SSC GD Constable Previous Year Paper (Held on: 17th November 2021 Shift 3)

The logic followed here is :-

HIDDEN is written as IJECDM.

Similarly,

FELLOW will be written as :

Hence, the correct answer is "GFMKNV".

Calculation of compound interest for half-yearly CI₁ = P(1 + r₁/100)²ⁿ - P

Calculation of compound interest for quarterly of year CI₂ = P(1 + r₂/100)⁴ⁿ - P

Given :

Principle = 40,000

Rate of interest = 20%

∴ r₁ for half-yearly = 10%

∴ r₂ for quarterly of year = 5%

⇒ n = 1 year

Difference between the compound interest on ₹40,000 at 20% per annum compounded half - yearly and compounded quarterly for a period of one year is :

⇒ CI₁ -CI₂ = [P(1 + r1/100)2n - P] - [P(1 + r2/100)4n - P]

⇒ P(1 + 10/100)² - P - P(1 + 5/100)⁴ + P

⇒ P(1 + 1/10)² - P(1 + 1/20)⁴

= 40000(11/10)² - 40000(21/20)⁴

= 40000[(11/10)² - (21/20)⁴]

or

= 40000 [(21/20)⁴ - (11/10)²]

= 40000(1.05⁴ - 1.1²)

= 40000(1.21550625 - 1.21)

= 40000 (0.00550625)

= 220.25

Hence, the correct answer is "₹ 220.25".

Given :- T _ D S _ R _ S T R D _ T _ D S _ R _ S

By checking options and substituting accordingly.

1. R, T, D, T, R, D, T → T R D S - T R D S - T R D T - T R D S - D R T S 2. D, T, D, S, S, S, T → T D D S - T R D S - T R D S - T S D S - S R T S

3. R, T, D, S, R, T, D → T R D S - T R D S - T R D S - T R D S - T R D S

• Here TRDS is repeated. 4. D, T, R, S, R, T, D → T D D S - T R R S - T R D S - T R D S - T R D S
• Option (3) gives a pattern of : T R D S - T R D S - T R D S - T R D S - T R D S

Hence, the correct answer is "R, T, D, S, R, T, D".

According to the given information:

Six people, F, G, H, I, J and K , are standing opposite to each other in a circle, facing towards the center.

2. F and K are opposite to each other.

3. K is second to the left of H and H is opposite to I.

4. F and G are adjacent to each other and J is opposite to G.

∴ Here, 'G' is standing between Fand I.

Hence, the correct answer is "G".

The logic followed here is :-

By using BODMAS RULE :

Given :

 

Given equation is : 15 S 2 P 2 (11 S 2) D 75 V 15 D 4 (9 S 4)

By inserting the symbols in given equation the expression is as follows : 

= 15 × 2 + 2 (11 × 2) - 75 ÷ 15 - 4 (9 × 4)

= 15 × 2 + 2 (22) - 75 ÷ 15 - 4 (36)

= 15 × 2 + 44 - 75 ÷ 15 - 144

= 15 × 2 + 44 - 5 - 144

​= 30 + 44 - 5 - 144

= 74 - 149

= -75

Hence, the correct answer is "-75".

The logic followed here is :-

'TWO' is coded as '3' → Number of letters in word TWO is 3,

and

'FIVE' is coded as '4' → Number of letters in word FIVE is 4.

Similarly,

'EIGHT' be coded as → Number of letters in word EIGHT is 5.

Hence, the correct answer is "5".

The logic followed here is :-

First number² + 6 = Second number

      ♦  15 : 231 → 15² + 6 = 225 + 6 = 231

Similarly,

      ♦  16 : ? → 16² + 6 = 256 + 6 = 262

Hence, the correct answer is "262".

The arrangement of the given words in the order in which they appear in an English dictionary is as follows :

Ma is common in all the words.

4. Mammal
5. Manager
6. Mandible
7. Manicure
8. Manner

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

The logic followed here is :-

1. YUSR

2. GDBA

3. IFDC

4. ZWUT

∴ Here, 'YUSR' is different from other three alternatives given.

Hence, the correct answer is "YUSR".

The logic followed here is:

Printer is a hardware device that accepts text and graphic output from a computer and transfers the information to paper.

Similarly,

Web Browser is a type of software that allows us to find and view websites.

Hence, the correct answer is "software".

Family chart :

Family diagram :

Given :

1. 'P × Q' means 'P is the wife of Q'.

2. 'P + Q' means 'P is the father of Q'.

3. 'P ÷ Q' means 'P is the daughter of Q'.

4. 'P - Q' means 'P is the son of Q'. 

The given expression is : 

'E ÷ F + G - H ÷ I' → E is the daughter of F, F is the father of G, G is the son of H and H is the daughter of I.

∴ Here, E is the grand daughter of I.

Hence, the correct answer is "Granddaughter".

The logic followed here is :-

Eleven people are sitting across a rectangular table. Four persons are sitting on each longest side of the table.

1. Boss is sitting alone at one side of the table.

2.  N and O are sitting beside each other on one of the shortest side of table.

Case (i) :

Case (ii) :

3. H is sitting opposite to E and between G and N.

Case (i) :

Case (ii) :

4. B is opposite to D and between C and G.

Case (i) :

Case (ii) :

5. A is sitting opposite to C and between M and D.

Case (i) :

Case (ii) :

6. F is sitting opposite to G.

Case (i) :

Case (ii) :

∴ Here, 'M' is Boss among them.

Hence, the correct answer is "M".

The figure that will come next in the following figure series is as shown below :

• Circle which is darken moves in anti-clockwise from one corner to other corner by one step.

• Rhombus which is darken moves in anti-clockwise.

• Figure 1 to figure 2 one darken rhombus moves 3 steps anti-clockwise and other darken rhombus is added.

• Figure 2 to figure 3 darken rhombus moves 3 steps anti-clockwise and other darken rhombus is removed.

• Figure 3 to figure 4 one darken rhombus moves 3 steps clockwise and other darken rhombus is added.

• Figure 4 to figure 5 darken rhombus moves 3 steps clockwise and other darken rhombus is removed as shown in figure.

Hence, the correct answer is "Option 3".

In first dice and second dice, A and B is common in both dice.

Moving dice1 in anti-clockwise direction the other adjacent side of A, B appeared is 'E'.

Moving again dice2 in anti-clockwise direction the other adjacent side of A,E appeared is 'F'.

Moving dice3 in anti-clockwise direction the other adjacent side of A, F will appear as 'C'.

As, from above three dices the opposite faces of give cube is as follows : 

 

∴ Here, the next possible position will be A, F adjacent with side 'C'.

Hence, the correct answer is "Option 2".

The mirror image of the given figure is as follows :

Hence, the correct answer is "Option 4".

After unfolding the paper the figure formed is as shown below :

Hence, the correct answer is "Option 3".

LOGIC: Sum of first two numbers × 2 = last number (Column wise)

Column(1): (15 + 16) × 2 = 31 × 2 = 62

Column(2):  (30 + 26) × 2 = 56 × 2 = 112

Similarly,

Column(3): (33 + 19) × 2 = 52 × 2 = 104

Hence, 104 is the correct answer.

The logic followed here is :-

Hence, the correct answer is "91".

The logic followed here is :-

FEW : GYH

Similarly,

YOU : ?

Hence, the correct answer is "QWA".

From the given information :-

∴ Here, the colour of 'Stop' signal is red, which is called green.

Hence, the correct answer is "green".

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

• Some Girls are Students.
• Some Boys are students.

Hence, the correct answer is "Option 1".

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

Conclusions :

I. All tulips are flowers → False (As All flowers are tulips so, All tulips are flowers, hence, False)

II. Some tulips are whites → False (As No tulips are whites so, Some tulips are whites, hence, False)

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

The logic followed here is :-

Hence, the correct answer is "NRU".

The logic followed here is :-

Hence, the correct answer is "92".

The image that is embedded in given figure is as below :

Hence, the correct answer is "Option 1".

The correct answer is 1947.

Key Points

• Exchange control  was introduced in India under the Defence of India Rules on September 3, 1939, on a temporary basis.
• The statutory power for exchange control was provided by the Foreign Exchange Regulation Act (FERA) of 1947, which was subsequently replaced by a more comprehensive Foreign Exchange Regulation Act, 1973.
• Liberalization was introduced in 1991 and this Act was amended as a new Foreign Exchange Regulation (Amendment) Act 1993.
• Significant developments in the external sector, such as a substantial increase in foreign exchange reserves, growth in foreign trade, rationalization of tariffs, current account convertibility, liberalization of Indian investments abroad, etc, resulted in a changing environment.
• In view of this changing environment, the Foreign Exchange Management Act (FEMA) was enacted in 1999 to replace FERA.
• FEMA became effective on June 1, 2000.

Additional Information 

• FEMA aims at facilitating external trade and payments and for promoting the orderly development and maintenance of foreign exchange markets in India.
• Emphasizing the shift in focus, the Reserve Bank in due course also amended (since January 31, 2004) the name of its department dealing with the foreign exchange transactions to the Foreign Exchange Department from Exchange Control Department.

The correct answer is These tides are the lowest.

Key Points

• Tides refer to the rise and fall in sea levels caused by the combination of gravitational forces exerted by the Moon and the Sun and the rotation of the Earth.
• There are two types of Tides: Spring Tides and Neap Tides.
• Spring Tides occur when the Sun, the Moon, and the Earth are in a straight line.
• High tides are higher and low tides are lower than average. 
• Spring tides occur twice a month.
• One during the full moon period and
• another during the new moon period.

1. Neap Tides occur when the Sun and the Moon are at right angles to each other and the forces of the sun and the moon tend to counteract one another.

• These tides also occur twice a month. However, there is a 7-day interval between Spring and Neap tides.

Important Points

• Spring tides are the tide just after a new or full moon, when there is the greatest difference between high and low water.
• So the difference between the new moon and full moon is 15 days. Hence the tides are fortnightly.
• In New Moon Syzygy, the high-high tide at a position will be higher than the high-high tide on the same position during Full Moon Syzygy.
• It is so because, in the new moon syzygy, the moon is between the Sun and Earth.
• So there will be a combined direct pull of the Sun and moon on that face of the earth.
• Hence a higher high-high tide.

The correct answer is Madhya Pradesh

Key Points

• Gau Cabinet’ for the protection and promotion of cattle.
• The first meeting of the Cabinet will be held on ‘Gopashtami’ on November 22
• at the Cow Sanctuary in Agar-Malwa district named ‘Kamdhenu Gau Abhyaranya
• The Animal Husbandry, Forest, Panchayat and Rural Development would be part of the Cabinet.​

Additional Information​​

• Madhya Pradesh is the first state who s introduce a Gau cabinet in India
• Madhya Pradesh.
• ​Mp chief minister is Mohan Yadav.
• The Governor of MP is Mangubhai C.patel
• Lok sabha sit 29
• Rajya sabha sit 11

The correct answer is 1858.

Key Points

• Bahadur Shah Zafar was the last Mughal Emperor who participated and was a symbolic head of the Revolt of 1857.
• He was born on 24 October 1775.
• He became Emperor in 1837 at the age of 62.
• He succeeded his father, Emperor Akbar Shah II.
• He was also a poet.
• After the revolt of 1857, he was found guilty and sent to exile in Burma (present Myanmar).

Additional Information Revolt of 1857-​

• The revolt of 1857 started due to the British policy of Doctrine of lapse, High land revenue, higher taxation and mistreatment of Indian sepoys.
• It was the 1st major revolt that took place against Britisher and was also called as First War of Independence by V.D.Sawarkar.

The correct answer is Iqbal Chand Malhotra and Maroof Raza.

Key Points

• Iqbal Chand Malhotra had completed their degree in Economics from Queens College, University of Cambridge.
• As of August 2022, Iqbal Chand Malhotra is Chairman & Producer, AIM Television Pvt. Ltd.
• Iqbal Chand Malhotra also worked as an advisor to  India to media mogul Rupert Murdoch.
• Maroof Raza was a former Indian Army officer and commentator on military and security issues.

 Additional Information

The correct answer is 14 January.

Key Points

• The Armed forces Veterans day is observed each year on January 14 since 2017.
• The Armed forces veterans day recognizes the service rendered by field Marshal KM Cariappa,
• The  Marshal KM Cariappa of the first Indian commander-in-chief of the Indian Armed forces​

Additional Information

• Indian armed forces
• The Indian Armed Forces are the military forces of the Republic of India.
• It consists of three professional uniformed services: the Indian Army, Indian Navy, and Indian Air Force
• The Indian Armed forces Headquarters in New Delhi.

Important Points

The correct answer is January 2020

Key Points

• Parliament passed the Transgender person (protection of right )Bill,2019 on 26 Nov 2019
• It defines a transgender person whose gender does not match the gender assigned at birth
• It provides every transgender person with the right to live an equal
• The Bill | States that transgender persons will have the right to “self-perceived” gender identity
• The Bill |  Enforces a minor’s right of residence compelling any transperson below 18 to cohabit with their natal family.

Additional Information

• The Transgender Persons (Protection of Rights) Bill, 2019 was introduced in Lok Sabha on July 19, 2019.
• The Minister for Social Justice and Empowerment, Mr Thaawarchand Gehlot introduced the bill.
• Japan was the first country to legalise transgender people in July 2003.
• Christine Jorgensen (USA)  was the first transgender in the world, in 1954.
• Naaz Joshi is the first transgender in India

Important Points

• In our constitution to Article 79 (part-v) mention BILL,ACT

The correct answer is MDH.

Key Points

• Mahashay Dharampal Gulati was the founder of MDH.
• MDH is an Indian spice company.
• He was awarded Padma Bhushan, in 2019.
• He is also called Spice King
• MDH was opened in 1919 in Sialkot (now in Pakistan).

Additional Information

The correct answer is 2018.

Key Points

• The Central Govt has repealed "The National Commission for Backward Classes Act, 1993" with effect from 15.8.2018.
• National Commission for Backward Classes (NCBC) was initially constituted by the Central Government by "The National Commission for Backward Classes Act, 1993" dated 2.4.1993.
• So far the Commission had been reconstituted 7 times up to 2016.

Additional Information

• The Present Commission (8th) has been accorded Constitutional Status through “The Constitution (One Hundred and Second Amendment) Act, 2018” Act dated 11.8.2018.
• Article 338B has been inserted, forming a Commission for the socially and educationally backward classes to be known as NCBC.
• The Commission consists of a Chairperson, Vice-Chairperson, and three other Members in the rank & pay of Secretary to the Government of India.
• Chairman - Shri Hansraj Gangaram Ahir and the 3 Members Shri Achary Thalloju, Dr. Sudha Yadav, Shri Kaushlendra Singh Patel. For more:- link
• Vice-Chairman- Dr. Lokesh Kumar Prajapati
• Secretary-Shri Rajeev Ranjan.
• Headquarters - New Delhi

The correct answer is K L Rahul

Key Points

• The K L Rahul player of the king's Eleven Punjab won the IPL 2020 orange cap
• The Indian batsman was the first time to cross the 600 mark  run
• IPL 19 David warner won the orange cap team of sun rises Hyderabad

Additional Information

• The Indian premier league
• established in 2008 is an annual Twenty20 cricket tournament.
• Administrator**-BCCI**
• Number,s of teams10

​

The correct answer is 1526

Key Points

• The first battle of Panipat was fought in 1526 between Babur and Ibrahim Lodi.
• ​In 1526, the Mughal forces of Babur, the Timurid ruler of Kabulistan, defeated the much larger ruling army of Ibrahim Lodi, Sultan of Delhi.​
• Panipat was a legendary location where after 1526, multiple battles were fought between the Mughals and varying other forces.
• Babur was invited by Daulat Khan, the governor of Punjab, to invade the region and unsettle Ibrahim Lodi.
• Lodi’s army relied heavily on cavalry and especially on elephants, which in earlier times, could shock the enemy and rout them.
• This battle made the foundation of the Mughal dynasty in India.
• Panipat is a historic city in Haryana, India.

Additional Information

• Second Battle of Panipat (1556):​
• It was fought between Hemu Vikramaditya and Akbar.
• Date: November 5, 1556.
• Third Battle of Panipat (1761):
• It was fought between Marathas and Ahmad Shah Durrani.
• Date: 14 January 1761.

The correct answer is Sur.

Key Points

• Sur dynasty was founded by Sher Shah Suri after defeating Mughal king Humayun in The Battle of Chausa in 1539.
• Sur originally belongs to Afghanistan.
• Sur ruled North India from 1540 to 1556.
• Sur last ruler Adil Shah Suri was defeated by Akbar in the 2nd battle of Panipat in 1556.

Important Points

• The period from 1206 A.D. to 1526 A.D. came to be known as the Delhi Sultanate period.

Additional Information

The correct answer is Keratin.

Key Points

• Human nails and hairs are made up of Keratin.
• Keratinocytes produce keratin, a type of protein that forms the basic component of hair, skin, and nails.
• Keratin in the skin's outer layer helps create a protective barrier.
• Keratin is a type of protein that forms the cells that make up the tissue in nails, hairs, and other parts of the body.
• It makes hair strong and resilient.

Important Points

• Laminin functions as a sticky glue, which holds cells and ECM together.
• It has active domains for collagen binding, cell adhesion, heparin-binding, and neurite outgrowth fragment.
• It modulates cell growth, motility, and signaling pathways.
• Cell types used are epithelial cells, endothelial cells, muscle cells, schwannoma, and hepatocytes.
• Collagen is the most abundant protein in mammals.
• In cell culture, it is used to study the growth, differentiation, and migration of cells.
• Collagen Type I is used for fibroblasts or endothelial cells.
• Collagen Type II may be used for Chondrocytes and epithelial cells.
• Fibronectin is a multifunctional protein involved in cell adhesion and spreading.
• It also regulates cellular morphology, cell migration, cytoskeletal organization, hemostasis, and wound repair.
• For cell types such as epithelial cells, mesenchymal cells, neuronal cells, fibroblasts cells, and endothelial cells you may use fibronectin.

The correct answer is Sumit Nagal.

Key Points

• Sumit Nagal became the first Indian tennis player to win a round at a Grand Slam in seven years when he downed American Bradley
• Someday verman was the last Indian to win a main draw match, it was in 2013 when he beat Slovakia Lukas Lacko
• Sumit Nangal is from Harayana, Jhajjar districts

Additional Information

• According to tennis history, a grand slam is a term used to represent all majors collectively.
• Don Budge became the first tennis player to win the four major championships in one year and thus capture the grand slam
• The Novak Djokovic is the grandest single wons ( 22).

Important Points

• Types of Grand Slam

The correct answer is Cooperative Societies.

Key Points 

1. Cooperative societies are the other major source of low-cost finance in rural areas.
2. Forms of cooperative societies are farmers cooperatives, weavers cooperatives, industrial workers cooperatives, Credit Cooperative Society, Consumer Cooperative Society, Producer Cooperative Societies, Marketing Cooperative Society, Housing Cooperative Society.
3. Cooperative Societies are formed for the mutual benefit of its members. Hence, the Credit Cooperative Society provides low-cost finance or cheap credit to its members at very nominal rate of interest.
4. Example of Credit Cooperative Society - Krishak Cooperative
5. Krishak Cooperative provides loans for construction of houses, fishery loans, loans for agricultural trade and cultivation, loans for the purchase of agricultural implements, and loans for a variety of other expenses.
6. The Cooperative also obtains a large loan from the bank, with these deposits from their members as collateral.
7. Loans to members are given from these funds.
8. Another round of lending can take place, once these loans are repaid.

Additional Information Other features of Cooperative Society are

1. It needs to be registered mandatorily under Societies Registration Act, 1860, or the Cooperative Societies Act, 1912.
2. There shall be at least 7 members with a draft of Memorandum of Association to register a Cooperative Society.
3. It is governed by a managing committee that is elected democratically by its members.
4. Audits are performed in cooperative societies, hence it is managed professionally.
5. Its formation and participation of members are voluntary by nature.
6. It is mutually beneficial to members of low and middle-income groups.
7. Reduced financial risk.

The correct answer is Karnataka

Key Points

• Yakshagana is a traditional theatre form of Karnataka.
• The literal meaning is "The Song of Yaksha"
• It was developed in Udupi District.
• It is a temple art form that reflects mythological stories, Ramayana, Mahabharat, and other Hindu epics.
• It is strongly influenced by Vaishnav Bhakti Movement.
• Usually recited in Kannada, Malayalam, and Tuliu.

Important Points

• Other dance forms
• Andhra Pradesh - Kuchipudi
• Telangana - Perini
• Kerala - Mohiniyattam

The correct answer is Silver Iodide

Key Points

1. Artificial rain is created by seeding clouds with Silver Iodide.
2. Seeding of Clouds refers to the process of making precipitation fall using substances like dry ice, and silver iodide.
3. Cloud seeding chemicals include silver iodide, potassium iodide and dry ice.
4. Cloud seeding is an artificial way to create moisture in the clouds so as to cause rainfall.

Important Points

The correct answer is Dominic Thiem.

Key Points

• Dominic Thiem won his first Men's Singles Grand Slam at US Open 2020
• He defeats Alexander Zverev to win the title.
• He is an Austrian professional tennis player.

Additional Information

• There are Four Grand Slams in Tennis which are the Australian Open, French Open, Wimbledon and US Open.
• Don Budge was the first tennis player to win all four Grand Slams.
• Rafael Nadal has won the maximum number of Grand Slams (22) in Men's.
• Serena Williams has won the maximum number of Grand Slams (23) in females.

Winner 2020

 

Winner 2021

 

Winner 2022 (July)

The correct answer is Badminton.

Key Points

1. Jwala Gutta is a left-handed Indian Badminton Player.
2. She was born in Wardha, Maharashtra on 7th September 1983.
3. She received India’s second-highest sporting honor ‘Arjuna Award’ in 2011.

Additional Information

1. Jwala Gutta
2. She played her debut match in India Asia Satellite Tournament, in 2002.
3. Her favorite shot was "Forehand Service and Left Handed Stroke Play".
4. Career Best Ranking - 6th (Mixed Doubled) and 10th (Womens' Doubles)
5. In her career spanning over a decade, she had a total of 165 wins and 167 losses to her credit.
6. She is India's most successful doubles specialist and has won the National Badminton Championships fourteen times.
7. She has won medals at all major international tournaments.

The correct answer is Malnad.

Key Points

• The Karnataka Plateau is divided into two parts Malnad and Maidan.
• The Malnad region is a hilly region whereas the Maidan is the plain region of low hills.
• The Highest peak of the Karnataka plateau is Mulangiri in Baba Budan Hills.
• The Karnataka plateau has an origin in the Kaveri river from the Bramhagiri hills.
• The Karnataka plateau has also the origin of Jog falls and Shivasamudram falls.
• The Karnataka plateau is made of lava which is famous for Black soil.

Additional Information

The correct answer is Punjab.

Key Points

• Empowered Action Group (EAG) states are the states who lagged behind in the demographic transition and have the highest infant mortality rates in the country.
• As per census 2011, Eight states are listed under Empowered Action Group (EAG) states which are Bihar, Chhattisgarh, Jharkhand, Madhya Pradesh, Orissa, Rajasthan, Uttaranchal and Uttar Pradesh.

Additional Information

• Census is the process of collecting, compiling, analysing, evaluating and publishing data related to a Population.
• Census is conducted by the Office of the Registrar General and Census Commissioner, Ministry of Home Affairs.
• The first census was conducted under British rule on February 17, 1881, under Lord Ripon.
• 2011 was the 15th census conducted in India and the 16th census which was to be conducted in 2021 was postponed due to the outbreak of covid-19.

The correct answer is 2012

Key Points 

• The Buddhist chanting of Ladhak is a form of musical verse
• It is 2012 it was included in the representative list of Humanity's intangible cultural Heritage
• The Buddhist chanting of Ladakh refers to the recitation of sacred Buddhist texts in the state of Jammu and Kashmir's trans-Himalayan Ladakh region
• The chanting is a highly orchestral drama.
• The chanting meant for peace and prosperity of a large of the world​​

 Additional Information

• UNESCO
• Formation 16 November 1945
• Type -United nation specialised agency
• Headquarters France
• present head -Audrey Azoulay

Important Points

• The first Indian UNESCO site was the Ajanta caves, Ellora caves, Agra fort, and Taj Mahal 1983.
• list of UNESCO World Heritage sites in India.

The correct answer is Imperial Japanese forces and British Indian forces

Key Points

• The Battle of Kohima was the turning point of the Japanese U-Go offensive into India in 1944, during World War II .
• This battle was fought in three stages from April 4 to June 22, 1944, around the town of Kohima
• The Japanese defeat at Kohima and Imphal was the largest up until that time
• In March 1944, the Japanese came in through the dense jungles of the region from Burma into India.

Additional Information

• The plan was to attack the northeast of India through Burma.
• There was a British garrison at Kohima, today the capital of the state of Nagaland.
• The Japanese forces wished to attack the garrison and take Kohima after which they would take Assam and then march on to Delhi
• During the Battle of Kohima, the British and Indian forces had lost 4,064 men, dead, missing and wounded
• One such slice of history is the Battle for Kohima-Imphal, which was a decisive turning point in the war.
• It ended with the first major defeat suffered by Japanese forces in the Burma theatre and thwarted their ambitious plans to invade India

Important Points

• World War II or the Second World War, often abbreviated as WWII or WW2, was a global war that lasted from 1939 to 1945
• It involved the vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies and the Axis powers
• In a total war directly involving more than 100 million personnel from more than 30 countries,
• the major participants threw their entire economic, industrial, and scientific capabilities
• The Axis powers—Germany, Italy, and Japan—and the Allies—France, Great Britain, the United States, the Soviet Union,
• The Axis power defeated by the Allies' power

The correct answer is Blood Pressure.

Key Points

• A Sphygmomanometer is a device used to measure Blood Pressure.
• It consists of an inflatable cuff, a measuring unit, the mercury manometer, and a mechanism for inflation which may be manually operated bulb and valve or a pump electrically operated.
• It was invented in 1881 by Samuel Siegfried Karl Ritter Von Basch.

Additional Information

• Electric Current is measured by Ammeter.
• Wind speed is measured by Anemometer.
• Humidity is measured by Hygrometers.

The correct answer is Pigovian.

Key Points

• Pigouvian taxes are taxes levied against private individuals or businesses for engaging in a specific activity that causes a certain negative effect on a commercial activity which affects other parties without this being reflected. Ex- Causing environmental pollution.
• Tax is named after economist Arthur C. Pigou, who mention or draw the idea from his book The Economics of Welfare, 1920.
• Arun Jaitley announced an increase in securities transaction taxes on equity options from 0.017% to 0.05%.

Additional InformationTax Definition

• A tax is a legal fee or financial charge levied by the government on an individual or an organization.

​Type of Taxes

• **Direct tax -**Direct taxes are those in which the point of impact and point of the incident will fall on the same entity. A direct tax cannot be transferred by an individual to another person, example-Income tax and corporate tax.
• **Indirect tax-**Indirect tax is a type of tax where the point of incident and impact does not fall on the same entity. The burden of tax can be transferred by the taxpayer to another person, for example- GST and Custom Duty.

Given:

Ratio of Men and Women = 5 : 4

Men are increased by 16%

Women are increased by 15%

Concept used:

Percentage increase = original quantity × Rate of % increase

Increased quantity = original quantity × (1 + Rate of % increase)

Calculation:

Let number of men = 50

And number of women = 40

Now, 16% of 50 = 50 × 16/100 = 8

 Increased men = 50 + 8 = 58

15% of 40 = 40 × 15/100 = 6

Increased women = 40 + 6 = 46

New ratio of men and women = 58 : 46

⇒ 29 : 23

∴ The new ratio of men and women is 29 : 23.

Alternate MethodLet men be 5X and women be 4X

Increased men = 5X × (1 + 0.16) = 5X × 1.16 (∵ 16% increase)

Increased women = 4X × (1 + 0.15) = 4X × 1.15 (∵ 15% increase)

New ratio = 5X × 1.16 : 4X × 1.15

⇒ 5 × 116 : 4 × 115

⇒ 29 : 23

∴ The new ratio of men and women is 29 : 23.

Shortcut Trick

For three numbers a, b, and c to be in continued proportion after adding a number x, the direct formula is:

x = (b² − a × c) ÷ (a + c − 2b)

Here, a = 15, b = 9, and c = 5.

x = (9² − 15 × 5) ÷ (15 + 5 − 2 × 9)

x = (81 − 75) ÷ (20 − 18) = 6 ÷ 2 = 3

∴ The correct answer is 3.

Alternate Method

Given:

The numbers are 15, 9, and 5.

Formula Used:

If three numbers A, B, and C are in continued proportion, then A : B :: B : C, which means the product of extremes equals the product of means (B² = A × C).

15 + x

:

9 + x

::

9 + x

:

5 + x

Product of Means

Product of Extremes

Calculations:

⇒ Let the number to be added be x.

⇒ According to the continued proportion condition:

⇒ (15 + x) : (9 + x) :: (9 + x) : (5 + x)

⇒ (15 + x) ÷ (9 + x) = (9 + x) ÷ (5 + x)

⇒ (15 + x) × (5 + x) = (9 + x)²

⇒ 75 + 15x + 5x + x² = 81 + 18x + x²

⇒ 75 + 20x = 81 + 18x

⇒ 20x − 18x = 81 − 75

⇒ 2x = 6

⇒ x = 3

∴ The correct answer is 3.

Additional Information

Continued Proportion

Three quantities a, b, and c are in continued proportion if a : b = b : c. Here, b is called the mean proportional between a and c, and c is the third proportional to a and b.

Mean Proportional

For any two numbers a and c, the mean proportional is given by the square root of their product: √(a × c).

Fourth Proportional

If a : b :: c : d, then d is the fourth proportional to a, b, and c, calculated as d = (b × c) ÷ a.

Componendo and Dividendo

A useful property of proportions states that if a ÷ b = c ÷ d, then (a + b) ÷ (a − b) = (c + d) ÷ (c − d).

Shortcut TrickSP = Rs. 900  and discount = 40% SP = (100 - Discount)/100 × MP

⇒ 900 = (100 - 40)/100 × MP

⇒ 900 = 60/100 × MP

⇒ MP = 1500.

Alternate MethodGiven:

Selling Price = Rs.900

Discount = 40%

Formula used:

Discount (D) = MP - SP

Discount percent (D%) = (D/MP) × 100

Where SP = selling price

MP = marked price

Calculation:

SP = Rs.900

D% = 40%

D% = (MP - SP)/MP × 100

⇒ 40 = (MP - 900)/MP × 100

⇒ 40/100 = 1 - 900/MP

⇒ 900/MP = 1 - 2/5 = 3/5

⇒ MP = 900 × 5/3

⇒ MP = Rs.1500

∴ The marked price is Rs.1500.

Given:

Total amount deposited in the name of his son and daughter = Rs.328000

Age of daughter = 18 years and Age of son = 19 years

Formula used:

Amount = Principal(1 + Rate /100)ⁿ, where n = time 

Calculation:

Let P₁ = amount deposited by Rameshwar in his daughter's account, Time (n) for compound interest = (21 - 18) years = 3 years

P₂ = amount deposited by Rameshwar in his son's account, Time (n) for compound interest = (21 - 19) years = 2 years

Now, according to the question, both will get the same amount after 21 years 

Amount of daughter = Amount of son

⇒ P₁ × (1 + 5/100)³ = P₂ × (1+ 5/100)²

⇒ P₁ × (105/100)³ = P₂ × (105/100)²

⇒ P₁ × (105/100) = P2

⇒ P₁/P₂ = 100/105 = 20/21

⇒ P₁ + P₂ = 20 + 21 = 41 units

But, according to question,  P1 + P2 = Rs.328000

⇒ 41 units = Rs.328000

⇒ 1 unit = 8000

⇒ Daughter's share (P₁ = 20 unit) = 20 × 8000 = Rs.160000

∴ Rameshwar invested Rs.1,60,000 in the name of his daughter.

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

3 × 4 ÷ 3 of 24 - 3 ÷ 2 × (3 - 4) × 2 + 6 ÷ 4 of 3

⇒ 3 × 4 ÷ 3 of 24 - 3 ÷ 2 × (-1) × 2 + 6 ÷ 4 of 3

⇒ 3 × 4 ÷ 72 - 3 ÷ 2 × (-1) × 2 + 6 ÷ 12

⇒ 3 × 4 × 1/72 - 3/2 × (-2) + 1/2

⇒ 1/6 + 3 + 1/2 = (1 + 18 + 3)/6

⇒ 22/6 = 11/3 

⇒ 3 $\frac{2}{3}$

∴ The value of 3 × 4 ÷ 3 of 24 - 3 ÷ 2 × (3 - 4) × 2 + 6 ÷ 4 of 3 is $3\frac{2}{3}$

Shortcut Trick

Number 6523678pq is divisible by 99, so it must be divisible by 9 and 11.

For divisibility by 9: Sum of digits (6+5+2+3+6+7+8+p+q) = 37 + p + q must be a multiple of 9.

Possible values for p + q are 8 or 17. Checking options: (1) 4+4=8, (2) 6+2=8, (3) 2+6=8, (4) 3+5=8. All satisfy 9.

For divisibility by 11: (q+8+6+2+6) − (p+7+3+5) = (22 + q) − (15 + p) = 7 + q − p must be 0 or 11.

If 7 + q − p = 11, then q − p = 4. From options, only p = 2, q = 6 gives 6 − 2 = 4.

∴ The correct answer is p = 2, q = 6.

Alternate Method

Given: Number = 6523678pq, Divisor = 99.

Formula Used: Divisibility rules of 9 and 11.

⇒ Condition 1 (Sum of digits for 9): 6 + 5 + 2 + 3 + 6 + 7 + 8 + p + q = 37 + p + q

⇒ For 37 + p + q to be divisible by 9, p + q = 8 (since 37 + 8 = 45) or p + q = 17.

⇒ Condition 2 (Difference for 11): (q + 8 + 6 + 2 + 6) − (p + 7 + 3 + 5) = 0, 11, ...

⇒ (22 + q) − (15 + p) = 7 + q − p

⇒ For 11 divisibility: 7 + q − p = 11 ⇒ q − p = 4

⇒ Solving p + q = 8 and q − p = 4:

⇒ 2q = 12 ⇒ q = 6 and p = 8 − 6 = 2.

∴ The correct answer is p = 2, q = 6.

Additional Information

Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Divisibility by 11

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

Composite Divisibility

If a number is divisible by two co-prime numbers a and b, it is also divisible by their product (a × b).

Shortcut Trick

Area of floor of a cube = a² = 192 m².

Longest rod in a cube = Body Diagonal = a√3.

⇒ a√3 = √(a² × 3) = √(192 × 3).

⇒ √576 = 24 m.

∴ The correct answer is 24 m.

Alternate Method

Given:

Area of the floor of the cubical room = 192 m².

Formula Used:

1. Area of floor (square) = a²
2. Longest rod (diagonal of cube) = a√3

Calculations:

⇒ Let the side of the cubical room be 'a'.

⇒ a² = 192

⇒ a = √192 = √(64 × 3) = 8√3 m

⇒ Length of the longest rod = a√3

⇒ Length = (8√3) × √3

⇒ Length = 8 × 3

⇒ Length = 24 m

∴ The correct answer is 24 m.

Additional Information

Volume of Cube

The volume of a cube with side 'a' is given by V = a³.

Total Surface Area

The Total Surface Area (TSA) of a cube is 6a², representing the area of all six square faces.

Diagonal of a Cuboid

For a cuboid with dimensions l, b, and h, the longest rod length is √(l² + b² + h²).

Given:

The average weight of 6 people increases by 1.5 kg

A person weighing 65 kg is replaced by a new person.

Concept used:

Average of N number of quantities = (Sum of N quantities)/(Total number of quantities)

Calculations:

Total increase in weight = 6 × 1.5 = 9 kg

This increment of weight is because of the replacement of a person of 65 kg with a new person

This implies that the new person has a weight of 9 kg more than the person whose weight is 65 kg

∴ The weight of new person = 65 + 9 = 74 kg.

Alternate Method Let the weight of the new person be x kg

And the average weight of 6 persons be A kg

Sum of weights of all persons = Average weight of all persons × Number of persons

⇒ A × 6 - 65 + x = (A + 1.5) × 6

⇒ A × 6 - 65 + x = A × 6 + 9

⇒ x - 65 = 9

⇒ x = 9 + 65 = 74 kg

∴ The weight of the new person is 74 kg.

Given:

$\frac{312÷26 + 60 ÷ (42 - 55 of 4 ÷ 10) × 2}{9 + (12 - 2 of 4)}$

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

$\frac{312÷26 + 60 ÷ (42 - 55 of 4 ÷ 10) × 2}{9 + (12 - 2 of 4)}$

(312 ÷ 26 + 60 ÷ (42 - 220 ÷ 10) × 2)/[9 + (12 - 8)]

⇒ (312 ÷ 26 + 60 ÷ (42 - 22) × 2)/(9 + 4)

⇒ (312 ÷ 26 + 60 ÷ 20 × 2)/13

⇒ (12 + 3 × 2)/13

⇒ (12 + 6)/13

⇒ 18/13

⇒ 1$\frac{5}{13}$

∴ The value is 1$\frac{5}{13}$.

Given:

Selling price = Rs.254.38

Gain % = 10.6% 

Final selling price = Rs.224.25

Formula used:

CP = SP/(100 + Gain%) × 100

Gain % = {(SP - CP)/CP} × 100

Loss % = {(CP - SP)/CP} × 100, where

CP = cost price

SP = selling price

Calculation:

According to the question,

Gain % = 10.6 = (254.38 - CP)/CP × 100

⇒ 10.6/100 = (254.38 - CP)/CP

⇒ CP × 0.106 = 254.38 - CP

⇒ 1.106 × CP = 254.38

⇒ CP = 254.38/1.106

⇒ CP = Rs.230

Now, final SP = 224.25

Loss % = {(CP - SP)/CP} × 100

Loss % = {(230 - 224.25)/230} × 100

⇒ (5.75/230) × 100

⇒ Loss % = 2.5%

∴ If the article is sold for 224.25, then the loss % will be 2.5%.

Shortcut TrickSP = 254.38 & Gain = 10.6%

Now, CP = SP/(100 + Gain%) × 100

⇒ CP = 254.38/(100 + 10.6) × 100 

⇒ CP = 254.38/110.6 × 100

⇒ CP = 230 then,

Final SP = 224.25 and CP = 230

Loss % = (230 - 224.25)/230 × 100

⇒ Loss % = 2.5%

Given:

Marked price = Rs.7500

First discount = 10%

Selling price = Rs.5805

Concept used:

Discount = Marked price - Selling price

Discount % = (Discount/MP) × 100

Successive discount percent = X + Y - (X × Y)/100

Where X% and Y% are the two successive discount percentages.

Calculation:

According to the question,

Marked price (MP) = Rs.7500

Discount = 7500 × 10% = Rs.750

Price after first discount = 7500 - 750 = Rs.6750

Let the second discount be x

Now, Selling price = Price after first discount - Second discount

⇒ 5805 = 6750 - x% × 6750

⇒ 5805 = 6750 ×  (1 - x%)

⇒ 1 - x% = 5805/6750 = 43/50

⇒ x% = 1 - (43/50) = 7/50

⇒ x = 7/50 × 100 = 14%

∴ The second discount % is 14%.

Shortcut TrickFirst discount be 10% and MP = 7,500

First Discount = 7500 × 10% = 750

Price after 1st discount = 7500 - 750 = 6750

Then, final SP = 5805

Second discount = 6750 - 5805 = 945.

% of 2nd discount = 945/6750 × 100 

⇒ % of 2nd discount = 14%.

Shortcut Trick

Divisibility by 88 requires the number to be divisible by both 8 and 11.

For 8, last three digits 5y2 must be divisible by 8 ⇒ Largest y = 9 (592 ÷ 8 = 74).

For 11, (Sum of digits at odd places) − (Sum of digits at even places) = 0 or 11.

(6 + 3 + 1 + 4 + 9) − (4 + x + 1 + 5 + 2) = 23 − (12 + x) = 11 − x.

For divisibility, 11 − x = 11 ⇒ x = 0.

Value of 2x − 3y = 2(0) − 3(9) = −27.

∴ The correct answer is − 27.

Alternate Method

Given: A 10-digit number 643x1145y2 is divisible by 88.

Method: Divisibility rules for 8 and 11.

⇒ Divisibility by 8: The last three digits (5y2) must be divisible by 8.

⇒ Possible values for y: If y = 1 (512), y = 5 (552), y = 9 (592).

⇒ Largest value of y = 9.

⇒ Divisibility by 11: The difference between the sum of digits at odd positions and even positions must be 0 or a multiple of 11.

⇒ Sum of digits at odd positions (from right): 2 + 5 + 1 + x + 4 = 12 + x.

⇒ Sum of digits at even positions (from right): y + 4 + 1 + 3 + 6 = 14 + y = 14 + 9 = 23.

⇒ Difference = 23 − (12 + x) = 11 − x.

⇒ For 11 − x to be divisible by 11, x must be 0 (since 11 − 0 = 11).

⇒ Value of (2x − 3y) = 2(0) − 3(9) = 0 − 27 = − 27.

∴ The correct answer is − 27.

Additional Information

Divisibility by 8

A number is divisible by 8 if its last three digits form a number that is divisible by 8.

Divisibility by 11

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

Composite Divisibility

If a number is divisible by two coprime numbers a and b, then it is also divisible by their product (a × b). For 88, the coprime factors are 8 and 11.

Given:

Principal = Rs.3000 and Rate % = 5% per annum

Formula used:

Amount = Principal × (1 + R/100)ⁿ

Compound Interest (CI) = [P × (1 + R/100)ⁿ - P]

Where P = principal, R = rate %, n = time

Effective Rate of interest when compounded half yearly at R % for one year

⇒ R_effective = R% + R% + R%²/100

Calculation:

According to the question,

When compounded yearly, rate = 5%, n = 1

CI = 3000 × (1 + 5/100) - 3000

⇒ CI (yearly) = 3000 × 5/100 = 150

When compounded half-yearly,

Rate = 5/2% = 2.5%, n = 2

CI = 3000 × [(1 + 2.5/100)² - 1]

⇒ 3000 × (1.025² - 1) = 3000 × .050625

⇒ CI (half yearly) = 151.875

CI (half yearly) - CI (yearly) = 151.875 - 150

⇒ 1.875 = Rs. $1\frac{7}{8}$ 

∴ The difference between the compound interest compounded half yearly and yearly is Rs. $1\frac{7}{8}$

Alternate MethodRate of interest when compounded yearly = 5%

When compounded half-yearly, 

Rate (half yearly) = 5/2 = 2.5%

As this will be compounded every 6 months for 1 year, 

Hence the effective rate of interest will be = 2.5% + 2.5% + 2.5%²/100

⇒ R_effective= 5.0625%

∴ Difference in CI = 3000 × (R_effective - R)

⇒ 3000 × (5.0625% - 5%) = 3000 × 0.0625/100

⇒ 1.875 = Rs. $1\frac{7}{8}$

∴ The difference between the compound interest compounded half yearly and yearly is Rs. $1\frac{7}{8}$

Given:

Height = 24 m

Slant height = 30 m

Formula used:

The curved surface area of Cone = 1/2 × (perimeter of base) × (slant height)

⇒ π × r × l

Where π = 22/7

r = radius of cone

l = slant height of the cone

The relation between r, h, and l is given by the Pythagoras theorem,

⇒ l² = r² + h²

Here, h = height of the cone

Calculation:

l = 30 m, h = 24 m

We know the Pythagorean triplet = (3, 4, 5)

If we multiply the triplet by 6, we get

⇒ (3 × 6, 4 × 6, 5 × 6) = (18, 24, 30)

According to the question, 

h = 24 m, l = 30 m and r = 18 m

Now, the curved surface area of the cone

⇒ π × r × l

⇒ 22/7 × 18 × 30

⇒ 1697.143 m2

∴ The curved surface area of the given cone is 1697.143 m2.

Alternate Method l = 30 m, h = 24 m

Using Pythagoras theorem, l2 = r2 + h2

⇒ 30² = r² + 24² 

⇒ r² = 30² - 24² = 900 - 576 = 324

⇒ r = √324 = 18 m

Now, the curved surface area of the cone

⇒ π × r × l ⇒ 22/7 × 18 × 30

⇒ 1697.143 m²

∴ The curved surface area of the given cone is 1697.143 m².

Important PointsPythagoras theorem: The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. i.e.,

(AC)² = (AB)² + (BC)²

Where AC = hypotenuse of the triangle

AB and BC are the other two sides of the triangle

The numbers which satisfy this relation, are called Pythagorean triplets.

e.g., (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), (11, 60, 61), (12, 35, 37), (16, 63, 65), (20, 21, 29), (28, 45, 53), (33, 56, 65)

All the multiples (or submultiples) of Pythagorean triplets also satisfy the relation. e.g., (6, 8, 10), (15, 36, 39) etc.

Given:

A complete the work in 60 days

B completes the work in 30 days

C completes the work in 20 days

Concept used:

Work done = Efficiency × time taken

Calculation:

A's efficiency = 1/60

B's efficiency = 1/30

C's efficiency = 1/20

Work done in 4 days (done by A alone) = 4× 1/60 = 1/15

5th day work (done by A + B + C) = 1/60 + 1/30 + 1/20

⇒ (1 + 2 + 3)/60 = 6/60 = 1/10

Work done in 5 days

⇒ 1/15 + 1/10 = (2 + 3)/30 = 5/30 = 1/6

⇒ 1/6 unit = 5 days

⇒ 1 unit = 5 × 6 = 30 days

∴ The work will be completed in 30 days.

Alternate Method 

Work done in 4 days (by A only) = 4 units

Work done on 5th day (by A + B + C together) = 1 + 2 + 3 = 6 units

Total work done in 5 days = 4 + 6 = 10 units

In 5 days 10 unit work is done

1 unit work done in = 5/10 = 1/2 days

Time to complete 60 units work = 1/2 × 60 = 30 days

∴ The work will be completed in 30 days.

Given:

The selling Price of 40 dozen bananas is Rs.1440

Gain % = 20%

Formula used:

Profit (P) = SP - CP

CP = SP/(100 + Gain%) × 100

SP = CP/100 × (100 + Gain%), where

SP = Selling price

CP = Cost price

Calculation:

According to the question,

SP of 40 dozen bananas = Rs.1440 and profit % = 20%

CP = 1440/(100 + 20) × 100

⇒ CP = 1440/120 × 100 

⇒ CP = 1200

CP of 40 dozen bananas = Rs.1200

CP of 20 dozen bananas = 1200/2 = Rs.600

SP of 20 dozen bananas for 30% gain

⇒ SP = 600/100 × 130

⇒ SP = Rs.780

∴ To get  30% gain, he should sell 20 dozen bananas for Rs.780.

Given:

Rate = r% p.a.

Time is 3 years and 19 years

Formula used:

Simple interest = (P × r × t)/100

Amount = Simple interest + Principal, where

P = principal 

r = rate of interest

t = time 

Calculation:

According to the question,

The amount for 3 years at r% = Simple interest for 19 years at r%

P +  (P × r × t)/100 = (P × r × t)/100

⇒ P + (P × r × 3)/100 = (P × r × 19)/100

⇒ P(100 + 3 × r)/100 = (P × r × 19)/100

⇒ 100 + 3 × r = r × 19

⇒ 16 × r = 100

⇒ r = 100/16 = 6.25

∴ The value of r is 6.25%.

Given:

Pipe A can empty the tank in 16 hours

Pipe B can empty the tank in 24 hours

Pipe C can fill the tank in 4 hours

Concept used:

Work = Efficiency × Time

Efficiency ∝ 1/Time

Calculation:

According to the question,

Efficiency of A = -3units/hr

Efficiency of B = -2 units/ hr

Efficiency of C = 12 units/hr

Here negative sign indicates the emptying nature of the pipes.

Total work = 48 units

35% of work = (35/100) × 48 = 16.8 units

Time to fill the tank by A, B, and C together =  16.8/(12 - 3 - 2)

⇒ 16.8/7 = 12/5

⇒ 2$\frac{2}{5}$ hrs

∴ A, B, C together will fill the tank in 2$\frac{2}{5}$ hrs.

Alternate Method A's efficiency = 1/16

B's efficiency = 1/24

C's efficiency = 1/4

Total efficiency = 1/4 - 1/24 - 1/16 (pipes A and B are the emptying the tank Hence their efficiency is taken negatively here)

⇒ (12 - 3 - 2)/48 = 7/48

The time taken to fill the 100% tank = 48/7 hrs

Time taken to fill 35% of the tank = 48× 35/(7 × 100) 

⇒ 12/5 hrs 

⇒ 2$\frac{2}{5}$ hrs

∴ A, B, C together will fill the tank in 2$\frac{2}{5}$ hrs.

Given:

80% of 3/4 of a number is 63

Calculation:

Let the number be X

According to the question,

⇒ X × 80/100 × 3/4 = 63

⇒ X = 63 × 10/8 × 4/3

⇒ 21 × 5 = 105

∴ The required number is 105.

Given:

Total packets = 360

Cost Price per packet = Rs.15

Selling price of 60% of packets = Rs.18 per packet

Selling price of 40% of packets = Rs.20 per packet

Formula used:

Profit = Selling price - Cost price

Profit % = Profit/Cost price × 100, where 

SP = selling price and CP = cost price

Calculation:

According to the question,

CP of 360 packets = 360 × 15 = Rs.5400 

60% of packets = 360 × 60/100 = 216 packets

SP of 216 packets = 216 × 18 = Rs.3888

SP of remaining 144 packets = 144 × 20 = Rs.2880

Total SP (360 packets) = 3888 + 2880 = Rs.6768

Gain = 6768 - 5400 = Rs.1368

Gain % = 1368/5400 × 100 = 25.33%

∴ Gain percent in the transaction is 25.3%.

Alternate Method Ratio of number of packets sold at Rs.18 per packet and Rs.20 per packet = 60% : 40%

⇒ 3 : 2

So, let the total packets be 5

SP of 3 packets = 3 × 18 = Rs.54

SP of 2 packets = 2 × 20 = Rs.40

Total SP = Rs.94

Total CP = 5 × 15 = Rs.75

Profit % = (94 - 75)/75 × 100

⇒ 19/75 × 100 = 76/3

⇒ 25.3%

∴ Gain percent in the transaction is 25.3%.

Given:

When x is subtracted from each of 43, 38, 11 and 10, then the numbers so obtained in this order are in proportion.

Concept used:

If a, b, c, and d are in proportion,

Then a/b = c/d

Mean proportion of two numbers a and b is = √(a × b)

Calculation:

(43 - x)/(38 - x) = (11 - x)(10 - x)

⇒ (43 - x)(10 - x) = (11 - x)(38 - x)

⇒ 430 - 43x - 10x + x² = 418 - 11x - 38x + x²

⇒ 430 - 53x = 418 - 49x

⇒ 4x = 430 - 418 = 12

⇒ x = 12/4 = 3

Now, mean proportional between (11x + 3) and (9x - 2) is

⇒ √(11x + 3)(9x - 2)

⇒ √(33 + 3)(27 - 2) = √(36 × 25)

⇒  30

∴ The mean proportional between (11x + 3) and (9x - 2) is 30.

Given :

Distance = 900 km

Average speed is reduced by 300 km/h 

Time of flight is increased by 30 min. 

Concept used:

Distance = Speed × Time

Average speed = Total distance/Total time

Calculation:

Let the original time of flight be T hrs

So, original average speed = 900/T 

When average speed is reduced by 300 km/h and time of flight is increased by 30 min.

According to the question,

Reduced average speed = 900/T - 300

New time of flight = (T + 1/2) hrs

New average speed = 900/(T + 1/2)

Equating average speed, we get

⇒ (900/T) - 300 = 900/(T + 0.5)

⇒ (3/T) - 1 = 3/(T + 0.5)

⇒ (3 - T)/T = 3/(T + 0.5)

⇒ (3 - T)(T + 0.5) = 3T 

⇒ T² + 0.5T - 1.5 = 0

⇒ 2T² + T - 3 = 0

⇒ (T - 1)(2T + 3) = 0

⇒ T - 1 = 0 ⇒ T = 1 hr

∴ The original time of flight is 1 hr.

Shortcut TrickIn such type of problems, use the formula directly

(S1 × S2)/(S1 - S2) × Time difference (in hours) = Distance (in km)

where S1 and S2 are the initial and final average speeds (in km/hr)

⇒ Let original average speed be S km/hr

⇒ S × (S - 300)/300 × 1/2 = 900

⇒ S × (S - 300) = 900 × 600

⇒ On comparing, we can tell directly that S = 900 km/hr

∴ The original time of flight = 900/900 = 1 hr.

Given:

If average speed = 50 km/h, then time taken is 10 minutes early than the scheduled time

If average speed = 30 km/h, then time taken is 10 minutes late from the scheduled time

Concept used:

Distance = Speed × Time

Average speed = Total distance/Total time

If the distance is constant, then

Speed ∝ 1/Time

Calculation:

Let the distance be X km, and the scheduled time be T min.

According to the concept,

X = 50 × (T - 10)

also, X = 30 × (T + 10)

Equating the above two equations,

50 × (T - 10) = 30 × (T + 10)

⇒ (T + 10)/(T - 10) = 5/3

⇒ T/10 = 4 = 40

⇒ T = 40 min.

X = 50 × [(40 - 10)/60] = 50 × 1/2

⇒ X = 25 km

∴ The distance covered by Akhil is 25 km.

Alternate MethodDistance is constant, therefore speed ∝ 1/time

The ratio of average speed = 5 : 3

Ratio of Time = 3 : 5

Difference between the time = 5 - 3 = 2 unit

According to question difference between the time is = T + 10 - (T - 10) = 20 minutes

Here T is the scheduled time

⇒ 2 units = 20 minutes

⇒ 3 units = 30 minutes or 1/2 hr

Akhil takes 30 minutes or half an hour when he drives at 50 km/hr

Distance covered by Akhil = 50 × 1/2 = 25 km

Shortcut TrickIn this type of problem, use the direct formula.

Distance (in km) = (S1 × S2)/(S1 - S2) × Time difference (in hrs)

Where, S1 and S2 are the two given average speeds.

S1 = 50 km/h, S2 = 30 km/h, Time difference = 20 minutes = 1/3 hr

⇒ Distance = (50 × 30)/20 × 1/3

⇒ 75/3 = 25 km

∴ The distance covered by Akhil is 25 km.

Given:

Average of 7 consecutive positive integers = 259

Concept used:

Average of N integers = Sum of all integers/Total number of integers

Calculation:

According to the question,

Let the 7 consecutive integers be

a, a + 1, a + 2, a + 3, a + 4, a +5, a + 6 and next 5 consecutive odd integers are a + 7, a + 9, a + 11, a + 13, a + 15

Sum  of first seven integers = 7a + 21

Sum = Average × Total integers

⇒ 7a + 21 = 259 × 7

⇒ a = (1813 - 21)/7 = 256

Sum of all the integers = 12a + 76 

Average = (12a + 76)/12

⇒ a + 76/12

⇒ 256 + 6.33

⇒ Average = 262.33

∴ The average of all the numbers is 262.33

Additional InformationAverage of N consecutive integers = (N + 1)/2

Average of N consecutive even integers = N+1

Average of N consecutive odd integers = N

Where N = number of terms

Shortcut Trick

Cancel out the % sign and solve directly:

⇒ 3(3X + 2Y) = 2(2X + 6Y)

⇒ 9X + 6Y = 4X + 12Y

⇒ 5X = 6Y ⇒ X/Y = 6/5

⇒ Required Ratio = (3 × 6) : (2 × 5) = 18 : 10 = 9 : 5

∴ The correct answer is 9 : 5.

Alternate Method

Given:

Sum of 3% of X and 2% of Y = ²/₃ × (Sum of 2% of X and 6% of Y)

Ratio Visualization

3X

18 units

2Y

10 units

Ratio = 18 : 10 = 9 : 5

Calculations:

⇒ ³/₁₀₀ × X + ²/₁₀₀ × Y = ²/₃ × (²/₁₀₀ × X + ⁶/₁₀₀ × Y)

⇒ 3X + 2Y = ²/₃ × (2X + 6Y)

⇒ 3 × (3X + 2Y) = 2 × (2X + 6Y)

⇒ 9X + 6Y = 4X + 12Y

⇒ 9X − 4X = 12Y − 6Y

⇒ 5X = 6Y

⇒ ^X/_Y = ⁶/₅

We need to find the ratio of 3X to 2Y:

⇒ ^3X/_2Y = ³/₂ × ^X/_Y

⇒ ^3X/_2Y = ³/₂ × ⁶/₅

⇒ ^3X/_2Y = ¹⁸/₁₀ = ⁹/₅

∴ The correct answer is 9 : 5.

Additional Information

Ratio & Proportion

Four numbers a, b, c, and d are in proportion if a:b = c:d. The product of means equals the product of extremes (b × c = a × d).

Componendo & Dividendo

If a/b = c/d, then by the rule of componendo and dividendo, (a+b)/(a−b) = (c+d)/(c−d).

Duplicate & Sub-duplicate Ratio

The duplicate ratio of a:b is a²:b², and the sub-duplicate ratio is √a:√b.

The correct answer is 'crumble'.

Key Points 

• Let us look into the meaning of the words in the options - 
• Collapse - (of a structure) suddenly fall down or give way.
• Slump - sit, lean, or fall heavily and limply.
• Sag - sink, subside, or bulge downwards under weight or pressure or through lack of strength.
• Crumble - break or fall apart into small fragments, especially as part of a process of deterioration.
• From the above meanings it is clear that crumble is the best word to substitute for the given group of words.
• Hence, option 4 is the correct answer.

The erroneous part is 'of learning'.

Key Points

• There is an error in preposition usage in the part of learning.
• Of is a preposition that is used for the following - 
• Of (to indicate relating to, belonging to) — I always dreamed of being famous.
• Of (to indicate reference) — This is a picture of my last birthday.
• Of (to specify the number or an amount) — A good number of people understand Hindi.
• None of the above usage points can be applied in the context of the given sentence.
• So, option 2 is the correct answer as it contains the erroneous part of learning.
• The correct preposition in the context of the given sentence is in as it is used to indicate opinion, belief, feeling, etc.

Correct sentence - Shilpi has / a keen interest / in learning / a foreign language.

The correct spelling is 'Procedure'. 

Key Points 

• Precipetation, Labaling , and Precoutions do not exist in the English language.
• So, we can say that there are spelling mistakes in these words.
• Procedure is a correct English word and means an established or official way of doing something.
• Hence, the correct answer is option 3.

Additional Information

• The correct spelling of the other three options given below along with their meanings -
• Precipitation - rain, snow, sleet, or hail that falls to or condenses on the ground.
• Labeling - attach a label to (something).
• Precautions - a measure is taken in advance to prevent something dangerous, unpleasant, or inconvenient from happening.

The correct answer is 'were sleeping'.

Key Points

• There is an error in verb tense in the underlined portion of the sentence.
• Are sleep is an incorrect form of tense.
• We need to use the present participle sleeping to make it correct.
• The sentence implies that the action of sleeping occurred in the past and that it was continuous (as the inmates did not wake up).
• In such a case we need to use the **past continuous tense (**were sleeping) to make the sentence correct.
• Hence, option 4 or were sleeping is the most appropriate option that can substitute the underlined segment in the given sentence.

Correct sentence - The inmates of the house were sleeping when the thief entered.

The correct answer is 'fur'.

Key Points  

• Let us look into the meaning of the words in the options - 
• Bristles - a short, stiff hair on an animal's skin or a man's face.
• Kenosis - the renunciation of the divine nature.
• Fur - the short, fine, soft hair of certain animals.
• Grizzly hair - grey or grey-haired.
• From the above meanings it is clear that fur is the best word to substitute for the given group of words.
• Hence, option 3 is the correct answer.

The erroneous part is 'Kavya didn't wanted'.

Key Points

• 'Didn't' is a contraction of 'did' and 'not'.
• 'Did' is a modal and a modal is always followed by the base form of a verb.
• Hence, 'want' (base form) must replace 'wanted' to make the sentence grammatically correct.
• So, option 1 is the correct answer.

Correct sentence - Kavya didn't want / any help / in painting.

The erroneous spelling is 'Robery'. 

Key Points

• The correct spelling for the word is robbery which means the action of taking property unlawfully from a person or place by force or threat of force.
• The meanings of the other options are as follows - 
• Rotten - suffering from decay.
• Rotate - move or cause to move in a circle around an axis or center.
• Round - shaped like a circle or cylinder.
• Hence, option 1 is the correct answer.