SSC CGL 2020 Tier-I Official Paper (Held On : 18 Aug 2021 Shift 1) (Previous Year Paper)

The logic followed here is:

Option (1)   Arthritis → It is a disease of bone.

Option (2)   Gout → It is a disease of bone.

Option (3)   Hypertension → It is not a disease of bone.

Option (4)   Rickets → It is a disease of bone.

Hence, “Hypertension” is an odd one.

Additional Information

• The main symptoms of arthritis are joint pain and stiffness, which typically worsen with age.
• Gout is a disorder in which deposits of uric acid crystals accumulate in the joints because of high blood levels of uric acid (hyperuricemia).
• Rickets is the softening and weakening of bones in children, usually because of an extreme and prolonged vitamin D deficiency. Rickets is a condition that affects bone development in children.
• Hypertension ̶ or elevated blood pressure ̶ is a serious medical condition that significantly increases the risks of heart, brain, kidney and other diseases.

The table is alphabets place value:

The pattern followed here is:

Step 1: All consonant place value in the alphabet series is coded as numeric values.

Step 2: Opposite letter place values of vowels are coded as numeric values.

'FORENSIC' is coded as '61218221419183'

'DORM' is coded as '4121813'

Similarly, 

CARAMEL = ?

Hence, the correct answer is "3261826132212".

Let the numbers is x, y and z.

Given :-

The total of three numbers is 240

So, x + y + z = 240 → eq. (i)

The second number is four times the first number.

y = 4x

The third number is three times the first number.

z = 3x

Put the value of y and z in eq. (i)

x + 4x + 3x = 240

8x = 240

x = 30

So,

Second number is y = 4x = 4 × 30 = 120

Third number is z = 3x = 3 × 30 = 90

Average of numbers = Sum of total number ÷ total numbers

(30 + 120 + 90) ÷ 3 = 240 ÷ 3 = 80

Hence, average of that three number is ‘80’

 Shortcut Trick

Average of numbers = Sum of total number ÷ total numbers

Sum of total number is given 240

So,

Average of numbers = 240 ÷ 3 = 80

Hence, average of that three number is ‘80’.

Opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surface are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces:-

 

Option (1): D and F → Yes, they are opposite to each other.

Option (2): A and D → No, they are not opposite to each other.

Option (3): E and B → No, they are not opposite to each other.

Option (4): E and C → No, they are not opposite to each other.

So, when the table will be constructed, the letters ‘D and F’ will be opposite to each other.

Hence, ‘D and F’ is correct answer.

Given:

Statements:

Some bowls are cups.

All cups are glasses.

Some glasses are plates.

All plates are utensils.

The least possible diagram for the given statements is as follows

Conclusions:

I. All bowls cannot be utensils → False (It is possible but not definite)

II. All glasses cannot be utensils → False (It is possible but not definite)

Hence, neither conclusion I nor II follows.

​The image obtained when the paper is unfolded is,

Hence, option 3 is the correct answer.

Given:

39 : 27

The pattern followed here is,

39 → 3 × 9 = 27

Similarly,

43 : ?

43 → 4 × 3 = 12

Hence, "12" is correct answer.

The logic followed here is:

Swan : Cygnet → A baby swan is called a cygnet.

Similarly,

Turkey : Poult →  A baby turkey is called poults.

Hence, ‘Turkey : Poult’ is the correct answer.

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

Hence, "option (3)" is the correct answer.

The logic followed here is:

Pauper : Rich → Opposite of Pauper is Rich.

Similarly,

Vengeful : forgiving/ remissive → Opposite of Vengeful is forgiving/remissive .

Hence, ‘Remissive’ is the correct answer.

The codes have been assigned as follows,

YOU TOOK MY PLACE IN’ is written as ‘COU POON LC QVAKE IJ’ →

Each word is given a particular code as per which the above alphabets are coded.

Similarly,

COMPILE →

Alternate Method

Y = C

O = O

U = U

T = P

O = O

O = O

K = N

M = L

Y = C

P = Q

L = V

A = A

C = K

E = E

I = I

N = J

For the desired answer we can get the code from the above codes:

C = K

O = O

M = L

P = Q

I = I

L = V

E = E

Hence, COMPILE is coded as ‘KOLQIVE’.

Given :- r_ uktrj_ kt_ juk_rju_trj_kt

By checking options and substituting accordingly.

1. u, j, r, t, j, u → r u u k t - r j j k t - r j u k t - r j u j t - r j u k t

2. j, r, u, k, t, u → r j u k t - r j r k t - u j u k k - r j u t t - r j u k t

3. j, r, u, t, u, k → r j u k t - r j r k t - u j u k t - r j u u t - r j k k t

4) j, u, r, t, k, u → r j u k t - r j u k t - r j u k t - r j u k t - r j u k t

• Option (4) gives a pattern of r j u k t - r j u k t - r j u k t - r j u k t - r j u k t

Hence, ‘j, u, r, t, k, u’ is the correct answer

The Logic here is as follows:

(First Number × second number) × 4 = Third Number

In (7, 9, 252)

(First Number × second number) × 4

= (7 × 9) × 4

= 63 × 4

= 252 = Third Number

Now check the all options,

Option (1) (6, 9, 188)

(First Number × second number) × 4

= (6 × 9) × 4

= 54 × 4

= 216 ≠ Third Number

Option (2) (12, 10, 260)

(First Number × second number) × 4

= (12 × 10) × 4

= 120 × 4

= 480 ≠ Third Number

Option (3) (8, 11, 352)

(First Number × second number) × 4

= (8 × 11) × 4

**= 88 **× 4

**= 352 = **Third Number

Option (4) (6, 8, 212)

(First Number × second number) × 4

= (6 × 8) × 4

= 48 × 4

= 192 ≠ Third Number

Hence, the correct answer is "(8, 11, 352)".

Alternate MethodThe pattern followed here is:

(1st number + 2nd number)² - (1st number - 2nd number)² = 3rd number

(7, 9, 252) → (7 + 9)² - (7 - 9)² = 256 - 4 = 252

Similarly, 

Option 3) (8, 11, 352)

(8 + 11)² - (8 - 11)² = 361 - 9 = 352

Hence, the correct answer is "(8, 11, 352)".

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

1. Centre figure is rotated in 90° Anti-clockwise direction.

2. Triangle shape is move in each corner of square Anti-clockwise direction and every time when it is move has become dark or no fill respectively.

Hence, ‘option 4’ is the correct answer.

The table of alphabets place value:

The pattern followed is,

All follow the same pattern, except ‘ZTOI’.

Hence, “ZTOI” is the odd – cluster.

According to the sequence in the dictionary:

The correct order of the given words is:

2. Recede
3. Recliner
4. Recognition
5. Reconcile
6. Recorder
7. Recreation

Hence, the correct answer is "2, 4, 6, 5, 3, 1".

The logic is here is:

Sum of all digits both sides should be equal.

Option (1): 406321 : 493

Now, follow the logic:

4 + 0 + 6 + 3 + 2 + 1 : 4 + 9 + 3

16 : 16 (LHS = RHS)

Option (2): 324335 : 577

Now, follow the logic:

3 + 2 + 4 + 3 + 3 + 5 : 5 + 7 + 7

20 : 19 (LHS ≠ RHS)

Option (3): 253471 : 778

Now, follow the logic:

2 + 5 + 3 + 4 + 7 + 1 : 7 + 7 + 8

22 : 22 (LHS = RHS)

Option (4): 111617 : 278

Now, follow the logic:

1 + 1 + 1 + 6 + 1 + 7 : 2 + 7 + 8

17 : 17 (LHS = RHS)

The option (2) is ratio not equal to other option.

Hence, pair “324335 : 577” is an odd one.

The embedded part of this image is:

Hence, option (2) is the correct answer.

Table show alphabet serial number –

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The logic is shown below –

Hence, “ZACP” is complete in that series.

According to BODMAS rule

Given equation 14 * 7 * 39 * 133 * 19 * 130

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

14 ÷ 7 + 39 - 133 × 19 = 130

By BODMAS rule

2 + 39 – 133 × 19 = 130

2 + 39 – 2527 = 130

41 – 2527 = 130

-2486 = 130 (LHS ≠ RHS)

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

14 × 7 - 39 + 133 ÷ 19 = 130

14 × 7 - 39 + 7 = 130

98 - 39 + 7 = 130

105 – 39 = 130

66 = 130 (LHS ≠ RHS)

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

14 × 7 + 39 - 133 ÷ 19 = 130

14 × 7 + 39 - 7 = 130

98 + 39 – 7 = 130

137 – 7 = 130

130 = 130 (LHS = RHS)

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

14 ÷ 7 - 39 + 133 × 19 = 130

2 - 39 + 133 × 19 = 130

2 - 39 + 2527 = 130

2529 - 39 = 130

2490 = 130 (LHS ≠ RHS)

Hence, the answer is “×, +, -, ÷, =”.

Given:

 

Here the pattern followed in each column is:

1^st number × 2^nd number = 3^rd number

Column 1: 3 × 23 = 69

Column 2: 5 × 27 = 135

Similarly

Column 3: 7 × 31 = 217

Hence, “217” is correct answer.

The Venn diagrams best represent the relationship between - Universe, Pluto, Solar system

figures are shown below:

.

Pluto is a part of the solar system and the solar system is eventually part of the universe.

Hence, ‘option 1’ is the correct answer.

Note: In the official answer key of SSC CGL, option 2 was given as the answer which is wrong. According to NASA, dwarf planets are considered a part of the solar system. 

Confusion PointsAlthough, Pluto is not a planet now; but, according to the definition of the Solar system given by NASA,  Our solar system consists of our star, the Sun, and everything bound to it by gravity – the planets Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune; dwarf planets such as Pluto; dozens of moons; and millions of asteroids, comets, and meteoroids.

The logic is shown below –

Hence, “510” is the missing term that completes the series

Preparing the family tree using the following symbols,

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

1. Ramesh is the father of Manideep.

2. Ramesh has only two children. Manideep is the brother of Niharika.

3. Niharika is the daughter of Kavita.

4. Ananya is the granddaughter of Kavita. Sujit is the father of Ananya.

Hence, Sujit is “Brother-in-law” of Manideep.

The number of triangles in the given figure is:

 

So, there are a total of 12 triangles in the figure.

Hence, ‘12’ is the correct answer.

Mistake PointsHere both are not triangles.

The correct answer is 1944.

• In 1944, Japan invade India resulting in the Battle of Imphal.

Key Points

• The Battle of Imphal took place from March to July 1944 in the vicinity of the city of Imphal, the capital of the state of Manipur in northeastern India.
• Japanese forces attempted to destroy the Allied forces at Imphal and invade India, but were driven back to Burma with heavy losses.
• Together with the Battle of Kohima on the road, by which the Allied forces at Imphal were relieved, the battle was the turning point of the Burma Campaign, which was part of the South-East Asian Theater of World War II.
• The defeats at Kohima and Imphal were the largest defeats to date in Japanese history, with many Japanese deaths from hunger, disease and exhaustion during their retreat.

Additional Information

• The operation to take Imphal was named U-go by the Japanese Army.
• It consisted of elements from the 31st Infantry Division of the Japanese Army and as well as units from the Indian National Army, who were in primarily support and scouting roles.
• The Japanese Army crossed into India on the night of 7th March and engaged the British Indian forces guarding the frontiers the morning of 8th March 1944.

The correct answer is Narendra Modi.

• Prime Minister Narendra Modi received the Global Goalkeeper award by the Bill and Melinda Gates Foundation for the Swachh Bharat Abhiyan.

Key Points

• The Goalkeepers Award program rewards winners for their work and inspires more action and innovation at a time when it is needed most.
• The Campaign Award celebrates an individual that has raised awareness or built a community in support of a Global Goal-related cause, inspiring action and creating change.

Additional Information

• Narendra Modi:
• He is an Indian politician serving as the 14th prime minister of India since 2014.
• Narendra Modi was the chief minister of Gujarat from 2001 to 2014 and is a Member of Parliament from Varanasi.
• Modi led the BJP in the 2014 general election which gave the party a majority in the Indian lower house of parliament, the Lok Sabha, the first time for any single party since 1984.
• Narendra Modi became the first Prime Minister born after India's independence from the British Empire in 1947.

Important Points

The correct answer is Lewis Hamilton.

• In 2020, Lewis Hamilton became the most successful F1 driver with the most career wins, overtaking Michael Schumacher.

Key Points

• Six-times world champion Lewis Hamilton became the most successful Formula One driver of all time in terms of race wins with a dominant 92nd career victory at the Portuguese Grand Prix.
• Lewis Hamilton was born on 7 January 1985 in Stevenage, Hertfordshire, England.
• He currently competes in Formula One for Mercedes, having previously driven for McLaren from 2007 to 2012.
• Hamilton began his car racing career in the 2001 British Formula Renault Winter Series, finishing fifth in the standings.

Additional Information

Lewis Hamilton Awards are:

The correct answer is Pilibhit Tiger Reserve.

• In 2020, Pilibhit tiger reserves won the ‘TX2 Award’ for its efforts to increase the tiger population.

Key Points

• The Pilibhit Tiger Reserve (PTR - Uttar Pradesh) has bagged the international award TX2 for doubling the number of tigers in the past four years. 
• ​Pilibhit Tiger Reserve is located in the Pilibhit district of Uttar Pradesh and was notified as a tiger reserve in 2014.
• It lies along the India-Nepal border in the foothills of the Himalayas and the plains of the Terai in Uttar Pradesh. It is part of the Terai Arc Landscape.
• About TX2 Award:
• ​Launched recently, these awards were open to submissions from any site in a tiger range country that has achieved remarkable measurable progress since 2010.
• It goes to one site that has achieved a remarkable and measurable increase in its tiger population since 2010.

Additional Information

 

In 2021

• TX2 Award: Bardia National Park, Nepal
• TX2 Award: Sathyamangalam Tiger Reserve, India
• Conservation Excellence Award: Khata Forest Conservation Area (India & Nepal)

The correct answer is Trade and Industry.

• Rajnikant Devidas Shroff was awarded the Padma Bhushan in the field of Trade and Industry in January 2021.

Key Points

• Rajnikant Devidas Shroff is an Indian businessperson and is the founder and chairman and UPL Limited.
• In 2020, he was ranked as the 93rd richest person in India, with a net worth of $1.5 billion, according to Forbes.
• Shroff is the only industrialist to receive Padma Bhushan in 2021.
• He is considered India's Crop Protection King.

Additional Information

• Padma Vibhushan **(**2021):
• Shinzo Abe
• S. P. Balasubrahmanyam (posthumous)
• Belle Monappa Hegde
• Narinder Singh Kapany (posthumous)
• Wahiduddin Khan
• B. B. Lal
• Sudarshan Sahoo

The correct answer is The net magnetic flux through any closed surface is zero.

Key Points

• The net magnetic flux through any closed surface will be zero.

Additional Information

• Gauss' Law for Magnetism:
• Gauss' Law for magnetism applies to the magnetic flux through a closed surface. In this case, the area vector points out from the surface.
• Because magnetic field lines are continuous loops, all closed surfaces have as many magnetic field lines going in as coming out. Hence, the net magnetic flux through a closed surface is zero.
• Net flux = ∫ B • dA = 0
• Gauss' Law for charges was a very useful method for calculating electric fields in highly symmetric situations.
• Gauss' Law for magnetism is considerably less useful, but we'll come up with another law that enables us to calculate magnetic fields in highly symmetric situations.

Magnetic flux:

• Magnetic flux is defined as the number of magnetic field lines passing through a given closed surface.
• It provides the measurement of the total magnetic field that passes through a given surface area.
• It is a scalar quantity.
• The SI unit of magnetic flux is Weber (Wb).

​Magnetic flux associated with any area is given as,

⇒ ϕB = BAcosθ

Where ϕB = magnetic flux, B = magnetic field intensity, A = area, and θ = angle between B and A

The correct answer is Bengal.

• Alivardi Khan was a Nawab of  Bengal.

Key Points

• Alivardi Khan was the Nawab of Bengal from 1740 to 1756.
• He toppled the Nasiri dynasty of Nawabs and assumed power himself.
• He is also known for his victory during the Battle of Burdwan against the Maratha Empire during the Maratha invasions of Bengal.

Additional Information

The correct answer is Desert.

• Plants grown in Desert places take up carbon dioxide during the night.

Key Points

• The desert plants which grow in semi-arid conditions fix atmospheric CO₂ to form malic acid in the dark.
• These plants accumulate organic acid intermediate during the night to be used during the daytime.
• This pathway is called Crassulacean acid metabolism (CAM) and the plants which carry out crassulacean metabolism are termed CAM plants.

Additional Information

• Different Parts of a Plant: A detailed description of each of the parts of plants is mentioned below:
• Roots: Roots are the most important part of a plant as they are responsible for transferring the necessary nutrients to the plant. They are the agents responsible for delivering water and minerals to the plants.
• Stems: Stems are also support systems for the plants. Their main function is to act as delivery agents for the nutrients and water stored in the roots and transfer them to the other plant parts in the form of glucose.
• Leaves: Leaves are a fundamental part of a plant as all the necessary food for the plants are stored in the leaves.
• Flowers: Flowers are known as the reproductive products of plants. They are mostly responsible for producing fruits.
• Fruits: Fruits are the products of reproduction in plants. The most essential component from which reproduction starts, that is the seed, is present in the fruit.
• Seeds: Seeds are the main agents for reproduction. They can be found most commonly in fruits from where they germinate and develop into new plants.

The correct answer is Silver.

• Bombay Stock Exchange became the first stock exchange in India to launch commodity derivatives contracts in gold and silver.

Key Points

• Bombay Stock Exchange (BSE), is an Indian stock exchange located on Dalal Street in Mumbai.
• Bombay Stock Exchange is Established in 1875 by cotton merchant Premchand Roychand.
• Bombay Stock Exchange is the oldest stock exchange in Asia, and also the tenth oldest in the world.
• The Bombay Stock Exchange is the 9th largest stock exchange with an overall market capitalization of more than Rs 255.003 lakh crore, as of October 2021.

Additional Information

• BSE is Asia's first and the Fastest Stock Exchange in the world with a speed of 6 microseconds and one of India's leading exchange groups.
• In 2013, BSE upgraded its technology platform to Bolt Plus, which is based on the business architecture of the global giant Deutsche Borse.
• As of now January 2022 the chairman of the Bombay Stock Exchange is Vikramajit Sen.

The correct answer is IFSC.

• IFSC is an alphanumeric code that uniquely identifies a bank-branch participating in the NEFT system.

Key Points

• National Electronic Funds Transfer (NEFT) is a mode of online funds transfer that is introduced by the Reserve Bank of India (RBI).
• It quickly transfers money between banks throughout India.
• A bank branch must be NEFT enabled for a customer to be able to transfer the funds to another party.
• It was started in November 2005, the setup was established and maintained by Institute for Development and Research in Banking Technology.

Additional Information

• IFSC (Indian Financial System Code) is an 11 digit alphanumeric code that is used to identify the bank branch of your account.
• The first 4 characters of the IFSC code represent the name of the bank, the fifth character is 0 and the last 6 numbers define the branch code of the bank.

Important Points

• STP: Segmentation, targeting, and positioning.
• SFMS: Structured Financial Messaging System.
• RTGS: Real-Time Gross Settlement.

The correct answer is Breathing root.

• A breathing root is NOT a storage root.

Key Points

• Breathing roots are respiratory roots found in halophytes such as mangroves.
• They often grow in saline swamps, so breathing roots come out of the water to consume oxygen.
• Pneumatophores, commonly found in mangrove species that grow in saline mudflats, are lateral roots that grow upward out of the mud and water to function as the site of oxygen intake for the submerged primary root system.

Additional Information

The correct answer is Samhita.

• The main collections of Vedic hymns are called Samhita.

Key Points

• The Rigveda Samhita is the oldest extant Indic text.
• It is a collection of 1,028 Vedic Sanskrit hymns and 10,600 verses in all, organized into ten books (Sanskrit: mandalas).
• The hymns are dedicated to Rigvedic deities.
• Samhitas are ritualistic texts, and they explain the social and religious importance of rituals.
• Each Samhita has added texts called Brahmanas, which have commentaries on the hymns and rituals.
• Each brahmana has an Aranyaka (forest text) and an Upanishad.
• The Aranyakas contain mystical ritual instructions to be undertaken in secret by the sages who live in the forests.
• Upanishads deal with philosophical inquiries.

Important Points

• Sutra:
• ​Sutra in Indian literary traditions refers to an aphorism or a collection of aphorisms in the form of a manual or, more broadly, a condensed manual or text.
• Sutras are a genre of ancient and medieval Indian texts found in Hinduism, Buddhism and Jainism.
• Pad:
• Pad refers to a word or foot in the context of Vedic texts. In particular, each verse (Rik) of a hymn can be broken down into multiple padas (feet).
• ​Mukh:
• Mukh means face or mouth in Sanskrit.

The correct answer is 1952.

• In 1952, the Rajya Sabha was first constituted.

Key Points

• The Council of States also known as Rajya Sabha first constituted on 3 April 1952.
• Elections were held in 1952 to elect members from various states of Independent India.
• Dr. S Radhakrishnan was the First Chairman of the Rajya Sabha, also the First Vice President of the Nation.

Additional Information

• On 23 August 1954, the Chairman of Rajya Sabha made an announcement in the House that the Council of States would now be called Rajya Sabha in Hindi.
• The Rajya Sabha met for the first time on 13 May 1952.
• Dr. S. Radhakrishnan was the first Chairman of the Rajya Sabha.
• Shri S. V Krishnamoorthy Rao was the first Deputy Chairman of Rajya Sabha.
• At that time, Two hundred and fifty (250), out of which 238 are to be elected and 12 are to be nominated by the President of India is the maximum strength of Rajya Sabha.

The correct answer is Sigmund Freud.

• Sigmund Freud is the founder of the field of psychoanalysis.

Key Points

• Psychoanalysis, a method of treating mental disorders, is shaped by psychoanalytic theory, which emphasizes unconscious mental processes and is sometimes described as depth psychology.
• The primary assumption of psychoanalysis is the belief that all people possess unconscious thoughts, feelings, desires, and memories.
• Freud’s psychoanalytic theory explains human personality as a series of stages that are formed through inner conflicts.

Additional Information

The correct answer is Maharashtra.

• The ‘Lezim’ dance form is peculiar to Maharashtra states.

Key Points

• Lezim is a group dance that is performed in formations of two or four in the villages of Maharashtra.
• Lezim performed in colorful costumes, the dance involves a dholki and all the dancers carry Lezim which an instrument with jingling cymbals.
• It is often played during the Ganesh festival.
• Other important dances of Maharashtra: Lavani, Nakata, Koli, Gafa, Dahikala.

Additional Information

The correct answer is green.

• The color of an emerald is generally is green.

Key Points

• Emeralds are prized for their vibrant green colors.
• Almost all natural emeralds have eye-visible inclusions. Inclusions are tiny growths that occur within the emerald as it is forming.
• In Rajasthan, emeralds have been found to occur at a number of places in districts Udaipur, Rajsamand, and Ajmer.

The correct answer is Brazil.

• ISRO’s Polar Satellite Launch Vehicle (PSLV) successfully launched a remote sensing satellite of Brazil country on 28th February 2021.

Key Points

• India’s Polar Satellite Launch Vehicle PSLV-C51 successfully launched Amazonia-1 along with 18 co-passenger satellites on February 28, 2021, from Satish Dhawan Space Centre SHAR, Sriharikota.
• Amazonia-1 is the optical earth observation satellite of the National Institute for Space Research (INPE).
• This satellite will provide remote sensing data to users for monitoring deforestation in the Amazon region and analysis of diversified agriculture across the Brazilian territory.

Additional Information

• ISRO:
• The Indian Space Research Organisation is the national space agency of India, headquartered in Bengaluru.
• It operates under the Department of Space (DOS) which is directly overseen by the Prime Minister of India, while the Chairman of ISRO acts as the executive of DOS as well.
• ISRO was established on 15 August 1969 and ISRO founder is Vikram Sarabhai.

Important Points

The correct answer is Gujarat.

• Gujarat states renamed the dragon fruit as ‘Kamalam’ in January 2021.

Key Points

• Dragon fruit is the fruit of a species of wild cactus indigenous to South and Central America, where it is called pitaya or pitahaya.
• Vietnam is the world’s largest producer and exporter of dragon fruit.
• The word Kamalam is Sanskrit for the Lotus.

Additional Information

• Gujarat:
• Animal - Asiatic Lion
• Bird - Greater Flamingo
• Flower - Marigold
• Tree - Banyan

The correct answer is Tropical deciduous forests.

• Sandalwood grows in Tropical deciduous forests.

Key Points

• The Sandalwood is a dry deciduous forest species native to China, India, Indonesia, Australia, and the Philippines.
• This small tropical tree grows to 20m high with redwood and a variety of dark colors of bark (dark brown, reddish and dark grey).
• Sandalwood occurs extensively mostly in the Eastern Ghats ranging from the Vellore district in the Northeast of Tamil Nadu to the Nilgiris in the west in the dry deciduous forests of the region.
• In Tamilnadu, only dead and drying sandal trees are brought to depots for rough cleaning and final cleaning.
• The final cleaned sandalwood is sold in a public auction in three sandalwood depots at Tiruppattur, Salem, and Sathyamangalam at regular intervals.

Additional Information 

The correct answer is Achanta Sharath Kamal.

• Achanta Sharath Kamal was the first Indian table tennis player ever to become nine times senior national champion as of January 2021.

Key Points

• Achanta Sharath Kamal is a professional table tennis player from India.
• He is the first Indian table tennis player ever to become nine times Senior National Champion hence breaking the record of eight times National Champion Kamlesh Mehta.
• In 2019 he was awarded the Padma Shri, India's fourth-highest civilian award.
• In the year 2007, he was the first Indian to win the Pyongyang Invitational Tournament held at Pyongyang, North Korea.

Additional Information

The correct answer is Karewas.

Key Points

• Karewas are thick deposits of glacial clay and other materials embedded with moraines.
• The Kashmir Himalayas are famous for Karewa formations, which are useful for the cultivation of Zafran, a local variety of saffron.
• Moraines are accumulations of dirt and rocks that have fallen onto the glacier surface or have been pushed along by the glacier as it moves.

Additional Information

• Duars:
• ​The Duars are the alluvial floodplains in eastern-northeastern India that lie south of the outer foothills of the Himalayas and north of the Brahmaputra River basin.
• Bhabars:
• ​Bhabhar is a region south of the Lower Himalayas and the Sivalik Hills in the Uttarakhand state of India.
• Duns:
• The longitudinal valley that lies in the middle of lesser Himalaya and the Shivalik is known as Duns.​

The correct answer is Kuchipudi.

• Siddhendra Yogi, a doyen of the Kuchipudi dance form, was lauded as Adi Guru.
• ​Kuchipudi, one of eight classical dance styles of India.
• Kuchipudi is indigenous to the state of Andhra Pradesh and differs from the other five classical styles by the inclusion of singing.
• Kuchipudi is a dance-drama performance art that originated in a village of Krishna district of Andhra Pradesh, India.

Key Points

• Siddhendra Yogi was an exceptional scholar and artist of the 14th century AD.
• The dance form of Kuchipudi saw a revolution during the Bhakti movement between the 11th and 13th centuries.
• Siddhendra Yogi covers the principles of dance of Natya Shastra, the Bible of all Indian classical dance styles.​

Additional Information

The correct answer is Prakash Javadekar.

• As of January 2021, Prakash Javadekar is the Union Minister for Information and Broadcasting.

Confusion Points

• As of January 2022, Anurag Thakur is the Union Minister for Information and Broadcasting.

Additional Information

The correct answer is Nandas.

• Chandragupta Maurya led a revolt against the Nandas and overthrew them.

Key Points

• In the 4th century B.C., Nanda kings ruled the Magadha dynasty and this dynasty was the most powerful kingdom of the north.
• A Brahman minister called Chanakya also known as Kautilya trained a young man i.e.Chandragupta Maurya.
• Chandragupta organized his own army and overthrew the Nanda king Dhana Nand in 322 B.C.In the 4th century B.C.

Additional Information

• Chandragupta Maurya:
• He was the architect of the Maurya Empire which controlled the plains of both the Indus and the Ganges, and which extended to the eastern and western oceans.
• He laid the foundation for an extensive and efficient system of centralized administration and tax-collection which formed the basis of his empire.
• Trade and agriculture were reformed and regulated, with the creation of infrastructure and standardization of weights and measures, and provisions were made for a large standing army.

Important Points

The correct answer is Force.

• Force is the external agency applied on a body to change its state of rest or uniform motion.

Key Points

• Newton's first law of motion:
• Newton's first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.
• This postulate is known as the law of inertia.
• The law of inertia was first formulated by Galileo Galilei for horizontal motion on Earth and was later generalized by René Descartes.

Additional Information

• In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter.
• Power is defined as the rate of doing work.
• It is the ratio of work done (W) and time taken (t).
• The SI unit of power is the watt (W), in honor of the physicist James Watt.
• In physics, energy is the quantitative property that must be transferred to a body or physical system to perform work on the body, or to heat it.

Total number of students appeared from school Q in 2017 = 350

Total number of students appeared from school S in 2018 = 400

Total = 750

Total number of students passed from school R in 2018 = 405

Total number of students passed from school T in 2014 = 225

Total = 630

Ratio = 750 : 630

⇒ 25 : 21

∴ Required answer is 25 : 21

Given:

$\rm (sin37^\circ cos53^\circ + cos37^\circ sin53^\circ)-\frac{4cos^237^\circ-7+4cos^253^\circ}{tan^247^\circ +4-cosec^243^\circ}$

Concept used:

<br>

 

<br>

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

$sinA.cosB + cosA.sinB = sin(A+B)$

Calculation:

$\rm (sin37^\circ cos53^\circ + cos37^\circ sin53^\circ)-\frac{4cos^237^\circ-7+4cos^253^\circ}{tan^247^\circ +4-cosec^243^\circ}$

⇒ $sin (53^\circ+37^\circ)-\frac{4sin^253^\circ-7+4cos^253^\circ}{tan^247^\circ +4-sec^247^\circ}$

⇒ 1 - (4 - 7)/(4 - 1) [sin2θ + cos2θ = 1 and sec2θ - tan2θ = 1]

⇒ 1 - (- 3/3)

⇒ 1 + 1 = 2

∴ Required answer is 2

Given:

∠ACB = 102°

Concept Used:

When a quadrilateral is inscribed in a circle, the opposite angles of it are supplementary angles.

The angle subtended at the center is always double the angle subtended at the remaining arc.

The radius from the center of the circle to the point of tangency is perpendicular to the tangent line.

Calculation:

Point D is taken on the major arc of the circle. Then, A & D, B & D, C & B, and A & C are joined.

∠ACB = 102°

Now,

∠ADB = (180 – 102)° = 78°

Now,

∠AOB = (78 × 2)° = 156°

Since OA = OB, ΔAOB is an isosceles triangle and ∠OBA = ∠OAB.

Now,

∠AOB + ∠OBA + ∠OAB = 180°

⇒ 2 × ∠OBA = (180 – 156)°

⇒ ∠OBA = 12°

Now,

∠OBA = 12°

∠OAB = 12°

Now,

∠OAP = ∠OAB + ∠BAP

⇒ 90° = 12° + ∠BAP

⇒ ∠BAP = 78°

Now,

∠OBP = ∠OBA + ∠ABP

⇒ 90° = 12° + ∠ABP

⇒ ∠ABP = 78°

Now,

∠APB + ∠ABP + ∠BAP = 180°

⇒ ∠APB + 78° + 78° = 180°

⇒ ∠APB = 180° - (2 × 78)°

⇒ ∠APB = 24°

∴ The required measure of ∠APB is 24°.

Alternate MethodEquivalent discount for Shruti = 10 + 5 - (10 × 5)/100 = 14.5%

Let the CP be Rs. 100

MP = 100 + 25 = 125

SP (For shopkeeper) = [125 × (100 - 14.5)]/100 = 106.875% = 2394

⇒ 1% = 22.40

⇒ 100% = Rs. 2240.

∴ The cost price is Rs. 2240.

Traditional method:

Given:

The Shopkeeper marked every item 25% above the cost price and allowed a 10% discount.

Shruti being a regular customer got a 5% additional discount.

She paid a bill of Rs. 2394.

Concept Used:

Percentage calculation

Calculation:

Let the cost price of the item purchased by Shruti be P.

Now,

Marked price

⇒ P + P × 25%

⇒ P (1 + 0.25)

⇒ (P × 1.25)

After 10% discount

⇒ (P × 1.25) - (P × 1.25) × 10%

⇒ (P × 1.25) (1 – 0.1)

⇒ (P × 1.25) × 0.9

⇒ (P × 1.125)

After addition 5% discount

⇒ (P × 1.125) - (P × 1.125) × 5%

⇒ (P × 1.125) (1 – 0.05)

⇒ (P × 1.125) × 0.95

⇒ (P × 1.06875)

According to the question,

(P × 1.06875) = 2394

⇒ P = 2394 ÷ 1.06875

⇒ P = 2240

∴ The cost price of the item purchased by Shruti is Rs. 2240.

Given:

Average of 5x + 7y = 37

Average of 7x + 5y = 35

Concept used:

Average = Sum of elements/No. of elements

Calculation:

5x + 7y = 37 × 12      ----(1)

7x + 5y = 35 × 12      ----(2)

By subtracting eq (2) from eq (1)

2y - 2x = 12 × 2

⇒ y - x = 12

⇒ 5y - 5x = 60     ----(3)

Adding eq (3) with eq (1)

So,

5x + 7y + 5y - 5x = 444 + 60

⇒ 12y = 504

⇒ y = 42

∴ The value of y is 42

Shortcut Trick

Let the total number of students in the examination be 100.

Number of boys = 45, which means number of girls = 55.

Boys who failed = (100 − 60)% of 45 = 40% of 45 = 18.

Girls who failed = (100 − 70)% of 55 = 30% of 55 = 16.5.

Total failed percentage = 18 + 16.5 = 34.5%.

∴ The correct answer is 34.5%.

Alternate Method

Given:

Total students considered = 100%

Percentage of boys = 45%

Passed boys = 60%

Passed girls = 70%

Formula Used:

Failed % = 100% − Passed %

Total Students = 100

Boys = 45

Girls = 55

Pass (60%) 27

Fail (40%) 18

Pass (70%) 38.5

Fail (30%) 16.5

Total Failed = 18 + 16.5 = 34.5%

Calculations:

⇒ Percentage of girls = 100% − 45% = 55%

⇒ Number of boys failed out of 100 = 40% of 45 = (40 ÷ 100) × 45 = 18

⇒ Number of girls failed out of 100 = 30% of 55 = (30 ÷ 100) × 55 = 16.5

⇒ Total failed students = 18 + 16.5 = 34.5

⇒ Percentage of students who failed = (34.5 ÷ 100) × 100% = 34.5%

∴ The correct answer is 34.5%.

Additional Information

Percentage Change

Percentage change is calculated as ((New Value − Old Value) ÷ Old Value) × 100.

Successive Percentage

When a value is changed by a% and then by b%, the net percentage change is given by (a + b + (a × b) ÷ 100)%.

Base Shift Rule

If A is R% more than B, then B is (R ÷ (100 + R)) × 100% less than A.

Given:

18 ÷ [26 - {25 - (15 - 5) ÷ 2}] of 12 + 2 - 2 ÷ 4 × 16

Concept used:

Calculation:

18 ÷ [26 - {25 - (15 - 5) ÷ 2}] of 12 + 2 - 2 ÷ 4 × 16

⇒ 18 ÷ [26 - {25 - 10 ÷ 2}] of 12 + 2 - 2 ÷ 4 × 16

⇒ 18 ÷ [26 - {25 - 5}] of 12 + 2 - 2 ÷ 4 × 16

⇒ 18 ÷ [26 - 20] of 12 + 2 - 2 ÷ 4 × 16

⇒ 18 ÷ 6 of 12 + 2 - 2 ÷ 4 × 16

⇒ 18 ÷ 72 + 2 - 2 ÷ 4 × 16

⇒ 1/4 + 2 - 1/2 × 16

⇒ 1/4 + 2 - 8

⇒ (1 + 8 - 32)/4

⇒ - 23/4

∴ Requried answer is - 23/4

Shortcut Trick

Net Simple Interest (SI) rate for 2.4 years at 10% = 10% × 2.4 = 24%.

Successive rates for Compound Interest (CI): 10%, 10%, and (10 × 2/5)% = 4%.

Net CI rate = 10 + 10 + (10 × 10)/100 = 21%; then 21 + 4 + (21 × 4)/100 = 25.84%.

Difference in percentage = 25.84% − 24% = 1.84%.

Difference in value = 1.84% of ₹8000 = 80 × 1.84 = ₹147.20.

∴ The correct answer is ₹147.20.

Alternate Method

Given: Principal (P) = ₹8000, Rate (R) = 10% p.a., Time (T) = 2²/₅ years = 2.4 years.

Formula Used: SI = (P × R × T) / 100 | CI Amount (A) = P(1 + R/100)ⁿ

⇒ Simple Interest (SI) = (8000 × 10 × 2.4) / 100

⇒ SI = 80 × 24 = ₹1920

⇒ Compound Interest Amount (A) = 8000 × (1 + 10/100) × (1 + 10/100) × (1 + 4/100)

⇒ A = 8000 × 1.1 × 1.1 × 1.04

⇒ A = 8000 × 1.21 × 1.04 = 9680 × 1.04 = ₹10067.20

⇒ Compound Interest (CI) = 10067.20 − 8000 = ₹2067.20

⇒ Difference = 2067.20 − 1920 = ₹147.20

∴ The correct answer is ₹147.20.

Additional Information

CI and SI Difference (2 Years)

For a period of 2 years, the difference is calculated as: Diff = P(R/100)².

CI and SI Difference (3 Years)

For a period of 3 years, the difference is: Diff = P(R/100)² × (3 + R/100).

Fractional Time Period CI

If time is T = n + a/b years, Amount = P(1 + R/100)ⁿ × (1 + (a/b × R)/100).

Concept used:

x4 + y4 + x2y2 = (x2 + y2 - xy)(x2 + y2 + xy)

Calculation:

Given that, 

x4 + y4 + x2y2 = 21   -----(1)

x2 + y2 - xy = 7         -----(2)

We know that,

x4 + y4 + x2y2 = (x2 + y2 - xy)(x2 + y2 + xy)

Using equation (1) & (2)

⇒ 21 = 7(x2 + y2 + xy)

⇒ (x2 + y2 + xy) = 3      ----(3)

Now.

(x2 + y2 + xy) + (x2 + y2 - xy) = 3 + 7

⇒ x2 + y2 = 5

Put this value in equation (3)

⇒ 5 + xy = 3

⇒ xy = - 2

Now, $\frac{x}{y}+\frac{y}{x} = \frac{ x^2 + y^2}{xy}$

⇒ ​$\frac{x}{y}+\frac{y}{x}$​  = - 5/2

∴ The required answer is - 5/2

Total numbers of boys in Commerce = 35 + 32 + 36 + 28 + 39

⇒ 170

Average = 170/5 = 34

Total numbers of girls in Arts = 36 + 43 + 42 + 46 + 43

⇒ 210

Average = 210/5 = 42

So, difference = 42 - 34 = 8

∴ Requried answer is 8

Total number of students passed from school Q in 2014 and 2018 = 240 + 320 = 560

Total number of students appeared from school R and S in 2017 = 800

Difference = 800 - 560 = 240

So, Percentage = (240/800) × 100

⇒ 30%

∴ Required percentage is 30%

Given:

3 sin2 θ - cos θ - 1 = 0

Concept used:

x2 – (sum of roots)x + product of roots = 0

Calculation:

3 sin2 θ - cos θ - 1 = 0

⇒ 3 - 3cos2θ - cosθ - 1 = 0

⇒ 3cos2θ + cosθ - 2 = 0

⇒ 3cos2θ + 3cosθ - 2cosθ - 2 = 0

⇒ 3cos(cosθ + 1) - 2(cosθ + 1) = 0

⇒ (cosθ + 1)(3cos - 2) = 0

⇒ cosθ = - 1, 2/3

⇒ cosθ = - 1, 2/3

cos180° = - 1

But we can not take this as 180° > 90° 

So, cosθ = 2/3

Now, cosθ = B/H

So, P2 = h2 - b2

⇒ P2 = 9 - 4

⇒ P2 = 5

⇒ P = √5

cot θ + cosec θ = 2/√5 + 3/√5

⇒ 5/√5 or √5

∴ Requried answer is √5

Total exports of company B in 2011 and 2014 = 75 + 200

⇒ 275

Total exports of company A in 2012 and 2015 = 120 + 220

⇒ 340

Ratio = 275 : 340

⇒ 55 : 68

∴ Required ratio is 55 : 68

Given:

x + y = 3

1/x + 1/y = - (3/10)

Concept Used:

(A + B)² = A² + 2AB + B²

Calculation:

1/x + 1/y = - (3/10)

⇒ (x + y)/xy = - (3/10)

⇒ xy = (-10)

Now,

x + y = 3

⇒ (x + y)² = 9 (Squaring both side)

⇒ x2 + y2 + 2xy = 9

⇒ x2 + y2 = 9 - 2xy

⇒ x2 + y2 = 9 – 2 × (-10)

⇒ x² + y² = 29

∴ The required value of x² + y² is 29.

Given:

$\frac{(375+125)^2-(125-375)^2}{375\times375-125\times125}$

Concept Used:

(A + B)2 - (A - B)2 = 4AB

A2 - B2 = (A + B) (A - B)

Calculation:

Let 375 be A & 125 be B.

Now, 

{(A + B)² - (B - A)²} ÷ (A × A - B × B)

⇒ {(A + B)2 - (A - B)2} ÷ (A² - B²)

⇒ (4 × AB) ÷ {(A + B) (A - B)}

⇒ (4 × 375 × 125) ÷ {(375 + 125) (375 - 125)}

⇒ $\frac{4 × 375 × 125 } {500 \times 250}$

⇒ 375/250

⇒ 3/2

∴ The value of given expression in 3/2.

Given:

A = 2C

A + B in 20 days

B + C in 24 days

Concept used:

Total work = LCM of time taken by the workers

Calculation:

LCM of 20 and 24 is 120

So, efficiency of A and B = 120/20 = 6 and efficiency of B and C = 120/24 = 5

Now 2C + B = 6 and B + C = 5

So, C = 1

B = 4

40% of the work = 120 × 2/5 = 48 units

So, B will take 48/4 = 12 days

∴ B alone do 40% of the same work in 12 days

Shortcut Trick

Now 2C + B = 6 and B + C = 5

So, C = 1

B = 4

So,

A, B and C = 2, 4, and 1

40% of the work = 120 × 2/5 = 48 units

So, B will take 48/4 = 12 days

GIven:

∠APB = 80°

Concept used:

• The radius from the center of the circle to the point of tangency is perpendicular to the tangent line.
• Angles opposite the equal sides of a triangle are equal.
• Sum of all angles of quadrilateral = 360°

 

Calculation:

In the given figure,

BOAP is a  quadrilateral, ∠OAP and ∠OBP = 90°

So, ∠AOB + ∠APB + 90° + 90° = 360° 

⇒ ∠AOB = 100°

In an Δ OAB, 

OA = OB = radius

⇒ ∠ OAB = ∠ OBA

∠OAB = (180 - 100)/2 = 80/2 = 40°

∴ ∠OAB is equal to 40°

Given:

Akhil takes 30 minutes i.e., 1/2 hour extra to cover a distance of 150 km if he drives 10 km/h slower than his usual speed.

Concept used:

Time = D/S

D = Distance

T = Time 

Calculation:

Let the usual speed of Akhil be S km/h.

After a 10kmph reduction, the speed of Akhil = (S - 10) km/h

According to the question,

150/(S - 10) - 150/S = 1/2

⇒ 150 {1/(S - 10) - 1/S} = 1/2

⇒ 150 {(S - S + 10)/ {S × (S -10)} = 1/2

⇒ 150 {10/ {S × (S - 10)} = 1/2

⇒ S × (S - 10) = 2 × 150 × 10

⇒ S = 60

Now,

Time taken by Akhil to drive 90 km at (60 - 15) km/h i.e. 45km/h

⇒ (90/45) hours

⇒ 2 hours

∴ Time taken by Akhil to drive 90 km if he drives 15 km per hour slower than his usual speed is 2 hours.

Shortcut Trick

In right-angled ▵OMA, AM = √(10² − 8²) = 6 cm.

In ▵OAP, using the property of similarity (or altitude in a right triangle):

AP/OA = AM/OM

⇒ AP/10 = 6/8

⇒ AP = 60/8 = 7.5 cm.

∴ The correct answer is 7.5 cm.

Alternate Method

Given: Radius (OA) = 10 cm, distance from centre (OM) = 8 cm.

Formula Used: In a right-angled triangle, the tangent is perpendicular to the radius. Pythagoras Theorem: H² = P² + B².

In ▵OMA, ∠OMA = 90° (Perpendicular from centre to chord).

⇒ AM² = OA² − OM²

⇒ AM² = 10² − 8² = 100 − 64 = 36

⇒ AM = 6 cm.

In right-angled ▵OAP, AM is the altitude to the hypotenuse OP (as OP bisects AB perpendicularly).

From similarity of ▵OMA and ▵AMP (or properties of right triangles):

⇒ AM/OM = AP/OA

⇒ 6 / 8 = AP / 10

⇒ AP = (6 × 10) ÷ 8

⇒ AP = 60 ÷ 8 = 7.5 cm.

∴ The correct answer is 7.5 cm.

Additional Information

Tangent-Radius Property

A tangent at any point of a circle is perpendicular to the radius through the point of contact (∠OAP = 90°).

Right Triangle Proportionality

In ▵OAP with altitude AM, the legs and altitude satisfy: OA² = OM × OP and AP² = PM × PO.

Chord Bisection

The line joining the external point P and the centre O is the perpendicular bisector of the chord of contact AB.

Shortcut Trick

Perimeter of a semi-circle = r(π + 2)

Given π = 3.14, Perimeter = r(3.14 + 2) = 5.14r

5.14r = 25.7 ⇒ r = 25.7 ÷ 5.14 = 5 cm

Diameter = 2 × r = 2 × 5 = 10 cm

∴ The correct answer is 10 cm.

Alternate Method

Given: Perimeter of semi-circle = 25.7 cm, π = 3.14

Formula Used: Perimeter = πr + 2r

⇒ r(π + 2) = 25.7

⇒ r(3.14 + 2) = 25.7

⇒ 5.14r = 25.7

⇒ r = 25.7 ÷ 5.14

⇒ r = 5 cm

⇒ Diameter = 2r = 2 × 5 = 10 cm

∴ The correct answer is 10 cm.

Additional Information

Area of a Semi-circle

The area is half the area of a full circle: Area = (πr²) ÷ 2.

Circle Properties

For a full circle, Circumference = 2πr and Diameter = 2r.

Sector of a Circle

Perimeter of a sector with angle θ = ( θ / 360 ) × 2πr + 2r.

Given:

sin4 30° + cos4 30° - sin 25° cos 65° - sin 65° cos 25°

Concept used:

sin(90° - θ) = cosθ 

cos(90° - θ) = sinθ 

sin²θ + cos²θ = 1

Calculation:

sin4 30° + cos4 30° - sin 25° cos 65° - sin 65° cos 25°

⇒ (1/2)⁴ + (√3/2)⁴ - sin 25° sin 25° - cos 25° cos 25°

⇒ 1/16 + 9/16 - sin² 25° - cos²25°

⇒ 1/16 + 9/16 - 1(sin2 25° + cos225°)

⇒ 10/16 - 1

⇒ (10 - 16)/16

⇒ - 6/16

⇒ - 3/8

∴ Required answer is - 3/8

Alternate MethodFormula used:

Sin(A+B) = Sin A Cos B + Cos A Sin B

sin4 30° + cos4 30° - (sin 25° cos 65° + sin 65° cos 25°)

⇒ (1/2)4 + (√3/2)4 - sin(25° + 65°)

⇒ 1/16 + 9/16 - sin(90°)

⇒ 1/16 + 9/16 - 1 

⇒ 10/16 - 1

⇒ (10 - 16)/16

⇒ - 6/16

⇒ - 3/8

∴ The required answer is - 3/8

Given:

Numbers are 12, 16, 6

4, and 6

Concept used:

If x is the fourth proportion of a, b and c

⇒ a/b = c/x

If x is the third proportion of a & b then

a/b = b/x

Calculation:

Let fourth proportion be x

And y be the third proportion

So,

12/16 = 6/x

⇒ x = 8

4/6 = 6/y

⇒ y = 9

So, ratio = 8 : 9

∴ Ratio is 8 : 9

Given:

888x53y4 is divisible by 72

Concept used:

Divisibility rule of 8 → If the last three digits of a number are divisible by 8, then the number is completely divisible by 8

Divisibility rule of 9 →  If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9

Calculation:

3y4 is divisible by 8

y = 0, 4 or 8

So, y = 8    (for maximum value of y)

8 + 8 + 8 + x + 5 + 3 + 8 + 4 = 44 + x is divisible by 9

So, x = 1

Now,

(7x + 2y) = 7 × 1 + 2 × 8

⇒ 7 + 16 = 23

∴ Required answer is 23