SSC CGL 2021 Tier-I (Held On : 11 April 2022 Shift 2) (Previous Year Paper)

The position of the English alphabet letters is given below:

    

Hence, the correct answer is "MXJY".

1. Pamila is the granddaughter of Akun who is married to Nikita.

2. Murali is the brother-in-law of Akun who has two daughters but no son.

3. Uday and Vanmay are the sons-in-law of Nikita.

4. Vanmay is married to Yamini and they have two daughters and one son.

5. Uday has one son and one daughter.

6. Tina and Smita are the daughters of Yamini.

7. Rahul is the cousin of Kamal and brother of Pamila.

8. Murali is unmarried.

Hence, Yamini is "Aunt" of Rahul.

Table show alphabet serial number –

The pattern followed is,

 

All follow the same pattern, except 'ZCGLS’.

Hence, “ZCGLS” is the odd one.

The image obtained when the paper is unfolded is,

Hence, "option 1" is the correct answer.

The logic here is,

PATELS : BQFUTM

Similarly,

NECTAR : ?

Hence, "FOUDSB" is the correct answer.

The table is alphabets place value:

The pattern followed here is:

MONEY is written as PRQHB

Similarly,

'CREDIT' = ?

Hence, 'CREDIT' is coded as "FUHGLW".

Statements:

No pink is yellow.

No yellow is white.

All reds are yellows.

The least possible diagram for the given statements is as follows

Conclusions:

I. No red is pink → True (Because no pink is yellow and all red is yellow)

II. No red is white → True (Because no white is yellow and all red is yellow)

III. No white is yellow → True (Because no yellow is white)

Hence, “All the conclusions follow".

The logical and meaningful order of the given words is as follows:

LOGIC: The organisms have been arranged according to their size

1. Starfish
2. Penguin
3. Giant Tortoise
4. Shark
5. Blue Whale

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

According to the BODMAS rule:

Option 1 : 24 and 48, × and ÷

Given:

24 ÷ 16 - 96 + 48 × 12 = 195

After interchange the numbers and signs;

48 × 16 - 96 + 24 ÷ 12 = 195

By BODMAS rule

48 × 16 - 96 + 2 = 195

768 - 96 + 2 = 195

770 – 96 = 195

674 = 195 (LHS ≠ RHS)

Option 2 : 24 and 16, - and ÷

Given: 

24 ÷ 16 - 96 + 48 × 12 = 195

After interchange the numbers and signs;

16 - 24 ÷ 96 + 48 × 12 = 195

By BODMAS rule

16 – 0.25 + 48 × 12 = 195

16 – 0.25 + 576 = 195

592 – 0.25 = 195

591.75 = 195 (LHS ≠ RHS)

Option 3: 12 and 16, × and ÷

Given:

24 ÷ 16 - 96 + 48 × 12 = 195

After interchange the numbers and signs;

24 × 12 - 96 + 48 ÷ 16 = 195

By BODMAS rule

24 × 12 - 96 + 3 = 195

288 – 96 + 3 = 195

291 – 96 = 195

195 = 195 (LHS = RHS)

Option 4: 12 and 48, × and +

Given:

24 ÷ 16 - 96 + 48 × 12 = 195

After interchange the numbers and signs;

24 ÷ 16 - 96 × 12 + 48 = 195

By BODMAS rule

1.5 – 96 × 12 + 48 = 195

1.5 – 1152 + 48 = 195

49.5 – 1152 = 195

• 1102.5 = 195 (LHS ≠ RHS)

Hence, the answer is “12 and 16, × and ÷”.

The correct mirror image of the given figure when the mirror is held at the right side is:

Detailed Explanation:

• The line PQ is the mirror
• The given word “% O V e R t H R o W &" ends with ‘&’. So the mirror image will start with “

" → Option 2 is eliminated.

• The mirror image of O is incorrect → Option 3 is eliminated.
• The mirror image of e is incorrect  → Option 4 is eliminated.

 

Hence, option (1) is the correct answer.

According to the BODMAS rule:

Option 1 : 6 and 9

Given:

384 ÷ 16 - 72 + 9 × 10 = 2

After interchanging the digits;

384 ÷ 19 - 72 + 6 × 10 = 2

By BODMAS rule

20.21 - 72 + 6 × 10 = 2

20.21 - 72 + 60 = 2

80.21 – 72 = 2

8.21 = 2 (LHS ≠ RHS)

Option 2 : 4 and 8

Given:

384 ÷ 16 - 72 + 9 × 10 = 2

After interchanging the digits;

348 ÷ 16 - 72 + 9 × 10 = 2

By BODMAS rule

21.75 - 72 + 9 × 10 = 2

21.75 - 72 + 90 = 2

111.75 - 72 = 2

39.75 = 2 (LHS ≠ RHS)

Option 3: 3 and 7

Given:

384 ÷ 16 - 72 + 9 × 10 = 2

After interchanging the digits;

784 ÷ 16 - 32 + 9 × 10 = 2

By BODMAS rule

49 - 32 + 9 × 10 = 2

49 - 32 + 90 = 2

139 - 32 = 2

107 = 2 (LHS ≠ RHS)

Option 4: 7 and 9

Given:

384 ÷ 16 - 72 + 9 × 10 = 2

After interchanging the digits;

384 ÷ 16 - 92 + 7 × 10 = 2

By BODMAS rule

24 - 92 + 7 × 10 = 2

24 – 92 + 70 = 2

94 – 92 = 2

2 = 2 (LHS = RHS)

Hence, the correct answer is “7 and 9”.

Given:

A side of a square-shaped park is 12 m.

• If a square-shaped garden with a side of 24 m is developed around the park, then the garden with the park will look like the picture below:

Formula:

Area of square = Side × Side

Calculation:

=> Total area of the park including the garden = Area of the outer square = 24 × 24

=> Area of square = 576 m2

Hence, the total area of the park including the garden is 576 m².

Given:

Here the pattern followed in each row is:

(1^st number)³ – (2^nd number)² = 3^rd number

Row 1: (1^st number)³ – (2^nd number)² = 3^rd number

7³ - 13² = 343 - 169 = 174

Row 2: (1^st number)³ – (2^nd number)² = 3^rd number

9³ - 25² = 729 - 625 = 104

Similarly

Row 3: (1^st number)³ – (2^nd number)² = 3^rd number

11³ - 30² = 1331 - 900 = 431

Hence, “431” is correct answer.

Given:

Logic: If two dice have 2 faces in common then the third face of dice 1 is opposite to the third face of dice 2.

In the third dice and fourth dice.

Numbers 4 and 2 are common.

Hence, the number "3" will be on the face opposite to the one having the number '1'.

Given: _ L H _ _ U _ H _ _ U _ H _ N U _ _ E N

Let's check each option:

1)  E, U, N, L, N, E, L, E, H, L → E L H U N  - U L H N E - U L H E N - U H L E N

2)  U, E, L, E, N, N, L, H, N, E → U L H E L - U E H N N - U L H H N - U N E E N

3)  U, E, N, L, E, N, L, E, L, H → U L H E N - U L H E N - U L H E N - U L H E N

4)  U, E, N, L, E, L, H, L, E, H → U L H E N - U L H E L - U H H L N - U E H E N

So, In option 3 "U L H E N" is repeating itself.

Hence, ‘U, E, N, L, E, N, L, E, L, H’ is the correct answer.

According to the given information,

 

‘okay’ is coded as "6".

Hence, '6’ is the correct answer.

The pattern followed here is:

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Hence, '2006' is the correct answer.

Given figure:

Important Points

• The image must not be rotated.

Hence, option (3) is the correct answer.

• The shaded part represents Indian police officers who are graduates but NOT females.

 

• The number representing Indian police officers who are graduates but NOT females = 11

Hence, ‘11’ is the correct answer.

The pattern followed here is:

Code = positional value × 2

• 'RAKHI' is coded as 36 - 2 - 22 - 16 - 18

And,

'SHALU' is coded as 38 - 16 - 2 - 24 - 42

Similarly,

MANJU = ?

Hence, 'MANJU' is coded as "26 - 2 - 28 - 20 - 42".

The pattern followed here is,

• (1st number - 2)² = 2nd number

Now,

• 23 : 441

=> (23 - 2)² = 21² = 441 = 2nd number

Similarly,

• 28 : ?

**=> **(28 - 2)² = 26² = 676 = 2nd number

Hence, "676" is the correct answer.

Given:

→ Here we can see that the faces with the digits 7, 6, and 4 are adjacent to each other.

 - 7 and 4 are opposite 2.  - 7 and 6 are opposite 3.  - 7, 6, and 4 are adjacent 4.  - 6 and 4 are opposite

Hence, option 3 is the correct answer.

Given:

• Five persons are sitting in a row facing the north

1. One of the two persons at the extreme ends is an introvert and the other one is an extrovert.

2. A weak person is sitting to the immediate left of the extrovert person.

3. The intelligent person is sitting exactly between the introvert and the thin persons.

4. A thin person is sitting to the immediate right of an intelligent person.

"Thin" person is sitting at the centre.

 

Hence, the correct answer is "Thin".

The figure that will replace the question mark (?) in the following figure series is shown below:

1. Figure 1 to 2 - flag rotates 45 degrees in the anti-clockwise direction.
2. Figure 2 to 3 - flag rotates 90 degrees in the anti-clockwise direction.
3. Figure 3 to 4 - flag rotates 135 degrees in the anti-clockwise direction.
4. Figure 4 to 5 -  flag rotates 180 degrees in the anti-clockwise direction.

Hence, ‘option 1’ is the correct answer.

The pattern followed here is:

 

Hence, '157' is the correct answer.

The correct answer is Rs. 50 lakh, Rs. 10 lakh.

Key Points

• Dispute Resolution Committee to be set up for taxpayers with taxable income up to Rs. 50 lakh and disputed income up to Rs. 10 lakh.
• In the Union Budget 2021-22, the Union Finance Minister-Nirmala Sitharaman reduced the time limit for the reopening of income tax assessment cases from six years to three years.
• The time limit will be 10 years for serious tax fraud cases where concealment of income is Rs 50 lakh or more with the approval of the Principal Chief Commissioner.
• The tax department will notify rules to remove hardships of double taxation faced by non-resident Indians (NRIs).
• She also announced that senior citizens above 75 years of age having an only pension and interest income would not be required to file income tax returns.
• Banks paying the interest would deduct the tax on their behalf.
• 1.10 lakh taxpayers have availed of the Direct Tax Vivad Se Vishwas scheme to resolve tax disputes.

The correct answer is ​National Infrastructure Pipeline.

Key Points

• NIP stands for National Infrastructure Pipeline.
• The National Infrastructure Pipeline (NIP) was announced in December 2019 by Finance Minister Nirmala Seetharaman.
• The NIP was launched with 6835 projects; and as Union Budget 2021-22, the project pipeline has now expanded to 7,400 projects.
• Around 217 projects worth Rs. 1.10 lakh crores under some key infrastructure Ministries have been completed.
• In the Union Budget 2021-22, the government propose to take the following steps

1. by creating the institutional structures;
2. by a big thrust on monetizing assets,
3. by enhancing the share of capital expenditure in central and state budgets.

The correct answer is sewage.

Key Points

• The process of wastewater treatment is commonly called sewage treatment.
• Cleaning of water is a process of removing pollutants before it enters a water body or is reused.
• There are mainly three types of sewage treatment stages primary, secondary or biological, and tertiary sewage treatments.

Additional Information

• Primary treatment (Physical process):
• It is the process of physically removing small and large particles from sewage.
• The floating debris is first removed by filtration through wire mesh screens in a sequential filtration.
• Secondary or biological sewage treatment:
• It is the removal of biodegradable organic matter from sewage or similar types of wastewater.
• This is usually done with the help of microorganisms, hence it is called biological treatment.
• Tertiary treatment (Chemical process):
• Biological treatment precedes chemical treatment in the treatment process.
• Chemical treatment is now considered as a tertiary treatment that can be more broadly defined as “treatment of wastewater by a process involving chemical treatment”.

The correct answer is Krishna.

Key Points

• Musi River is a tributary of the Krishna River in the Deccan Plateau flowing through Telangana.
• Musi River is also known as Musinuru or moosa River or Muchukunda.
• Hyderabad is situated on the banks of the Musi river.
• Osman Sagar and Himayat Sagar are dams built on it that used to act as a source of water for Hyderabad.

Additional Information

• The following table shows the different aspects of rivers of east flowing in a tabular manner:

The correct answer is The Constituent Assembly adopted the National Anthem in January 1950.

Key Points 

• The National Flag of the Indian Union was adopted on 22 July 1947.
• The National Anthem of the Indian Union was adopted on 24 January 1950.
• The Constitution was passed and adopted by the assembly on 26 November 1949.
• On 24 Jan1950, The Indian Constituent Assembly adopted "Vande Mataram " as a national song.
• The Constituent Assembly ratified India's membership of the Commonwealth in May 1949.
• Hence, Statement one is correct.

Additional Information

• The Constituent Assembly was constituted in November 1946 under the scheme formulated by the Cabinet Mission Plan.
• The elections to the Constituent Assembly were held in July-August 1946.
• The Constituent Assembly held its first meeting on December 9, 1946.
• Dr Sachchidanand Sinha, the oldest member, was elected as the temporary President of the Assembly, following the French practice.
• On December 13, 1946, Jawahar Lal Nehru moved the historic Objectives Resolution in the Assembly that laid down the fundamentals and philosophy of the constitutional structure.

The correct answer is 20.

Key Points

• The Atharvaveda is a collection of 20 khandas.
• The Atharva Veda is the "knowledge storehouse of atharvaṇas, the procedures for everyday life".
• The text is the fourth Veda but has been a late addition to the Vedic scriptures of Hinduism.
• It is a collection of 730 hymns with about 6,000 mantras, divided into 20 books.
• About a sixth of the Atharvaveda texts adapts verses from the Rigveda, and except for Books 15 and 16, the text is in poem form deploying a diversity of Vedic matters.
• Two different recensions of the text – the Paippalada and the Śaunakiya – have survived into modern times.

Additional Information

The correct answer is Her husband.

Key Points

• As per the Hindu Succession Act 1956, Her husband has the first right over the property of a Hindu woman who dies intestate.
• The Hindu Succession (Amendment) Act, 2005 (39 of 2005) was enacted to remove gender discriminatory provisions in the Hindu Succession Act, 1956.
• Under the amendment, the daughter of a coparcener shall by birth become a coparcener in her own right in the same manner as the son.
• The daughter shall now have the same rights in the coparcenary property (ancestral property of the Hindu undivided family) as a son.
• This amendment also repeals Section 23 of the Hindu Succession Act which disentitled a female heir to ask for partition in respect of a dwelling house, wholly occupied by a joint family, until the male heirs choose to divide their respective shares.
• Section 24 of the Act which denied the rights of a widow to inherit her husband's property upon her re-marriage has been repealed.
• This Act has brought about a central amendment that is applicable to all state governments.

The correct answer is three.

Key Points

• The 'Pradhan Mantri Annadata Aay Sanrakshan Abhiyan' (PM-AASHA) has three components to rationalise the government agricultural produce price and policy for efficiency, savings by way of reduction of wastages and leakages in storage and making fiscal gains.
• It is a scheme that guarantees a Minimum support price (MSP) to the farmers.
• The scheme is an effort of the government’s commitment to ensure remunerative prices to farmers for their produce as announced in the Union Budget for 2018.

Additional Information

• The scheme comprises three sub-schemes:
• Price Support Scheme (PSS)
• ​Under this, physical procurement of pulses, oilseeds, and Copra is to be done by Central Nodal Agencies in collaboration with state governments.
• Price Deficiency Payment Scheme (PDPS)
• ​This is based on the recommendations of NITI Aayog which suggested “Price Deficiency Payment” for implementation of MSP in crops where procurement is poor.
• Direct payment of the difference between the MSP and the selling price will be made to pre-registered farmers selling their produce in the notified market yard and thus it does not involve any physical procurement.
• The pilot of the Private Procurement & Stockist Scheme (PPPS)
• Under this scheme, participation of the private sector in procurement operations will be piloted.
• States have the option to roll out the scheme on a pilot basis in selected districts/APMCs involving private stockists.

The correct answer is Acorn.

Key Points

• Acorn is the nut of an oak tree.
• Acorns are usually seated in or surrounded by a woody cupule.
• They mature within one to two seasons, and their appearance varies depending on the species of oak.​

Additional Information

• The chestnuts are the deciduous trees and shrubs in the genus Castanea.
• The kola nut is the fruit of the kola tree (Cola acuminata and Cola nitida), indigenous to West Africa.
• Macadamia is a genus of four species of trees in the flowering plant family Proteaceae.

The correct answer is 74.05%.

Key Points

• 74.05% of rural child population to the total child population of the country in India as per Provisional population Totals of Census 2011.
• As per the Provisional Population Totals of Census 2011, the total population of India was 1210.2 million.
• Of this, the rural population stands at 833.1 million and the urban population at 377.1 million.
• According to Census 2001, over 70% lived in rural areas.
• By the 2001 census, 35 urban agglomerations in India with a population of 1 million or more.

Additional Information

• Population data is collected through a Census operation held every 10 years in our country.
• The first population Census in India was conducted in 1872
• 1872 - The first census was conducted in India non-synchronously in different parts.
• The first complete Census was conducted only in 1881.
• Theme of Census 2021- Janganana se Jan Kalyan.
• The theme of Census 2011 - Our Census, Our future.

The correct answer is Arikamedu.

Key Points

• Arikamedu was an ancient Roman trade centre and coastal settlement in Pondicherry.
• Arikamedu, an archaeological site in Kakkayanthope, Puducherry was formerly a major Chola port dedicated to bead making and trading with Roman traders and was believed to be the only town to have ties with Rome.
• The ancient city was first excavated by French archaeologists residing at Pondicherry, Jouveau Dubreuil, and Dr A. Aiyappan, the Superintendent of the Government Museum in Madras, four years before Wheeler came there.

Additional Information

• Lothal is a port city in Gujarat, located on the banks of the Bhogava River, a right tributary of the Sabarmati River.
• Pulakeshin ruled from the Chalukyan capital of Badami which was the main power in the south of the Narmada river.

The correct answer is ​Article 324.

Key Points

• Article 324 deals with provisions with regard to the election commission of India.
• The Election Commission of India is an autonomous constitutional body responsible for administering Union and State election processes in India.
• Part XV of the constitution of India deals with elections and establishes a commission for these matters.
• Article 324 to 329 of the constitution of India deals with powers, function, tenure, eligibility, etc of the commission and the member.

Additional Information

• State Emergency is provided in Article 356 and is popularly known as Presidents Rule.
• ​National Emergency is provided in Article 352 and the President of India can declare a national emergency.
• Article 101 deals with the Vacation of Seats in the parliament.

The correct answer is Allahabad.

Key Points

• After Mahatma Gandhi's release from prison in January 1931, Congress leaders met at Allahabad to plan the future course of action.
• Gandhi Ji began his Dandi March from his Asharam in Sabarmati in order to break the salt law, by manufacturing their own salt in Dandi.
• Salt March also known as Dandi March was initiated by Mahatma Gandhi.
• It was started on 12 March 1930 and rallied for 24 days at Sabarmati near Ahmedabad.
• Gandhiji and more than thousands of people got arrested while making their own salt as a protest against British rule and British taxation of salt production to make it legal and tax-free.
• It ultimately turned into a victory when the British unleashed the protesters from prison and granted the people to make their own salt.

The correct answer is Nuthalapati Venkata Ramana.

Key Points

• Justice Nuthalapati Venkata Ramana was appointed Chief Justice of the Supreme Court of India with effect from 24th April 2021.
• The Chief Justice of India is appointed by the president of India after consultation with the judges of the Supreme Court and high courts.
• Justice Nuthalapati Venkata Ramana has been appointed as the 48th Chief Justice of India (CJI).
• He is also the former Chief Justice of Delhi High Court and acting Chief Justice of Andhra Pradesh High Court.

Important Points

• The current and 50th Chief Justice is Justice Dhananjaya Y. Chandrachud, who entered office on 9 November 2022.

Additional Information

• At present, the Supreme Court consists of 34 judges (one chief justice and thirty-three other judges).
• The judges of the Supreme Court are appointed by the President.
• The President of India is the head of the Indian State.
• He is a part of the Union Executive (Article 52-78) along with the Vice-President, Prime Minister, Council of Ministers, and Attorney-General of India.

The correct answer is As. 

Key Points

• The chemical formula of arsenic is As.
• Arsenic:
• Atomic number: 33
• Atomic mass: 74.93 u
• Arsenic is an element that causes arsenicosis.
• It is found in water that has flowed through arsenic-rich rocks.
• Arsenic and fluoride have been recognized by the World Health Organization (WHO) as the most serious inorganic contaminants in drinking water on a worldwide basis.

Additional Information

• There are 7  metalloids in the modern periodic table.
• The seven commonly recognized metalloids are:-
• Boron (B), Silicon (Si), germanium (Ge), arsenic (As), antimony (Sb), tellurium (Te), and Polonium*.*
• Metalloids Silicon and Germanium are widely used in the semiconductor industry.

The correct answer is the United States of America.

Key Points

• Rajeev Ram is a professional tennis player from the United States of America.
• Ram is a four-time major champion, having won the :
• 2020 Australian Open and
• 2021 US Open in men's doubles with Joe Salisbury,
• Australian Open mixed doubles titles in 2019 and 2021 alongside Barbora Krejčíková.

The correct answer is Notochord is present.

Key Points 

• Characteristics of Chordates Are:
• Presence of Notochord: 
• In the embryonic stage of chordate animals, there is a solid stick-like structure (Just below the central nervous system and above the alimentary canal), this is called the notochord.
• Presence of dorsal tubular nerve cord: 
• In chordates, the nervous system is present at the dorsal surface of the body. The nerve cord is the hollow, tubular structure present just below the body wall and above the notochord.
• Presence of pharyngeal gill clefts: 
• In every chordate, there is a presence of a pair of lateral gill clefts in the wall of the pharynx for respiration.
• These may be present in any stage of its life span like in higher chordates gill clefts are present only in the embryonic stage not in adults.
• Post anal tail:
• It is the post-anal part of the body.
• The tail is reduced or absent in many adult chordates.

Fig: Chordata characteristics

The correct answer is Bengaluru FC.

Key Points

• The former Indian football captain Sunil Chhetri played for Bengaluru FC in 2021.
• Sunil Chhetri has become the highest goalscorer in Indian football, known as the 'Goal Machine'.
• With 47 goals in six editions, the poster boy of Indian football is the top goal-scoring Indian in the Indian Super League.

Additional Information

• Important Indian footballer:
• Baichung Bhutia is a retired Indian footballer of the Sikkim-Bhutia dynasty.
• PK Banerjee was declared India's greatest footballer in the 20th century by FIFA.
• Former Indian striker IM Vijayan is a footballer who made his India debut in the 90s.

The correct answer is Kerala.

Key Points

• Makaravilakku is an annual festival held on Makar Sankranti in the Kerala state.
  

Makaravilakku is an annual festival held on Makara Sankranti at the Sabarimala Ayyappa temple in Kerala.

• Makara Jyothi is a star that appears in the sky on Makara Samkramam, when the Sun moves from dhanu Rasi (Sagittarius) to Makaram Rasi (Capricorn) on the first day of the Malayalam month of Makaram, January 14 (Makara Sankranti) this year.
• Onam is the most important and popular festival in Kerala. Celebrated with much pomp and fervor, Onam is a harvest festival.

Additional Information 

• Important festivals:

The correct answer is Sulphur.

Key Points

• Sulphur in petroleum can cause corrosion to parts of internal combustion engines and refineries.
• So, H₂S0₄ is used in the refining of petroleum to remove sulphur and other compounds.
• Sulphuric acid treatment results in partial or complete removal of unsaturated hydrocarbons, sulphur, oxygen and nitrogen compounds.
• Sulfur:
• Symbol: S
• Atomic number: 16
• Atomic mass: 32 u

The correct answer is Complex pasts: Diverse Futures.

Key Points

• World Heritage Day 
• World Heritage Day is celebrated every year on 18 April.
• Its aim is to preserve the human heritage and to recognize all the efforts of relevant organizations.
• The International Council on Monuments and Sites (ICOMOS) 1982 announced 18 April World Heritage Day.
• The aim of the day is to enhance awareness about the importance of cultural heritage, and monuments and conserving them.
• Complex Pasts: Diverse Futures was the theme of International day for Monuments and Sites i.e World Heritage Day 2021.

Additional Information

• Heritage and Climate is the theme for 2022.
• Shared Cultures, Shared Heritage and Shared Responsibility were the themes for World Heritage Day 2020.
• Rural Landscapes was the theme for World Heritage Day 2019

The correct answer is Soil erosion.

Key Points

• Badlands are a type of dry terrain where softer sedimentary rocks and clay-rich soils have been extensively eroded.
• Badlands are arid regions where the hills are badly eroded under the action of water due to occasional rainstorms or the flow of river streams.
• Gullies and ravines represent them.
• Badland is rugged topography, usually of relatively low relief.
• Badland is associated with the arid and semi-arid regions.

Additional Information

• Types of Erosion are as follows
• Rain Drop Erosion - Due to falling raindrops on the soil surface.
• Sheet Erosion- Uniform removal of soil in thin layers from the surface.
• Rill Erosion - Erosion takes place through numerous narrow streamlets.
• Gully Erosion - Occurs due to runoff of surface water causing the removal of soil and forming gullies due to erosion.
• Stram Bank Erosion- Nothing but away from banks of a stream or a river.

The correct answer is Ethanol.

Key Points

• Ethanol, anhydrous ethyl alcohol has a chemical formula of C2H5OH or CH3CH2OH.
• It can be produced from sugarcane, maize, wheat, etc which are having high starch content.
• Ethanol can be mixed with the gasoline to form different blends.
• As the ethanol molecule contains oxygen, it allows the engine to completely combust the fuel, resulting in fewer emissions and thereby reducing the occurrence of environmental pollution.

Additional Information

The correct answer is Dadabhai Naoroji.

Key Points

• Dadabhai Naoroji wrote the book 'Poverty and Un British Rule in India'.
• Dadabhai Naoroji was popularly known as the 'Grand Old Man of India'.
• He is the first Indian to become a member of the British Parliament.
• He helped found the London Indian Society and East India Association.
• In 1885, Naoroji became a vice-president of the Bombay Presidency Association.
• He was Congress president thrice, in 1886, 1893, and 1906.

Additional Information 

• Major writings of Dada Bhai Naoroji were as follows:
• Poverty in India
• The manners and customs of the Parsees
• Condition of India
• Admission of educated natives into the ICS
• The wants and means of India
• An Era of Darkness is a book written by Shashi Tharoor.
• The Light of Asia: The Poem that Defined The Buddha is a book written by Jairam Ramesh.
• The Ancient Wisdom, Man Whence How and Whithera and Man and His Bodies (Dodo Press) are some books written by Annie Besant.

The correct answer is Violin.

Key Points 

• Dwaram Venkataswamy Naidu used to play the Violin.
• He was probably the first to show that the violin can be used to play Carnatic music as well as other traditional instruments like Veena.
• He is not just another great musician and violinist of the 20th century, but perhaps the one primarily responsible for solo violin performances.
• Naidu used to play the compositions of famous German musicians like Mendelssohn and Johann Sebastian Bach.

Additional Information

• Indian Music Instruments and Players:
• Mridangam: Palakkad Mani Iyer, T.R. Murthy, Guruvayoor Doraiswami, Karaikudi R.Mani, Umayalpuram Shivaraman, Velloor A. Ramabhadran, Mavelikara Krishnan Kutty Nair.
• Sitar: Ravi Shankar, Mushtaq Ali Khan, Vilayat Khan, Uma Shankar Mishra, Nikhil Banerjee, Raiz Khan, Harashankar Bhattacharya, Budhaditya Mukherjee, Abdul Halim Jaffer Khan
• Sarod : Amjad Ali Khan, Ali Akbar Khan, Rajiv Taranath
• Violin : V.G. Jog, Lalgudi Jayaraman, T.N. Krishnan, Yehudi Mennuhin, M. S. Gopalakrishnan, Kunnukkudi Vaidyanathan, Kalyana Krishna Bhagavatar, L. Subramaniam, Chandayya, Kantha Devi, Gajannan Rao Joshi (Hindustani), Zubin Mehta (Western).
• Santoor: Shiv Kumar Sharma, Tarun Bhattacharya, Bhajan Sopperi.
• Flute: N.Ramani, Hariprasad Chaurasia, T.R. Mahalingam, Pannalal Ghosh, T. S. Shankaran, Sikkil Sisters
• Mandolin: U. Srinivas, S. Balamurali Krishna.
• Piano : Surojeet Chatterji, Kaikhosh Shapurji, Sorabjee.
• Shehnai: Bismillah Khan, Bagheshwari Gamar, Bade Gulam Ali.
• Tabla: Alla Rakha, Zakir Hussian, Shankar Ghosh, Abad Mistry, Rimba Shiva, Santha Prasad, Sheikh Dawood, Sharafat Ahmed Khan, Kishan Maharaj, Ahmed, Tirkuva, Pt. Samta Prasad.

Given:

The length of the pole = 23 m

The first window is 3√5 m above the ground and the second window is 4√15 m above the ground.

Formula used:

In a right-angled triangle,

Base = √(Hypotenuse² - Perpendicular²)

Calculation:

Here, the width of the street = BC

In ΔABO,

BO = √(AO² - AB²)

= √(232 - 3√52)

= √(529 - 45)

= √484

= 22 m

In ΔOCD,

CO = √(DO2 - DC2)

= √(232 - 4√152)

= √(529 - 240)

= √289 = 17 m

Then, BC = BO + CO

= 22 + 17

= 39 m

∴ The width (in m) of the street is 39 m

Given:

There are the exports of cars of type A and B (in Rs. millions) from 2014 to 2018 in the given bar graph.

Total number of years = 5

Concept used:

Average = The sum of the terms/Number of terms

Calculation:

The average exports (per year) of cars of type B (in Rs. millions) = (225 + 250 + 200 + 275 + 325)/5 = 1275/5 = 255 (in Rs. millions)

The exports of cars of type A in 2014 (in Rs. millions) = 200

Here, 255 - 55 = 200 (in Rs. millions)

Therefore, The exports of cars of type A in 2014 is Rs. 55 million less than the average exports (per year) of cars of type B over the five years

Given:

Each side of the equilateral triangle = 8 cm

Formula used:

The height of an equilateral triangle = (√3/2) × Side

Calculation:

The height of the equilateral triangle = (√3/2) × 8

= 4√3 cm

∴ The height (in cm) of an equilateral triangle whose each side is 8 cm is 4√3 cm

Given:

Diameter of the circle = 20 cm

OT = 26 cm

Concept used:

Radius = Diameter/2

The radius of a circle is always perpendicular to the tangent on the circle.

In a right-angled triangle, Base = √(Hypotenuse² - Perpendicular²)

Calculation:

OT = 26 cm

Radius (OA) = 20/2 = 10 cm

OA is perpendicular to TA

So, ∠OAT = 90°

In ΔOAT, TA = √(262 - 102)

= √(676 - 100)

= √576

= 24 cm

∴ The length (in cm) of the tangent TA is 24 cm

Given:

The angle of elevation of the top of the tower from the top of the pole = 60º

The angle of depression of the bottom of the tower from the top of the pole = 30º

Calculation:

Let, the height of the pole (AB) = CD = x m

So, the height of ED = (76 - x) m

So, In ΔACD, tan 30° = CD/AD

⇒ 1/√3 = x/AD

⇒ AD = √3x   .....(1)

In ΔAED, tan 60° = ED/AD

⇒ √3 = (76 - x)/√3x

⇒ 76 - x = 3x

⇒ 3x + x = 76

⇒ 4x = 76

⇒ x = 76/4 = 19

∴ The height (in m) of the pole is 19 m

Given:

There are the exports of cars of type A and B (in Rs. millions) from 2014 to 2018 in the given bar graph.

Total number of years = 5

Calculation:

The total exports of cars of type B from 2014 to 2017 (in Rs. millions) = 225 + 250 + 200 + 275 = 950

The total exports of cars of type A from 2015 to 2018 (in Rs. millions) = 150 + 275 + 175 + 300 = 900

The difference (in Rs. millions) = 950 - 900 = 50

The percentage = (50/900) × 100 = 5.55...% ≈ 5.6%

∴ The total exports of cars of type B from 2014 to 2017 is 5.6% more than the total exports of cars of type A from 2015 to 2018

Shortcut Trick

Area of outer path around a square = 4w(s + w), where w = width and s = side of field.

105.75 = 4 × 4.5 × (s + 4.5)

105.75 = 18 × (s + 4.5) ⇒ s + 4.5 = 5.875 ⇒ s = 1.375 m

Perimeter = 4s = 4 × 1.375 = 5.5 m

Cost = 5.5 × 100 = Rs. 550

∴ The correct answer is Rs. 550.

Alternate Method

Given: Width of path (w) = 4.5 m, Area of path = 105.75 m², Rate = Rs. 100/m.

Formula Used: Area of path = (s + 2w)² − s²; Cost = Perimeter × Rate

⇒ Let the side of the square field be s.

⇒ Area of path = (s + 2 × 4.5)² − s²

⇒ 105.75 = (s + 9)² − s²

⇒ 105.75 = s² + 81 + 18s − s²

⇒ 105.75 − 81 = 18s

⇒ 24.75 = 18s

⇒ s = 24.75 ÷ 18 = 1.375 m

⇒ Perimeter of the field = 4 × s = 4 × 1.375 = 5.5 m

⇒ Total Cost of fencing = 5.5 × 100 = Rs. 550

∴ The correct answer is Rs. 550.

Additional Information

Area of Path (Outer)

For a square of side 's' and path width 'w' outside: Area = 4w(s + w).

Area of Path (Inner)

For a square of side 's' and path width 'w' inside: Area = 4w(s − w).

Fencing Cost

Total Cost = Perimeter of the region to be fenced × Rate per unit length.

Shortcut Trick

Initial non-silver part (copper + nickel) = 100% − 40% = 60%.

Final non-silver part = 100% − 50% = 50%.

Since the quantity of non-silver remains constant: Initial Total × 60% = Final Total × 50%.

25 × 60 = Final Total × 50 ⇒ Final Total = 30 kg.

Silver added = Final Total − Initial Total = 30 − 25 = 5 kg.

∴ The correct answer is 5 kg.

Alternate Method

Given: Initial weight = 25 kg, Initial Silver = 40%, New Silver = 50%.

⇒ Initial Silver = 40% of 25 = 10 kg.

⇒ Initial Others (Copper + Nickel) = 25 − 10 = 15 kg.

⇒ Let x kg of silver be added.

⇒ New Silver = 10 + x, New Total = 25 + x.

⇒ According to question: (10 + x) / (25 + x) = 50 / 100

⇒ (10 + x) / (25 + x) = 1 / 2

⇒ 2 × (10 + x) = 25 + x

⇒ 20 + 2x = 25 + x

⇒ x = 5 kg.

∴ The correct answer is 5 kg.

Additional Information

Mixture Constant Property

When one component is added to a mixture, the quantity of the other components remains constant. Formula: Initial Total × Initial % of Constant Part = Final Total × Final % of Constant Part.

Alligation Method

Silver in mixture (40%) and pure silver added (100%) result in a mean of 50%. The ratio of quantities is (100−50) : (50−40) = 50 : 10 = 5 : 1. If 5 units = 25 kg, then 1 unit = 5 kg.

Given:

The given expression = ${{{(a^2-4b^2)}^3} + 64 {{(b^2 - 4c^2)}^3} + {{(16c^2 -a^2})^3}} \over {{(a-2b)^3} +{(2b-4c)^3} +{(4c-a)^3}}$

Formula used:

If a + b + c = 0 then a³ + b³ + c³ = 3abc

Calculation:

${{{(a^2-4b^2)}^3} + 64 {{(b^2 - 4c^2)}^3} + {{(16c^2 -a^2})^3}} \over {{(a-2b)^3} +{(2b-4c)^3} +{(4c-a)^3}}$

= ${{{(a^2-4b^2)}^3} + {{(4b^2 - 16c^2)}^3} + {{(16c^2 -a^2})^3}} \over {{(a-2b)^3} +{(2b-4c)^3} +{(4c-a)^3}}$

Let, a² - 4b² = x; 4b² - 16c² = y; 16c² - a² = z

Here, x + y + z = a2 - 4b2 + 4b2 - 16c2 + 16c2 - a2 = 0

Then, (a2 - 4b2)³ + (4b2 - 16c2)³ + (16c2 - a2)³ = 3 (a2 - 4b2) (4b2 - 16c2) (16c2 - a2)

Let, a - 2b = p; 2b - 4c = q; 4c - a = r

Here, p + q + r = a - 2b + 2b - 4c + 4c - a = 0

Then, (a - 2b)³ + (2b - 4c)³ + (4c - a)³ = 3 (a - 2b) (2b - 4c) (4c - a)

Now, ${{{(a^2-4b^2)}^3} + {{(4b^2 - 16c^2)}^3} + {{(16c^2 -a^2})^3}} \over {{(a-2b)^3} +{(2b-4c)^3} +{(4c-a)^3}}$ = $\frac{3(a^2-4b^2)(4b^2-16c^2)(16c^2-a^2)}{3(a-2b)(2b-4c)(4c-a)}$

= $\frac{(a+2b)(a-2b)(2b+4c)(2b-4c)(4c+a)(4c-a)}{(a-2b)(2b-4c)(4c-a)}$  [Using a² - b² = (a + b) (a - b) formula]

= (a + 2b) (2b + 4c) (4c + a)

= 2 (a + 2b) (b + 2c) (4c + a)

∴ The value of the expression is 2 (a+ 2b) (b + 2c) (4c + a)

Alternate Method ${{{(a^2-4b^2)}^3} + 64 {{(b^2 - 4c^2)}^3} + {{(16c^2 -a^2})^3}} \over {{(a-2b)^3} +{(2b-4c)^3} +{(4c-a)^3}}$ 

We know that a + b + c = 0 then a³ + b³ + c³ = 3abc

First, we satisfy the numerator and denominator with this equation.

⇒ (a² - 4b²) + (4b² - 16c²) + (16c² - a²) = 0

Now, (a - 2b) + (2b - 4c) + (4c - a) = 0

${{{(a^2-4b^2)}^3} + 64 {{(b^2 - 4c^2)}^3} + {{(16c^2 -a^2})^3}} \over {{(a-2b)^3} +{(2b-4c)^3} +{(4c-a)^3}}$

⇒ ${3{(a^2-4b^2)}{(4b^2 - 16c^2)}{(16c^2 -a^2})} \over {3{(a-2b)}{(2b-4c)}{(4c-a)}}$ = ${(a-2b)(a+2b)(2b-4c)(2b+4c)(4c-a)(4c+a)}\over{(a-2b)(2b-4c)(4c-a)}$ 

⇒ (a + 2b){2(b + 2c)}(4c + a)

⇒ 2(a + 2b)(b + 2c)(4c + a)

∴ The value of the expression is 2(a + 2b)(b + 2c)(4c + a).

Given:

There is the monthly expenditure of a family on different heads is shown in the following pie chart.

Income of the family = Rs. 108000/month

Calculation:

The total angle of all expenditures = 75° + 60° + 70° + 65° + 50° + 40° = 360°

The difference between Misc. Expenses and spent on Children's Education = 75° - 70° = 5°

So, the amount differences = (5/360) × 108000 = Rs. 1500

∴ The money (in Rs.) spent on Misc. Expenses are Rs. 1500 more than that spent on Children's Education.

Given:

The selling price at profit = Rs. 832

The selling price at loss = Rs. 448

Required loss = 10%

Formula used:

S.P. = (100 - Loss%)/100 × C.P.

Where, C.P. = Cost price; S.P. = Selling price

Calculation:

Let, the profit = loss = x

So, 448 + x = 832 - x

⇒ x + x = 832 - 448

⇒ 2x = 384

⇒ x = 384/2 = 192

∴ The cost price = (448 + 192) = (832 - 192) = Rs. 640

So the selling price = (100 - 10)/100 × 640 = Rs. 576

∴ The selling price of the article will be Rs. 576

Given:

The given numbers are 108, 124 and 156

After dividing by the greatest number x, the remainder in each case is the same.

Concept used:

The greatest number that will divide a, b, and c and leaving the same remainder in each case is given by the HCF of |a - b|, |b - c|, and |c - a|

Calculation:

Here, |108 - 124| = |- 16| = 16

|124 - 156| = |- 32| = 32

|156 - 108| = 48

Prime factors of 16 = 2 × 2 × 2 × 2

Prime factors of 32 = 2 × 2 × 2 × 2 × 2

Prime factors of 48 = 2 × 2 × 2 × 2 × 3

So, HCF of 16, 32, and 48 = 2 × 2 × 2 × 2 = 16

∴ The greatest number is 16

Shortcut Trick

Total work = 92 units (LCM of 46, 92, and 23)

Efficiency = Work/Time

Total efficiency = 2 + 1 + 4 = 7 units

X complete in 2 days = 2 × 2 = 4 work

X and Y complete in 6 days = 6 × (2 + 1) = 18 work

The remaining work = 92 - (4 + 18) = 92 - 22 = 70 work

Time is taken by X, Y, and Z to complete remaining work = 70/7 = 10 days

Total work done by X = 8 + 10 = 18 days

∴ X work the total of 18 days

Alternate Method

Given:

X, Y, and Z can do a piece of work in 46 days, 92 days, and 23 days respectively.

Calculation:

X can finish in 1 day = 1/46 work

Y can finish in 1 day = 1/92 work

Z can finish in 1 day = 1/23 work

X and Y can finish in 1 day = (1/46) + (1/92) = 3/92 work

X, Y, and Z can finish together in 1 day = (1/46) + (1/92) + (1/23) = 7/92 work

X can do in 2 days = 2/46 = 1/23 work

X and Y can do in 6 days =  6 × (3/92) = 9/46 work  [∵ Z joined them after 8 days from the beginning]

The remaining work = 1 - [(1/23) + (9/46)] = 1 - (11/46) = 35/46 work

Time is taken by X, Y, and Z to finish the work = (35/46) ÷ (7/92) = (35/46) × (92/7) = 10 days

Total time of work of X = 8 + 10 = 18 days

∴ X work the total of 18 days

Given:

8√3sin30º tan60º - 3cos0º + 3sin245º + 2cos230º

Calculation:

8√3sin30º tan60º - 3cos0º + 3sin245º + 2cos230º

⇒ [8√3 × $1\over2$ × √3] - 3 × 1 + 3 × ($1\over{\sqrt2}$)² + 2 × ($\sqrt3\over2$)²

⇒ 12 - 3 + (3 × $1\over2$) + (2 × $3\over4$)

⇒ 12 - 3 + $3\over2$ + $3\over2$

⇒ 9 + $3+3\over2$ = 9 + 3 = 12

The value of the expression is 12

Given:

There is the histogram shows the daily wages ( in Rs.) of workers in a factory.

Calculation:

The number of workers with daily wages less than Rs. 180 = 55 + 80 + 108 = 243

The number of workers with daily wages is more than Rs. 190 = 150 + 105 + 70 = 325

The percentage = (243/325) × 100 = 74.76...% ≈ 74.8%

∴ The number of workers with daily wages less than Rs. 180 is 74.8% of the number of workers with daily wages more than Rs. 190

Given:

cos (A - B) = ${\sqrt3}\over 2$

secA = 2

0º $\leq$ A $\leq$ 90º

Calculation:

sec A = 2

⇒ secA = sec60° (sec60° = 2)

⇒ A = 60°

Also, cos (A - B) = √3/2

⇒ cos (A - B) = cos 30°  [∵ cos 30° = ${\sqrt3}\over 2$]

⇒ A - B = 30°

⇒ 60° - B = 30°  [∵ A = 60°]

⇒ B = 60° - 30° = 30°

∴ The measure of B is 30°

Given:

∠ROS = 42º

Concept used:

The sum of the angles of a triangle = 180°

Exterior angle = Sum of opposite interior angles

Angle made by an arc at the centre = 2 × Angle made by the same arc at any point on the circumference of the circle

Calculation:

Join RQ and RS

According to the concept,

∠RQS = ∠ROS/2

⇒ ∠RQS = 42°/2 = 21°   .....(1)

Here, PQ is a diameter.

So, ∠PRQ = 90°  [∵ Angle in the semicircle = 90°]

In ΔRQT, ∠PRQ is an exterior angle

So, ∠PRQ = ∠RTQ + ∠TQR

⇒ 90° = ∠RTQ + 21°  [∵ ∠TQR = ∠RQS = 21°]

⇒ ∠RTQ = 90° - 21° = 69°

⇒ ∠PTQ = 69°

∴ The measure of  ∠PTQ is 69°

Given:

The given expression = 980 ÷ 35 x 16 + 4 - 2 x 2

Calculation:

980 ÷ 35 x 16 + 4 - 2 x 2

= 28 x 16 + 4 - 2 x 2

= 448 + 4 - 4

= 452 - 4

= 448

∴ The value of the expression is 448

Given:

The Sum becomes Rs. 7800 in 3 years and Rs. 11232 in 5 years

Formula used:

At compound interest, the final amount = $P\left(1+\frac{r}{100} \right)^{n}$

Where, P = The sum of the amount

r = Rate of interest

n = Time (years)

Calculation:

Here, Rs. 7800 becomes Rs. 11232 at compound interest in two years.

Let, the rate of interest = R

So, 11232 = $7800\left(1+\frac{R}{100} \right)^2$

⇒ [(100 + R)/100]² = 11232/7800

⇒ [(100 + R)/100]2 = 144/100

⇒ [(100 + R)/100]2 = (12/10)²

⇒ [(100 + R)/100] = (12/10)

⇒ 100 + R = 1200/10 = 120

⇒ R = 120 - 100 = 20

∴ The rate per cent is 20%

Given:

The car covers 275 km with a speed = 50 km/h

The car covers 315 km with a speed = 70 km/h

Formula used:

Average speed = Total Distance/Total time

Calculation:

Time is taken to covers 275 km = 275/50 = 11/2 hours

Time is taken to covers 315 km = 315/70 = 9/2 hours

The average speed = (275 + 315)/(11/2 + 9/2) km/h

= 590/10 km/h

= 59 km/h

∴ The average speed (in km/h) for the entire journey is 59 km/h

Shortcut Trick

Ratio of Profit = Ratio of (Investment × Time).

A's investment = (29 × 4) + (26 × 8) = 116 + 208 = 324 units.

B's investment = 25 × 12 = 300 units.

C's investment = (25 × 6) + (37 × 6) = 150 + 222 = 372 units.

Ratio A : B : C = 324 : 300 : 372 = 27 : 25 : 31.

Total units = 27 + 25 + 31 = 83 units → Rs. 33,200. 1 unit = 400.

C's share = 31 × 400 = Rs. 12,400.

∴ The correct answer is Rs. 12,400.

Alternate Method

Given: Initial investments of A, B, and C are Rs. 29,000, Rs. 25,000, and Rs. 25,000. Changes occur at 4 and 6 months. Total Profit = Rs. 33,200.

Formulas: Profit Share = Investment × Time Period | Total Profit = ∑ Individual Profits.

⇒ A's Equivalent Capital = (29,000 × 4) + (26,000 × 8) = 1,16,000 + 2,08,000 = Rs. 3,24,000.

⇒ B's Equivalent Capital = 25,000 × 12 = Rs. 3,00,000.

⇒ C's Equivalent Capital = (25,000 × 6) + (37,000 × 6) = 1,50,000 + 2,22,000 = Rs. 3,72,000.

⇒ Ratio of Profit = 324 : 300 : 372 = 27 : 25 : 31.

⇒ C's share = (31 ÷ 83) × 33,200 = 31 × 400 = Rs. 12,400.

∴ The correct answer is Rs. 12,400.

Additional Information

Partnership Basics

In a compound partnership, the profit is distributed according to the product of capital and the time duration of the investment.

Capital Adjustments

When a partner withdraws or adds capital, calculate the effective capital for each time interval separately before summing them up for the total ratio.

Given:

The numbers are from 500 to 650 which are divisible neither by 3 nor by 7

Calculation:

The total numbers up to 500 are divisible by 3 = 500/3 → 166 (Quotient)

The total numbers up to 500 are divisible by 7 = 500/7 → 71 (Quotient)

The total numbers up to 500 are divisible by 21 = 500/21 → 23 (Quotient)

The total numbers up to 650 are divisible by 3 = 650/3 → 216 (Quotient)

The total numbers up to 650 are divisible by 7 = 650/7 → 92 (Quotient)

The total numbers up to 650 are divisible by 21 = 650/21 → 30 (Quotient)

⇒ The total number divisible by 3 between 500 and 650 = 216 - 166 = 50

⇒ The total number divisible by 7 between 500 and 650 = 92 - 71 = 21

⇒ The total number divisible by 21 between 500 and 650 = 30 - 23 = 7

The total numbers from 500 to 650 = 150 + 1 = 151

∴ The required numbers = 151 - (50 + 21 - 7) = 151 - 64 = 87

∴ The are total 87 numbers from 500 to 650 (including both) which are neither divisible by 3 nor by 7

Shortcut Trick

Runs scored in 10 overs = 10 × 7.2 = 72 runs.

Remaining runs needed = 272 − 72 = 200 runs.

Required run rate = 200 ÷ 40 = 5.

∴ The correct answer is 5.

Alternate Method

Given:

Initial Overs = 10 | Initial Run Rate = 7.2 | Target = 272 runs | Remaining Overs = 40

Formula Used:

Total Runs = Run Rate × Overs

Required Run Rate = (Target − Runs Scored) ÷ Remaining Overs

Calculations:

⇒ Runs scored in first 10 overs = 10 × 7.2 = 72 runs

⇒ Remaining runs to be scored = 272 − 72 = 200 runs

⇒ Remaining overs = 40 overs

⇒ Required average run rate = 200 ÷ 40

⇒ Required average run rate = 5

∴ The correct answer is 5.

Additional Information

Run Rate Calculation

Run Rate is the average number of runs scored per over. Formula: Run Rate = Total Runs ÷ Total Overs.

Weighted Average in Cricket

The overall run rate for the entire match is the weighted average of the run rates in different phases: (R₁O₁ + R₂O₂) ÷ (O₁ + O₂).

Shortcut Trick

Length = 8% increase (108/100 = 27/25)

Breadth = 10% decrease (90/100 = 9/10)

Area of a rectangle = Length × Breadth

The decrease = 250 - 243 = 7

The decrease percentage = (7/250) × 100 = 2.8%

∴ The percentage of decrease in area is 2.8%

Alternate Method

Given:

The length of the rectangle increased = 8%

The breadth of the rectangle decreased = 10%

Formula used:

Area of a rectangle = Length × Breadth

Calculation:

Let, the length of the rectangle = x

The breadth of the rectangle = y

So, the initial area of the rectangle = xy

The final area of the rectangle = (108x/100) × (90y/100) = 243xy/250

The decrease in area = xy - (243xy/250) = 7xy/250

The percentage = [(7xy/250)/xy] × 100 %

= (7/250) × 100 %

= 14/5 %

= 2.8%

∴ The percentage of decrease in area is 2.8%

Alternate Method Use successive increment and decrements method

Total change = A + B + A × B/100

Where, A and B are successive increments and decrements 

So, total percentage increment and decrements = 8 - 10 - 8 × 10/100 = - 2.8%

( ∵ " - " sign denotes the decrement)

∴ The percentage of decrease in area is 2.8%

Given:

(4x + 2y)³ + (4x - 2y)³ = 16 (Ax³ + Bxy²)   .....(1)

Formula used:

a³ + b³ = (a + b) (a² + b² - ab)

(a + b)2 + (a - b)2 = 2 (a2 + b2)

a2 - b2 = (a + b) (a - b)

Calculation:

(4x + 2y)3 + (4x - 2y)3 = (4x + 2y + 4x - 2y) [(4x + 2y)2 + (4x - 2y)2 - (4x + 2y) (4x - 2y)]

(4x + 2y)3 + (4x - 2y)3 = 8x [2 (16x² + 4y²)] - (16x² - 4y²)

(4x + 2y)3 + (4x - 2y)3 = 8x (32x² + 8y² - 16x2 + 4y2)

(4x + 2y)3 + (4x - 2y)3 = 8x (16x2 + 12y2)

(4x + 2y)3 + (4x - 2y)3 = 16 (8x3 + 6xy2)   .....(2)

Justifying equations (1) and (2),

A = 8 and B = 6

So, (1/2) √(A² + B²) = (1/2) √(82 + 62)

= 1/2 × √(64 + 36)

= 1/2 × √100

= 1/2 × 10 = 5

∴ The value of (1/2) √(A2 + B2) is 5

Alternate Method

(4x + 2y)3 + (4x - 2y)3 = 16 (Ax3 + Bxy2) –––––––– (1)

(a +b)³ = a³ + b³ + 3ab(a + b) 

(4x + 2y)³ = 64x³ + 8y³ + 24xy(4x + 2y)

⇒ 64x3 + 8y3 + 96x²y + 48xy² –––––––– (2)

And, (4x – 2y)3 = 64x3 – 8y3 – 24xy(4x – 2y)

⇒ 64x3 – 8y3 – 96x2y + 48xy²  –––––––– (3)

Adding the equation 1 and 2, we have

 (4x + 2y)3 + (4x - 2y)³ = 128x³ + 96xy² = 16(8x³ + 6xy²) –– (4)

Justifying equations (1) and (4), we have

A = 8, and B = 6

${1\over 2 }{(√{A^2 +B^2})}$ = $1\over2$ $\sqrt{A^2+B^2}$ = $1\over2$ $\sqrt{8^2+6^2}$ 

⇒ $1\over2$ × 10 = 5

∴ The value of $1\over2$(\sqrt{A^2+B^2}\) is 5

The erroneous part is 'during he was'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'when he was' should be used instead of 'during he was'.
• Use “when + sentence”. So, we need a subject and a verb.
• We can use this at the beginning or in the middle of a sentence.
• Example: She is quiet when she is angry.
• Whereas, we use “during + noun”.
• We can use this at the beginning or end of a sentence.
• Example: She cried during the movie.
• Thus, the correct answer is Option 4.
  

Correct Sentence: We stayed in Jim's flat when he was on holiday.