SSC GD Constable Previous Year Paper (Held on: 1st December 2021 Shift 2)

Let, the total number of students are x.

If 3 students are absent, then the rest of the students can be divided equally into 7 groups.

Equal parts are (x - 3)/7

If 7 students are absent, then the rest of the students can be divided equally into 9 groups. 

Equal parts are (x - 7)/9

According to the question,

(x - 3)/7 = (x - 7)/9 + 4

⇒ (9x - 27 - 7x + 49)/ 63 = 4

⇒ 2x + 22 = 63 × 4

⇒ 2x = 252 - 22

⇒ 2x = 230

⇒ x = 115.

Hence, the correct answer is "115".

Alternate Method By option elimination:

Option (1): 115

If 3 students are absent, then the rest of the students can be divided equally into 7 groups. 

Equal parts are (115 - 3)/7 =112 / 7 = 16

If 7 students are absent, then the rest of the students can be divided equally into 9 groups. 

Equal parts are (115 - 7)/9 = 108 / 9 = 12 

Therefore two conditions are satisfied. 

Option (2): 140

If 3 students are absent, then the rest of the students can be divided equally into 7 groups. 

Equal parts are (140 - 3)/7 =137 does not divide by 7.

Option (3): 87

If 3 students are absent, then the rest of the students can be divided equally into 7 groups. 

Equal parts are (87 - 3)/7 = 84/7 = 12.

If 7 students are absent, then the rest of the students can be divided equally into 9 groups. 

Equal parts are (87 - 7)/9 = 80 does not divide by 9.

Option (4): 101

If 3 students are absent, then the rest of the students can be divided equally into 7 groups. 

Equal parts are (101 - 3)/7 = 98/7 = 14.

If 7 students are absent, then the rest of the students can be divided equally into 9 groups. 

Equal parts are (101 - 7)/9 = 94 does not divide by 9.

Hence, the correct answer is "115".

The logic followed here is:

Similarly,

Hence, 'CPVKUGRVKE' 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:

i. Facet

iii. Facile

ii. Facility

iv. Fact

v. Faculty

Hence, 'i, iii, ii, iv, v' is the correct answer.

The logic followed here is:

• ‘Up’ is related to ‘Down’ → Up is antonym of Down.

Similarly,

• ‘Cold’ is related to ‘________’ → Cold is antonym of Hot.

Hence, 'Hot' is the correct answer.

The paper when unfolded will appear as shown below:

Hence, 'option 4' is the correct answer.

The logic followed here is:

(11, 13, 17) → All the three numbers are prime numbers.

Similarly,

(41, 43, 53) → All the three numbers are prime numbers.

Hence, '(41, 43, 53)' is the correct answer.

Seven people, Gaurav, Manish, Rahul, Anish, Meeta, Priya, and Preeti, are sitting in a circle.

1. Preeti is the neighbour of Meeta and Priya and sitting second to the left of Anish.

Case I:

Case II:

2. Anish is not the neighbour of Meeta and Rahul.

(According to this Case 1 is eliminated because in case 1 Anish is the neighbour of meeta)

Case II:

3. Gaurav is the neighbour of Manish and Rahul.

Case II:

1. Fourth to the right of Priya → Rahul is fourth to the right of Priya.
2. Second to the right of Anish → Gaurav is second to the right of Anish.
3. Between Manish and Gaurav → No one is between Manish and Gaurav.
4. Immediate left to Preeti → Priya is to the immediate left to Preeti.

Clearly, the position of Rahul is fourth to the right of Priya.

Hence, 'Fourth to the right of Priya' is the correct answer.

The faces opposite to each other is shown below:

→ Can be formed.

→ Can be formed.

 → Cannot be formed as % and # are faces opposite to each other.

 → Cannot be formed as % and # are faces opposite to each other.

Hence, 'only A and B' is the correct answer.

The logic followed here is:

Hence, '176' is the correct answer.

The Venn diagram that best illustrates the relationship between Teachers, Mothers, and Females is shown below:

All mothers are females. Some females and mothers are teachers.

Hence, 'option 3' is the correct answer.

The logic followed here is:

Similarly,

Hence, 'DMMXCS' is the correct answer.

The logic followed here is:

Logic: In a column - 1st number × 2nd number × 5 = 3rd number

• 11 × 8 × 5 = 440
• 9 × 12 × 5 = 540

Similarly,

• 7 × 14 × 5 = 490

Hence, '490' is the correct answer.

The logic followed here is:

Hence, 'L' is the correct answer.

The logic followed here is:

Similarly,

Hence, 'FOPVHI' is the correct answer.

All six friends are sitting in a row and facing north.

1. A and D is sitting at extreme ends.

2. H is sitting between D and G whereas B is sitting between L and A.

Clearly, L is sitting between G and B.

Hence, 'L' is the correct answer.

The logic followed here is:

'FRUSTRATION' is coded as '11'

• Number of letters in the word FRUSTATION is 11.

'TOPICAL' is coded as '7'

• Number of letters in the word TOPICAL is 7.

Similarly,

'RESURGENCE' is coded as '10'.

• Number of letters in the word RESURGENCE is 10.

Hence, '10' is the correct answer.

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

Clearly, N is the uncle of R.

Hence, ‘Uncle’ is the correct answer.

The correct mirror image of the given figure when the mirror is placed at the right side is shown below:

Hence, 'option 1' is the correct answer.

The least possible Venn diagram is:

Conclusions:

I) Some laptops are desktops. → Follow (As, All computers are desktops and Some computers are laptops)

II) All desktops are laptops. → Do not follow (As, All computers are desktops and Some computers are laptops → All desktops are laptops)

Hence, Only conclusion I follows.

The figure from among the given options that can replace the question mark(?) in the following series is shown below:

1st figure is rotate 180º clockwise in the 3rd figures.

Similarly, 

2nd figure is rotate 180º clockwise in the 4th figures.

Hence, 'option 2' is the correct answer.

The logic followed here is:

1. KOSWA → K + 4 = O; O + 4 = S; S + 4 = W; W + 4 = A
2. EIMQU → E + 4 = I; I + 4 = M; M + 4 = Q; Q + 4 = U
3. NRUZE → N + 4 = R; R + 3 = U; U + 5 = Z; Z + 5 = E
4. AEIMQ → A + 4 = E; E + 4 = I; I + 4 = M; M + 4 = Q

Hence, 'NRUZE' is the odd one out.

(14 R 9) S 6 P 40 Q 1

After replacing letters by their meaning, we get:

(14 × 9) ÷ 6 + 40 - 1

= 126 ÷ 6 + 40 - 1

= 21 + 40 - 1

= 61 - 1

= 60

Hence, '60' is the correct answer.

The logic followed here is:

Hence, 'DGI' is the correct answer.

Hence, the correct answer is "Option 2".

The logic followed here is:

Difference between the numbers is series of alternate prime numbers.

Hence, '38' is the correct answer.

The correct answer is apiculture.

Key Points

• Apiculture or beekeeping may be a kind of occupation that involves nurturing and looking after bees for the purpose of acquiring bee products like beeswax, honey, secretion, flower pollen, and bee pollen.
• Apiculture generally implies the maintenance of bees belonging to the genus Apis which are honeybees.
• However, in apiculture, even bees that aren't likely to sting are kept for preservation.

Additional Information

• Sericulture:
• Sericulture is the rearing of silkworms (i.e., the production of cocoons) for the commercial production of silk.
• Though a variety of species produce silk, only a few are used for sericulture.
• The word Sericulture springs from the Greek ‘Sericos’ meaning ‘silk’ and the English ‘culture’ meaning ‘rearing’.
• It's a multidisciplinary program.
• Pisciculture:
• The breeding, rearing, and transplantation of fish by artificial means is named pisciculture.
• Pisciculture may be a process of growing fish and selling it or using its products for domestic or commercial use.
• Floriculture:
• Floriculture may be a division of ornamental horticulture that deals with growing, selling, and arranging flowers and decorative plants.
• It encompasses flower production, processing, marketing, and distribution.

The correct answer is Aurangzeb.

Key Points

• The battle of Samugarh was fought between Aurangzeb and Dara Shukoh.
• It had been a decisive battle in the struggle for the throne during the Mughal war of succession.
• During this battle, Dara was finally defeated by Aurangzeb.
• Then, Aurangzeb went on to rule the Mughal empire.

Additional Information

• Bairam Khan:
• Bairam Khan was an unprecedented military general who served Mughal emperors Humayun and his son Akbar and had great contributions to expanding their kingdom.
• Bairam led Akbar to his victory against Hemu in the second battle of Panipat.
• Sher Shah:
• Farid, who later came to be called Sher Khan and subsequently Sher Shah, was the son of a Jagirdar under the dominion of Jaunpur.
• His father Hasan Khan Sur held the jagir of Sasaram in Bihar during the rule of Lodis.
• After defeating Humayun he became sovereign ruler within the year 1540 and assumed the title of Sher Shah.
• Muhammad Azam:
• Azam was Aurangzeb’s eldest son.
• Aurangzeb’s other son Prince Muhammad Akbar died, he was younger than Azam.

The correct answer is 9 November.

Key Points

• Uttarakhand Foundation Day also referred to as Uttarakhand Diwas or Uttarakhand Day is celebrated on November 9.
• On November 9, 2000, Uttarakhand was declared because of the 27th state.
• Within the year 2007, it acquired the name Uttrakhand rather than Uttaranchal.
• The stories of this state are associated with the great dynasties of Kushanas, Kudinas, Kanishka, Samudragupta, Kataria, Palas, Chandras, and Pawaras.

Important Points

• About Uttarakhand:
• The state is found at the foothills of the Himalayan mountain ranges, it's largely a hilly State, having international boundaries with China (Tibet) in the north and Nepal in the east.
• It also houses the four most sacred and revered Hindu temples also referred to as the Char Dham of Uttarakhand.

1. Badrinath
2. Kedarnath
3. Gangotri and
4. Yamunotri.

• Summer capital - Gairsain.
• winter capital - Dehradun.

The correct answer is 1 November.

Key Points

• Every year on November 1, Chattisgarh formation and foundation day is observed.
• The center-eastern state of Chhattisgarh in India celebrates its formation day on All Saints' Day.
• On this day, Madhya Pradesh was carved out of Chattisgarh.
• This may be the 21st anniversary of the state of Chhattisgarh.

Important Points

• About Chhattisgarh:
• It is the ninth largest state in India with 135,194 sq km of the world and has a population of about 25.5 million.
• The celebrations to mark the 17th state foundation day will be celebrated in Naya Raipur, per annum.
• The center-eastern state borders
• Madhya Pradesh in the northwest
• Uttar Pradesh in the north
• Jharkhand within the northeast
• Maharashtra within the southwest
• Telangana and Andhra Pradesh in the south, and
• Odisha in the southeast.

The correct answer is Borobi, a blue surfing koala.

Key Points

• The mascot for the 2018 Commonwealth Games within the Gold Coast was Borobi, the Blue koala.
• The features of Borobi included blue fur and coloured ears, a crimson nose, sunscreen, and Indigenous markings on hands and feet.
• The name springs from the word for a koala in the indigenous language Yugambeh.
• The 2018 Commonwealth Games started on April 4th and lasted until the 15th of April. which year the venue in Gold Coast, Australia- which can be hosting the games for the 5th time.
• Sporting talents from quite 71 countries will be participating in this spectacle that happens once in 4 years.
• New Delhi hosted the 2010 edition while in 2014 the games were conducted in Glasgow, Scotland, and therefore the 2022 edition was hosted in Birmingham, England.

Important Point

• Birmingham hosted Commonwealth Games in 2022.
• The Commonwealth Games is an international multi-sport event that was first held in 1930.
• The 2022 Commonwealth Games is officially known as the XXII Commonwealth Games.
• It will be the third time England will host the Commonwealth Games, after London in 1934 and Manchester in 2002.
• The Birmingham Organising Committee for the 2022 Commonwealth Games is responsible for the planning and operational delivery of the Games.
• This includes sport, venue, and competition management, ticket sales, all ceremonies, and the Queen’s Baton Relay.

The correct answer is February.

Key Points

• Surajkund Crafts Mela is one of the largest crafts fairs in India that is held every year in the Surajkund district of Haryana.
• The fair is actually the most popular among all fairs and festivals in Haryana and attracts visitors in large numbers from all parts of the country.
• Even several tourists from the planet over arrive at the Surajkund Crafts Mela every year to witness the glorious culture and heritage of India.

Important Points

• The fair is aimed at bringing to light the enormous talent of artisans and craftsmen in India who display their exquisite handlooms and handicrafts before a large audience at the fair.
• Every product is artistically produced after much painstaking effort and is actually a masterpiece.
• At the Haryana Surajkund Crafts Fair, several small thatch platforms are specially provided to create an authentic rustic ambiance.
• Under these thatched roofs, an outsized number of master craftsmen arriving from all parts of India gather to display their unique talent.

Additional Information

• Haryana:
• Capital- Chandigarh
• Chief Minister- Manoharlal Khattar
• Governor- Bandaru Dattatreya
• District- 22
• Lok Sabha Seat- 10
• Rajya Sabha seat- 5

The correct answer is 28.3.

Key Points

• In 2019, the infant mortality rate in India was at about 28.3 deaths per 1,000 live births, a significant decrease from previous years.
• The infant mortality rate is the number of deaths of children under one year of age per 1,000 live births.
• The infant mortality rate for India in 2020 was 29.848 deaths per 1000 live births, a 3.48% decline from 2019.
• The infant mortality rate for India in 2018 was 32.000 deaths per 1000 live births, a 4.24% decline from 2017.

Important Points

• In order to bring down Infant Mortality Rate (IMR) and Maternal Mortality Rate (MMR), the Ministry of Health and Family Welfare (MoHFW) is supporting all States/UTs in the implementation of Reproductive, Maternal, New-born, Child, Adolescent Health and Nutrition (RMNCAH+N) strategy under National Health Mission (NHM) supported the Annual Program Implementation Plan (APIP) submitted by States/ UTs.
• The interventions haunted by Govt. are:
• Interventions for improving Infant Mortality Rate (IMR):
• Facility-based newborn care
• Mother's absolute affection
• Universal immunization program
• Rashtriya Bal Swasthya Karyakaram
• Nutrition Rehabilitation Centres
• Intensified Diarrhoea Control Fortnight / Defeat Diarrhoea (D2) initiative
• Anaemia Mukt Bharat

The correct answer is Sandip Pradhan.

Key Points

• Deputy director general of the Sports Authority of India ( SAI ), Sandeep Pradhan, has been promoted to take over the top spot of the department.
• Pradhan will be taking charge of SAI as DG from August 1, as the former SAI chief Neelam Kapur will retire from her services on July 31.
• The tenure of Sandip Pradhan as Director General of the Sports Authority of India (SAI) has been extended by two years and it will come into effect from June 6, 2020.

Important Points

• Sports Authority of India:
• Sports Authority of India (SAI) was set up in 1984 to carry forward the legacy of the IXth Asian Games held in New Delhi in 1982 under the Department of Sports.
• SAl has been entrusted with the twin objectives of promoting sports and achieving sporting excellence at the national and international levels.
• SAI was set up as a Society registered of Societies Act, 1860 in pursuance of Resolution No. 1-1/83/SAI dated 25th January 1984 of the Department of Sports, Govt. of India with the objective of promotion of Sports and Games as detailed in the Resolution.

The correct answer is Santanu Das.

Key Points

• The winners of The Hindu Prize 2019 Fiction and Non-Fiction are Mirza Waheed ( Tell Her Everything ) and Santanu Das ( India, Empire, and First World War Culture: Writings, Images, and Songs ).
• The winners for both categories were selected by an eminent panel of judges.
• The citation describes Prof. Das’ work as “a sensitive exploration of the human dimensions of a major modern war that reshaped global politics and culture in fundamental ways” and as one that “helps to re-examine the scholarly and popular imaginations of the First World War which have tended to ignore the involvement of close to over a million Indians in it, and in particular, the tens of thousands among them who lost their lives.”

Important Points

• ​The Hindu Prize was instituted in 2010 to honour writers who have spent their lifetime mining the human spirit through their words and concepts.
• The prize is typically awarded at a ceremony during The Hindu’s annual literature festival Lit For Life.
• However, the 2020 edition had to be cancelled thanks to a challenging environment. a gift ceremony to be held on March 28 was also cancelled because of the COVID-19 pandemic.
• The Hindu Lit for all times will be back in January 2021.

The correct answer is 

Key Points

• Kharait is a martial dance performed with swords in the state of Himachal Pradesh.
• It is performed in Kullu district.
• This martial art is performed with swords and hurdles in circles at a fast tempo.

Additional Information

• Folk dances of the given states:
• Maharashtra- Lavani, Nakata, Koli, Lezim, Gafa, Dahikala Dasavtar or Bohada, Tamasha, Mauni, Powara, Gouricha.
• Himachal Pradesh- Kinnauri, Thoda, Jhora, Jhali, Chharhi, Dhaman, Chhapeli, Mahasu, Dangi, Chamba, Thali, Jhainta, Daf, Stick dance.
• Punjab- Bhangra, Giddha, Daff, Dhaman, Bhand, Nagual.
• Uttar Pradesh- Nautanki, Raslila, Kajri, Jhora, Chappeli, Jaita.

The correct answer is Hooghly.

Key Points

• The Battle of Plassey was a victory over the Nawab of Bengal and his French allies by the British East India Company, led by Clive.
• The combat ended on Midsummer Eve, 1757. the corporate was able to gain control of Bengal as a result of the conflict.
• British took control of most of the Indian subcontinent, Myanmar, and Afghanistan over the subsequent hundred years.
• The Conflict of Plassey is known as the battle that took place at Palashi.
• It occurred at the Hooghly River’s banks, around 150 kilometres north of Calcutta and south of Murshidabad.
• Murshidabad was the capital of Bengal Suba during that time.

Additional Information

• Bhagirathi:
• Originating from the Gaumukh is the source stream of the River Ganga that transforms into a turbulent river.
• The headwaters of the River Bhagirathi are born within the region of the Gangotri and Khatling Glaciers in the Garhwal Himalayas.
• From here, the river flows for about 205 kilometres before meeting the Alaknanda River within the town of Devprayag.
• Padma:
• The Padma is one of the major rivers of Bangladesh, and satellite imagery shows that it has been growing in size, transforming in shape, and changing in location for at least the past 30 years.
• It forms in India at the junction of the Ganges and Jamuna Rivers, then merges with the Meghna River and ultimately empties into the Bay of Bengal.
• Barakar:
• Barakar River originates from an area called Padma situated in the district of Hazaribagh in the state of Jharkhand.
• Barakar River runs down from west to east direction diagonally to the northern part of the Chota Nagpur tableland and pours across 225 kilometres of the area and later merges into Damodar situated near Dishergarh of the district of Bardhaman in West Bengal.

Important Points

• According to the official answer key of SSC Hooghly is the correct answer (SSC GD Constable Previous Year Paper Held on: 1st December 2021 Shift 2).

The correct answer is Article 352.

Key Points

• The constitution of India guarantees several fundamental rights to citizens of India.
• These rights help the individual to steer a life of welfare and dignity.
• However in certain cases these fundamental rights are often suspended.
• These cases are explained as follows –
• When the president makes a proclamation of Emergency under article 352, all the six “Right to Freedom” guaranteed under section 19 are automatically suspended.
• During the proclamation of emergency no law or executive order issued by state are often challenged on the ground that it is inconsistent with the rights guaranteed by article 19.
• The President can suspend other Fundamental Rights also through specific orders, but these orders must be approved by the parliament.
• It's going to be observed that such orders of the President may extend to the whole or any part of the territory of India.

Additional Information

• Article 353 (Effect of Proclamation of Emergency):
• The executive power of the Union extends to directing any state regarding the manner in which its executive power should be exercised.
• The Parliament becomes empowered to make laws on any subject enumerated in the State List.
• Article 354 ( Application of provisions relating to distribution of revenues while a Proclamation of Emergency is in operation):
• The President, by an order, can modify the constitutional distribution of revenues between the Centre and the states.
• It continues till the end of the financial year in which the Emergency ceases to operate.
• Such order has to be laid before each House of the Parliament.
• Article 351:
• “It shall be the duty of the Union to promote the spread of the Hindi language to develop it so that it may serve as a medium of expression for all the elements of the composite culture of India and to secure its enrichment by assimilating without interfering with its genius, the forms, style and expressions used in Hindustani and in the other languages of India specified in the 8th Schedule, and by drawing, wherever necessary or desirable, for its vocabulary, primarily, on Sanskrit and secondarily on other languages.”

The correct answer is Sinhala.

Key Points

• One of the official languages of Sri Lanka is Sinhalese.
• It's the Sinhalese people's native language, who total approximately 16 million.
• A further 4 million speak Sinhalese as a second language.
• This language belongs to the Indo-European family.
• Within that category, is a component of the Indo-Aryan branch.
• It's written with the Sinhalese alphabet which descends from the ancient Indian Brahmi writing.
• Modern-Sinhalese is traced to the Dravidian as well as Pali and the medieval version of Sinhalese.
• it's also borrowed words from Tamil, Portuguese, Dutch, and English.
• The Rodiya community within Sri Lanka speaks a dialect of Sinhalese called Rodiya.
• it's considered an indication of belonging to a lower-caste in the society.

Additional Information

• English:
• It is the official language of Arunachal Pradesh.
• It is not included in the schedule 8 of the Indian constitution.
• Malayalam:
• It is the official language of Kerala.
• It is derived from Sanskrit language.
• Tamil:
• It is the official language of Tamil Nadu.
• It is included in the Schedule 8 of the Indian Constitution.

The correct answer is Calcium nitrate.

Key Points

• Calcium nitrate, also called Norgessalpeter (Norwegian saltpetre), is a compound with the formula Ca (NO3)2.
• This colourless salt absorbs moisture from the air and is usually found as a tetrahydrate.

Additional Information

• Nitrous oxide:
• Nitrous oxide (N2O), commonly referred to as laughing gas or nos, is an anaesthetic gas with pain-relieving and anti-anxiety properties.
• It's been used recreationally and in medicine for over 200 years.
• It's become widely and easily available for recreational use as it can be legally bought and sold for the purpose of making whipped cream.
• Calcium nitrate:
• Calcium nitrate is an inorganic compound with the chemical formula Ca(NO3)2.
• Another name for this compound is Norgessalpeter.
• Potassium nitrate:
• Potassium nitrate also called saltpetre or nitre is a white solid soluble in water formed by fractional crystallisation of sodium nitrate and potassium chloride solutions.
• It occurs naturally as nitre in India, South Africa and Brazil rocks.

The correct answer is One.

Key Points

• Sikkim may be a rare state which only connects with one state of the country. the sole state of India that connects to Sikkim is West Bengal while other borders of Sikkim connect with countries like Nepal in the West, Bhutan in the East, and China in the north.
• The state is best known for its biodiversity and is the second smallest state in India.

Important Points

• About Sikkim:
• Capital: Gangtok
• Chief Minister: Prem Singh Tamang
• Governor: Lakshman Acharya
• Lok Sabha seats: 1
• Rajya Sabha seats: 1

The correct answer is Archimedes' principle.

Key Points

• The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.
• The value of thrust force is given by the Archimedes law which Archimedes of Syracuse of Greece discovered.
• When an object is partially or fully immersed in a liquid, the apparent loss of weight is equal to the weight of the liquid displaced by it.
• Lactometers, hydrometers, ships, and submarines are designed on this principle.

Additional Information

• The principle of gravitation:
• Newton’s law of universal gravitation states that any particle of matter in the universe attracts another one with a force varying directly as the product of the masses and inversely as the square of the distance between them.
• The Principle of relative density:
• The difference between the specific gravity and density is that at room temperature and pressure, 1gram per 1 cubic cm is the density of water this density is treated as a standard and the density of any other material (usual liquids) is calculated relative to this is called relative density or specific gravity.
• principle of buoyancy:
• The principle states that the buoyant force acting on an object immersed in or floating on a fluid is equal to the weight of the fluid displaced by the object.

The correct answer is Dr. Harsh Vardhan.

Key Points

• Dr. Harsh Vardhan, Union Minister for Health and Family Welfare digitally chaired the 147th session ofWHO Executive Board, through Video Conference.

Important Points

• WHO Executive Board:
• The Executive Board is composed of 34 technically qualified members elected for three-year terms.
• The annual committee meeting is held in January when the members agree upon the agenda for the World Health Assembly and the resolutions to be considered by the Health Assembly.
• A second shorter meeting takes place in May-June, as a follow-up to the Health Assembly.
• the most functions of the Board are to implement the decisions and policies of the Health Assembly and advise and usually to facilitate its work.

Additional Information

• Amit Shah:
• Amit Shah is the current Minister of Home Affairs and the first Minister of cooperation of India.
• The politician belongs to the Bharatiya Janata Party, and previously also served because of the President of the BJP from 2014 to 2020.
• Narendra Modi:
• Narendra Damodardas Modi is an Indian politician serving because the 14th and current prime minister of India since 2014.
• Modi was the chief minister of Gujarat from 2001 to 2014 and is the Member of Parliament from Varanasi.

The correct answer is Rajiv Kumar.

Key Points

• Rajiv Kumar, the senior-most member of the committee, took charge because of the 25th Chief Election Commissioner (CEC) of the country.
• The primary major task for Kumar, who will remain in this post till February 2025, is going to be to hold the elections of the President and the Vice President, slated for July-August.
• The 2024 Lok Sabha polls, several assembly elections, and Rajya Sabha elections also will be conducted under the watch of Kumar.
• Kumar has been a part of the poll panel as an election commissioner since September 1, 2020.
• He succeeds Sushil Chandra, who demitted from office on Saturday evening. Kumar will hold the post from May 15, 2022, to February 18, 2025.
• Kumar's 65th birthday is on February 19, 2025. consistent with the constitution, the term of election commissioners is six years or till the age of 65 years, whichever comes first.

Additional Information

• Election Commission of India (Article 324-329):
• The committee of India is a permanent constitutional body that conducts elections in the state and union territories.
• Get information on the election laws, instructions, political parties, current elections, past elections etc.
• Information on voters' registration is provided. Detailed information per bye-elections, results, star campaigners, and expenditure observers is provided.
• Users also can find guidelines on how to register a political party. Details about election reform proposals also are given.

The correct answer is India.

Key Points

• The 2018 Men's Hockey World Cup was the 14th edition of the Hockey World Cup, the quadrennial world championship for men's national hockey teams organized by the FIH.
• It had been held from 28 November to 16 December 2018, at the Kalinga Stadium in Bhubaneswar, India.

Important Points

• About Hockey World Cup:
• Every four years, the simplest teams in the world gathered to play for the Olympic gold, considered the very best honor in hockey.
• It had been dominated by the Asian teams, with India alone winning eight gold medals and Pakistan three.
• hockey was expanding its reach and it received a solid boost when the first edition of the men’s Hockey World Cup was staged in 1971.
• The thought of a hockey World Cup was first mooted jointly by India and Pakistan in an International Hockey Federation (FIH) council meeting in March 1969.

The correct answer is Giant African snail.

Key Points

• The snail population spread rapidly within the State, spurred by two more waves of invasion between the 1970s and in 2005.
• The import of timber from twenty-four snail-infested countries sped up their spread in Kerala.
• “In 2005, this snail was recorded only in Palakkad, Ernakulam, and Pathanamthitta.
• But by 2020, it's spread to all districts except Idukki,” said Dr. Keerthy.
• One of the worst invasive species declared by the International Union for Conservation of Nature (IUCN), the enormous African Snail is suspected to spread eosinophilic meningitis, septicemia, and peritonitis in humans.
• Many cases of eosinophilic meningitis were reported among children in Ernakulam and Thiruvananthapuram.

Additional Information

• Garden Snail:
• The snail ( Helix aspersa) is a terrestrial gastropod mollusk and one of the best-known species in the world.
• it's so common that it is one of the most proliferated terrestrial mollusks.
• Channeled apple snail:
• Ampullariidae, commonly known as the apple snails, is a family of large freshwater snails, aquatic gastropod mollusks with a gill, and an operculum.
• Chinese Snail:
• The shell of the Chinese mystery snail is large, spherical, and smooth. The outer shell is light to dark olive green to brownish.
• The inner shell is white to pale blue.

The correct answer is 63.

Key Points

• In the World Bank’s Ease of Doing Business Report 2020, India has made an interesting jump ranking 63rd among 190 countries.
• It's improved by 14 ranks from its rank of 77 in 2019.
• India has improved its rank in 7 out of 10 indicators and has moved closer to international best practices.
• The 2020 edition of the report acknowledges India together of the top 10 improvers, the third time in a row, with an improvement of 67 ranks in 3 years, said a government statement.
• The state has also taken the highest jump by any large country since 2011.

Important Points

• Ease of Doing Business Index:
• Economies are ranked on their simple doing business, from 1–190.
• A high simple doing business ranking means the regulatory environment is more conducive to the starting and operation of a local firm.
• The rankings are determined by sorting the mixture scores on 10 topics, each consisting of several indicators, giving equal weight to every top. The rankings for all economies are benchmarked to May 2019.
• Read the methodology, explaining how the convenience of doing business rankings and the ease of doing business scores are calculated (PDF), or download the ranking table (PDF).

The correct answer is Arya Samaj.

Key Points

• Lala Lajpat Rai was an eminent freedom fighter, a social activist, an educationist, and a lawyer who sacrificed his life for the independence of his motherland.
• He was a member of Arya Samaj since his college days and was an active volunteer in carrying out the social activities of Arya Samaj.
• He also joined Congress to fight for freedom, since he belonged to the Extremist group of the Congress party.

Additional Information

• Vaishnavism:
• Vaishnavism is the largest branch of modern Hinduism. Its devotees worship Vishnu, or one among his avatars, because the Supreme God.
• It has numerous sects and their beliefs vary. all Vaishnavas believe that there's one Supreme God over all creation.
• And like other Hindu branches, they believe in the existence of many lower deities under that Supreme God.
• Buddhism:
• Buddhism is one of the world’s major religions.
• It originated in India in 563–483 B.C.E. with Siddhartha Gautama, and over the subsequent millennia, it spread across Asia and the rest of the world.
• Buddhists believe that human life may be a cycle of suffering and rebirth, but that if one achieves a state of enlightenment (nirvana), it's possible to escape this cycle forever.
• Jainism:
• The Jaina doctrine is far older than Buddhism. In Jainism, ‘Tirthankara’ refers to 24 enlightened spiritual masters who are believed to possess achieved perfect knowledge through asceticism.
• Jainas don’t see Mahavira because of the founder of their religion but as the 24th Tirthankara in a long history of spiritual masters.

The correct answer is the Equator.

Key Points

• The currents which be due to the low latitudes in Tropical Zones towards the high latitudes in the Temperate and Subpolar Zones are called warm currents.
• Warm water is brought into cold water areas by them.
• The cold and hot currents meet an important fog and this creates rich fish ground.
• The Oyashio and Kuroshio currents and Gulf stream and labrador Currents produce such conditions.

Important Points

• The Torrid Zone:
• This zone stretches between twenty-three and a half degree N and S latitudes and more or less receives the vertical rays of the sun.
• A moderately warm climate throughout the year is experienced by this region.
• The cold currents originate at the poles and move toward the equator.
• warm currents originate at the equator and move towards the poles which are colder.

Additional Information

• Arctic Circle:
• The Arctic is the northern polar region of the Earth, which encompasses the Arctic Ocean and various adjacent seas, also as portions of Canada, Finland, Greenland, Iceland, Norway, Russia, Sweden, and therefore the United States (Alaska).
• Tropic of Cancer:
• The Tropic of Cancer lies at latitude 23.50 on the north of the equator and runs through several countries on three continents including Africa, Asia, and Europe.
• Antarctic circle:
• The Antarctic Circle is the most southerly of the five major circles of latitude that mark maps of Earth. The region south of this circle is understood as the Antarctic, and therefore the zone immediately to the north is called the Southern Temperate Zone.

The correct answer is Gujarat.

Key Points

• Amul was founded in 1946 in Anand, Gujarat with a mission to prevent the exploitation of the farmers by middlemen.
• The Gujarat Co-operative Milk Marketing Federation Ltd manages Amul.
• Amul spurred the White Revolution in India, which placed India at the highest of milk-producing nations.
• Amul is present in over 50 countries, and India alone has quite 7200 exclusive parlors.
• In 1999, Amul was awarded the “Best of All” Rajiv Gandhi National Quality Award“ for maintaining the utmost quality in its plants.
• Amul has been awarded the Guinness record for the longest-running advertising campaign.

Important Points

• White Revolution in India:
• The Government of India initiated Operation Flood known as the White Revolution after witnessing the huge success of the Green Revolution, which resulted in an immense increase in wheat and rice production.
• The white revolution in India started with the motive of accelerating milk production to make the country one of the largest producers of milk in the world.
• It created a national milk grid linking producers throughout India to consumers in over 700 towns and cities and reducing seasonal and regional price variations while ensuring that producers get a serious share of the profit by eliminating the middlemen.
• Today, India is the world’s largest producer of milk, and Dr. Verghese Kurien is known as the father of the White Revolution in India.

The correct answer is Vacuum.

Key Points

• A sound may be a type of energy that results from an object's or body's vibration.
• Sound travels through air particles and wishes a medium to go through.
• The vacuum, as we all know, is an empty space barren of all stuff.
• It is a place where the gaseous pressure is significantly lower than the atmospheric pressure.
• The sound may be a mechanical wave and requires a medium to travel. during a vacuum, sound cannot travel because there are not any molecules that can vibrate or convey the wave. Hence, sound cannot travel in a vacuum.

Important Points

• Mechanical Wave:
• A mechanical wave may be a wave that is a vibration in matter, transferring energy through a cloth.
• Not all waves are like this. for instance, electromagnetic waves like visible light are not mechanical because they can travel through the vacuum of space to reach us from the sun.
• Mechanical waves include water waves, sound waves, earthquake waves, and lots more.
• Like all waves, those of the mechanical variety have peaks, crests, and troughs.
• They even have a frequency, which is the number of waves that pass by per second, and a wavelength, which is the distance from one peak to the next, or one trough to the subsequent.

Given:

The average age of a company A of 5 members is 44.8 years

The average age of another company B of 4 members is 48 years.

Concept used:

Total = Average × Number of Entities

Calculation:

Total age of Company A = 44.8 × 5 = 224 years

Total age of Company B = 48 × 4 = 192 years

Total age of company B is less than the total age of company A

⇒ $\frac {224 - 192}{224} \times 100\%$ = $\frac {100}{7}\%$

∴  The total age of company B is less than the total age of company A by $\frac {100}{7}\%$.

Given:

The product of two numbers is 19440 and their HCF is 18

Concept used:

If P is the HCF of A and B then

A = (P × m) & B = (P × n)

Where m and n are arbitrary positive integers and co-prime to each other.

Calculation:

Let the two numbers be 18a and 18b respectively

According to the question,

18a × 18b = 19440

⇒ ab = 19440/324

⇒ ab = 60

Possible pairs of a and b = (1, 60), (3, 20), (4,15), (5, 12)

∴ The possible number of pairs of such numbers is 4.

Given:

Selvaraj paid ₹38,00,000 as a one-time payment

Before the handover, he had to pay 5% to make the full payment

Calculation:

Payment done before taking the keys = (100 - 5) = 95%

The full cost for flat = 38,00,000 ÷ 95% = ₹40,00,000

Additional amount to be paid

⇒ 40,00,000 - 38,00,000 = ₹2,00,000

∴ The additional amount to be paid is ₹2,00,000.

Given:

0.2 × 2 +${ {1} \over 2}$ ÷ 2 × ${ {5} \over 2}$ of 2 - 1.5 + 3 × ${ {1} \over 3}$ ÷ ${ {2} \over 3}$ - ${ {2} \over 5}$

Concept used:

Calculation:

0.2 × 2 +${ {1} \over 2}$ ÷ 2 × ${ {5} \over 2}$ of 2 - 1.5 + 3 × ${ {1} \over 3}$ ÷ ${ {2} \over 3}$ - ${ {2} \over 5}$

⇒ 0.2 × 2 +${ {1} \over 2}$ ÷ 2 × 5 - 1.5 + 3 × ${ {1} \over 3}$ ÷ ${ {2} \over 3}$ - ${ {2} \over 5}$

⇒ 0.2 × 2 +${ {1} \over 2}$ × ${ {1} \over 2}$ × 5 - 1.5 + 3 × ${ {1} \over 3}$ × ${ {3} \over 2}$ - ${ {2} \over 5}$

⇒ 0.2 × 2 +${ {5} \over 4}$ - 1.5 + ${ {3} \over 2}$ - ${ {2} \over 5}$

⇒ 0.4 + ${ {5} \over 4}$ - 1.5 + ${ {3} \over 2}$ - ${ {2} \over 5}$

⇒ ${ {2} \over 5}$ + ${ {5} \over 4}$ - ${ {3} \over 2}$ + ${ {3} \over 2}$ - ${ {2} \over 5}$

⇒ $\frac {5} {4}$

∴ The simplified answer is $\frac {5} {4}$.

Given:

[12 ÷ (2 × 3)] ÷ [24 ÷ (8 - 5)]

Concept used:

Calculation:

[12 ÷ (2 × 3)] ÷ [24 ÷ (8 - 5)]

⇒ [12 ÷ 6] ÷ [24 ÷ 3]

⇒ 2 ÷ 8

⇒ ${ {1} \over 4}$

∴ The value of [12 ÷ (2 × 3)] ÷ [24 ÷ (8 - 5)] is ${ {1} \over 4}$.

Shortcut Trick

$\frac{MP}{CP}$ = $\frac{100-Loss}{100-Doscount}$ = $\frac{100-15}{100-30}$ = $\frac{85}{70}$

MP = ₹850 → 85 units = ₹850 → 1 unit = ₹10

Thus, CP = 70 × 10 = ₹700

Alternate Method

Given:

The marked price of an article is ₹850

Article is sold at 15% loss after giving a 30% discount

Concept used:

SP = MP × ($\frac{100-Discount}{100}$)

SP = CP × ($\frac{100-Loss}{100}$)

Calculation:

SP = 850 × $\frac{100-30}{100}$ = 850 × $\frac{70}{100}$ = Rs 595

CP = 595 × $\frac{100}{100-15}$ =  595 × $\frac{100}{85}$ = Rs 700

∴ The CP of the article is Rs 700.

Shortcut Trick

1 day earning of 5M + 3W = 8400 ÷ 4 = ₹2100   ... (i)

1 day earning of 9M + 7W = 28700 ÷ 7 = ₹4100   ... (ii)

Solve (i) × 7 − (ii) × 3: (35M + 21W) − (27M + 21W) = 14700 − 12300

8M = 2400 ⇒ M = ₹300, and substituting M gives W = ₹200.

Daily earning of 8M + 5W = 8(300) + 5(200) = ₹3400.

Total days to earn ₹30600 = 30600 ÷ 3400 = 9 days.

∴ The correct answer is 9 days.

Alternate Method

Given:

Earning of 5 men and 3 women in 4 days = ₹8,400

Earning of 9 men and 7 women in 7 days = ₹28,700

Calculations:

Let the daily earning of 1 man be M and 1 woman be W.

⇒ (5M + 3W) × 4 = 8400

⇒ 5M + 3W = 2100   ---- (Equation 1)

⇒ (9M + 7W) × 7 = 28700

⇒ 9M + 7W = 4100   ---- (Equation 2)

Multiplying Equation 1 by 7 and Equation 2 by 3:

⇒ 35M + 21W = 14700   ---- (Equation 3)

⇒ 27M + 21W = 12300   ---- (Equation 4)

Subtracting Equation 4 from Equation 3:

⇒ 35M − 27M = 14700 − 12300

⇒ 8M = 2400

⇒ M = 300

Substitute M = 300 in Equation 1:

⇒ 5(300) + 3W = 2100

⇒ 1500 + 3W = 2100

⇒ 3W = 600

⇒ W = 200

Calculate the daily earning of 8 men and 5 women:

⇒ 8M + 5W = 8(300) + 5(200)

⇒ Total daily earning = 2400 + 1000 = ₹3400

Number of days required to earn ₹30,600:

⇒ Required Days = Total Target Earning ÷ Daily Earning

⇒ Required Days = 30600 ÷ 3400 = 9 days

∴ The correct answer is 9 days.

Additional Information

Work & Wages Rule

Wages are distributed in direct proportion to the work done by individuals. When individuals work for the same number of days, their total wages are shared in the ratio of their daily efficiencies or one-day earnings.

Simultaneous Linear Equations

For a system of two variables, equations can be solved by scaling one or both equations to equalize the coefficients of one variable, then adding or subtracting to eliminate it and solve for the remaining unknown.

Unitary Method Application

The fastest way to equate different groups working for different time periods is to calculate the earnings or work done for exactly 1 unit of time (1 day) to establish a common proportional base.

Given:

In a school, the total students (boys and girls only) are 720. Boys and girls are in the ratio 7 : 5. In another school, there are 560 students (boys and girls only) and the ratio of boys and girls is 3 : 5. 

Calculation:

Number of boys in the first school = 720 × 7/(7 + 5) = 420

Number of girls in the first school = 720 × 5/(7 + 5) = 300

Number of boys in the second school = 560 × 3/(3 + 5) = 210

Number of girls in the second school = 560 × 5/(3 + 5) = 350

Now, The ratio of boys and girls in the total strength of the two schools

⇒ (420 + 210) : (300 + 350)

⇒ 630 : 650

⇒ 63 : 65

∴ The ratio of boys and girls in the total strength of the two schools is 63 : 65.

Shortcut Trick

By successive method

Value after 2 years = 250000 × $\frac{90}{100}$ × $\frac{90}{100}$ = ₹2,02,500

∴ After 2 years the value of the machine will be ₹2,02,500.

Alternate Method

Given:

A machine depreciates by 10% per year

The present worth of the machine is ₹2,50,000

Concept used:

In case of the compound interest,

Amount = P(1 + R/100)^N

CI = P(1 + R/100)^N - P

Where, P = Principal, R = Rate of Interest, N = Time in years

Calculation:

After 2 years the value of the machine will be

⇒ 250000(1 - 10/100)²

(Here, the depreciation is considered as negative growth)

⇒ 250000 × 0.81

⇒ ₹2,02,500

∴ After 2 years the value of the machine will be ₹2,02,500.

Given

By selling an item at (4/5)th of CP one loses 16%

Concept used:

CP = SP ×  $\frac{100}{100-Loss}$

Gain = SP - CP

Gain% =$\frac{Gain}{CP} × 100$

\()Calculation:\()

Let the original SP be Rs x.

Latest SP = $x × \frac{4}{5} \space = \space \frac{4x}{5}$

CP = $(\frac{4x × 100}{(1000-16) × 5})$ = $\frac{80x}{84}$ = $\frac{20x}{21}$

Gain = \()\(x-\frac{20x}{21}\) = $\frac{x}{21}$

Gain% at the original SP = $\frac{x}{21} × \frac{21}{20x} × 100$

⇒ $\frac {1}{20} × 100\%$ = 5%

∴ The original gain percentage is 5%.

Shortcut Trick

By successive method

CP for manufacturer = 21252 × $\frac{100}{115}$ × $\frac{100}{112}$ × $\frac{100}{110}$ = ₹15,000

∴ The cost price of the item for the manufacturer was ₹15,000.

Alternate Method

Given:

A manufacturer sells an item to a wholesaler at a profit of 10%

The wholesaler sells the same item to a retailer at a profit of 12%

The retailer sells the same item to a customer at a profit of 15%

The customer paid ₹21,252 for the item

Concept used:

SP = CP × $\frac{100+Profit}{100}$

Calculation:

CP to the retailer = 21252 × $\frac{100}{115}$ = ₹18,480

CP to the wholesaler = 18480 × $\frac{100}{112}$ = ₹16,500

CP to the manufacturer = 16500 × $\frac{100}{110}$ = ₹15,000

∴ The cost price of the item for the manufacturer was ₹15,000.

Shortcut Trick

Average speed for two equal halves of a journey = (2 × S₁ × S₂) ÷ (S₁ + S₂)

Average speed = (2 × 21 × 24) ÷ (21 + 24) = 1008 ÷ 45 = 22.4 km/h

Total Distance = Average Speed × Total Time

Total Distance = 22.4 × 12 = 268.8 km

∴ The correct answer is 268.8 km.

Alternate Method

Given:

Speed for first half (S₁) = 21 km/h

Speed for second half (S₂) = 24 km/h

Total time (T) = 12 hours

Formula Used:

Time = Distance ÷ Speed

Let the total distance be D km.

⇒ Time for first half = (D ÷ 2) ÷ 21 = D ÷ 42 hours

⇒ Time for second half = (D ÷ 2) ÷ 24 = D ÷ 48 hours

⇒ Total Time = D ÷ 42 + D ÷ 48 = 12

⇒ (8D + 7D) ÷ 336 = 12 [LCM of 42 and 48 is 336]

⇒ 15D ÷ 336 = 12

⇒ 15D = 12 × 336

⇒ 15D = 4032

⇒ D = 4032 ÷ 15

⇒ D = 268.8 km

∴ The correct answer is 268.8 km.

Additional Information

Average Speed

It is the total distance traveled divided by the total time taken. Average Speed = Total Distance ÷ Total Time.

Conversion of Units

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Proportionality Rule

If distance is constant, speed is inversely proportional to time (S ∝ 1/T). If time is constant, distance is directly proportional to speed (D ∝ S).

Shortcut Trick

By successive method

Final SP = 1200 × $\frac{70}{100}$ × $\frac{75}{100}$ = ₹630

∴ The final sale price of the shirt is ₹630.

Alternate Method

Given:

A store announces two successive discounts of 30% and 25%

Concept used:

Effective discount of two successive discounts = $(A + B - {AB \over 100})\%$

SP = MP × $\frac{100-Discount}{100}$

Calculation:

Final discount% = 30 + 25 - (30 × 25)/100 = 47.5%

Final SP of the shirt = 1200 × $\frac{100-47.5}{100}$ = 1200 × $\frac{52.5}{100}$ = ₹630

∴ The final sale price of the shirt is ₹630.

Shortcut Trick

Shortcut: LCM = HCF × Product of Ratio Parts

Ratio = 3 : 5 and HCF = 6

∴ LCM = 6 × (3 × 5)

∴ LCM = 6 × 15 = 90

∴ The correct answer is 90.

Alternate Method

Given: Ratio of two numbers = 3 : 5 and HCF = 6

Formula Used: Number = HCF × Ratio Part

Ratio: 3

Ratio: 5 HCF Multiplier = 6

Num 1 = 3 × 6 = 18

Num 2 = 5 × 6 = 30 LCM(18, 30) = 90

⇒ Let the two numbers be 3x and 5x.

⇒ The HCF of 3x and 5x is x (since 3 and 5 are co-prime).

⇒ Given HCF = 6, so x = 6.

⇒ First number = 3 × 6 = 18

⇒ Second number = 5 × 6 = 30

⇒ LCM of 18 and 30:

⇒ 18 = 2 × 3 × 3

⇒ 30 = 2 × 3 × 5

⇒ LCM = 2 × 3 × 3 × 5 = 90

∴ The correct answer is 90.

Additional Information

Fundamental Relation

For any two numbers A and B, Product of numbers = HCF × LCM. ⇒ A × B = HCF(A, B) × LCM(A, B).

LCM of Fractions

LCM of (a/b, c/d) = LCM(a, c) ÷ HCF(b, d).

Co-prime Numbers

If two numbers are co-prime, their HCF is always 1 and their LCM is always their product.

Property of Ratio

If the ratio of two numbers is a : b and their HCF is H, the numbers are Ha and Hb, and their LCM is H × a × b.

Given:

A, B and C individually can complete a work in 12, 10 and 15 days respectively

All three work together and after 3 days, B and C leave the work.

Concept used:

Total work = Efficiency × Total Time

Calculation:

LCM (12, 10, 15) = 60

Let the total work be 60 units (∵ LCM of 12, 10, 15 = 60)

Efficiency of A = 60/12 = 5 units/day

Efficiency of B = 60/10 = 6 units/day

Efficiency of C = 60/15 = 4 units/day

Work done in 3 days by A, B, C = 3 × (5 + 6 + 4) = 45 units

Time required by A to complete the remaining work

⇒ (60 - 45)/5 = 3 days

∴ The remaining work will be completed by A in 3 days.

Given:

A certain sum becomes double in 2 years at a certain rate per annum compound interest.

Concept used:

In case of the compound interest,

Amount = P(1 + R/100)^N

CI = P(1 + R/100)^N - P

Where, P = Principal, R = Rate of Interest, N = Time in years

Calculation:

Let the rate of interest and principal be R% and P respectively

According to the question,

P(1 + R/100)² = 2P

⇒ (1 + R/100)2 = 2

⇒ (1 + R/100)4 = 2² (Squaring both sides)

⇒ P(1 + R/100)4 = 22 × P (Multiplying P on both sides)

⇒ P(1 + R/100)4 = 4 × P      ....(1)

Now, from (1), we can clearly conclude in 4 years the principal will become 4 times in amount at the same rate of interest.

∴ The number of years it will become 4 times at the same compound interest rate is 4 years.

Given:

A cuboidal metal plate of 1 cm thickness, 9 cm breadth and 81 cm length is melted to form a cube

Concept used:

1. Volume of a Cuboid = Length × Breadth × Height

2. Volume of a Cube = Side³

3. Total surface area of Cube = 6(Side)²

The volume of the cube should be equal to the volume of the cuboidal metal plate.

Calculation:

Volume of the cuboidal metal plate = 1 × 9 × 81 = 729 cm³

Let the measure of each side of the cube be Q.

Volume of the cube = Q³

Total surface area of the cube = 6Q²

According to the concept,

Q3 = 729

⇒ Q = 9

⇒ Q² = 81

⇒ 6Q² = 486

∴ The total surface area of the cube is 486 cm².

Given:

A certain sum amounts to ₹8,571.50 in $4{{1} \over 2}$years at 8.5% p.a. at simple interest.

The simple interest on the same sum will be ₹x in $6{{2} \over 3}$ years at 10${ {1} \over 2}$% p.a.

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

Where, P = Principal, R = Rate of Interest

Calculation:

Let the principal amount be P

According to the concept,

P + (P × 4.5 × 8.5)/100 = 8571.5

⇒ 1.3825P = 8571.5

⇒ P = 8571.5/1.3825

⇒ P = 6200

Now, the simple interest on ₹6,200 in $6{{2} \over 3}$ years at 10${ {1} \over 2}$% p.a.

⇒ (6200 × 20/3 × 21/2) ÷ 100

⇒ ₹4,340

∴ The value of x is ₹4,340.

Given:

X% of Y is 100 and Y% of Z is 400.

Calculation:

According to the question,

X% of Y = 100

⇒ XY/100 = 100

⇒ XY = 10000      ....(1)

According to the question,

Y% of Z = 400

⇒ YZ/100 = 400

⇒ YZ = 40000      ....(2)

(1) ÷ (2)

X/Z = 1/4

⇒ X : Z = 1 : 4

∴ The ratio between X and Z is 1 : 4.

Given:

At the start of a session, the number of students in grades 6, 7 and 8 in a school was 120, 150 and 130 respectively.

Later on, 10 students were admitted in grades 6 and 7 and 10 students were transferred from grade 8. 

Calculation:

Total number of students initially = 120 + 150 + 130 = 400

Final number of students grade 6 = 120 + 10 = 130

Final number of students grade 7 = 150 + 10 = 160

Final number of students grade 8 = 130 - 10 = 120

Total number of students at the end = 130 + 160 + 120 = 410

Now, the ratio of the number of students at the start and those at the end of the session

⇒ 400 : 410 = 40 : 41

∴ The ratio of the number of students at the start and those at the end of the session is 40 : 41.

Given:

The length and breadth of a rectangular field are in the ratio 4 : 3.

The cost of cultivating the field at ₹2 per m2 is ₹600

Concept used:

Area of a rectangle = Length × Breadth

Cultivation takes place across the area of a field

Calculation:

Let the length and breadth of the rectangular field be 4x and 3x respectively.

Area of the field = 4x × 3x = 12x²

According to the question,

12x2 × 2 = 600

⇒ x² = 25

⇒ x = 5 (considering the positive value only)

Now, the length of the field = 4 × 5 = 20m

∴ The length of the field is 20m.

Shortcut Trick

Let the sum of the last five numbers be 3 units.

The first number = 2/3 × 3 = 2 units.

Total sum of six numbers = 2 + 3 = 5 units.

Given Average of 6 numbers = 12.5 ⇒ Total Sum = 12.5 × 6 = 75.

5 units = 75 ⇒ 1 unit = 15.

Sum of last five numbers = 3 units = 3 × 15 = 45.

Average of last five numbers = 45 ÷ 5 = 9.

∴ The correct answer is 9.

Alternate Method

Given:

Average of 6 numbers = 12.5

Let the first number be x and the sum of the last five numbers be S.

Formula Used:

Sum = Average × Number of terms

Calculations:

⇒ Total Sum = 12.5 × 6 = 75

⇒ x + S = 75

⇒ According to the question, x = (2/3) × S

⇒ (2/3)S + S = 75

⇒ (5/3)S = 75

⇒ S = (75 × 3) ÷ 5 = 15 × 3 = 45

⇒ Average of last five numbers = S ÷ 5

⇒ Average = 45 ÷ 5 = 9

∴ The correct answer is 9.

Additional Information

Basic Average Formula

Average = (Sum of all observations) ÷ (Total number of observations).

Weighted Average

If two groups have averages A₁ and A₂ with n₁ and n₂ terms, Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Sum of First n Natural Numbers

Sum = [n(n + 1)] ÷ 2. Average = (n + 1) ÷ 2.

Given:

A shopkeeper sold 100 pencils at ₹24 for 10 pencils. 

Profit earned = 20%

Concept used:

SP = CP × $\frac{100+Gain}{100}$

Calculation:

SP of 100 pencils = 24 × 100/10 = ₹240

CP of 100 pencils = 240 × $\frac{100}{100+20}$ = 240 × $\frac{100}{120}$ = ₹200

CP of each pencil = 200/100 = ₹2

∴ The cost price of each pencil is ₹2.

Given:

While covering a distance of 24 km, a man noticed that after walking for 1 h 20 min, the distance covered by him was ${{ 7} \over 11}$ of the remaining distance. 

Concept used:

Distance = Speed × Time

Calculation:

1 hour 20 minutes = (1 + 20/60) hours

⇒ 4/3 hours

Let the remaining distance be 11x km.

Distance cover by him walking = 11x × ${{ 7} \over 11}$ = 7x

According to the question,

11x + 7x = 24

⇒ 18x = 24

⇒ x = 24/18 = 4/3

So, the distance covered by him walking = 7 × 4/3 = 28/3 km

Now, his speed = ${\frac {28}{3}} \div {\frac {4}{3}}$

⇒ 7 km/h

∴ His speed was 7 km/h.

Given:

Two positive numbers are in the ratio 5 : 8.

The sum of their squares is 356.

Calculation:

Let the positive numbers be 5x and 8x respectively

Sum of these numbers = 5x + 8x = 13x

According to the question,

(5x)² + (8x)² = 356

⇒ 25x² + 64x² = 356

⇒ 89x² = 356

⇒ x² = 356/89

⇒ x² = 4

⇒ x = +2 (∵ given numbers are positive only)

⇒ 13x = 26

∴ The sum of those two numbers is 26.

The erroneous segment is 'owing for'.

Key Points

• The given sentence is not grammatically correct.
• The error lies in Part A of the sentence.
• Here, the error lies in the erroneous usage of the preposition 'for' after owing.
• The correct preposition after owing is 'to'.
• If something is owing to another thing, it is a result of that thing.
• Therefore, the correct substitution for the erroneous part is 'owing to'.
• Hence, the correct answer is option 3.

The correct answer is 'archary'.

Key Points

• We have to choose the erroneous spelling as our marked option.
• From the given options, archery is spelled incorrectly.
• Its correct spelling is 'archery' which means art, practice, or skill of shooting with a bow and arrow.
• Therefore, the correct answer is option 2.

Additional Information

• Orchard: An orchard is a piece of land where fruit trees are grown.
• The term is typically used to refer to a location where apples, peaches, pears, cherries, or similar fruit trees are cultivated in quantity.
• Example: We picked apples in my grandfather's orchard.
• Archary: This seems to be a misspelled or incorrect word.
• It does not exist in the English language as per my knowledge up to the cut-off in 2021.
• You might be referring to "archery," which is the practice or sport of shooting arrows with a bow.
• Example: I am taking archery lessons this summer.
• Anarchy: Anarchy is a state of society without government or law.
• It can also refer to political and social disorder due to the absence of governmental control.
• Example: After the overthrow of the government, the country was thrown into anarchy.
• Monarch: A monarch is a sovereign head of state, especially a king, queen, or emperor.
• In a different context, the Monarch is also a type of large and beautiful butterfly, known for its long migrations.
• Example: The United Kingdom is ruled by a monarch, Queen Elizabeth II.

The correct answer is 'since the hurricane made landfall'.

Key Points

• The given sentence is not grammatically correct.
• The underlined segment is erroneous here.
• We need to substitute the underlined segment with the sentence from the following options:
• The given sentence is in the present perfect tense and in this case since will be used to introduce an action or an event as a reason for something related in the past.
• Therefore, we will substitute since here in the underlined segment and,  thus the correct answer is option 2.
  

Correct Sentence: There have been heavy rains in the city since the hurricane made landfall.

The correct answer is 'Accomplice'.

Key Points

• The one word for the given group of words 'A partner in crime' is Accomplice.
• Let us explore the meanings of all options :
• Companion means a person who associates with or accompanies another or others.
• Follower means a person who follows or supports a person, belief, etc.
• Opponent means a person who disagrees with something and speaks against it or tries to change it.
• The marked option accomplice means a person who helps another in committing a crime.
• So, from the meanings of the given options, it is clear that the one word is 'Accomplice.'
• Therefore, the correct answer is option 4.

The correct answer is 'fond'.

Key Points

• The given sentence 'She is so ______ of plants that she can spend her entire day in a garden.' implies that the person is so affectionate of plants that she can spend her entire day in a garden.
• So, we have to choose an option which is having a similar meaning to the word 'affectionate'.
• Hence, from the given options 'fond' is the synonym of the word 'affectionate'.
• Therefore, the correct answer is option 4.

The correct answer is 'Nectar'.

Key Points

• We need to substitute the given group of words with  one word from the following options:
• Let's explore the meanings :
• Euphoria means an extremely strong feeling of happiness.
• Nectar means a sweet liquid produced by flowers, which bees and other insects collect
• Ambrosia means something especially delicious to taste or smell.
• Juice means the liquid that comes from a piece of meat when it is cooked.
• From the meanings of the given options, it is clear that 'nectar' is the one word for the given group of words

Thus, the correct answer is option 2.

The correct answer s 'Accelerate'.

Key Points

• The one word for 'move faster' from the given options is-
• The marked option 'accelerate' means to move faster.
• Hence, the one word for 'move faster' is 'accelerate.'
• Thus, the correct answer is option 1.