SSC CGL 2021 Tier-I (Held On : 19 April 2022 Shift 3) (Previous Year Paper)

The pattern followed here is:

Logic: First number + 1111 =  Second number.

3824 : 4935

⇒3824 + 1111 = 4935

Similarly,

5716 : ?

⇒ 5716 + 1111 = 6827

Hence, the correct answer is "6827".

The position of letters according to the English alphabet series:

'COLOUR' is written as 'FQOQXT'

And,

'VIOLET' is written as 'YKRNHV'

Similarly,

'PURPLE' be written '?'

Hence, the correct answer is "SWUROG".

BODMAS Rule:

Let us first decode the given sign:

Given:- 9 @ 114 $ 19 % 5 # 21

After interchanging the symbol with mathematical sign we get:

⇒ 9 + 114 ÷ 19 × 5 - 21

⇒ 9 + 6 × 5 - 21

⇒ 9 + 30 - 21

⇒ 39 - 21 

⇒ 18

Hence, the correct answer is "18".

The correct mirror image is shown below:

Hence, the correct answer is "Option 3".

Mistake Points The question asked, Which of the option figures will be the same as the given question figure after Rotation.

So, Rotate the options figure not the question figure.

The pattern followed here is:

First rotate 135° clockwise, then rotate 45° anticlockwise means rotate (135° - 45°) clockwise  = rotate 90° clockwise 

Note: It is asked in the question which option figure rotated to find the given figure.

Hence, the correct answer is "Option 3".

The position of letters according to the English alphabet series:

The pattern followed here is:

Hence, the correct answer is "TVF".

The pattern followed here is:

1. The given leaf  is rotate 45º clockwise in next figure.

Hence, the correct answer is "Option 4".

The logic followed here is 

In a Row:

(First Number + 1) × {(second number + 1) ÷ 2} = Third number

First Row:

(14 + 1) × {(21 + 1) ÷ 2} 

= 15 × (22 ÷ 2) 

= 15 × 11

= 165 =Third number

Third Row:

(10 + 1) × {(17 + 1) ÷ 2} 

= 11 × (18 ÷ 2) 

= 11 × 9

=  99 = Third number

Second Row:

(13 + 1) × {(19 + 1) ÷ 2} 

= 14 × (20 ÷ 2) 

= 14 × 10

=  140 

Hence, the correct answer is "140".

Six Children: G, H, I, J, K, and L, are sitting around a circular table facing towards the centre

1) J and K are sitting to the immediate left and right of G, respectively. L is sitting to the immediate left of J, but not to the immediate right of H.

Clearly, H is sitting immediate right of K.

Hence, the correct answer is "H".

Given:

Hence, the correct answer is 

"Option 3".

The logic followed here is:

From the given two different cubes the adjacent sides are as shown below:

As 10 is common in both dice, it is clear that 15, 20, 25  and 30 are adjacent to it and remaining number i.e., 5 will opposite to it.

Opposite pairs:

25 → 20

30 → 15

10 → 5

So, the opposite side '15' is '30'.

Hence, the correct answer is "30".

The least possible Venn diagram is given below.

Conclusions:

I. All cats are rabbits → Does not follow → As all rabbits are cows and some rabbits are cats. So, all cats are rabbits is not definite true.

II. Some cows are rabbits → Follow → As all rabbits are cows so some cows are rabbits is definite ture.

Hence, the correct answer is "Only Conclusion II follows".

The pattern followed here is:

The prime number series followed here which start with 19.

Hence, the correct answer is "174".

The position of letters according to the English alphabet series:

Logic: (1) Code = Position value of consonant + consecutive odd number(i.e. 1,3,5 etc) respectively.

           (2) Vowel changes to next vowel in cyclic way(i.e. A → E → I → O → U).

Hence, the correct answer is "RAS".

According to the given information:

Clearly, take medicine coded as '85'

Hence, the correct answer is "85".

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

• All Omnivores and deer is a living organisms.
• Deer is not a Omnivores. Deer is Herbivores.
• Planet is different form all.

Hence, the correct answer is "Option 2".

Additional Information1. Omnivores → An animal that eat both plants and meat.

2. Herbivores → An animal that eat only plants and grass.
3. Carnivores → An animal that eat only meat.

BODMAS Rule: 

Option 1) - and +

Given Equation: 45 ÷ 15 × 5 + 15 −11 = 39

After interchanging sign we get: 

⇒ 45 ÷ 15 × 5 - 15 + 11 = 39

⇒ 3 × 5 - 15 + 11 = 39

⇒ 15 - 15 + 11 = 39

⇒ 26 - 15 = 39

⇒ 11 ≠ 39

⇒ LHS ≠ RHS

Option 2) - and ×

Given Equation: 45 ÷ 15 × 5 + 15 −11 = 39

After interchanging sign we get: 

⇒ 45 ÷ 15 - 5 + 15 × 11 = 39 

⇒ 3 - 5 + 15 × 11 = 39

⇒ 3 - 5 + 165 = 39

⇒ 168 - 5 = 39

⇒ 163 ≠ 39

⇒ LHS ≠ RHS

Option 3) + and ×

Given Equation: 45 ÷ 15 × 5 + 15 −11 = 39

After interchanging sign we get: 

⇒ 45 ÷ 15 + 5 × 15 −11 = 39

⇒ 3 + 5 × 15 - 11 = 39

⇒ 3 + 75 - 11 = 39

⇒ 78 - 11 = 39

⇒ 67 ≠ 39

⇒ LHS ≠ RHS

Option 4) ÷ and +

Given Equation: 45 ÷ 15 × 5 + 15 −11 = 39

After interchanging sign we get: 

⇒ 45 + 15 × 5 ÷ 15 −11 = 39

⇒ 45 + 15 × 0.33 - 11 = 39

⇒ 45 + 5 - 11 = 39

⇒ 50 - 11 = 39

⇒ 39 = 39

⇒ LHS = RHS

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

The position of letters according to the English alphabet series:

1) LGS : PLY

Similarly,

2) MKB : ?

Hence, the correct answer is "QPH".

The position of letters according to the English alphabet series:

Logic: Addition of place of alphabet × 2 =  Number.

‘LILY’ is coded as 116

And,

‘LOTUS’ is coded as 174

Similarly,

‘TULIP’ be coded as '?'

Hence, the correct answer is "156".

The position of letters according to the English alphabet series:

Option 1) YRLGC

Option 2) HAUPL

Option 3) ATNIE

Option 4) GZTNK

Hence, the correct answer is "GZTNK".

The correct meaningful order is given below:

4. Script → First of all the story of a movie or video is written in script form. 2. Rehearsal → Rehearsal are done based on the script written. 1. Recording → Recording is done after the rehearsal. 5. Video Editing → Then video editing of the recording. 3. Viewers → Finally it is ready for viewers.

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

Given:

Three years from today, Ravish will be three times as old as Kailash.

So, Age of Ravish = 3 × Age of Kailash

Let, age of Kailash = x and age of Ravish = 3x.

We know that, difference between the age of two persons always remains same.

As, three years ago, the difference between the age of Ravish and the age of Kailash was 18 years. So, after three years the difference between the age of Ravish and the age of Kailash will 18 years.

According to the question, 

Age of Ravish - Age of Kailash = 18

⇒ 3x - x = 18

⇒ 2x = 18

⇒ x = 9

Therefore, age of Ravish = 3x = 3 × 9 = 27 year [After three years] 

So, present age of Ravish is 27 - 3 = 24 year.

Hence, the correct answer is "24".

The pattern followed here is:

Hence, the correct answer is "2474".

According to the given information:

1. Niraj is the father of Rinku.

2. Jiya and Tiya are the daughters of Ruby, who is the only sister of Rinku.

3. Vishnu is the son of Rinku and Gita.

Clearly, Niraj is Maternal grandfather of Tiya.

Hence, the correct answer is "Maternal grandfather".

The pattern followed here is:

Hence, the correct answer is "Option 1".

The correct answer is Anjali Bhardwaj.

Key Points

• Anjali Bharadwaj is an Indian social activist working on issues of transparency and accountability.
• She is one of the 12 "courageous" individuals named by the Biden administration for the newly-instituted International Anti-Corruption Champions Award.
• Bharadwaj is the founder of the Satark Nagrik Sangathan (SNS).
• SNS is a citizens' group with a mandate to promote transparency and accountability in government and encourage the active participation of citizens.
• She is also a convener of the National Campaign for Peoples' Right to Information.
• She successfully advocated for the creation of an anti-corruption ombudsman and the Whistle Blowers' Protection Act, offering protection to those who expose corruption and abuse of power.​

Important Points

• International Anti-Corruption Champions Award.
• ​Recognizes individuals who have worked tirelessly, often in the face of adversity, to defend transparency, combat corruption, and ensure accountability in their own countries.
• ​In addition to Bharadwaj, the other honourees are:
• Ardian Dvorani of Albania.
• Diana Salazar of Ecuador.
• Sophia Pretrick of Micronesia.
• Juan Francisco Sandoval Alfaro of Guatemala.
• Ibrahima Kalil Gueye of Guinea.
• Dhuha A Mohammed of Iraq.
• Bolot Temirov of Kyrgyz Republic.
• Mustafa Abdullah Sanalla of Libya.
• Victor Sotto of The Philippines.
• Francis Ben Kaifala of Sierra Leone.
• Ruslan Ryaboshapka of Ukraine.

Additional Information

• Medha Patkar
• An Indian social activist and former Politician working on various crucial political and economic issues raised by tribals, Dalits, farmers, laborers, and women facing injustice in India.
• She is an alumnus of TISS, a premier institute of social science research in India.
• Flavia Agnes
• ​Flavia Agnes is an Indian women's rights lawyer with expertise in marital, divorce, and property law.
• She has published articles in the journals Subaltern Studies, Economic and Political Weekly.
• Archana Borthakur
• ​Archana Borthakur is an Indian social activist from Assam.
• Founded social welfare society Priyobondhu in pursuit of community development and social change.

The correct answer is red seaweeds.

Key Points

• ‘Hypnea indica’ and ‘Hypnea bullata’ are types of red seaweeds.
• Marine biologists from the Central University of Punjab have discovered two new native species of marine algae, also called seaweeds, from the coasts of Gujarat, Diu, and Tamil Nadu.
• The species are named Hypnea indica and Hypnea bullata.
• Named Hypnea indica (after India) and Hypnea bullata (because of the blisterlike marks on its body – bullate).
• The seaweeds are part of the genus Hypnea or red seaweeds.
• The red seaweed species are economically important as:
• They contain carrageenan, an important biomolecule that is used widely in the food industry.​​

Important Points

• Seaweed:
• They are the primitive, marine non-flowering marine algae without roots, stems, and leaves, which play a major role in marine ecosystems.
• Large seaweeds form dense underwater forests known as kelp forests, which act as underwater nurseries for fish, snails, and sea urchins.
• ​Seaweeds are abundant along the Tamil Nadu and Gujarat coasts and around Lakshadweep and Andaman & Nicobar Islands.

The correct answer is Qila Mubarak in Bathinda.

• Qila Mubarak fort served as a prison for Empress Razia Sultana after she was defeated by her rebellious general, Malik Ikhtiar-ud-din Altunia.

Key Points

• Razia Sultana Born: 1205 ​Reign: 1236 – 1240
• She was Iltutmish’s daughter.
• She is also the first and last Muslim woman to rule over Delhi.
• She was defeated by Malik Ikhtiar-ud-din Altunia, the governor of Bathinda.
• After which sultana was prisoned at Qila Mubarak fort.
• She later married to Malik Ikhtiar-ud-din Altunia.
• She was reportedly killed by her brother’s forces.
• She was succeeded by her brother Muizuddin Bahram Shah.​

Additional Information

• Golconda fort in Golconda
• ​Golconda Fort is built by the Qutb Shahi dynasty as the capital of the Golconda Sultanate, located in Hyderabad, Telangana, India.
• This is one of the most magnificent fortress complexes in India.
• Mehrangarh fort in Jodhpur​
• ​Mehrangarh Fort in Jodhpur was built by Rao Jodha, who was the founder of Jodhpur city.
• Considered one of the most formidable and magnificent forts of Rajasthan, was built in the year 1459.
• ​Jaigarh fort in Jaipur 
• ​Jaigarh Fort is known as the victory fort which was built by king Sawai Maan Singh III in 1726.
• It was built in order to protect the amber fort and the palace complex within it.

The correct answer is 1.33 g.

Key Points

• Every sample of carbon monoxide contains 16.0 g of oxygen for every 12.0 g of carbon.
• This is a mass ratio of oxygen to carbon of 1.33 to 1.
• In carbon dioxide, there is exactly twice as much oxygen present as there is in carbon monoxide.
• This illustrates the law of multiple proportions:
• whenever the same two elements form more than one compound, the different masses of one element that combine with the same mass of the other element are in the ratio of small whole numbers.
• In carbon monoxide, there is 1.333g oxygen for every 1g carbon.
• In carbon dioxide, there is 2.666g oxygen for every gram of carbon.
• So **the ratio of oxygen in the two compounds is 1:2, a small whole-number ratio.**​

Important Points

• Carbon monoxide is a deadly gas.
• It is formed from the incomplete combustion of some carbon-containing materials (such as wood and gasoline).
• It will attach to haemoglobin in the red blood cells and block the binding of oxygen to those cells.
• If oxygen does not bind, it cannot be carried to the cells of the body where it is needed, and death can occur.
• Carbon dioxide, on the other hand, is not toxic like carbon monoxide is.
• However, it can displace oxygen in systems since it is heavier.
• Carbon dioxide fire extinguishers cut off the flow of oxygen in a fire, putting out the fire.

The correct answer is 8000 meters.

Key Points

• Climbers while climbing some of the world's tallest mountains, enter the “death zone” when they are 8,000 meters from sea level, where oxygen is 34% the concentration it is on the ground below.
• Most climbers are not accustomed to the high altitude and low oxygen levels and rely on bottled oxygen they bring along.
• Climbers who spend long periods in this region can develop altitude sickness and even brain swelling.
• Mount Everest is 29,029 feet tall.
• The final 4,029ft of the ascent is known as the Death Zone:
• Above 25,000ft the body can no longer acclimatize to the altitude.
• The lungs can't get enough oxygen and cells begin to die.
• The Himalayan and the Karakoram ranges of Asia are home to all 14 of Earth’s 8,000-meter (26,247-foot) peaks.

The correct answer is 22.4 Litre.

Key Points

• At standard temperature and pressure (STP) one mole of any gas occupies a volume of 22.4 L.
• The standard temperature is 0°C (273.15 K) and the standard pressure is 1 atm.

Important Points

Avogadro’s hypothesis states that:

• Equal volumes of any gas at the same temperature and pressure contain the same number of particles.

The ideal gas equation is:

• PV = nRT
• n=Number of moles
• R=The gas constant.
• The SI value for R is 8.31441 J K-1 mol-1.

The correct answer is Dr. Soumya Swaminathan.

Key Points

• 'Till we win: India's fight against the Covid-19 pandemic' is a formidable book by Dr. Chandrakant Lahariya, Dr. Gagandeep Kang, and Dr. Randeep Guleria – three medical experts at the forefront of India’s fight against Covid-19.
• The book was about:
• the misinformation that surrounded the pandemic.
• the need to provide key information to citizens about how the pandemic emerged and grew – what was done, what continues to be done, and what the future may hold for India.
• It also aimed to capitalize on the increased interest in the health system among the policy audience, as the country readies for the "new normal".

Additional Information

• Dr. Soumya Swaminathan
• ​Soumya Swaminathan is an Indian paediatrician and clinical scientist known for her research on tuberculosis and HIV.
• Since March 2019, Swaminathan has served as the Chief Scientist at the World Health Organization.​
• Dr. Randeep Guleria
• ​Randeep Guleria is an Indian pulmonologist and the current director of the All India Institute of Medical Sciences, New Delhi.
• He is credited with the establishment of India's first center for pulmonary medicines and sleep disorders at AIIMS.
• Dr. Gagandeep Kang
• ​Gagandeep Kang is an Indian Microbiologist and virologist.
• She is the Professor in the Department of Gastrointestinal Sciences at the Christian Medical College, Vellore, India.
• She is a leading researcher with a major research focus on viral infections in children and the testing of rotaviral vaccines.
• Dr Chandrakant Lahariya
• ​Chandrakant Lahariya is an Indian medical doctor, epidemiologist, vaccinologist, public health, policy expert, and writer.
• His work centres around strengthening health systems, and public policy interventions to address health inequities and develop innovative models for health service delivery.

The correct answer is Naomi Osaka.

Key Points

• Naomi Osaka is the world's highest-paid female athlete, ranked first on Forbes’ list of ‘Highest-Paid Female Athletes 2020’.
• The Japanese star raked in $57.3 million in prize money and endorsements over the last year.
• The four-time Grand Slam champion has commercial deals with the likes of Tag Heuer and Louis Vuitton, in addition to partnerships with Nike, Beats by Dre, and Mastercard, among others.
• She also owns equity stakes in BodyArmor and Hyperice as well as becoming an investor in the professional women's soccer team, North Carolina Courage.
• She has helped raise awareness of mental health issues in sports.​

Additional Information

• Fellow tennis players Serena Williams ($45.9 million) and older sister Venus ($11.3 million) were next on the list.
• American gymnast Simone Biles ($10.1 million) and Spanish tennis player Garbine Muguruza ($8.8 million) rounded out the top five.
• Naomi Osaka is the Highest-Paid Woman Athlete in 2022 (Again).​

The correct answer is four.

Key Points

• The Central Board of Directors of the Reserve Bank of India is appointed for a term of four years.
• The overall direction of the RBI lies with the 21-member central board of directors, composed of:
• The governor,
• Four deputy governors,
• Two finance ministry representatives,
• Ten government-nominated directors,
• Four directors who represent local boards for Mumbai, Kolkata, Chennai, and Delhi.
• The Government of India appoints the directors for a four-year term.
• The Central Board of Directors of the RBI recommended aligning the accounting year of RBI with the financial year of the government (April-March), from 2020-21.
• The Reserve Bank's affairs are governed by a central board of directors.
• The board is appointed by the Government of India in keeping with the **Reserve Bank of India Act.**​

Additional Information

• RBI (Reserve Bank of India):
• The Reserve Bank of India was established on April 1, 1935, in accordance with the provisions of the Reserve Bank of India Act, 1934.
• This central banking institution was established based on the suggestions of the “Royal Commission on Indian Currency & Finance” in 1926.
• The Reserve Bank of India (RBI) is India's central bank and regulatory body.
• It is responsible for the issue and supply of the Indian rupee and the regulation of the Indian banking system.
• It also manages the country's main payment systems and works to promote its economic development.
• Governor: Shaktikanta Das
• Headquarters: Mumbai, Maharashtra

The correct answer is 338B (1).

Key Points

• The 102nd Amendment Act of 2018 inserted Article 338-B and gave constitutional status to the National Commission for Backward Classes (NCBC).
• 338B(1):
• There shall be a Commission for the socially and educationally backward classes to be known as the National Commission for Backward Classes.
• 338B(1): 
• There shall be a Commission for the socially and educationally backward classes to be known as the National Commission for Backward Classes.
• The primary objective of the commission is:
• To provide constitutional and other legal safeguards for the socially and educationally backward classes.
• Recommending various welfare measures for the overall development of backward classes to state and central government.
• Policy matters affecting the socially and educationally backward classes are required to be consulted by central and state governments with NCBC.
• **NCBC has all the powers of a civil court while investigating any matter or inquiring about any complaint.**​

Important Points

• Article 124A (1):
• Article 124 deals with the establishment and constitution of the Supreme Court.
• (1) There shall be a Supreme Court of India constituting of a Chief Justice of India and, until Parliament by law prescribes a larger number, of not more than seven other Judges.
• **Article 243Y (1):**​
• The Finance Commission constituted under article 243 (I) shall also review the financial position of the Municipalities and make recommendations to the Governor.
• Article 243S (1):
• There shall be constituted Wards Committees, consisting of one or more Wards, within the territorial area of a Municipality having a population of three lakhs or more.​

The correct answer is Badruddin Tyabji – Bombay Presidency Association.

Key Points

• Bombay Presidency Association
• Pherozeshah Mehta, Badruddin Tyabji, and K. T. Telang were largely responsible for the formation of the Bombay Presidency Association in 1885.
• Bombay Presidency Association was a body that championed Indian interests and hosted the first meeting of the Indian National Congress in Bombay at the end of 1885.
• Madras Mahajana Sabha
• ​Ramaswami Mudaliar and P. Anandacharlu established the Madras Mahajana Sabha in 1884.
• The first meeting took place on December 29, 1884.
• Madras Mahajana Sabha was a Madras Presidency-based Indian nationalist organization.
• East India Association
• ​The East India Association was founded by Dadabhai Naoroji in 1866, in collaboration with Indians and retired British officials in London.
• It superseded the London Indian Society.
• It was a platform for discussing matters and ideas about India, and providing representation for Indians to the Government.
• Poona Sarvajanik Sabha
• ​The Poona Sarvajanik Sabha was founded in 1870 at Poona.
• It was founded by Mahadev Govind Ranade, Ganesh Vasudeo Joshi, and S. H. Chiplunkar.

The correct answer is Tripura.

Key Points

• As per National Family Health Survey 5, Tripura is the only state with a sex ratio at birth for children born in the last five years (urban + rural), above 1,000.
• The first phase of the fifth round of the National Family Health Survey (NFHS-5) was conducted in 2019-20 and its findings were released in December 2020.
• The NFHS provides estimates on key indicators related to population, family planning, child and maternal health, nutrition, adult health, and domestic violence, among others.
• In the first phase of the fifth round, the findings for 22 states and union territories (17 states and 5 union territories) have been presented.

Important Points

• The sex ratio at birth for children born in the last five years is below 950 for seven (of the 17) states.
• The sex ratio at birth is the number of female children born per 1,000 male children born.
• In three states, the ratio is below 900 (Goa: 838, Himachal Pradesh: 875, and Telangana: 894).
• The ratio has declined in seven states.
• The most notable decline was in Goa (from 966 to 838), and Kerala (from 1,047 to 951).
• Only Tripura has a sex ratio at birth above 1,000 (i.e., more females born than males).​

The correct answer is wheat.

Key Points

• The system of MSP (Minimum Support Price) was first introduced for wheat in 1966-67 and later expanded to include other essential food crops.
• When the Green Revolution started in the 1960s, India was actively looking to shore up its food reserves and prevent shortages.
• The MSP system finally started in 1966-67 for wheat and was expanded further to include other essential food crops.
• This was then sold to the poor at subsidized rates under the public distribution system.

Important Points

• MSP (Minimum Support Price)
• Form of market intervention by the Government of India to insure agricultural producers against any sharp fall in farm prices.
• Announced on the basis of the recommendations of the Commission for Agricultural Costs and Prices (CACP).
• Government announces minimum support prices (MSPs) for 22 mandated crops and fair and remunerative prices (FRP) for sugarcane.
• The mandated crops are 14 crops of the Kharif season, 6 rabi crops, and two other commercial crops.
• The list of crops is as follows:
• Cereals (7) - paddy, wheat, barley, jowar, bajra, maize and ragi
• Pulses (5) - gram, arhar/tur, moong, urad and lentil
• Oilseeds (8) - groundnut, rapeseed/mustard, toria, soyabean, sunflower seed, sesamum, safflower seed, and nigerseed.
• Raw cotton
• Raw jute
• Copra
• De-husked coconut
• Sugarcane (Fair and remunerative price)
• Virginia flu-cured (VFC) tobacco

The correct answer is Bhawaiya.

Key Points

• Bhawaiya is a major genre of folk song popular throughout the entire sub-Himalayan belt of northern West Bengal, western Assam and parts of Bangladesh.
• Its origin is drawn from various theatrical and matriarchal ritual folk music traditions.
• Bhawaiya has developed into a socially conscious yet lyrical song tradition that is a mainstay of the culture of the Rajbanshi, Koch and other communities of North Bengal.
• Mostly written from the perspective of the woman.
• Songs speak of love not socially mandated but arising unbidden between men and women thrown together by the vagaries of a marginalized socio-economic existence.
• The woman in a bhawaiya song is often a loner, a young widow or a woman in the full bloom of youth who is yet to find a loving husband.

Additional Information

• Rekham Pada
• ​Rekham Pada is a folk dance popular in Arunachal Pradesh.
• It is one of the main dance forms of the Nishi Tribe.
• Both men and women participate in this dance.
• Rekham Pada is accompanied by a song, which is sung normally in chorus.
• The tribe members dance Rekham Pada during important rituals, during festivals, and also for recreation occasionally.
• Chalo
• ​The Chalo dance is part of Arunachal Pradesh's most awaited festival, called Chalo Loku.
• This festival is a grand celebration in the state and takes place every year in October and November.
• It is a celebration of the Nocte tribe.
• The name “Chalo Loku” translates to paddy cultivation season in English.
• Roppi
• ​Roppi is one of the popular folk dances of Arunachal Pradesh.
• It is mainly performed by the tribal group of the state.

The correct answer is 1928.

• In 1928 Motilal Nehru (Chairman) and eight other Congress leaders draft a constitution for India.

Key Points

• Nehru Report (1928 AD):
• Nehru report was tabled in 1928 AD by Motilal Nehru.
• It remains memorable as the first major Indian effort to draft a constitutional framework for India.
• The recommendations evoked a debate concerning the goal of India-Dominion status of complete independence.
• Other members of the committee were:
• **Tej Bahadur Sapru, Ali Imam, M.S. Aney, Mangal Singh, Sohaib Qureshi, G.R. Pradhan, and Subhash Chandra Bose.**​

Important Points

• Recommendations of the Nehru Report:
• Dominion status Rejection of separate electorates.
• Linguistic provinces.
• Nineteen fundamental rights including equal rights for women.
• Full protection of cultural and religious interests of Muslims.
• Complete dissociation of religion from the state.
• Jinnah, the leader of the Muslim League did not accept the Nehru Report and drew up a list of fourteen demands, which became famous as the 14 points of Jinnah.

The correct answer is Platyhelminthes.

Key Points

• Animals belonging to the phylum Platyhelminthes are also called flatworms due to their dorsoventrally flattened bodies.
• Examples are a liver fluke, tapeworm, etc.
• They are found as endoparasites in human beings.
• About 80 percent of all flatworms are parasitic—i.e., living on or in another organism and securing nourishment from it.
• They are bilaterally symmetrical (i.e., the right and left sides are similar) and lack specialized respiratory, skeletal, and circulatory systems.
• The body cavity (coelom) is absent.
• The body is not segmented; spongy connective tissue (mesenchyme) constitutes the so-called parenchyma and fills the space between organs.
• Flatworms are generally hermaphroditic—functional reproductive organs of both sexes occurring in one individual.

Additional Information

• Ctenophora
• ​Ctenophora is a phylum of exclusively marine invertebrates.
• Ctenophora means “comb-bearing”.
• They are commonly known as comb jellies or sea walnuts.
• The distinguishing feature of the phylum is the presence of comb plates with cilia that are used for locomotion.
• They are radially symmetrical and diploblastic.
• Porifera​
• ​These are pore-bearing multicellular animals.
• The body has no organs.
• They exhibit holozoic nutrition.
• The body is radially symmetrical.
• They can regenerate their lost parts.
• Cnidaria
• ​Mostly marine animals, the cnidarians include the corals, hydras, and jellyfish.
• Radial symmetry.
• Diploblastic animals.
• Tissue level of organization.
• Presence of cnidoblasts with stinging nematocysts on the tentacles.

The correct answer is Rottela Panduga.

Key Points

• Rotiyaan ki eid or Rottela Panduga is an annual three-day festival held at Bara Shaheed Dargah in Nellore in Andhra Pradesh.
• The annual event is observed in the month of Muharram as the festival of 12 martyrs whose mortal remains are buried in the compound.
• People visit the shrine from far-off locations.
• Women who visit the shrine, exchange their rotis (flat Indian breads) at Nellore Tank (Swarnala Cheruvu) in fulfilment of their wishes.​

Additional Information

• Bheldiya
• Bheldiya is celebrated in the state of Assam.
• This is a festival celebrated in the month of May to worship the River Goddess by farmers, fishermen, and boatmen, whose lives and livelihoods essentially depend on the rivers.
• On this occasion, the devotees accompanied by the chanting of the names of Lord Vishnu and readings from the Bhagavata text float beautifully decorated ritual boats made out of the peels of the Banana plants and pay their obeisance to the rivers. ​
• Ali Ai Ligang
• This festival is also celebrated in the state of Assam.
• ​This 5-day festival associated with the commencement of agricultural operation with the sowing of seeds is celebrated every year in the spring season (February-March) by the members of the Mishing community with traditional songs, dance and feast.
• Baishagu
• This festival is also celebrated in the state of Assam.
• ​This is a new year festival celebrated every year by the Bodo Kacharis in the month of Baisakh (mid-April).
• The festival begins with the worship of cows on the first day and continues with the worship of their supreme God, Bathou (identified with Lord Shiva).
• Community feast and dancing on the second day before it is concluded with a prayer at a designated place called girjasali.

The correct answer is Duke of Edinburgh.

Key Points

• Titles held by Prince Phillip, the late husband of Queen Elizabeth II, until his death in April 2021 were:
• ​Duke of Edinburgh.
• Earl of Merioneth and Baron Greenwich.
• Prince of Greece and Denmark.
• ​Philip’s father was Prince Andrew of Greece and Denmark (1882–1944).
• His mother was Princess Alice (1885–1969), granddaughter of Queen Victoria.
• Philip was educated at Gordonstoun School, near Elgin, Moray, Scotland, and at the Royal Naval College, Dartmouth, Devon, England.
• From January 1940 to the end of World War II, he served with the Royal Navy in combat in the Mediterranean and the Pacific.
• His marriage to his distant cousin Princess Elizabeth took place in Westminster Abbey on November 20, 1947.

The correct answer is 10%.

Key Points

• Hon’ble Prime Minister Shri Narendra Modi on May 12th, 2020, announced the Special economic and comprehensive package of Rs. 20 lakh crore - equivalent to 10% of India’s GDP – to fight the COVID-19 pandemic in India.
• He gave a clarion call for Aatma Nirbhar Bharat or Self-Reliant India Movement.
• He also outlined five pillars of Aatma Nirbhar Bharat:–
• Economy.
• Infrastructure.
• System.
• Vibrant Demography.
• Demand.
• Minister for Finance & Corporate Affairs **Smt. Nirmala Sitharaman laid down the details of the Aatma Nirbhar Bharat Package.**​

The correct answer is 101^st.

Key Points

• GST stands for Goods and Services Tax
• ​GST was passed as the 101st amendment act.
• It came into force on 1st July 2017.
• GST is a comprehensive indirect tax on the manufacture, sale, and consumption of goods and services throughout India.
• It will replace existing multiple taxes levied by the central and state governments.
• The concept of GST was first introduced in the Parliament by P. Chidambaram in 2005.
• France is the first country to introduce GST.
• The different tax slabs under the GST are 0%, 5%, 12%, 18%, and 28%.
• **"One nation, one tax, and one market" is the motto of the GST.**​

Additional Information

• Taxes are of two types;
• Direct taxes:
• They are paid in entirety by a taxpayer directly to the government.
• The tax where the liability, as well as the burden to pay it, resides on the same individual.
• Direct taxes include tax varieties such as income tax, corporate tax, wealth tax, gift tax, expenditure tax etc.​
• Types of direct tax include :
• Income Tax: Levied on and paid by the same person according to tax brackets as defined by the income tax department.
• Corporate Tax: Paid by companies and corporations on their profits.
• Wealth Tax: Levied on the value of the property that a person holds.
• Estate Duty: Paid by an individual in case of inheritance.
• Gift Tax: An individual receiving the taxable gift pays tax to the government.
• Fringe Benefits Tax: Paid by an employer that provides fringe benefits to employees, and is collected by the state government.
• Indirect tax:
• Taxes, where the liability to pay the tax, lies on a person who then shifts the tax burden to another individual.
• Types of indirect taxes are :
• Excise Duty: Payable by the manufacturer who shifts the tax burden to retailers and wholesalers.
• Sales Tax: Paid by a shopkeeper or retailer, who then shifts the tax burden to customers by charging sales tax on goods and services.
• Customs Duty: Import duties levied on goods from outside the country, ultimately paid for by consumers and retailers.
• Entertainment Tax: Liability is on the cinema owners, who transfer the burden to cinemagoers.
• Service Tax: Charged on services rendered to consumers, such as food bills in a restaurant.

The correct answer is Teesta.

Key Points

• Teesta River is a 414 km long river that rises in the Pauhunri Mountain of the eastern Himalayas.
• It flows through the Indian states of Sikkim and West Bengal through Bangladesh and enters the Bay of Bengal.
• Teesta is one of the right tributaries of Brahmaputra.
• Before going to the Bay of Bengal through Bangladesh Teesta flows through West Bengal and Sikkim.
• River Rangeet originates in Sikkim which is the largest river in Sikkim and also a tributary of the river Teesta.​

Additional Information

• Koshi 
• ​The Kosi or Koshi flows through China, Nepal, and India.
• The Kosi River has another name, the Sorrow of Bihar.
• It drains the terrains of northern Bihar with one of its main tributaries like the Gandak River.
• Hooghly
• ​Hugli River is also spelt Hooghly.
• river in West Bengal state, northeastern India.
• An arm of the Ganga River, it provides access to Kolkata (Calcutta) from the Bay of Bengal.
• Sone
• ​Son River is a perennial river located in central India.
• It originates near Amarkantak Hill in the Annupur district of Madhya Pradesh.
• Merges with the Ganges River near Patna in Bihar.
• Sone River is the second-largest southern tributary of the Ganges' after the Yamuna River.

The correct answer is 88.89%.

 Key Points

• A sample of pure water, whatever the source always contains 88.89% by mass of oxygen and 11.1%by mass of hydrogen.
• This is according to the law of constant composition.
• Water (H₂O) molecule consists of two hydrogen atoms of relative mass 1 and one oxygen atom of relative mass 16.
• Therefore, the ratio in which 2 atoms of hydrogen and one atom of oxygen are combined is 1: 8.
• It will always be the same irrespective of the source of water.
• The total amount of percentage is 100, therefore they are divided in a constant ratio.
• As 2 atoms of hydrogen and one atom of oxygen are divided in a ratio of 1:8.
• Therefore the mass of Oxygen in percentage terms in the compound is 88.89%.

 Important Points

• The chemical formula of water is H2O.
• Water contains two hydrogen atoms and one oxygen atom.
• The molar mass of water, = 2×atomic mass of hydrogen + 1×atomic mass of oxygen.
• Therefore, the molar mass of water= 2×1+16=18g.
• Mass of oxygen in water: 16 g.
• Mass of hydrogen in water: 2 g.
• The formula for calculating the percent composition of any element in a given compound is:
• The mass percent of element = (Mass of that element in the compound/ Molar mass of compound)×100.
• So, mass % of hydrogen in H2O = (mass of hydrogen in H2O/Molar mass of H2O)×100
• = (2/18)×100
• =11.1%.
• Now, mass % of oxygen in H2O = (Mass of oxygen in H2O/Molar mass of H2O)×100

                  =(16/18)×100

                   =88.8%.

 Additional Information

• Law of constant composition
• In a given compound, the elements always combine in the same proportion as each other.
• This implies that any pure sample of a compound, no matter the source, will always consist of the same elements present in the same ratio by mass.
• For example, pure water always contains hydrogen and oxygen in a fixed mass ratio.

The correct answer is Bal Gangadhar Tilak.

Key Points

• Bal Gangadhar Tilak gave the slogan 'Freedom is my birthright and I Shall have it'.
• Lokmanya Bal Gangadhar Tilak roused the Indian people and injected fresh life into our liberation cause with his electrifying phrase, "Swaraj is my birthright and I shall have it."
• Bal Gangadhar Tilak worked valiantly to aid the country's independence from British domination.
• Bal Gangadhar Tilak, a member of the Lal-Bal-Pal troika.
• He was dubbed the "Father of Indian Unrest" by British colonial rulers.
• Lokmanya Tilak founded and published two newspapers:
• The (Marathi) Kesari
• The (English) Mahratta.
• To criticize the colonial overlords, he used his pen as a weapon.

Additional Information

The correct answer is Ankita Raina.

Key Points

• Ankita Ravinderkrishan Raina (born 11 January 1993) is an Indian professional tennis player.
• Raina has won one title on the WTA Tour and one at WTA 125 tournaments (both in doubles).
• Along with 11 singles and 20 doubles titles on the ITF Circuit.
• Raina has also won gold medals in the women's singles and mixed doubles events at the 2016 South Asian Games.
• And won a bronze medal in singles at the 2018 Asian Games.
• Raina is one of only two women representing India who has won a WTA-level title.​

Additional Information

• Bala Devi
• ​Bala Devi is an Indian women's footballer.
• She plays as a forward for Scottish Women's Premier League club Rangers and India women's national football team.
• Shanti Mallick​
• Shanti Mallick is the first female footballer in India to have been awarded the Arjuna award in 1983.
• ​Aditi Chauhan
• ​Aditi Chauhan is an Indian women's professional footballer who plays as a goalkeeper for the Indian national team.

Concept:

Environmental policy:

• It is a kind of measure or unit that is taken by a different kind of organization like government and private regarding a different kind of effect of human activities on the environment.
• This is majorly created for the prevention of human-made effects on the ecosystem.
• Different kinds of environmental policies are ecosystem management, waste management, natural resources protection, and biodiversity conservation.

Explanation:

Extended Producer Responsibility:

• This policy's concept was first introduced by the Swedish Ministry of Environment in 1990.
• Today's world is facing an increasing amount of waste and its effect on the environment.
• Different governments around the world are trying to control this problem with the post-consumer phase by environmental policy.
• The correct answer is Extended Producer Responsibility.
• EPR refers to an environmental policy that sees producers responsible for the safe disposal of their products.
• It is the responsibility, that the waste generated during the production processes should be taken care of in a proper way, from an environmental and resource-saving point of view.
• Before the manufacturing of a product is commenced it should be known how the waste, which is a result of the production process, should be treated, as well as how the product should be taken care of when discarded.
• The ultimate goal of EPR is sustainable development through environmentally responsible product development and product recovery.
• Its main objective is to divert and reduce waste.
• Here producers of a product take full responsibility for their products' whole lifecycle including recycling, reuse, final disposal, and packaging.

Thus, extended producer responsibility is an environmental policy under which producers are given a significant responsibility - financial and/or physical - for the treatment or disposal of products that are no longer useful to the consumer.

Given data:

Calculations:

Number of people visiting Mall A on Thursday, Saturday and Sunday = 460 + 1280 + 1500 = 3240

Number of people visiting Mall B on Thursday, Saturday and Sunday = 750 + 1100 + 1350 = 3200

Ratio = 3240 : 3200 = 81 : 80

∴ The ratio is 81 : 80.

Formula:

M₁ × D₁ = M₂ × D₂, where

M1 and M₂ = Number of men working on D1 and D₂.

D1 and D₂ = Days for which M1 and M₂ worked respectively.

Calculations:

Total work days = 20 × 30 = 600 man-days

Total work done in 10 days = 20 × 10 = 200 man-days

Total work remaining = 600 - 200 = 400 man-days

Total time needed to complete the remaining work = 400 ÷ 16 = 25

Total time needed to complete the whole work = 25 + 10 = 35 days

∴ The work would be completed in 35 days.

Concept:

We need to find a common multiple for a set of numbers i.e., LCM of the numbers. This is followed by division with the largest three-digit number and addition of the remainder. 

Calculations:

LCM of 3, 4, 5, and  8 = 120

Greatest three-digit number = 999

Largest three-digit number that is exactly divisible by 120 = 960 (120 × 8 = 960)

Greatest three-digit number that would leave remainder 2 when divided by 120 = 960 + 2 = 962

∴ The largest three-digit number that would leave remainder 2 when divided by 3, 4, 5, and 8 is 962.

Given data:

Length of medians = 7 cm and 4√6 cm.

Calculation:

In Δ ABC, AE = BE and BD = DC

⇒ ED = $1\over2$ AC

Let BE = x and BD = y

⇒ BC = 2y

Applying Pythagora's theorem to the Δ BEC

BE² + BC² = EC²

Substituting the value, we get-

x² + (2y)² = (4√6)²

⇒ 96 = x2 + 4y2 - (Equation 1)

Applying Pythagora's theorem to the Δ ABD

AB2 + BD2 = AD2

Substituting the value, we get-

(2x)2 + y2 = 72

⇒ 49 = 4x2 + y2 - (Equation 2)

Adding Equation 1 and Equation 2, we get-

⇒ 5x² + 5y² = 145

⇒ x2 + y2 = 29

In Δ BED, x2 + y2 = ED²

⇒ ED = √29.

AC = 2ED = 2√29.

∴ The length of the hypotenuse of the triangle is 2√29.

Shortcut Trick

In right angled Δ ABC, if AD and CE are the medians then,

⇒ 4(AD² + CE²) = 5AC²

Now, AD = 7 cm and CE = 4√6

⇒ 4[(7)² + (4√6)²] = 5AC²

⇒ 4(49 + 96) = 5AC²

⇒ 5AC² = 580

⇒ AC = 2√29

∴ The length of the hypotenuse of the triangle is 2√29.

Additional Information ⇒ AD² + CE² = 5ED²

Concept used:

(a + b)³ = a³ + b³ + 3ab (a + b)

(a - b)³  = a³ - b³ - 3ab (a - b)

Calculations:

(x + y)3 - (x - y)3 - 3y(2x2 - 3y2) = ky3

⇒ x3 + y3 + 3x²y + 3xy² - x3 + y3 + 3x²y - 3xy² - 6yx² + 9y³ = ky³

⇒ 11y3 = ky3

⇒ k = 11

∴ The value of k is 11.

Given data:

Length of pole = 9 m

Length of shadow of the pole = 3√3 m

Calculation:

In the right-angled triangle ABC

tan θ = AC / BC

⇒ tan θ =  9 / 3√3

⇒ tan θ = √3

∴ θ = 60º

∴ The angle of the elevation of the sun is 60º.

Concept used:

B = Bar/Bracket

O = Off

D = Division

M = Multiplication

A = Addition

S = Subtraction

Calculation:

\(\frac{{1\frac{2}{3} \div \frac{5}{6} × 6 + \frac{4}{5} × \frac{1}{2} + \frac{2}{3}}}{{2 - \left[ {1\frac{1}{3} × \left( { - \frac{3}{5}} \right) - 6\left{ {\frac{3}{5} - \left( {3 - \frac{3}{{10}}} \right)} \right}} \right]}}\)

⇒ \(\frac{{\frac{5}{3} \div \frac{5}{6} × 6 + \frac{4}{5} × \frac{1}{2} + \frac{2}{3}}}{{2 - \left[ {\frac{4}{3} × \left( { - \frac{3}{5}} \right) - 6\left{ {\frac{3}{5} - \left( {3 - \frac{3}{{10}}} \right)} \right}} \right]}}\)

⇒ \(\frac{{\frac{5}{3} × \frac{6}{5} × 6 + \frac{4}{5} × \frac{1}{2} + \frac{2}{3}}}{{2 - \left[ {\frac{4}{3} × \left( { - \frac{3}{5}} \right) - 6\left{ {\frac{3}{5} - \left( {\frac{27}{{10}}} \right)} \right}} \right]}}\)

⇒ \(\frac{{\frac{5}{3} × \frac{6}{5} × 6 + \frac{4}{5} × \frac{1}{2} + \frac{2}{3}}}{{2 - \left[ {\frac{4}{3} × \left( { - \frac{3}{5}} \right) - 6\left{ {\frac{-21}{10} } \right}} \right]}}\)

⇒ $\frac{{12 + \frac{2}{5} + \frac{2}{3}}}{{2 - \left[ {\frac{-4}{5} + \frac{63}{5}} \right]}}$

⇒ $\frac{{ \frac{196}{15} }}{{2 + {\frac{4}{5} - \frac{63}{5}} }}$

⇒ $\frac{{ \frac{196}{15} }}{{{\frac{-49}{5} } }}$

⇒ $196\over 15$ × $-5\over49$ = $-4\over3$

∴ The answer to the expression is $-4\over3$.

Formula used:

cot α × tan α = 1

(a + b)² = a² + b² - 2ab

Calculation:

cot2 α + tan2 α = 2

Subtracting 2 from both sides, we get-

⇒ cot2 α + tan2 α - 2 = 2 - 2

⇒ cot2 α + tan2 α - 2 × cot α × tan α = 0

⇒ (cot α - tan α)² = 0

⇒ cot α = tan α 

⇒ tan² α  = 1

⇒ α = 45°

∴ The value of α is 45°.

Calculation:

Cost of one pencil = Rs $5\over 4$

Cost of 60 pencil = $5\over 4$ × 60 = Rs 75

Cost of single second-type pencil = Rs $3\over 2$

Cost of 60 second-type pencil = $3\over 2$ × 60 = Rs 90

Total cost price = 75 + 90 = Rs 165.

Selling price of one pencil = Rs $4\over 3$

Total selling price = $4\over 3$ × 120 = Rs 160

Total loss = 165 - 160 = Rs 5

Loss% = $5\over165$ × 100 = 3$1\over 33$%

∴ The loss incurred is  3$1\over 33$%.

Shortcut Trick Average cost price of both pencils = ${5\over 4} +{3\over 2} \over 2$ = $11\over 8$ 

Selling price of pencils = $4\over 3$

Loss = $11\over 8$ - $4\over 3$ = $1\over 24$

Loss % = $1\over 24$ × $8\over 11$ × 100 = 3$1\over 33$%.

Calculations:

Students with marks less than 100 = 10 + 18 + 32 + 45 = 105

Students with marks 120 and above = 75 + 55 + 40 + 15 = 185

Difference = 185 - 105 = 80

Difference % = $80\over 185$ × 100 = 43.2%

∴ The answer is 43.2%.

Given data:

DC = 2BD

AC - AB = 5 cm

Calculation:

AD is the bisector of ∠BAC

⇒ $AB\over AC$ = $BD\over DC$

Substituting the values, we get-

⇒ $AB\over AB+5$ = $BD\over 2BD$

⇒ $AB\over AB+5$ = $1\over 2$

⇒ 2AB = AB + 5

⇒ AB = 5 cm.

∴ The length of AB is 5 cm.

Given data:

Formula used:

Gains = Receipts - Expenditure

Calculation:

∴ In the year 2020, the company gained the maximum amount.

Shortcut Trick

Total Distance = 12 + 6 = 18 km

Total Time = (12 ÷ 16) + (6 ÷ 20) = 3/4 + 3/10 = (15 + 6) / 20 = 21/20 hours

Average Speed = Total Distance ÷ Total Time = 18 ÷ (21/20) = 18 × 20 / 21 = 120 / 7 km/h

Average Speed = 17(1/7) km/h

∴ The correct answer is 17(1/7) km/h.

Alternate Method

Given:

Distance₁ (d₁) = 12 km, Speed₁ (s₁) = 16 km/h

Distance₂ (d₂) = 6 km, Speed₂ (s₂) = 20 km/h

Formula Used:

Average Speed = (Total Distance) / (Total Time)

Time = Distance / Speed

⇒ Time taken for first part (t₁) = 12 / 16 = 3/4 hours

⇒ Time taken for second part (t₂) = 6 / 20 = 3/10 hours

⇒ Total Time (T) = 3/4 + 3/10 = (15 + 6) / 20 = 21/20 hours

⇒ Average Speed = 18 / (21/20)

⇒ Average Speed = (18 × 20) / 21 = 360 / 21 = 120 / 7

⇒ Average Speed = 17(1/7) km/h

∴ The correct answer is 17(1/7) km/h.

Additional Information

Average Speed (Equal Distances)

When two equal distances are covered at speeds x and y, the average speed is 2xy / (x + y).

Relative Speed

If two objects move in opposite directions, relative speed is the sum of speeds (s₁ + s₂). In the same direction, it is the difference |s₁ − s₂|.

Conversion Factor

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

Formula:

P = $SI×100\over R× T$

A = P × (1 + $R\over 100$)^T

CI = A - P

where-

P = Principal

SI = Simple Interest

R = Rate

T = Time

CI = Compound Interest

A = Amount

Effective rate = r1 + r2 + $r_1 × r_2 \over 100$

Where “r₁” and “r₂” are rate of interest during successive years.

Calculation:

P = $4800×100\over 8× 12$ = Rs 5000

Effective discount = 10 + 10 + $10 × 10 \over 100$ = 21%

Final effective discount = 21 + 10 + $21 × 10 \over 100$ = 33.1%

CI = $5000× 33.1× 1\over100$ = Rs 1655.

∴ The compound interest on the sum is Rs 1655.

Formula Used:

Effective discount = d1 + d2 - $d_1 × d_2 \over 100$

Where “d1” and “d2” are successive discounts offered.

Calculation:

Effective discount = 20 + 25 - $20 × 25 \over 100$ = 40%

⇒ 40% discount on MP = Rs 250

MP = $250 \over 40$ × 100 = Rs 625

MP is 25% above the CP i.e., Cost Price

⇒ CP = $625 \over 125$ × 100 = Rs 500.

∴ The cost price of the article is Rs 500.

Calculation:

$\frac{{\cos A}}{{1 - \tan A}} + \frac{{\sin A}}{{1 - \cot A}} - \sin A$

⇒ $\frac{{\cos A}}{{1 - \tan A}} + \frac{{\sin A}}{{1 - {1\over tan A}}} - \sin A$ 

⇒ $\frac{{\cos A}}{{1 - \tan A}} + \frac{{\sin A \times tan A}}{{tan A - 1}} - \sin A$

⇒ $\frac{{\cos A}}{{1 - \tan A}} - \frac{{\sin A \times tan A}}{{1- tan A}} - \sin A$

⇒ $\frac{{\cos A - sin A\times tan A -sin A + sin A \times tan A}}{{1 - \tan A}}$

⇒ $\frac{{\cos A -sin A}}{{1 - {sinA \over{cos A}}}}$

⇒ $\frac{cos A\times [{\cos A -sin A]}}{{cos A -sin A }}$

⇒ cos A

∴ The answer for the expression is cos A.

Shortcut Trick

Net deviation of first 4 numbers = 4 × (44 − 42) = +8

Net deviation of last 5 numbers = 5 × (40 − 42) = −10

Sum of 5th, 6th, and 7th numbers = (3 × 42) − (8 − 10) = 126 + 2 = 128

Let 6th number be x, then (x + 6) + x + (x + 5) = 128 ⇒ 3x = 117 ⇒ x = 39

Average of 6th (39) and 7th (44) = (39 + 44) ÷ 2 = 41.5

∴ The correct option is D.

Alternate Method

Given:

Average of 12 numbers = 42

Average of first 4 numbers = 44

Average of last 5 numbers = 40

6th number is 6 less than 5th and 5 less than 7th.

Formula Used:

Sum = Average × Number of observations

First 4 (Avg 44) 5, 6, 7 (Avg ?) Last 5 (Avg 40) Total of 12 Numbers (Avg 42)

Remaining Sum (5th+6th+7th) = 128

Calculations:

⇒ Total sum of 12 numbers = 12 × 42 = 504

⇒ Sum of first 4 numbers = 4 × 44 = 176

⇒ Sum of last 5 numbers = 5 × 40 = 200

⇒ Sum of 5th, 6th, and 7th numbers = 504 − (176 + 200) = 504 − 376 = 128

⇒ Let 6th number = x

⇒ 5th number = x + 6

⇒ 7th number = x + 5

⇒ (x + 6) + x + (x + 5) = 128

⇒ 3x + 11 = 128 ⇒ 3x = 117 ⇒ x = 39

⇒ 6th number = 39, 7th number = 39 + 5 = 44

⇒ Average of 6th and 7th numbers = (39 + 44) ÷ 2 = 83 ÷ 2 = 41.5

∴ The correct option is D.

Additional Information

Average Concept

Average = (Sum of all observations) ÷ (Total number of observations). It represents the central value of a data set.

Deviation Method

The sum of deviations of all observations from the actual mean is always zero. This property helps in finding missing values quickly.

Weighted Average

When two or more groups are combined, the new average A = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂), where n is the count and a is the individual group average.

Given data:

a + b + c = 11

ab + bc + ac = 28

Formula used:

a3 + b3 + c3 - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ac)

(a + b + c)² = a² + b² + c² + 2 × (ab + bc + ac)

Calculations:

Substituting the values, we get-

(a + b + c)2 = a2 + b2 + c2 + 2 × (ab + bc + ac)

⇒ 121 = a2 + b2 + c2 + 2 × 28

⇒ a2 + b2 + c2 = 121 - 56 = 65

a3 + b3 + c3 - 3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ac)

⇒ a3 + b3 + c3 - 3abc = 11 × (65 - 28)

⇒  a3 + b3 + c3 - 3abc = 11 × 37 = 407

∴ The value of the expression is 407.

Given:

∠ABO = 40°

Concept:

The angle subtended by an arc at the center is double than subtended by it on other parts of the circle. In the figure below, ∠ AOB = 2∠ACB

 

Calculation:

In the figure ∠ABO = ∠BAO (angles formed by the radius are equal)

In Δ AOB, ∠ABO + ∠BAO + ∠BOA = 180°

⇒ ∠BOA = 180° - (40 + 40) = 100°

⇒ ∠BOA (external) = 360° - 100° = 260°.

∠ACB = $1\over 2$ ∠BOA (external) (since angle formed by the arc at the center is double compared to the angle formed by the arc at other points on the circumference).

∴ ∠ACB = $1\over 2$ × 260° = 130°

∴ The angle formed by ∠ACB is 130°.

Concept:

The divisibility test for 6 states that for a number to be divisible by 6, it should be divisible by 2 and 3.

Calculation:

The number k53206k would be divisible by 2 if k is an even number i.e., 2, 4, 6, or 8.

The number k53206k would be divisible by 3, if the sum of the digits is divisible by 3.

⇒ sum of digits = k + 5 + 3 + 2 + 0 + 6 + k = 16 + 2k 

⇒ If k = 4, 16 + 2k is divisible by 3.

∴ The value of k is 4.

Mistake PointsThe value of k cannot be 0 since k is present at the start of the digit. If the value of k is 0, it will make the number a 6-digit number instead of a 7-digit number.

Shortcut Trick

Profit Ratio = (Investment_A × Time_A) : (Investment_B × Time_B)

5 : 9 = (I_A × 8) : (36,000 × 12)

I_A = (5 ÷ 9) × (36,000 × 12 ÷ 8)

I_A = 5 × 4,000 × 1.5 = 30,000

∴ The correct answer is 30,000.

Alternate Method

Given: Investment of B = Rs. 36,000 | Time for A = 8 months | Time for B = 12 months | Profit Ratio A : B = 5 : 9

Formula Used: Profit = Investment × Time

⇒ Profit_A ÷ Profit_B = (Inv_A × Time_A) ÷ (Inv_B × Time_B)

⇒ 5 ÷ 9 = (I_A × 8) ÷ (36,000 × 12)

⇒ 5 ÷ 9 = (8 × I_A) ÷ 432,000

⇒ 8 × I_A × 9 = 5 × 432,000

⇒ 72 × I_A = 2,160,000

⇒ I_A = 2,160,000 ÷ 72

⇒ I_A = 30,000

∴ The correct answer is 30,000.

Additional Information

Profit Distribution Rule

In any partnership, the ratio of profits is directly proportional to the product of capital invested and the time duration: P₁ : P₂ = C₁T₁ : C₂T₂.

Capital Calculation

If profits and time periods are known, the ratio of investments is: C₁ : C₂ = (P₁/T₁) : (P₂/T₂).

Working vs Sleeping Partner

A working partner manages the business and may receive a salary or fixed percentage of profit before the remaining profit is divided based on the investment ratio.

Given data:

Students with either Grade D or Grade E = 11 + 8 = 19%

Total students = 1800

Calculation:

Total students with either Grade D or Grade E = $19\over100$ × 1800 = 342

∴ Total students with either Grade D or Grade E is 342.

Given data:

Radius = 13 cm

Length of one chord = 10 cm

Distance between chords = 17 cm

Calculation:

BF = $1\over 2$ AB = 5 cm

Applying Pythagora's theorem in the Δ BOF 

BF² + OF² = BO²

⇒ OF2 = 13² - 5² = 12²

∴ OF = 12 cm.

⇒ OE = 17 - 12 = 5 cm

Applying Pythagora's theorem in Δ OED

⇒ ED2 + OE2 = OD2

⇒ ED2 = 132 - 52 = 122

∴ ED = 12 cm.

⇒ CD = 2 × 12 = 24 cm

Difference between the length of the chords = 24 - 10 = 14 cm

∴ The difference between the length of the chords is 14 cm.

Calculation:

Let the initial oranges with the fruit seller be x.

1st selling = 0.45x + 1

Remaining = x - (0.45x + 1) = 0.55x - 1

2nd selling = $1\over 5$ × (0.55x - 1) = 0.11x - 0.2 + 2 = 0.11x + 1.8

Remaining after second selling = 0.55x - 1 - (0.11x + 1.8) = 0.55x - 0.11x - 1 - 1.8 = 0.44x - 2.8

3rd selling = 90% × (0.44x - 2.8)

Remaining after 3rd selling = 0.1 × (0.44x - 2.8) = 0.044x - 0.28

According to the question-

⇒ 0.044x - 0.28 = 5

⇒ 0.044x = 5.28

⇒ x = $5.28\over 0.044$ = 120

∴ The number of oranges was 120. 

Alternate Method

At last, he sells 90% of the remaining oranges after selling the oranges to a second customer, then he has 10% of the remaining oranges.

10% of the remaining oranges after selling the oranges to the second customer = 5

So remaining oranges after selling the oranges to the second customer = 100% of the remaining oranges after selling the oranges to the second customer = 50 oranges

He gave 2 extra oranges to the second customer, so the remaining oranges = 50 + 2

He sells 20% of the remaining oranges to the second customer, so he has 80% of the remaining oranges = 52

100% of remaining oranges after selling the oranges to the first customer = (52/4) * 5 = 65 oranges

He gave 1 extra orange to the first customer, so the total oranges after selling 45% of the oranges = 65 + 1 = 66 oranges

(100% - 45% = 55%) of total oranges = 66

so

100% of oranges = (66/55) * 100 = 120 oranges

Given data:

Radius of wire (r) = 0.1 mm

Diameter of solid copper sphere (D) = 6 cm

Concept:

Wire could be considered a miniature cylinder that is to be formed from a solid copper sphere. Hence, the volume of wire drawn would be equal to the volume of the solid copper sphere.

Formula used:

Volume of cylinder = π × r2 × l, where

r = radius of wire

l = length of wire

Volume of solid sphere = $4\over 3$ × π × R3, where

R = Radius of the solid sphere

Calculation:

Volume of solid sphere = $4\over 3$ × 3.14 × 3 × 3 × 3 = 113.04 cm³

Let the length of wire be "l".

Volume of wire = 3.14 × $1\over 100$ × $1\over 100$ × l

According to the question-

Volume of wire = Volume of solid sphere

⇒ 3.14 × $1\over 100$ × $1\over 100$ × l = 113.04 cm³

⇒ l = 113.04 ×$10,000\over 3.14$ = 360000 cm 

∴ The length of wire formed is 360000 cm.

The correct answer is "make up"

Key Points

• In the given sentence, the use of the phrasal verb is incorrect.
• A phrasal verb is a combination of a verb and preposition, adverb, or sometimes both.
• The meaning of a phrasal verb may vary significantly from its literal meaning.
• The meaning is not formed from the individual words but in their combined usage.
• Let's look at the given phrasal verbs.
• Make up: to make a decision about something.
• Made out: assert or imply something about a particular person or thing.
• Make on: to turn on, light, or ignite
• As per the meaning of given phrasal verbs, "make up" is the appropriate word choice.
• Example: Rajat can't make up his mind about whether to pursue medicine or engineering.
• In the given sentence, the speaker has to take a decision regarding the vacation, so "make up" is appropriate.

The correct sentence is: I can’t make up my mind about taking a vacation in winter.

Hence, the correct answer is option 2.

The erroneous segment is "a doctor of"

Key Points

• In the given sentence, the usage of the preposition 'of' is incorrect.
• We use the preposition 'of' usually to talk about quantification, the relation of an object with a noun, and for reference.
• Example: He is the owner of the restaurant.
• We use the preposition 'at' to talk about time, location or activity.
• Example: She was watching a theatrical performance at the Siri Fort Auditorium.
• In the given sentence, we need to use the preposition 'at' as we are giving details about the place where the doctor was working.

The correct sentence is: He was formerly a doctor at the corporate hospital.

Hence, the correct answer is option 4.