SSC CGL 2020 Tier-I Official Paper (Held On : 24 Aug 2021 Shift 3) (Previous Year Paper)

Statements:

All lemons are plums.

All plums are dates.

Some dates are mangoes.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some lemons are mangoes → False (It is possible but not definite)

II. Some mangoes are plums → False (It is possible but not definite)

III. All lemons are dates → True (because all lemons are plums and all plums are dates so definitely all lemons are also dates)

IV. Some mangoes are dates → True (because some dates are mangoes so, definitely some mangoes are also dates)

Hence, “Both conclusions III and IV follow”.

Additional Information 

Table show alphabet serial number –

The pattern followed is,

Hence, “MVQF” is the term that completes the series.

According to the sequence in the dictionary:

The correct order of the given words is:

5. Perturb
6. Pneumonia
7. Precision
8. Puberty
9. Publicity

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

Given:

 

Here the pattern followed in each row is:

{(2^nd number)² + (3^rd number)² } ÷ 2 = 1^st number

Row 1: 45, 9, 3

{(2^nd number)² + (3^rd number)² } ÷ 2

= (9² + 3²) ÷ 2

= (81 + 9) ÷ 2

= 90 ÷ 2

= 45 = 1^st number

Row 2: 122, 10, 12

{(2^nd number)² + (3^rd number)² } ÷ 2

= (10² + 12²) ÷ 2

= (100 + 144) ÷ 2

= 244 ÷ 2

= 122 = 1^st number

Similarly,

Row 3: 116, 6, ?

{(2^nd number)² + (3^rd number)² } ÷ 2 = 116

= (6² + ?²) ÷ 2 = 116

= (36 + ?²) = 232

= ?² = 232 - 36 = 196

= ? = 14 = 1^st number

Hence, “14” is correct answer.

The pattern followed here is:

1. Middle shape is rotating 90° Anticlockwise and 180° Anticlockwise direction alternatively in each step.

2. Top, left, and bottom shape (total 3 shapes) are rotating 180° clockwise/anticlockwise direction and right shape (total 1 shape) is the same in 1st figure to 2nd figure.

3. Right and bottom shapes (total 2 shapes) are rotating 180° clockwise/anticlockwise direction and top and left shapes (total 2 shapes) are the same in 2nd figure to 3rd figure.

4. Top, left and right shapes are (total 3 shapes) are rotating 180° clockwise/anticlockwise direction and bottom shape (total 1 shape) is the same in 3rd figure to 4th figure.

5. Left and bottom shapes (total 2 shapes) are rotating 180° clockwise/anticlockwise direction and top and right shapes (total 2 shapes) are the same in 4th figure to 5th figure.

6) Top, right and bottom shapes are (total 3 shapes) are rotating 180° clockwise/anticlockwise direction and left shape (total 1 shape) is the same in 5th figure to 6th figure.

Hence, the correct answer is "Option 3".

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

Hence, "option (4)" is the correct answer.

Additional Information

In Mirror image left side and right side changed vice-versa where top and bottom remain same.

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

Given:

Libya : Tripoli → Tripoli is the capital of Libya

Similarly, 

Dublin → Dublin is the capital and largest city of Ireland.

Hence, the correct answer is "Dublin".

Additional Information

Moscow → Moscow is the capital of Russia.

Oslo → Oslo is the capital of Norway.

Madrid → Madrid is the capital of Spain.

We put all the option in blank area and check who create particular pattern

Option (1) t, t, q, p, n, l, d

d q _ p l n _ q t _ l n d _ t p l _ d q _ p _ n

After filling the blanks with the letters/numbers in the option given above, we get:

d q t p l n / t q t q l n / d p t p l n / d q l p d n

No particular pattern is repeating itself when the sequence is divided into equal parts.

Option (2) t, p, d, q, l, n, t

d q _ p l n _ q t _ l n d _ t p l _ d q _ p _ n

After filling the blanks with the letters/numbers in the option given above, we get:

d q t p l n / p q t d l n / d q t p l l / d q n p t n

No particular pattern is repeating itself when the sequence is divided into equal parts.

Option (3) t, d, p, q, n, t, l

d q _ p l n _ q t _ l n d _ t p l _ d q _ p _ n

After filling the blanks with the letters/numbers in the option given above, we get:

d q t p l n / d q t p l n / d q t p l n / d q t p l n

A particular pattern is repeating itself when the sequence is divided into equal parts.

Option (4) d, l, n, p, q, t, t

d q _ p l n _ q t _ l n d _ t p l _ d q _ p _ n

After filling the blanks with the letters/numbers in the option given above, we get:

d q d p l n / l q t n l n / d p t p l q / d q t p t n

No particular pattern is repeating itself when the sequence is divided into equal parts.

Hence, ‘t, d, p, q, n, t, l’ is the correct answer.

Income → Aswath : Sunita : Ramdin → 12x : 9x : 7x

Expenditures → Aswath : Sunita : Ramdin → 15y : 9y : 8y

Savings = Income - Expenditures

Aswath : Sunita : Ramdin → 12x - 15y : 9x - 9y : 7x - 8y

Given:

Aswath saves 25% of his income for future investments

12x - 15y = 25% of 12x

=> 12x - 15y = 3x

=> 9x = 15y

=> x / y = 15 / 9

So, x = 15; y = 9

Put the value of x and y saving of Aswath, Sunita and Ramdin.

=> 12x -15y : 9x - 9y : 7x - 8y

=> (12 × 15 - 15 × 9) : (9 × 15 – 9 × 9) : (7 × 15 - 8 × 9)

=> (180 - 135) : (135 - 81) : (105 - 72)

=> 45 : 54 : 33

Divided by 3,

=> 15 : 18 : 11

Hence, ‘15 : 18 : 11’ is the ratio of the savings of Aswath, Sunita and Ramdin.

Table show alphabet serial number –

The pattern for the code is as follows,

'MONTHLY' is written as 'DGMOSJR'

Similarly,

HEADING = ?

Hence, ‘HEADING’ is coded as ‘LINYFZM’.

The logic followed here is:

Except option 3, all words are the synonyms of each other whereas abuse is the antonyms of these words.

Option (1) Disrespect → Disrespect word is synonyms of Insult.

Option (2) Abuse → Abuse word is synonyms of Insult.

Option (3) Respect → To admire or have a high opinion of somebody.

Option (4) Contempt → Contempt word is synonyms of Insult.

Hence, “Respect” is an odd one.

The image obtained when the paper is unfolded is,

Hence, option 4 is the correct answer.

Confusion Points

• Right bottom position of U is different in Option 3 and 4 figure.
• Double CC in bottom part are the same direction in option figure 1.

Here in option 3 and option 4 the right bottom position of U is different.

Given:

Here the pattern followed in each column is:

(1^st number × 2^nd number) + 2^nd number = 3^rd number

Column 1: (23 × 3) + 3 = 69 + 3 = 72 = 3^rd number

Column 2: (32 × 4) + 4 = 128 + 4 = 132 = 3^rd number

Similarly

Column 3: (16 × 5) + 5 = 80 + 5 = 85 = 3^rd number

Hence, “85” is correct answer.

The number of triangles in the given figure is:

So, there are a total of 19 triangles in the figure.

Hence, ‘19’ is the correct answer.

Shortcut TrickGiven figure:

The number of triangles = 8 × 2 = 16

Now, 

The number of triangles = 1 + 2 = 3

Total the number of triangles = 16 + 3 = 19

Hence, the correct answer is "19".

The embedded part of this image is:

Hence, option (2) is the correct answer.

Preparing the family tree using the following symbols,

Given:

"She is my mother-in-law's only son’s niece"

We can draw following Family Tree from the information given above:

Hence, the girl's mother is "Sister-in-law" of Deepika.

The pattern followed here is:

Hence, '63' is the correct answer.

The table is alphabets place value:

The pattern followed here is:                                

Sum of the positional values of the opposite alphabets letters × Total number of vowels in word = number.

LABOUR → Total number of vowels (A, O, U) in the word is 3.           

Opposite alphabets of a given word are

=> Sum of the positional values of the opposite alphabets letters × Total number of vowels in word = number

=> (15 +26 + 25 + 12 + 6 + 9) × 3 = 93 × 3 = 279

And,

EXHALE → Total number of vowels (E, A, E) in the word is 3.           

Opposite alphabets of given word is

=> Sum of the positional values of the opposite alphabets letters × Total number of vowels in word = number

=> (22 + 3 + 19 + 26 + 15 + 22) × 3 = 107 × 3 = 321

Similarly,

CAUTIOUS → Total number of vowels (A, U, I, O, U) in the word is 5.           

Opposite alphabets of given word is

=> Sum of the positional values of the opposite alphabets letters × Total number of vowels in word = number

=> (24 + 26 + 6 + 7 + 18 + 12 + 6 + 8) × 5 = 107 × 5 = 535

Hence, CAUTIOUS will be written as “535”.

The pattern followed here is,

Let (1^st number : 2^nd number)

2^nd number ÷ 33 = 1^st number

Now follow the steps:

21 : 693

=> 2^nd number ÷ 33 = 1^st number

=> 693 ÷ 33 = 21 = 1^st number

Similarly,

? : 792

=> 2^nd number ÷ 33 = 1^st number

=> 792 ÷ 33 = 24 = 1^st number

Hence, "24" is correct answer.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except ‘NRIP’.

Hence, “NRIP” is the odd one

The logic is here is:

(1^st number × 4) + 2 = 2^nd number.

Option (1): 6 ∶ 26

Now, follow the logic:

(6 × 4) + 2 = 24 + 2 = 26 = 2^nd number

This option follows the pattern.

Option (2): 5 ∶ 24

Now, follow the logic:

(5 × 4) + 2 = 20 + 2 = 22 ≠ 2^nd number

This option do not follow the pattern.

Option (3): 8 ∶ 34

Now, follow the logic:

(8 × 4) + 2 = 32 + 2 = 34 = 2^nd number

This option follows the pattern.

Option (4): 7 ∶ 30

Now, follow the logic:

(7 × 4) + 2 = 28 + 2 = 30 = 2^nd number

This option follows the pattern.

Hence, pair “5 ∶ 24” is an odd one.

The game should be the first word and the field should be the second.

The logic followed here is:

Golf : Course → Golf is played on a course.

Similarly,

Cycling : Velodrome → Cycling racing track called a velodrome.

Hence, ‘Cycling : Velodrome’ is the correct answer. 

Mistake Points The sequence/ordering of game and field is wrong in the fourth option.

Additional Information

The Venn diagrams best represent the relationship between - Men, Lyricists, Extroverts figures are shown below:

Some men are lyricists and some men are extroverts.

Hence, ‘option 2’ is the correct answer.

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

In first dice and second dice.

Letter 'Q' is common.

The left letter will be opposite to each other writing them clockwise starting from X.

 

Hence, the correct answer is “P”.

Shortcut TrickThe pattern followed here is:

When a similar number/letter is on a similar surface, the remaining similar surfaces are opposite to each other and the letter/number which is not visible will be opposite to the same letter/number

Dice 1 and 2:

 

Hence, the correct answer is “P”.

According to BODMAS rule

Given equation 512 * 32 * 9 * 100 * 6 * 25 * 2

Option 1 : Using the combination +, ×, ÷, =, -, ×

512 + 32 × 9 ÷ 100 = 6 - 25 × 2

By BODMAS rule

512 + 32 × 0.09 = 6 - 25 × 2

512 + 2.88 = 6 - 50

514.88 = - 44 (LHS ≠ RHS)

Option 2 : Using combination ÷, ×, +, -, =, ×

512 ÷ 32 × 9 + 100 - 6 = 25 × 2

16 × 9 + 100 - 6 = 25 × 2

144 + 100 - 6 = 50

244 – 6 = 50

238 = 50 (LHS ≠ RHS)

Option 3 : Using the combination ÷, ×, +, =, -, ×

512 ÷ 32 × 9 + 100 = 6 - 25 × 2

16 × 9 + 100 = 6 - 25 × 2

144 + 100 = 6 - 50

244 = - 44 (LHS ≠ RHS)

Option 4 : Using the combination ÷, ×, -, +, =, ×

512 ÷ 32 × 9 - 100 + 6 = 25 × 2

16 × 9 - 100 + 6 = 25 × 2

144 - 100 + 6 = 50

44 + 6 = 50

50 = 50 (LHS = RHS)

Hence, the answer is “÷, ×, -, +, =, ×”.

The correct answer is 1963.

Key Points

• The first rocket launched in India:
• Sounding rockets are one or two-stage solid propellant rockets used for probing the upper atmospheric regions and for space research.
• They also serve as easily affordable platforms to test or prove prototypes of new components or subsystems intended for use in launch vehicles and satellites.
• With the establishment of the Thumba Equatorial Rocket Launching Station (TERLS) in 1963 at Thumba, a location close to the magnetic equator, there was a quantum jump in the scope for aeronomy and atmospheric sciences in India.
• The launch of the first sounding rocket from Thumba near Thiruvananthapuram, Kerala on 21 November 1963, marked the beginning of the Indian Space Programme. Hence, Option 3 is correct.
• Sounding rockets made it possible to probe the atmosphere in situ using rocket-borne instrumentation.
• The first rockets were two-stage rockets imported from Russia (M-100) and France (Centaure).
• While the M-100 could carry a payload of 70 kg to an altitude of 85 km, the Centaure was capable of reaching 150 km with a payload of approximately 30 kg.

Additional Information

• ISRO:
• It is the space agency under the Department of Space of Government of India, headquartered in the city of Bengaluru, Karnataka.
• Its vision is to harness space technology for national development while pursuing space science research and planetary exploration.
• Antrix Corporation Limited (ACL) is a Marketing arm of ISRO for promotion and commercial exploitation of space products, technical consultancy services, and transfer of technologies developed by ISRO.
• The space research activities were initiated in India under Dr. Vikram Sarabhai, the founding father of the Indian space programme, during the 1960s.

The correct answer is Article 368.

Key Points

• Amendment of Indian Constitution:
• Under Article 368, the parliament can amend the Constitution. Hence, Option 1 is correct.
• Amending the constitution of India is the process of making amendments to the fundamental law or supreme law of the country.
• The amendment process in the constitution is set out in Part XX (Article 368) of the Indian Constitution.
• This procedure preserves the sanctity of India's Constitution and holds a check on the Indian Parliament's arbitrary power.
• Article 368 does not set down the legislative process to be followed at various points of the amendment.

Additional Information

The correct answer is the flow channel.

Key Points

• Flow channel
• These are also called gravity irrigation.
• It is the type of irrigation in which water is available at a higher level to enable supply to the land by gravity flow. Hence, Option 4 is correct.

Additional Information

The correct answer is ​Abul Fazl.

Key Points

• Abul Fazl 
• He was the author of Akbarnama, the official history of Akbar’s reign in 3 volumes. Hence, Option 4 is correct.
• The third volume of the above work is known as Ain-i-Akbari, which is the administrative report of Akbar’s reign.
• Another important work of Abul Fazl was Ruqaat, which is a collection of letters to the princes of Akbar and other contemporaries.

Additional Information

The correct answer is Keibul Lamjao National Park.

Key Points

• Keibul Lamjao National Park: 
• It is a national park in the Bishnupur district of the state of Manipur in India.
• The national park is characterized by many floating decomposed plant materials locally called phumdis.
• The park which was initially declared to be a sanctuary in 1966, was subsequently declared to be a national park in 1977 through a gazette notification.
• Kishtwar National Park is a national park located in the Kishtwar district of Jammu and Kashmir, India.
• Khangchendzonga National Park also Kanchenjunga Biosphere Reserve is a National Park and a Biosphere reserve located in Sikkim, India.
• Khirganga National Park is a national park in Himachal Pradesh, India established in 2010.
• Jim Corbett National Park is a forested wildlife sanctuary in northern India’s Uttarakhand State.

Additional Information

The correct answer is remittances.

Key Points

• Remittances:
• Remittances are usually understood as financial or in-kind transfers made by migrants to friends and relatives back in communities of origin.
• These are the sum of two main components:
• Personal Transfers in cash or in-kind between resident and non-resident households and Compensation of Employees, which refers to the income of workers who work in another country for a limited period.
• Remittances help in stimulating economic development in recipient countries, but this can also make such countries over-reliant on them.

Additional Information

• According to the World Bank’s Migration and Development Brief, India has become the world’s largest recipient of Remittances, receiving USD 87 billion (a gain of 4.6 % from the previous year) in 2021.
• India is followed by China, Mexico, the Philippines, and Egypt.
• The United States is the biggest source, accounting for over 20% of all Remittances.

The correct answer is 23 January.

Key Points

• Parakram Diwas
• The central government has decided to observe Subhas Chandra Bose Jayanti as 'Parakram Diwas' to be celebrated on 23^rd January. Hence, Option 4 is correct.
• A high-level committee headed by the Prime Minister has also been formed to plan year-round programmes to mark the anniversary of Bose.
• Recently the Government of India has also instituted Subhash Chandra Bose Aapda Prabandhan Puraskaar to recognise the excellent work done by the individuals and institutions in the field of disaster management.

Additional Information

• Subhash Chandra Bose:
• Subhas Chandra Bose was born on 23^rd January 1897, in Cuttack, Orissa Division, Bengal Province, to Prabhavati Dutt Bose and Janakinath Bose.
• In 1919, he had cleared the Indian Civil Services (ICS) examination. Bose, however, resigned later.
• He was highly influenced by Vivekananda's teachings and considered him as his spiritual Guru.
• His political mentor was Chittaranjan Das.
• He stood for unqualified Swaraj (independence) and opposed Motilal Nehru Report which spoke for dominion status for India.
• He actively participated in the Salt Satyagraha of 1930 and vehemently opposed the suspension of the Civil Disobedience Movement and the signing of the Gandhi-Irwin Pact in 1931.
• In the 1930s, he was closely associated with left politics in Congress along with Jawaharlal Nehru and M.N. Roy.
• Bose won the congress presidential elections at Haripura in 1938.
• Again in 1939 at Tripuri, he won the presidential elections against Gandhi's candidate Pattabhi Sitarammayya.
• Due to ideological differences with Gandhi, Bose resigned and left congress. Rajendra Prasad was appointed in his place.
• He found a new party, 'the Forward Bloc'. The purpose was to consolidate the political left and major support base in his home state Bengal.

The correct answer is Phosphine.

Key Points

• Phosphine:
• It is the simplest phosphorus hydride.
• It is a colourless and extremely toxic gas.
• Some people think it smells like rotting fish; it reminds others of the odour of garlic.
• In any case, pure phosphine is actually odourless; an impurity, diphosphine (P2H4), is responsible for its foul scent.
• It is formed naturally via the anaerobic decay of phosphorus-containing organic matter. Hence, Option 3 is correct.
• The earliest reported preparation was made by Antoine Lavoisier’s student Philippe Gengembre in the late 18th century.
• It is made industrially from white phosphorus by hydrolysis with an alkali metal hydroxide or an aqueous acid-catalyzed disproportionation reaction.
• The industrial product is normally shipped as liquefied gas.

Hence the phosphine is formed naturally via anaerobic decay of phosphorus-containing organic matter.

The correct answer is 600.

Key Points

• The third phase of Pradhan Mantri Kaushal Vikas Yojana: 
• It was launched on January 15, 2021, in 600 districts across all states of India.
• The third phase will be spearheaded by the Ministry of Skill Development and Entrepreneurship (MSDE).
• It will focus on new-age India and COVID-related skills.
• Based on the learnings gained from the first and second phases of the mission, the Ministry has improved the newer version of the scheme to match the current policy doctrine and energize the skilling ecosystem affected due to the COVID-19 pandemic.
• Pradhan Mantri Kaushal Vikas Yojana's third phase (PMKVY 3.0) will focus on training eight lakh candidates during the scheme period of 2020-2021 with an outlay of Rs. 948.90 crore.
• Prime Minister Narendra Modi had launched Skill India Mission on July 15, 2015.
• The mission gained momentum through the launch of Pradhan Mantri Kaushal Vikas Yojana (PMKVY), its flagship scheme.
• The third phase of the scheme will be launched by Union Skill Development Minister Mahendranath Pandey, in the presence of the Minister of State, Raj Kumar Singh.

The correct answer is Lord Padmasambhava. 

Key Points

• Hemis Festival:
• It Brings the colourful shades of festivities in the barren, deserted land of Ladakh.
• Hemis festival is one event that greatly represents the analogy of Ladakh culture.
• Like the other popular festivals in Leh Ladakh, the Hemis Festival in Ladakh also marks the victory of good over evil.
• Just past the harsh winters of Ladakh, the Hemis festival feels like a welcome respite, that lures thousands of tourists to this remote place.
• And what better way to understand the people and culture of a region, other than its festivals.
• Dedicated to the birth of Buddhist Lord Padmasambhava, who is the founder of Vajrayana Buddhism in Ladakh. Hence, Option 3 is correct.
• Hemis festival is celebrated on the 10th day of the Tibetan lunar month.
• Evident from its name, the celebrations of this renowned festival take place in the Hemis Gompa or monastery, which, along with holding a sacred status, is also the largest of its kind in Ladakh.

The correct answer is Harisena. 

Key Points

• Allahabad pillar Inscription or Prayag Prasasti:
• Samudra Gupta court poet and minister Harisena composed the Allahabad pillar Inscription or Prayag Prasasti. Hence, Option 3 is correct.
• The Pillar was an Asokan Pillar erected by Asoka six centuries before him.
• This Inscription is a eulogy of Samudra Gupta and mentions the conquests of Samudra Gupta and the boundaries of the Gupta Empire.
• As per this inscription, Samudra Gupta defeated 9 kings in the North, 12 Kings in the South, reducing all the Atavika states to vassalage.
• Allahabad Prasasti, composed by Harishena, does not bear any date and for this reason, historians have presumed that it was composed probably before the Ashwamedha Yajna performed by Samudragupta.

Additional Information

• Samudragupta:
• He was a ruler of the Gupta Empire of Ancient India.
• As a son of the Gupta emperor Chandragupta I and the Lichchhavi princess Kumaradevi, he greatly expanded his dynasty's political power.
• Reigned from 335/336 CE to 375 CE.
• He Called ‘Napolean of India’ by VA Smith (Irish Indologist and Art Historian).
• His campaigns are mentioned in the Eran inscription (Madhya Pradesh).

The correct answer is Dmitri Mendeleev.

Key Points

• The Periodic Law, as we know it today owes its development to the Russian chemist, Dmitri Mendeleev (1834-1907) and the German chemist, Lothar Meyer (1830-1895).
• Working independently, both the chemists in 1869 proposed that on arranging elements in the increasing order of their atomic weights, similarities appear in physical and chemical properties at regular intervals.

Important Points

• Modern Periodic Table:
• The Modern Periodic Table is classified into the following elements - p-block, s-block, d-block, and f-block.
• The p-block elements include chalcogens, pnictogens, halogens, inert gases.
• The 18th group is known as Inert gas, zero groups, Nonreactive gases.
• The 17th group is known as Halogen.
• The 16th group is known as Chalcogen.
• The 15th group is known as Pnictogen.
• The s-block elements include alkali metals and alkaline earth metals.
• The d-block elements include Transition elements.
• The f-block elements include Inner Transition Elements.

The correct answer is oneirology.

Key Points

• Oneirology
• ​It is the scientific study of dreams. Hence, Option 2 is correct.
• Current research seeks correlations between dreaming and current knowledge about the functions of the brain, as well as an understanding of how the brain works during dreaming as pertains to memory formation and mental disorders.
• The study of oneirology can be distinguished from dream analysis in that the aim is to quantitatively study the process of dreams instead of analyzing the meaning behind them.
• The discipline is generally agreed to have begun with the discovery by Nathaniel Kleitman and his student Eugene Aserinsky in 1955 of regular cycles in human sleep, in the sleep laboratory at the University of Chicago.

Additional Information

The correct answer is 1925.

Key Points

• Kakori Robbery/Conspiracy case:
• It was a train robbery that took place on 9 August 1925 against the British Indian Government. Hence, Option 4 is correct.
• It was organized by the Hindustan Republican Association.
• The idea behind the Kakori conspiracy was to secure money belonging to the government.
• The train was carrying money bags belonging to the British Government.
• The people included here were Swaran Singh, Ram Prasad Bismil, Ashfaqulla Khan, Rajendra Lahiri, Durga Bhagavati Charan Vohra, Roshan Singh, Sachindra Bakshi, Chandrasekhar Azad, Vishnu Sharan Dublish, Keshab Chakravarthy, Banwari Lal, Mukundi Lal, Sachindra Nath Sanyal, and Manmathnath Gupta.

The correct answer is Mumbai and Hyderabad.

Key Points

• United Nations Educational, Scientific and Cultural Organization (UNESCO) has included Mumbai and Hyderabad in its network of 'Creative Cities' among the 66 cities selected on the occasion of World Cities Day 2019 (31st October). Hence, Option 3 is correct.
• With the addition of 66 new cities, the UNESCO Creative Cities Network counts a total of 246 cities.
• Mumbai has been designated as Creative City of Films and Hyderabad as a Creative City of Gastronomy.
• Earlier, Indian cities like Chennai and Varanasi have been included in UNESCO Cities of Music while Jaipur has been included in the City of Crafts and Folk Arts.​

Important Points

• UNESCO Creative Cities Network (UCCN):
• It was created in 2004.
• Currently (2019), 246 cities make up this network which aims towards a common objective of placing creativity and cultural industries at the heart of their development plans at the local level and cooperating actively at the international level.
• The UNESCO Creative Cities aims to achieve Sustainable Development Goals through innovative thinking and action.
• Also, cities are championing sustainable development actions that directly benefit communities at the urban level.
• Sustainable Development Goal 11 aims for Sustainable Cities and Communities.
• The network covers seven creative fields: crafts and folk arts, media arts, film, design, gastronomy, literature, and music.

The correct answer is Hills.

Key Points

• Terrace Farming:
• This is practiced on hill slopes that do not have enough flat terrain for growing crops. Hence, Option 4 is correct.
• In this, the slopes of the hills are converted into horizontal terraces of regular intervals which allow the cultivation of crops.
• They also reduce the surface runoff along the slopes and help in preventing soil erosion.

Additional Information

• Contour Bunding
• In this, a series of checks are put in place across the slope of a hilly surface.
• The bunds divide the entire slope into numerous smaller segments which help in reducing the runoff along the slopes, ensure greater absorption of rainwater on the slopes thus controlling soil erosion.
• Sometimes, the bunds can be in the form of retaining walls.
• Contour Ploughing
• On slopy areas, ploughing of land must be done across the contours, at right angles to the slope.
• This will prevent the formation of gullies along the slopes which could erode the topsoil through runoff.
• This also helps in ensuring that the crops along the slopes get adequate water.

The correct answer is Shashi Tharoor.

Key Points

• The Paradoxical Prime Minister:
• The Paradoxical Prime Minister: Narendra Modi And His India is a Non-fiction book written by senior Indian National Congress parliamentarian Shashi Tharoor. Hence option 1 is correct.
• The book talks about prime minister Narendra Modi's life and his time.
• It is divided into five sections comprising 50 chapters.
• It will release on 26th October 2018.

Additional Information

• Shashi Tharoor:
• He is an Indian former international diplomat, politician, writer, and public intellectual who has been serving as a Member of Parliament, Lok Sabha from Thiruvananthapuram, Kerala, since 2009.
• He was formerly Under-Secretary-General of the United Nations and ran for the post of Secretary-General in 2006.

The correct answer is Rishabh Pant.

Key Points

• Rishabh Pant:
• Jindal South West (JSW) Steel has appointed Indian cricketer Rishabh Pant as its brand ambassador. Hence, Option 4 is correct.
• Pant will help promote JSW’s steel products which include Colouron+ colour-coated sheets and JSW Neosteel TMT bars, for a three-year period.
• He is an Indian cricketer who plays as a middle-order wicket-keeper batsman for India, Delhi, and the Delhi Capitals in the Indian Premier League.
• He was the vice-captain of the India U-19 team for the 2016 Under-19 Cricket World Cup.

Additional Information

• JSW Steel Ltd:
• It is an Indian multinational steel-making company based in Mumbai, Maharashtra.
• It is a subsidiary of JSW Group.
• It is one of the fastest-growing companies in India with a global footprint in over 140 countries.

The correct answer is Sandeep Aggarwal.

Key Points

• Sandeep Aggarwal:
• He has been appointed as the new Chairman of the Telecom Equipment and Services Export Promotion Council (TEPC). Hence, Option 1 is correct.
• He is the MD of Paramount Communications Ltd., a cable manufacturer.
• He will take over from Shyamal Ghosh, ex-Telecom Secretary.

Additional Information

• Telecom Equipment and Services Export Promotion Council (TEPC)
• It has been set up by the Government of India to promote and develop the export of Telecom Equipment and Services.
• TEPC as a Council plays a critical role in the furtherance of Telecom export from India and assists Indian member companies in easy facilitation of their respective exports.
• The Council caters to the complete Telecom Ecosystem including Telecom Hardware Manufacturing, Telecom Service Provision, Telecom Software, and Consultancy.
• It thus represents the strength of Equipment Manufacturers, System Integrators, Service Providers, and other stakeholders in the telecom domain.

The correct answer is Siddhartha Mohanty.

Key Points

• Siddhartha Mohanty:
• The Appointments Committee of the Cabinet (ACC) has approved the appointment of Siddhartha Mohanty as the new Managing Director of the Life Insurance Corporation (LIC) of India. Hence, Option 1 is correct.
• He is currently serving as the Managing director (MD) and chief executive officer (CEO) of LIC Housing Finance. Siddhartha Mohanty has replaced TC Suseel Kumar, who retired on January 31, 2021. LIC has four Managing Directors and one Chairman.

Additional Information

• LIC: 
• It is fully owned by the central government and governed by the Life Insurance Corporation Act, 1956. Every LIC policy is guaranteed by the government.
• It has the highest market share in the life insurance segment in India.
• LIC policyholders enjoy a sovereign guarantee (under Section 37 of the Act) on the sum assured and the bonus declared. This has been one of the main selling points for LIC policies.
• LIC pays 5% of its surplus to the government and the balance 95% to policyholders. Compared to this, private players pay around 90% to policyholders.
• A large part of LIC's investment is in equities, bond markets, and government-dominated instruments.
• LIC now also holds a 51% stake in IDBI bank thus making it the only insurer in India to own a bank.
• LIC is the biggest institutional investor in the Indian equity markets. LIC’s gross investments in equity are set to touch an all-time high of ₹72,000 crores in the financial year 2019-20.
• The government has used LIC on many occasions to stabilize the markets. Eg an offer for the sale of Oil and Natural Gas Corporation Limited (ONGC) in 2012 is a classic example of a LIC bailout.

The correct answer is 2014.

Key Points

• Target Olympic Podium (TOP) Scheme:
• It was formulated in July 2014 under the overall ambit of the National Sports Development Fund (NSDF) with the aim to identify, groom and prepare potential medal prospects for Olympic and Paralympic Games. Hence, Option 2 is correct.
• About 54.40 % of the total expenditure of the National Sports Development Fund (NSDF) has been incurred on TOP Scheme.
• Target Olympic Podium (TOP) Scheme was formulated in 2014 under the overall ambit of the National Sports Development Fund (NSDF) with the aim to identify, groom, and prepare potential medal prospects for the Olympic and Paralympic Games.
• The high priority category has been created to put focus on those sports disciplines played in the Olympics in which India has won medals in the last conducted Asian Games as well as Commonwealth Games or in which India has a good chance of winning medals.

Additional Information

• Presently, nine sports disciplines viz.,
• (i) Athletics,
• (ii) Badminton
• (iii) Hockey
• (iv) Shooting
• (v) Tennis
• (vi) Weightlifting
• (vii) Wrestling,
• (viii) Archery
• (ix) Boxing
• The National Sports Development Fund (NSDF) was established in November 1998 under the Charitable Endowments Act, 1890 with the aim of promoting sports and games in the country.

The correct answer is Dadabhai Naoroji.

Key Points

• Dadabhai Naoroji: 
• He wrote the book 'Poverty and Un British Rule in India'. Hence, Option 4 is correct.
• Dadabhai Naoroji was popularly known as the 'Grand Old Man of India'.
• He is the first Indian to become a member of the British Parliament.
• He helped found the London Indian Society and East India Association.
• In 1885, Naoroji became a vice-president of the Bombay Presidency Association.
• He was Congress president thrice, in 1886, 1893, and 1906.

Additional Information

• Major writings of Dada Bhai Naroji were as follows:
• Poverty in India
• The manners and customs of the Parsees
• Condition of India
• Admission of educated natives into the ICS
• The wants and means of India

The correct answer is Raman Effect.

Key Point

• Raman Effect:
• It states that there is a change in the wavelength of light that occurs when a light beam is deflected by molecules.
• This is caused due to the molecules of gases, liquids, or solids when they are excited to vibrational energy levels.
• The Raman Effect is the phenomenon of scattering of light by molecules present in a medium.​ Hence, Option 3 is correct.
• When a beam of light travels through a transparent object, a small fraction of the light gets scattered in directions other than where it should.
• The scattering occurs due to the difference in wavelength of light as it enters into the medium.
• The Raman effect is defined as the scattering of photons by the excited molecules that are at higher energy levels.
• Raman effect is also known as Raman scattering.
• Raman effect, change in the wavelength of light that occurs when a light beam is deflected by molecules.
• When a beam of light traverses a dust-free, transparent sample of a chemical compound, a small fraction of the light emerges in directions other than that of the incident (incoming) beam.
• Most of this scattered light is of unchanged wavelength.
• A small part, however, has wavelengths different from that of the incident light its presence is a result of the Raman effect.

The correct answer is Justice Gita Mittal.

Key Points

• Gita Mittal:
• The Indian Broadcasting Foundation (IBF) has appointed Justice Gita Mittal as the new chairperson of the Broadcasting Content Complaints Council (BCCC).
• Justice Mittal succeeds former Supreme Court Judge, Justice Vikramajit Sen, whose tenure as BCCC chairperson has ended.
• Having served as the 1st woman Chief Justice of Jammu & Kashmir High Court, she is also the first woman chairperson of BCCC.
• Former Chief Justice of Jammu & Kashmir High Court, Justice Gita Mittal, has been declared as one of the two recipients of the Arline Pacht Global Vision Award for 2021. The Award will be presented at IAWJ’s Biennial Conference during the virtual opening ceremony on May 7, 2021. She shares the honour with Margarita Luna Ramos from Mexico.
• International Association of Women Judges (IAWJ) instituted this award in 2016. Justice Mittal would be the first Indian judge to receive the award. Award is presented to a sitting/retired woman judge to recognize her contribution to IAWJ.

Additional Information

• Indian Broadcasting and Digital Foundation (IBDF):
• IBDF is a unified representative body of television broadcasters in India.
• The organisation was founded in the year 1999. Over 250 Indian television channels are associated with it.
• Recently, in May 2021, The Indian Broadcasting Foundation (IBF), the apex body of broadcasters, was expanded to cover digital streaming platforms and renamed the Indian Broadcasting and Digital Foundation (IBDF).
• The move brought the broadcasters and OTT (over-the-top) platforms, which had seen a substantial jump in their viewership base after the pandemic, under one roof.
• IBDF also formed a self-regulatory body named as Digital Media Content Regulatory Council (DMCRC) for digital OTT platforms.
• DMCRC is a second-tier mechanism at the appellate level and is similar to Broadcast Content Complaint Council (BCCC), which IBF had implemented for the linear broadcasting sector way back in 2011.
• The IBDF is the parent organisation of the Broadcasting Content Complaints Council (BCCC) which was set up in the year 2011. The BCCC examines content-related complaints relating to all non-news general entertainment channels in India.

The correct answer is Article 265.

Key Points

• The system of taxation:
• It is the backbone of a nation’s economy which keeps revenue consistent, manages growth in the economy, and fuels its industrial activity.
• India’s three-tier federal structure consists of the Union Government, the State Governments, and the Local Bodies which are empowered with the responsibility of the different taxes and duties, which are applicable in the country.
• The local bodies would include local councils and the municipalities.
• The government of India is authorized to levy taxes on individuals and organisations according to the Constitution.
• However, Article 265 of the Indian constitution states that the right to levy/charge taxes hasn’t been given to any except the authority of law. Hence, Option 3 is correct.
• The 7th schedule of the constitution has defined the subjects on which Union/State or both can levy taxes.
• As per the 73rd and 74th amendments of the constitution, limited financial powers have been given to the local governments which are enshrined in Part IX and IX-A of the constitution.

Given:

$\left(5-\frac{x^2}{3}\right)^3$

Concept used:

(A - B)³ = A³ - 3A²B + 3AB² - B³

Calculation:

$\left(5-\frac{x^2}{3}\right)^3$

⇒ 125 - (25x²) + (5x⁴/3) - (x⁶/27)

∴ (-25) is the coefficient of x2 in the expansion of $\left(5-\frac{x^2}{3}\right)^3$.

The total number of male teachers in the districts East, North, West taken together = 1650 + 1075 + 1280 = 4,005

The total number of female teachers in the districts East and South = 2375 + 1085 = 3,460

Difference between them = 4005 - 3460 = 545

∴ The difference between the total number of male teachers in the districts East, North, West taken together and the total number of female teachers in the districts East and South is 545.

Given:

sec 31° = x

Concept used:

Sin (90° - θ) = Cosθ

Cosecθ = 1/Sinθ

Cosθ = 1/Secθ

Calculation:

$\rm sin^259^\circ+\frac{1}{sec^231^\circ}-\frac{1}{sin^259^\circ cosec^259^\circ}$

⇒ Sin² (90 - 31)° + (1/Sec²31°) - {1 / (Sin²59° × 1/Sin²59°)

⇒ Cos² 31° + (1/Sec231°) - 1

⇒ (1/Sec231°) + (1/Sec231°) - 1

⇒ (2/Sec231°) - 1

⇒ (2/x²) - 1

⇒ (2 - x²)/x²

∴ The required value of $\rm sin^259^\circ+\frac{1}{sec^231^\circ}-\frac{1}{sin^259^\circ cosec^259^\circ}$ is (2 - x2)/x2.

Production increased in 2016 compared to 2015 = (1400 - 1250)/1250 × 100% = 12%

Since in the given options there is no such option that includes 2016 except option A, we don't need to check any further. Because 2016 is a valid year where production increased by more than 10%, it has to be there in the answer.

∴ The production increased by more than 10% of that in the previous year in 2016.

Marks obtained by E in English = 54% × 50 = 27

Marks obtained by E in Maths = 64% × 150 = 96

Marks obtained by E in Science = 55% × 80 = 44

Marks obtained by E in Science = 72% × 75 = 54

Marks obtained by E in Social Studies = 85% × 100 = 85

Total marks obtained by E in all five subjects = 27 + 96 + 44 + 54 + 85 = 306

∴ Total marks obtained by E in all five subjects is 306.

Given:

Principal amount = Rs. 12000

Time = 18 months

Rate of interest = 20%

Concept used:

Simple interest = (Principal × Time × Rate) ÷ 100

In the case of compound interest,

A = P × (1 + r/100)n

C.I = A - P

Here, A = Amount, P = Principal, r = Rate of interest. n = Time, C.I = Compound interest

Calculation:

When interest is compounded yearly,

Principal = Rs. 12,000

At the end of the first year, the principal becomes = 12000 × 1.2¹ = Rs. 14400

Then, after 6 months the interest accumulated on the principal amount of Rs. 14400

⇒ (14400 × 20 × 6/12) / 100

⇒ 1440

So, after 8 months the initial principal amount becomes = 14400 + 1440 = Rs. 15840

Interest accumuted in 18 months = Rs. (15840 - 12000) = Rs. 3840

When interest compounded half-yearly,

Rate of interest (R) = 20/2 % = 10%

Time (n) = 18 ÷ 6 = 3

Principal = 12,000

So, after 18 months the principal becomes

⇒ 12000 (1 + 10/100)³

⇒ Rs. 15972

Interest accumuted in 18 months = Rs. (15972 - 12000) = Rs. 3972

So, the difference between the interest accumulated = Rs. (3972 - 3840) = Rs. 132

∴ The difference between the compound interest compounded yearly and compounded half yearly for 18 months at 20% per annum on a sum of Rs. 12,000 is Rs. 132.

Alternate Method Formulae used:

CI_{half yearly} – CI_yearly = P[(1 + (r/200))²ⁿ – (1 + (r/100))ⁿ]

CIhalf yearly – CIyearly = 12000[(1 + (20/200))2(1.5) – (1 + (20/100))1.5]

CIhalf yearly – CIyearly = 12000 [(1 + (1/10))³– (1 + (1/5))1.5]

CIhalf yearly – CIyearly = 132

Shortcut Trick Put θ = 45° 

$\rm \frac{(sin 45+sec45)^2+(cos45+cosec45)^2}{(1+sec45 \ cosec45)^2}$

⇒ $\rm \frac{(1/\sqrt 2 + \sqrt 2)^2+(1/\sqrt 2+ \sqrt 2)^2}{(1+ \sqrt 2 \sqrt 2)^2}$

⇒ $\rm \frac{(3/\sqrt 2)^2+(3/\sqrt 2)^2}{(1+ 2)^2}$

⇒ [(9/2) + (9/2)]/9

⇒ (9/9) = 1

Alternate Method

Given:

0° < θ < 90°

Concept used:

1/Sinθ = Cosecθ

1/Cosθ = Secθ

Sin²θ + Cos²θ = 1

(A + B)² = A² + 2AB + B²

Calculation:

Now,

(Sinθ + secθ)² + (Cosθ + Cosecθ)²

⇒ (Sinθ + 1/Cosθ)² + (Cosθ + 1/Sinθ)²

⇒ Sin²θ + 2 × Sinθ × (1/Cosθ) + 1/Cos²θ + Cos2​θ + 2 × Cosθ × (1/Sinθ) + 1/Sin²θ

⇒ (Sin2θ + Cos2​θ) + {(2Sinθ/Cosθ) + (2Cosθ Sinθ)} + (1/Cos2θ + 1/Sin2θ)

⇒ 1 + {2/(Cosθ × Sinθ)} + {1/(Cos2θ × Sin2θ)}

⇒ (1 + 2 × Secθ × Cosecθ + Sec²θ × Cosec²θ)

⇒ (1 + Secθ Cosecθ)²

So,

$\rm \frac{(sin θ+secθ)^2+(cosθ+cosecθ)^2}{(1+secθ \ cosecθ)^2}$

⇒ (1 + Secθ Cosecθ)2/(1 + Secθ Cosecθ)2

⇒ 1

∴ The required value of $\rm \frac{(sin θ+secθ)^2+(cosθ+cosecθ)^2}{(1+secθ \ cosecθ)^2}$ is 1.

Given:

Cost price of the article = Rs. 920

Marked price of the article = Rs. 1472

Discount = x%

Gain = 20%

Concept used:

Selling price = Cost price × (1 + Gain percentage/100)

Selling price = Marked price (1 - discount percentage/100)

Cost price/Marked price = (100 - Discount%)/(100 + Gain%)

Calculation:

So, the selling price of the article = 920 × 1.2 = Rs. 1,104

According to the question,

1472 (1 - x%) = 1104

⇒ (1 - x%) = 0.75

⇒ x = 25

∴ The required value of x is 25.

 Shortcut Trick

Cost price/Marked price = (100 - Discount%)/(100 + Gain%)

⇒ 920/1472 = (100 - Discount%)/(100 + 20) 

⇒ (920/1472) × 120 = 100 - Discount%

⇒ 75 = 100 - Discount%

⇒ Discount% = 100 - 75 = 25

∴ The required value of x is 25.

Given:

The surface area of the cube is 13.5 m2

Concept used:

If the A unit is the measure of a cube's each side, then its surface area is 6A² unit² and the measure of its longest diagonal is A√3 unit. 

Calculation:

Let the measure of each side of the cube be A meter.

According to the question,

6 × A² = 13.5 

⇒ A = 1.5 

∴ Longest diagonal = A√3 = 1.5√3

∴ The length of its diagonal is 1.5√3 m.

Given:   

x4 - 62x2 + 1 = 0

x > 0

Concept used:

(x + y)2 = x2 + y2 + 2xy

(x + y)3 = x3 + y3 + 3xy(x + y)

Calculation:

x4 - 62x2 + 1 = 0

⇒ x² - 62 + x^-2 = 0 (Multiplying both side by x^-2)

⇒ x2 + x-2 + 2 = 62 + 2 

⇒ (x + x^-1)² = 64

⇒ (x + x-1) = 8      ....(1)

⇒ (x + x-1)3 = 512 (Taking cube on both sides)

⇒ x³ + x^-3 + 3 × (x + x-1) = 512

⇒ x3 + x-3 + 3 × 8 = 512 (From 1)

⇒ x3 + x-3 = 512 - 24

⇒ x3 + x-3 = 488

∴ The required value of (x3 + x-3) is 488.

Given:

AB is the diameter of the circle whose centre is at O.

AB has been extended to P.

PT is the tangent at C.

∠BPT = 28°

Concept used:

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

The sum of all angles of a triangle is 180°. 

Calculation:

OC⊥PT at C

So, ΔOCP is a right-angled triangle at C.

Then, ∠COP = 90° - 28° = 62° 

Here, OA = OB = Radii of the circle

So, ΔOBC is an isosceles triangle.

Then, ∠BCO = ∠CBO = (180 - 62)° ÷ 2 = 59° 

Here, ABP is a straight line.

So, ∠CBP = (180 - 59)° = 121° 

Here, ΔBCP is triangle.

So,

∠BCP + ∠CBP + ∠BPC = 180°

⇒ ∠BCP = 180° - 28° - 121° 

⇒ ∠BCP = 31°

∴ The measure of ∠BCP is 31°.

Given: 

x8 - 34x4 + 1 = 0

x > 0

Concept used:

(x + y)² = x² + y² + 2xy

(x - y)³ = x³ - y³ - 3xy(x - y)

Calculation:

x8 - 34x4 + 1 = 0

⇒ x⁴ - 34 + x^-4 = 0 (Multiplying both side by x-4)

⇒ x4 + x-4 = 34

⇒ x4 + x-4 + 2 = 34 +2 

⇒ (x² + x^-2)² = 36

⇒ (x2 + x-2) = 6

⇒ x2 + x-2 - 2 = 6 - 2

⇒ (x - x^-1)² = 4

⇒ (x - x-1) = 2

⇒ (x - x-1)³ = 2³

⇒ (x³ - 3 × (x - x^-1) - x^-3) = 8

⇒ (x3 - (3 × 2) - x-3) = 8

⇒ (x3- x-3) = 8 + 6

⇒ (x3- x-3) = 14

∴ The required value of (x3- x-3) is 14.

Shortcut TrickIf x4 + 1/x4 = P, then x2 + 1/x2 = √{P + 2}

If x2 + 1/x2 = Q, then x - 1/x = √{Q - 2} =

x8 - 34x4 + 1 = 0 

divided by x4 on both sides,

x4 + 1/x4 = 34 

x2 + 1/x2 = √{P + 2} = √{34 + 2} = √36 = 6

x - 1/x = √{P - 2} = √{6 - 2} = 2

x3 - 1/x3 = (x - 1/x)3 + 3(x - 1/x)

⇒ (2)3 + 3 × 2 = 8 + 6 = 14

Given:

Original selling price = Rs. 455

If he sells it for Rs. 490, then he would gain an amount four times the loss.

Desired gain = 25%

Concept used:

Loss = Cost price - Selling price

Gain = Selling price - Cost price

Selling price = Cost price × (1 + gain percentage/100)

Calculation:

let the cost price of the article be CP.

According to the question,

4 × (CP - 455) = (490 - CP)

⇒ CP = 462

Now, to make 25%, the shopkeeper has to it at  = (462 × 1.25) = Rs. 577.50

∴ At Rs. 577.50 he should sell the article to gain 25%.

Given:

The tank is filled in 4 hours by three pipes A, B, and C.

Pipe C is $1\frac{1}{2}$ times as fast as B and B is 3 times as far as A

Concept used:

The capacity of that tank  = the rate of flow of pipe C × time taken by the pipe

Calculation:

Given that, rate of flow C = (3/2)B and B = 3A

Let, pipe A fills the tank = 2Q unit per hour

Pipe B fills the tank = 3A = 3 × 2Q = 6Q unit per hour

Pipe C fills the tank = (3/2)B = (3/2) × 6Q = 9Q unit per hours

Together they can fill = (2Q + 6Q + 9Q) = 17Q unit per hour

Now, the capacity of that tank = 4 × 17 = 68Q unit per hour

So, Pipe A will take to fill that tank = 68Q ÷ 2Q = 34 hours

∴ 34 hours will pipe A alone take to fill the tank.

Shortcut TrickEfficiency of the pipes,

So, total work = 17 × 4 = 68 units

A will take 68/2 = 34 hours

Calculation:

Marks obtained by C in science = 85% × 80 = 68

Marks obtained by D in science = 75% × 80 = 60

Marks obtained by F in science = 65% × 80 = 52

Total marks obtained by C,D & F in science = 68 + 60 +52 = 180

Marks obtained by B in science = 75% × 80 = 60

Marks obtained by B in Hindi = 68% × 75 = 51

Marks obtained by B in Social studies = 49% × 100 = 49

Total marks obtained by B in Science, Hindi & Social Studies = 60 + 51 + 49 = 160

So,

The total marks obtained by students C, D, and F in Science is more than the total marks obtained by B in Science, Hindi and Social Studies by 

⇒ {(180 -160) /160} × 100%

⇒ 12.5%

∴ The total marks obtained by students C, D and F in Science is more than the total marks obtained by B in Science, Hindi, and Social Studies by 12.5%.

Given:

$\rm\left(\frac{3}{4}-\frac{1}{4}÷\frac{1}{4}\ of\ \frac{2}{5}\right)÷\left(\frac{3}{4}÷\frac{2}{3}\ of\ \frac{3}{5}\right)$

Concept used:

Calculation:

$\rm\left(\frac{3}{4}-\frac{1}{4}÷\frac{1}{4}\ of\ \frac{2}{5}\right)÷\left(\frac{3}{4}÷\frac{2}{3}\ of\ \frac{3}{5}\right)$

⇒ (3/4 - 1/4 ÷ 1/10) ÷ (3/4 ÷ 2/5)

⇒ (3/4 - 5/2) ÷ (15/8)

⇒ (-7/4) ÷ (15/8)

⇒ (-14/15)

∴ The required value of $\rm\left(\frac{3}{4}-\frac{1}{4}÷\frac{1}{4}\ of\ \frac{2}{5}\right)÷\left(\frac{3}{4}÷\frac{2}{3}\ of\ \frac{3}{5}\right)$ is (-14/15).

Given: 

The ratio among A, B, C, and D is 4 ∶ 12 ∶  30 ∶ 45 respectively.

The difference between the shares of A and D is Rs. 5535

Concept used:

Ratio proportion

Calculation:

Let the common ratio among them be P.

So, 

The share of A = Rs. 4P

The share of B = Rs. 12P

The share of C = Rs. 30P

The share of D = Rs. 45P

Total sum = (45 + 30 + 12 + 4)P = Rs. 91P

According to the question,

45P - 4P = 5535

⇒ 41P = 5535

⇒ P = 135

⇒ 91P = 12285

∴ The total sum is Rs. 12285.

Given:

The boat takes 16 hours to 150 km downstream and 150 km upstream.

Speed of the motorboat in the still water is 20 kmph

Concept used:

When going downstream, the speed of the boat and the flow of the river are added to calculate the net speed.

When going upstream, we take the difference between the speed of the boat and the flow of the river as the net speed. 

Time = Distance / Speed

(A + B) (A - B) = A² - B²

Calculation:

Let the flow of the river be R kmph.

According to the question,

{150 / (20 + R)} + {150 / (20 - R)} = 16

⇒ {150 × (20 + R + 20 - R)} / (20² - R²) = 16

⇒ (150 × 40) / (202 - R2) = 16

⇒ 400 - R² = 375

⇒ R² = 25

⇒ R = 5

∴ The flow of the river is 5 kmph.

Given:

9 digit number 7698x138y is divisible by 72

$√{4x+y}$

Concept used:

A number is divisible by 8 when the number formed by the last three digits of the number is divisible by 8.

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

Calculation:

7698x138y is divisible by 72 when it is divisible by 8 as well as 9.

So, it must be divisible by 8 as well as 9.

By divisibility rule of 8, we can clearly say that y is equal to 4. Since in the range of 380 to 389, there is only one number that is divisible by 8, and that is 384.

So, the given number becomes 7698x1384.

Now, the sum of digits of 7698x1384 = 46 + x

So, in order to be divisible by 9, x has to be (54 - 46) = 8 (∵The nearest multiple of 9 to 46 is 54)

Now,

√(4x + y)

⇒ √36

⇒ 6

∴ The required value of $√{4x+y}$ is 6.

Given:

$\rm \frac{sinθ+cosθ}{sinθ-cosθ}=5$

Concept used:

Sin² θ = 1 - Cos² θ

Sec² θ = 1 + tan² θ

Sin θ / Cos θ = tan θ

Componendo - Dividendo method

For any fraction p/q = r/s

(p + q) / (p - q) =  (r + s) /  (r - s)

Calculation:

$\rm \frac{sinθ+cosθ}{sinθ-cosθ}=5/1$

Using Componendo - Dividendo method

⇒ {(Sin θ + Cos θ) + (Sin θ - Cos θ)} / {(Sin θ + Cos θ) - (Sin θ - Cos θ)}  = (5 + 1) / (5 - 1)

⇒ Sin θ / Cos θ = 3/2

⇒ tan² θ = 9/4

Now,

Sec² θ = 1 + 9/4 = 13/4

Cos² θ = 4/13

So, Sin² θ = 1 - (4/13) = 9/13

Then,

$\frac{4sin^2θ+3}{2cos^2θ+2}$

⇒ (4 × 9/13 + 3) / (2 × 4/13 + 2)

⇒ 75/34

∴ The required value of $\frac{4sin^2θ+3}{2cos^2θ+2}$ is 75/34.

Given:

ΔABC is a right-angled triangle at B.

BD = 5 cm

AD = 13 cm

AC = 37 cm

Concept used:

If ΔABC is a right-angled triangle at B & AC is the hypotenuse, then according to Pythagoras theorem,

AB2 + BC2 = AC2

Calculation:

Here, ΔABD is also a right-angled triangle.

So,

AB² + BD² = AD²

⇒ AB2 = 169 - 25

⇒ AB = 12

We know,

AB2 + BC2 = AC2

⇒ BC² = AC2 - AB2

⇒ BC2 = 37² - 12²

⇒ BC = 35

⇒ BD + DC = 35

⇒ DC = 30

∴ The measure of DC is 30 cm.

Given:

Centre O

The points A, B, C, and D in this order are concyclic.

BD is the diameter

∠BAC = 22°

Concept used:

The angle formed on circumference forming on diameter is 90° 

The angle at the center formed on the same arc is twice the angle on the same arc forming at the circumference. 

Calculation:

Here, according to the concept, 

∠ BAD = 90°

⇒ ∠ BAC + ∠ CAD = 90° 

⇒ ∠ CAD = 90° - 22° = 68° 

Now we know that, 

∠ COD = 2 × ∠ CAD 

⇒ ∠ COD = 2 × 68 = 136°   

∴ The measure of ∠COD is 136°.

Given:

The reciprocal of a positive fraction got typed in place of itself, and thereby its value got reduced to $\frac{175}{4}\%$.

Concept used:

Application of percentage 

Calculation:

Let the original number be x.

So, the reciprocal of the original number = 1/x

According to the question,

 $x - \frac{1}{x}=\frac{175x}{400}$

⇒ $\frac{x^2 - 1}{x}=\frac{175x}{400}$ 

Cross multiplying

400(x² - 1) = 175x²

400x² - 175x2 = 400

⇒ (x)2 = 400/225

⇒ (x) = 20/15 (∵ the fraction should be positive)

⇒ (x) = 4/3

∴ The value of the fraction is 4/3.