SSC CHSL Tier-1 2023: Official Paper (Held On: 08 Aug, 2023 Shift 2) (Previous Year Paper)

Select the correct mirror image of the given figure when the mirror is placed at MN as shown.

Hence, 'option 4' is the correct answer.

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

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

Clearly, B is grandmother i.e., Mother's mother of E.

Hence, ‘Mother's mother’ is the correct answer.

The logic followed here is:

Difference between the numbers is prime number series from 71 to 83.

Hence, '346' is the correct answer.

Given equation: 5 - 9 × 8 ÷ 12 + 4 = ?

 If '+' and '÷' are interchanged and '×'and '-'are interchanged, then the equation becomes:

5 × 9 - 8 + 12 ÷ 4 = ?

By BODMAS rule:

⇒ 5 × 9 - 8 + 12 ÷ 4 = ?

⇒ 5 × 9 - 8 + 3 = ?

⇒ 45 - 8 + 3 = ?

⇒ 48 - 8 = ?

⇒ 40 = ?

Hence, '40' is the correct answer.

The logic followed here is:

Hence, '423' is the correct answer.

The logic followed here is:

Hence, '53' is the correct answer.

The logic followed here is:

• 
• 

Similarly,

• 

Hence, 'EHHHUZM' is the correct answer.

The logic followed here is:

Hence, 'NSUA' is the correct answer.

The logic followed here is:

Hence, 'GB 23' is the correct answer.

The code for each word is shown below:

Clearly, 'come' is written as 'fi' in the given language.

Hence, 'fi' is the correct answer.

The least possible Venn diagram is: 

Conclusion (I): Some tulips are orchids → Does not follow (As, there is no definite relation between tulips are orchids. Hence, false)

Conclusion (II): No orchid is a rose → Follows (Since all orchids are lilies and no lily is a rose, it is definite that no orchid is a rose)

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

The logic followed here is:

1. RSU → R + 1 = S; S + 2 = U
2. XYA → X + 1 = Y; Y + 2 = A
3. DEG → D + 1 = E; E + 2 = G
4. ZAB → Z + 1 = A; A + 2 = C ≠ B

Hence, 'ZAB' is the correct answer.

The logic followed here is:

Hence, 'ZF 50' is the correct answer.

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

  

  

Thus, there are total 19 triangles in the given figure.  

Hence, "19" is the correct answer.

According to given figure:

The figure will appear when it is opened as follows:

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

Given : 15^th January 1996 was a Monday

Explanation :

The number of odd days from 15^th January 1996 to 30^th March 1997 :

∴ The number of odd days from 15^th January 1996 to 30^th March 1997 ⇒ 6

⇒So, Six odd day get added to Monday because day asked in future.

∴ Sunday was the day of the week on the 30^th March 1997.

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 : (1^st number × 9) - 8 = 2^nd number

Given :

• (42, 370)

(42 × 9) - 8 = 370

378 - 8 = 370

370 = 370 (LHS = RHS)

• (57, 505)

(57 × 9) - 8 = 505

513 - 8 = 505

505 = 505 (LHS = RHS)

So,

• Option - (1) : (29, 253)

(29 × 9) - 8 = 253

261 - 8 = 253

253 = 253 (LHS = RHS)

• Option - (2) : (31, 288)

(31 × 9) - 8 = 288

279 - 10 = 288

279 ≠ 288 (LHS ≠ RHS)

• Option - (3) : (49, 449)

(49 × 9) - 8 = 449

441 - 8 = 449

433 ≠ 449 (LHS ≠ RHS)

• Option - (4) : (84, 747)

(84 × 9) - 8 = 747

756 - 8 = 747

748 ≠ 747 (LHS ≠ RHS)

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

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

1. For '

' element → Alternately replacing with '

' element.

2. For '

' element → → Alternately replacing with '

' element.

Final series is

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

Given : 71 - 11 × 484 ÷ 88 + 30 = ?

According to the question, after replacing the signs :

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

So,​​

71 + 11 ÷ 484 × 88 - 30 = ?

71 + 0.022 × 88 - 30 = ?

71 + 2 - 30 = ?

73 - 30 = ?

Hence, "43" is the correct answer.

Given :

Statement given : P × Q + R - S ÷ T

So,

• P × Q → P is the father of Q.

• Q + R → Q is the wife of R.

• R - S → R is the brother of S.

• S ÷ T → S is the mother of T.

​

Thus, according to the final family tree :-

1. Option - (1) : T is the son of S ⇒ As T can be either son or daughter of S, therefore this statement is false.
2. Option - (2) : Q is the sister of S ⇒ Q is the sister-in-law of S, therefore this statement is false.
3. Option - (3) : R is T's mother's brother ⇒ R is maternal uncle of T, therefore this statement is true.
4. Option - (4) : P is the father of R ⇒ P is the father-in-law of R, therefore this statement is false.

Here, "R is T's mother's brother" statement is true.

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

Logic : [1^st number × (1^st number + 4)] = 2^nd number

So,

• Option - (1) : 5:45

5 × (5 + 4) = 45

5 × 9 = 45

45 = 45 (LHS = RHS)

• Option - (2) : 2:10

2 × (2 + 4) = 10

2 × 6 = 10

12 ≠ 10 (LHS ≠ RHS)

• Option - (3) : 3:21

3 × (3 + 4) = 21

3 × 7 = 21

21 = 21 (LHS = RHS)

• Option - (4) : 4:32

4 × (4 + 4) = 32

4 × 8 = 32

32 = 32 (LHS = RHS)

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

The logic followed here is :-  (2) is added to the position value according to English alphabetic series.

​So,

• 'JOSV’ is written as 'LQUX'

​

And,

• 'EJNQ' is written as 'GLPS'

​

​Similarly,

• 'DIMP' is written as

​

Hence, "FKOR" is the correct answer.

Given : 72 - 33 × 605 ÷ 110 + 70 = ?

According to the question, after replacing the signs :

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

So,​​

72 + 33 ÷ 605 × 110 - 70 = ?

72 + 0.054 × 110 - 70 = ?

72 + 6 - 70 = ?

78 - 70 = ?

8 = ?

Hence, "8" is the correct answer.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some directors are writers → Does not Follow (As, all directors are actors and some actors are writers. So, it is possible but not definitely true.)

II. No producer is a director → Does not Follow (As, all directors are actors, some actors are writers and no writer is a producer. So, it is possible but not definitely true.)

So, Neither conclusion I nor II follows.

Hence, the correct answer is "Neither conclusion I nor II follows".

Given : 19 December 1992 was Saturday

Explanation :

The number of odd days from 19 December 1992 to 22 December 2009 :

∴ The number of odd days from 19 December 1992 to 22 December 2009 ⇒ 3

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

∴ Tuesday was the day of the week on the 22 December 2009.

Hence, "Tuesday" 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 correct answer is French.

 Key Points

• Joseph Francois Dupleix:-
• He was the Governor General of the French East India Company in India.
• He served as the Governor General from 1742 to 1754.
• Dupleix was known for his ambitious plans to expand French influence in India and played a key role in the Carnatic Wars.
• Under his leadership, the French East India Company established a strong presence in India and competed with the British East India Company for dominance.

The correct answer is Triple jump indoor.

Key Points

• Praveen Chithravel:-
• He is associated with the sport of Triple Jump Indoor.
• He missed out on a medal at the Commonwealth Games 2022 but made a strong comeback to win silver at the Asian Championships with a national indoor record.
• Praveen Chithravel's silver medal at the Asian Championships with a national indoor record is a significant achievement in the sport of Triple Jump Indoor.
• Triple Jump Indoor:-
• It is a track and field event in which athletes jump as far as possible with a hop, step, and jump technique.

Additional Information

• Shot Put Indoor:-
• It is a track and field event in which athletes throw a heavy spherical object as far as possible.
• Long Jump Indoor:-
• It is a track and field event in which athletes jump as far as possible from a running start.
• 800m Indoor:-
• It is a middle-distance running event in which athletes run two laps of a 400m track indoors.

The correct answer is consumption goods and capital goods.

Key Points

• Final goods:-
• These are those goods that are ready for consumption or use by the end consumer.
• Consumption goods:-
• These are those goods that are used for immediate satisfaction of human needs and wants, such as food, clothing, and electronics.
• Capital goods:-
• These are those goods that are used to produce other goods and services, such as machinery and equipment.

Additional Information

• Raw materials:-
• These are those materials that are used to produce goods, while semi-finished goods are those goods that are partially completed but still require further processing to become final goods.
• Single goods:-
• These are those goods that are not composed of multiple parts or components, while composite goods are those goods that are composed of multiple parts or components.

The correct answer is Mohiniyattam.

Key Points

• Neena Prasad:-
• She was awarded the Sangeet Natak Akademi Award 2021 for her contribution to Mohiniyattam, a classical dance form from Kerala.
• Neena Prasad is a renowned Mohiniyattam dancer and choreographer, who has been actively promoting and preserving the art form for several years.
• Mohiniyattam:-
• ​It is known for its graceful movements, subtle expressions, and intricate hand gestures.

Additional Information

• Bharatanatyam:-
• It is a classical dance form from Tamil Nadu, characterized by its fast footwork, complex rhythms, and dramatic expressions.
• Kuchipudi:-
• It is a classical dance form from Andhra Pradesh, known for its dynamic movements, intricate footwork, and dramatic storytelling.
• Odissi:-
• It is a classical dance form from Odisha, characterized by its fluid movements, curved postures, and intricate hand gestures.

The correct answer is Mizoram.

Key Points

• Pawl Kut:-
• It is a thanksgiving festival celebrated by the Mizos, an ethnic group belonging to the state of Mizoram in India.
• It is usually celebrated in the month of February and is a harvest festival that marks the end of the agricultural year.
• The festival is characterized by traditional dances, music, and feasting, where people gather to express gratitude for a bountiful harvest and seek blessings for the coming year.
• The festival also has religious significance as it involves the offering of prayers to the deity of harvest and fertility, called Pathian.

The correct answer is Indian federation was the result of an agreement by sovereign units to join it.

Key Points

• 'Union of States':-
• It is mentioned in the Preamble of the Constitution of India, which describes India as a 'sovereign socialist secular democratic republic' that is a 'Union of States'.
• The Union of States structure has several implications for the governance of India:
• Division of power: The Constitution clearly divides power between the central government and the states. The central government has exclusive power over certain subjects, such as defense, foreign affairs, and currency. The states have exclusive power over other subjects, such as public order, education, and health. There is also a concurrent list of subjects, where both the central government and the states have power to legislate.
• Cooperative federalism: The relationship between the central government and the states is not adversarial but rather cooperative. Both levels of government need to work together to achieve common goals, such as economic development and social welfare.
• Unity in diversity: India's vast diversity is one of its greatest strengths. The Union of States structure allows for a balance between national unity and regional diversity. Each state has its own unique culture, language, and traditions, but they are all bound together by a common Indian identity.

The correct answer is Hermann Kolbe.

Key Points

• Hermann Kolbe:-
• He is a German chemist who used the technique of preparing hydrocarbons by electrolysis of solutions of salts of fatty acids. He discovered this method in 1845.

Additional Information

• Cecilia Payne:-
• She was an astronomer who made groundbreaking discoveries about the composition of stars.
• She determined that stars are mostly composed of hydrogen and helium, which was a revolutionary idea at the time.
• Marcellin Berthelot:-
• He was a French chemist who made significant contributions to the fields of thermochemistry and organic chemistry.
• He is known for his work on the synthesis of organic compounds and the study of chemical reactions.
• Giulio Natta:-
• He was an Italian chemist who won the Nobel Prize in Chemistry in 1963 for his work on the stereospecific polymerization of propylene.
• This work led to the development of new types of plastics and materials.

The correct answer is 2^nd Five Year Plan.

Key Points

• Mahalanobis Plan:-
• It was implemented during the 2^nd Five Year Plan from 1956-1961.
• It was named after the Indian statistician Prasanta Chandra Mahalanobis who played a key role in its formulation.
• The plan focused on the development of heavy industries and infrastructure, with an emphasis on import substitution.
• The Mahalanobis Plan was criticized for its reliance on centralized planning and neglect of agriculture.

Additional Information

• 1^st Five Year Plan (1951-1956):-
• It focused on agriculture, with a goal of achieving food self-sufficiency.
• 3^rd Five Year Plan (1961-1966):-
• It was also known as the "Gadgil-Yojana" after its chief architect, V.K.R.V. Rao.
• 4^th Five Year Plan (1969-1974):-
• It was the first plan to be formulated after the devaluation of the Indian rupee in 1966, which had a significant impact on the country's economy.

The correct answer is Surendranath Banerjee.

Key Points 

• Indian Association:-
• It was founded in 1876 in Calcutta (now Kolkata) by Surendranath Banerjee and Anand Mohan Bose.
• Indian Association was a political organization that aimed to promote the interests of the Indian community and to work towards the attainment of political rights and freedom from British rule.Indian Association played a significant role in the Indian National Movement and was one of the first organizations to demand self-government and representation for Indians in the British colonial administration.
• Surendranath Banerjee:-
• He was a prominent Indian nationalist leader and a member of the Indian National Congress.
• He was also a journalist, lawyer, and a member of the Bengal Legislative Council.

Additional Information

• Dada Bhai Naoroji:-
• He was a prominent Indian nationalist leader and a member of the Indian National Congress.
• He was also a scholar, social reformer, and a member of the British Parliament.
• He is known for his theory of the "drain of wealth" from India to Britain and his advocacy for Indian self-rule.
• Gopal Krishna Gokhale:_
• He was a prominent Indian nationalist leader and a member of the Indian National Congress.
• He was also a social reformer, educator, and a member of the Bombay Legislative Council.
• He is known for his advocacy for constitutional reforms, education, and social justice.
• Pheroz Shah Mehta:-
• He was a prominent Indian nationalist leader and a member of the Indian National Congress.
• He was also a lawyer, journalist, and a member of the Bombay Legislative Council.
• He is known for his advocacy for civil liberties, education, and social reform.

The correct answer is Only iii is correct.

Key Points

• The value of money is determined by the demand and supply of money in the economy.
• The price level is determined by the demand and supply of goods and services in the economy.
• Therefore, the value of money and the price level have an indirect relationship.
• When the price level increases, the value of money decreases and vice versa.

The correct answer is Public affairs.

Key Points

• Padma Vibhushan:-
• Padma Vibhushan is the second-highest civilian award in India, after Bharat Ratna.
• It is awarded for exceptional and distinguished service in any field including art, literature, science and engineering, sports, medicine, social work, public affairs, civil service, trade and industry.
• Mulayam Singh Yadav received the Padma Vibhushan award in 2023 in the category of Public Affairs.
• Mulayam Singh Yadav:-
• He was a prominent Indian politician who served as the Chief Minister of Uttar Pradesh three times and was also the founder of the Samajwadi Party.

The correct answer is Only A.

Key Points

• Increase repo rate:
• This is the rate at which commercial banks borrow money from the Reserve Bank.
• By increasing the repo rate, the Reserve Bank makes it more expensive for banks to borrow money, which reduces the amount of money in circulation and helps to control inflation.

The correct answer is Jaychand and Muhammad Ghori.

 Key Points

• Battle of Chandawar:-
• It took place in 1194 AD.
• The battle was fought between the Hindu king Jaychand and the Muslim invader Muhammad Ghori.
• It was a significant battle in the history of India as it marked the end of the Chauhan dynasty and the beginning of the Muslim rule in Northern India.

Additional Information

• Mahmood Gaznavi:-
• He was a ruler from the 10^th century and had no involvement in the Battle of Chandawar.

The correct answer is Vitamin D.

Key Points

• Vitamin D:-
• It is the vitamin that is synthesized in the presence of sunlight in our body.
• When the skin is exposed to sunlight, a type of cholesterol present in the skin is converted into vitamin D.
• Vitamin D is essential for bone health as it helps the body absorb calcium and phosphorus.
• Deficiency of vitamin D can lead to rickets in children and osteoporosis in adults.

Additional Information

• Vitamin B:
• There are several types of vitamin B such as B1, B2, B6, B12, etc.
• These vitamins are essential for maintaining good health and well-being.
• They play a crucial role in the metabolism of energy, red blood cell production, and brain function.
• Vitamin C:
• Also known as ascorbic acid, vitamin C is an antioxidant that helps protect cells from damage caused by free radicals.
• It is also important for the growth and repair of tissues in the body.
• Vitamin A:
• This vitamin is important for maintaining good vision, skin health, and immune function.
• It is found in animal products such as liver, fish, and eggs, as well as in some plant-based foods like carrots and sweet potatoes.

The correct answer is Koneru Humpy.

Key Points

• Koneru Humpy:-
• She won the India's first ever silver medal at FIDE World Rapid and Blitz Championship 2022.
• She is a renowned Indian chess grandmaster who has won several accolades and titles in her career.

Additional Information

• Harika Dronavalli:-
• She is another Indian chess grandmaster who has won several international tournaments and represented India in the Chess Olympiad.
• Bhakti Kulkarni:-
• She is an Indian chess player who has won several national and international tournaments and is a former National Women's Premier Chess Champion.
• Tania Sachdev:-
• She is an Indian chess player who has won several international tournaments and represented India in the Chess Olympiad.
• FIDE World Rapid and Blitz Championship:-
• It is an international chess tournament organized by the World Chess Federation (FIDE) where players compete in rapid and blitz chess games.

The correct answer is intervention to expand or reduce the demand.

Key Points

• Stabilisation function:-
• It is aimed at maintaining economic stability by adjusting the level of aggregate demand in the economy.
• The stabilization function of the government budget is a macroeconomic concept that deals with the management of the overall level of economic activity in the economy.

Additional Information

• Fiscal policy tools:-
• These are used by the government to influence the level of aggregate demand in the economy. Expansionary fiscal policy involves increasing government spending, reducing taxes, and increasing borrowing to stimulate economic growth. In contrast, contractionary fiscal policy involves reducing government spending, increasing taxes, and reducing borrowing to slow down economic growth.
• Allocation of resources:-
• It is an important function of the government, which involves the distribution of resources among different sectors of the economy to achieve economic efficiency and equity.
• Production of public goods:-
• It is another important function of the government, which involves the provision of goods and services that are not provided by the private sector, such as national defense, public health, and education.
• Distribution of income in society:-
• It is an important issue that involves the fair distribution of income among different groups in the economy. The government can use taxation and social welfare programs to achieve a fair distribution of income.

The correct answer is The Satpura Range is in the South of the Plateau.

Key Points

• Deccan Plateau:-
• It is a large plateau in southern India, covering most of the southern part of the country.
• It is bordered by the Eastern Ghats to the east, the Western Ghats to the west, the Satpura Range to the north, and the Nilgiri Hills to the south.
• The Deccan Plateau is known for its rich cultural and historical heritage, with several ancient kingdoms and empires having ruled over the region.

Additional Information

• Eastern Ghats:-
• These are a range of mountains that run parallel to the east coast of India, and are known for their scenic beauty and biodiversity.
• Western Ghats:-
• These are a UNESCO World Heritage Site and are known for their unique and diverse ecosystems, including rainforests, grasslands, and wetlands.
• Vindhya Range:-
• This is a range of hills and mountains that run parallel to the northern edge of the Deccan Plateau and are known for their mineral wealth and scenic beauty.

The correct answer is Phthalaldehyde.

Key Points

• Phthalaldehyde:-
• It is the dialdehyde referred to in the question, which has two formyl groups attached to adjacent carbon centers on a benzene ring.
• It forms fluorescent conjugation products with primary amines, making it useful in various analytical and diagnostic applications.

Additional Information

• Acetaldehyde:-
• ​It is a simple aldehyde with a characteristic pungent odor, commonly used in the production of chemicals and plastics.
• Valeraldehyde:-
• It is a five-carbon aldehyde with a fruity odor, used in the production of fragrances and flavors.
• Isobutyraldehyde:-
• It is a four-carbon aldehyde with a pungent odor, used in the production of chemicals and solvents.

The correct answer is Kerala.

Key Points

• Chavittukali:-
• It is a traditional folk dance form that originated in the state of Kerala, India.
• It is believed to have been introduced by the Portuguese during their colonial rule in the region.
• The dance is characterized by its use of distinct footwear called "chavittu" that produces a rhythmic sound when struck against the ground.
• Chavittukali is typically performed during Christian festivals and celebrations in Kerala.

The correct answer is 117 per sq km.

Key Points

• Census 1951:-
• There were approximately 117 people living in every square kilometer of land in India in 1951.
• The density of population has increased significantly since then, with the latest Census of 2011 reporting a density of 382 per sq km.

Additional Information

• Density of population:-
• It refers to the number of people living in a particular area, usually measured as the number of people per square kilometer of land.

The correct answer is Jawaharlal Nehru.

 Key Points

• Jawaharlal Nehru:-
• He made the statement that the Constitution of free India must be framed without outside interference by a constituent assembly elected on the basis of adult franchise.
• This statement was made in the context of India's struggle for independence from British colonial rule and the need to establish a democratic and representative government.

Additional Information

• MN Roy:-
• He was a political philosopher and activist who was associated with the Communist Party of India and advocated for socialist principles.
• Sardar Patel:-
• He was a prominent leader in the Indian independence movement and played a key role in the integration of princely states into the newly independent India.
• Mahatma Gandhi:-
• He was a spiritual and political leader who was instrumental in India's nonviolent struggle for independence and advocated for principles of truth, nonviolence, and self-reliance.

The correct answer is Rajasthan and Madhya Pradesh.

Key Points

• Chambal Project:-
• The joint venture of Chambal Project involves the states of Rajasthan and Madhya Pradesh.
• The Chambal River flows through these two states, and the project aims to harness its water resources for various purposes such as irrigation, power generation, and drinking water supply.
• Rajasthan and Madhya Pradesh have equal shares in the project, with each state contributing towards the construction and maintenance of the infrastructure.
• The project has been successful in achieving its objectives, and has benefited the farmers and residents of the region.

The correct answer is Ricky Kej.

Key Points

• Ricky Kej:-
• He is an Indian music composer who won the Grammy Award for Best New Age Album in the year 2015 for his album "Winds of Samsara".

 Additional Information

• MM Keeravani:-
• He is a popular Indian music composer who has won several awards for his work in Telugu cinema.
• He is known for composing music for films like Baahubali and Magadheera.
• Aby Tom Cyriac:-
• He is a relatively unknown music composer from Kerala who has composed music for a few Malayalam films.
• AR Rahman:-
• He is a legendary Indian music composer who has won several awards including Oscars, Grammys and BAFTAs.
• He is known for his work in films like Slumdog Millionaire, Roja and Dil Se.

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

Key Points

• Jhuming:-
• It is a type of shifting agriculture practiced in the North Eastern region of India.
• Dahiya:-
• It is a type of shifting agriculture practiced in Madhya Pradesh.
• Penda:-
• It is a type of shifting agriculture practiced in Andhra Pradesh.
• Kumari:-
• It is a type of shifting agriculture practiced in the Western Ghats.

Additional Information

• Shifting agriculture:-
• It is a traditional method of farming where farmers move from one place to another after a few years to allow the land to regenerate.

The correct answer is 2020.

Key Points

• Val Barker Cup:-
• It is a prestigious award given to the most outstanding boxer in the Olympics Games.
• However, the cup was not awarded in the Olympics Games of 2020.
• The cup was awarded in the previous three Olympics Games of 2016, 2012, and 2008.
• The decision to not award the cup in 2020 might have been due to the COVID-19 pandemic and the changes in the schedule and format of the games.
• The Val Barker Cup is named after a British sports journalist who covered boxing in the early 1900s and was known for his fair and unbiased reporting.

Given

Amount = 2.10 lakh

Rate = 5%

Formula used

Amount = P(1 + r/100)ⁿ

Calculation

⇒ 2.1 = P(1 + 5/100)²

⇒ 2.1 = P × 21/20  × 21/20

⇒ P = 2.1 × 400/441

⇒ P = 1.905 lakh

The present income would be 1.905 lakh.

Given

x² - 5√ 5x + 1 = 0

Formula used

(a - b)² = (a + b)² - 4ab

(a - b)³ = a³ - b³ - 3ab(a - b)

Calculation

If we simplify the given equation,x2 - 5√ 5x + 1 = 0, by dividing it by x.

⇒ x + 1/x = 5√ 5

Applying the above-mentioned formula:

⇒ (x - 1/x)2 = (x + 1/x)2 - 4x × 1/x

⇒ (x - 1/x)2 = 125 - 4

⇒ (x - 1/x)2 = 121

⇒ x - 1/x = 11

⇒ x3 - 1/x³ = (x - 1/x)³ + 3x × 1/x(x + 1/x)

⇒ x3 - 1/x3 = (11)3 + 3(11)

⇒ x3 - 1/x3 = 1331 + 33

⇒ x3 - 1/x3 = 1364

The answer is 1364.

Given

Discount = 25%

Profit = 70%

New Discount = 50%

Formula used

Profit% = (Profit/Cost price) × 100

Discount % = (Discount /Mark price) × 100

Calculation

Let the Cost price of the table be 100a

Since he gains a profit of 70%, the selling price = 100a + (70/100) x 100a = 170a

M.P = 170a x 100/75

⇒ 170a x 4/3 = 680a/3

Now, if he sells the table at a 50% discount

⇒ New selling price will be = 680a/3 x 1/2

⇒ New selling price = 340a/3

His new profit percentage will be = (340a/3 - 100a)100a x 100

⇒ 40/300 x 100

⇒ 40/3 or 13(1/3)%

The answer is 13(1/3)%.

Given

The total number of students in the college in 2021 = 60000

The total number of students in the college in 2022 = 75000

Concept

The degree-to-percentage conversion, multiply by 5/18

Calculation

The number of students opting for the mathematical sciences from 2021 = 68.4 × 5/18

⇒ 19% of 60000

= 11400

The number of students opting for the mathematical sciences from 2022 = 61.2 × 5/18

⇒ 17% of 75000

= 12750

The percentage change = (12750 - 11400)/11400 × 100

= 12%

The answer is 12%.

Given:

Volume of cube = 729 cm³

Formula:

The total surface area of the cube = 6a²

Calculation:

Let the side of the cube be A, then

A³ = 729

⇒ A = ∛729

⇒ A = ∛(9 × 9 × 9)

⇒ A = 9 cm

∴ The total surface area of the cube

⇒ 6a² 

⇒6 × 9 × 9

⇒ 486 cm²

The answer is 486 cm2

Calculation

The sales of shirts manufactured by companies C1 = 190 + 225 + 240 + 215 + 205

= 1075

The sales of shirts manufactured by companies C2 = 226 + 244 + 235 + 175 + 210

= 1090

The sales of shirts manufactured by companies C3 = 184 + 214 + 235 + 260 + 265

= 1158

The sales of shirts manufactured by companies C4 = 202 + 202 + 275 + 200 + 245

= 1124

∴ The Company C3 sold the most shirts in these five weeks.

Given 

A and B  together can complete work = 15 days 

B can complete work = 21 days 

Formula Used 

Work = time × efficiency 

Calculation 

Take LCM of (15, 21) = 105

Let the total work be 105 

Efficiency of A and B = 105/15 = 7      ----(1)

Efficiency of B  = 105/21 = 5      ----(2)

From (1) and (2) 

⇒ A + B  - B = 2 

By using (3), efficiency of A  =2,

 A alone can complete the work in days = 105/2 = 52(1/2) days 

∴ A alone can complete the work in days 52(1/2) days.

Given:

The circumference of a circle = 132 cm

Formula used:

Circumference(C) of a circle = 2πr

Area of a circle = πr²

Where, r = radius

Calculation:

According to the question,

C = 2 × 22/7 × r

⇒ 132 = 44r/7

r = 21 cm

Now,

Area of a circle = πr2

⇒ 22/7 × 21 × 21 = 1386 cm²

 

∴ The area of circle is 1386 cm2.

Given:

A bus travels 3 hours at a speed of = 60 km/h

A bus travels 4 hours at a speed of = 50 km/h

A bus travels 5 hours to cover the distance = 50 km/hr

Concept:

Average speed = Total distance/ Total time

Calculation:

Total distance covered by bus in 3 hrs at a speed of 60 km/h = (60 × 3) = 180 km

Total distance covered by bus in 4 hrs at a speed of 50 km/h = (4 × 50) = 200 km

Total distance covered by bus in 5 hrs  = (5 × 50) =  250km

Total distance covered = (180 + 200 + 250) km = 630 km

Total time taken = (3 + 4 + 5) hours = 12 hours

Average speed = 630/12 = 52.5 km/h

∴ The average speed for the whole journey is 52.5 km/hr

Given:

There is a provision of food for 70 boys for 36 days

50 more boys join the camp.

Calculation:

Let the food be enough for x days for 50 more boys.

⇒ 70 × 36 = 120 × x

⇒ 2520 = 120x

⇒ x = 21

∴ The food will be enough for 21 days.

Shortcut Trick

Using Fermat's Little Theorem: a^p−1 ≡ 1 (mod p) for any prime p.

Here p = 7, so 3⁶ ≡ 1 (mod 7).

We can write 3⁸ = 3⁶ × 3².

So, 3⁸ ≡ 1 × 9 ≡ 9 (mod 7).

When 9 is divided by 7, the remainder is 2.

∴ The correct answer is 2.

Alternate Method

Given:

Expression: 3⁸ ÷ 7

Concept Used:

Properties of remainders: (A × B) mod N = [(A mod N) × (B mod N)] mod N

Calculation:

⇒ The given expression 3⁸ can be written as (3²)⁴.

⇒ (3²)⁴ = 9⁴

⇒ Find the remainder when the base 9 is divided by 7.

⇒ 9 ÷ 7 leaves a remainder of 2.

⇒ Now, replace 9 with its remainder in the original power expression: 2⁴

⇒ 2⁴ = 16

⇒ Finally, divide 16 by 7 to get the final remainder.

⇒ 16 = 7 × 2 + 2

⇒ The remainder is 2.

∴ The correct answer is 2.

Additional Information

Fermat's Little Theorem

It states that if p is a prime number, then for any integer a, the number a^p−1 − 1 is an integer multiple of p. The formula is expressed as a^p−1 ≡ 1 (mod p).

Euler's Totient Theorem

It generalizes Fermat's theorem, stating a^φ(n) ≡ 1 (mod n) where a and n are coprime, and φ(n) represents Euler's totient function.

Successive Squaring Concept

Large powers can be calculated efficiently by repeatedly squaring the base and taking the remainder at each step to keep the numbers small and manageable.

Given:

Area of a sector of a circle = 616 cm² 

Angled formed at the centre by arc = 10° 

Concepts used:

Area of a sector of circle = πr² × (θ/360°) 

Where,

θ → Angle formed at the centre

r → Radius of circle

Calculation:

Let the radius of the circle be r cm.

Area of sector of circle = πr2 × (θ/360°) 

⇒ 616 cm² = πr² ×  (10°/360°) 

⇒ 616 cm² = (1/36) × (22/7) × r² 

⇒ 616 cm² = (22/28) × r² 

⇒ r² = (616 × 36 × 7)/22

⇒ r = √ (28 × 36 × 7)

⇒ r = 84 cm.

∴ The radius of the circle is 84 cm.

Given

√a = 3b

Calculation

⇒ √a = 3b

On squaring both sides;

⇒ a = 9b²

⇒ a/b² = 9

The answer is 9.

Given

2: 9 :: 4: x

Concept used

Product of mean = Product of extremes

Calculation

⇒ 2 × x = 9 × 4

⇒ x = 18

The answer is 18.

Given

$\frac{cot^3 A - 1}{cot A - 1}$

Formula used

a³ - b³ = (a - b)(a² + ab + b²)

cosec²A = cot2A +1

Calculation

⇒ cot³A - 1³ = (CotA - 1)(cot²A + cotA + 12)

⇒ (cot3A - 1³)/(cotA - 1) = (CotA - 1)(cot2A + cotA + 12)/(cotA - 1)

⇒ (cot2A + cotA + 12)

⇒ cosec2A + cotA

The answer is cosec2A + cotA.

Given

$\frac{(0.25)^4 + 2 \times (0.25)^2 + 1 - (0.25)^2}{(0.25)^2 + 0.25 + 1}$

Formula used

a⁴ + a² + 1 = (a² + a + 1)(a² - a + 1)

Calculation

Let 0.25 = a,

$\frac{(0.25)^4 + 2 \times (0.25)^2 + 1 - (0.25)^2}{(0.25)^2 + 0.25 + 1}$ = (a4 + a2 + 1)/ (a2 + a + 1) ​= (a2 - a + 1)

⇒ 0.25² - 0.25 + 1

⇒ 1.0625 - 0.25

⇒ 0.8125

The answer is 0.8125.

Given

A trader sells two LED sets at the same price.

There is a gain of 20% on one LED and 20% loss on the second LED.

Formula used

S.P = (100 + Gain)/100 × C.P

S.P = (100 - Loss)/100 × C.P

Calculations:

Let the selling price of LED be '100x'

For 1^st LED

Cost price + 20 % of cost price = 100x

⇒120 % cost price = 100x

⇒ Cost price = (100x) × (100/120)

⇒ 250/3 x

Similarly cost price of 2^nd LED

Cost price - 20 % cost price = 100x

⇒ 80% of cost price = 100x

⇒ Cost price = (125)x

⇒ Total cost price = (250/3)x + (125)x

⇒ (250 + 375)/3)x

⇒ (625/3)x

Total selling price = 100x + 100x

⇒ 200x

⇒ (600/3)x

So,

Loss% = [(cost price - selling price)/ cost price)] × 100

⇒ (25/625) × 100

⇒  4%

∴ The correct choice will be option 4.

Given

tan θ + sec θ = a

Formula used

if sec θ + tan θ = a, then sec θ - tan θ = 1/a

Calculation

tan θ + sec θ = a

i.e. sec θ + tan θ = a   ---(1)

So, sec θ - tan θ = 1/a  ---(2)

Add (1) and (2),

sec θ + tan θ + sec θ - tan θ = a + 1/a

⇒ 2 sec θ = a + 1/a

⇒ 2 sec θ = (a² + 1)/a

⇒ sec θ = (a² + 1)/2a

∴ The correct answer is option (4).

Given: 

Selling price of the mixture = 30 per kg 

Profit percent = 10% 

Formula used:

Profit percent = [(SP - CP)/ CP]× 100 

⇒ 10 = [(30 - CP)/ CP] × 100 

⇒ 10 CP = 3000 - 100 CP 

⇒ 110 CP = 3000 

⇒ CP = Rs. 300/11

Let the quantity of the first variety of tea = x

Let the quantity of the second variety of tea = y 

According to the question: 

26 × x + 32 × y = (x + y) 300/11

(26x + 32y) × 11 = 300x + 300y 

52y = 14x 

x : y = 26 : 7

∴ The required ratio is 26: 7

Given

Speed = 63 km/h

Formula Used:

Speed = Distance ÷ Time

⇒ Time = Distance ÷ Speed

⇒ 1 hour = 60 minutes = 3600 seconds

Calculation:

Speed of car is 63 km/hr = 63 × 5/18 m/sec = 35/2 km/sec

Distance = 35/2 × 10

Distance = 175 m

The answer is 175 m.

Given:

Shyam purchased a packet of 16 pens and got 4 pens free with it

Marked percentage = 20%

Selling price = Marked price

Formula used:

SP = CP × [(100 + Profit%)/100]

Discount = free item/Total item × 100

Calculation: 

Let the cost price of 16 pens and getting 4 pens free with it be Rs. 100x

Discount = free item/Total item × 100

= 4/20 × 100

= 20%

Shyam's C.P = 100x × 80/100

= 80x

Marked price = 100x × 120/100

= 120x

M.P = S.P

Profit% = (120x - 80x)/80x × 100

= 50%

The answer is 50%.

Given

cos θ = 11/17

Concept used

tan θ = P/B

cos θ = B/H

P2 + B2 = H2

Calculation

112 + P2 = 172

P2 = 289 - 121

P2 = 168

P = 2√42

tan θ = P/B = 2√42/11

The answer is 2√42/11.

Calculation

The students in all the given classes liking Hockey = 70% of 260 + 90% of 180 + 90% of 240 + 80% of 60

= 182 + 162 + 216 + 48

= 608

The answer is 608.

Given:-

ΔABC ∼ ΔPQR and PQ = 4.8 cm

Perimeter of ΔABC/Perimeter of ΔPQR = 3:2

Formula used:-

Perimeter of ΔABC/Perimeter of ΔPQR = AB/PQ = BC/QR = AC/PR

Calculation:-  

According to the question -

⇒ Perimeter of ΔABC/Perimeter of ΔPQR = 3/2 = AB/PQ

⇒ AB = (4.8 × 3)/2

⇒ AB = 7.2 cm

∴ The required value of AB is 7.2 cm.

Given

Two triangles XYZ and UVW are congruent

The area of ΔXYZ = 58 cm2

Concept used

Two triangles are said to be congruent if their sides have the same length and their angles have the same measure.

Thus, two triangles can be superimposed side to side and angle to angle.

Calculation

Congruent triangles are triangles having corresponding sides and angles to be equal.

Congruence is denoted by the symbol “≅”.  From the above concept, we can write XYZ ≅ UVW.

They have the same area and the same perimeter.

The answer is 58.

The correct answer is "Certainty."

 Key Points

• The given word is misconception, which means a mistaken belief or idea. ((किसी बात के विषय में) भ्रांत धारणा, ग़लतफ़हमी)
• Example: It is a proper misconception.
• The opposite of "misconception" is "certainty."
• Certainty means a state of being completely sure or confident. (अवश्‍यंभाविता, निश्चितता)
• Example: We can’t say with certainty that there is life on other planets.
• The correct answer is option 4.

 Additional Information

• Option 1: Illusion means a false idea or belief. (निराधार विचार, धारणा या प्रभाव; भ्रम)
• Option 2: Hallucination means seeing or hearing things that are not really there. ((बीमारी या नशे में होने वाला) दृष्टिभ्रम या मतिभ्रम, (ऐसी बातें देखना या सुनना जो वस्‍तुतः हैं नहीं); निर्मूलभ्रम)
• Option 3: Fallacy means a mistaken belief or idea. (झूठा विश्‍वास या भ्रांत धारणा)

The correct answer is "Co-worker."

 Key Points

• "Colleague" means a person with whom one works, especially in a profession or business. (सहकर्मी)
• Example: He is my colleague.
• "Co-worker" is a person who works with another person towards a common goal. (एक व्यक्ति जो किसी अन्य व्यक्ति के साथ एक सामान्य लक्ष्य की दिशा में काम करता है)
• Example: He is my co-worker.
• The synonym of colleague is co-worker.
• The correct answer is Option 1.

Additional Information

• Option 2 (Consult) means to seek information or advice from someone with expertise in a particular area. ((किसी के विषय में) किसी से जानकारी या सलाह माँगना अथवा पुस्‍तक आदि में जानक��री ढूँढ़ना)
• Option 3 (Distend) means to swell or expand by pressure from inside. (अंदरूनी दबाव के कारण फूलना या फुलाना, अफरना या अफराना)
• Option 4 (Exempt) means to free someone or something from an obligation or liability imposed on others. (आधिकारिक रूप से छूट देना)

The correct answer is "Dangerous."

 Key Points

• "Perilous" means dangerous or risky. (ख़तरनाक, जोखिम-भरा)
• Example: The country roads are quite perilous.
• Synonyms of perilous are dangerous, hazardous, unsafe, precarious, and risky.
• "Dangerous" means likely to cause injury or damage. (ख़तरनाक, भयंकर)
• Example: Climbing the mountain without proper gear is dangerous.
• The correct answer is Option 2.

Additional Information

• Option 1) Convenient means easy or comfortable. (विशेष उद्देश्‍य की दृष्टि से उपयुक्त या व्‍यावहारिक; आसान, सुविधाजनक)
• Option 3) Helpful means useful or beneficial. (सहायता करने वाला, सहायतापूर्ण, सहायक, सहायता के लिए तत्‍पर)
• Option 4) Suitable means appropriate or fitting. ((किसी के लिए) सही या उचित या उपयुक्त)

Here, the erroneous part is "the accident occurring blast."

 Key Points

• The phrase "occurring blast" is not grammatically correct.
• It should be either "accident" or "blast," but not both.
• The sentence can be corrected to "Nobody from the gathering of odd people could guess the accident or the blast occurring."
• The correct answer is Option 1.

The correct answer is "nail: a small metal spike, driven into wood to join things together or to serve as a hook."

 Key Points

• The sentence suggests that the key was hanging on something near the door.
• The word "nail" in Option 2 fits the context perfectly as it refers to a small metal spike that can be used to hang things. (कील)
• Example: She was hammering a nail.
• The correct answer is Option 2.

Correct sentence: The key was hanging on a nail by the door.

Additional Information

• Option 1 - This meaning of "nail" is used in phrases like "nail someone for something" which means to catch someone doing something wrong or guilty. (किसी को कुछ गलत या दोषी करते हुए पकड़ना)
• Option 3 - This meaning of "nail" refers to the hard part at the end of fingers and toes that can be trimmed and painted. (the hard part at the end of fingers and toes that can be trimmed and painted.)
• Option 4 - This meaning of "nail" is used in phrases like "nail the exam" which means to do the exam successfully. (परीक्षा को सफलतापूर्वक करना)

The correct answer is "Surrugocy."

 Key Points

• The correct spelling of the word is "Surrogacy."
• The incorrect option, "Surrugocy", has "u" instead of "o" and "o" instead of "a."
• "Surrogacy" means the action or state of being a surrogate. (सरोगेट होने की क्रिया या अवस्था)
• Example: Surrogacy is frequently denounced as exploitation.
• The correct answer is Option 3.

Additional Information

• Option 1: "Obdurate" means stubborn or unyielding. (लोगों की इच्छानुसार अपना विचार बदलने से मना करना; हठधर्मी, ज़िद्दी)
• Option 2: "Cryptic" means mysterious or puzzling. (गुप्‍त अर्थ वाला; रहस्‍यमय)
• Option 4: "Drastic" means extreme or severe. (अत्‍यधिक और भरपूर असरदार, उग्र, प्रचंड)

The correct answer is "RQPS."

 Key Points

• The sentence talks about a memoir exploring the impact of the authors' upbringing on their identity and journey of self-discovery.
• Part R has the structure, subject + verb, so it must be the first part.
• Part Q provides an object to the first part of the sentence, so it must follow R.
• The rest of the sentence is the object that is present in the pair PS. So the last pair must be PS.
• The correct answer is Option 1.

Correct sentence: The memoir explores (R), the authors' journey of self-discovery and the impact of their (Q), upbringing on their identity (P), and (S) is missing from the given options.

Here, the erroneous part is "a Leaning Tower of Pisa is a."

 Key Points

• The error lies in the part "a Leaning Tower of Pisais a ."
• As per grammatical rules, the definite article "the" is used before a place name if it consists of an adjective followed by a noun.
• "Leaning Tower" is the name of a place.
• The article "the" should be used before the proper noun "Leaning Tower of Pisa."
• The correct answer is Option 2.

Correct sentence: I have read that the Leaning Tower of Pisa is a popular tourist attraction in the world.

The correct answer is "One who takes an opposing position for the sake of argument."

 Key Points

• "Devil's advocate" is an idiom that refers to someone who takes a contrary position in order to stimulate discussion or test the strength of an argument. (कोई व्यक्ति जो चर्चा को प्रोत्साहित करने या किसी तर्क की ताकत का परीक्षण करने के लिए विपरीत रुख अपनाता है)
• Example: I don't really believe all that - I was just playing devil's advocate.
• The term comes from the Catholic Church, where a person would argue against the canonization of a saint to ensure that all possible objections had been considered.
• The Devil's advocate is not necessarily arguing for their own beliefs, but rather playing a role to challenge others and promote critical thinking.
• The correct answer is Option 1.