SSC CGL 2024 Tier-I Official Paper (Held On: 11 Sept, 2024 Shift 2) (Previous Year Paper)

Given equation: 8 + 6 ÷ 51 – 17 × 13 = ?

According to the question, after ‘÷’ and ‘–‘ are interchanged and ‘×’ and ‘+’ are interchanged:

8 + 6 ÷ 51 – 17 × 13 = ? ⇒ 8 × 6 - 51 ÷ 17 + 13 = ?

⇒ 8 × 6 - 51 ÷ 17 + 13 = ?

⇒ 8 × 6 - 3 + 13 = ?

⇒ 48 + 13 - 3 = ?

⇒ 61 - 3 = ?

⇒ 58 = ?

Hence, "Option 2" is the correct answer.

The logic followed here is:

8-17-35

2 × (17 - 8) = 35 - 17

2 × 9 = 18

18 = 18 (LHS = RHS) 

And,

23-47-95

2 × (47 - 23) = 95 - 47

2 × 24 = 48

48 = 48 (LHS = RHS) 

So, checking each option one by one:

Option 1) 9-20-41

2 × (20 - 9) = 41 - 20

2 × 11 = 21

22 ≠ 21 (LHS ≠ RHS)

Option 2) 12-25-51

2 × (25 - 12) = 51 - 25

2 × 13 = 26

26 = 26 (LHS = RHS)

Option 3) 13-29-55

2 × (29 - 13) = 55 - 29

2 × 16 = 26

32 ≠ 26 (LHS ≠ RHS)

Option 4) 16-32-62

2 × **(**32 - 16) = 62 - 32

2 × 16 = 30

32 ≠ 30 (LHS ≠ RHS)

Thus, out of all the options, '12-25-51' follows the same logic as given.

Hence, "Option 2" is the correct answer.

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

Conclusions:

(I) All apples are lemons → Follow (As all apples are mangoes and all mangoes are lemons. As wholes apples comes in mangoes which whole comes in lemons, therefore it is true.)

(II) All mangoes are kiwis → Follow (As all mangoes are lemons and all lemons are kiwis. As wholes mangoes comes in lemons which whole comes in kiwis, therefore it is true.)

∴ Here, Both conclusions I and II follow.

Hence, "Option 4" is the correct answer.

The logic followed here is:

Option 1) 90 – 144

90 × 1.6 = 144

144 = 144 (LHS = RHS)

Option 2) 75 – 120

75 × 1.6 = 120

120 = 120 (LHS = RHS)

Option 3) 45 – 70

45 × 1.6 = 70

72 ≠ 70 (LHS ≠ RHS)

Option 4) 65 – 104

65 × 1.6 = 104

104 = 104 (LHS = RHS)

Thus, out of all the options, '45 – 70' is the odd one out.

Hence, "Option 3" is the correct answer.

The logic followed here is:

(34, 15, 64)

34 + 15 × 2 = 64

34 + 30 = 64

64 = 64 (LHS = RHS)

And,

(29, 17, 63)

29 + 17 × 2 = 63

29 + 34 = 63

63 = 63 (LHS = RHS)

Option 1) (44, 32, 98)

44 + 32 × 2 = 98

44 + 64 = 98

108 ≠ 98 (LHS ≠ RHS)

Option 2) (31, 23, 54)

31 + 25 × 2 = 54

31 + 50 = 54

81 ≠ 54 (LHS ≠ RHS)

Option 3) (25, 14, 53)

25 + 14 × 2 = 53

25 + 28 = 53

53 = 53 (LHS = RHS)

Option 4) (24, 28, 76)

24 + 28 × 2 = 76

24 + 56 = 76

70 ≠ 76 (LHS ≠ RHS)

Thus, out of all the options, '(25, 14, 53)' follows the same logic as given.

Hence, "Option 3" is the correct answer.

The logic followed here is:

1. All elements shift in the anticlockwise direction.

2. Elements shifts by skipping parts i.e. 0, 1, 2, and 3 parts.

Thus, the final series is:

Hence. "Option 4" is the correct answer.

The logic followed here is:

​

Hence, "Option 3" is the correct answer.

The logic followed here is:

​'BUZZY' is coded as '10'

Number of letter in 'BUZZY' → 5 × 2 = 10

And,

'KING' is coded as '8'

Number of letter in 'KING' → 4 × 2 = 8

Similarly,

'ABROAD' is coded as

Number of letter in 'ABROAD' → 6 × 2 = 12

Hence, "Option 4" is the correct answer.

The logic followed here is:

Logic: 1^st number - 83 = 2^nd number.

Now,

for, 186 : 103

→ 186 - 83 = 103,

for, 156 : 73

→ 156 - 83 = 73,

Similarly, for 95 : 12

→ 95 - 83 = 12.

Hence, "Option 4" is the correct answer.

The logic followed here is:

Hence, "Option 2" is the correct answer.

The logic followed here is:

1. First box series:

First row corner elements interchange positions.

First two elements of third row and center element shift anticlockwise.

The rest of the elements shift anticlockwise. 

2. Second box series:

Third column elements shift to the corner opposite sides.

Second column elements shift anticlockwise.

First column elements shift to the corner opposite sides diagonally.

Top left corner element is replaced by new element.

Thus, the final series is:

Hence. "Option 1" is the correct answer.

Given equation: 41 − 54 × 6 ÷ 9 + 7 = ?

According to the question, after '+' and '−' are interchanged and '×' and '÷' are interchanged:

41 − 54 × 6 ÷ 9 + 7 = ? ⇒ 41 + 54 ÷ 6 × 9 - 7 = ?

⇒ 41 + 54 ÷ 6 × 9 - 7 = ?

⇒ 41 + 9 × 9 - 7 = ?

⇒ 41 + 81 - 7 = ?

⇒ 122 - 7 = ?

⇒ 115 = ?

Hence, "Option 4" is the correct answer.

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

Conclusions:

(I) Some pins are pens→ Does not follow (As all pens are pages and some pages are pins. So it is possible but not definite.)

(II) Some boards are pages → Does not follow (As some pages are pins and some pins are boards. So it is possible but not definite.)

(III) Some pens are boards → Does not follow (As all pens are pages, some pages are pins and some pins are boards. So it is possible but not definite.)

∴ Here, None of the conclusions follow.

Hence, "Option 2" is the correct answer.

Decoding symbols:

Given: P − Q + R ÷ S × T

P − Q → P is the son of Q.

Q + R → Q is the wife of R.

R ÷ S → R is the father of S.

S × T → S is the husband of T.

Thus, P is T's husband’s brother or brother-in-law

Hence, the correct answer is "Option 3"

The logic followed here is:

‘Lavish’ is antonym of ‘Austere’.

Similarly,

‘Prejudiced’ is antonym of ‘Impartial'.

Hence, "Option 1" is the correct answer.

Additional InformationLavish → It means luxurious or extravagant.

Austere → It means simple or strict.

Prejudiced → It means showing partiality or bias.

Impartial → It means fair or unbiased.

Compromised → It means exposed to risk or weakened or to settle a dispute by mutual concessions.

Thoughtful → It means showing  consideration or careful thinking.

Careful → It means taking precautions to avoid harm, error, or risk.

The image embedded in the given figure is as shown below :

∴ Here, the given figure is embedded in option Figure - 3.

Hence, the correct answer is "Option 3".

Given word: JEALOUS

According to the question all the letters in the word given are arranged in English alphabetical order:

Thus, according to the final arrangement, three letter's i.e. E, L and O positions remains unchanged.

Hence, "Option 3" is the correct answer.

Given series: _ C _ W _ _ _ C _ W _ _

Option 1) WCCWWWCC→ W C C W C W W C W W C C → (It doesn't follow any pattern)

Option 2) WWCWWWCW → W C W W C W W C W W C W → (It follows the pattern of: WCW - WCW - WCW - WCW)

Option 3) CWCWWCCW → C C W W C W W C C W C W → (It doesn't follow any pattern)

Option 4) CCWWCCWC → C C C W W W C C C W W C → (It doesn't follow any pattern)

Hence, "Option 2" is the correct answer.

For find the opposite surface of '1', we need to compare the common surface in the given dices,

Now,

From the given Dice,

 

→ 6 is the common surface in both Dice, and 2, 3, 4,and 5 are the adjacent surfaces, so the remaining surface '1' is the opposite surface of '6'.

Here, '6' is opposite to the face containing '1'.

Hence, the correct answer is "Option 1".

The logic followed here is:

TRAINER : VTCIQHU

And,

RADIANT : TCFIDQW

Similarly,

CUSHION : ?

Hence, "Option 1" is the correct answer.

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

Thus, as marked there are a total of 10 triangles.

Hence, "Option 4" is the correct answer.

The logic followed here is:

VAIN' is written as 'OKBY'

And,

'VAST' is written as 'UUBY'

Similarly,

'VERB' is written as

Hence, "Option 2" is the correct answer.

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

Here. option figure 1 shows the mirror image of the given figure.

Hence, the correct answer is "Option 1".

The logic followed here is:

Option 1) GDI​

Option 2) XUZ

Option 3) LKP

Option 4) SPU

Thus, out of all the options, 'LKP' is the odd one out.

Hence, "Option 3" is the correct answer.

The figure which will look like the paper when unfolded is shown below:

Thus, option Figure 3 will look like the paper when unfolded.

Hence, "Option 3" is the correct answer.

The correct answer is Himachal Pradesh

Key Points

The Himalayan Yew :

• The Himalayan Yew (Taxus wallachiana) is a medicinal plant found in various parts of Himachal Pradesh and Arunachal Pradesh.
• The plant holds an important place in traditional medicine and its products are used by the local populations for treating common infections.
• A chemical compound called ‘taxol’ is extracted from the bark, needles, twigs and roots of this tree, and it has been successfully used to treat some cancers – the drug is now the biggest selling anti-cancer drug in the world.
• The species is under great threat due to over-exploitation.
• In the last decade, thousands of yew trees have dried up in various parts of Himachal Pradesh and Arunachal Pradesh.
• Yew has undergone a recent, range-wide population decline of at least 50% as per IUCN.
• Due to the illegal cutting of plant parts and other anthropogenic pressures, Himalayan yew is endangered, and threatened with extinction, in Himalaya.
• Throughout its range in the western Himalayas, it is declining in response to a range of threats.
• In Afghanistan, up to 50% of the forests where it occurs have been destroyed or heavily logged (UNEP 2003) over the last 30 years.
• In northwest India and western Nepal, exploitation associated with Taxol production has led to a national decline of up to 90% in Taxus populations throughout the country.
• Also, in other countries such as Pakistan, overexploitation for fuel, fodder, and medicinal use has led to a significant decline.
• The decline is continuing and while the causes are largely understood, in many areas they will not be reversible. On this basis, an assessment of Endangered is warranted.

The correct answer is Nucleus: Lipid metabolism.

Key Points

• The nucleus is the control center of the cell, storing the cell's DNA and coordinating cellular activities such as growth, metabolism, and reproduction.
• Lipid metabolism is primarily associated with the smooth endoplasmic reticulum and not the nucleus.
• The nucleus is responsible for the transcription of DNA to mRNA, which is then translated into proteins by ribosomes.
• The nucleus also contains the nucleolus, which is involved in ribosome synthesis and assembly.

Additional Information

• Lysosomes:
• Lysosomes are membrane-bound organelles that contain enzymes to break down biomolecules.
• They are often referred to as the "suicidal bags" of the cell because they can digest cellular components when the cell is damaged.
• They play a key role in the degradation and recycling of cellular waste, cellular signaling, and energy metabolism.
• Mitochondria:
• Mitochondria are known as the "powerhouses of the cell" because they generate most of the cell's supply of adenosine triphosphate (ATP), used as a source of chemical energy.
• They are involved in other processes such as signaling, cellular differentiation, and cell death, as well as the control of the cell cycle and cell growth.
• Mitochondria have their own DNA and are thought to have originated from ancestral prokaryotes through endosymbiosis.
• Ribosomes:
• Ribosomes are the molecular machines responsible for protein synthesis.
• They translate messenger RNA (mRNA) into amino acid sequences to build proteins.
• Ribosomes can be found floating freely in the cytoplasm or bound to the endoplasmic reticulum, forming the rough ER.
• They are made up of ribosomal RNA (rRNA) and proteins and consist of two subunits, a large and a small one.

The correct answer is Battle of Plassey.

Key Points

• The Battle of Plassey was fought on 23 June 1757, in the eastern part of India.
• This battle marked the beginning of British colonial rule in India.
• It was fought between the British East India Company and the Nawab of Bengal, Siraj ud-Daulah.
• The British victory in this battle was largely due to the betrayal of Nawab's commander, Mir Jafar, who sided with the British.

Additional Information

• First Carnatic War
• The First Carnatic War (1746-1748) was fought between the British and the French in India.
• It was mainly a result of the War of Austrian Succession in Europe.
• The war ended with the Treaty of Aix-la-Chapelle in 1748, resulting in a status quo ante bellum.
• Battle of Wandiwash
• The Battle of Wandiwash was fought on 22 January 1760 between the British and the French.
• The British, under Sir Eyre Coote, decisively defeated the French forces.
• This battle marked the end of French colonial ambitions in India.
• Battle of Buxar
• The Battle of Buxar was fought on 22 October 1764 between the British East India Company and the combined forces of the Nawab of Bengal, Nawab of Awadh, and the Mughal Emperor.
• The British victory established their supremacy in the eastern parts of India.
• This battle was crucial for the British as it consolidated their power after the Battle of Plassey.

The correct answer is Mizoram.

Key Points

• Mizoram is a state in Northeast India, known for its scenic beauty and cultural heritage.
• As of 2022, Mizoram has only one operational airport, which is Lengpui Airport.
• Lengpui Airport is located near Aizawl, the capital city of Mizoram, and is the primary airport serving the state.
• Due to the state's hilly terrain and lower population density, the development of multiple airports has been limited.

Additional Information

• Operational Airports in India:
• India has a network of airports spread across its vast geography, including both international and domestic airports.
• The Airports Authority of India (AAI) is responsible for the development, maintenance, and management of civil aviation infrastructure in the country.
• As of 2022, some states like Maharashtra and Karnataka have multiple operational airports due to their larger land area and higher population density.
• Lengpui Airport:
• Lengpui Airport is the only operational airport in Mizoram and serves as the main gateway to the state.
• It is situated approximately 32 km from Aizawl, the state capital.
• The airport is equipped to handle both domestic flights and is known for its picturesque approach due to the surrounding hills.
• Lengpui Airport was inaugurated in 1998 and has since been a crucial part of Mizoram's connectivity.
• Challenges in Airport Development in Hilly Regions:
• Constructing and maintaining airports in hilly terrains like Mizoram presents unique challenges, including difficult topography and limited flat land availability.
• High construction costs and environmental concerns also play significant roles in limiting the number of airports.
• However, such regions can benefit greatly from air connectivity in terms of tourism and economic development.
• Importance of Air Connectivity:
• Air connectivity is crucial for the socio-economic development of any region, providing faster and more efficient transportation options.
• It facilitates trade, tourism, and cultural exchange, contributing to the overall growth of the region.
• For states like Mizoram, with challenging road infrastructure, air connectivity becomes even more important.

The correct answer is K C Wheare.

Key Points

• K C Wheare was a distinguished constitutional scholar known for his work on federalism and constitutional law.
• He praised the Indian Constitution's amending process for its variety and flexibility, which he considered wise and unique.
• Wheare emphasized that such variety in the amending process is rare among the world's constitutions.
• His observations highlight the robustness and adaptability of the Indian Constitution in accommodating changes.

Additional Information

• Granville Austin
• Granville Austin was an American historian who studied the Indian Constitution extensively.
• He is known for his seminal work, "The Indian Constitution: Cornerstone of a Nation," which examines the making and functioning of the Indian Constitution.
• Austin's work is highly regarded for its in-depth analysis and insight into the Indian constitutional process.
• Ivor Jennings
• Sir Ivor Jennings was a British lawyer and academic who made significant contributions to the study of constitutional law.
• He was involved in the drafting of several constitutions in the Commonwealth countries, including India.
• Jennings emphasized the importance of conventions and practices in the functioning of a constitution.
• HM Seervai
• H.M. Seervai was a prominent Indian jurist and constitutional expert.
• He authored the influential book "Constitutional Law of India," which is a comprehensive commentary on the Indian Constitution.
• Seervai's work is widely cited in legal circles and has greatly contributed to the understanding of the Indian constitutional law.
• Amending Process in the Indian Constitution
• The Indian Constitution provides a detailed procedure for its amendment in Part XX, Article 368.
• The amending process is categorized into three types: simple majority, special majority, and special majority with ratification by states.
• This flexibility allows the Constitution to be both rigid and flexible, accommodating necessary changes while maintaining stability.
• Amendments require different levels of parliamentary support and, in some cases, ratification by state legislatures, ensuring a broad consensus.

The correct answer is Padma Vibhushan.

Key Points

• Ustad Zakir Hussain, a renowned tabla player, was awarded the Padma Vibhushan by the Government of India in 2023.
• The Padma Vibhushan is the second-highest civilian award in India, recognizing exceptional and distinguished service in any field including service rendered by Government servants.
• Ustad Zakir Hussain is globally acclaimed for his virtuosity and contributions to Indian classical music.
• He has previously been awarded the Padma Shri in 1988 and the Padma Bhushan in 2002.

Additional Information

• Padma Awards:
• The Padma Awards are one of the highest civilian honors of India announced annually on the eve of Republic Day.
• The awards are given in three categories: Padma Vibhushan (for exceptional and distinguished service), Padma Bhushan (distinguished service of a high order), and Padma Shri (distinguished service).
• The awards recognize achievements in all fields of activities or disciplines where an element of public service is involved.
• The Padma Awards were instituted in the year 1954 and are announced every year on Republic Day (26^th January).
• Ustad Zakir Hussain:
• Ustad Zakir Hussain is an Indian tabla virtuoso, composer, percussionist, music producer, and film actor.
• He is the son of legendary tabla player Ustad Alla Rakha.
• He has been awarded the Sangeet Natak Akademi Award, the highest Indian recognition given to practicing artists.
• In addition to his work in Indian classical music, he has also collaborated with many international artists and has contributed to various genres of music.

The correct answer is Kirana

Key Points

• Gangubai Hangal and Prabha Atre were exponents of the Kirana Gharana.
• The Kirana Gharana is known for its focus on perfect intonation and the intricate use of microtones (shrutis).
• Gangubai Hangal was an Indian classical singer of the khyal genre of Hindustani classical music.
• Prabha Atre is also a renowned Indian classical vocalist from the same Gharana, known for her innovative approach and contributions to classical music.

Additional Information

• Other Gharanas
• Rampur Gharana is known for its mix of Dhrupad and Khayal styles.
• Jaipur Gharana is recognized for its intricate and complex singing style.
• The Mewati gharana is a Hindustani classical music apprenticeship tribe that was founded in the late 19^th century by brothers Ghagge Nazir Khan and Wahid Khan of Indore.
• Key Exponents - Pandit Jasraj, Ustad Rais Khan, Mohd Shafi  etc.

The correct answer is Neeraj Chopra.

Key Points

• Neeraj Chopra is an Indian track and field athlete who competes in the javelin throw.
• He created history by becoming the first Indian to win a gold medal in athletics at the Olympic Games when he won the men's javelin throw at the Tokyo 2020 Olympics.
• On 8^th September 2022, Neeraj Chopra became the first Indian to win the Zurich Diamond League final with a throw of 88.44 meters.
• He has consistently performed well in international competitions, bringing laurels to India in the field of athletics.

Important Points 

• Zurich Diamond League
• The Diamond League is an annual series of elite track and field athletic competitions comprising fourteen of the best invitational athletics meetings.
• It was founded in 2010, and the Zurich meeting is one of the most prestigious events in this series.
• Athletes accumulate points at each Diamond League meet and the top performers in each event compete in the final, where the winner is crowned the Diamond League champion.
• Javelin Throw
• Javelin throw is a track and field event where the javelin, a spear about 2.5 meters in length, is thrown.
• The objective is to throw the javelin as far as possible; the athlete with the longest valid throw wins.
• It has been a part of the modern Olympic Games since its inception for men in 1908 and for women in 1932.
• Neeraj Chopra's Career Highlights
• Neeraj Chopra won the gold medal at the 2018 Commonwealth Games and the 2018 Asian Games, where he also set a new Indian national record.
• He made his mark internationally by becoming the World Junior Champion in 2016.
• He is also the first Indian to win a Diamond League title, which he achieved in August 2022 in Lausanne before winning the Zurich final.

The correct answer is 19^th World Championships, 1952.

Key Points

• The 19^th World Table Tennis Championships were held in Bombay (now Mumbai), India, in 1952.
• This event marked the first time that the World Table Tennis Championships were hosted in India.
• The Championships featured both men's and women's events, including singles, doubles, and mixed doubles competitions.
• India's hosting of the event was significant in promoting the sport within the country and the region.

Additional Information

• Table Tennis World Championships:
• The Table Tennis World Championships are an international event organized by the International Table Tennis Federation (ITTF).
• The first World Championships were held in London in 1926.
• The Championships include events for both individual players and national teams.
• Over the years, the Championships have been held in various countries around the world, showcasing the global popularity of the sport.
• International Table Tennis Federation (ITTF):
• The ITTF is the governing body for all international table tennis associations.
• It was founded in 1926 and is responsible for the organization of numerous international competitions, including the World Table Tennis Championships.
• The ITTF oversees the rules and regulations of the sport, ensuring fair play and standardization across the globe.
• Significance of Hosting International Events:
• Hosting international sports events can significantly boost a country's visibility and reputation in the global arena.Such events often encourage the development of sports infrastructure and facilities within the host country.
• They also inspire local athletes and increase public interest and participation in the sport.
• Hosting events like the World Table Tennis Championships can have long-term economic benefits through tourism and international partnerships.

The correct answer is option 1.

Key Points

• Devaluation refers to the official reduction in the external value of a country's currency, which is often done by the government or monetary authorities to improve the country's trade balance. Therefore, it matches with description 5.
• Depreciation indicates a decline in the market rate of exchange for a currency. This is generally due to market forces and does not involve official action. Thus, it matches with description 1.
• Deflation is characterized by a contraction of home currency. It is associated with a decrease in the general price level of goods and services, making the value of money higher. Therefore, it matches with description 2.
• Exchange control involves foreign exchange rationing where the government restricts the amount of foreign currency or local currency that can be used or exchanged. Thus, it matches with description 3.

Additional Information

• Devaluation
• It is a deliberate downward adjustment to the value of a country's currency relative to another currency, group of currencies, or standard.
• This is often used as a tool to enhance the competitiveness of a country's exports by making them cheaper in the global market.
• Devaluation can lead to inflation as import prices become more expensive.
• Depreciation
• Depreciation is the decrease in the value of a currency in the context of the foreign exchange market.
• This can occur due to changes in market dynamics, such as shifts in investor sentiment or economic fundamentals.
• Unlike devaluation, depreciation is not a result of an official policy decision by the government.
• Deflation
• Deflation is the decline in the general price level of goods and services.
• It can increase the real value of money, allowing consumers to buy more with the same amount of money.
• However, deflation can also lead to reduced consumer spending and investment, potentially resulting in economic recession.
• Exchange Control
• Exchange control involves regulating the use of foreign exchange by the government or central bank.
• It can include measures such as limiting the purchase of foreign currency, restricting the amount of foreign currency that can be brought into or taken out of the country, and controlling the exchange rate.
• The objective is often to stabilize the currency, manage the balance of payments, and control inflation.

The correct answer is Grignard reagent.

Key Points

• When haloalkanes and aryl and vinyl halides react with magnesium metal, they yield Grignard reagents.
• Grignard reagents are of the form RMgX, where R is an alkyl or aryl group and X is a halogen.
• These reagents are essential in organic synthesis for forming carbon-carbon bonds.
• Grignard reagents are highly reactive and can react with a variety of electrophiles to form new compounds.
• The reaction typically occurs in an anhydrous ether solvent to stabilize the Grignard reagent.

Additional Information

• Hinsberg reagent is used to distinguish between primary, secondary, and tertiary amines.
• Tollens' reagent is used to detect aldehydes, where it forms a silver mirror on the test tube.
• Fehling reagent is another test for aldehydes, particularly in distinguishing between aldehydes and ketones.

The correct answer is 2.

Key Points

• Fishes have a two-chambered heart consisting of one atrium and one ventricle.
• The blood flows in a single circuit, from the heart to the gills for oxygenation and then to the rest of the body.
• The two-chambered heart is efficient for the aquatic life of fishes, supporting their metabolism and oxygen needs.
• Having a two-chambered heart is a characteristic feature of most fish species.

Additional Information

• Chambers of the Heart
• Atrium: The atrium receives deoxygenated blood from the body and sends it to the ventricle.
• Ventricle: The ventricle pumps the deoxygenated blood to the gills for oxygenation.
• Circulatory System in Fishes
• Fishes have a single circulatory system, meaning blood passes through the heart only once during each complete circuit of the body.
• After oxygenation in the gills, the oxygen-rich blood is delivered directly to the tissues without returning to the heart.
• This system is different from mammals and birds, which have a double circulatory system.
• Gills
• Gills are the respiratory organs in fishes that allow them to extract oxygen from water.
• Blood flows through the gill filaments where gas exchange occurs – carbon dioxide is released into the water and oxygen is absorbed.
• Adaptations
• The two-chambered heart and single circulatory system are highly adapted to an aquatic environment where oxygen levels can vary.
• These adaptations ensure efficient oxygen delivery to support the metabolism and activity levels of fishes.

The correct answer is Kerala.

Key Points

• According to the NITI Aayog report of 2023, Kerala has the lowest percentage of the total population that is multidimensionally poor.
• Kerala's robust health and education infrastructure contribute significantly to its low multidimensional poverty rate.
• The state has consistently performed well in various human development indices, including literacy and life expectancy.
• Kerala's social policies and investments in public services have played a crucial role in reducing poverty.

Additional Information

• Multidimensional Poverty Index (MPI)
• The MPI is a measure that captures the multiple deprivations that people face in their daily lives, including poor health, lack of education, and inadequate living standards.
• It is an international measure developed by the Oxford Poverty and Human Development Initiative (OPHI) and the United Nations Development Programme (UNDP).
• The MPI assesses poverty at the individual level by considering various factors like nutrition, child mortality, years of schooling, school attendance, cooking fuel, sanitation, drinking water, electricity, housing, and assets.
• The MPI helps policymakers target resources and interventions more effectively to address the specific needs of the poor.
• NITI Aayog
• NITI Aayog (National Institution for Transforming India) is the premier policy think tank of the Government of India, providing both directional and policy inputs.
• It was established in 2015, replacing the Planning Commission of India, with the aim to foster cooperative federalism through structured support initiatives and mechanisms with the states on a continuous basis.
• NITI Aayog's primary objectives include promoting sustainable development, enhancing the use of technology, and improving governance and policy implementation.
• It plays a crucial role in designing strategic and long-term policies and programs for the Government of India.
• Human Development Index (HDI)
• The HDI is a composite statistic of life expectancy, education, and per capita income indicators, which are used to rank countries into four tiers of human development.
• It is a measure of a country's social and economic development, developed by the United Nations Development Programme (UNDP).
• HDI scores are used to assess and compare the level of human development across countries and regions.
• The HDI helps in understanding the broader picture of development and guiding policy decisions to improve living conditions.

The correct answer is Diopter.

Key Points

• The diopter (D) is the unit of measurement for the optical power of a lens or curved mirror.
• It is defined as the reciprocal of the focal length (f) measured in meters (i.e., D = 1/f).
• A lens with a focal length of 1 meter has an optical power of 1 diopter.
• Lenses with positive diopters are converging lenses, while those with negative diopters are diverging lenses.

Additional Information

• Optical Power:
• Optical power, also known as lens power, is the degree to which a lens converges or diverges light.
• It is an important concept in optics and is essential in the design of optical systems such as glasses, cameras, and telescopes.
• Focal Length:
• The focal length of a lens is the distance from the lens at which parallel rays of light converge to a single point.
• It determines the magnifying power of the lens and is crucial in the formation of clear images.
• Converging and Diverging Lenses:
• Converging lenses (positive diopters) focus light to a point and are used in applications like magnifying glasses and corrective lenses for hyperopia (farsightedness).
• Diverging lenses (negative diopters) spread light outwards and are used in devices like peepholes and corrective lenses for myopia (nearsightedness).

The correct answer is Up to 74%.

Key Points

• The Government of India has allowed automatic approval of up to 74% Foreign Direct Investment (FDI) by the Reserve Bank of India in nine categories of industries.
• This move was aimed at simplifying the investment process and making it more attractive for foreign investors.
• FDI is a major source of non-debt financial resource for the economic development of India.
• Automatic approval means that foreign investors do not need prior approval from the government for investment up to 74% in these industries.

Additional Information

• Foreign Direct Investment (FDI):
• FDI refers to the investment made by a firm or individual in one country into business interests located in another country.
• It usually involves participation in management, joint-venture, transfer of technology and expertise.
• FDI is considered crucial for the economic development of a country as it brings in capital, technology, and expertise.
• Automatic Route:
• Under the automatic route, foreign investment does not require prior approval from the government or the Reserve Bank of India.
• Investors are only required to inform the Reserve Bank's regional office within 30 days of receipt of inward remittances and file the required documents.
• Reserve Bank of India (RBI):
• The RBI is the central banking institution of India, which controls the issuance and supply of the Indian rupee and oversees the country's monetary policy.
• It also plays an essential role in regulating the financial system and ensuring its stability.
• Industries Eligible for 74% FDI:
• The government has specified nine categories of industries where up to 74% FDI is allowed under the automatic route.
• These categories include sectors like pharmaceuticals, telecommunications, and various manufacturing industries.

The correct answer is Ibrahim Lodi.

Key Points

• Ibrahim Lodi was the last ruler of the Delhi Sultanate from the Lodi dynasty.
• He reigned from 1517 until his defeat and death in the First Battle of Panipat in 1526.
• Ibrahim Lodi was the son of Sikandar Lodi and ascended to the throne after his father's death.
• His rule marked the end of the Delhi Sultanate and the beginning of the Mughal Empire in India.

Additional Information

• Delhi Sultanate
• The Delhi Sultanate was a Muslim kingdom that ruled over large parts of the Indian subcontinent for over 300 years, from 1206 to 1526.
• It was established by Qutb-ud-din Aibak after the defeat of Prithviraj Chauhan and marked the beginning of Muslim rule in India.
• The Sultanate saw the rise and fall of several dynasties including the Mamluks, Khaljis, Tughlaqs, Sayyids, and Lodis.
• It played a crucial role in shaping the culture, architecture, and administration of India during the medieval period.
• First Battle of Panipat
• The First Battle of Panipat was fought on April 21, 1526, between the forces of the Mughal ruler Babur and the Lodi dynasty's Sultan Ibrahim Lodi.
• The battle marked the end of the Delhi Sultanate and the beginning of the Mughal Empire in India.
• Babur's use of innovative military tactics and artillery was instrumental in his victory.
• This battle is considered one of the most significant events in Indian history as it led to the establishment of Mughal rule, which lasted for over three centuries.
• Mughal Empire
• The Mughal Empire was an empire that controlled large parts of the Indian subcontinent from the early 16^th to the mid-19^th century.
• It was founded by Babur, a descendant of Timur and Genghis Khan, after his victory in the First Battle of Panipat.
• The Mughal Empire is known for its rich cultural contributions, including significant developments in art, architecture, and cuisine.
• Some of the most famous Mughal rulers include Akbar, Shah Jahan, and Aurangzeb.

The correct answer is Durand Cup.

Key Points

• The Durand Cup is a football competition in India.
• It is one of the oldest football tournaments in the world, having been founded in 1888.
• The competition is named after Sir Mortimer Durand, the then Foreign Secretary in charge of India.
• The Durand Cup is not associated with cricket and is instead a significant event in Indian football.

Additional Information

• Duleep Trophy
• The Duleep Trophy is a first-class cricket tournament in India.
• It was named after Kumar Shri Duleepsinhji of Nawanagar, an Indian cricket player.
• The competition started in 1961-62 and is played between teams representing geographical zones of India.
• The Duleep Trophy is an important event in the Indian domestic cricket calendar.
• Deodhar Trophy
• The Deodhar Trophy is a List A cricket competition in Indian domestic cricket.
• It was named after Prof. D. B. Deodhar, who is known as the Grand Old Man of Indian cricket.
• The tournament started in 1973-74 and is played between teams selected by the national selectors from the best of the domestic players.
• The Deodhar Trophy is a significant tournament for aspiring cricketers in India.
• Ranji Trophy
• The Ranji Trophy is a first-class cricket championship played in India.
• The competition is named after the famous Indian cricketer Ranjitsinhji.
• It was founded in 1934 and is played between various regional teams across India.
• The Ranji Trophy is considered the premier first-class cricket tournament in India.

The correct answer is when the sun and moon are at right angles to each other.

Key Points

• Neap tides occur when the gravitational forces of the moon and the sun are perpendicular to one another with respect to the Earth.
• These tides are characterized by the least difference between high and low tide levels, making them weaker compared to spring tides.
• Neap tides occur during the first and third quarters of the moon phase, approximately every two weeks.
• During neap tides, the tidal range is reduced because the sun's gravitational pull partially cancels out the moon's gravitational pull on the Earth's oceans.

Additional Information

• Spring Tides
• Spring tides occur when the Earth, moon, and sun are aligned, leading to the highest high tides and the lowest low tides.
• This alignment occurs during full moon and new moon phases.
• The combined gravitational force of the moon and sun leads to a greater tidal range.
• Gravitational Forces
• The gravitational forces of the moon and sun both affect the Earth's oceans, causing tides.
• The moon's gravitational force has a more significant impact due to its proximity to Earth.
• Tidal Range
• The tidal range is the difference in height between consecutive high and low tides.
• It varies depending on the alignment of the Earth, moon, and sun.
• Phases of the Moon
• The moon goes through different phases (new moon, first quarter, full moon, third quarter) as it orbits the Earth.
• These phases affect the gravitational pull on the Earth's oceans, leading to different types of tides.

The Correct Answer is Yakshagana dance.

Key Points

• Chittani Ramachandra Hegde was associated with Yakshagana, a traditional dance-drama form from Karnataka, India.
• He was a legendary figure in Yakshagana, particularly known for his brilliant portrayal of heroic and villainous characters, bringing vibrancy and depth to the art form.
• Hegde was widely regarded as one of the finest exponents of Yakshagana and was honored with several awards for his contribution to the art, including the prestigious Padma Shri in 2012.

The correct answer is Jagannath, Balabhadra and Subhadra.

Key Points

• The Jagannath Temple in Puri is dedicated to Lord Jagannath (a form of Lord Vishnu).
• The temple also houses idols of Balabhadra (Lord Jagannath's elder brother) and Subhadra (their sister).
• This temple is one of the four Hindu pilgrimage sites known as the Char Dham.
• The idol of Jagannath is made of wood and is ceremoniously replaced every twelve or nineteen years in a process known as Nabakalebara.

Additional Information

• Jagannath Temple
• Located in Puri, Odisha, the Jagannath Temple is a famous Hindu temple dedicated to Lord Jagannath.
• The temple is an important pilgrimage destination for Hindus, especially Vaishnavas.
• It is famous for its annual Ratha Yatra or Chariot Festival, where the three principal deities are pulled on huge and elaborately decorated temple cars.
• Non-Hindus are not allowed to enter the temple premises, but they can view the temple from the nearby Raghunandan Library.
• Char Dham
• Char Dham refers to the four holy pilgrimage sites for Hindus, which include Badrinath, Dwarka, Puri, and Rameswaram.
• These sites are highly revered and are visited by devotees to attain spiritual salvation.
• The pilgrimage to Char Dham is considered a way to cleanse oneself of sins and attain Moksha (liberation).
• Nabakalebara
• Nabakalebara is a ritual that involves the renewal of the wooden idols of Jagannath, Balabhadra, Subhadra, and Sudarshana.
• This ritual is performed when there are two Ashadha months in a year, which happens according to the Hindu calendar approximately every 12 to 19 years.
• During Nabakalebara, new idols are carved from specially chosen neem trees, and the old idols are buried in a sacred place within the temple premises.

The Correct Answer is Kerala.

Key Points

• Anna Chandy, the first Indian woman to serve as a judge at a high court, was appointed to the Kerala High Court.
• She served as a High Court judge from 9 February 1959 to 5 April 1967.
• Anna Chandy was also one of the first female judges in the Commonwealth countries.
• Her appointment to the Kerala High Court marked a significant milestone in the Indian judiciary and for women's representation in the legal profession.
• Anna Chandy passed away in the year 1996.

The correct answer is Ministry of Education.

Key Points

• The NIPUN Bharat Scheme was launched by the Ministry of Education in July 2021.
• NIPUN stands for National Initiative for Proficiency in Reading with Understanding and Numeracy.
• The aim of the NIPUN Bharat Scheme is to ensure that every child in India attains foundational literacy and numeracy by the end of Grade 3, by 2026-27.
• The scheme is an essential part of the National Education Policy (NEP) 2020 which focuses on early education and foundational learning.

Important Points 

• National Education Policy (NEP) 2020
• The NEP 2020 is a comprehensive framework to guide the development of education in the country.It emphasizes universal access to education at all levels and aims to transform the education system by 2040.
• One of the key focuses of NEP 2020 is foundational literacy and numeracy.
• It also aims to promote multilingualism and the use of technology in education.
• Foundational Literacy and Numeracy (FLN)
• FLN refers to the basic reading, writing, and arithmetic skills that form the foundation of a child's education.
• The NIPUN Bharat scheme specifically targets the attainment of FLN by children at the primary level.
• FLN is crucial for the overall cognitive development of a child and impacts their ability to learn more complex subjects in higher grades.
• Implementation of NIPUN Bharat
• The scheme is implemented by the Department of School Education and Literacy under the Ministry of Education.
• It involves the training of teachers, the development of age-appropriate learning materials, and regular assessments to track progress.
• The initiative promotes a participatory approach involving parents, community members, and local bodies to ensure the effective implementation of the scheme.

The correct answer is Article 57.

Key Points

• Article 57 of the Constitution of India states that a person who holds, or who has held, office as President shall, subject to the other provisions of this Constitution, be eligible for re-election to that office.
• This article ensures that there is no restriction on the number of times a person can be re-elected as President of India.
• The President of India is elected by an electoral college consisting of the elected members of both Houses of Parliament and the elected members of the Legislative Assemblies of States.
• Article 57 is part of the chapter on the Executive, which is detailed in Part V of the Indian Constitution.

Additional Information

• Article 56
• Article 56 of the Constitution of India deals with the term of office of the President.
• According to this article, the President shall hold office for a term of five years from the date on which he enters upon his office.
• The President may resign from his office by writing under his hand addressed to the Vice-President of India.
• The President may, for violation of the Constitution, be removed from office by impeachment in the manner provided in Article 61.
• Article 58
• Article 58 lays down the qualifications for election as President of India.
• A person shall be eligible for election as President if he is a citizen of India, has completed the age of thirty-five years, and is qualified for election as a member of the House of the People.
• The person should not hold any office of profit under the Government of India or the Government of any State or under any local or other authority subject to the control of any of the said Governments.
• Article 59
• Article 59 deals with the conditions of the President's office.
• The President shall not be a member of either House of Parliament or of a House of the Legislature of any State, and if a member of either House of Parliament or of a House of the Legislature of any State be elected President, he shall be deemed to have vacated his seat in that House on the date on which he enters upon his office as President.
• The President shall not hold any other office of profit.
• The President shall be entitled to such emoluments, allowances, and privileges as may be determined by Parliament by law and, until provision in that behalf is so made, such emoluments, allowances, and privileges as are specified in the Second Schedule.
• The emoluments and allowances of the President shall not be diminished during his term of office.

The correct answer is Champaran.

Key Points

• Champaran is famous for the Champaran Satyagraha of 1917 where Mahatma Gandhi led a movement against the British planters who forced local farmers to grow indigo under harsh conditions.
• This movement marked Gandhi's first active involvement in the Indian freedom struggle and was a significant milestone in India's path to independence.
• The success of the Champaran movement brought Gandhi to the forefront of the Indian independence movement.
• The indigo planters in Champaran were exploiting the farmers by forcing them to grow indigo on a portion of their land and sell it at fixed prices, which was economically detrimental to the farmers.

Additional Information

• Mahatma Gandhi
• Mohandas Karamchand Gandhi, popularly known as Mahatma Gandhi, was a prominent leader of the Indian independence movement against British rule.
• He is known for his philosophy of non-violence (Ahimsa) and civil disobedience, which he employed to lead India to independence.
• Gandhi's methods inspired movements for civil rights and freedom across the world.
• He is often referred to as the "Father of the Nation" in India for his pivotal role in the country's struggle for independence.
• Indigo Cultivation
• Indigo was a valuable dye in the textile industry during the colonial period.
• British planters in India forced local farmers to grow indigo under the Tinkathia system, where farmers had to grow indigo on 3/20^th (or roughly 15%) of their land.
• This system was highly exploitative as the indigo crop depleted the soil, and the farmers received very low prices for their produce.
• The Champaran Satyagraha was a protest against this system and highlighted the plight of the farmers.
• Satyagraha
• Satyagraha is a form of nonviolent resistance or civil resistance.
• The term was coined and developed by Mahatma Gandhi during the Indian independence movement.
• Satyagraha is based on the principle of nonviolence and seeks to bring about social and political change through passive resistance and peaceful protests.
• It emphasizes the power of truth and the need to adhere to ethical principles in the face of injustice.

The correct answer is Vanaprastha.

Key Points

• Vanaprastha is the third stage in the Ashrama system of Vedic life, typically starting around the age of 50 when a person withdraws from worldly responsibilities.
• This stage is characterized by retirement from household duties and the beginning of a spiritual journey.
• Individuals in the Vanaprastha stage often spend their time in forests or secluded places for meditation and spiritual practices.
• The Vanaprastha stage serves as a transition from the Grihastha (householder) stage to Sanyasa (renunciation), emphasizing detachment from material possessions and societal roles.

Additional Information

• Brahmacharya

• This is the first stage of life in the Ashrama system, focusing on education and celibacy.

• It typically lasts until the age of 25, during which an individual is expected to live a disciplined life of study and self-control.

• Grihastha

• The second stage of life, starting around the age of 25 and lasting until about 50.

• It involves marriage, family responsibilities, and contributing to society through work and raising children.

• Sanyasa

• The fourth and final stage of life, marked by renunciation of worldly possessions and responsibilities.

• Individuals in this

• • Individuals in this stage dedicate their lives to spiritual pursuits and often become wandering ascetics.

• dedicate their lives to spiritual pursuits and often become wandering ascetics.

• Ashrama System

• The Ashrama system is a framework for the stages of life in Hindu philosophy, guiding an individual's journey from birth to death.

• The four stages are Brahmacharya (student life), Grihastha (householder life), Vanaprastha (hermit or forest-dweller life), and Sanyasa (renounced life).

• This system aims to provide a balanced and meaningful life by addressing different phases and responsibilities.

Shortcut Trick

When the mid-points of two sides of a triangle are joined, the area of the smaller triangle formed is 1/4 of the total area.

The remaining quadrilateral area will be 3/4 of the total area of the original triangle.

Area of MNRQ = (3 ÷ 4) × Area of ΔPQR

Area = (3 ÷ 4) × 46 = 34.5 cm²

∴ The correct answer is 34.5 cm².

Alternate Method

P Q R

M N

S

Area = 1/4 Area = 3/4

Given:

Area of ΔPQR = 46 cm².

M, N, and S are mid-points of sides PQ, PR, and QR respectively.

Concept Used:

By the Mid-point Theorem, the line segment connecting the mid-points of two sides of a triangle is parallel to the third side and is half its length.

Hence, ΔPMN ∼ ΔPQR.

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Calculation:

⇒ MN / QR = 1 / 2

⇒ Area of ΔPMN / Area of ΔPQR = (MN / QR)²

⇒ Area of ΔPMN / Area of ΔPQR = (1 / 2)² = 1 / 4

⇒ Area of ΔPMN = (1 / 4) × 46 = 11.5 cm²

⇒ Area of quadrilateral MNRQ = Area of ΔPQR − Area of ΔPMN

⇒ Area of quadrilateral MNRQ = 46 − 11.5 = 34.5 cm²

∴ The correct answer is 34.5 cm².

Additional Information

Mid-Point Theorem

The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of its length.

Area of Similar Triangles

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides: Area₁ / Area₂ = (Side₁ / Side₂)².

Medians and Triangle Area

A median of a triangle divides it into two smaller triangles of equal area. All three medians intersect at the centroid, dividing the triangle into six equal smaller areas.

Shortcut Trick

Net percentage change formula: a + b + (a × b) ÷ 100

Here, a = +25% (increase) and b = −12% (decrease).

⇒ Net change = 25 − 12 + (25 × −12) ÷ 100

⇒ Net change = 13 − 3 = +10%

Positive sign indicates an overall increase.

∴ The correct answer is 10% increase.

Alternate Method

Given:

Initial salary increase = 25%

Subsequent salary decrease = 12%

Calculations:

Let the initial salary of the worker be 100.

⇒ Salary after 25% increase = 100 + (25 ÷ 100 × 100) = 125

⇒ Decrease amount = 12% of 125 = (12 ÷ 100) × 125 = 15

⇒ Final salary = 125 − 15 = 110

⇒ Overall change = Final salary − Initial salary = 110 − 100 = +10

⇒ Percentage change = (10 ÷ 100) × 100% = 10% increase

∴ The correct answer is 10% increase.

Additional Information

Successive Percentage Change

When a value is subjected to successive percentage changes of a% and b%, the net change can be found using the formula: Net % = a + b + (a × b) ÷ 100.

Multiplying Factor Method

For successive changes, the final value can be directly calculated as: Final Value = Initial Value × (1 ± f₁) × (1 ± f₂), where f represents the fractional equivalent of the percentage.

Percentage Change Formula

Percentage change = [(Final Value − Initial Value) ÷ Initial Value] × 100. A positive result denotes an increase, while a negative result indicates a decrease.

Shortcut Trick

If a pipe fills a tank in x hours and due to a leak it takes y hours to fill, the leak alone can empty the tank in (x × y) ÷ (y − x) hours.

Here, x = 6 hours and y = 6 + 2 = 8 hours.

Required time = (6 × 8) ÷ (8 − 6) = 48 ÷ 2 = 24 hours.

∴ The correct answer is 24 hours.

Alternate Method

Given:

Time taken by Pipe A to fill the tank = 6 hours

Time taken by Pipe A and Leak together = 6 + 2 = 8 hours

Calculations:

⇒ Efficiency of the leak = Efficiency of (Pipe A + Leak) − Efficiency of Pipe A

⇒ Efficiency of the leak = 3 − 4 = −1 unit/hr

⇒ The negative sign indicates that the leak empties the tank at the rate of 1 unit/hr.

⇒ Time taken by the leak to empty the full tank = Total Work ÷ Efficiency of leak

⇒ Time = 24 ÷ 1 = 24 hours

∴ The correct answer is 24 hours.

Additional Information

Pipes and Cisterns Basics

If a pipe can fill a tank in x hours, its efficiency is considered positive (+1/x). If a pipe (or leak) empties it in y hours, its efficiency is considered negative (−1/y).

Combined Work with an Emptying Pipe

When an inlet pipe and an outlet pipe operate together, the net part of the tank filled in 1 hour is given by (1/x) − (1/y).

Emptying a Full Tank

If the filling capacity is less than the emptying capacity, the tank will eventually empty. Time taken to empty = Total capacity ÷ Net emptying rate.

Shortcut Trick

Convert cosine terms into sine using the complementary angle rule: cos(90° − θ) = sin θ.

cos 34° = sin(90° − 34°) = sin 56° and cos 59° = sin(90° − 59°) = sin 31°.

Substitute these into the expression to get: (cosec 56° × sin 56°) − (sin 31° × cosec 31°).

Since cosec θ and sin θ are reciprocal to each other (cosec θ × sin θ = 1), the expression simplifies to 1 − 1 = 0.

∴ The correct answer is 0.

Alternate Method

Given:

cosec 56° × cos 34° − cos 59° × cosec 31°

Formula Used:

cos(90° − θ) = sin θ

sin θ × cosec θ = 1

Calculations:

⇒ cosec 56° × cos(90° − 56°) − cos(90° − 31°) × cosec 31°

⇒ cosec 56° × sin 56° − sin 31° × cosec 31°

⇒ 1 − 1

⇒ 0

∴ The correct answer is 0.

Additional Information

Trigonometric Ratios of Complementary Angles

sin(90° − θ) = cos θ | cos(90° − θ) = sin θ | tan(90° − θ) = cot θ.

Reciprocal Relations

sin θ × cosec θ = 1 | cos θ × sec θ = 1 | tan θ × cot θ = 1.

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1 | sec²θ − tan²θ = 1 | cosec²θ − cot²θ = 1.

Given:

Sales of manufacturer M₂ (in hundreds) from 2016 to 2019 = 160, 170, 180, 190

Sales of manufacturer M₄ (in hundreds) from 2016 to 2019 = 200, 210, 220, 230

Formula used:

Total sales = Sum of sales for the years

Difference = Total sales of M₄ - Total sales of M₂

Calculations:

Total sales of M₂:

⇒ 160 + 170 + 180 + 190 = 700 (hundreds)

⇒ Total sales of M₂ = 700 × 100 = 70,000

Total sales of M₄:

⇒ 200 + 210 + 220 + 230 = 860 (hundreds)

⇒ Total sales of M₄ = 860 × 100 = 86,000

Difference:

⇒ 86,000 - 70,000 = 16,000

∴ The difference is 16,000. Option (4) is correct.

Given:

Marks obtained and total marks for each subject:

English: 73/100

Hindi: 56/80

Science: 45/75

Mathematics: 90/125

IT: 45/60

Formula used:

Percentage = (Marks obtained / Total marks) × 100

Calculations:

English:

⇒ (73 / 100) × 100 = 73%

Hindi:

⇒ (56 / 80) × 100 = 70%

Science:

⇒ (45 / 75) × 100 = 60%

Mathematics:

⇒ (90 / 125) × 100 = 72%

IT:

⇒ (45 / 60) × 100 = 75%

∴ Akshay scored the highest marks in IT with 75%.

Shortcut Trick

Total Simple Interest = Amount − Principal = ₹11,928 − ₹8,400 = ₹3,528

Simple Interest for 1 year = 7% of 8,400 = ₹588

Time = Total Interest ÷ Interest per year = 3528 ÷ 588 = 6 years

∴ The correct answer is 6 years.

Alternate Method

Given:

Principal (P) = ₹8,400

Amount (A) = ₹11,928

Rate (R) = 7% per annum

Formula Used:

Simple Interest (SI) = Amount − Principal

SI = (P × R × T) ÷ 100

Principal ₹8,400

• SI at 7% p.a. T = ? years

Amount ₹11,928

SI = ₹11,928 − ₹8,400 = ₹3,528

Calculations:

⇒ SI = 11,928 − 8,400 = 3,528

⇒ 3,528 = (8,400 × 7 × T) ÷ 100

⇒ 3,528 = 84 × 7 × T

⇒ 3,528 = 588 × T

⇒ T = 3,528 ÷ 588

⇒ T = 6

∴ The correct answer is 6 years.

Additional Information

Compound Interest (CI) Formula

When interest is compounded annually, Amount = P × (1 + R/100)^T. The CI is the difference between the Amount and the Principal.

Difference Between SI and CI for 2 Years

For a given principal P and rate R, the difference between CI and SI over 2 years is calculated as: D = P × (R/100)².

Rule of 72

A quick rule of thumb used to estimate the number of years required to double the invested money at a given annual fixed interest rate. Time ≈ 72 ÷ R.

Shortcut Trick

The area of a square can be directly calculated if the length of its diagonal is known.

Area of square = (Diagonal)² ÷ 2

Area = (4.8)² ÷ 2

Area = 23.04 ÷ 2 = 11.52 m²

∴ The correct answer is 11.52 m².

Alternate Method

Given:

Length of the diagonal of the square (d) = 4.8 m

Formula Used:

Diagonal of a square = √2 × Side

Area of a square = (Side)²

Calculations:

⇒ Side of the square = Diagonal ÷ √2

⇒ Side = 4.8 ÷ √2 m

⇒ Area of the square = (4.8 ÷ √2)²

⇒ Area = (4.8 × 4.8) ÷ (√2 × √2)

⇒ Area = 23.04 ÷ 2

⇒ Area = 11.52 m²

∴ The correct answer is 11.52 m².

Additional Information

Perimeter of a Square

The perimeter is the total continuous length of the boundary of the square. It is calculated as P = 4 × Side.

Diagonal and Side Relation

A diagonal divides the square into two identical right-angled isosceles triangles. Applying Pythagoras theorem, the relationship formed is Diagonal = √2 × Side.

Circumcircle of a Square

The diagonal of the square is equal to the diameter of its circumscribed circle. The Circumradius (R) is given by R = Diagonal ÷ 2.

Shortcut Trick

For a number to be divisible by both 2 and 5, it must be divisible by their Lowest Common Multiple (LCM).

The LCM of 2 and 5 is 10.

A number is divisible by 10 if and only if its last digit is 0.

Looking at the given options, only 63840 has a last digit of 0.

∴ The correct answer is 63840.

Alternate Method

Given:

Numbers to check: 63840, 20792, 37915, 37254

Concept Used:

Divisibility by 2: The last digit must be an even number (0, 2, 4, 6, 8).

Divisibility by 5: The last digit must be 0 or 5.

Calculations:

⇒ For a number to be divisible by both 2 and 5, the last digit must satisfy both rules simultaneously.

⇒ The only digit that is even and also satisfies the rule of 5 is 0.

⇒ Option 1: 63840 ends with 0, hence it is divisible by both 2 and 5.

⇒ Option 2: 20792 ends with 2, so it is divisible by 2 but not by 5.

⇒ Option 3: 37915 ends with 5, so it is divisible by 5 but not by 2.

⇒ Option 4: 37254 ends with 4, so it is divisible by 2 but not by 5.

∴ The correct answer is 63840.

Additional Information

Divisibility by 3 and 9

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

Divisibility by 4 and 8

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

Divisibility by 11

A number is divisible by 11 if the difference between the sum of digits in odd places and the sum of digits in even places is 0 or a multiple of 11.

Divisibility by Composite Numbers

To check divisibility by a composite number (like 6, 12, or 15), factorize it into co-prime factors. For example, a number is divisible by 6 if it is divisible by both 2 and 3.

Shortcut Trick

Convert the mixed fraction to an improper fraction: 7 1/5 = 36/5

Mean proportional = √(36/5 × 245) = √(36 × 49) = 6 × 7 = 42

The only even prime number in mathematics is 2.

Required quotient = 42 ÷ 2 = 21

∴ The correct answer is 21.

Alternate Method

Given:

First number (a) = 7 1/5 = 36/5

Second number (b) = 245

Formula Used:

Mean proportional between two numbers a and b = √(a × b)

Calculation:

⇒ Mean proportional = √(36/5 × 245)

⇒ Mean proportional = √(36 × 49)

⇒ Mean proportional = 6 × 7 = 42

⇒ The only even prime number is 2.

⇒ Required quotient = 42 ÷ 2 = 21

∴ The correct answer is 21.

Additional Information

Mean Proportional

The mean proportional (or geometric mean) of two numbers a and b is given by the formula √(a × b). It acts as the middle term in a continuous proportion where a : x = x : b.

Third and Fourth Proportionals

For two numbers a and b, the third proportional is evaluated as b² ÷ a. For three separate numbers a, b, and c, the fourth proportional is evaluated as (b × c) ÷ a.

Even Prime Number

A prime number is a positive integer greater than 1 that has exactly two distinct divisors: 1 and itself. The number 2 is uniquely the smallest prime number and the only even prime number.

Given:

October: 200,189

November: 204,933

December: 211,885

Formula used:

Final Value = Initial Value × (1 + r)ⁿ

Where:

r = Monthly growth rate (as a decimal)

n = Number of months (in this case, n = 2 months)

Final Value = December value (211,885)

Initial Value = October value (200,189)

Calculations:

211,885 = 200,189 × (1 + r)²

⇒ (1 + r)² = 211,885 / 200,189

⇒ (1 + r)² = 1.0586

⇒ 1 + r = √1.0586 ≈ 1.029

⇒ r = 1.029 - 1 = 0.029

⇒ r ≈ 0.029, or 2.9%

∴ The average growth rate is 2.9%.

Calculation:

$1020 \div \left[ \frac{4}{3} \text{ of } (26 + 4) - 11 \frac{2}{3} \right]$

⇒ $1020 \div \left[ \frac{4}{3} \text{ of } (30) - 11 \frac{2}{3} \right]$

⇒ $1020 \div \left[40 - 11 \frac{2}{3} \right]$

⇒ $1020 \div \left[40 - \frac{35}{3} \right]$

⇒ 1020 × 3/85

⇒ 36

∴ The correct answer is 36.

Shortcut Trick

For two similar triangles, the ratio of their corresponding sides is simply the square root of the ratio of their areas.

Ratio of sides = √(Area₁ / Area₂)

⇒ Ratio of sides = √(25 / 144)

⇒ Ratio of sides = 5 : 12

∴ The correct answer is 5 : 12.

Alternate Method

Given:

Ratio of areas of two similar triangles (A₁ : A₂) = 25 : 144

Formula Used:

If two triangles are similar, the ratio of their areas is strictly equal to the square of the ratio of their corresponding sides.

A₁ / A₂ = (S₁ / S₂)²

Ratio of Areas = S₁² : S₂²

A₁ = 25

S₁

A₂ = 144

S₂

Calculation:

⇒ (S₁ / S₂)² = 25 / 144

⇒ S₁ / S₂ = √(25 / 144)

⇒ S₁ / S₂ = 5 / 12

∴ The correct answer is 5 : 12.

Additional Information

Properties of Similar Triangles

When two triangles are similar, their corresponding interior angles are exactly equal, and the ratio of their corresponding side lengths remains constant.

Perimeters and Altitudes Ratio

The ratio of perimeters, corresponding altitudes, angle bisectors, and medians of two similar triangles is strictly equivalent to the ratio of their corresponding sides.

Volumes of Similar Figures

For any three-dimensional similar geometric shapes, the ratio of their total volumes is equal to the cube of the ratio of their corresponding linear 1D dimensions.

Formula used:

Plastic Bats = 1,00,000 - Wooden Bats

Brand B Plastic Bats = $\dfrac{B}{A + B} \times \text{Total Plastic Bats}$

where A and B are the parts of the Brand A: Brand B ratio.

Calculation:

Company P:

Wooden Bats = 65% of 1,00,000 = 65,000

Plastic Bats = 1,00,000 - 65,000 = 35,000

Brand A : Brand B ratio = 3 : 7

Brand B Plastic Bats = $\dfrac{7}{10} \times 35,000 = 24,500$

Company Q:

Wooden Bats = 70% of 1,00,000 = 70,000

Plastic Bats = 1,00,000 - 70,000 = 30,000

Brand A : Brand B ratio = 7 : 8

Brand B Plastic Bats = $\dfrac{8}{15} \times 30,000 = 16,000$

Company R:

Wooden Bats = 60% of 1,00,000 = 60,000

Plastic Bats = 1,00,000 - 60,000 = 40,000

Brand A : Brand B ratio = 19 : 6

Brand B Plastic Bats = $\dfrac{6}{25} \times 40,000 = 9,600$

Company S:

Wooden Bats = 70% of 1,00,000 = 70,000

Plastic Bats = 1,00,000 - 70,000 = 30,000

Brand A : Brand B ratio = 7 : 8

Brand B Plastic Bats = $\dfrac{8}{15} \times 30,000 = 16,000$

Company T:

Wooden Bats = 50% of 1,00,000 = 50,000

Plastic Bats = 1,00,000 - 50,000 = 50,000

Brand A : Brand B ratio = 2 : 3

Brand B Plastic Bats = $\dfrac{3}{5} \times 50,000 = 30,000$

Total number of Brand B plastic bats:

Total Brand B Plastic Bats = 24,500 + 16,000 + 9,600 + 16,000 + 30,000 = 96,100

∴ The total number of Brand B plastic bats manufactured by all companies is 96,100.

Shortcut Trick

The prime numbers between 50 and 76 are 53, 59, 61, 67, 71, and 73.

Let the assumed average be 60.

Net deviation = (−7) + (−1) + (+1) + (+7) + (+11) + (+13) = +24

Average deviation = +24 ÷ 6 = +4

Actual average = 60 + 4 = 64

∴ The correct answer is 64.

Alternate Method

Given:

The range of numbers lies between 50 and 76.

Formula Used:

Average = Sum of observations ÷ Total number of observations

53

59

61

67

71

73

Avg

Sum = 384, Average = 64

Calculations:

⇒ The prime numbers lying between 50 and 76 are: 53, 59, 61, 67, 71, and 73.

⇒ Total number of prime numbers in this range (n) = 6

⇒ Sum of these prime numbers = 53 + 59 + 61 + 67 + 71 + 73

⇒ Sum = 384

⇒ Average = 384 ÷ 6 = 64

∴ The correct answer is 64.

Additional Information

Prime Numbers

A prime number is a natural number greater than 1 that is completely divisible only by 1 and itself. The number 2 is the smallest and the only even prime number.

Deviation Method for Averages

Assume an arbitrary average (A). The Actual Average = A + (Sum of deviations ÷ Number of terms). This method is highly effective for quickly calculating averages of large, closely grouped numbers without complex addition.

Combined Average

If two separate groups contain n₁ and n₂ items with averages A₁ and A₂ respectively, their combined average is calculated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

In a right-angled triangle at B, the sum of acute angles ∠A and ∠C is 90°.

⇒ ∠C = 90° − ∠A

Taking cosine on both sides gives cos C = cos(90° − A).

Using the complementary angle identity cos(90° − θ) = sin θ, we directly get cos C = sin A.

Given sin A = 1/2, it follows that cos C = 1/2.

∴ The correct answer is 1/2.

Alternate Method

Given:

In ΔABC, ∠B = 90° and sin A = 1/2.

Formula Used:

sin θ = Perpendicular / Hypotenuse

cos θ = Base / Hypotenuse

Pythagoras Theorem: Hypotenuse² = Perpendicular² + Base²

Calculations:

⇒ sin A = BC / AC = 1 / 2

⇒ Let BC = 1 unit and AC = 2 units.

⇒ By Pythagoras theorem, AB = √(AC² − BC²) = √(2² − 1²) = √3 units.

⇒ We need to find cos C.

⇒ For angle C, Base = BC and Hypotenuse = AC.

⇒ cos C = Base / Hypotenuse = BC / AC = 1 / 2

Alternatively, using exact angle values:

⇒ sin A = 1 / 2 ⇒ ∠A = 30°

⇒ In ΔABC, ∠C = 180° − (90° + 30°) = 60°

⇒ cos C = cos 60° = 1 / 2

∴ The correct answer is 1/2.

Additional Information

Complementary Angles in Trigonometry

If two angles A and B sum up to 90°, they are complementary. The trigonometric ratios shift exactly such that sin A = cos B, tan A = cot B, and sec A = cosec B.

Trigonometric Ratios for 30°, 60°, 90° Triangles

In a right-angled triangle with angles 30°-60°-90°, the sides are always in the ratio 1 : √3 : 2 respectively opposite to the angles.

Pythagoras Theorem

For any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Formula: Hypotenuse² = Perpendicular² + Base².

Shortcut Trick

The given expression follows the standard algebraic identity: (a³ − b³) ÷ (a² + ab + b²) = a − b

Here, a = 4.2 and b = 1.2

Simply calculate the difference: 4.2 − 1.2 = 3

∴ The correct answer is 3.

Alternate Method

Given:

Expression: (4.2³ − 1.2³) ÷ (4.2² + 5.04 + 1.2²)

Formula Used:

a³ − b³ = (a − b)(a² + ab + b²)

Calculation:

⇒ Let a = 4.2 and b = 1.2

⇒ Check the middle term of the denominator: a × b = 4.2 × 1.2 = 5.04

⇒ So, the denominator is perfectly in the form of a² + ab + b²

⇒ The given expression becomes: (a³ − b³) ÷ (a² + ab + b²)

⇒ Substituting the formula for a³ − b³:

⇒ [(a − b)(a² + ab + b²)] ÷ (a² + ab + b²)

⇒ The common term (a² + ab + b²) in the numerator and denominator cancels out.

⇒ Remaining expression = a − b

⇒ Result = 4.2 − 1.2 = 3

∴ The correct answer is 3.

Additional Information

Sum of Cubes Identity

Similar to the difference of cubes, the sum of cubes formula is useful in simplifications: a³ + b³ = (a + b)(a² − ab + b²).

Difference of Squares

Another highly used algebraic identity in exams is a² − b² = (a − b)(a + b).

Decimal Multiplication Shortcut

When checking terms like 4.2 × 1.2, you can multiply 42 × 12 = 504, and then place the decimal point two places from the right to get 5.04.

Shortcut Trick

For linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂, directly check their coefficient ratios.

Ratio of x-coefficients (a₁/a₂) = 0.4 ÷ 0.3 = 4/3

Ratio of y-coefficients (b₁/b₂) = 0.16 ÷ 0.12 = 4/3

Ratio of constants (c₁/c₂) = 1.7 ÷ 3.4 = 1/2

Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel and never intersect.

∴ The correct answer is no solution.

Alternate Method

Given:

0.4x + 0.16y = 1.7

0.3x + 0.12y = 3.4

Formula Used:

For a system of linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂:

If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the system represents parallel lines and has no solution.

Calculations:

⇒ To simplify, multiply the first equation by 100 to remove decimals:

⇒ 40x + 16y = 170

⇒ Multiply the second equation by 100:

⇒ 30x + 12y = 340

⇒ Now, compare the coefficients with standard form:

⇒ a₁ = 40, b₁ = 16, c₁ = 170

⇒ a₂ = 30, b₂ = 12, c₂ = 340

⇒ Find the ratio a₁/a₂ = 40 ÷ 30 = 4/3

⇒ Find the ratio b₁/b₂ = 16 ÷ 12 = 4/3

⇒ Find the ratio c₁/c₂ = 170 ÷ 340 = 1/2

⇒ We can observe that a₁/a₂ = b₁/b₂ ≠ c₁/c₂

⇒ This means the equations represent distinct parallel lines, so they will never intersect.

∴ The correct answer is no solution.

Additional Information

Unique Solution (Intersecting Lines)

If a₁/a₂ ≠ b₁/b₂, the lines intersect at exactly one point, giving a single unique solution.

Infinitely Many Solutions (Coincident Lines)

If a₁/a₂ = b₁/b₂ = c₁/c₂, the lines overlap entirely, resulting in infinitely many common points or solutions.

No Solution (Parallel Lines)

If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines have the same slope but different intercepts, making them parallel with no point of intersection.

Shortcut Trick

Let the borrowed amount from R be 100%.

Interest paid to R = 8%.

Net profit earned by S after settling the debt = 5%.

Total return generated by the scheme = Interest to R + Profit to S = 8% + 5% = 13%.

If R invested directly, he would receive the entire 13% return generated by the scheme.

∴ The correct answer is 13%.

Alternate Method

Given:

Interest promised to R = 8%

S's profit from the scheme after paying R = 5%

Calculations:

Flow of Investment and Returns

Investment 100 Units

Paid to R 108 Units

S's Profit 5 Units

Total Scheme Yield = 108 + 5 = 113 Units

⇒ Let the principal amount borrowed by S be 100 units.

⇒ Amount to be paid back to R = Principal + 8% Interest = 100 + 8 = 108 units.

⇒ S earned a net profit of 5% on the principal = 5 units.

⇒ Total return generated from the scheme = Amount paid to R + S's profit.

⇒ Total return from the scheme = 108 + 5 = 113 units.

⇒ If R invested the 100 units directly in the scheme, the return would be 113 units.

⇒ R's direct gain = Total Return − Principal = 113 − 100 = 13 units.

⇒ R's gain percentage = (13 ÷ 100) × 100 = 13%.

∴ The correct answer is 13%.

Additional Information

Percentage Base Rule

Unless otherwise stated explicitly, profit or loss percentage is always calculated on the initial principal or the cost price of the investment.

Successive Investment Chain

When money passes through an intermediary, the ultimate yield of an asset or scheme is equivalent to the sum of the intermediary's borrowing cost (interest) and their net profit margin.

Shortcut Trick

Put direct values: tan 60° = √3, cos 30° = √3/2, sec 30° = 2/√3, cot 60° = 1/√3.

Numerator = 4/3 × 3 + 3 × 3/4 − 2 × 4/3 − 3/4 × 1/3 = 4 + 9/4 − 8/3 − 1/4 = 6 − 8/3 = 10/3.

Denominator uses formula: sin A cos B − cos A sin B = sin(A − B).

Denominator = sin(60° − 30°) = sin 30° = 1/2.

Total Value = (10/3) ÷ (1/2) = 20/3 = 6 2/3.

∴ The correct answer is 6 2/3.

Alternate Method

Given:

[4/3 tan²60° + 3 cos²30° − 2 sec²30° − 3/4 cot²60°} ÷ [sin 60° cos 30° − cos 60° sin 30°]

Formula Used:

sin(A − B) = sin A cos B − cos A sin B

Calculations:

⇒ Numerator = 4/3 × (√3)² + 3 × (√3/2)² − 2 × (2/√3)² − 3/4 × (1/√3)²

⇒ Numerator = 4/3 × 3 + 3 × 3/4 − 2 × 4/3 − 3/4 × 1/3

⇒ Numerator = 4 + 9/4 − 8/3 − 1/4

⇒ Numerator = 4 + (9 − 1)/4 − 8/3 = 4 + 8/4 − 8/3

⇒ Numerator = 4 + 2 − 8/3 = 6 − 8/3 = (18 − 8) ÷ 3 = 10/3

⇒ Denominator = sin 60° cos 30° − cos 60° sin 30°

⇒ Denominator = sin(60° − 30°) = sin 30° = 1/2

⇒ Total Value = Numerator ÷ Denominator = (10/3) ÷ (1/2)

⇒ Total Value = 10/3 × 2 = 20/3 = 6 2/3

∴ The correct answer is 6 2/3.

Additional Information

Trigonometric Compound Angles

sin(A ± B) = sin A cos B ± cos A sin B | cos(A ± B) = cos A cos B ∓ sin A sin B

Important Trigonometric Values

sin 30° = 1/2, sin 60° = √3/2, cos 30° = √3/2, cos 60° = 1/2, tan 30° = 1/√3, tan 60° = √3.

Pythagorean Identities

sin²θ + cos²θ = 1, sec²θ − tan²θ = 1, cosec²θ − cot²θ = 1.

Shortcut Trick

Since AB = AC, the triangle is isosceles and angles opposite to equal sides are equal (∠B = ∠C).

∠B = (180º − ∠A) ÷ 2

∠B = (180º − 80º) ÷ 2 = 100º ÷ 2 = 50º

∴ The correct answer is 50º.

Alternate Method

Given:

In ΔABC, AB = AC

∠A = 80º

80º

?

?

A B C

Formula Used:

Sum of all internal angles of a triangle is 180º.

Angles opposite to equal sides of an isosceles triangle are equal.

Calculation:

⇒ In ΔABC, AB = AC

⇒ Therefore, ∠B = ∠C

⇒ ∠A + ∠B + ∠C = 180º

⇒ 80º + ∠B + ∠B = 180º

⇒ 2 × ∠B = 180º − 80º

⇒ 2 × ∠B = 100º

⇒ ∠B = 100º ÷ 2

⇒ ∠B = 50º

∴ The correct answer is 50º.

Additional Information

Isosceles Triangle Properties

A triangle with two equal sides is an isosceles triangle. The angles opposite to the equal sides are always equal.

Angle Sum Property

The sum of all interior angles of any triangle is always equal to 180º.

Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two opposite interior angles: ∠Ext = ∠Int₁ + ∠Int₂.

Shortcut Trick

Let the Marked Price (MP) be 100 units.

Cost Price (CP) = 75% of 100 = 75 units.

Selling Price (SP) after 15% discount = 100 − 15 = 85 units.

Profit = SP − CP = 85 − 75 = 10 units.

Profit % = (10 ÷ 75) × 100 = 13.33%.

∴ The correct answer is 13.33%.

Alternate Method

Given:

Cost Price of the bat = 75% of MP

Discount allowed = 15%

Formula Used:

Selling Price (SP) = MP × (100 − Discount %) ÷ 100

Gain % = (Gain ÷ CP) × 100

Calculations:

⇒ Let Marked Price (MP) = 100x

⇒ Cost Price (CP) = 75% of 100x = 75x

⇒ Discount = 15% of 100x = 15x

⇒ Selling Price (SP) = 100x − 15x = 85x

⇒ Gain = SP − CP = 85x − 75x = 10x

⇒ Gain % = (10x ÷ 75x) × 100

⇒ Gain % = (2 ÷ 15) × 100 = 40 ÷ 3 = 13.33%

∴ The correct answer is 13.33%.

Additional Information

Marked Price and Discount

Discount is always calculated on the Marked Price (MP) unless explicitly stated otherwise. Formula: SP = MP × (1 − D/100).

Direct Relation Between CP and MP

When Profit/Loss % and Discount % are given, the ratio of Cost Price to Marked Price is given by: CP/MP = (100 − Discount%) ÷ (100 ± Profit/Loss%).

Successive Discounts

When two successive discounts of a% and b% are given, the equivalent single discount is calculated as: Equivalent Discount = a + b − (a × b)/100.

Shortcut Trick

When two triangles are given as congruent, the order of their letters directly shows the corresponding parts.

For ▵ABC ≅ ▵RPQ, simply match the positions of the letters.

The letters P and Q are at the second and third positions in RPQ.

The letters at the second and third positions in ABC are B and C.

Therefore, side PQ corresponds to side BC.

∴ The correct answer is BC.

Alternate Method

Given:

▵ABC ≅ ▵RPQ

Concept Used:

Two triangles are congruent if their corresponding sides and angles are equal in measure. The sequence of the vertices in the congruence statement specifies the exactly matched parts.

A B C

R P Q

Corresponding Sides: BC & PQ

⇒ Based on the congruency statement ▵ABC ≅ ▵RPQ, we establish the following exact vertex correspondence:

⇒ Vertex A corresponds to Vertex R

⇒ Vertex B corresponds to Vertex P

⇒ Vertex C corresponds to Vertex Q

⇒ The side formed by connecting vertices P and Q in ▵RPQ naturally corresponds to the matching vertices in ▵ABC.

⇒ Since P → B and Q → C, the side PQ corresponds to the side BC.

∴ The correct answer is BC.

Additional Information

CPCTC Theorem

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent". It simply implies that once you have proven two triangles are congruent, all of their corresponding angles and sides are equal.

Conditions for Congruency

Two triangles can be proven congruent using five major geometric criteria: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and RHS (Right angle-Hypotenuse-Side).

Similarity vs Congruence

Congruent triangles have the exact same shape and size (ratio of sides is exactly 1). Similar triangles have the same shape but may differ in size, meaning their corresponding angles are equal, but corresponding sides are only proportional.

Shortcut Trick

Relative speed = 11 − 10 = 1 km/h = 1000 ÷ 60 m/min = 50/3 m/min.

Relative distance covered in 9 mins = (50/3) × 9 = 150 m.

Remaining distance = Initial distance − Distance covered = 200 − 150 = 50 m.

∴ The correct answer is 50 m.

Alternate Method

Given:

Initial distance between policeman and thief = 200 m

Speed of policeman = 11 km/h

Speed of thief = 10 km/h

Time = 9 minutes

Formula Used:

Relative Speed (when moving in the same direction) = S₁ − S₂

Distance = Speed × Time

1 km/h = 5/18 m/s

Calculations:

⇒ Relative speed = 11 − 10 = 1 km/h

⇒ Relative speed in m/s = 1 × (5/18) = 5/18 m/s

⇒ Time in seconds = 9 × 60 = 540 seconds

⇒ Distance covered by policeman relative to thief = Relative speed × Time

⇒ Relative distance = (5/18) × 540 = 5 × 30 = 150 m

⇒ Remaining distance between them = Initial distance − Relative distance

⇒ Remaining distance = 200 − 150 = 50 m

∴ The correct answer is 50 m.

Additional Information

Relative Speed (Same Direction)

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

Relative Speed (Opposite Direction)

When two objects move in opposite directions, their relative speed is the sum of their individual speeds: S_rel = S₁ + S₂.

Speed Conversion

To convert speed from km/h to m/s, multiply the speed value by 5/18. To convert from m/s to km/h, multiply by 18/5.

Shortcut Trick

Identify the form of the expression: a² + b² + ab, where a = 1.55 and b = 0.55.

Using the standard algebraic identity: a³ − b³ = (a − b)(a² + b² + ab).

Here, a − b = 1.55 − 0.55 = 1.

Therefore, a² + b² + ab = a³ − b³ directly.

∴ The correct answer is 1.55³ − 0.55³.

Alternate Method

Given:

The expression: 1.55² + 0.55² + 1.55 × 0.55

Formula Used:

a³ − b³ = (a − b)(a² + ab + b²)

Calculation:

⇒ Let a = 1.55 and b = 0.55

⇒ The given expression takes the form: a² + b² + ab

⇒ Rearranging the formula for the difference of cubes, we get: a² + ab + b² = (a³ − b³) ÷ (a − b)

⇒ Find the value of the denominator: a − b = 1.55 − 0.55 = 1

⇒ Substitute the numerical values back into the rearranged formula:

⇒ 1.55² + 1.55 × 0.55 + 0.55² = (1.55³ − 0.55³) ÷ 1

⇒ 1.55² + 1.55 × 0.55 + 0.55² = 1.55³ − 0.55³

∴ The correct answer is 1.55³ − 0.55³.

Additional Information

Sum of Cubes Identity

The formula for the sum of cubes is a³ + b³ = (a + b)(a² − ab + b²).

Difference of Squares

A fundamental algebraic identity is a² − b² = (a + b)(a − b).

Perfect Square Trinomials

The expansion of squared binomials follows the identities (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

The correct answer is 4 i.e. this part of the sentence contains a grammatical error.

Key Points

• The phrase "his health is not more good" is grammatically incorrect.
• The correct phrase should be "their health is not good anymore" or "their health is no longer good".

Hence, the correct answer is option 4.

Correct sentence: Neither my brother nor my brothers-in-law attended the meeting as their health is not good anymore.

Additional Information

• "More good" is incorrect; "better" should be used for comparisons, or expressions like "not good anymore" should be used to indicate a negative change in state.
• When talking about health deterioration, "not good anymore" indicates the current state effectively.

The correct answer is Option (3) i.e. QRPO

Key Points

• Q in a world that can be" begins the sentence by setting up the context.
• R harsh and challenging" continues the context by describing the nature of the world.
• P kindness and empathy" introduces the key elements that are needed in such a world.
• O bring light and positivity" concludes the sentence by describing the effect of kindness and empathy.

Therefore, the correct answer is QRPO.

Additional Information

• Option 1 (PORQ): This option places kindness and empathy first, which doesn't provide the necessary context before introducing the main subject.
• Option 2 (ROQP): This option disrupts the logical flow by starting with the description of the world before introducing kindness and empathy.
• Option 4 (QROP): This option is close but ends with the incomplete phrase "bring light and positivity" instead of the intended effect.

The correct answer is: Option 1 i.e. 'recieved'.

Key Points

• The word "recieved" is incorrectly spelt; the correct spelling is "received". (प्राप्त किया)
• Example: She received an award for her outstanding performance.
• "Received" refers to being given or presented with something. (प्राप्त किया)
• Example: He received a letter from his old friend yesterday.

Therefore, the correct answer is: Option 1 i.e. 'recieved'.

Additional Information

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

• Award (पुरस्कार): A prize or other mark of recognition given in honor of an achievement.
• Example: She won an award for her excellent research work.
• Performance (प्रदर्शन): The action or process of performing a task or function.
• Example: His performance in the play was outstanding.
• Outstanding (उत्कृष्ट): Exceptionally good.
• Example: She did an outstanding job on the project.

The correct answer is: Option 4.

Key Points

• The idiom "To read between the lines" means to understand more than what the words suggest; it involves perceiving the hidden or underlying meaning behind the words. (शब्दों से अधिक समझना)
• Example: When she said she was fine, he read between the lines and knew she was actually upset.
• "To underline some words" refers to physically drawing a line under words for emphasis. (कुछ शब्दों को रेखांकित करना)
• Example: The teacher asked us to underline the important points in the text.
• "To read differently" refers to interpreting or understanding text in a different manner. (अलग तरीके से पढ़ना)
• Example: She read the poem differently, finding new meanings in the verses.
• "To read aloud to public" means to read something out loud for an audience to hear. (जनता के सामने जोर से पढ़ना)
• Example: The author read aloud her new book to the audience at the event.

Therefore, the correct answer is: Option 4.

Additional Information

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

• To underline some words (कुछ शब्दों को रेखांकित करना): Drawing a line under words for emphasis.
• Example: The teacher asked us to underline the important points in the text.
• To read differently (अलग तरीके से पढ़ना): Interpreting or understanding text in a different manner.
• Example: She read the poem differently, finding new meanings in the verses.
• To read aloud to public (जनता के सामने जोर से पढ़ना): Reading something out loud for an audience to hear.
• Example: The author read aloud her new book to the audience at the event.

The correct answer is: Option 3.

Key Points

• The word "Deficient" means lacking in some necessary quality or element; not enough in amount or degree. (अपर्याप्त)
• Example: The diet was deficient in vitamins, leading to health problems.
• "Ample" refers to being more than enough in quantity, size, or scope; fully sufficient or more than adequate. (प्रचुर)
• Example: There was ample space in the room for all the guests to sit comfortably.
• Hence, we can infer that the opposite of 'Deficient' is 'Ample'.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Skimpy (अल्प): Lacking in size, fullness, or quantity; meager.
• Example: The portions of food served were quite skimpy, leaving everyone still hungry.
• Broken (टूटा हुआ): Separated into parts or pieces due to being damaged.
• Example: The broken vase lay in fragments on the floor.
• Terrible (भयानक): Extremely or distressingly bad or serious.
• Example: The weather was so terrible that we decided to stay indoors all day.