SSC CGL 2021 Tier-I (Held On : 19 April 2022 Shift 1) (Previous Year Paper)

The logic followed here is:

Logic: (First number × 4) + 7 = Second Number

1. 5 : 27

⇒ 5 × 4 + 7 = 20 + 7 = 27

And,

2. 8 : 39

⇒ 8 × 4 + 7 = 32 + 7 = 39

Similarly,

3. 7 : ?

⇒ 7 × 4 + 7 = 28 + 7 = 35

Hence, the correct answer is "35".

BODMAS rule:

Let's check each option one by one.

Option 1) 17 and 5. So the equation will become:

⇒ 119 + 11 × 17 - 153 ÷ 5 = 201

⇒ 119 + 11 × 17 - 30.6 = 201

⇒ 119 + 187 - 30.6 = 201

⇒ 306 - 30.6 = 201

⇒ 275.4 ≠ 201

⇒ LHS ≠ RHS

Option 2) 119 and 17. So the equation will become:

⇒ 17 + 11 × 5 - 153 ÷ 119 = 201

⇒ 17 + 11 × 5 - 1.2857 = 201

⇒ 17 + 55 - 1.2857 = 201 

⇒ 72 - 1.2857 = 201

⇒ 70.7143 ≠ 201

⇒ LHS ≠ RHS

Option 3) 119 and 153. So the equation will become:

⇒ 153 + 11 x 5 - 119 ÷ 17 = 201

⇒ 153 + 11 x 5 - 7 = 201

⇒ 153 + 55 - 7 = 201

⇒ 208 - 7 = 201

⇒ 201 = 201

⇒ LHS = RHS

Option 4) 11 and 17. So the equation will become:

⇒ 119 + 17 × 5 - 153 ÷ 11 = 201

⇒ 119 + 17 × 5 - 13.90 = 201

⇒ 119 + 85 - 13.90 = 201

⇒ 204 - 13.90 = 201

⇒ 190.1 ≠ 201

⇒ LHS ≠ RHS

Hence, the correct answer is "119 and 153".

Given:

The ratio of the share of A, B and C respectively = 11 : 23 : 25

Calculation:

Let the share of A, B and C be 11x, 23x and 25x respectively.

According to the question

⇒ 11x + 23x + 25x = 1003

⇒ 59x = 1003

⇒ x = 17

Now B get more than A =  B -A = 23 - 11 = 12

⇒ Now, 17 × 12 = 204

Hence, the correct answer is "204".

Eight person: Bindu, Krunal, Manoj, Nilima, Omkar, Piyush, Renu and Sundar are sitting around a circular table facing the centre.

1. Sundar sits second to the right of Piyush.

2. Only two persons sit between Sundar and Krunal.

 

3) Omkar sits opposite to Bindu, who is not an immediate neighbour of Krunal and Piyush.

4. Manoj sits third to the right of Bindu.

5)  Nilima is the immediate neighbour of Krunal and Bindu.

6. Only one position left for Renu.

Clearly, Nilima sits opposite the one who sits to the immediate left of Renu. 

Hence, the correct answer is "Nilima sits opposite the one who sits to the immediate left of Renu".

Given:

Hence, the correct answer is "Option 1".

The pattern followed here is:

FASTER : AEFRST

Similarly,

KINGDOM : ?

Hence, the correct answer is "DGIKMNO".

The paper unfolded will appear as shown below:

  

Hence, the correct answer is "Option 3".

The pattern followed here is:

1. Number of triangle is decrease by two in every next figure.

2. Number of quadrilateral is increase by one in every next figure.

 

Hence, the correct answer is "Option 4".

The pattern followed here is:

Hence, the correct answer is "54"

The correct order of the given words according to the English dictionary is:

1. Hatchability 4. Hatchback 2. Hatchel 3. Hatchers 5. Hatchings

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

The pattern followed here is:

Hence, the correct answer is "367".

The faces opposite to each other is shown below:

The opposite sides are:

1 → 6

2 → 5

4 → 3

Clearly, 5 is opposite to 2.

Hence, the correct answer is "2".

The position of letters according to the English alphabet series:

Logic: 

• Consonant - Subtract of - 6 in every consonant.
• Vowel - Addition of + 5 in every alphabet.

‘BUILDER’ is written as ‘VZNFXJL’

Similarly,

‘PARKING’ be written as '?'

Hence, the correct answer is "JFLENHA".

Let us first decode the given data:

Given: C12m$S5m*G3m&J6m%K!JT 

According to the Pythagoras theorem,

(Hypotenuse)² = Base² + Height²

⇒ CS is Height = (12)²

⇒ GS is the Base = (5)²

⇒ GC is the Hypotenuse = ?

Therefore,

⇒ (GC)² = (GS)² + (CS)² 

⇒ (GC)2 = (5)² + (12)²

⇒ (GC)2 = 25 + 144

⇒ (GC)² = 169

⇒ GC = **√**169

⇒ GC = 13

Hence, the correct answer is "13 m".

The least possible Venn diagram is shown below:

Conclusions:

I. Some erasers are markers → Does not follow → (As all calculators are marker, some pencil are marker and some eraser are pencil. So, some eraser are markers is possibility but not definite true)

II. Some pencils are calculators → Does not follow → (As all calculators are marker and some pencil are marker. So, some pencils are calculators is possibility but not definite true)

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

The position of letters according to the English alphabet series:

Hence, the correct answer is "CARC".

Given: A_GGA_GGAN

1. GNNG →  GANG-GANG-GANG
2. NGNG →  NAGG-GANG-GANG
3. TGTG →  TAGG-GATG-GANG
4. SGSA →  SAGG-GASG-GANA

• Option 1 is followed the cycle of GANG

Hence, the correct answer is "GNNG".

The position of letters according to the English alphabet series:

Logic: Given alphabet is coded as reverse value × Number of vowel = Code

‘GLOVE’ is coded as 148

⇒ 20 + 15 + 12 + 5 + 22 = 74 × 2 = 148

Similarly,

‘OBDURATE’ is coded as '?'

⇒ 12 + 25 + 23 + 6 + 9 + 26 + 7 + 22 = 130 × 4 = 520

Hence, the correct answer is "520".

The logic followed here is:

• Here 'Sohan' is coded as 'Dig'.

Hence, the correct answer is "Dig".

Format of Question:

The logic followed here is: 

Here middle number = 4 + 4 = 8

And 

​

Here middle number = 5 + 3 = 8

Similarly,

Here middle number(?) = 7 + 4 = 11 

Hence, the correct answer is "11".

The position of letters according to the English alphabet series:

Logic: first letter + 4 = second letter then, third letter is opposite of second letter.

1. PSH

⇒ P(16) + 3 = S(19)

⇒ S(19) opposite value is H(8)

2. SWD 

⇒ S(19) + 4 = W(23) 

⇒ W(23) opposite value is D(4)

3. LPK

⇒ L(12) + 4 = P(16)

⇒ P(16) opposite value is K(11)

4() FJQ

⇒ F(6) + 4 = J(10)

⇒ J(10) opposite value is Q(17)

Cleary, PSH is different from all.

Hence, the correct answer is "PSH".

The pattern followed here is:

Detailed Explanation:

• The line PQ is the mirror.
• The word "

 the given is "

" it is not the mirror image⇒ Option 1 is eliminated.

• The word "

" the fifth letter is "C". So, the mirror image should be "

" ⇒ Option 2 is eliminated.

• The word "

 "the given is "

" it is not the mirror image ⇒ Option 3 is eliminated.

Hence, the correct answer is "Option 4".

Let us first decode the given data:

Family Chart:-

Given: W % O – B ? C ? D

Option 1) % and – 

After interchanging we get: W % O – B % C - D

1. W % O means W is the son-in-law of O.

2. O - B means B is the wife of O.

3. B % C means B is son-in-law of C. (Here B is not a son-in-law of C because B is a female)

4. C - D means D is wife of C.

It is false because, here B is the female and given relation is wrong.

Option 2)  $ and +

After interchanging we get: W % O – B $ C + D

1. W % O means W is the son-in-law of O.

2. O - B means B is wife of O.

3. B $ C means C is father of B.

4. C + D means D is son of C.

It is false because, here D is the uncle of W.

Option 3) + and #

After interchanging we get: W % O – B + C # D

1. W % O means W is the son-in-law of O.

2. O - B means B is wife of O.

3. B + C means C is son of B.

4. C # D means D is only sister of C.

It is true, here D is the wife of W.

Option 4) + and -

After interchanging we get: W % O – B + C - D

1. W % O means W is the son-in-law of O.

2. O - B means B is wife of O.

3. B + C means C is son of B.

4. C - D means D is wife of C.

It is false because here, D is the sister-in-law of W. 

Hence, the correct answer is "+ and #".

Shortcut Trick D has to be the wife of W which means she needs to be female and going by all symbols we can see that only the - and # symbols represent female but the "-" symbol means wife and that is not possible because this would mean D is the wife of C so the only symbol left is # and the answer is 3rd.

BODMAS rule:

Option 1) 5 and 6

After interchanging the digits we get: 

⇒ 37 + 1162 × 8 ÷ 758 - 47 = 22

⇒ 37 + 1162 × 0.010 - 47 = 22

⇒ 37 + 12.26 - 47 = 22

⇒ 49.26 - 47 = 22

⇒ 2.26 ≠ 22

⇒ LHS ≠ RHS

Option 2) 4 and 5

After interchanging the digits we get: 

⇒ 37 + 1142 × 8 ÷ 768 - 57 = 22

⇒ 37 + 1142 × 0.010 - 57 = 22

⇒ 37 + 11.42 - 57 = 22

⇒ 48.42 - 57 = 22

⇒ -8.58 ≠ 22

⇒ LHS ≠ RHS

Option 3) 3 and 4

After interchanging the digits we get:

⇒ 47 + 1152 × 8 ÷ 768 - 37 = 22

⇒ 47 + 1152 × $\frac{8}{768}$ - 37 = 22

⇒ 47 + 3 × $\frac{8}{2}$ - 37 = 22

⇒ 47 + 12 - 37 = 22

⇒ 59 - 37 = 22

⇒ 22 = 22

⇒ LHS = RHS

Option 4) 2 and 3

After interchanging the digits we get:

⇒ 27 + 1152 × 8 ÷ 768 − 47 = 22

⇒ 27 + 1152 × 0.010 - 47 = 22

⇒ 27 + 11.52 - 47 = 22

⇒ 38.52 - 47 = 22 

⇒ - 8.48 ≠ 22

⇒ LHS ≠ RHS

Hence, the correct answer is "3 and 4".

The tax-payers who also are blood donors is shown below:

Number of tax-payers who also are blood donors is 27 + 36 = 63

Hence, the correct answer is "63"

The correct answer is music.

Key Points

• Kishori Amonkar was an Indian classical vocalist.
• She belonged to the Jaipur Gharana.
• Birth- April 10, 1932.
• Death- April 3, 2017.
• She also won Padma Bhushan (1987) and Padma Vibhushan (2002).

Additional Information 

• Jaipur Gharana :
• The Jaipur-Atrauli Gharana emerged from Alladiya Khan's family which originated from Atrauli and migrated to Jaipur.
• The Jaipur-Atrauli Gharana is Hindustani music founded by Alladiya Khan (1855–1946) in the late 19th century.
• The Gharana is known for its distinctive vocal aesthetics, raga repertoire, and technical aptitude.
• The chief exponents of the Jaipur Gharana are Alladiya Khan, Mallikarjun Mansur, Kesarbhai Kerkar, Kishori Amonkar, and Shruti Sadolikar, Padma Talwalkar and Ashwini Bhide Deshpande.

The correct answer is Shehnai.

Key Points 

Shehnai:

• It is a reed instrument in which there are seven holes along the tube which are used for playing the melody by opening and closing them with the fingers.
• It is known as a Mangal Vadya and is usually played on all auspicious occasions in north India such as marriages, temple festivals, etc.
• The Shehnai is considered to have come to India from West Asia, there are other scholars who believe that this instrument travelled to China from India.
• It is now a popular instrument in concerts, the sound is very sweet and suited for playing Raga Sangeet.
• In the early fifties of this century, Ustad Bismillah Khan is credited for popularizing this instrument.
• Today, Pt. Anant Lal and Pt. Daya Shankar is also a noted Shehnai player.

​

The correct answer is 2005.

Key Points 

• Right to Information (RTI),2005, is an act set up by the Parliament of India that frames the procedures and rules for the right to information to the citizen.
• RTI has replaced the Freedom of information act, 2002.

The following are the features of the RTI Act:

• It promotes accountability and transparency in every public authority.
• It promotes effective and timely dissemination of correct information by the public authority to any individual.
• It promotes the establishment of district, state, and central level information commissions as an appellate body.
• It may be written by hand or online.
• To maintain all the records which are appropriate to be computerized and should be connected with the network so that all the records are easily accessible.
• To prepare reports which include the number of report requests made by the general public to each authority.
• It is transparent and shows the amount collected by public authority as a charge from this act.

The correct answer is Laszlo Lovasz.

Key Points

• Abel Prize is presented by the King of Norway and is often called the Nobel Prize in Mathematics.
• The Abel Prize was established on 1 January 2002.
• The purpose is to award the Abel Prize for outstanding scientific work in the field of mathematics.
• The prize amount is 7.5 million NOK and was awarded for the first time on 3 June 2003.
• The prize is awarded by the Norwegian Academy of Science and Letters.
• The Abel Prize 2021 was awarded to Avi Wigderson, and Laszlo Lovasz.

Additional Information 

The correct answer is Blight.

Key Points

• Blight refers to a type of plant disease caused by fungal or bacterial pathogens.
• These pathogens cause cell death or necrosis, and when large areas of plants have been quickly killed, the disease is described as blight.
• There are different types of blight that can affect your plants and understanding how to best treat them is crucial for their health.
• Early blight, also known as target spot, is a common disease of tomatoes and potatoes.
• The fungus can infect the leaves, stems and fruit of tomatoes and may explain why your tomatoes are dying.

Additional Information

The correct answer is Maharashtra.

Key Points 

• Maharashtra topped the Khelo India Youth Games of the year 2020 with a total of 256 medals.
• Haryana and Delhi were in the 2nd and 3rd positions.
• Avinash Joshi, CEO of the "Khelo India Games 2020" event has announced that lawn bowls and cycling will be included in the Khelo India for the first time.
• The "Khelo India Games 2020" event is the 3rd edition of the games that have taken place between the dates of 10th January 2020 to 22nd January 2020 in Guwahati, Assam.
• Under the Khelo India Event for the year 2020, the youth participated across 20 disciplines of sports.
• 6500 athletes from 37 teams from all over the country have presented their talent in front of the nation.
• The motive of giving financial aid is to provide a chance to athletes of India for an Olympic event.

Additional Information 

• About Khelo India Youth Games
• Khelo India Youth Games previously known as Khelo India School Games are national-level multidisciplinary games that are organized for two categories viz. under-17 school students and under-21 college students.

In News

• The Khelo India Youth Games 2021 concluded on 13 June 2022 at Panchkula in Haryana.
• The closing ceremony was organised at Indradanush Auditorium in  Panchkula.
• This was the fourth edition of the Khelo India Youth Games.
• Haryana emerged as champion by getting the top position in the medal tally with a total of 137 medals while Maharashtra got the second position by winning 125 medals.
• At 13, Jharkhand’s Eitu Mandal is the youngest kabaddi entrant in the Khelo India Youth Games (KIYG) 2021.
• JAIN (Deemed-to-be University) became the winner of the Khelo India University Games 2021 on 3 May 2022.

The correct answer is Chennai.

Key Points

• The first two Test matches of the IND vs ENG Test series were held at the MA Chidambaram Stadium, also known as Chepauk Stadium, in Chennai.
• India and England have faced each other in 9 Test matches at 'Chepauk', with the hosts registering five wins and England winning three matches.
• The Test match in 1982 ended in a draw.
• Overall, India has played 32 Test matches against all comers at Chepauk, registering 14 wins, losing 6 matches, and drawing 11.

In News

• India Tour of England 2022 is scheduled to begin on Thu Jul 7, 2022, to be hosted by England as per the cricket schedule announced.
• The 1st T20 match between England vs India was played at The Rose Bowl, Southampton on Jul 7, 2022.

The correct answer is Two.

Key Points 

• Sodium Peroxide
• It is an inorganic compound with the formula Na2O2.
• This yellowish solid is the product of sodium ignited in excess oxygen.
• It is a strong base.
• This metal peroxide exists in several hydrates and peroxyhydrates.

Additional Information

• Sodium
• It is a chemical element with the symbol Na and atomic number 11.
• ​Sodium is silver-white colour metal with malleable and ductile properties.
• It is a metal that can easily be cut with a knife.
• It is a good conductor of heat and electricity.

The correct answer is Federal.

Key Points

• The preamble is the introductory part of the Constitution which sets out the principles on which the Constitution is based.
• The preamble declares India to be a sovereign, socialist, secular and democratic republic.
• The word Federal is nowhere mentioned in the Indian constitution.
• The ideals behind the Preamble to India’s Constitution were laid down by Jawaharlal Nehru’s Objectives Resolution, adopted by the Constituent Assembly on January 22, 1947.
• The date is mentioned in the preamble when it was adopted i.e. November 26, 1949.

Keywords in Preamble

• We, the people of India:
• It indicates the ultimate sovereignty of the people of India.
• Sovereign:
• The term means that India has its own independent authority and it is not a dominion of any other external power.
• Socialist:
• The term means the achievement of socialist ends through democratic means.
• It holds faith in a mixed economy where both private and public sectors co-exist side by side.
• It was added to the Preamble by the 42nd Amendment, 1976.
• Secular:
• The term means that all the religions in India get equal respect, protection and support from the state.
• It was incorporated into the Preamble by the 42nd Constitutional Amendment, 1976.
• Democratic:
• The term implies that the Constitution of India has an established form of Constitution which gets its authority from the will of the people expressed in an election
• Republic:
• ​The term indicates that the head of the state is elected by the people.
• In India, the President of India is the elected head of the state.

The correct answer is Partition of Bengal.

Key Points 

• Partition of Bengal 
• Lord Curzon announced the partition of Bengal on 20th July 1905.
• The partition came into effect on 16th October 1905.
• At that time of partition, Bengal was the biggest province of British India that included Bihar and parts of Orissa.
• The British argued that the division was for administrative convenience.
• The partition of the Bengal is an example of the British policy of divide and rule.
• The main reason for the partition of Bengal was to destroy the political influence of the educated middle class among whom the Bengali intelligentsia was the most prominent.
• The swadeshi movement started to protest against the partition of Bengal.
• Bengal partition was finally cancelled by Lord Hardinge in 1911.

Additional Information 

• In the Lahore session, The Indian National Congress, on 19 December 1929, passed the historic resolution 'Purna Swaraj' (total independence).
• A public declaration was made on 26 Jan 1930- a day which the Congress Party urged Indians to celebrate as 'Independence Day.'
• Jawaharlal Nehru was elected as President of the Indian National Congress in December 1929 at its annual session in the city of Lahore.
• The Chauri Chaura incident took place on 4 February 1922 in Chauri Chaura in the Gorakhpur district of the British Union Province of India (present-day Uttar Pradesh). 
• Due to the incident, Mahatma Gandhi called off the ‘Non-cooperation Movement’ on 12 February 1922.
• Gandhi-Irwin Pact was a political agreement signed by Mahatma Gandhi and the Viceroy of India, Lord Irwin in March 1931 before the Second Round Table Conference in London.
• The main purpose of this pact was to make Congress participate in the Second Round Table Conference.

The correct answer is Atoll.

• Atoll is a group of islands found in the tropical oceans consisting of coral reefs and a central depression​

Key Points

• An atoll is a ring-shaped coral reef, island, or series of islets.
• An atoll surrounds a body of water called a lagoon.
• The term “atoll” is derived from a Maldivian (divehi) word, atolu.
• Atolls develop with underwater volcanoes, called seamounts.
• Atolls consist of ribbons of reefs that may not always be circular but whose broad configuration is a closed shape up to dozens of kilometres across.
• The most extensive groups of atolls occur in the Pacific Ocean but there are also numerous atolls in the central Indian Ocean.

Additional Information 

The correct answer is the Industrial Finance Corporation of India.

Key Points 

• Industrial Finance Corporation of India
• ​It was established on July 1, 1948
• The primary goal of establishing this development bank was to help the industrial sector meet its medium- and long-term financial demands.
• The IFCI's authorized capital is 250 crores.
• People's deposits are not accepted
• When a firm issues shares or debentures, the Industrial Finance Corporation of India may choose to underwrite securities.
• The IFCI also insures the loans that these industrial enterprises take out.
• It also ensures deferred payments for loans taken out in foreign currency from foreign banks.

Additional Information 

• The National Housing Bank Act,1987 envisaged the setting up of National Housing Bank (NHB) in 1988.
• National Housing Bank is an apex-level financial institution for promoting the housing sectors at both regional and local levels.
• The Head office of NHB is in New Delhi.
• The Export-Import Bank of India (EXIM Bank) is a financial institution of India that was established on 1 January 1982 under the Export-Import Bank of India Act 1981.
• Its main objective is to provide financial assistance to promote Indian exports.
• Industrial Development Bank of India was established in 1964 and came into operation on July 1, 1964, to provide credit and other financial facilities for the development of industries in India.
• IDBI Bank has been categorized as a private sector bank by the Reserve Bank of India, with effect from January 21, 2019.

The correct answer is Plant.

Key Points 

• Biotic Factor:
• The word ‘biotic’ refers to having to do with living organisms.
• They refer to the biological component of the ecosystem, consisting of a population of plants, animals and micro-organisms in complex communities.
• The biotic factors influencing an organism, viruses and other parasitic organisms cause diseases.
• These are all parts of an organism’s biotic environment.
• The biotic component consists of three distinct groups of organisms, producers, consumers and decomposers.
• Examples of biotic factors are fungi, bacteria, yeast, etc.

Additional Information 

• Abiotic Factor:
• Factors other than the biotic factors which are important for the atmosphere are called abiotic factors.
• Other physical factors include climate, temperature, precipitation, types of soil present (sandy or clay, dry or wet, fertile or infertile), and wind.
• In the ecosystem, the abiotic (non-living) components perform the important function of providing water and oxygen for organisms.

The correct answer is Buddhists.

Key Points

• Sangken Festival is one of the important festivals celebrated by Khamtis, one of the oldest tribes of the Lohit District of Arunachal Prades.
• The festival is a Buddhist festival celebrated with respect where Buddha is worshipped for humanity's welfare.
• The celebration takes place for three consecutive days when the images of Lord Buddha are provided with a bath ceremoniously.
• The festival's main attraction is splashing clean water, which is the symbol of peace and purity.
• Sangken Festival is celebrated in April when the natives welcome the New Year with splendour and magnificence.

The correct answer is 100%.

Key Points  As per the Economic Survey of India 2021, SENSEX and NIFTY resulted in India’s market-cap to GDP ratio crossing 100% for the first time since October 2010. 

• This, however, raises concerns about the disconnect between the financial markets and the real sector.
• The central theme of this year’s Economic Survey is the “Agile approach”, implemented through India’s economic response to the COVID-19 Pandemic shock.
• As per the Agile approach, short-term policy responses can be tailored to an evolving situation rather than what a model may have predicted.
• Economic Survey 2021-22 estimates that the Indian economy (GDP) may grow by 9.2 per cent in real terms in 2021-22 (as per first advanced estimates) subsequent to a contraction of 7.3 per cent in 2020-21.
• GDP is projected to grow by 8- 8.5 per cent in real terms in 2022-23.

Additional Information SENSEX

• Sensex stands for Stock Exchange Sensitivity Index. It consists of the top 30 companies listed with BSE for trading.
• The Sensex, the market index of BSE which is also known as S&P BSE Sensex, is one of the oldest market indices in India.
• The Sensex is calculated by using the free-float market capitalisation method and through this, the performance of thirty companies gets reflected.

NIFTY

• Nifty, a stock market index of the National Stock Exchange, stands for National Stock Exchange Fifty.
• Nifty comprises the top 50 companies that are traded in the NSE.
• The method used to calculate Nifty is the same as Sensex, i.e., the free-float market capitalisation method.

The correct answer is Jaimini.

 Key Points

• Mimamsa-sutra was written by Jaimini encompasses the Nyaya-vaisheshika systems and emphasises the concept of valid knowledge**.**
• According to Purva Mimamsa, Vedas are eternal and possess all knowledge.​
• According to Mimamsa's philosophy, Vedas are eternal and possess all knowledge, and religion means the fulfilment of duties prescribed by the Vedas.
• It says that the essence of the Vedas is dharma. By the execution of dharma, one earns merit which leads one to heaven after death.

Additional Information Schools of Indian Philosophy

The correct answer is Nitrogen dioxide.

Key PointsChemical Wastewater Treatment

• The chemical used in this process is Aluminium Sulfate (Alum), Polyaluminium chloride (PAC), and Aluminium chloride.
• Chemicals are used during wastewater treatment in an array of processes to expedite disinfection.
• Specialized chemicals such as chlorine, hydrogen peroxide, sodium chlorite, and sodium hypochlorite (bleach) act as agents that disinfect, sanitize, and assist in the purification of wastewater at treatment facilities.
• There are several distinct chemical unit processes that can be applied to wastewater during cleaning.
• Chemical coagulation
• Chemical precipitation
• Chemical oxidation
• Advanced oxidation
• Ion exchange
• Chemical neutralization and stabilization
• The chemical coagulant process involves destabilizing wastewater particles so that they aggregate during chemical flocculation.
• Fine solid particles dispersed in wastewater carry negative electric surface charges (in their normal stable state), which prevent them from forming larger groups and settling.
• Chemical coagulation destabilizes these particles by introducing positively charged coagulants that then reduce the negative particles’ charge.

The correct answer is: 'low and nearly equal birth and death rates'.

Key Points

• The post-transitional stage of demographic transition is characterised by low and nearly equal birth and death rates.
• This statement is correct.
• The post-transition stage marks the stabilization of population growth. Both birth rates and death rates are low and relatively equal. This results in negligible or even negative population growth.
• Examples of such societies include Japan and Germany, where birth rates are well below replacement levels, and population decline is observed.
• High and nearly equal birth and death rates
• This statement is incorrect.
• High birth and death rates typically describe the pre-transition stage of demographic transition, not the post-transitional stage.
• In the pre-transition stage, both rates are high, leading to low net population growth. As societies move forward in the transition, these rates fall and eventually stabilize at lower levels.
• Falling birth rates and high death rates
• This statement is incorrect.
• Falling birth rates and high death rates are characteristics of the early transition stage.
• As death rates begin to fall due to improvements in healthcare and living conditions, birth rates typically remain high for some time before beginning to decline.
• Falling death rates and high birth rates
• This statement is incorrect.
• Falling death rates and high birth rates characterize the early transition stage, where population growth accelerates due to improved healthcare and nutrition, but birth rates remain high due to cultural and social factors.

Additional Information

• Demographic Transition Stages:
• Stage 1: Pre-transition - Both birth rates and death rates are high, leading to low population growth.
• Stage 2: Early transition - Death rates fall due to improvements in healthcare, while birth rates remain high, causing rapid population growth.
• Stage 3: Late transition - Birth rates start to decline, and population growth begins to slow down.
• Stage 4: Post-transition - Both birth rates and death rates are low, leading to stable or shrinking population size.

The correct answer is English.

Key Points 

• The East India Company sent Captain William Hawkins to the court of Emperor Jahangir in 1608 to seek permission to open a factory at Surat.
• He was well versed with Turkish and Jahangir also knew some of it since it was the native tongue of Mughal Emperor Babur.
• He was called 'English Khan' by Jahangir.
• William Hawkins was the commander of Hector, the first ship of the British East India Company to anchor at Surat in 1608.
• Sir Thomas Roe, who was an English diplomat sent by James I to the court of Emperor Jahangir in 1615.
• Roe successfully secured a firman, or royal decree, that provided the English the right to trade and establish a factory in Surat.
• English set up business centers at Agra, Ahmedabad and Broach.

Additional Information 

• Jahangir (AD 1605-1627) was Akbar's son and the fourth Mughal Emperor.
• he executed the fifth Sikh Guru, Arjun Dev.
• He is famous for his 'golden chain of justice'.
• Captain Hawkins and Sir Thomas Roe visited his court.

The correct answer is bread.

Key Points

• Saccharomyces cerevisiae is the best-studied eukaryote and a valuable tool for most aspects of basic research on eukaryotic organisms.
• S. cerevisiae's biotechnological usefulness resides in its unique biological characteristics, i.e.,
• Its fermentation capacity is accompanied by the production of alcohol and CO2 and its resilience to adverse conditions of osmolarity and low pH.
• Among the most prominent applications involving the use of S. cerevisiae are the ones in the food, beverage -especially wine- and biofuel production industries.
• It is a type of budding yeast.
• That can ferment sugar into carbon dioxide and alcohol and is commonly used in the baking and brewing industries, hence used in the making of bread.

Additional Information

• Thermophilic species such as:
• Streptococcus thermophiles, Lactobacillus helveticus, and Lactobacillus delbrueckii ssp are associated with Swiss- and Italian-type cheeses.
• Yoghurt cultures are mainly composed of the bacteria Lactobacillus delbrueckii subsp. bulgaricus and Streptococcus thermophilus.

The correct answer is Scorpion.

Key Points

• Phylum Arthropoda is the largest phylum in the animal kingdom.
• It was first created by Von Seibold in 1845.
• Around two-thirds of all named species on earth come under phylum arthropods.
• The body of arthropods is covered by a chitinous exoskeleton.
• Phylum Arthropoda has jointed appendages.
• Respiratory organs of arthropods are gills, book gills, book lungs, or tracheal system.
• The circulatory system in Arthropoda is of open type.
• Excretion in Arthropoda takes place through malpighian tubules.
• Examples of Phylum Arthropoda are Cockroach, Prawn, Crab, Scorpion, Centipede, Housefly, Ticks, and Mites.

Important Points 

• All arthropods lay eggs except Scorpion who directly gives birth to young.

Popular species of Arthropods

The correct answer is Gurudev Rabindranath Tagore’s. 

• The Economic Survey of 2020-21 mentions that India’s fiscal policy should reflect Gurudev Rabindranath Tagore’s sentiment of ‘a mind without fear'.

Key Points

• India’s willingness to pay is unquestionably demonstrated through its zero sovereign default history.
• India’s ability to pay can be gauged by low foreign currency-denominated debt and forex reserves.
• Sovereign credit rating changes for India have no or weak correlation with macroeconomic indicators.
• India’s fiscal policy should reflect Gurudev Rabindranath Tagore’s sentiment of ‘a mind without fear.
• Sovereign credit rating methodology should be made more transparent, less subjective and better attuned to reflect economies’ fundamentals.
• The fundamental theme of the Economic Survey 2020-21 is #Saving Lives and Livelihoods.

Important Point

• Economic Survey is usually presented a day before the Union Budget is presented in the Parliament.
• Economic Survey is the flagship annual document of the Ministry of finance.
• India's first Economic Survey was presented in the year 1950-51.
• Up to 1964, it was presented along with the Union Budget.
• From 1964 0nwards, it has been delinked from the Budget.
• It is presented every year in the Parliament during the Budget Session.

Additional Information

• Economic Survey 2021-22:
• The Economic Survey 2021-22, in the Prices and Inflation Section, mentioned the following points:
• Wholesale Price Index (WPI) rose to 12.5% during 2021-22 (April to December)
• The average CPI-Combined inflation moderated to 5.2% in 2021-22 (April-December) from 6.6% in 2020-21
• Food inflation averaged at a low of 2.9% in 2021-22 (April to December) as against 9.1% in 2020-21
• The Economic Survey 2021-22 also mentioned the Divergence between CPI-C and WPI Inflation:
• The divergence peaked at 9.6 percentage points in May 2020.
• In 2021-22 there was a reversal in divergence with retail inflation falling below wholesale inflation by 8.0 percentage points in December 2021.

The correct answer is conditions,** health, prevent.**

• According to World Health Organization (WHO), “Hygiene refers to conditions and practices that help to maintain health and prevent the spread of diseases.

Key Points

• Hygiene refers to conditions and practices that help to maintain health and prevent the spread of diseases.
• Medical hygiene, therefore, includes a specific set of practices associated with this preservation of health, for example, environmental cleaning, sterilization of equipment, hand hygiene, water and sanitation and safe disposal of medical waste.
• Personal hygiene refers to maintaining the body's cleanliness.

Additional Information

• World Health Organization (WHO)
• WHO is the United Nations agency that connects nations, partners and people to promote health, keep the world safe and serve the vulnerable – so everyone, everywhere can attain the highest level of health.
• Working with 194 Member States across 6 regions and on the ground in 150+ locations, the WHO team works to improve everyone’s ability to enjoy good health and well-being.
• India is a member of WHO.​
• Establishment: April 7th, 1948
• Headquarters: Geneva, Switzerland.

The correct answer is Credential Committee.

• Alladi Krishnaswami Ayyar was the chairman of the Credential Committee of the Constituent Assembly of India.
• He served as the Advocate General of Madras State from 1929 to 1944.

• IMPORTANT COMMITTEES OF THE CONSTITUENT ASSEMBLY AND THEIR CHAIRMEN

The correct answer is S Hareesh.

Key Points 

• Malayalam author S Hareesh won the coveted JCB Prize for Literature 2020 for his novel, ‘Moustache’.
• Translated in English by Jayasree Kalathil and published by HarperCollins India, the book has been praised for its impeccable confluence of myth and magic.
• The winner was announced by JCB chairman Lord Bamford in a virtual ceremony.
• The prize, worth Rs 25 lakh, is one of the most prestigious literary awards in India.
• Hareesh has won a host of prizes in the past, including the Kerala Sahitya Akademi Award, Thomas Mundassery Prize, and the VP Sivakumar Memorial Prize.

Given:

A takes 3 hours more than B to walk 'd' km.

If A doubles his speed, then he can make it in 1 hour less than B.

Concept used:

Time = Distance/speed

Calculation:

Let the speed of the A be a and B be b

According to the question,

(d/a) - (d/b) = 3      ----(i)

Again,

(d/b) - (d/2a) = 1      ----(i)

By adding eq (i) and eq (ii) we get,

d/2a = 4

⇒ d/a = 4 × 2 = 8

So, it will take 8 hours by A to cover the distance d

∴ A requires 8 hours to walk 'd' km.

Given:

Profit % = 60% on capital

Donation = 50% of total capital(initial amount + profit)

Concept used:

Total capital = Initial amount + profit

Calculation:

Let the captial at the starting be 100a

After 1st year, his capital = 100a + 100a × 60%

⇒ 160a

After donating, his capital = 160a - 160a × 50%

⇒ 80a

After 2nd year, his capital = 80a + 80a × 60%

⇒ 128a

After donating, his capital = 128a - 128a × 50%

⇒ 64a

After 3rd year, his capital = 64a + 64a × 60%

⇒ 102.4a

After donating, his capital = 102.4a - 102.4a × 50%

⇒ 51.2a

Here, in the question 51.2a = Rs. 15360

⇒ a = 300

⇒ 100a = 300 × 100 = Rs. 30000

So, his capital at the starting was Rs. 30000

∴ The initial amount (in Rs.) with which the man started his business was 30000.

Given:

A = 60°

Concept used:

Calculation:

$\frac{{{\rm{10 \ sin }}\frac{{\rm{A}}}{{\rm{2}}}{\rm{ \ + \ 8cosA}}}}{{{\rm{7\ sin }}\frac{{{\rm{3A}}}}{{\rm{2}}}{\rm{ \ - \ 12cosA}}}}$

⇒ $\frac{{{\rm{10 \ sin }}\frac{{\rm{60°}}}{{\rm{2}}}{\rm{ \ + \ 8cos60°}}}}{{{\rm{7\ sin }}\frac{{{\rm{180°}}}}{{\rm{2}}}{\rm{ \ - \ 12cos60°}}}}$

⇒ $\frac{{{\rm{10 \ sin }}{{\rm{30°}}}{{\rm{}}}{\rm{ \ + \ 8cos60°}}}}{{{\rm{7\ sin }}{{{\rm{90°}}}}{{\rm{}}}{\rm{ \ - \ 12cos60°}}}}$

⇒ $\frac{{{\rm{10 \times\frac{1}{2} }}{{\rm{}}}{{\rm{}}}{\rm{ \ + \ 8\times\frac{1}{2}}}}}{{{\rm{7\times1 }}{{{\rm{}}}}{{\rm{}}}{\rm{ \ - \ 12\times\frac{1}{2}}}}}$

⇒ $\frac{{{\rm{5 }}{{\rm{}}}{{\rm{}}}{\rm{ \ + \ 4}}}}{{{\rm{7 }}{{{\rm{}}}}{{\rm{}}}{\rm{ \ - \ 6}}}}$

⇒ $\frac{9}{1}$

⇒ 9

∴ Required answer is 9.

Given:

BC = 14.4 cm

CA = 15.2 cm

AB = 12.4 cm

Concept used:

Midpoint theorem - The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

Calculation:

F and E are the mid point of AB and AC

So, according to the concept,

FE = (BC/2)

Similarly,

DE = (AB/2) and FD = (AC/2)

Now,

Perimeter of ΔDEF = DE + FE + FD

⇒ (BC/2) + (AB/2) + (AC/2)

⇒ 1/2(BC + AB + AC)

⇒ 1/2(14.4 + 12.4 + 15.2)

⇒ 1/2(42)

⇒ 21

∴ The perimeter (in cm) of the ΔDEF is 21.

Shortcut Trick When Profit at SP1 equals Loss at SP2, the Cost Price (CP) is the average: CP = (SP1 + SP2) ÷ 2. CP = (832 + 448) ÷ 2 = 1280 ÷ 2 = 640. To gain 10% profit, required SP = CP × 1.10. SP = 640 × 1.1 = 704. ∴ The correct answer is 704.

Alternate Method Given: SP1 = 832, SP2 = 448, Profit = Loss, New Profit% = 10%. Formulas: Profit = SP − CP | Loss = CP − SP | SP = CP × (100 + P%) ÷ 100.

⇒ Let CP be x. According to the question: 832 − x = x − 448. ⇒ 2x = 832 + 448 ⇒ 2x = 1280 ⇒ x = 640. ⇒ Cost Price = 640. ⇒ New Selling Price for 10% profit = 640 + (10% of 640). ⇒ New SP = 640 + 64 = 704. ∴ The correct answer is 704.

Additional Information Profit and Loss Basics Profit occurs when SP > CP, and Loss occurs when CP > SP. Both are calculated on CP unless specified otherwise. Percentage Calculations To increase a value by x%, multiply it by (1 + x/100). For a 10% increase, the multiplier is 1.10.

Given:

MP of the item = Rs. 400

Discount % for 1st and 2nd = 10%

Concept used:

SP = MP - (MP × Discount%)

Calculation:

Price after 1st discount = 400 - (400 × 10%)

⇒ 360

Price after 2nd discount = 360 - (360 × 10%)

⇒ 324

So, the cost price of the customers after two discounts = Rs. 324

∴ The item is available to customers at Rs. 324.

Shortcut Trick

Ratio of Height to Shadow = 30 : 10√3

Simplified ratio = 3 : √3 = √3 : 1

Since tan θ = √3, the value of θ must be 60°.

∴ The correct answer is 60°.

Alternate Method

Given:

Height of the tree (AB) = 30 m

Length of the shadow (BC) = 10√3 m

Formula Used:

tan θ = Perpendicular ÷ Base

Calculations:

⇒ tan θ = AB ÷ BC

⇒ tan θ = 30 ÷ 10√3

⇒ tan θ = 3 ÷ √3

⇒ tan θ = √3

⇒ θ = tan⁻¹(√3)

⇒ θ = 60°

∴ The correct answer is 60°.

Additional Information

Trigonometric Ratios at 60°

For an angle of 60°, tan 60° = √3, sin 60° = √3/2, and cos 60° = 1/2.

Angle of Elevation

It is the angle formed by the line of sight with the horizontal when looking up at an object.

Standard Triangle Ratios

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

Given:

3sin²θ + 4cosθ - 4 = 0

Formula used:

sin²θ + cos²θ = 1

Hypotenuse(H)² = Perpendicular(P)² + Base(B)² 

Calculation:

3sin2θ + 4cosθ - 4 = 0

⇒ 3(1 - cos2θ) + 4cosθ - 4 = 0

⇒ 3 - 3cos2θ + 4cosθ - 4 = 0

⇒ - 3cos2θ + 4cosθ - 1 = 0

⇒ 3cos2θ - 4cosθ + 1 = 0

⇒ 3cos2θ - 3cosθ - cosθ  + 1 = 0

⇒ 3cosθ(cosθ - 1) - 1(cosθ  - 1) = 0

⇒ (cosθ - 1)(3cosθ - 1) = 0

⇒ cosθ = 1, 1/3

But cosθ = 1 is not possible because it is given 0° < θ  < 90° and cos0° = 1

So, cosθ = 1/3

Now,

Cosθ = B/H

So,

H² = B² + P²

⇒ 3² = 1² + P²

⇒ 9 = 1 + P2

⇒ 9 - 1 = P2

⇒ 8 = P2

⇒ 2√2 = P

So, cosec2θ + cot2θ = (3/2√2)² + (1/2√2)²

⇒ (9/8) + (1/8)

⇒ (9 + 1)/8

⇒ 10/8 = 5/4

∴ The value of (cosec2 θ + cot2 θ) is $\frac{5}{4}$.

Given:

a3 + b3 = 218

a + b = 2

Concept used:

a3 + b3 = (a + b)(a2 + b2 - ab)

(a + b)2 = a2 + b2 + 2ab

Calculation:

a3 + b3 = 218

⇒ 2(a² + b² - ab) = 218

⇒ a2 + b2 - ab = 109      ----(i)

Again,

a + b = 2

⇒ (a + b)² = 2²

⇒ a² + b² + 2ab = 4      ----(ii)

By subtracting eq (i) from eq (ii) we get,

3ab = - 105

⇒ ab = - (105/3)

⇒ ab = - 35

Now,

$\sqrt {1 - ab}$ = $\sqrt {1 - (-35)}$

⇒ $\sqrt {1 +35}$

⇒ $\sqrt {36}$

⇒ 6

∴ Required answer is 6.

Given:

Edge of cube = 7cm

Concept used:

Volume of a cube = a³

Volume of a sphere = (4/3)πr³

Here,

a = side or edge of the cube

r = radius of the sphere

Calculation:

Let the radius of the sphere be x cm

According to the question,

a³ - (4/3)πr³ = ${\rm{163}}\frac{{\rm{1}}}{{\rm{3}}}$

⇒ 7³ - $\frac{4}{3}$πr³ = ${\rm{}}\frac{{\rm{490}}}{{\rm{3}}}$

⇒ 343 - ${\rm{}}\frac{{\rm{490}}}{{\rm{3}}}$ = $\frac{4}{3}$πr3

⇒ ${\rm{}}\frac{{\rm{1029,-,490}}}{{\rm{3}}}$ = $\frac{4}{3}$πr3

⇒ ${\rm{}}\frac{{\rm{539}}}{{\rm{3}}}$ = $\frac{4}{3}$πr3

⇒ 539 = 4πr3

⇒ (539 × 7)/(22 × 4) = r3

⇒ 42.875 = r3

⇒ r = 3.5 cm

So, diameter = 3.5 × 2 = 7 cm

∴ The diameter (in cm) of the sphere is 7.

Given:

\(\rm \frac{{\left[ {\frac{3}{8}, - ,\left{ {\frac{3}{8}, - ,\left( {\frac{5}{8}, - ,\frac{3}{8}} \right)} \right}} \right],of,4.8, - ,0.9}}{{4\frac{1}{6}, \div ,2.5, \times ,0.2, \div ,\frac{1}{5},of,50, + ,\left( {\frac{3}{4}, - ,\frac{1}{8}} \right)}}\)

Concept used:

Calculation:

\(\rm \frac{{\left[ {\frac{3}{8}, - ,\left{ {\frac{3}{8}, - ,\left( {\frac{5}{8}, - ,\frac{3}{8}} \right)} \right}} \right],of,4.8, - ,0.9}}{{4\frac{1}{6}, \div ,2.5, \times ,0.2, \div ,\frac{1}{5},of,50, + ,\left( {\frac{3}{4}, - ,\frac{1}{8}} \right)}}\)

⇒ \(\rm \frac{{\left[ {\frac{3}{8}, - ,\left{ {\frac{3}{8}, - ,\left( {\frac{5, - ,3}{8}} \right)} \right}} \right],of,4.8, - ,0.9}}{{4\frac{1}{6}, \div ,2.5, \times ,0.2, \div ,\frac{1}{5},of,50, + ,\left( {\frac{6, - ,1}{8}} \right)}}\)

⇒ \(\rm \frac{{\left[ {\frac{3}{8}, - ,\left{ {\frac{3}{8}, - ,\left( {\frac{1}{4}} \right)} \right}} \right],of,4.8, - ,0.9}}{{4\frac{1}{6}, \div ,2.5, \times ,0.2, \div ,\frac{1}{5},of,50, + ,\left( {\frac{5}{8}} \right)}}\)

⇒ \(\rm \frac{{\left[ {\frac{3}{8}, - ,\left{ {\frac{3}{8}, -, {\frac{1}{4}}} \right}} \right],of,4.8, - ,0.9}}{{4\frac{1}{6}, \div ,2.5, \times ,0.2, \div ,\frac{1}{5},of,50, + ,{\frac{5}{8}}}}\)

⇒ \(\rm \frac{{\left[ {\frac{3}{8}, - ,\left{ {\frac{3, -,2}{8} {}} \right}} \right],of,4.8, - ,0.9}}{{4\frac{1}{6}, \div ,2.5, \times ,0.2, \div ,\frac{1}{5},of,50, + ,{\frac{5}{8}}}}\)

⇒ $\rm \frac{{\left[ {\frac{3}{8}, - , {\frac{1}{8} {}}} \right],of,4.8, - ,0.9}}{{4\frac{1}{6}, \div ,2.5, \times ,0.2, \div ,\frac{1}{5},of,50, + ,{\frac{5}{8}}}}$

⇒ $\rm \frac{{\left[ {\frac{3, - ,1}{8}} \right],of,4.8, - ,0.9}}{{4\frac{1}{6}, \div ,2.5, \times ,0.2, \div ,\frac{1}{5},of,50, + ,{\frac{5}{8}}}}$

⇒ $\rm \frac{{\frac{1}{4},of,4.8, - ,0.9}}{{4\frac{1}{6}, \div ,2.5, \times ,0.2, \div ,\frac{1}{5},of,50, + ,{\frac{5}{8}}}}$

⇒ $\rm \frac{{1.2, - ,0.9}}{{\frac{25}{6}, \div ,2.5, \times ,0.2, \div ,10, + ,{\frac{5}{8}}}}$

⇒ $\rm \frac{{1.2, - ,0.9}}{{\frac{25}{6,\times,2.5}, \times ,\frac{0.2}{10}, + ,{\frac{5}{8}}}}$

⇒ $\rm \frac{{1.2, - ,0.9}}{{\frac{1}{30} + ,{\frac{5}{8}}}}$

⇒ $\rm \frac{{1.2, - ,0.9}}{{\frac{4,+,75}{120}}}$

⇒ $\rm \frac{{0.3}}{{\frac{79}{120}}}$

⇒ $\frac{{36}}{{79}}$

∴ Required answer is $\frac{{36}}{{79}}$.

Shortcut Trick

Ratio of investments: C = 100 units, B = 60 units (40% less), A = 78 units (30% more than B).

Total units = 100 + 60 + 78 = 238 units.

Average = 238 ÷ 3 units ≈ 79.33 units.

Given 100 units = ₹8,000 ⇒ 1 unit = ₹80.

Average value = 80 × 79.33 ≈ ₹6,346.67.

∴ The correct answer is ₹6,347.

Alternate Method

Given: C's investment = ₹8,000; B = 40% less than C; A = 30% more than B.

Formula Used: Average = (Sum of all investments) ÷ (Number of persons)

⇒ Investment of C = ₹8,000

⇒ Investment of B = 8,000 − (40% of 8,000) = 8,000 × 0.60 = ₹4,800

⇒ Investment of A = 4,800 + (30% of 4,800) = 4,800 × 1.30 = ₹6,240

⇒ Total Investment = 6,240 + 4,800 + 8,000 = ₹19,040

⇒ Average = 19,040 ÷ 3 = ₹6,346.666...

⇒ Nearest Rupee ≈ ₹6,347

∴ The correct answer is ₹6,347.

Additional Information

Percentage Change Formula

To find a value after a percentage increase or decrease: New Value = Original Value × (1 ± R/100).

Average of Grouped Data

The average of n numbers is calculated by dividing the total sum of all numbers by n.

Rounding Rules

When rounding to the nearest whole number, if the decimal part is 0.5 or greater, round up to the next integer.

Given:

PQ = 14 cm

RS = 48 cm

O is the centre

Concept used:

The perpendicular from the center of a circle to a chord bisects the chord.

Pythagoras theorem = Hypotenuse² =  Perpendicular² + Base²

Calculation:

Let OX ⊥ RS and OY ⊥ PQ

Let OX be d

And XY = 17

So,

OY = (d + 17)

Applying pythagoras theorem in ΔOXS

OS² = OX² + XS²

⇒ OS² = d² + 24²

Again,

In ΔOYQ

OQ² = OY² + YQ²

⇒ OQ2 = (d + 17)² + 72

Now,

d2 + 242 = (d + 17)2 + 72 [∵ OS = OQ = radius of the circle]

⇒ d2 + 576 = d² + 172 + 2 × d × 17 + 49

⇒ 576 = 289 + 34d + 49

⇒ 34d = 576 - 289 - 49

⇒ 34d = 238

⇒ d = 238/34

⇒ d = 7

So,

OS2 = 72 + 242

⇒ OS2 = 49 + 576

⇒ OS2 = 625

⇒ OS = 25

So, radius of the circle = 25 cm

∴ The radius (in cm) of the circle is 25 cm.

Calculation:

Number of exports of cars of type A in 2016 = 275

Number of exports of cars of type A in 2018 = 300

Total numbers of exports of cars of type A in 2016 and 2018 = 275 + 300

⇒ 575

Number of exports of cars of type B in 2014 = 225

Number of exports of cars of type B in 2017 = 275

Total numbers of exports of cars of type B in 2014 and 2017 = 225 + 275

⇒ 500

Ratio of type A cars and type B cars = 575 : 500

⇒ 23 : 20

∴ Required answer is 23 : 20.

Given:

Sum = Rs. 18000

Amount = Rs. 21780

Time = 2 years

Concept used:

A = P(1 + r/100)^t

I = P(1 + r/100)t - P

Here,

A = amount

P = principal and sum

r = rate

t = time

I = interest

Calculation:

Let the rate of interest be r

So,

21780 = 18000(1 + r/100)²

⇒ 21780/18000 = (1 + r/100)2

⇒ 1089/900 = (1 + r/100)2

⇒ (33/30)² = (1 + r/100)2

⇒ 33/30 = (1 + r/100)

⇒ 33/30 = [(100 + r)/100]

⇒ 3300 = 3000 + 30r

⇒ 30r = 300

⇒ r = 300/30

⇒ r = 10

So, rate of interest = 10%

New rate = 15%

So,

I = 18000(1 + 15/100)² - 18000

⇒ I = 18000(1 + 3/20)2 - 18000

⇒ I = 18000[(20 + 3)/20]2 - 18000

⇒ I = 18000[(23/20]2 - 18000

⇒ I = 18000 × (529/400) - 18000

⇒ I = 23805 - 18000

⇒ I = 5805

So, interest for the new rate = Rs. 5805

∴ Required compound interest is Rs. 5805.

Given:

14 men can complete a work in 15 days

Concept used:

M1 × D1 = M2 × D2

Here,

M1 = Men at the 1st case

D1 = Time at the 1st case

M2 = Men at the 2nd case

D2 = Time at the 2nd case 

Calculation:

According to the concept,

M1 = 14

D1 = 15

M2 = 21

Let D2 be x

So,

14 × 15 = 21 × x

⇒ 210 = 21x

⇒ x = 210/21

⇒ x = 10

So, D2 = 10 days

∴ They will complete the same work in 10 days.

Given:

Average of three numbers = 112

Concept used:

Average = sum of elements/no of elements

Calculation:

Total of three numbers = 112 × 3

⇒ 336

Let 2nd number be 3a

According to the question,

1st number × 1/3 = 3a 

⇒ 1st number = 3a × 3 = 9a

Again,

3rd number × 3/4 = 3a

⇒ 3rd number = 3a × (4/3) = 4a

Now,

9a + 3a + 4a = 336

⇒ 16a = 336

⇒ a = 336/16

⇒ a = 21

Smallest among three = 3 × 21 = 63

∴ The smallest number is 63.

Calculation:

1. Cars during 6 to 7 = 70

Cars during 7 to 8 = 105

Increase in number of cars = 105 - 70 = 35

Percentage change = (35/70) × 100

⇒ 50% increase

 

2. Cars during 8 to 9 = 130

Increase in number of cars = 130 - 105 = 25

Percentage change = (25/105) × 100

⇒ 23.809% ≈ 23.81% increase

 

3. Cars during 9 to 10 = 115

Decreased in number of cars = 130 - 115 = 15

Percentage change = (15/130) × 100

⇒ 11.538% ≈ 11.54% decrease

 

4. Cars during 10 to 11 = 95

Decreased in number of cars = 115 - 95 = 20

Percentage change = (20/115) × 100

⇒ 17.391% ≈ 17.39% decrease

 

5. Cars during 11 to 12 = 45

Decreased in number of cars = 95 - 45 = 50

Percentage change = (50/95) × 100

⇒ 52.631% ≈ 52.63% decrease

∴ Required answer is 52.63% decrease.

Calculation:

Number of students studying humanities in the year 2019 = 2000 × (21/100)

⇒ 420

Number of students studying humanities in the year 2020 = 2400 × (19/100)

⇒ 456

Total number of students studying humanities in the year 2019 and 2020 = 420 + 456

⇒ 876

Percentage of students studying humanities in the year 2019 and 2020 = [876/(2000 + 2400)] × 100

⇒ [876/4400] × 100

⇒ 876/44

⇒ 19.909 ≈ 19.91

∴ Requried answer is 19.91%.

Given:

Two numbers 516 and 525 are divided by 6, the remainders are R1 and R2 respectively.

Concept used:

If a number in the form of (b - 1)ⁿ is divided by b

Then,

Remainder = 1 if n is an even number

Remainder = (b - 1) if n is an odd number

Calculation:

516 = (6 - 1)¹⁶

So, remainder = $\frac{(6 - 1)^{16}}{6}$ = 1 i.e R₁

again,

525 = (6 - 1)25

So, remainder = $\frac{(6 - 1)^{25}}{6}$ = (6 - 1) = 5 i.e R2

Now, 

\(\frac{{{{\rm{R}}{\rm{1}}}{\rm{ + }}{{\rm{R}}{\rm{2}}}}}{{{{\rm{R}}_{\rm{2}}}}}\) = $\frac{1,+,5}{5}$

⇒ $\frac{6}{5}$

∴ Required answer is $\frac{6}{5}$.

Given:

(Area of ΔABC) : (Area of ΔPQR) = 121 : 64

QP = 14.4 cm

PR = 12 cm

AC = 18 cm

Concept used:

If, ΔXYZ∼ΔPTR,

then $\rm\frac{XY^2}{PT^2} =\frac{YZ^2}{TR^2} = \frac{XZ^2}{PR^2} = \frac{Area of \Delta XYZ}{Area of \Delta PTR}$

Calculation:

As ΔABC ~ ΔQPR

So, AB²/QP² = 121/64

⇒ AB/QP = 11/8

⇒ AB/14.4 = 11/8

⇒ 8AB = 11 × 14.4

⇒ AB = (11 × 14.4)/8

⇒ AB = 19.8 cm

∴ The length of AB is 19.8 cm.

Additional InformationHere we do not need to work on the values of other sides as in the question only AB is asked.

Shortcut Trick

Let the common factor (HCF) be x.

LCM of ratio terms (3, 8, 15) = 120.

We know: HCF × LCM of ratio parts = Actual LCM

x × 120 = 8280

x = 69

∴ The correct answer is 69.

Alternate Method

Ratio & LCM Concept

3x

8x

15x

LCM = 120x = 8280

Given:

Three numbers are in the proportion of 3 : 8 : 15.

The LCM of the numbers = 8280.

Concept Used:

If numbers are given in a ratio a : b : c, they can be written as ax, bx, and cx where x is their HCF.

The LCM of (ax, bx, cx) is x × LCM(a, b, c).

Calculations:

⇒ Let the three numbers be 3x, 8x, and 15x respectively.

⇒ LCM of the ratios (3, 8, and 15) = 120

⇒ LCM of the actual numbers = 120x

⇒ We are given that the LCM is 8280.

⇒ 120x = 8280

⇒ x = 8280 ÷ 120

⇒ x = 69

The common multiplier x is the Highest Common Factor (HCF) among the three numbers.

∴ The correct answer is 69.

Additional Information

LCM and HCF of Co-prime Numbers

If two numbers a and b are co-prime, their Highest Common Factor (HCF) is 1 and their Least Common Multiple (LCM) is their product (a × b).

Product Rule for Two Numbers

For any two positive integers, the product of the numbers is always equal to the product of their HCF and LCM. Formula: First Number × Second Number = HCF × LCM. This applies generally to two numbers, not three.

LCM and HCF of Fractions

LCM of fractions = LCM of numerators ÷ HCF of denominators. HCF of fractions = HCF of numerators ÷ LCM of denominators.

Calculation:

Total sales of potatoes, tomatoes, beans = 80 + 70 + 45

⇒ 195

Total sales of onions, others = 90 + 75

⇒ 165

Ratio of them = 195 : 165

⇒ 13 : 11

∴ Required answer is 13 : 11.

Additional InformationHere we do not need to calculate the central angle of the total because the angle is calculated on the basis of 360° so, it will be cancelled out at the time of calculating the ratio.

Given:

BC is a diameter

∠ABC = 42°

Concept used:

Alternate segment theorem = The angle between a tangent and a chord is equal to the angle in the alternate segment.

Diameter makes an angle of 90 degree on circumference

Calculation:

According to the concept,

∠BAC = 90°

So, ∠BCA = 180° - 42° - 90° 

⇒ 48°

Now, according to the concept,

∠MAB = ∠BCA

So, ∠MAB = 48°

∴ The measure of ∠MAB is 48°.

Given:

x + y + z = 7

xy + yz + zx = 8

Formula used:

a³ + b³ + c³ - 3abc = (a + b + c)[(a + b + c)² - 3(ab + bc + ac)]

Calculation:

Putting the values in the formula we get

x3 + y3 + z3 - 3xyz = 7 × (72 - 3 × 8)

⇒ 7 × (49 - 24)

⇒ 7 × 25

⇒ 175

∴ The value of x3 + y3 + z3 - 3xyz is 175.

The correct answer is "Convert"

Key Points

• Let's see the meanings of the given words-
• Commute- to reduce (a judicial sentence, especially a sentence of death) to another less severe one or to travel some distance between one's home and place of work on a regular basis
• Synonyms of commute are: trade, swap, exchange, change, substitute, shift, switch, interchange, replace, etc.
• Condense- make (something) denser or more concentrated.
• Convert- change the form, character, or function of something.
• Conserve- protect (something, especially something of environmental or cultural importance) from harm or destruction.
• Consume- eat, drink, or ingest (food or drink).
• Hence, according to the meanings of the given words, the correct answer is "Convert" i.e. Option 2.

Hinglish

• आइए देखें दिए गए शब्दों के अर्थ-
• Commute- एक न्यायिक सजा को कम करना, विशेष रूप से मौत की सजा को कम गंभीर सजा देना; अपने घर और कार्यस्थल के बीच नियमित रूप से कुछ दूरी तय करना
• Synonyms: trade, swap, exchange, change, substitute, shift, switch, interchange, replace, etc.
• Condense-  (कुछ) सघन या अधिक केंद्रित करना।
• Convert- किसी चीज़ के रूप, चरित्र या कार्य को बदलना।
• Conserve- रक्षा करना, सुरक्षित रखना
• Consume- खाना, काम में लाना

The correct answer is "Agreement"

Key Points

• Let's see the meanings of the given words-
• Altercation- a noisy argument or disagreement, especially in public.
• Quarrel- a heated argument or disagreement, typically about a trivial issue and between people who are usually on good terms.
• Agreement- harmony or accordance in opinion or feeling.
• Controversy- a prolonged public disagreement or heated discussion.
• Argument- an exchange of diverging or opposite views, typically a heated or angry one
• Hence, according to the meanings of the given words, the correct answer is Option 2 i.e. Agreement.

Hinglish

• आइए देखें दिए गए शब्दों के अर्थ-
• Altercation- एक शोर तर्क या असहमति, विशेष रूप से सार्वजनिक रूप से।
• Quarrel- एक गर्म तर्क या असहमति, आमतौर पर एक तुच्छ मुद्दे के बारे में और उन लोगों के बीच जो आमतौर पर अच्छी शर्तों पर होते हैं।
• Agreement- सद्भाव या राय या भावना के अनुसार।
• Controversy- एक लंबे समय तक सार्वजनिक असहमति या गर्म चर्चा।
• Argument- अलग-अलग या विपरीत विचारों का आदान-प्रदान, आमतौर पर एक गर्म या गुस्से में एक

The correct answer is "Hard work is being done by the children."

Key Points

• The given sentence has a present continuous tense. Also, it is in the Active voice.
• The structure of present continuous tense in the passive voice is- Object (in active voice) + be(forms) + V₁ -ing + Subject (in active voice).
• Let's see an example-
• Active: He is playing football.
  

Passive: Football is being played by him.

So the correct passive voice is- Hard work is being done by the children.