akademi award from the state of Manipur.
• CV Chandrasekhar is an Indian classical dancer and choreographer, who has won several awards for his contributions to the field of dance.
• In 1992, he retired from his position as Head of the M.S. University, Baroda Faculty of Performing Arts.
• Raja Reddy is a famous Kuchipudi dancer, who has also been honored with many awards for his achievements in the field of dance.

The correct answer is B and D.

Key Points

• Directive Principles of State Policy (DPSP) are guidelines and principles laid down in the Indian Constitution for the government to follow while making laws and policies.
• DPSPs are positive in nature, meaning they outline the positive actions that the government should take to promote the welfare of the people.
• DPSPs have moral and political sanctions, which means that while they are not enforceable by the courts, they are still considered important principles for the government to follow.
• DPSPs promote the welfare of all sections of the society, not just the rich.
• They aim to promote social, economic and political justice, and ensure equality of opportunity and status for all citizens.

Additional Information

• The Directive Principles of the Irish Constitution, which address social fairness, economic well-being, foreign policy, and legal and administrative issues, served as the model for the DPSC's principles.
• The following categories comprise Directive Principles: Environmental, Justice and Legal, Political and Administrative, Economic and Socialistic, Peace and Security, and Monument Protection.
• The concept of such policies "can be traced to the Declaration of the Rights of Man and of the Citizen proclaimed by Revolutionary France and the Declaration of Independence by the American Colonies."
• The Universal Declaration of Human Rights by the United Nations has had an impact on the Indian constitution.

The correct answer is Magh Bihu.

Key Points

• Makar Sankranti is a Hindu festival celebrated on the 14^th of January every year, marking the transition of the sun into the zodiac sign of Capricorn (Makar Rashi).
• Magh Bihu is the festival celebrated on Makar Sankranti day in Assam.
• It is also known as Bhogali Bihu or Maghar Domahi.
• Magh Bihu is a harvest festival and is celebrated with great enthusiasm and feasting.
• It marks the end of the harvesting season and the beginning of a new agricultural cycle.

Additional Information

• Kati Bihu is celebrated in October/November and is also known as Kongali Bihu or Kangali Bihu.
• It is celebrated during the sowing season and is a festival of prayers for a good harvest.
• Bohag Bihu or Rongali Bihu is celebrated in April and is also known as the Assamese New Year.
• It marks the beginning of the Assamese calendar and the onset of spring.
• Raksha Bandhan is an annual ritual or ceremony that serves as the centerpiece of the South Asian festival of the same name.
• Sisters of all ages bind the rakhi, a talisman or charm, around their brothers' wrists on this day.
• They give them a present in exchange for their symbolic protection, and customarily give the brothers a portion of the duty for their possible upbringing.

The correct answer is Opening the largest number of bank accounts in one week.

 Key Points

• In August 2014, the PMJDY opened 18,096,130 bank accounts in one week, which was recognized by the Guinness Book of World Records.
• The Department of Financial Services, Government of India, has declared that the "Most bank accounts opened in one week as part of the Financial Inclusion Campaign is 18,096,130."

Additional Information

• The Pradhan Mantri Jan Dhan Yojana (PMJDY) was launched in August 2014 by the Indian government.
• Its aim of providing financial inclusion and banking services to all households in India.
• The scheme offers basic savings bank deposit accounts (BSBDA) with no minimum balance requirement, a RuPay debit card, and insurance coverage.
• As of August 2021, the PMJDY has opened over 43 crore (430 million) bank accounts and mobilized over Rs 1.5 lakh crore (1.5 trillion) in deposits.

The correct answer is Vinai Kumar Saxena.

Key Points

• Vinai Kumar Saxena was appointed as the Lieutenant Governor of Delhi in May 2022 by President Ram Nath Kovind.
• Vinai Kumar Saxena is a retired Indian Administrative Service (IAS) officer of the 1983 batch from the Assam-Meghalaya cadre.
• He has served as the Chairman of the Agricultural and Processed Food Products Export Development Authority (APEDA) and the Khadi and Village Industries Commission (KVIC) in the past.

Additional Information

• Manoj Sinha is a politician from the Bharatiya Janata Party (BJP).
• He is currently serving as the Lieutenant Governor of Jammu and Kashmir.
• Admiral D K Joshi is a retired Indian Navy officer.
• He served as the Chief of Naval Staff from 2012 to 2014.
• Dr Tamilisai Soundararajan is a politician from the BJP.
• She served as the second Governor of Telangana, and also served as Lieutenant Governor of Puducherry from 18 February 2021 to 18 March 2024.

The correct answer is 1869.

Key Points

• Mohandas Karamchand Gandhi was born in 1869.
• This means that he lived during a time when India was under British colonial rule.
• Gandhi played a crucial role in the Indian independence movement through non-violent civil disobedience and peaceful protests.
• During its fight for independence, he led the nation in the non-cooperation movement in 1922, the Salt March in 1930, and the Quit India movement in 1942.
• His legacy continues to inspire people around the world to fight for justice, equality, and freedom.

Additional Information

• Mohandas Karamchand Gandhi was an Indian independence activist who is widely known as Mahatma Gandhi.
• He was a prominent figure in India's struggle for independence from British rule.
• Gandhi was born in Porbandar, a coastal town in present-day Gujarat, India.
• His birthday, October 2^nd, is celebrated as a national holiday in India as Gandhi Jayanti.

The correct answer is Pandit Shivkumar Sharma.

Key Points

• Pandit Shivkumar Sharma is associated with Santoor.
• He is a renowned Indian classical musician who is known for his mastery in playing the santoor, a stringed musical instrument.
• He is one of the pioneers of Indian classical music fusion and has collaborated with many renowned musicians from India and abroad.
• He has been honored with several awards and accolades, including the Padma Shri, Padma Bhushan, and Padma Vibhushan.
• Apart from his musical career, he has also composed music for several Bollywood movies.

Additional Information

• Pandit Jasraj was a renowned Indian classical vocalist who belonged to the Mewati gharana.
• He was known for his soulful renditions of classical ragas and was honored with several awards, including the Padma Vibhushan and the Sangeet Natak Akademi Award.
• Pandit Bhimsen Joshi was a legendary Indian classical vocalist who belonged to the Kirana gharana.
• He was known for his powerful voice and his ability to evoke emotions through his music.
• He was honored with several awards, including the Bharat Ratna, Padma Vibhushan, and Padma Bhushan.
• Hari Prasad Chaurasia is a renowned Indian classical flautist who is known for his mastery in playing the bansuri, a bamboo flute.
• He has collaborated with many renowned musicians and has been honored with several awards, including the Padma Shri, Padma Bhushan, and Padma Vibhushan.

The correct answer is Chlamydomonas.

Key Points

• Chlamydomonas is a type of haploid unicellular eukaryote cell that has a diameter of approximately 10 μm.
• Half of its volume is occupied by cup-shaped chloroplasts, which are responsible for photosynthesis.
• Chlamydomonas is found in freshwater environments and is capable of both sexual and asexual reproduction.
• It is commonly used as a model organism in genetic and biochemical research.

Additional Information

• Hydrodictyon is a genus of green algae that forms a net-like structure.
• It is commonly known as the water net.
• Ulva is a genus of green algae that is commonly known as sea lettuce.
• It is often found in marine environments.
• Oedogonium is a genus of filamentous green algae.
• It is commonly found in freshwater environments.

The correct answer is Kaolinite.

 Key Points

• Orthoclase is a type of feldspar mineral that is commonly found in igneous rocks.
• Hydrolysis of orthoclase results in the formation of kaolinite, which is a type of clay mineral.
• Kaolinite is commonly used in the production of ceramics, paper, and other industrial applications.

Additional Information

• Limonite is a type of iron ore.
• It is formed by the weathering of iron-rich rocks and soils.
• Magnesite is a mineral composed of magnesium carbonate.
• It is commonly used in the production of refractory materials.
• Gypsum is a mineral composed of calcium sulfate. 
• It is commonly used in the production of plaster and drywall.

The correct answer is To avoid generation of private profit.

 Key Points

• Poor savings capacity of the public:
• This was one of the main reasons why the public sector played a dominant role in establishing the industrial sector in India post-independence.
• The private sector did not have enough capital to invest in large-scale industries, and the government had to step in to fill this gap.
• Absence of a large enough market for output:
• Another reason why the public sector played a dominant role was that there was not a large enough market for the output of the industries.
• The private sector would have found it difficult to sustain their businesses in such a scenario, and the government had to step in to provide the necessary infrastructure and support.
• Lack of adequate capital with private industrialists:
• As mentioned earlier, the private sector did not have adequate capital to invest in large-scale industries.
• The government had to provide the necessary capital through various means such as subsidies, tax incentives, and loans.
• To avoid the generation of private profit:
• This option is incorrect because it goes against the basic principles of capitalism and entrepreneurship.
• The private sector is driven by the profit motive, and this is what encourages innovation, efficiency, and growth.
• The government's role is to facilitate this process by creating a conducive environment for businesses to thrive.

Additional Information

• Industrial sector in India post-Independence:
• The Indian government adopted a socialist approach to economic development after Independence in 1947.
• The focus was on building a self-sufficient economy through import substitution and state-led industrialization.
• Private sector in India:
• ​The private sector was largely absent in the early years of Independence, as the government had nationalized many key industries.
• It was only in the 1980s and 1990s that the government started liberalizing the economy and allowing private participation in various sectors.
• Public sector in India:
• ​The public sector played a dominant role in the Indian economy for several decades after Independence.
• The government set up various public sector enterprises in key industries such as steel, coal, power, and telecommunications.
• These enterprises were supposed to be the engines of growth and development for the country.

The correct answer is Maharashtra.

Key Points

• Saurashtra defeated Maharashtra by 8 wickets in the final match of the Vijay Hazare Trophy 2022.
• This was Saurashtra's second Vijay Hazare Trophy title, having previously won in 2019-20.
• Karnataka and Delhi were both semi-finalists in the tournament but were not the teams that Saurashtra defeated in the final.
• Andhra did not make it past the group stage of the tournament.

Additional Information

• The Vijay Hazare Trophy is a domestic one-day cricket competition in India.
• The competition bears the name of the renowned Indian cricket player from the 20^th century, Vijay Hazare.
• It was inaugurated in the 2002–03 season.
• Tamil Nadu has won the trophy five times, making them the most successful team.
• Saurashtra is a cricket team from the state of Gujarat.

The correct answer is Gopal Krishna Gokhale.

Key Points

• The Deccan Sabha was founded by Gopal Krishna Gokhale, who was a prominent Indian nationalist and social reformer.
• Gokhale was a member of the Indian National Congress and played a key role in the early stages of the Indian independence movement.
• The Deccan Sabha was a political organization founded in 1896 in Pune, India.
• The organization aimed to promote social and political reforms in the Deccan region of India and played a key role in the Indian independence movement.
• Other prominent members of the Deccan Sabha included Gopal Krishna Gokhale's mentor, Mahadev Govind Ranade, and the social reformer, Dhondo Keshav Karve.

Additional Information

• Born in Bombay, Sir Pherozeshah Merwanjee Mehta was an Indian politician and attorney. 
• In 1873, he was elected as the Bombay Municipality's municipal commissioner and served as its president four times.
• During British rule, Surendranath Banerjee led the Indian nationalist movement.
• In order to unite Hindus and Muslims for political action, he formed the Indian National Association, a nationalist group.
• Dadabhai Naoroji was an Indian politician, academic, writer, and trader.
• From 1886 to 1887, 1893 to 1894, and 1906 to 1907, he presided over the Indian National Congress as its second, ninth, and twenty-second president.

The correct answer is Sher Shah Suri.

Key Points

• Sher Shah Suri, a medieval ruler, focused on the construction of sarai for the convenience of travelers.
• Sarai were shelters that provided food, water, and lodging for travelers, especially those on long journeys.
• Sher Shah Suri built a network of saris along the main roads and highways in his empire, which facilitated travel and trade.
• The construction of saris was a significant achievement of Sher Shah Suri's reign, as it improved the infrastructure of the empire and benefited the common people.

Additional Information

• Babur was more interested in military conquests.
• The Mughal Empire in the Indian subcontinent was founded by Babur.
• Akbar was interested in religious tolerance and administrative reforms.
• The reign of Akbar, the third Mughal emperor, lasted from 1556 to 1605.
• Humayun was interested in restoring his lost empire.
• From 1530 to 1540 and again from 1555 until his death in 1556, Humayun, the second Mughal emperor, ruled over regions that are today Eastern Afghanistan, Bangladesh, Northern India, and Pakistan.

The correct answer is Li and Mg.

 Key Points

• Lithium (Li) and Magnesium (Mg) show a diagonal relationship as they are located diagonally opposite to each other in the periodic table.
• Both Li and Mg have similar atomic radii, electronegativities, and ionization energies due to the similarities in their electronic configurations.
• A diagonal relationship refers to the similarities in properties between elements that are diagonally opposite to each other in the periodic table.

Additional Information

• Diagonal relationship is a result of the similarities in the electronic configurations of these elements.
• Be and B do not show a diagonal relationship as they are not located diagonally opposite to each other in the periodic table.
• Similarly, Be and Mg do not show a diagonal relationship as they belong to the same group and have different electronic configurations.
• Na and Mg also do not show a diagonal relationship as they belong to different periods and have different electronic configurations.

The correct answer is Wages in cash.

 Key Points

• Operating surplus is the excess revenue generated by a business after deducting operating expenses.
• Rent, profit, and interest are all included in the operating surplus because they are sources of revenue for the business.
• Wages in cash, on the other hand, are an operating expense and would be deducted from revenue to calculate operating surplus.

Additional Information

• Rent refers to the amount of money paid by a business for the use of a property or space.
• Profit is the amount of money a business earns after deducting all expenses, including operating expenses.
• Interest is the amount of money paid by a business for borrowing money or the amount earned by a business for lending money
• Wages are the amount of money paid to employees for their work.
• They are an expense for the business and would not be included in operating surplus.

The correct answer is Los Angeles.

Key Points

• Los Angeles City was awarded the right to host the 2028 Olympic Games by the International Olympic Committee (IOC) in 2017.
• Paris and Tokyo were also in the running for the 2024 Olympic Games, but Los Angeles withdrew its bid for 2024 and agreed to host the 2028 Games instead.
• Amsterdam has not been in contention for hosting the 2028 Olympic Games, as the Netherlands has not submitted a bid to the IOC for any upcoming Olympic Games.
• It is worth noting that the 2020 Olympic Games, originally scheduled to take place in Tokyo, were postponed to 2021 due to the COVID-19 pandemic.

Additional Information

• The Olympic Games are a major international multi-sport event, featuring thousands of athletes from around the world competing in various sports over a period of several weeks.
• The event is held every four years, alternating between the Summer and Winter Games.
• The current Olympic Games were founded by Baron Pierre de Coubertin.
• Greece's Athens hosted the first modern Olympics in 1896.

The correct answer is Bhuvan Kumar.

Key Points

• Bhuvan Kumar won the Sangeet Natak Akademi Award 2021 for his contribution to the 'Chhau' dance.
• Chhau is a traditional dance form originating from eastern India.
• It is particularly from the states of Jharkhand, Odisha, and West Bengal.

Additional Information

• Bijay Kumar Jena is a renowned Odissi dancer and choreographer.
• He has been awarded the Padma Shri and Sangeet Natak Akademi Award for his contribution to the field of dance.
• Rabindra Atibudhi is a renowned folk music singer from Odisha.
• He has been awarded the Sangeet Natak Akademi Award for his contribution to the field of music.
• Trilochan Mohanta is a renowned sculptor and artist from Odisha.
• He has been awarded the Padma Shri and National Award for his contribution to the field of art.

The correct answer is Government Spending.

 Key Points

• Government spending is not a monetary policy instrument of RBI.
• It is a fiscal policy instrument used by the government to influence the economy.
• The bank rate is the rate at which RBI lends money to commercial banks.
• It is a monetary policy instrument used to regulate credit growth and inflation.
• Open market operations refer to the buying and selling of government securities by RBI in the open market.
• It is a monetary policy instrument used to inject or withdraw liquidity from the market.
• The Cash Reserve Ratio (CRR) is the percentage of deposits that banks are required to keep with RBI.
• It is a monetary policy instrument used to regulate the money supply in the economy.
• RBI uses a combination of monetary policy instruments to achieve its objectives of maintaining price stability, promoting economic growth, and ensuring financial stability.

Additional Information

• Government spending is a tool used by the government to influence the economy.
• It refers to the amount of money spent by the government on goods and services, such as infrastructure development, social welfare programs, defense, etc.
• The bank rate is an important tool used by RBI to regulate credit growth and inflation.
• A higher bank rate makes borrowing expensive, which reduces credit growth and inflation, while a lower bank rate stimulates borrowing and economic growth.
• Open market operations are used by RBI to inject or withdraw liquidity from the market.
• When RBI buys government securities, it injects liquidity into the market, while selling government securities withdraws liquidity from the market.
• The Cash Reserve Ratio (CRR) is used by RBI to regulate the money supply in the economy.
• A higher CRR reduces the amount of money that banks can lend, which reduces credit growth and inflation, while a lower CRR stimulates credit growth and economic activity.

The correct answer is Money spent on purchasing shares of a company.

 Key Points

• Investment is defined as the purchase of goods that are not consumed today but are used in the future to create wealth.
• In addition to residential construction, machinery and equipment employed by a firm, and inventories of raw materials stocked by a firm are all components of investment as they are used to generate future income.
• Money spent on purchasing shares of a company is not a component of investment as it does not directly create wealth or generate future income.
• However, investing in shares can indirectly contribute to wealth creation through dividends and capital gains.
• It is important to note that investment can take various forms, including financial assets like stocks and bonds, as well as physical assets like real estate and machinery.

Additional Information

• Addition to residential construction: This is a component of investment as it involves spending money on building or improving a property, which can generate future income through rent or sale.
• Machinery and equipment employed by a firm: This is a component of investment as it involves spending money on tools and equipment that can increase productivity and generate future income for the firm.
• Inventories of raw materials stocked by a firm: This is a component of investment as it involves spending money on goods that can be used to produce finished products and generate future income for the firm.

The correct answer is Leh.

Key Points

• Leh experiences the lowest temperature in India due to its high altitude and proximity to the Himalayas.
• The average temperature in Leh during winter can drop to -20 degrees Celsius.
• Leh is a city in the disputed Kashmir region of Ladakh, which is administered by India.
• It is Ladakh's largest city and joint capital.

Additional Information

• Jaisalmer experiences extreme heat during summers with temperatures soaring above 45 degrees Celsius.
• Munnar is a hill station in Kerala.
• It experiences moderate temperatures throughout the year.
• Bundelkhand is a region spanning across Madhya Pradesh and Uttar Pradesh.
• It experiences hot and dry summers with temperatures rising above 40 degrees Celsius.

The correct answer is Francium.

 Key Points

• Francium is a highly radioactive metal.
• It is the second rarest element in the Earth's crust.
• It was discovered in 1939 by Marguerite Perey.
• It is named after France.

Additional Information

• Meitnerium (Mt) is a synthetic element.
• It was first synthesized in 1982.
• Dubnium (Db) was first synthesized in 1967.
• It is named after the Russian city of Dubna.
• Seaborgium (Sg) was first synthesized in 1974.
• It is named after Glenn T. Seaborg, a nuclear chemist.

Shortcut Trick

Let the total number of votes be x.

Total → Turnout → Valid → A's Share

x × 80% × 98% × 60% = 9408

x × 0.8 × 0.98 × 0.6 = 9408

x × 0.4704 = 9408

x = 9408 ÷ 0.4704 = 20000

∴ The correct answer is 20,000.

Alternate Method

Given:

Turnout = 80% of total votes

Invalid = 2% of casted votes

A's votes = 9,408 (60% of valid votes)

Formula Used:

Valid votes = Total votes × Turnout % × (100 − Invalid %)

Total Voters (100%)

Voted (80%)

Valid (98% of Voted)

A's Share (60%) = 9408

B's Share (40%)

⇒ Let Valid Votes = V

⇒ 60% of V = 9408

⇒ V = (9408 × 100) ÷ 60 = 15680

⇒ Let Casted Votes = C

⇒ 98% of C = 15680

⇒ C = (15680 × 100) ÷ 98 = 16000

⇒ Let Total Votes = T

⇒ 80% of T = 16000

⇒ T = (16000 × 100) ÷ 80 = 20000

∴ The correct answer is 20,000.

Additional Information

Successive Percentage

When a value is changed by a%, b%, and c% successively, the final value is Initial × (1 ± a/100) × (1 ± b/100) × (1 ± c/100).

Election Terminology

Valid Votes = Total Casted Votes − Invalid Votes. Winner's Margin = Winner's Votes − Runner-up's Votes.

Base Value Concept

Always identify the base for percentage calculation. Here, 2% invalid is based on casted votes, and 60% share is based on valid votes.

Given:

(5a + $\frac{4}{a}$ - 2) = 13

Concept used:

(a + b)² = a² + b² + 2ab 

Calculation:

⇒ (5a + $\frac{4}{a}$) = 13 + 2

⇒ (5a + $\frac{4}{a}$) = 15

Squaring both sides

⇒ (5a + $\frac{4}{a}$)² = 15²

⇒ 25a² + (16/a²) + 2 × 5a × (4/a) = 225

⇒ 25a2 + (16/a2) + 40 = 225

⇒ 25a2 + (16/a2)  = 225 - 40

⇒ (25a2 + $\frac{16}{a^2}$) = 185

∴ The correct answer is 185.

Shortcut Trick

For a number to be divisible by 6, it must be even and the sum of its digits must be divisible by 3.

Sum of digits of 3426x = 3 + 4 + 2 + 6 + x = 15 + x. For this to be a multiple of 3, x can be 0, 3, 6, or 9.

Since the number must be even, x must be 0 or 6. Since it is NOT divisible by 5, x cannot be 0.

∴ The correct answer is 6.

Alternate Method

Given: The number is 3426x. It is divisible by 6 but NOT divisible by 5.

Formula Used: Divisibility rules for 2, 3, 5, and 6.

⇒ For divisibility by 2, the last digit x must be even: {0, 2, 4, 6, 8}.

⇒ For divisibility by 3, sum of digits = 3 + 4 + 2 + 6 + x = 15 + x. This sum must be divisible by 3.

⇒ Possible values for x from the sum condition: {0, 3, 6, 9}.

⇒ Combining both (divisibility by 6), x must be in the intersection: {0, 6}.

⇒ For divisibility by 5, the last digit must be 0 or 5. Since 3426x is NOT divisible by 5, x ≠ 0.

⇒ From the remaining possible values {0, 6}, we exclude 0, leaving x = 6.

∴ The correct answer is 6.

Additional Information

Divisibility by 3

A number is divisible by 3 if the sum of all its digits is a multiple of 3.

Divisibility by 6

A number is divisible by 6 if it satisfies the divisibility rules for both 2 (ends in 0, 2, 4, 6, 8) and 3 simultaneously.

Divisibility by 5

A number is divisible by 5 if its unit digit is either 0 or 5.

Divisibility by 4

A number is divisible by 4 if the last two digits of the number are divisible by 4 or are 00.

Shortcut Trick

Use the net deviation method from the average price (₹612).

Deviation for 1^st variety: 504 − 612 = −108

Deviation for 2^nd variety: 540 − 612 = −72

Total deficit for 2 parts of 3^rd variety = 108 + 72 = 180

Surplus required per unit of 3^rd variety = 180 ÷ 2 = 90

Price of 3^rd variety = 612 + 90 = ₹702

∴ The correct answer is ₹702.

Alternate Method

Given:

Price of Variety 1 = ₹504 per kg | Price of Variety 2 = ₹540 per kg

Mixing Ratio = 1 : 1 : 2 | Mean Price of mixture = ₹612 per kg

Formula Used:

Weighted Average Price = (n₁c₁ + n₂c₂ + n₃c₃) ÷ (n₁ + n₂ + n₃)

Let the price of the third variety be ₹X per kg.

⇒ Total Weight = 1 + 1 + 2 = 4 kg

⇒ Total Cost = (1 × 504) + (1 × 540) + (2 × X)

⇒ Total Cost = 1044 + 2X

⇒ Mean Price × Total Weight = 612 × 4

⇒ 1044 + 2X = 2448

⇒ 2X = 2448 − 1044

⇒ 2X = 1404

⇒ X = 1404 ÷ 2

⇒ X = 702

∴ The correct answer is ₹702.

Additional Information

Weighted Average Concept

When items with different quantities (w₁, w₂) and prices (p₁, p₂) are mixed, the average price P = (w₁p₁ + w₂p₂) ÷ (w₁ + w₂).

Rule of Alligation

It is a faster way to find the ratio of mixing two ingredients: (Cheaper Quantity) / (Dearer Quantity) = (Dearer Price − Mean Price) / (Mean Price − Cheaper Price).

Three Variety Mixing

To solve for three varieties, they can be treated as two separate pairs using alligation, where each pair result is balanced against the common mean price.

Formula used:

(a³ - b³) = (a - b) × (a² + ab + b²)

(a² - b²) = (a + b) × (a - b)

Calculation:

$\frac{(x^3-y^3)(x+y)}{x^2+xy+y^2}$

⇒ {(x - y) × (x² + xy + y²) × (x + y)}/(x2 + xy + y2)

⇒ (x - y) × (x + y)

⇒ (x2 - y2)

∴ The correct answer is (x2 - y2).

Calculation:

There are only 3 tangent possible if two circle touches each other externally.

∴ The correct option is 1.

Given:

2(tan2A cos2A + cos2A)

Formula used:

Sec² θ = tan² θ + 1

cos2 θ × sec2 θ = 1

Calculation:

⇒ 2 × (tan2A cos2A + cos2A)

⇒ 2 × Cos² A (tan²A + 1)

⇒ 2 × cos² A × sec² A

⇒ 2 × 1 = 2

∴ The correct answer is 2.

Given:

Tan(A + B - C) = 1/√3

Cos(B + C - A) = 1/2

sin(C + A - B) = 1/√2

Formula used:

Tan 30° = 1/√3 ; cos 60° = 1/2

and sin 45° = 1/√2

Calculation:

Tan(A + B - C) = 1/√3

⇒ Tan (A + B - C) = tan 30°

⇒ (A + B - C) = 30°

⇒ C = A + B - 30 -------- (1)

Cos(B + C - A) = 1/2

⇒ Cos(B + C - A) = cos 60° 

⇒ (B + C - A) = 60°

Now putting the value of c in the equation:

⇒ (B + A + B - 30 - A) = 60°

⇒ 2B = 60 + 30 = 90

⇒ B = 45° 

sin(C + A - B) = 1/√2

⇒ sin(C + A - B) = sin 45° 

⇒ C + A - B = 45°

Now putting the value of c in the equation:

⇒ A + B - 30 + A - B = 45°

⇒ 2A = 75

⇒ A = 37.5°

Now,  C = A + B - 30

⇒ 37.5 + 45 - 30

⇒ 52.5

Required sum:

⇒ A + B + C =  37.5 + 45 + 52.5

⇒ 135

∴ The correct answer is 135°. 

Shortcut TrickCalculation:

 Tan(A + B - C) = 1/√3

⇒ Tan (A + B - C) = tan 30°

⇒ (A + B - C) = 30° -------- (1)

Cos(B + C - A) = 1/2

⇒ Cos(B + C - A) = cos 60° 

⇒ (B + C - A) = 60° ------- (2)

sin(C + A - B) = 1/√2

⇒ sin(C + A - B) = sin 45° 

⇒ C + A - B = 45° -------- (3)

From eq. (1) + (2) + (3) 

⇒ B + C - A + C + A - B + A + B - C = 30 + 60 + 45

⇒ A + B + C = 135°

∴ The correct answer is 135°.

Calculation:

Average number of female athletes from England = (480 + 420 + 130 + 250)/4

⇒ 1280/4 = 320

Average number of female athletes from France = (280 + 120 + 160 + 600)/4

⇒ 1160/4 = 290

Required ratio = 320 : 290

⇒ 32 : 29 

∴ The correct option is 4.

Given:

a + 5b = 13

and ab = 9

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

⇒ a + 5b = 13

Squaring both sides

⇒ (a + 5b)² = (13)²

⇒ a² + 25b² + 2 × a × 5b = 169

⇒ a2 + 25b2 + 10ab = 169

⇒ a2 + 25b2 + (10 × 9) = 169

⇒ a2 + 25b2 = 169 - 90 

⇒ a2 + 25b2 = 79

∴ The correct answer is 79.

Given:

In △ABC

8 × ∠A = 6 × ∠B = 3 × ∠C

Concept used:

The sum of 3 angles is 180°.

Calculation:

8 × ∠A = 6 × ∠B = 3 × ∠C = K

∠ A = K/8 ; ∠B = K/6 ; ∠C = K/3

∠A : ∠B : ∠C = 3K : 4K : 8K

∠A : ∠B : ∠C = 3 : 4 : 8

Now,

(3 + 4 + 8) = 15 units = 180°

1 unit = 180/15 = 12°

⇒ ∠A = 3 units = 12 × 3 = 36°

∠B = 4 units = 12 × 4 = 48°

∠C = 8 units = 12 × 8 = 96°

∴ The correct option is 3.

Shortcut Trick

For numbers 8, 6, 2, 9 to be in proportion after subtracting P, use the formula: P = (ad − bc) / [(a + d) − (b + c)]

⇒ P = (8 × 9 − 6 × 2) / [(8 + 9) − (6 + 2)] = (72 − 12) / (17 − 8) = 60 / 9 = 20/3

First term = 3P − 6 = 3(20/3) − 6 = 14; Second term = 9P − 4 = 9(20/3) − 4 = 56

Mean proportional = √(14 × 56) = √(14 × 14 × 4) = 14 × 2 = 28

∴ The correct answer is 28.

Alternate Method

Given: Numbers are 8, 6, 2, and 9. After subtracting P, they are in proportion.

Formula: If a, b, c, d are in proportion, then a/b = c/d or ad = bc.

⇒ (8 − P) / (6 − P) = (2 − P) / (9 − P)

⇒ (8 − P)(9 − P) = (6 − P)(2 − P)

⇒ 72 − 17P + P² = 12 − 8P + P²

⇒ 72 − 12 = 17P − 8P

⇒ 60 = 9P ⇒ P = 60/9 = 20/3

⇒ Term 1 = 3P − 6 = 3(20/3) − 6 = 20 − 6 = 14

⇒ Term 2 = 9P − 4 = 9(20/3) − 4 = 60 − 4 = 56

⇒ Mean proportional = √(14 × 56) = √(784)

⇒ Mean proportional = 28

∴ The correct answer is 28.

Additional Information

Mean Proportional

The mean proportional (or geometric mean) between two numbers 'a' and 'b' is given by the formula x = √(a × b).

Continued Proportion

Three numbers a, b, and c are in continued proportion if a/b = b/c, which implies b² = ac.

Fourth Proportional

If four numbers a, b, c, and d are in proportion (a:b :: c:d), then 'd' is the fourth proportional and is calculated as d = (b × c) / a.

Shortcut Trick

Pankaj time = 140 ÷ 2.5 = 56 seconds.

Arun distance = 140 − 20 = 120 m (given 20 m start).

Arun time = 56 + 4 = 60 seconds (since he lost by 4 sec).

Arun speed = 120 ÷ 60 = 2 m/s.

∴ The correct answer is 2 m/s.

Alternate Method

Given: Total Race Distance = 140 m, Pankaj speed = 5/2 m/s = 2.5 m/s, Start given to Arun = 20 m, Beating time = 4 seconds.

Formula: Time = Distance ÷ Speed | Speed = Distance ÷ Time

⇒ Time taken by Pankaj = 140 ÷ (5/2) = (140 × 2) ÷ 5 = 280 ÷ 5 = 56 seconds.

⇒ Time taken by Arun = Time of Pankaj + Time defeat = 56 + 4 = 60 seconds.

⇒ Distance covered by Arun = Total Race − Start given = 140 − 20 = 120 m.

⇒ Speed of Arun = 120 ÷ 60 = 2 m/s.

∴ The correct answer is 2 m/s.

Additional Information

Head Start (Distance)

If A gives B a start of x meters in a race of L meters, B only needs to cover (L − x) meters to reach the finish line.

Beating by Time

If A beats B by t seconds, it means B takes t seconds more than A to complete his designated distance.

Dead Heat

A race is called a dead heat if all contestants reach the finish line at exactly the same time.

Calculation:

Let the run score by the team A in 7^th over = x

Run score by the team A in 8^th over = (x - 5)

Run score by the team A in 9^th over = (x + 6)

Average run scored in first nine overs = 9

⇒ {4 + 15 + 8 + 7 + 10 + 3 + x + (x - 5) + (x + 6)}/9 = 9

⇒ 48 + 3x = 9 × 9

⇒ 3x = 81 - 48 

⇒ x = 33/3 = 11

Run score by the team in 8^th over = (x - 5)

⇒ (11 - 5) = 6

∴ The correct answer is 6.

Given:

The customer gets 7 books free on buying 13 books.

Formula used:

Discount% = (free item × 100)/total item

Calculation:

Discount% = (7 × 100)/(13 + 7)

⇒ (7 × 100)/20

⇒ 7 × 5 = 35%

∴ The correct answer is 35%.

Given:

Principal = Rs.3,20,000

Amount = Rs.4,05,000

Rate = 12.5%

Formula used:

Amount = P × (1 + R%)^T

Where, P = principal ; T = time ; R = rate

Calculation:

Amount = P × (1 + R%)T

⇒ 405000 = 320000 × {1 + (12.5/100)}^T

⇒ 81 = 64 × {1 + (12.5/100)}^T

⇒ 81/64 = {112.5/100}T

⇒ {9/8}T = (9/8)²

So, time (T) = 2 years

∴ The correct answer is 2 years.

Given:

A can finish a work = 24 days

B can finish a work = 30 days

Concept used:

Total work = efficiency × time

Calculation:

Total work complete in 11 days = (5 + 4) × 11 = 9 × 11 = 99 units

Percentage of work to be completed = {100 - (99 × 100)/120}

⇒ {100 - (33 × 5)/2}

⇒ (100 - 82.5)% = 17.5%

∴ The correct answer is 17.5%.

Given:

ΔLMN ∼ ΔPQR

∠L = 40°, ∠N = 80°

PQ = 7.5 cm, LN = 8 cm

Concept used:

If ΔABC ∼ ΔDEF then their corresponding side's ratio are equal.

AB/DE = BC/EF = AC/DF

The sum of all angles in a triangle is 180°.

Calculation:

ΔLMN ∼ ΔPQR then,

⇒ LM/PQ = LN/PR

⇒ 6/7.5 = 8/x

⇒ 6x = 8 × 7.5

⇒ x = 60/6 = 10 cm

In ΔLMN

⇒ ∠L + ∠M + ∠N = 180°

⇒ 40° + ∠M + 80° = 180°

⇒ ∠M = 180 - 120 = 60°

ΔLMN ∼ ΔPQR then,

⇒ ∠M = ∠Q = 60° 

∴ The correct option is 4.

Given:

O₂E (r2)= 2.4 cm

O₁D (r1) = 4 cm

Distance between centers (d) = O1O2 = 6.5 cm

Formula used:

Common tangent = √{d² - (r₁ - r₂)²}

Calculation:

 

Common tangent (DE) = √{d2 - (r1 - r2)2}

⇒ √{(6.5)2 - (4 - 2.4)2}

⇒ √{(42.25 - (1.6)2}

⇒ √{(42.25 - 2.56}

⇒ √39.69 = 6.3 cm

∴ The correct answer is 6.3 cm.

Given:

​$\frac{(1 + secθ)}{secθ}$ × (1 - cosθ)

Formula used:

Sec² θ - 1 = tan² θ

A² - B² = (A + B) × (A - B)

Tan θ = sin θ/cos θ  

Calculation:

$\frac{(1 + secθ)}{secθ}$ × (1 - cosθ)

⇒ $\frac{(1 + secθ)}{secθ}$ ×  (1 - 1/secθ)

⇒ $\frac{(1 + secθ)}{secθ}$ ×  (sec θ - 1)/sec θ

⇒ (sec² θ - 1)/sec² θ

⇒ Tan² θ × cos² θ

⇒ (sin² θ × cos2 θ)/cos2 θ 

⇒ sin² θ

∴ The correct answer is sin2 θ. 

​

Calculation:

From the table above we can say

H is the second highest run scorer among all 8 other batsmen.

∴ The correct option is 4.

Shortcut Trick

Extra interest is generated solely by the increased rate over the time period.

Total percentage increase in interest = 6% × 4 years = 24%

Given, 24% of Principal (P) = Rs. 600

⇒ P = 600 ÷ 0.24 = Rs. 2,500

Value of 2.5 P = 2.5 × 2,500 = Rs. 6,250

∴ The correct answer is Rs. 6,250.

Alternate Method

Given:

Principal = Rs. P | Time (T) = 4 years | Increase in Rate (ΔR) = 6% | Increase in Interest (ΔI) = Rs. 600

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ ΔInterest = (P × ΔRate × Time) ÷ 100

⇒ 600 = (P × 6 × 4) ÷ 100

⇒ 600 = 24P ÷ 100

⇒ P = (600 × 100) ÷ 24

⇒ P = 25 × 100 = Rs. 2,500

⇒ Value of 2.5 P = 2.5 × 2,500

⇒ 2.5 P = Rs. 6,250

∴ The correct answer is Rs. 6,250.

Additional Information

Relationship between Interest and Rate

Simple Interest is directly proportional to the Rate of interest. If the rate increases by r% for t years, the interest increases by (r × t)% of the principal.

Amount Formula

The total Amount (A) in simple interest is given by A = P + SI = P × (1 + RT/100).

Rate of Interest Calculation

The Rate (R) can be found if other variables are known using R = (SI × 100) ÷ (P × T).

Shortcut Trick

Use the Successive Percentage formula for Net Gain/Loss: Net % = a + b + (ab / 100)

Here, a = +90 (Markup) and b = −40 (Discount).

Net Change = 90 − 40 + [90 × (−40) / 100]

Net Change = 50 − 36 = 14%.

∴ The correct answer is 14%.

Alternate Method

Given:

Markup Percentage = 90%

Discount Percentage = 40%

Let the Cost Price (CP) of the goods be 100.

⇒ Marked Price (MP) = CP + 90% of CP

⇒ MP = 100 + (90/100) × 100 = 190

⇒ Discount = 40% of MP

⇒ Discount = (40/100) × 190 = 76

⇒ Selling Price (SP) = MP − Discount

⇒ SP = 190 − 76 = 114

⇒ Gain = SP − CP = 114 − 100 = 14

⇒ Gain Percentage = (Gain / CP) × 100

⇒ Gain % = (14 / 100) × 100 = 14%

∴ The correct answer is 14%.

Additional Information

Markup Percentage

It is the extra price added to the Cost Price to arrive at the Marked Price. Formula: Markup % = [(MP − CP) / CP] × 100.

Discount and Selling Price

Discount is always calculated on the Marked Price (MP). Formula: SP = MP × [1 − (Discount % / 100)].

Relationship between CP, MP, and Profit

The ratio of MP to CP can be expressed as: MP / CP = (100 + Profit %) / (100 − Discount %).

Given:

Selling price (S.P) of A = Rs.4860

Loss% for A = 19%

Concept used:

If profit is P%, then

Selling price (S.P) = Cost price (C.P) × (100 + P)%

If the loss is L%, then

Selling price (S.P) = Cost price (C.P) × (100 - L)%  

Calculation:

C.P for A = (4860 × 100)/(100 - 19)

⇒ (4860 × 100)/81

⇒ 60 × 100 = 6000

S.P of B = 6000 × 117% = Rs.7020

Gain for B = (7020 - 4860) = Rs.2160

∴ The correct answer is Rs.2160.

Shortcut Trick

Base circumference = 2 × π × r = 154 cm

⇒ r = 154 ÷ (2 × 22 ÷ 7) = 24.5 cm

⇒ Curved Surface Area (CSA) of hemisphere = 2 × π × r² = Circumference × r

⇒ CSA = 154 × 24.5 = 3773 cm²

⇒ Total painting cost = (3773 ÷ 100) × 4 = 150.92

∴ The correct answer is Rs. 150.92.

Alternate Method

Given:

Circumference of the dome base = 154 cm

Cost of painting = Rs. 4 per 100 cm²

Formula Used:

Circumference of base = 2 × π × r

Curved Surface Area (CSA) of hemisphere = 2 × π × r²

Total Cost = (CSA ÷ 100) × Rate

Calculations:

⇒ 2 × π × r = 154

⇒ 2 × (22 ÷ 7) × r = 154

⇒ r = (154 × 7) ÷ 44

⇒ r = 24.5 cm

⇒ Area to be painted (CSA) = 2 × (22 ÷ 7) × 24.5 × 24.5

⇒ CSA = (44 ÷ 7) × 600.25

⇒ CSA = 44 × 85.75 = 3773 cm²

⇒ Total Cost = (3773 ÷ 100) × 4

⇒ Total Cost = 37.73 × 4 = 150.92

∴ The correct answer is Rs. 150.92.

Additional Information

Total Surface Area (TSA) of a Hemisphere

The total surface area includes the curved surface and the flat circular base. Formula: TSA = 3 × π × r².

Volume of a Hemisphere

It represents the capacity or space occupied by the hemisphere. Formula: Volume = (2 ÷ 3) × π × r³.

Surface Area of a Full Sphere

The total curved surface of a complete sphere is double the CSA of a hemisphere. Formula: Surface Area = 4 × π × r².

The correct answer is: "Who wrote these letters?"

Key Points

• In the passive voice, the focus is on the receiver of the action, and the doer is often placed in a prepositional phrase.
• Structure: Subject + Verb + Agent +?
• In the active voice, the emphasis is on the doer of the action, resulting in a more direct and concise sentence.
• Structure: Subject + Verb + Object + ?
• In the original sentence, "By whom" is the passive construction, indicating that the action (writing the letters) is being done to the letters by an unidentified person.
• In the active voice transformation, "Who" becomes the subject, and "wrote" is the active verb, clearly identifying the doer of the action.
• The emphasis shifts from the letters to the person who wrote them, resulting in a more direct and straightforward sentence.

Thus, option 4 is the correct answer.

The correct answer is: "The cat chased the mice."

Key Points

• Passive Voice: "The mice were chased by the cat."
• Structure: Subject (The mice) + Verb (were chased) + Object (by the cat)
• The mice (Subject) receive the action of being chased.
• "Were chased" is the passive verb phrase.
• "By the cat" is a prepositional phrase indicating the doer of the action.
• Active Voice: "The cat chased the mice."
• Structure: Subject (The cat) + Verb (chased) + Object (the mice)
• The cat (Subject) performs the action of chasing.
• "Chased" is the active verb.
• "The mice" is the direct object receiving the action.
• In the passive voice, the focus is on the mice (the receiver of the action), and the cat (the doer) is placed in a prepositional phrase.
• In the active voice, the emphasis shifts to the cat as the doer of the action, resulting in a more straightforward and direct sentence.

Therefore, the correct answer is option 1.

The correct answer is: "It is imperative in understanding."

Key Points

• The error is in the use of the phrase "in understanding." It should be "to understand" instead.
• "To understand" is more direct and clear, specifying the action that is imperative.
• "Imperative to" is a more common and idiomatic construction when expressing the necessity or importance of an action.
• The use of "to understand" maintains grammatical consistency with the structure of the sentence.
• The construction "to understand" is an example of the "to + infinitive" form of the verb.
• In English, the infinitive form of a verb is the base form preceded by the particle "to."
• By using "to understand," the sentence flows more smoothly and conveys the idea that understanding the rising importance of artificial intelligence is imperative for achieving the desired outcomes in the public sector.

Thus, option 2 is the correct answer.

The correct answer is: "accept; except".

Key Points

• Accept: This means to agree to receive or undertake something that is offered. (जो कुछ प्रस्तावित किया गया है उसे प्राप्त करने या करने के लिए सहमत होना)
• In the sentence, the person is willing to receive any job offer.
• Except: This means excluding or not including. (शामिल करना या न करना)
• In the context of the sentence, the person is willing to accept any job offer except for the one that involves working on weekends.
• So, the sentence conveys that the person is open to considering and agreeing to most job offers but has a specific condition regarding working on weekends.

Therefore, the correct answer is option 4.

The correct homophones to fill in the blanks are: I will accept any job offer except for the one that requires me to work on weekends.

The correct answer is: B, A, D, C

Key Points

 

• Sentence B introduces the topic of the paragraph, which is the changes in the teaching-learning process in the educational sector.
• Sentence A explains that these changes were bound to happen due to technological advancements.
• Sentence D provides further explanation by stating that the constant evolution in academics has also contributed to these changes.
• Sentence C concludes the paragraph by suggesting that educators must willingly accept and embrace these changes to excel in their profession.

Therefore, the correct answer is option 3.

The correct answer is: "If he expresses"

Key Points

• In English, conditional sentences often use the present simple tense in the "if" clause.
• This is because the action in the "if" clause (expressing love impressively, in this case) is generally a habitual or factual condition.
• Therefore, the usage of "if he expresses" is more appropriate than "if he will express."
• "Expresses" is in the present simple tense and is commonly used in conditional sentences to indicate a general truth or habitual action.
• This emphasizes that the person (he) is actively involved in expressing his feelings.

Thus, option 3 is the correct answer.

The correct answer is: Certainty

Key Points

• The given sentence talks about being aware of the possibility of natural disasters.
• Potential: The capability or possibility for something to happen or develop; having the capacity or ability. (किसी चीज़ के घटित होने या विकसित होने की क्षमता या संभावना; क्षमता या योग्यता होना)
• Example: His potential as a leader became evident when he successfully led the team to victory.
• Marked option Certainty: The state of being certain, sure, or confident about something; the quality of being definite or unquestionable. (किसी चीज़ के बारे में निश्चित, सुनिश्चित या आश्वस्त होने की अवस्था; निश्चित या निर्विवाद होने का गुण)
• Example: The scientific experiment yielded conclusive results, providing a high level of certainty about the hypothesis.
• Hence, the antonym of 'potential' is 'certainty'.

Thus, option 2 is the correct answer.

Additional Information

• Maze: A complex network of paths or passages. (पथों या मार्गों का एक जटिल नेटवर्क)
• Knot: A fastening made by tying a piece of string, rope, or something similar. (डोरी, रस्सी या ऐसी ही किसी वस्तु को बांधकर बनाया गया बंधन)
• Neuter: Having no gender. (जिसका कोई लिंग न हो)

The correct answer is: Spoil somebody's chance of doing something.

Key Points

• The idiom "queer pitch" means to spoil somebody's chance of doing something, especially in a sly or underhanded way. (किसी के कुछ करने के अवसर को ख़राब करना, विशेष रूप से धूर्ततापूर्वक या गुप्त तरीके से)
• The word "queer" in this context means strange or suspicious.
• The word "pitch" refers to a situation or opportunity.
• Example: The rival team's coach tried to queer our pitch by bribing the referees.

Therefore, option 4 is the correct answer.

The correct answer is: "He has bigger fish to fry."

Key Points

• The phrase "bigger fish to fry" means that someone has more important or pressing matters to attend to. (किसी के पास ध्यान देने के लिए अधिक महत्वपूर्ण या अत्यावश्यक मामले हैं)
• The phrase is a common idiom in the English language.
• Example: He had bigger fish to fry, so he didn't get involved in the minor office disputes.

Thus, option 2 is the correct answer.

Substituted sentence: Ravindra has left the friends' meeting saying that he has bigger fish to fry.