SSC CGL 2021 Tier-I (Held On : 20 April 2022 Shift 1) (Previous Year Paper)

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

The one letter P is common in all words, so we will start from the second letter from starting.

3. Pancytopenia 2. Pandemonium 5. Panegyric 4. Panelist 1. Pediculate

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

The position of letters according to the English alphabet series:

Option 1) QPJ

Option 2) YXS

Option 3) RQL

Option 4) SRM

Hence, the correct answer is "QPJ".

Five friends: Prakash, Qadir, Ramesh, Saurabh and Tariq are friends.

1) Ramesh is taller than Qadir but shorter than Saurabh.

⇒ Saurabh > Ramesh > Qadir

2) Prakash is the shortest, and Tariq is taller than Saurabh.

⇒ Tariq > Saurabh > Ramesh > Qadir > Prakash

Clearly, Tariq is the tallest among all.

Hence, the correct answer is "Tariq".

The pattern followed here is:

1. & shifted their position in right upper corner in second figure, then shifted right lower bottom corner in third figure at last shift left lower bottom corner in the last figure.

2) 

increase the number of triangle by one in every next figure.

3) 

Rotate 90º clockwise in every next figure.

Hence, the correct answer is "Option 2".

The pattern followed here is:

Hence, the correct answer is "258".

The pattern followed here is:

Logic: In column = First number × Second number - 2 = Third number

In column 1

⇒ 9 × 5 = 45 - 2 = 43

And,

In column 2

⇒ 7 × 4 = 28 - 2 = 26

Similarly,

In column 3

⇒ 9 × 7 = 63 - 2 = 61 

Hence, the correct answer is "61".

Formula:

Area of a circle = πr²

Given = r = 90cm

⇒ A = π(90)² = 8100π

Now, the radius of this circle is increased to 99.

Let A' be the new area as X be the % increase in area.

A' = π(99)2 = 9801π

X = (A' - A/A) × 100

X = (9801π - 8100π/ 8100π) × 100

X = 1701π/ 81π

X = 21

Hence, the correct answer is "21%".

The pattern followed here is:

Logic: Every alphabet is coded with a unique number.

1) ‘FILE’ is coded as 8357

And,

2)  ‘SINK’ is coded as 9364

Similarly,

3) ‘NIKE’ be coded as '?'

Hence, the correct answer is "6347".

The position of letters according to the English alphabet series:

1) CARNATIC ∶  SBDMZDJU

Similarly,

2) FREEDOMS ∶  ?

Hence, the correct answer is "FSGVWTNP".

Given:

Hence, the correct answer is "Option 3".

Given:

1) Vijendra walks a certain distance, say X metres, from his home towards the west.

2) Then he turns left and walks 23 metres.

3) After that, he turns left and walks 36 metres.

4) Then he turns left again to walk 23 metres.

5) He finally turns left and walks 18 metres to reach his home.

Final figure according to the given information.

⇒ BC - ED = 36 - 18 = 18 m 

Hence, the correct answer is "18".

The least possible Venn diagram is given below:

• Some buckets are made up of plastic.
• Some photo frames are also made up of plastic.

Hence, the correct answer is "Option 3".

The logic followed here is:

Clearly, the code of Radha is "Jig".

Hence, the correct answer is "JIG".

Given: X _ U _ B _ O _ Z _ X _ U _ B

1. O Z X U B O Z → X O U Z B - X O U Z B - X O U Z B
2. O Z X U B Z O → X O U Z B - X O U Z B - X Z U O B
3. O X Z U B O Z → X O U X B - Z O U Z B - X O U Z B
4. O Z X B U O Z → X O U Z B - X O B Z U - X O U Z B

Option 1) followed the cycle of XOUZB

Hence, the correct answer is "O Z X U B O Z".

The correct mirror image is shown below:

Hence, the correct answer is "Option 2".

The pattern followed here is:

Hence, the correct answer is "NZW".

The paper look when it is unfolded is shown below:

 

= 

Hence, the correct answer is "Option 4".

The pattern followed here is:

Hence, the correct answer is "110".

The logic followed here is:

Logic: First number + 75 = Second number.

1) 147 ∶  222

⇒ 147 + 75 = 222

Similarly,

2. 158 : ?

⇒ 158 + 75 = 233

Hence, the correct answer is "233".

BODMAS Rule:

Given: 22 * 110 * 392 * 49 * 18 * 12

Option 1) +, ÷, =, –, ×

After putting all mathematical sign in given equation we get:

⇒ 22 + 110 ÷ 392 = 49 - 18 × 12

⇒ 22 + 0.280 = 49 - 288

⇒ 22.28 ≠ - 239

⇒ LHS ≠ RHS

Option 2) +, =, ÷, ×, –

After putting all mathematical sign in given equation we get:

⇒ 22 + 110 = 392 ÷ 49 × 18 - 12 

⇒ 132 = 8 × 18 - 12

⇒ 132 = 144 - 12

⇒ 132 = 132

⇒ LHS = RHS

Option 3) =, –, +, ÷, ×

After putting all mathematical sign in given equation we get:

⇒ 22 = 110 - 392 + 49 ÷ 18 ×  12 

⇒ 22 = 110 - 392 + 2.722 × 12

⇒ 22 = 110 - 392 + 32.664

⇒ 22 = 142.664 - 392 

⇒ 22 = - 249.33

⇒ LHS ≠ RHS

Option 4) =, ×, +, ÷, – 

After putting all mathematical sign in given equation we get:

⇒ 22 = 110 × 392 + 49 ÷ 18 - 12

⇒ 22 = 110 × 392 + 2.722 - 12

⇒ 22 = 43,120 + 2.722 - 12

⇒ 22 = 43,122.722 - 12

⇒ 22 ≠ 43,110.722

⇒ LHS ≠ RHS

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

The position of letters according to the English alphabet series:

Logic: Step 1: Alphabet are arranged in alphabetical order.

Step 2: Addition and subtraction of 3 in alternate manner.

‘NORMAL’ is written as ‘DIPKRO’

And,

‘SOUND’ is written as ‘GKRPX

Similarly,

‘CLUSTER’ is written as '?'

Hence, the correct answer is "FBOOVQX".

Preparing the family tree using the following symbols:

As per the given data, the blood relation diagram is:

1. Vinita and Amita are the sisters of Gaurav.

2. Ashish is the father of Vinita. Ansh is the son of Amita.

Clearly, Ashish is the Maternal grandfather of Ansh.

Hence, the correct answer is "Maternal Grandfather".

BODMAS Rule:

Given: 189 ÷ 27 − 3 + 29 × 2 = 48

Option 1) - and ×

After interchanging the sign we get:

⇒ 189 ÷ 27 × 3 + 29 - 2 = 48

⇒ 7 × 3 + 29 -2 = 48

⇒ 21 + 29 - 2 = 48

⇒ 50 -2 = 48

⇒ 48 = 48

⇒ LHS = RHS 

Option 2) + and × 

After interchanging the sign we get:

⇒ 189 ÷ 27 − 3 × 29 + 2 = 48 

⇒ 7 - 3 × 29 + 2 = 48

⇒ 7 - 87 + 2 = 48

⇒ 9 - 87 = 48

⇒ - 78 ≠ 48

⇒ LHS ≠ RHS

Option 3) ÷ and -

After interchanging the sign we get:

⇒ 189 - 27 ÷ 3 + 29 × 2 = 48

⇒ 189 - 9 + 29 × 2 = 48

⇒ 189 - 9 + 58 = 48

⇒ 247 - 9 = 48

⇒ 238 ≠ 48

⇒ LHS ≠ RHS

Option 4) − and +

After interchanging the sign we get:

⇒ 189 ÷ 27 + 3 - 29 × 2 = 48

⇒ 7 + 3 - 29 × 2 = 48

⇒ 7 + 3 - 58 = 48

⇒ 10 - 58 = 48

⇒ - 48 ≠ 48

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 1".

A cube of side 18 cm is painted yellow on all the faces and then cut into smaller cubes of sides 3 cm each.

Cube is divided into 18/3 = 6 equal parts, hence n = 6.

Number of cubes with 2 sides painted = 12 (n - 2)

= 12 (6 - 2)

= 12 × 4

= 48 

Hence, '48' is the correct answer.

The least possible Venn diagram is shown below:

Conclusions:

I. Some mobiles are laptops → Does not follow → (As, all mobiles are tablets and some tablets are laptops, So some mobile are laptop is possible but not definite true)

II. All telephones are tablets → Does not follow → (As, some telephones are mobiles, all mobiles are tablets and some tablets are laptops. So, all telephone being tablets are possibility but not definite true)

III. Some telephones are tablets → Follow → (As, some telephones are mobiles and all mobiles are tablets. So, some telephone are tablets are definite true)

Hence, the correct answer is "Only conclusion III follows".

The correct answer is 2030.

Key Points

• During the union budget, 2021- 2022 the Finance Minister announces that Indian Railways have prepared a national rail plan for India 2030.
• The plan is to create a ‘future-ready’ railway system by 2030.
• The main aim of the national rail plan is to bring down the logistics cost.
• It is expected that Western Dedicated Freight Corridor (DFC) and Eastern DFC will be commissioned by June 2022.
• It also announces the 100% electrification of broad gauge rail tracks by December 2023.

Additional Information

• The Passenger convenience and safety measures proposed in the union budget 2021- 2022 are:
• Introduction of aesthetically designed Vista Dome LHB coach on tourist routes.
• Introduction of an indigenously developed automatic train protection system that eliminates train collision due to human error.
• The budget also provided a record sum of Rs. 1,10,055 crore for Railways of which Rs. 1,07,100 crore is for capital expenditure.

The correct answer is a tool.

Key Points

• A celt is a tool from the Neolithic period.
• The tools and weapons of the Neolithic Age were better and sharper than the Paleolithic Age.
• A polished stone called a celt was used to make tools.
• Some newly developed **tools like sickles, bows, arrows and improved axes were made in the Neolithic Age.**​

Important Points

• Salient features of the Neolithic period
• ​In India, the period occurs between 7,000 B.C. to 1,000 B.C.
• Development of settled agriculture and the use of tools and weapons made of polished stones.
• The major crops grown during this period were ragi, horse gram, cotton, rice, wheat, and barley.
• One of the remarkable achievements of the Neolithic Period was the invention of the wheel.
• It brought rapid progress in man's life.
• The wheel was used in horse carts and bullock carts that helped man a lot to carry heavy loads.
• Therefore, in this period transport became quite easy and quick.
• The wheel was also used for spinning and weaving.
• It also helped in pottery.
• Man-made beautiful pots to keep food grains and store water.

The correct answer is Jowar.

Key Points

• Jowar is the main food crop in semi-arid areas of central and southern India.
• Maharashtra alone produces more than half of the total jowar production of the country.
• It is both Kharif and Rabi crops in Southern India.
• It is a Kharif crop in northern India.
• Other leading producer states of jowar are **Karnataka, Madhya Pradesh, Andhra Pradesh, and Telangana.**​

Additional Information

• Ragi
• ​'Ragi' also known as Finger Millet, is a popular food grain crop in India.
• It is a Kharif crop.
• It is called dry land crops, mostly cultivated by the people of Andhra Pradesh, Karnataka, and Tamil Nadu & Kerala.
• Grown in both tropical and sub-tropic regions.
• Maize​
• In India, maize is the third most important food crop after rice and wheat.
• Maize in India contributes nearly 9 % to the national food basket.
• Maize also serves as a basic raw material as an ingredient in thousands of industrial products including:
• starch, oil, protein, alcoholic beverages, food sweeteners, pharmaceuticals, cosmetics, film, textiles, gum, etc.
• The predominant maize-growing states are Andhra Pradesh (20.9 %), Karnataka (16.5 %), and Rajasthan (9.9 %), Maharashtra (9.1 %).
• Bajra​
• ​In India, Bajra is an essential food crop in the millet category after Jowar.
• It is cultivated in a warm and dry climate between June and October.
• It is a Kharif crop.
• Bajra requires light soil with proper water drainage.
• However, it can be grown in all types of soils.
• Out of the whole Bajra production in the country, 85% is grown in Rajasthan.
• India is in first place in Bajra production in the world.

The correct answer is the dog.

Key Points

• The scientific name for the domestic dog is Canis lupus familiaris.
• Dog is a domestic mammal of the family Canidae (order Carnivora).
• It is a subspecies of the gray wolf (Canis lupus) and is related to foxes and jackals.

Additional Information

• Cat 
• ​Felis silvestris catus is the scientific name for the domestic, or house cat.
• The closest relative is the species Felis silvestris lybica , the African Wild Cat.
• Buffalo​
• ​The scientific name generally used for water buffalo is Bubalus Bubalis.
• Belongs to the Bovidae family which also includes other cloven-hoofed ruminants such as goats, sheep, and antelopes.
• Found on the Indian subcontinent, China, Southeast Asia, Australia, Europe, North America, and South America.
• ​Cow
• Domesticated cows (Bos taurus) belong to the family Bovidae.
• Cattle are mostly raised for milk, meat, and leather.
• Cows are also used as **draft animals (animals that pull carts or plough agricultural fields).**​

The correct answer is Devdutt Padikkal.

Key Points

• Online food delivery service Eat. fit has landed IPL franchise Royal Challengers Bangalore and Karnataka top-order batsman Devdutt Padikkal as the company’s brand ambassador.
• Eat. fit, one of India’s largest healthy food platforms, is a subsidiary of the fitness and wellness startup Cure. fit.
• The strategic collaboration with the 20-year-old is an association for four years is due to many reasons:
• sensational performances in the past few years, especially in the IPL 2020.
• performance in the last IPL 2020 with the franchise’s top-scoring batsman with 473 runs to his name.
• performance in the Vijay Hazare Trophy, where he scored 737 runs in 7 matches reflected on how **crucial a player he could be for the Indian team in the years to come.**​

Additional Information

The correct answer is 50.

Key Points

• As per an estimate by the ‘Food Waste Index Report 2021’, released by the United Nations Environment Programme (UNEP) in March 2021.
• India wastes approximately 50 kg of food per person per year.
• The household food waste estimate in the US is 59 kg per capita per year, or 19,359,951 tonnes a year.
• In China, these estimates are 64 kg per capita per year or 91,646,213 tonnes a year.
• The United Nations Environment Programme (UNEP) and WRAP released the Food Waste Index Report 2021.
• **According to this report, 931 million tonnes of food were wasted globally in 2019.**​

Additional Information

• UNEP Headquarters: Nairobi, Kenya.
• UNEP Head: Inger Andersen.
• UNEP Founder: Maurice Strong.
• UNEP Founded: 5 June 1972, Nairobi, Kenya.

The correct answer is London Marathon.

Key Points

• Sunday 22 April 2018 marks the 11th consecutive year that Guinness World Records has partnered with the Virgin Money London Marathon, providing on-the-finish-line record verification for a huge variety of costumed runners.
• An unprecedented 90 record titles are being attempted this year, featuring a total of 98 runners – the highest number yet.
• A team of Guinness World Records adjudicators will be on hand at the 26-mile race, to check costumes, verify times and confirm records.
• In 2008, Michelle Frost became the first person to set the record for the Fastest marathon on stilts.

The correct answer is Helping the visually challenged.

Key Points

• Helping the visually challenged will not help in the motor development of a student.
• Motor development means the physical growth and strengthening of bones, muscles, and the ability to move and touch his/her surroundings.
• Motor development falls into two categories:
• fine motor.
• gross motor.
• Fine motor skills refer to small movements in the hands, wrists, fingers, feet, toes, lips, and tongue.
• Gross motor skills involve the motor development of muscles. 
• It develops through activities such as 
• attending yoga sessions,
• doing push-ups,
• walking,
• running,
• playing cricket,
• joining a dance class.

The correct answer is Bhagirathi.

Key Points

• Koteshwar Dam
• It is a gravity dam on the Bhagirathi River, located 22 km from the Tehri Dam in Tehri District, Uttarakhand.
• The dam is part of the Tehri Hydropower Complex and serves to regulate the Tehri Dam's tailrace for irrigation and create the lower reservoir of the Tehri Pumped Storage Power Station.
• Bhagirathi​
• The Bhagirathi river is a Himalayan river that flows in Uttarakhand State.
• It is one of the two headstreams of the pious Ganga river.
• It originates from Gaumukh Glacier and flows about 193 km before merging with Alaknanda to form River Ganga at Devprayag.

Additional Information

• Gomati
• The Gomti river is a Monsoon and Groundwater fed river.
• That originated from Gomat Taal (earlier known as Fulhaar jheel) near Madho Tanda, Pilibhit district of Uttar Pradesh state.
• It is a tributary of the Ganges river.
• Its length extends 960 km through Uttar Pradesh and meets the Ganges river near Saidpur, and Kaithi 27 km from Varanasi district of Uttar Pradesh state.
• ​Koshi
• The Kosi is a 720 km long transboundary river which flows through Nepal, Tibet and India.
• It drains the northern slopes of Tibet and the southern slopes of Nepal.
• It is also known as Saptakoshi due to its seven upper tributaries, namely, the Indrawati, the Sun Koshi, the Tama Koshi, the Likhu, the Dudh Koshi, the Arun and the Tamor.
• Damodar
• The source of the Damodar river is Chota Nagpur Plateau (Palamau hills in Jharkhand) and the mouth is Hooghly River, Rupnarayan River.
• The river bifurcates into two channels at Beguahana.
• The main flow passes through the Mundeswari channel and discharges into Rupnarayan.
• The other one Amta channel carries discharge during high floods and outfalls into the Hooghly.
• The Damodar River in India has four main dams:
  

Tilaiya: Located on the Barakar River

Maithon: Located on the Barakar River

Panchet: Located on the Damodar River

Konar: Located on the Konar River

The correct answer 26th Amendment Act 1971.

Key Points

• Privy purses conferred ‘special status’ to the ruling class, which continued the British practice of ruler and ruled.
• ‘Privy purse’ was an added economic pressure on a newly born independent nation, that was ridden with poverty, hunger and security challenges.
• Therefore, the then Prime Minister, Indira Gandhi, argued the case for the abolition of the privy purse. So, by the 26th Amendment to the Constitution of India in 1971, ‘privy purse’ was abolished. The amendment leads to the omission of Articles 291 and 362.
• The payments of ‘privy purse’ were made to the former rulers under the constitutional provisions of Article 291 and Article 362.

Additional Information

• Article 291 dealt with Privy purse sums of Rulers and was repealed by the Constitution in (Twenty-sixth Amendment) Act, 1971.
• Article 362 dealt with the Rights and privileges of Rulers of Indian States and was repealed by the Constitution (Twenty-sixth Amendment) Act, 1971

The correct answer is Lava.

Key Points

• Lava is the folk dance form of Lakshadeep's Minicoy Island.
• It is a folk dance performed mainly by the Lakshadweep males.
• It is a renowned traditional style of dance performed on festive occasions.
• The word 'Lava' signifies the beautiful movement of music, song, and rhythm.
• Lava dance is the most popular dance on Lakshadweep Minicoy Island.
• First, line up the performers themselves in pairs or singles carrying drums, and launch a dance according to drum beating.

Additional Information

• Leshalaptu 
• ​It is a folk dance of Nagaland.
• This dance is performed by women.
• ​Moyashai
• ​It is also one of the folk dances of Nagaland.
• It is a victory dance performed by the Lotha tribe of Nagaland.
• Aaluyattu
• ​Aaluyattu is a folk dance form from the state of Nagaland.
• The dance is performed by the Konyak tribe.

The correct answer is Euglena.

Key Points

• Euglena belongs to the kingdom Protista.
• Euglena is a single-celled organism with a well-defined nucleus.
• It uses flagella for locomotion, all these characteristics are **similar to the organisms belonging to the kingdom Protista.**​

Additional Information

• The living organism is placed into five different kingdoms:
• Monera
• Prokaryotic organisms are placed.
• They are a primitive type of organism some are fed on the host cell some show symbiotic relations.
• They are called prokaryotes because their nucleus is present in cell cytoplasm without a nuclear membrane.
• Protista
• This kingdom acts as a connecting link between kingdom prokaryotes.
• Mostly aquatic and found in seas, freshwater, and moist soil.
• Fungi
• Kingdom consists of species that are heterotrophic, spore-forming, non-vascular, achlorophyllous, and eukaryotic organisms.
• Their cell wall is made up of chitin or fungal cellulose and glycogen is a reserve food material.
• The study of fungi is called mycology.
• Examples: Aspergillus, Mucor, Rhizopus.
• Plants
• It is the eukaryotic multicellular living organism that shows the photosynthetic process.
• Acts as the producer in the ecosystem
• Their body is divided into roots, shoots, and leaves.
• They are divided into crypto gramme (flower and seed-bearing plants) and phanerogamme (a plant with seeds and sex organs visible).
• Animalia
• Kingdom Animalia constitutes all animals.
• Amongst the five kingdoms, the largest kingdom is the animal kingdom.
• Animals are multicellular eukaryotes.
• However, like plants, they do not possess chlorophyll or a cell wall.

The correct answer is lawyer.

Key Points

• Prashant Bhushan is an Indian public interest lawyer in the Supreme Court of India.
• He was a member of India Against Corruption (IAC) movement known as Team Anna which supported Anna Hazare's campaign for the implementation of the Jan Lokpal Bill.
• He is one of the founders of Swaraj Abhiyan and Sambhaavnaa, an Institute of Public Policy and Politics.
• Prashant Bhushan is the oldest of the four children of Shanti Bhushan(former union Law minister) and Kumud Bhushan.
• Bhushan wrote "The Case that Shook India", a book on the case that set aside Indira Gandhi's election in 1974.
• He constantly works for the goodwill of society and is an activist who took up cases for social welfare.

The correct answer is Fluoridation.

Key Points

• Water fluoridation is the process of adjusting the amount of fluoride in drinking water to a level recommended for preventing tooth decay.
• Fluoride has been proven to protect teeth from decay.
• Bacteria in the mouth produce acid when a person eats sugary foods.
• This acid eats away minerals from the tooth’s surface, making the tooth weaker and increasing the chance of developing cavities.
• Fluoride helps to rebuild and strengthen the tooth’s surface, or enamel.
• Water fluoridation prevents tooth decay by providing frequent and consistent contact with low levels of fluoride.
• Fluoride stops cavities from forming and can even rebuild the tooth’s surface.

Additional Information

• Iodisation
• ​Salt iodization has been the preferred strategy to control and eliminate iodine deficiency disorders (IDD).
• The World Health Organization (WHO) recommends that the salt must have an iodine content of 15 parts per million (ppm) or more.
• Chlorination​
• ​Chlorination is the process of adding chlorine to drinking water to kill parasites, bacteria, and viruses.
• Chlorine levels up to 4 milligrams per liter (mg/L or 4 parts per million (ppm)) are considered safe in drinking water.
• Carbonization ​
• ​Carbonization is the conversion of organic matter like plants and dead animal remains into carbon through destructive distillation.
• The gradual process of coal formation from dead vegetation is known as carbonization.

The correct answer is the Atlantic Ocean.

Key Points

• On September 15, 2016, President Obama designated the first marine national monument in the Atlantic Ocean, the Northeast Canyons and Seamounts Marine National Monument.
• The area has been the subject of scientific exploration and discovery since the 1970s.
• This is the first and only national marine monument in the Atlantic Ocean.
• These undersea canyons and seamounts contain:
• fragile and largely pristine deep marine ecosystems and rich biodiversity.
• 54 species of deep-sea corals.
• endangered whales and sea turtles.
• other marine mammals and **numerous fish species.**​

Additional Information

• A Strait is a naturally formed, narrow, typically navigable waterway that connects two larger bodies of water.

Additional Information

• ​Atlantic Ocean
• ​The second-largest ocean on Earth.
• The Atlantic drives our weather patterns, including hurricanes.
• It is home to many species from sea turtles to dolphins.
• The Atlantic Ocean has been a key avenue of trade and travel.
• Arctic Ocean ​
• ​The Arctic Ocean is the smallest and shallowest of the world's five major oceans.
• It spans an area of approximately 14,060,000 km².
• It is known as the coldest of all the oceans.
• The Arctic Ocean is Earth's northernmost body of water.
• Red Sea​
• Saltiest sea of all the seas that connect to the ocean without even one river that meets the sea.
• A popular hypothesis about the origins of the Red Sea's name is that it contains cyanobacteria called Trichodesmium erythraeum, which turns the normally blue-green water reddish-brown.
• It is the major spot for scuba diving and snorkeling.
• It has more than 1200 fish species that including 44 sharks, which makes it the best place to get into marine life.
• Arabian Sea
• ​The Arabian Sea, the northwestern part of the Indian Ocean, lies between India and the Arabian Peninsula.
• It has an area of about 1,491,000 sq miles and an average depth of 8,970 feet.
• One of the world's busiest shipping lanes, primarily due to its proximity to the Red Sea and the Persian Gulf.

The correct answer is Suman Chakraborty.

Key Points

• Professor Suman Chakraborty has been selected for the 30th GD Birla Award for Scientific Research for:
• Outstanding contribution to engineering science and its applications in developing technologies for affordable healthcare.
• He is a faculty member at the Indian Institute of Technology (IIT), Kharagpur’s department of mechanical engineering.
• He is credited with establishing the first microfluidics laboratory: 
• to facilitate the study of how tiny volumes of fluids flow through small channels.
• Chakraborty has also invented technologies that have not only been patented but **also licensed to industrial houses for commercialization.**​

Additional Information

• ​GD Birla Award
• Started in 1991.
• Recognizes eminent Indian scientists below the age of 50 for their original and outstanding contributions to any branch of science or technology.
• It carries a cash prize of Rs. 5 lakh.
• The recipient is chosen by a selection board, whose present head is professor Chandrima Shaha, the president of the Indian National Science Academy (INSA).
• ​Narayan Pradhan has been selected for the 31st GD Birla Award,2022 for Scientific Research for his outstanding contribution in the field of material sciences.

The correct answer is 20.

Key Points

• Union Budget 2021-22 recommends voluntary scrapping of old vehicles.
• It is based on fitness tests over the period of 20 years for personal vehicles and 15 years for commercial vehicles.
• This will **help in reducing old and polluting vehicles off the road.**​

Important Points

• Highlights of the budget 2021-22
• ​Rs. 2,23,846 crore outlay for Health and Wellbeing in 2021-22 as against Rs. 94,452 crores in 2020-21 an increase of 137%.
• Rs. 35,000 crores for COVID-19 vaccine in 2021-22.
• Rs. 64,180 crore outlay over 6 years for PM AtmaNirbhar Swasth Bharat Yojana.
• Rs. 2,87,000 crore over 5 years for Jal Jeevan Mission (Urban) - to be launched with an aim to provide:
• 2.86 crore household tap connections.
• Universal water supply in all 4,378 Urban Local Bodies.
• Liquid waste management in 500 AMRUT cities.
• Mega Investment Textiles Parks (MITRA) scheme, in addition to PLI.
• 7 Textile Parks to be established over 3 years.
• Under the Rs. 5.35 lakh crore Bharatmala Pariyojana, more than 13,000 km length of roads worth Rs. 3.3 lakh crore was awarded for construction.
• To increase the permissible FDI limit from 49% to 74% and allow foreign ownership and control with safeguards.
• Agricultural credit target enhanced to Rs. 16.5 lakh crore in FY22 - animal husbandry, dairy, and fisheries to be the focus areas.
• Rural Infrastructure Development Fund to be enhanced to Rs. 40,000 crores from Rs. 30,000 crores.
• To double the Micro Irrigation Fund to Rs. 10,000 crores.
• ‘Operation Green Scheme’ to be extended to 22 perishable products, to boost value addition in agriculture and allied products.

Additional Information 

• About Budget 2022-23.
• India’s economic growth is estimated at 9.2% to be the highest among all large economies.
• 60 lakh new jobs are to be created under the productivity-linked incentive scheme in 14 sectors.
• PLI Schemes have the potential to create an additional production of Rs 30 lakh crore.
• Entering Amrit Kaal, the 25-year-long lead-up to India @100, the budget provides the impetus for growth along with four priorities:
• PM Gati Shakti
• Inclusive Development
• Productivity Enhancement & Investment,
• Sunrise opportunities,
• Energy Transition, and Climate Action.Financing of investments
• National Highways Network to be expanded by 25000 Km in 2022-23.
• Rs. 2.37 lakh crore direct payment to 1.63 crore farmers for procurement of wheat and paddy.
• Rs. 48,000 crores allocated for completion of 80 lakh houses in 2022-23 under PM Awas Yojana.
• Introduction of Digital Rupee by the Reserve Bank of India starting 2022-23.
• ​Total expenditure in 2022-23 is estimated at Rs. 39.45 lakh crore.
• Total receipts other than borrowings in 2022-23 are estimated at Rs. 22.84 lakh crore.
• The fiscal deficit in 2022-23 is estimated at 6.4% of GDP.

The correct answer is 1961.

Key Points

• Goa Liberation Day
• India attained independence from British rule back in 1947, but it would still take Goa, which was a Portuguese colony at the time-14 more years to be liberated from foreign control.
• On December 19, 1961, Indian armed personnel managed to wrest control of Goa from the Portuguese, ending around 450 years of colonial rule.
• The Goa Opinion Poll was a referendum held in the state of Goa, India on 16 January 1967, to decide the future of the Union Territory of Goa, Daman, and Diu within the Indian Union.
• The fight for freedom began in the 1940s as India inched closer to independence from British rule.
• The Portuguese colonized several parts of India in 1510 but by the end of the 19th century Portuguese colonies in India were limited to Goa, Daman, Diu, Dadra, Nagar Haveli, and Anjediva Island.
• On 30th May 1987, the territory was split and Goa was formed, Daman and Diu remained a Union Territory.​

Additional Information

• Goa (As of July 2022)
• Capital- Panaji
• Chief Minister- Pramod Sawant
• Governor- P.S. Sreedharan Pillai
• State Bird- Ruby Throated Yellow
• state Animal- Gaur
• State Flower- Jasmine
• State Tree- Terminalia Elliptica
• National Parks in Goa - Mollem National Park

The correct answer is Akbar.

Key Points

• Sikandra is the final resting place of Emperor Akbar.
• The monument is in Sikandra, Agra (previously known as Akbarabad, or the land of king Akbar).
• It is a fine example of Mughal architecture and was built during the peak of the Mughal rule.
• Its construction was started by Akbar in 1605 and completed by Jahangir.
• **Sikandra was named after Sikander Lodi.**​

Additional Information

The correct answer is Committee on the Functions.

Key Points

• GV Mavalankar was the Chairman of the Committee on the Functions of the Constituent Assembly of India.
• The Constituent Assembly met for the first time in New Delhi on 9 December 1946.
• The Constituent Assembly selected 22 committees to deal with diverse tasks of Constitution-making.
• Out of these, **10 were on procedural affairs and 12 on substantive affairs.**​

Important Points

The correct answer is 14 to 18.

Key Points

• Article 14 to Article 18 of the Constitution of India guarantees the right to equality for every citizen of India.
• This deals with the general principles of equality.
• Article 14 of the constitution states that:
• The State shall not deny to any person equality before the law or the equal protection of the laws within the territory of India.
• This article constitutes of 2 parts, being:
• Equality before law and
• Equal protection of the laws
• Article 15 prohibits discrimination against citizens on such specific grounds as religion, race, caste, sex, or place of birth.
• Article 16 guarantees equality of opportunity in matters of employment under the state. The right is available to citizens only.
• Article 17 deals with a peculiar problem in our country. Howsoever praiseworthy the caste system in its origin might have been, it certainly proved to be a disgrace to humanity, a threat to unity, and a serious hindrance to the social, educational, and economic progress of our country.
• Article 18 abolishes titles, other than a military or academic distinction.

The correct answer is Sarvatra.

Key Points

• The Swachh Swasth Sarvatra is an initiative to achieve better health outcomes through improved sanitation and increased awareness and healthy lifestyles.
• It is a joint initiative of the Ministry of Health and Family Welfare and the Ministry of Drinking Water and Sanitation
• It has been launched to strengthen Community Health Centres (CHCs) in 708 Open Defecation Free (ODF) blocks in India to enable them to achieve higher levels of cleanliness and hygiene.
• Under it, Rs. 10 lakh of financial assistance will be given to the CHCs
• to meet the standards of sanitation, hygiene, and infection control.
• The initiative is a part of the Swachh Bharat Mission, under the National Health Mission.
• It is focused on the twin objectives:
• constructing toilets.
• enabling behavioural change of individuals.
• It focused on the **goal of making India Open Defecation free by 2nd October 2019.**​

Additional Information

• Ministry of Health and Family Welfare
• ​Decide health policy in India.
• It is also responsible for all government programs relating to family planning in India.
• Minister: Mansukh Mandaviya.

The correct answer is tassuj.

Key Points

• Abul Fazl-i-Allami described in Ain-i-Akbari that during the period of Mughal Emperor Akbar, the gaz was used as the unit of measuring length.
• Each gaz was divided into 24 equal parts and each part was called Tassuj.
• Gaz was extensively used to measure land pieces, for the construction of buildings, houses, wells, gardens, and roads.
• The gaz was widely used as a unit of length till the metric system was introduced in 1956.
• Even today in many parts of our country, particularly **in the rural areas, gaz is being used as a unit of length.**​

Additional Information

• Angul
• Angul(finger) is a traditional unit of measurement used in India.
• It is used to measure a small length by a finger.
• One Aṅgula during the Maurya period is believed to be approximately equal to 1.763 centimeters.
• Rajahkan​
• The smallest unit of length was parmanu.The elements of measurement system and

definition of some of the units of length and their conversion may be written as

8 parmanu =1 rajahkan (dust particle coming from the wheel of a chariot)

8 rajahkan = 1 liksha (egg of lice)

​In ancient times the smallest unit of length was parmanu.

• The smallest unit of length was parmanu.The elements of measurement system and

definition of some of the units of length and their conversion may be written as

8 parmanu =1 rajahkan (dust particle coming from the wheel of a chariot)

8 rajahkan = 1 liksha (egg of lice)

8 parmanu = 1 rajahkan (dust particle coming out of chariot wheel).

• 8 rajahkan = 1 liksha (egg of Lice).
• Liksha
• ​Likṣha refers to the “egg of a louse”.
• It represents a type of absolute measurement, as defined in the texts dealing with silpa (arts and crafts), known as silpashastra.

The correct answer is six.

Key Points

• The Cabinet Committee on Economic Affairs, chaired by PM Narendra Modi, has approved the increase in the Minimum Support Prices (MSPs) for six mandated rabi crops for marketing season 2021-22.
• The highest increase in MSP has been announced for lentils (Rs. 300 per quintal).
• For gram and rapeseed & mustard, this increase is (Rs. 225 per quintal each) and safflower (Rs. 112 per quintal).
• For barley and wheat, an increase of Rs. 75 per quintal and Rs 50 per quintal respectively has been announced.
• The differential remuneration is aimed at encouraging crop diversification.
• Minimum Support Prices for all Rabi crops for marketing season 2021-22:

Additional Information

• Cabinet Committee on Economic Affairs (CCEA)
• The major function of the Cabinet Committee on Economic Affairs (CCEA):
• to review economic trends on a continuous basis.
• review the problems and prospects, with a view to evolving economic prospects.
• integrated economic policy framework for the country.
• The composition of the Cabinet Committee on Economic Affairs in 2021 is as follows:

The correct answer is fencer.

Key Points

• Tamil Nadu's Bhavani Devi, the 1st Indian fencer to qualify for the Olympics, was felicitated by Indian Fencing Association.
• The 27-year-old qualified for the Tokyo Olympics through the Adjusted Official Ranking (AOR) method.
• In March 2021 ending, Bhavani storms into the semifinals of the Women's sabre individual competition in the 31st Senior National Fencing Championships at Delhi Public School.

Additional Information

Calculation:

TV sets manufactured by company C = 70000

TV sets sold by company C = 82% of 70000 = 57400

TV sets manufactured by company D = 85000

TV sets sold by company D = 56% of 85000 = 47600

Total TV sold by C and D = 57400 + 47600 = 105000

Average TV sold by C and D = 105000/2 = 52500

TV sets manufactured by company E = 58000

Now, % = 52500/58000 × 100% ≈ 90.5%

∴ The average number of TV sets sold by companies C and D is 90.5% of the number of TV sets manufactured by company E.

Given:

(0.4x + $\frac{1}{x}$) = 5

Concept used:

(a)³ + (b)³ = (a + b)³ - 3ab(a + b)

Calculation:

(0.064x3 + $\frac{1}{{{x^3}}}$)

⇒ (0.4x)³ + ($\frac{1}{x}$)³

⇒ (0.4x + $\frac{1}{x}$)³ - 3 × 0.4x × $\frac{1}{x}$(0.4x + $\frac{1}{x}$)

⇒ (5)3 - 1.2(5)

⇒ 125 - 6

⇒ 119

∴ Required answer is 119.

Given:

A shopkeeper allows a 28% discount on the marked price of an article and still makes a profit of 20%.

He gains ₹30.80 on the sale of one article.

Concept used:

Selling price = Marked Price - Marked Price × Discount%

Selling Price = Cost Price + Cost Price × Gain%

Calculation:

Let the marked and cost price of the article be q and p. 

The selling price = q - q × 28% = 0.72q

According to the concept,

0.72q = p + p × 20%

⇒ 0.72q = 1.2p

⇒ 0.6q = p      ....(1)

According to the question,

0.72q = p + 30.80

⇒ 0.72q = 0.6q + 30.80 (From 1)

⇒ 0.12q = 30.80

⇒ q = 30.8/0.12

⇒ q = 770/3

Now, the selling price = 0.72 × 770/3 = ₹184.80

∴ The selling price of the article is ₹184.80.

Shortcut Trick Let the Marked price be Rs. 100

He gives 28% discount,

⇒ SP = 100 × (100 - 28)% = 100 × 72% = 72

He gains 20% on 72

CP = 72 × 100/120 = 72 × 5/6 = 60

According to the question, 

⇒ 72 - 60 = 12 = 30.80

SP = 72 = 12 × 6

⇒ SP = 30.80 × 6 = 184.80

∴ The selling price of the article is ₹184.80.

Given:

cosec4 A(1 - cos4 A) - 2 cot2 A - 1

Concept used:

Sin²A + Cos²A = 1

Cosec²A - Cot²A = 1

CosA/SinA = CotA

1/SinA = CosecA

A² - B² = (A + B) (A - B)

Calculation:

cosec4A(1 - cos4A) - 2cot2A - 1

⇒ cosec4A(1 - cos²A) (1 + cos2A) - 2cot2 A - 1

⇒ cosec4A × sin²A × (1 + cos2A) - cot2A - (cot2 A + 1)

⇒ cosec²A(1 + cos²A) - cot2 A - cosec²A

⇒ cosec2A + cosec²A × cos2A - cot2 A - cosec2A

⇒ cosec2A + cot²A - cot2 A - cosec2A

⇒ 0

∴ The simplified value is 0.

Given:

The difference between compound interest compounded annually and simple interest on a certain sum at a rate of 15% per annum for 2 years is ₹1,944.

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

where

P = Principal amount

R = Rate of interest per year

T = Time in years

In case of the compound interest,

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

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

where

P = Principal amount

R = Rate of interest per year

N = Time in years

Calculation:

Let the principal amount be P.

According to the question,

P(1 + 15/100)² - P = (P × 15 × 2)/100 + 1944

⇒ 1.3225P - P = 0.3P + 1944

⇒ 0.3225P - 0.3P = 1944

⇒ 0.0225P = 1944

⇒ P = 1944/0.0225

⇒ P = 86400

Now, the compound interest incurred on the same sum for the same period at a rate of 10% per annum

⇒ 86400(1 + 10/100)² - 86400

⇒ 104544 - 86400 = ₹18144

∴ The compound interest compounded annually (in ₹) on the same sum for the same period at a rate of 10% per annum is ₹18,144.

Shortcut Trick

Let Total Distance = 100 units and Total Time = 1 unit.

Average Speed = 130 km/h ⇒ Total Distance = 130 km.

Remaining Distance = 25% of 130 = 32.5 km.

Remaining Time = 1 − 2/3 = 1/3 of total time.

Speed X = Remaining Distance ÷ Remaining Time = 32.5 ÷ (1/3) = 97.5 km/h.

Value of X/2 = 97.5 ÷ 2 = 48.75 km/h.

∴ The correct answer is 48.75 km/h.

Alternate Method

Given: Average Speed = 130 km/h, First part = 75% distance in 2/3 time.

Formula Used: Speed = Distance ÷ Time | Average Speed = Total Distance ÷ Total Time

⇒ Let Total Distance = D and Total Time = T.

⇒ D/T = 130 km/h.

⇒ Remaining Distance = D − 0.75D = 0.25D.

⇒ Remaining Time = T − (2/3)T = (1/3)T.

⇒ Speed X = 0.25D ÷ (T/3) = 0.75 × (D/T).

⇒ X = 0.75 × 130 = 97.5 km/h.

⇒ X/2 = 97.5 ÷ 2 = 48.75 km/h.

∴ The correct answer is 48.75 km/h.

Additional Information

Average Speed Formula

Average Speed = Total Distance ÷ Total Time. For two equal distances with speeds a and b, Avg Speed = 2ab ÷ (a + b).

Relative Speed

When two objects move in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Given:

Manjeet bought a second-hand motorbike for ₹22,000 and spent ₹3,000 on its overhauling and maintenance.

He then sold it with a 12% profit.

Concept used:

Selling Price = Cost Price + Cost Price × Gain%

Profit% = ${(Selling\ Price\ -\ Cost\ Price) \over Cost Price} \times 100\%$

Calculation:

The total cost price occurred to Manjeet for the bike

⇒ 22000 + 3000 = ₹25000

The selling price = 25000 + 25000 × 12% = ₹ 28000

Had he sold the bike for ₹500 less, the selling price would have been

⇒ 28000 - 500 = ₹27500

Now, his profit percentage = ${{27500 - 25000} \over 25000} \times 100\%$

⇒ 10%

∴ HIs profit percentage would have been 10%.

Given:

2, 3, 10, 18 and 20

Concept used:

LCM is the smallest common multiple of two or more numbers.

Calculation:

The least or smallest number which is exactly divisible by 2, 3, 10, 18, and 20 is the LCM of 2, 3, 10, 18, and 20. 

LCM (2, 3, 10, 18, 20) = 180

180 = 2² × 3² × 5

So, to become a perfect square 180 needs to be multiplied by 5. 

Now, the least square number which is exactly divisible by 2, 3, 10, 18 and 20

⇒ 180 × 5 = 900

∴ The least-square number which is exactly divisible by 2, 3, 10, 18, and 20 is 900.

Given:

80% and 90% pure acid solutions are mixed to obtain 20 litres of 87% pure acid solution.

Calculation:

Let x litres and y litres be respectively the amount of 80% and 90% pure acid solutions. 

As per the given condition,

0.80x + 0.90y = 20 × 0.87

⇒ 0.80x + 0.90y = 20 × 0.87      ----(i) 

And  x + y = 20      ----(ii)

From (ii), substituting y = 20 – x in (i) we get 

0.80x + 0.90(20 – x) = 20 × 0.87

⇒ 0.80x + 0.90 × 20 – 0.90x = 20 × 0.87 

⇒ 0.10x = 0.90 × 20 – 20 × 0.87

⇒ 0.10x = 18 - 17.4

⇒ 0.10x = 0.6

⇒ x = 6

So, The quantity of 80% pure acid solution is 6 liters

∴ The quantity (in litres) of 80% pure acid solution taken to form the mixture is 6 liters.

Shortcut TrickWith the help of alligetaion method

So, ratio of quantity of 80% and 90% pure acid in the solution = 3 : 7

So, 80% pure acid = 20 × (3/10)

⇒ 6 liters.

Calculation:

Percentage change in the number of cars between 6AM and 7AM = (105 - 70)/70 × 100% = 50%

Percentage change in the number of cars between 7AM and 8AM = (130 - 105)/105 × 100% = 23.8%

Percentage change in the number of cars between 8AM and 9AM = (115 - 130)/130 × 100% = -11.54%

Percentage change in the number of cars between 10AM and 11AM = (95 - 115)/115 × 100% = -17.39%

Percentage change in the number of cars between 11AM and 12PM = (45 - 95)/95 × 100% = -52.63%

(Negative sign indicates percentage decrease)

∴ The minimum change percentage in the number of cars in comparison to the previous hour is 11.54%.

Given:

In a circle with centre O, PA and PB are tangents to the circle at point A and point B, respectively. C is a point on the major arc AB.

∠ACB = 50°

Concept used:

The angle subtended by an arc of a circle at its centre is twice the angle subtended by it at any point of the alternate segment of the circle.

The Sum of all internal angles of a quadrilateral is 360°.

Calculation:

According to the concept,

∠AOB = 2 × ∠ACB

⇒ ∠AOB = 2 × 50°

⇒ ∠AOB = 100°

Consider the quadrilateral AOBP, 

∠A + ∠O + ∠B + ∠P = 360°

⇒ 90° + 100° + 90° + ∠P = 360°

⇒ ∠P = 360° - 90° - 90° - 100°

⇒ ∠P = 80°

⇒ ∠APB = 80°

∴ The measure of ∠APB is 80°.

Given:

6tanA (tanA + 1) = 5 - tanA

0 < A < $\frac{\pi}{2}$ 

Concept used:

The Sridharacharya equation is given by ax² + bx + c = 0

where a, b, c are real numbers and a ≠ 0.

The solution of equation by the Sridharacharya formula is given as,

⇒ x = $-b \pm √ {b^2 - 4ac} \over 2a$

Calculation:

6tanA (tanA + 1) = 5 - tanA

⇒ 6tan²A + 7tanA - 5 = 0

According to the concept,

After applying the Sridharacharya equation we get,

tanA = 1/2 and tanA = -5/3

So, tanA = 1/2 (∵ 0 < A < $\frac{\pi}{2}$ )

∵ tanA = opposite/adjacent = 1/2

From Pythagoras Theorem 

∴ Hypotenuse = √(2² + 1²)

= √5

∴ cosA = adjacent/hypotenuse =  2/√5

and, sinA = opposite/hypotenuse = 1/√5

Now, (sinA + cosA)

⇒ 1/√5 + 2/√5 = $\frac{3}{{√ 5 }}$

∴ The value of (sinA + cosA) is $\frac{3}{{√ 5 }}$.

Calculation:

Number of employees of 28+ to 38 years = 25% × 2500 = 625

The number of corporate office employees in the age group of 38+ years

⇒ (30 + 15 + 10)% × 2500

⇒ 55% × 2500 = 1375

Now, % more = ${{1375 - 625} \over 625} \times 100\%$

⇒ 120%

∴ The number of corporate office employees in the age group of 38+ years and above is 120% more than that of 28+ to 38 years.

Given:

The number 3426k if the number is divisible by 6

Concept used:

Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if the last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.

Calculation:

6 = 3 × 2

According to the concept,

Only 4 and 6 from the options can be the value of k

Now,

3 + 4 + 2 + 6 + 4 = 19 i,e not divisible by 3

3 + 4 + 2 + 6 + 6 = 21 i,e divisible by 3

So, k = 6

∴ The value of k is 6.

Calculation:

The total exports of cars of type A from 2014 to 2016 = 200 + 150 + 275 = 625M

The total exports of cars of type B from 2015 to 2017 = 250 + 200 + 275 = 725M

Now, % less = ${{725M - 625M} \over 725M} \times 100\%$

⇒ 13.79% ≈ 13.8%

∴ The total exports of cars of type A from 2014 to 2016 is approximately 13.8% less than the total exports of cars of type B from 2015 to 2017.

Given:

ABC is a right-angled triangle BD is perpendicular to AC.

AD = 6 cm and DC = 5 cm

Concept used:

ΔABC is a right-angled triangle at B.

BD is perpendicular to AC.

So, ΔABD ~ ΔACB ~ Δ BCD

Now, BD2 = AD × DC and AB2 = AD × AC

Calculation:

According to the concept,

BD2 = AD × DC

⇒ BD2 = 6 × 5

⇒ BD2 = 30

According to the concept,

AB² = AD × AC

⇒ AB2 = 6 × (AD + CD)

⇒ AB2 = 6 × (6 + 5)

⇒ AB2 = 6 × 11

⇒ AB2 = 66

Now, AB2 + BD2 = 30 + 66 = 96

∴ The value of AB2 + BD2 is 96 cm.

Given:

x2 + $\frac{1}{x^2}$ = 18

Concept used:

If (a + $\rm \frac{1}{a}$) = k

Then,

a3 + $\rm \frac{1}{a^3}$ = k3 - 3k

Calculation:

x2 + $\frac{1}{x^2}$ = 18

By adding 2 in both sides

x2 + $\frac{1}{x^2}$ + 2 = 18 + 2

⇒ (x + $\frac{1}{x}$)² = 20

⇒ (x + $\frac{1}{x}$) = 2√5

Now,

x3 + $\frac{1}{x^3}$ = (2√5)³ - 3(2√5)

⇒ 40√5 - 6√5

⇒ 34√5

∴ The required answer is 34√5.

Given:

The inner circumference of a circular path enclosed between two concentric circles is 264 m. 

The uniform width of the circular path is 3 m.

Concept used:

Circumference of a circle = 2πr

Area of a circle = πr²

Where r = radius of the circle

Calculation:

Let the inner radius be R.

According to the question,

2πR = 264

⇒ R = 264/2π

⇒ R = 42

So, the outer radius of circular path = 42 + 3 = 45 m

Now, the area of the circular path

⇒ π (45² - 42²)

⇒ π × 261 = 820.28 ≈ 820 m²

∴ The area of the circular path is 820 m².

Given:

A and B are 30% and 50%, respectively, more than the number C

Calculation:

Let the the number C is 10c

Now,

A = 10c × 130%

⇒ 13c

B = 10c × 150%

⇒ 15c

So,

A : B = 13c : 15c

⇒ 13 : 15

∴ The ratio of A to that of B is 13 : 15.

Given:

A college hostel mess has provisions for 25 days for 350 boys.

At the end of 10 days, when some boys were shifted to another hostel, it was found that now the provisions will last for 21 more days.

Concept used:

Available provisions = Number of days × Number of boys

Calculation:

Available provisions = 25 × 350 = 8750 units

After 10 days the remaining provision = 8750 - 10 × 350

⇒ 5250 units

Let N number of boys shifted to another hostel.

According to the question,

(350 - N) × 21 = 5250

⇒ 350 - N = 5250/21

⇒ 350 - N = 250

⇒ N = 350 - 250

⇒ N = 100

∴ 100 boys were shifted to another hostel.

Shortcut Trick

For any triangle with sides a, b, and c (where c is the longest side), the type of triangle is determined by comparing a² + b² and c².

Here, the sides are proportional to 7, 24, and 30. Let a = 7, b = 24, and c = 30.

Calculate: 7² + 24² = 49 + 576 = 625.

Calculate: 30² = 900.

Since 900 > 625 (i.e., c² > a² + b²), the triangle is obtuse angled.

∴ The correct answer is obtuse angled.

Alternate Method

Given: The ratios of the lengths of the sides of a triangle are 7 : 24 : 30.

Formula Used:

1. Triangle Inequality: Sum of any two sides must be greater than the third side (a + c).
2. Cosine Property:

• If a² + b² > c² → Acute-angled triangle.

• If a² + b² = c² → Right-angled triangle.

• If a² + b² < c² → Obtuse-angled triangle.

Calculations:

⇒ Let the sides be a = 7k, b = 24k, and c = 30k.

⇒ First, check triangle validity: 7k + 24k = 31k. Since 31k > 30k, the triangle is possible.

⇒ Now, compare the squares of the sides: a² = (7k)² = 49k².

⇒ b² = (24k)² = 576k².

⇒ c² = (30k)² = 900k².

⇒ Sum of squares of smaller sides = 49k² + 576k² = 625k².

⇒ Comparing a² + b² and c²: 625k² < 900k².

⇒ Since a² + b² < c², the angle opposite to side c is obtuse (greater than 90°).

∴ The correct answer is obtuse angled.

Additional Information

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side (a + c).

Pythagorean Triplets

If a² + b² = c², the triangle is right-angled. Common examples include (3, 4, 5), (5, 12, 13), and (7, 24, 25).

Cosine Rule and Angles

For triangle ABC, cos C = (a² + b² − c²) ÷ (2ab). If the numerator is negative (a² + b² < c²), angle C is obtuse.

Given:

The tops of two poles of heights 18 m and 30.5 m are connected by a wire. 

The wire makes an angle of 30° with the horizontal.

Concept used:

ΔABC is a right-angled triangle at B, SinA = CB/CA

Calculation:

Let AB and CD be the towers of heights 30.5 and 18 m respectively and AC be the wire.

Here, CD = EB = 18 m and CE = DB

So, AE = 30.5 - 18 = 12.5 m

ΔAEC is a right-angled triangle at E. 

sin 30° = AE/AC

⇒ 1/2 = 12.5/AC

⇒ AC = 25

∴ The length of the wire is 25 m.

Given:

The average of eleven consecutive positive integers is d. 

Concept used:

Total = Average × Number of entities

Calculation:

Let the first integer of the series be N.

According to the question,

N + (N + 1) + (N + 2) + .... + (N + 10) = 11 × d

⇒ 11N + (1 + 2 + 3 + .... + 10) = 11d

⇒ 11N + 55 = 11d

⇒ N + 5 = d

⇒ N = d - 5      ....(1)

Let the new average be D.

According to the question,

N + (N + 1) + (N + 2) + .... + (N + 8) = 9 × D

⇒ 9N + (1 + 2 + 3 + .... + 8) = 9D

⇒ 9N + 36 = 9D

⇒ N + 4 = D

⇒ d - 5 + 4 = D (From 1)

⇒ D = d - 1

∴ The average will decrease by 1.

Given:

Points A and B are on a circle with centre O. PA and PB are tangents to the circle from an external point P. 

PA and PB are inclined to each other at 42°.

Concept used:

Sum of all internal angles of a triangle is 180°.

Sum of all internal angles of a quadrilateral is 360°.

Calculation:

Consider the quadrilateral AOBP, 

∠A + ∠O + ∠B + ∠P = 360°

⇒ 90° + ∠O + 90° + 42° = 360°

⇒ ∠O = 360° - 90° - 90° - 42°

⇒ ∠O = 138°

ΔOAB is an isosceles triangle since OA and OB are the radii of the circle.

So, ∠OAB = ∠OBA = R° (let)

2R° + 138° = 180° 

⇒ 2R° = 42° 

⇒ R = 21° 

⇒ ∠OAB = 21°

∴ The measure of ∠OAB is 21°.

Given:

[25 + 8 ÷ 2 - {16 + (14 of 7 ÷ 14) - (18 ÷ 12 of $\frac{1}{2}$)}] 

Concept used:

Calculation:

[25 + 8 ÷ 2 - {16 + (14 of 7 ÷ 14) - (18 ÷ 12 of $\frac{1}{2}$)}] 

⇒ [25 + 8 ÷ 2 - {16 + (98 ÷ 14) - (18 ÷ 6)}] 

⇒ [25 + 4 - {16 + 7 - 3}]

⇒ 25 + 4 - 20

⇒ 9

∴ The simplified value is 9.

The correct answer is "gadget"

Key Points

• Let's look at the meaning of the given words.
• gadget: a small mechanical or electronic device or tool, especially an ingenious or novel one.
• apparatus: the technical equipment or machinery needed for a particular activity or purpose.
• tool: a device or implement, especially one held in the hand, used to carry out a particular function.
• implement: a tool, utensil, or another piece of equipment that is used for a particular purpose.
• In the given sentence, the speaker is referring to the dishwasher which is an electronic device**.**
• Hence, the correct answer is option 1.
  

The complete sentence is: The latest gadget I have bought is a dishwasher.

The erroneous spelling is "Beggining"

Key Points

• Let's look at the correct spelling and meaning of the word.
• Beginning: the point in time or space at which something begins.
• Example: The movie theatre displayed a statutory warning at the beginning of the film regarding piracy.

Hence, the correct answer is option 2.

Hinglish

• Let's look at the correct spelling and meaning of the word.
• Beginning: समय या स्थान का वह बिंदु जिस पर कुछ शुरू होता है।

The erroneous segment is "even they were heavy"

Key Points

• In the given sentence, we need to use the conjunction "even though".
• Even though is a subordinate conjunction.
• It makes the fact in the main clause of the sentence look more surprising.
• In the given sentence, the usage of even though reveals that Alex is strong as he easily picks up the heavy boxes.

The correct sentence is: Alex picked up the boxes quite easily even though they were heavy.

Hence, the correct answer is option 2.

The erroneous segment is "My friends are gone"

Key Points

• In the given sentence, the verb form "gone" is incorrect in the erroneous segment.
• The given sentence is in the present tense.
• So we can't use the past participle of the verb 'go' which is "gone".
• We need to use the gerund form of the verb "go" which is "going" in the sentence.

The correct sentence is: My friends are going on a trip to Goa today.

Hence, the correct answer is option 3.

The correct answer is "As I heard "

Key Points

• In the given sentence, we need to use "As I heard" at the beginning to make it the simple past tense.
• The Past perfect tense is used when out of two actions it is necessary to emphasize that the preceding action was completely finished before the succeeding action started.
• There are two events in the given sentence. Both are in past tense but one is more recent than the other.
• The speaker had heard the lecture. This is the first event and hence, it takes the simple past tense.
• It is followed by remembering the book he had read two years ago. This is the second event and hence, it takes the past perfect tense.
• The past perfect tense is crucial for putting the events in the sequence in the past.

The correct sentence is: As I heard the lecture it reminded me of a book I had read two years ago.

Hence, the correct answer is option 4.

The correct answer is "sturdy"

Key Points

• Let's look at the meaning of the given word.
• Robust: strong and healthy; vigorous.
• Let's look at the meaning of the given options.
• round: shaped like a circle or cylinder.
• sturdy : (of a person or their body) strongly and solidly built.
• small: of a size that is less than normal or usual.
• weak:  lacking the power to perform physically demanding tasks; having little physical strength or energy.
• As per the meaning of the words, "sturdy" is the synonym for robust.
• Example: The jeep has a sturdy feel to it.

Hence, the correct answer is option 2.

Hinglish

• Let's look at the meaning of the given word.
• Robust: मजबूत और स्वस्थ; ज़ोरदार।
• Let's look at the meaning of the given options.
• round: एक वृत्त या बेलन के आकार का।
• sturdy: (किसी व्यक्ति या उनके शरीर का) दृढ़ता से और ठोस रूप से निर्मित।
• small: एक आकार का जो सामान्य या सामान्य से कम है।
• weak: शारीरिक रूप से मांग वाले कार्यों को करने की शक्ति की कमी; कम शारीरिक शक्ति या ऊर्जा होना।
• As per the meaning of the words, "sturdy" is the synonym for robust.

The correct answer is "Intentionally "

Key Points

• The meaning of the given idiom is "Deliberately or intentionally."
• We use the idiom "On purpose" to refer to an action by someone which is deemed intentional.
• Example: She felt her boss was rude to her on purpose.

Hence, the correct answer is option 2.

Hinglish

• The meaning of the given idiom is ."जानबूझकर"

The correct answer is "He should be asked to leave the room."

Key Points

• There are a few things to keep in mind before changing a sentence from active to passive voice.
• In the given sentence, the object pronoun "him" changes to "he" in the passive voice.
• In the passive voice, the object(who is receiving the action) is highlighted in the sentence.
• In the given sentence, "he" is the object which comes to the front in the passive voice.
• The main verb in the active voice which is the base form(V₁) takes the past participle form(V₃) in the passive voice.
• In the given sentence, "ask"(base form) changes to "asked"(past participle) in the passive voice.

The correct sentence is: He should be asked to leave the room.

Hence, the correct answer is option 4.