SSC CGL 2021 Tier-I (Held On : 18 April 2022 Shift 3) (Previous Year Paper)

Formula: Area of a circle = πr² , where π = 22/7

So,

• Area of Circle A = (22/7) × 4²
• Area of Circle B = (22/7) × 82

Ratio of the areas of two circles, i.e. Circle-A : Circle-B = (22/7) × 42 : (22/7) × 82 

= 16 : 64

= 1 : 4

Hence, '1 : 4' is the correct answer.

The correct option that indicates the arrangement of the given words in the order in which they appear in an English dictionary is:

5. Likeliest
6. Likelihood 
7. Likenesses
8. Likens
9. Likewise

Hence, '5, 1, 2, 4, 3' is the correct answer.

The logic followed here is: Alphabet are arranged according alphabet series.

• PRACTISE
• Alphabetical order of letters: A > C> E > I > P > R > S > T

Similarly,

• TECHNOLOGY
• Alphabetical order of letters: C > E > G > H > L > N > O > O > T > Y

Hence, 'CEGHLNOOTY' is the correct answer.

Anamika, Gopal, Nischal, Vanmayi, Shresta and Sripad are sitting in a straight line facing the north.

1. Sripad is at the second place from the right end.

2. Shresta is between Anamika and Sripad.

3. Nischal is to the immediate left of Gopal.

4. Four persons are sitting between Nischal and Vanmayi.

If Gopal and Sripad interchange their positions.

Then Gopal will be sitting between Vanmayi and Shresta.

Hence, 'Gopal' is the correct answer.

If

• 'sky' is called 'cloud'
• 'cloud' is called 'thunder'
• 'thunder' is called 'water'
• 'water' is called 'pot'
• 'pot' is called 'desert'
• 'desert' is called 'sky'

Fish lives in water and water is called pot.

• So, fish lives in pot.

Hence, 'pot' is the correct answer.

The paper when unfolded will appear as shown below:

Hence, 'option 2' is the correct answer.

At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika.

Here we see, Kritika is facing North.

Hence, 'North' is the correct answer.

The logic followed here is:

Similarly,

Hence, '33-45-24-27-39-3' is the correct answer.

The logic followed here is:

Hence, 'DZL' is the correct answer.

The least possible Venn diagram is:          

Conclusions:

I. Some animals are leopards. → Follow (As, Some lions are tigers, All tigers are leopards and All lions are animals) 

II. Some leopards are lions. → Follow (As, Some lions are tigers and All tigers are leopards)

III. Some animals are tigers. → Follow (As, Some lions are tigers and All lions are animals) 

Hence, All conclusions I, II and III follow.

The image embedded in given figure is as shown below:

Hence, 'option 3' is the correct answer.

Mistake Points

If Only two entities ask in the question, then Only those two parts are counted.

But,

If the question is asking for two entity then, you have to take all the common part which is included in that two areas.

Girls who are toppers and captains also are shown below:

Number of girls who are toppers and captains also = 8 + 5 = 13

Important Points Number of girls who are toppers and captains also - This statement means we should consider the numbers in the common region of intersection of Girls (triangle), Toppers (rectangle), and Captains (hexagon) = 8 + 5 = 13

Hence, '13' is the correct answer.

BODMAS rule:

Given equation: 63 * 90 * 42 * 230 * 46 * 3 

After replacing the *'s by the sequence of mathematical signs in each option, we get:

1. =, ×, +, ÷, – 

63 = 90 × 42 + 230 ÷ 46 - 3 

63 = 90 × 42 + 5 - 3

63 = 3780 + 5 - 3

63 = 3785 - 3

63 ≠ 3782

2. +, ÷, –, =, ×

63 + 90 ÷ 42 - 230 = 46 × 3

63 + 2.14 - 230 = 46 × 3

63 + 2.14 - 230 = 138

65.14 - 230 = 138

-164.86 ≠ 138

3. =, –, +, ÷, ×

63 = 90 - 42 + 230 ÷ 46 × 3

63 = 90 - 42 + 5 × 3

63 = 90 - 42 + 15

63 = 105 - 42

63 = 63

4. ×, ÷, =, –, +

63 × 90 ÷ 42 = 230 - 46 + 3

63 × 2.14 = 230 - 46 + 3

134.82 = 230 - 46 + 3

134.82 = 233 - 46

134.82 ≠ 187

Hence, '=, –, +, ÷, ×' is the correct answer.

Given sequence: d _ a _ b _ q d h _ a _ c q _ h _ a _ c q

1. h a c a b d a b → d h a a b c q - d h a a b c q - d h a a b c q
2. h a b a b d a b → d h a a b b q - d h a a b c q - d h a a b c q
3. h a c a b d q b → d h a a b c q - d h a a b c q - d h q a b c q
4. h a q a b d a b → d h a a b q q - d h a a b c q - d h a a b c q

• In option 1, dhaabcq is repeated.

Hence, 'h a c a b d a b' is the correct answer.

A cube of side 12 cm is painted green on all the faces and then cut into smaller cubes of sides 2 cm each.

Cube is divided into 12/2 = 6 equal parts, hence n = 6.

Number of cubes with 1 sides painted = 6(n - 2)²

= 6 (6 - 2)²

= 6 × 4²

= 6 × 16

= 96

Hence, '96' is the correct answer.

The logic followed here is:

578 - 1² = 578 - 1 = 577

577 - 32 = 577 - 9 = 568

568 - 52 = 568 - 25 = 543

543 - 72 = 543 - 49 = 494

Hence, '494' is the correct answer.

The mirror image of the given combination when the mirror is place at the right side is as shown below :

• The line PQ is the mirror.
• The given word "BRIGHTEN" is written as BRTGHIEN in option 1, positions of letters T and I are  interchanged ⇒ Option 1 is eliminated.
• The given word "BRIGHTEN" is written as BRTGHIEN in option 2, positions of letters T and I are  interchanged ⇒ Option 2 is eliminated.
• The given word "BRIGHTEN" is written same as the given combination BRIGHTEN in option 3 ⇒ Option 3 is eliminated.

Hence, 'option 4' is the correct answer.

Given expression: 441 D 7 A 21 B 6 C (189 D 7) A (46 C 12)

After replacing the letters by their meaning, we get:

441 ÷ 7 + 21 × 6 - (189 ÷ 7) + (46 - 12)

= 441 ÷ 7 + 21 × 6 - 27 + 34

= 63 + 21 × 6 - 27 + 34

= 63 + 126 - 27 + 34

= 223 - 27

= 196

Hence, '196' is the correct answer.

The logic followed here is:

Logic: Number : (Number)² + 7

• 16 : 263 → 16² + 7 = 256 + 7 = 263
• 22 : 491 → 222 + 7 = 484 + 7 = 491

Similarly,

• 18 : ? → 182 + 7 = 324 + 7 = 331

Hence, '331' is the correct answer.

The logic followed here is:

1. FCHP → F - 3 = C; C + 5 = H; H + 8 = P
2. JGLS → J - 3 = G; G + 5 = L; L + 7 = S
3. WTYF → W - 3 = T; T + 5 = Y; Y + 7 = F
4. NKPW → N - 3 = K; K + 5 = P; P + 7 = W

Hence, 'FCHP' is the odd one out.

The logic followed here is:

Logic followed by the differences between the numbers is:

4 × 1 = 4

4 + 3 = 7

7 × 5 = 35

35 + 7 = 42

42 × 9 = 378

378 + 11 = 389

So, the next number in the series will be 472 + 389 = 861

Hence, '861' is the correct answer.

The position of letters according to the English alphabet series:

The pattern followed here is:

Step: 1 All the alphabet are arranged in ascending order (i.e., alphabetical order A to Z) 

Step: 2 After arranging in ascending order all letters follow the pattern of +4, -4, +4, -4 and so on.

‘TEDIOUS’ is written as ‘HAMKWPY’

 

Similarly,

‘PROFUSE’ be written as '?'

Hence, the correct answer is "IBSLVOY".

The logic followed here is:

Logic: Column = Third number × (Second number - 10) = First number

• Column 1: 15 × (14 - 10) = 15 × 4 = 60
• Column 2: 19 × (18 - 10) = 19 × 8 = 152

Similarly,

• Column 3: ? × (17 - 10) = 161
• ? × 7 = 161
• ? = 161 ÷ 7
• ? = 23

Hence, '23' is the correct answer.

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

Taruni is Jahnavi’s sister

Dilip is Manoj’s paternal grandfather.

Clearly, Taruni is wife of Dilip.

Hence, 'Wife' is the correct answer.

The pattern followed here is:

1) 

is shifted two placed left  in second figure and remain in its place till the last figure.

2) 

is shifted three placed left  in third figure then lower side middle of the figure is last figure.

3) 

is shifted fourth placed left in third figure then shifted right bottom corner in fourth figure and remain its place till the last figure.

Hence, the correct answer is "Option 4".

The correct answer is Article 297.

• The 40^th Amendment Act of 1976 was applied to Article 297 of the constitution of India.

Key Points

• According to the  40^th Amendment Act of 1976:
• For Article 297 of the Constitution, the following article shall be substituted, namely:-
• Article 297(3).
• Article297(2)
• Article 297(1)
• ​These articles empowered the Parliament to specify ​from time to time,
• the limits of the territorial waters, the continental shelf, the Exclusive Economic Zone (EEZ), and the maritime zones of India.
• 40^th Amendment 1976, also included 64 more Central and state laws.
• Mostly relating to land reforms in the 9^th Schedule.

Additional Information

• Article 248
• It deals with the residuary powers of legislation.
• It states that parliament has exclusive power to make any law with respect to any matter not enumerated in the Concurrent List or State List.
• Article 245​
• ​Article 245 of the Indian constitution talks about the extent of laws made by Parliament and by the Legislatures of States.
• It gives Parliament the power to make laws and also gives the legislative body the power to repeal them.
• Article 226
• ​Article 226 of the Constitution empowers the Hon'ble High Courts to exercise power through the issuance of writs:
• Habeas Corpus
• Mandamus
• Quo Warranto
• Prohibition and certiorari or any appropriate writ.

The correct answer is Acoustics.

Key Points

• Acoustics is the study of the production and propagation of sound waves.
• Acoustics is the science concerned with the production, control, transmission, reception, and effects of sound.
• The term is derived from the Greek akoustos, meaning “heard.”
• Applications of acoustic technology are in the study of:
• Geologic,
• Atmospheric,
• Underwater phenomena.​

Additional Information

• Optics
• ​Optics is the branch of physics which is concerned with light and its behavioural pattern and properties.
• Optics is a branch of physics that deals with the determination of behaviour and the properties of light,
• It also studies the interactions of light with the matter and also with the instruments which are used to detect it.
• Photonics
• ​Photonics is the physical science of light waves.
• It deals with the science behind the generation, detection and manipulation of light.
• Light has a dual nature known as the wave-particle duality.
• Astrophysics
• ​Astrophysics is a branch of space science that applies the laws of physics and chemistry to seek to understand the universe.
• The field explores topics such as the birth, life and death of stars, planets, galaxies, nebulae and other objects in the universe.

The correct answer is Arthur C Clarke.

Key Points

• Arthur Charles Clarke was an author and inventor, most famous for his science fiction novel '2001: A Space Odyssey.'
• His work ranged from scientific discovery to science fiction, from technical application to entertainment.
• Arthur C Clarke, a famous science fiction writer held the position of a professor at the Physical Research Laboratory in Ahmedabad.
• He was also a radar instructor in the Royal Air Force after World War II began in the **year 1939.**​

Additional Information

• Isaac Asimov
• ​Isaac Asimov was an American writer and professor of biochemistry at Boston University.
• A prolific writer who is best known for the Foundation series and robot stories.
• Jules Verne 
• ​Jules Verne was a French novelist, poet, and playwright.
• Famous for his pioneering science-fiction novels, such as Journey to the Centre of the Earth (1864), From the Earth to the Moon (1865), and Twenty Thousand Leagues Under the Sea (1869–70).
• HG Wells ​
• ​H.G. Wells was an English novelist, journalist, sociologist, and historian.
• Best known for such science fiction novels as The Time Machine and The War of the Worlds and such comic novels as Tono-Bungay.

The correct answer is Cotton.

Key Points

• India lost a large proportion of cotton growing area to Pakistan during the partition.
• The industry suffered in several ways:
• India’s share in the output of raw cotton in undivided India was about 60%, while the corresponding share in the mill output was as high as 95%.
• Secondly, the areas growing high-quality long and medium staple cotton went to West Punjab and Sind.
• Thirdly, India lost a sizeable amount of its internal market because of the partition.
• The country also lost its earlier advantage as an exporter.
• Approximately 65 percent of Pakistan's cotton is grown in Punjab as the region has dry conditions.
• The rest is grown in Sindh, which has a more humid climate, with the negligible area under cotton in Khyber Pakhtunkhwa and Balochistan.
• **During the partition these areas went into Pakistan, hence India lost a huge proportion of its cotton production.**​

Important Points

• Conditions required for Cotton cultivation
• Cotton is a tropical or sub-tropical crop grown in semi-arid areas of the country (mainly in the Deccan Plateau).
• A hard frost is injurious to cotton cultivation and it requires at least 210 frost-free days.
• Only light rainfall (50 to 100 centimetres) is preferred.
• Cotton can also be cultivated under irrigated conditions.
• It requires high temperature and bright sunshine for its growth.
• Cotton requires a clear sky during the flowering stage.
• A light well-drained soil capable of retaining moisture is ideally suited for the cultivation of the crop.
• Black cotton soil is preferred.
• It is a Kharif crop and requires 6 to 8 months to mature.
• Now, India is the leading cotton-producing country.

The correct answer is 1951.

Key Points

• The First Amendment to the constitution of India was made in 1951.
• The first Amendment added the ninth schedule to the Indian constitution.
• It restricted the freedom of speech and expression.
• It was introduced to remove certain practical difficulties created by the court's decision in several cases such as Kameshwar Singh Case, Romesh Thapar Case, etc.
• The First Amendment protects us against government limits on our freedom of expression, but it doesn’t prevent a private employer from setting its own rules.
• It prevents the government from requiring you to say something you don't want to or keeping you from hearing or reading the words of others.
• It inserted articles 31A and 31B into the Indian constitution.

The correct answer is grammar.

• Ashtadhyayi was written by Indian grammarian Panini during the 6^th to 5^th century BCE.

Key Points 

• Ashtadhyayi sets the work standard for the Sanskrit language.
• It sums up in 4,000 sutras that had evolved in the Vedic religion.
• Panini divided his work into eight chapters, each of which is further divided into quarter chapters.
• Beyond defining the morphology and syntax of Sanskrit language, Ashtadhyayi distinguishes between usage in the spoken language and usage that is proper to the language of the sacred texts.

Additional Information 

• Vedavyasa: He is the author of Mahabharata.
• Shukadeva: He is the main narrator of Bhagavata Purana.
• Valmiki: He is the author of the epic Ramayana.

The correct answer is 2%.

Key Points

• India is expected to have a Current Account Surplus of 2 percent of GDP in FY21, a historic high after 17 years.
• Summary of Economic Survey-2020-21
• India’s real GDP to record an 11.0% growth in FY2021-22 and nominal GDP to grow by 15.4% – the highest since independence.
• The recovery in the second half of FY2020-21 is expected to be powered by government consumption, estimated to grow at 17% YoY.
• Exports are expected to decline by 5.8% and imports by 11.3% in the second half of FY21.
• India expected to have a Current Account Surplus of 2% of GDP in FY21, a historic high after 17 years.
• On the supply side, Gross Value Added (GVA) growth was pegged at -7.2% in FY21 as against 3.9% in FY20.
• Agriculture is set to cushion the shock of the COVID-19 pandemic on the Indian economy in FY21 with a growth of 3.4%.
• Industry and services are estimated to contract by 9.6% and 8.8% respectively during FY21.
• Agriculture remained the silver lining while contact-based services, manufacturing, and construction were hit hardest, and recovering steadily.
• India remained a preferred investment destination in FY 2020-21 with FDI pouring in amidst global asset shifts towards equities and prospects of quicker recovery in emerging economies.
• Net FPI inflows recorded an all-time monthly high of US$ 9.8 billion in November 2020, as investors’ risk appetite returned.
• India was the only country among emerging markets to receive equity FII inflows in 2020.​

Additional Information

• Current Account Surplus
• ​A current account surplus is a positive current account balance, indicating that a nation is a net lender to the rest of the world.
• A current account surplus will tend to boost domestic employment if:
• It is due to an improvement in competitiveness.
• Leading to higher demand for exports.
• If domestic demand is still relatively strong, consumers are buying domestic goods, rather than importing$.

The correct answer is Satriya.

Key Points

• Sattriya is a classical dance of Assam and it was introduced by Mahapurusha Sankaradeva.
• Mahapurusha Sankaradeva:
• He was born in 1449 AD in Nagaon, Assam.
• Sankardev inspired the Bhakti movement in Assam.
• He was the founder of Ekasarana Dharma.
• He is considered the father of the modern Assamese race.​

Additional Information

• Lavani:​
• It is a folk dance of Maharashtra.
• Women wearing ankle bells (Ghungroo) and 9-yard saree perform this dance on dholak beats.
• The performers are called 'Nauvari' and the style of saree wearing is called Kashta.
• It is performed on the themes of heroism, love devotion, sorrow, politics, and religion.
• Odissi:
• The caves of Udayagiri-Khandagiri provide some of the earliest examples of Odissi dance.
• It derives its name from the ‘Odra nritya’ mentioned in Natya Shastra.
• It was mainly practised by the ‘maharis’ and patronized by the Jain king Kheravela.
• The young boys were recruited and dressed as females for this dance form
• These boys in the art form came to be known as ‘Gotipuas’. ​
• Bihu:
• It is a festival of Assam.
• This festival is celebrated 3 times a year
• Rongali or Bohag Bihu: April
• Kati Bihu: October
• Bhogali or Magh Bihu: January
• Popir:
• Popir is the folk dance of Arunachal Pradesh.
• Performed by Galo tribe of Arunachal Pradesh.
• It is mainly performed by females.
• ​Ponung:
• ​It is a folk dance of Arunachal Pradesh.
• Performed by Adi tribe of Arunachal Pradesh.
• Ponung dance is an important religious celebration for the Adi tribe.

​

The correct answer is A Sharath Kamal.

• Achanta Sharath Kamal was the first Indian table tennis player ever to become nine times senior national champion as of April 2021.

Key Points 

• Achanta Sharath Kamal is a professional table tennis player from India.
• He is the first Indian table tennis player ever to become nine times Senior National Champion hence breaking the record of eight times National Champion Kamlesh Mehta.
• In 2019 he was awarded the Padma Shri, India's fourth-highest civilian award.
• In the year 2007, he was the first Indian to win the Pyongyang Invitational Tournament held at Pyongyang, North Korea.

Additional Information 

The correct answer is Entomology

• Entomology is the study of insects and their relationship to humans, the environment, and other organisms.
• Entomology is crucial to our understanding of the human disease, agriculture, evolution, ecology, and biodiversity.

​

Additional Information 

• Mycology is the study of fungi, their relationships to each other and other organisms. It is the unique biochemistry that sets them apart from other groups.
• Philology traditionally the study of the history of language, including the historical study of literary texts. It is also called comparative philology when the emphasis is on the comparison of the historical states of different languages.
• Phycology (also called algology) is the study of algae. It is a large heterogeneous group of chiefly aquatic plants ranging in size from microscopic forms to species as large as shrubs or trees.

The correct answer is Rs.7 lakh crore.

Key Points

• The payment made at MSP rates in the last 6 years is Rs. 7 lakh crore which is double that made by the previous government.
• The Cabinet Committee on Economic Affairs (CCEA) chaired by Prime Minister Shri Narendra Modi has approved the increase in the Minimum Support Prices (MSPs) for all mandated Rabi crops for marketing season 2021-22.
• This increase in MSP is in line with the recommendations of the Swaminathan Commission.
• The highest increase in MSP has been announced for:
• lentil (Rs. 300 per quintal).
• gram and rapeseed & mustard (Rs. 225 per quintal each).
• safflower (Rs. 112 per quintal).
• For barley and wheat, an increase of Rs. 75 per quintal and Rs 50 per quintal respectively.

Additional Information

• Minimum Support Price (MSP)
• Form of market intervention by the Government of India to insure agricultural producers against any sharp fall in farm prices.
• Announced on the basis of the recommendations of the Commission for Agricultural Costs and Prices (CACP).
• Government announces minimum support prices (MSPs) for 22 mandated crops and fair and remunerative prices (FRP) for sugarcane.
• The mandated crops are 14 crops of the Kharif season, 6 rabi crops, and two other commercial crops.
• The list of crops is as follows:
• Cereals (7) - paddy, wheat, barley, jowar, bajra, maize and ragi
• Pulses (5) - gram, arhar/tur, moong, urad and lentil
• Oilseeds (8) - groundnut, rapeseed/mustard, toria, soyabean, sunflower seed, sesamum, safflower seed, and nigerseed.
• Raw cotton
• Raw jute
• Copra
• De-husked coconut
• Sugarcane (Fair and remunerative price)
• Virginia flu-cured (VFC) tobacco

The correct answer is Man.

Key Points

• Hominidae includes the great apes:
• The orangutans (genus Pongo),
• The gorillas (Gorilla), and
• The chimpanzees and bonobos (Pan)
• Human beings (Homo).
• Hominidae has been a subject of much debate among taxonomists.
• Formerly, humans alone (with their extinct forebears) were placed in Hominidae.
• Earlier, the great apes were placed in a different family, Pongidae.
• However, morphological and molecular studies now indicate that humans are closely related to chimpanzees.
• Since classification schemes aim to depict relationships.
• It is logical to consider humans and great apes as hominids.
• That is members of the same zoological family, Hominidae.
• All members of Hominidae share complex cognitive attributes:
• ​For example, they all can learn to recognize themselves in mirrors (an ability indicating a degree of self-awareness).

The correct answer is 16.

Key Points

• The average atomic mass of oxygen is 15.9994(16) atomic mass units.
• However, this atomic mass is the average atomic mass of all the isotopes in nature.
• Hence, the atomic mass of oxygen is 16 u means that one atom of oxygen is 16 times heavier than 1/12 of a carbon-12 atom.

Oxygen is the chemical element with the symbol O and atomic number 8.

• It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as well as with other compounds.
• At standard temperature and pressure, two atoms of the element bind to form dioxygen, a colorless and odorless diatomic gas with the formula O2.

Diatomic oxygen gas currently constitutes 20.95% of the Earth's atmosphere, though this has changed considerably over long periods of time.

• Oxygen makes up almost half of the Earth's crust in the form of oxides.
• Oxygen was isolated by Michael Sendivogius before 1604, but it is commonly believed that the element was discovered independently by Carl Wilhelm Scheele, in Uppsala, in 1773 or earlier, and Joseph Priestley in Wiltshire, in 1774.
• Priority is often given to Priestley because his work was published first.

The correct answer is 1968.

Key Points

Green Revolution in India:

• The term green revolution was first used by William Gaud and Norman Borlaug is the Father of the Green Revolution.
• After Independence, Indian policy-makers adopted all measures to achieve self-sufficiency in food grains.
• In the year 1965, the government of India launched the Green Revolution with the help of a geneticist, now known as the father of the Green revolution (India) M.S. Swaminathan.
• The movement of the green revolution was a great success and changed the country’s status from a food-deficient economy to one of the world’s leading agricultural nations.
• It started in 1967 and lasted till 1978.
• India adopted a new strategy in agriculture, which resulted in the 'Green Revolution', especially in the production of wheat and rice.
• Indira Gandhi, the then Prime Minister of India, officially recorded the impressive strides of the Green Revolution in agriculture by releasing a special stamp entitled 'Wheat Revolution' in July 1968.
• The success of wheat was later replicated in rice.

Thus, to signify the achievements of the Green Revolution, a stamp was released by the then Prime Minister Mrs. Indira Gandhi entitled as ‘Wheat Revolution’ in July 1968.

The correct answer is a mobile water testing laboratory.​

 Key Points

• In October 2020, the Haryana government has launched a mobile water testing laboratory under the Jal Jeevan Mission scheme.
• It is fully equipped with a multi-parameter system containing analysers, sensors, probes and instruments meant for assessing water quality.
• Water quality in Haryana is mainly affected by constituents like total dissolved solids, fluoride, nitrate, iron and alkalinity.
• This testing lab is GPS-enabled for location tracking.
• Haryana: 
• Capital: Chandigarh
• Governor: Bandaru Dattatreya
• Chief minister: Manohar Lal Khattar
• Lok Sabha seats - 10.
• Rajya Sabha seats - 5.
• State Animal - Blackbuck.
• State Bird - Black francolin.

The correct answer is Mahendra Lal Sircar.

Key Points

• Indian Association for the Cultivation of Science in Calcutta was founded on July 29, 1876, by Dr Mahendra Lal Sircar, IACS is the oldest institute in India devoted to the pursuit of fundamental research in the frontier areas of basic sciences.
• Professor C V Raman worked at IACS from 1907 to 1933, and it is here that he discovered the celebrated Effect that bears his name and for which he was awarded Nobel Prize in Physics in 1930.
• The Indian Association for the Cultivation of Science (IACS) is a society registered under Act XXI of 1860.
• It has a Governing Council with a number of members elected or nominated and the Registrar as its Non-Member Secretary.
• The Institute is run by the Governing Council, which is the apex policy-making body.

Additional Information

• The Governing Council plays the following important role.
• The Council is the executive authority of the Association and would constitute the apex body responsible for the smooth running of the organization.
• The Council will ensure that the transactions in the Association are in accordance with the Regulations and Bye-Laws contained herein.
• It is the apex policy-making and decision-making authority of the Association. It has the complete power to run the affairs of the institute component of the Association.
• The Council is empowered to create posts in any category including supernumerary positions and or new departments/divisions/units subject to concurrence from the Department of Science & Technology, Government of India.
• The Council is also empowered to introduce new Bye-Laws for better running of the Association within the framework of the regulations.
• The Council is proactively engaged in entering into an arrangement with the government ministries and agencies, both in the centre and the state and also from industries and international sources for securing and accepting grants-in-aid to the Association on mutually agreed on terms and conditions.
• It is also empowered to undertake any other activity that might be deemed suitable for the progress of the Association.

The correct answer is Twinkle Khanna.

• Twinkle Khanna is the author of the book 'Mrs Funnybones: She's Just Like You and a Lot Like Me'.

Key Points 

The correct answer is Arunachal Pradesh.

Key Points

• According to Census-2011, the population density of Arunachal Pradesh is only 17 people per square km.
• According to the Census 2011, the population density of the states given in the option is -
• Sikkim - 86 per sq km.
• Nagaland - 119 per sq km.
• Assam - 398 per sq km.
• Among the states, Arunachal Pradesh has the lowest population density with 17 per sq km.
• **The highest population density is in the NCT of Delhi with 11297 people per sq km.**​

Additional Information

• The population density of India is 382.
• Earlier, in the 2001 Census, the total population density was 324.
• As per the 2011 Census:
• The most densely populated state in India is Bihar.
• Bihar has a total density of 1106.
• The least densely populated state in India is Arunachal Pradesh.
• Total Density: 17.
• Delhi is the most densely populated Union Territory in India.
• ​It has a total density of 11320.
• Andaman and Nicobar Islands is the least densely populated UT in India.
• Total Density: 46

The correct answer is 3.

Key Points

• The number of protons in the nucleus of lithium is 3.
• Lithium:
• Symbol: Li
• Atomic Number: 3
• Group: 1
• Period: 2
• Block: S
• Electronic configuration: [He] 2s1
• It is the lightest metal.
• Lithium is found only in Salt and Minerals.
• Lithium is used in battery industries.

The correct answer is Diwan-i-insha.

Key Points

• Diwan-i-Insha was the department of correspondence.
• Delhi Sultanate's administration was segregated into various parts – Central, Provincial, Judicial, Local, etc.
• There were many departments and officials who helped the Sultan in administration.

Important Points

• Administration under the Sultanate:
• It was also influenced by the Iranian system of administration.
• The situation in India and Indian traditions was kept in mind during these systems.
• Organs of the Government:
• Diwan-i-Wizarat: Department of revenue and finance headed by the Wazir.
• Diwan-i-Arz: Department of Military headed by Ariz-i-Mamalik.
• Diwan-i-Insha: Department of royal correspondence headed by Dabir-i-lnsha.
• Diwan-i-Risalat: Department of foreign affairs
• Diwan-i-bandagan: ​Diwan-i-bandagan (department of slaves).
• Diwan-i-Khairat: (charity department) was created by Firuz Shah Tughlaq.
• Diwan-i-mustakhraj: Diwan-i-mustakhraj (to realize arrears) was created by Alauddin Khiiji.
• Diwan- i-kohi: Diwan- i-kohi (department of agriculture) was created by Muhammad bin Tughluq.

The correct answer is Ibrahim Khan.

Key Points

• Chandannagar was established as a French colony in 1673.
• Obtained permission from Ibrahim Khan, the then Nawab of Bengal, to establish a trading post on the right bank of the river Hooghly.
• In 1730 Joseph Francois Dupleix was appointed governor of the city.
• In 1756 war broke out between France and Great Britain, and the British Navy captured Chandannagar on 23 March 1757.
• Chandernagore merged with West Bengal on 2^nd October 1954.

The correct answer is 24. 

• Article 24 
• Article 24 of the Indian constitution talks about the prohibition of the employment of children in factories.
• No child below the age of fourteen years shall be employed to work in any factory or mine or engaged in any other hazardous employment.

Important Points

• Article 23
• Trafficking of humans and forms of forced labour are prohibited and any contravention of this provision shall be an offence punishable in accordance with the law.
• Nothing in this article shall prevent the State from imposing compulsory service for public purposes, and in imposing such service the State shall not make any discrimination on grounds only of religion, race, caste or class or any of them.
• Article 25: 
• Freedom of Conscience of the free profession, practice and propagation of religion.
• Article 26:
• Freedom to manage religious affairs.
• Article 27:
• Freedom from taxation for the promotion of religion.
• Article 28:
• Freedom from attending religious instruction.
• Article 34:
• Article 34 says while Martial Law is in force in any area, fundamental rights can be restricted.
• Article 21A:
• Article 21A provides the Right to Education.
• Under Article 21A State provides free and compulsory education to all children between the ages of 6 to 14 years.
• Article 31:
• Article 31 says the right to property is no more a fundamental right.
• The Right to property though still, is a constitutional right, not a fundamental right.

The Correct Answer is Le Corbusier.

Key Points

• The monument built in Chandigarh by Legendary Architect, Le Corbusier is Open Hand Monument.
• The Open Hand Monument is a symbolic structure designed by the architect Le Corbusier and located in the Capitol Complex of the Indian city and union territory of Chandigarh.
• It is the emblem and symbol of the Government of Chandigarh and symbolizes "the hand to give and the hand to take, peace and prosperity, and the unity of mankind".
• The largest example of Le Corbusier's many Open Hand sculptures, it stands 26 meters high.
• The metal structure with vanes is 14 meters high, weighs 50 short tons, and was designed to rotate in the wind.

The correct answer is Mithali Raj.

Key Points 

• ​Mithali Raj is an Indian Cricketer and the Captain of the Indian Women's National Cricket team.
• Mithali Raj has moved up one place to occupy the number one spot in the ICC ODI rankings 2017.
• Mithali received the Arjuna award in 2013.
• Mithali Raj became the first Indian woman to score 10,000 runs in international cricket across all formats in March 2021.
• She is famously known as the "Lady Sachin".

Important Points

• International Cricket Council is the world governing body of cricket.
• It was founded at the Imperial Cricket Conference in 1909 by representatives from Australia, England, and South Africa.
• It was renamed the International Cricket Conference in 1965 and took up its current name in 1989.
• Chairman of ICC: Greg Barclay.
• CEO of ICC: Geoff Allardice.
• Headquarters of ICC: Dubai, United Arab Emirates.
• ICC Awards of the Decade 2020:
• Ellyse Perry wins the Rachael Heyhoe-Flint Award for ICC Female Cricketer of the Decade.
• Ellyse Perry is ICC Women’s T20 Cricketer of the Decade.
• Kyle Coetzer is ICC Men’s Associate Cricketer of the Decade
• Kathryn Bryce is ICC Women’s Associate Cricketer of the Decade.
• ​ICC Spirit of Cricket Award of the Decade: MS Dhoni (India)
• Garfield Sobers Award for ICC Male Cricketer of the Decade: Virat Kohli (India).
• ICC Men’s ODI Cricketer of the Decade: Virat Kohli (India)
• ICC Men’s T20I Cricketer of the Decade: Rashid Khan (Afghanistan)
• ICC Men’s Test Cricketer of the Decade: Steve Smith(Australia)
• ICC Men’s Associate Cricketer of the Decade: Kyle Coetzer (Scotland)
• Rachael Heyhoe Flint Award for ICC Female Cricketer of the Decade: Ellyse Perry (Australia)
• ICC Women’s ODI Cricketer of the Decade: Ellyse Perry(Australia)
• ICC Women’s T20I Cricketer of the Decade: Ellyse Perry (Australia)
• ICC Women’s Associate Cricketer of the Decade: Kathryn Bryce (Scotland)

Additional Information

• ICC Awards 2021:

The correct answer is Food items.

Key Points

Public Goods :

• In economics, a public good is a good that is both non-excludable and non-rivalrous.
• For such goods, users cannot be barred from accessing or using them for failing to pay for them.
• Also, use by one person neither prevents access of other people nor does it reduce availability to others.
• Examples - National defence, Roads, Government administration, etc.

Private Goods:

• In economics, private good is a good that is both excludable and rivalrous.
• For instance, food consumed automatically bars other people from consuming that portion.
• Food items are private food.

Hence Food items are NOT public goods.

Additional Information

Given data:

Formula used:

% difference = [(Difference in the number of workers having daily wages less than Rs 500 and those having wages Rs 650 and above) / (Workers with daily wages Rs 650 and above)] × 100

Calculations:

Workers with daily wages less than Rs 500 = 30 + 45 = 75

Workers with daily wages Rs 650 and above = 35

Difference in the number of workers having daily wages less than Rs 500 and those having wages Rs 650 and above = 75 – 35 = 40

% difference = ${40\over 35 }$ × 100 = 114.3%

The answer is 114.3 %.

Formula:

(x - y)² = x² + y² - 2xy

Calculations:

√x - $1\over √x$ = √3

Squaring both sides, we get-

⇒ (√x)² + ($1\over √x$)² - 2 × $\sqrt x$  × $1\over √x$ = (√3)²

⇒ x + $1\over x$ - 2 = 3

⇒ x + $1\over x$ = 5

Squaring both sides, we get-

⇒ x² + $1\over x^2$ + 2 = 25

⇒ x2 + $1\over x^2$ = 23

Squaring both sides, we get-

⇒ x4 + $1\over x^4$ + 2 = 529

⇒ x4 + $1\over x^4$ = 527

The answer for the expression is 527.

Shortcut Trick If √x - $1\over √x$ = √3 = p, then x + $\frac{1}{x}$ = p² + 2 = (√3)² + 2 = 5 = k (Let)

If  x + $\frac{1}{x}$ = k = 5, then x² + $\frac{1}{x^2}$ = k² - 2 = 5² - 2 = 23 m (Let)

 x2 + $\frac{1}{x^2}$ = m = 23, then x⁴ + $\frac{1}{x^4}$ = m² - 2 = (23)² - 2 = 527

Formula used:

sin 30º = $1\over 2$

cos 45º = $1 \over \sqrt2$

sin 45º = $1 \over \sqrt2$

cos 60º = $1\over 2$

Calculations:

Substituting the value of A as 10º in the equation-

⇒ $12 sin30+5cos (5\times 10-5)\over 9 sin {9\times 10\over 2}-4cos (5\times 10+10)$

⇒ $12 sin30+5cos 45\over 9 sin 45-4cos 60$

Substituting the values of trigonometric functions-

⇒ $12\times {1\over 2} + 5 \times { 1\over\sqrt2} \over9\times {1\over\sqrt2} -4\times {1\over 2}$

⇒ $6 + {5\over\sqrt2}\over {9\over\sqrt2}- 2$

Taking √2 as LCM and canceling the common denominator, we get-

⇒ $6\sqrt2 + 5\over 9- 2\sqrt2$

The answer is $6\sqrt2 + 5\over 9- 2\sqrt2$.

Given data:

Δ PQR area = 196 cm²

Δ MNT area = 169 cm2

Longest side of PQR = 28 cm

Concept used:

According to the Similarity theorem, two triangles are said to be similar, if their sides are in equal proportion along with their corresponding angles. The area of the similar triangle would also be in proportion to the square of their similar sides.

Hence, if Δ ABC ~ Δ DEF

⇒ $AB^2 \over DE^2$ = $ar Δ ABC \over ar Δ DEF$ 

Calculations:

Longest side of PQR i.e, PR = 28 cm

From the similarity theorem,

⇒ $PR^2\over MT^2$ = $ar PQR\over ar MNT$ 

Taking the square root of both the sides -

⇒ $28 \over MT$ = $14\over 13$

⇒ MT = 26 cm

∴ The length of the largest side of the smallest triangle Δ MNT is 26 cm.

Given data:

OD = OA = 15 cm (radius)

AB = 24 cm

AC = CB = 12 cm

Concept used:

Chord theorem circle states that if the radius of the circle is perpendicular to the chord of the circle, it bisects it and vice-versa.

In the circle, OA is the radius that bisects the chord BC perpendicularly.

Calculations:

In right-angled triangle OAC,

AC² + OC² = OA²  (From Pythagoras theorem)

Substituting the value of OA and AC 

⇒ OC² = 15² – 12² = 81 or OC = 9 cm

From the figure, CD = OD – OC

Since, OD = radius i.e., 15 cm

⇒ CD = 15 – 9 = 6 cm

∴ The length of CD is 6 cm.

Given data:

Profit % = 17%

Discount at Marked Price = 10%

Cost Price = Rs 500

Formula used:

MP × (100 - D%) = CP × (100 + G%) = SP

Where-

MP = Marked Price

CP = Cost Price

SP = Selling Price

D% = Discount offered at Marked Price

G% = Profit %

Calculations:

Substituting the values of D%, G%, and CP in the equation-

MP × (100 - D%) = CP × (100 + G%)

MP = CP × (100 + G%) / (100 - D%)

MP = 500 × (100+17) / (100 - 90)

MP = 500 × (117 / 90) = Rs 650

The Printed Price (Marked Price) is Rs 650.

Given data:

CP = tangent to the circle i.e., ∠OCP = 90º

∠APC = 38º

Calculations:

In Δ OCP, ∠OCP + ∠OPC + ∠COP = 180º

∠COP = 180º – (∠OCP + ∠OPC)

∠COP = 180º – (90º + 38º) = 52º

In isosceles triangle BOC, ∠BCO + ∠CBO + ∠COB = 180º

Since ∠BCO = ∠CBO (formed from same radius)

⇒ 2 ∠BCO = 180º – ∠COB

⇒ ∠BCO = $(180º - 52º)\over 2$ = 64º

From the figure, ∠PCB = 90º – ∠BCO

⇒ ∠PCB = 90º – 64º = 26º

∴ The measure of ∠PCB is 26º.

Given data:

Principal amount = Rs 17,200

Rate 1 = 8 %

Rate 2 = 10 %

Total interest received = Rs 3008

Time = 2 years

Formula used :

 SI = (P x R x T) / 100

Where-

P = Principal amount

R = Rate

T = Time

SI = Simple Interest

Calculation :

Let the amount lent on 8 % be a

⇒ Amount on 10 % = (17,200 - a)

SI on principal “a” = (a x 8 x 2) / 100 = $4a\over 25$

Similarly, SI on principal (17,200 - a) = $(17,200 - a) × 10 × 2\over 100$ = $17,200 – a \over 5$

According to the question, total interest accrued was Rs 3008

⇒ $4a\over 25$ + $17,200 – a \over 5$ = 3008

⇒ 4a + 86,000 - 5a = 3008 ×  25

⇒ - a + 86,000 = 75,200

⇒ a = Rs 10,800

∴ The amount lent at 8% rate was Rs 10,800.

Given data:

Volume of sphere = 4,851  cm³

Formula used:

V = $4\over3$π r³

Where-

V = volume of the sphere

R = radius of sphere

Calculations:

Volume of the sphere = 4851

⇒ $4\over3$ × $22\over 7$ ×  r3 = 4,851

⇒ r3 = $4851× 7× 3\over 22× 4$ = 1157.625 

Taking cube root of both sides, we get-

⇒ r = 10.5 cm

We know that diameter = 2 × r = 2 × 10.5 = 21 cm. 

∴ The diameter of the sphere is 21 cm.

Given data:

Angle of depression from cliff to the top of tower = 30º

Angle of depression from cliff to the bottom of tower = 60º

Height of cliff = 195 m

Formula used:

tan θ = p / b

Where “p” and “b” are perpendicular and base of a right-angled triangle.

Calculation:

Let, CE = (195 – x) m, and AB = y m

Now, for △CDE

tan30° = (△195 – x) / y

⇒ y = (195 – x)√3

And, for △ABC

tan60° = 195 / y

⇒ y = 195/ √3

Now,

Y = (195 – x)√3 = 195/ √3

⇒ 195 = 585 – 3x

⇒ 3x = 390

⇒ x = 130

∴ The height of tower is 130 m.

Given data:

% of voters who did not cast their vote = 5%

Invalid vote percentage = 10%

Winning candidate vote % = 60%

Total vote difference between winning and losing candidate = 17,271 votes

Calculation:

Let the total number of voters be a.

Since, 5% of the voters did not cast their vote

⇒ Votes polled = (100 - 5) = 95% of a.

Invalid votes = 10 %

⇒ Total valid votes = 90% × (95% of a).

Votes won by winning candidate = 60 % of  90% of (95% of a).

Votes won by losing candidate = 40 % of  90% of (95% of a).

According to the question-

⇒ 60% of [90% of (95% of a)] − 40% of [90% of (95% of a)] = 17,271

⇒ 20% of [90% of (95% of a)] = 17,271

⇒ $20\over 100$ × $90\over 100$ × $95\over 100$ × a = 17,271

⇒ a = 101,000 votes

∴ Total registered voters are 101,000.   

Shortcut TrickLet the total number of voters be 100

5% of them did not cast votes

⇒ 100 × 95/100 = 95 casted votes

10% of 95 pressed NOTA

90% of 95 casted votes,

⇒ 90/100 × 95 = 9/2 × 19

Winner gets 60% then looser must be getting 40%

Diiference between them is 60% - 40% = 20%

⇒ 20% of 9/2 × 19 = 17,271

⇒ 1/5 × 9/2 × 19 = 17,271

⇒ 1 = 1010

∴ Total voters = 100 = 100 × 1010 = 1,01,000

Shortcut Trick

Marked Price (MP) = 1,800

Successive Discounts = 15% and 8%

Net Selling Price = MP × (100 − d₁)% × (100 − d₂)%

Calculation = 1,800 × 0.85 × 0.92

Final Amount = 1,800 × 0.782 = 1,407.6

∴ The correct answer is 1,408.

Alternate Method

Given: Marked Price = 1,800, First Discount = 15%, Cash Discount = 8%.

Formulas: Price after discount = MP × (100 − Discount%) ÷ 100

⇒ Price after 15% discount = 1,800 − (15% of 1,800)

⇒ Price after 15% discount = 1,800 − 270 = 1,530

⇒ Cash discount on net payment = 8% of 1,530

⇒ Cash discount = 1,530 × 0.08 = 122.4

⇒ Final amount paid = 1,530 − 122.4 = 1,407.6

⇒ Rounding to the nearest rupee = 1,408

∴ The correct answer is 1,408.

Additional Information

Successive Discounts

When multiple discounts are applied, the second discount is calculated on the reduced price. Single equivalent discount = a + b − (a × b ÷ 100).

Rounding Off

If the decimal part is 0.5 or greater, round up to the next whole number.

Given data:

Length = 20 cm

Breadth = 10 cm

Height = 8 cm

Formula:

TSA = 2 × (l × b + b × h + l × h)

Where-

TSA = Total Surface Area

l = Length

b = Breadth

h = Height

Calculations:

TSA = 2 × (20 × 10 + 10 × 8 + 20 × 8) = 880 cm²

∴ The total cardboard area needed to make a closed box is 880 cm².

Given data:

Calculations:

Ratio of Income to expenditure for respective years-

∴ The income-expenditure ratio is the minimum in the year 2018.

Given data:

Calculation:

Let the speed of river be “x” and speed of boat be “y”.

Effective downstream speed = x + y

Effective upstream speed = x – y

$33\over x+y$+ $35 \over x-y$ = 8 (Eq. 1)

$44\over x+y$ + $28\over x-y$= 8 (Eq. 2)

Subtracting equation 1 from equation 2-

⇒ $44\over x+y$ - $33\over x+y$ + $28\over x-y$ - $35 \over x-y$= 0

⇒ $44\over x+y$ - $33\over x+y$ =  $35 \over x-y$ - $28\over x-y$

⇒ $11\over x+y$ = $7\over x-y$

⇒ 11 × (x - y) = 7 × (x + y)

⇒ 11 x - 11y = 7x + 7y

⇒ 4x = 18y

⇒ x = $9\over 2$y.

Putting the value of "x" in equation 1-

⇒ $33\over {9y\over 2}+y$ + $35\over {9y\over 2}-y$ = 8

⇒ $66\over 11y$ + $70\over 7y$ = 8 or $6\over y$ + $10 \over y$ = 8

⇒ y = 2 

Substituting the value of "y" in the value of "x" = 9

∴ Time required for 55 km downstream and 14 km upstream distance = $55\over x+y$+ $14\over x-y$

⇒ Time required for 55 km downstream and 14 km upstream distance = $55\over 9+2$+ $14\over 9-2$= 5 + 2 = 7 hours

The total time required for the distance to be traveled is 7 hours.

Shortcut TrickHere, according to the question, 

⇒ 33/(x + y) + 35/(x - y) = 8 & 44/(x + y) + 28/(x - y) = 8

As the number of required hours is a complete number hence 

The values of (x + y) & (x - y) should divide the respective numbers

For Downstream, that is 33 and 44 both are multiples of 11

and for Upstream, that is 35 and 28 both are multiples of 7

By value putting method, 

⇒ 33/11 + 35/7 = 3 + 5 = 8 & 44/11 + 28/7 = 4 + 4 = 8

⇒ x + y = 11 & x - y = 7

Required time, 

⇒ 55/11 + 14/7 = 5 + 2 = 7 hours

∴ The total time required for the distance to be traveled is 7 hours.

Concept used:

We would use the concept of BODMAS-

B – Bracket

O – Off

D – Divide

M – Multiplication

A – Addition

S – Subtraction

Calculation:

$(3\div1)\times 2+5-2\over (3\times 3)-2$

⇒$3\times 2+5-2\over 9-2$

⇒ $6+5-2\over 7$

⇒ $9\over 7$

 ∴ The answer to the expression is $9\over 7$.

Given:

Calculations:

Total people visiting Mall A on Monday, Tuesday, Friday and Sunday = 560 + 700 + 840 + 1500 = 3600

Total people visiting Mall B on Tuesday, Thursday, Saturday and Sunday = 700 + 750 + 1100 + 1350 = 3900

Percentage of people visiting Mall on A compared to Mall B = $3600\over 3900$ × 100 = 92.3%

The answer is 92.3%.

Shortcut Trick

Try standard values for θ: 30°, 45°, 60°.

If θ = 60°, then 2 sin² 60° + 3 cos 60° = 2(3/4) + 3(1/2) = 1.5 + 1.5 = 3. Condition satisfied.

Value = sec² 60° + cot² 60° = (2)² + (1/√3)² = 4 + 1/3 = 4(1/3).

∴ The correct answer is 4(1/3).

Alternate Method

Given: 2 sin² θ + 3 cos θ = 3

Formula: sin² θ = 1 − cos² θ

⇒ 2(1 − cos² θ) + 3 cos θ = 3

⇒ 2 − 2 cos² θ + 3 cos θ = 3

⇒ 2 cos² θ − 3 cos θ + 1 = 0

⇒ (2 cos θ − 1)(cos θ − 1) = 0

⇒ cos θ = 1/2 or cos θ = 1

⇒ Since 0° < θ < 90°, cos θ = 1/2 ⇒ θ = 60°

⇒ Required value = sec² 60° + cot² 60°

⇒ (2)² + (1/√3)² = 4 + 1/3 = 13/3 = 4(1/3)

∴ The correct answer is 4(1/3).

Additional Information

Trigonometric Identities

Fundamental relations include sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Standard Values

For θ = 60°: sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3, and cot 60° = 1/√3.

Given data:

Total family earning = Rs 108,000

Calculations:

Total central angle for food and transport = 65 + 50 = 115

Total expense for food and transport =  $115\over 360$ × 108,000 = Rs 34,500.

The family spends Rs 34,500 on food and transport together monthly.

Shortcut Trick

Ratio of HCF : LCM = 1 : 22

Total units = 1 + 22 = 23 units

23 units = 276 ⇒ 1 unit (HCF) = 12

LCM = 22 × 12 = 264

Other number = (LCM × HCF) ÷ Given number = (264 × 12) ÷ 132 = 24

∴ The correct answer is 24.

Alternate Method

Given:

LCM = 22 × HCF

LCM + HCF = 276

First number = 132

Formula Used:

Product of two numbers = LCM × HCF

HCF (1x)

LCM (22x)

Total Sum = 276 132 × Other Number = HCF × LCM

Calculations:

⇒ Let HCF = H

⇒ LCM = 22H

⇒ H + 22H = 276

⇒ 23H = 276

⇒ H = 276 ÷ 23 = 12

⇒ LCM = 22 × 12 = 264

⇒ 132 × Other Number = 12 × 264

⇒ Other Number = (12 × 264) ÷ 132

⇒ Other Number = 12 × 2 = 24

∴ The correct answer is 24.

Additional Information

HCF and LCM Relation

For any two numbers a and b, HCF(a, b) × LCM(a, b) = a × b.

HCF and LCM of Fractions

HCF = (HCF of Numerators) ÷ (LCM of Denominators) and LCM = (LCM of Numerators) ÷ (HCF of Denominators).

Co-prime Numbers

Two numbers are co-prime if their HCF is 1. In this case, their LCM is simply the product of the numbers.

Shortcut Trick

For consecutive integers, the Average lies exactly at the mid-point of the series.

Largest Integer = Average + (n − 1) ÷ 2

Largest Integer = 22.5 + (18 − 1) ÷ 2 = 22.5 + 8.5 = 31

∴ The correct answer is 31.

Alternate Method

Given: Number of terms (n) = 18, Average = 22.5

Formula: Average of AP = (First term + Last term) ÷ 2

⇒ Let the 18 consecutive integers be x, x+1, ..., x+17.

⇒ 22.5 = (x + x + 17) ÷ 2

⇒ 22.5 × 2 = 2x + 17

⇒ 45 = 2x + 17

⇒ 2x = 45 − 17 = 28

⇒ x = 14 (Smallest integer)

⇒ Largest integer = x + 17 = 14 + 17 = 31

∴ The correct answer is 31.

Additional Information

Consecutive Integers Average

For any Arithmetic Progression (AP), the average is always the middle term (if n is odd) or the mean of the two middle terms (if n is even).

Smallest and Largest Relation

The difference between the largest and smallest of n consecutive integers is always (n − 1).

Sum of Consecutive Integers

Sum = Average × Number of terms = [n ÷ 2] × [2a + (n − 1)d].

Shortcut Trick Substitute the smallest value of n that satisfies the condition. If n divided by 6 leaves remainder 2, let n = 2. Now calculate (n2 + n + 2) → (22 + 2 + 2) = 4 + 2 + 2 = 8. Remainder when 8 is divided by 6 → 8 ÷ 6 = 1 with Remainder 2. ∴ The correct answer is 2. Alternate Method Given: n ≡ 2 (mod 6) Formula: If a ≡ r (mod m), then f(a) ≡ f(r) (mod m).

⇒ Let n = 6k + 2, where k is any integer. ⇒ Expression = (6k + 2)2 + (6k + 2) + 2 ⇒ Expression = (36k2 + 24k + 4) + 6k + 2 + 2 ⇒ Expression = 36k2 + 30k + 8 ⇒ Expression = 6(6k2 + 5k + 1) + 2 ⇒ Since 6(6k2 + 5k + 1) is exactly divisible by 6, the remainder is 2. ∴ The correct answer is 2. Additional Information Divisibility Rule of 6 A number is divisible by 6 if it is divisible by both 2 (even number) and 3 (sum of digits is divisible by 3). Remainder Property of Powers If n % d = r, then nk % d = rk % d. This helps in simplifying polynomial remainders quickly. Euclid's Division Lemma For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b.