SSC CGL 2020 Tier-I Official Paper (Held On : 20 Aug 2021 Shift 2) (Previous Year Paper)

According to the sequence in the dictionary:

The correct order of the given words is:

5. Relatable
6. Related
7. Relation
8. Relatival
9. Relative

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

The logic is shown below –

Hence, “72” is the term that completes the series

The logic followed here is:

Cat : Kitten → A baby cat called kitten.

Similarly,

Cow : Calf → A baby cow called calf.

Hence, ‘Cow : Calf’ is the correct answer.

Additional Information

The logic is here is:

1^st number - 2^nd number = 118

Option (1): 727 : 609

Now, follow the logic:

727 – 609 = 118

This option follows the pattern.

Option (2): 373 : 255

Now, follow the logic:

373 - 255 = 118

This option follows the pattern.

Option (3): 191 : 177

Now, follow the logic:

191 – 177 = 14

This option do not follow the pattern.

Option (4): 797 : 679

Now, follow the logic:

797 – 679 = 118

This option follows the pattern.

Hence, pair “191 : 177” is an odd one.

Alternate Method The logic followed here is:-

Sum of digits of first number - Sum of digits of second number = 1

1. In 727 : 609

Sum of digits of first number = 7 + 2 + 7 = 16

Sum of digits of second number = 6 + 0 + 9 = 15

Sum of digits of first number - sum of digits of second number → 16 - 15 = 1

2. In 373 : 255

Sum of digits of first number = 3 + 7 + 3 = 13

Sum of digits of second number = 2 + 5 + 5 = 12

Sum of digits of first number - sum of digits of second number → 13 - 12 = 1

3. In 191 : 177

Sum of digits of first number = 1 + 9 + 1 = 11

Sum of digits of second number = 1 + 7 + 7 = 15

Here, sum of digits of second number > Sum of digits of first number

Also, Sum of digits of second number - sum of digits of first number → 15 - 11 = 4

4. In 797 : 679

Sum of digits of first number = 7 + 9 + 7 = 23

Sum of digits of second number = 6 + 7 + 9 = 22

Sum of digits of first number - sum of digits of second number → 23 - 22 = 1

As can be seen clearly from the above that 191 : 177 doesn't follow the logic and is the odd one out.

Hence, the correct answer is "191 : 177".

Table show alphabet serial number –

The pattern for the code is as follows,

Similarly,

Hence, ‘FLOWER’ is coded as ‘UELPVK’.

Preparing the family tree using the following symbols,

  

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

1. Swati is the daughter of Anil's only sister Akshara.

2. Anil's mother is Gauri. Kamini is Gauri's mother.

3. Kamini's husband is Gaurav. Poonam is Gaurav's mother-in-law.

Hence, Swati is the ‘great-granddaughter’ of Gaurav.

The possible diagram is,

Hence, Option(2) is the correct answer

The logic followed here is:

Swell : Sad → Sad is opposite word of Swell.

Similarly,

Chill : Provoke → Provoke is Opposite word of Chill.

Hence, ‘Provoke’ is the correct answer.

The triangles in the given figure are

 

So, total of 32 triangles in the figure.

Hence, ‘32’ is the correct answer.

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

Hence, "option (2)" 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.

Statements:

1. All fans are heaters.
2. Some coolers are fans.
3. All purifiers are coolers.

The least possible diagram for the given statements is as follows

Conclusions:

I, All purifiers are heaters → False (It is possible but not definite)

II. Some purifiers are heaters → False (It is possible but not definite)

Ill. Some heaters are coolers → True (because all fans are heaters and some fans are coolers so some heaters are also coolers)

IV. All coolers are heaters → False (It is possible but not definite)

Hence, Only conclusion III follow.

Additional Information

The embedded part of this image is:

Hence, option (2) is the correct answer.

Important Points

• Do not get tensed by the complexity of the figures.
• Carefully understand the structure of the given question figure.
• The embedded figure may not be of exact size. It may be small or big.
• Sometimes the rotation or reflection of the figures may be confusing.
• So think wisely before selecting the answer.

Given: ‘PRIVATE' is coded as '93236441540" and "SHORTEN' is coded as '1615383652840".

The logic followed here is:

1) Given word in a word are arranged in alphabetical order first three letter and last three letter are arranging in alphabets order.

2) After arrangement consonants letter place value multiplies by 2 and this number is used as number code.

3) Vowels place value is used as the number code.

‘PRIVATE' is coded as '93236441540"

And,

"SHORTEN' is coded as '1615383652840".

Similarly, 

**REFUSAL **= ?

Hence, "512362112438" is the correct answer.

Given:

 

Here the pattern followed in each row is:

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

Row 1: 7, 35, 13

(13 - 7)² - 1 = 6² - 1 = 36 – 1 = 35

Row 2: 9, 24, 14

(14 - 9)² - 1 = 5² - 1 = 25 – 1 = 24

Similarly

Row 3: 13, 120, ?

(? - 13)² - 1 = 120

= (? - 13)2 = 120 + 1

= (? - 13)2 = 121

= ? - 13 = 11

= ? = 11 + 13 = 24

Hence, “24” is correct answer.

The logic is here is:

Option (1): Hinder → Definition of HINDER is to stop someone or something from making progress.

Option (2): Forbid → FORBID to tell someone in a very strong way that they must not do something or that something is not allowed**.**

Option (3): Permit → PERMIT is to allow something, or make something possible.

Option (4): Impede → Definition of IMPEDE make something more difficult to do**.**

Hinder, Forbid and Impede all are antonyms word of Permit.

Hence, ‘Permit’ is the correct answer.

The pattern followed here is:

[1^st number × (1^st number + 1)] ÷ 3 = Second number.

Let (M : N)

Step 1 → M × (M + 1)  = A (A any number)

Step 2 → A ÷ 3  = N

Now follow the steps:

8 : 24

Step 1 → 8 × (8 + 1) = 8 × 9 = 72

Step 2 → 72 ÷ 3  = 24

Similarly,

18 : 114

Step 1 → 18 × (18 + 1) = 18 × 19 = 342

Step 2 → 342 ÷ 3  = 114

Similarly,

? : 52

Step 1 → 12 × (12 + 1) = 12 × 13 = 156

Step 2 → 156 ÷ 3  = 52

Hence, "12 : 52"  is correct answer.

Table show alphabet serial number –

The logic is shown below –

Hence, “XNE” is complete in the series.

Note:- Two opposite faces are never seen together or adjacent to each other.

In figure (A): None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

In figure (B): None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

In figure (C): None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

In figure (D): None of the opposite faces are seen together nor they are adjacent to each other. Thus, this cube can be made.

Hence, ‘All A, B, C and D’ is the correct answer.

Mistake PointsCube will form with these sides. Yes, it is confusing because there have three empty sides. In this type of question, you should focus on the possible case. We should ignore the empty sides which are opposite to symbols and try to form a dice with the other empty side.

The Logic here is as follows:

(First Number)2 + (Second Number)3 = Third number

In (4, 7, 359):

(First Number)2 + (Second Number)3 =

= (4)2 + (7)3

= 16 + 343

= 359 = Third Number

Similarly,

In (6, 8, 548):

(First Number)2 + (Second Number)3 =

= (6)2 + (8)3

= 36 + 512

= 548 = Third Number

Hence, the correct answer is "(6, 8, 548)".

The image obtained when the paper is unfolded is,

Hence, option 2 is the correct answer.

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

1. In series arrow rotating in a clockwise direction.

2. In series square change its position in each corner of figure and also change one by one shaded part to non-shaded part.

3. In series circle change its position in each corner of figure and also change one by one shaded part to non-shaded part.

Hence, ‘option 4’ is the correct answer.

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

Option (1) l, l, q, r, l, r, t

m _ t q _ m l _ q r m _ t q _ m _ t _ r

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

m l t q l / m l q q r / m r t q l / m r t t r

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

Option (2) l, q, r, l, l, r, t

m _ t q _ m l _ q r m _ t q _ m _ t _ r

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

m l t q q / m l r q r / m l t q l / m r t t r

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

Option (3) l, r, t, l, r, l, q

m _ t q _ m l _ q r m _ t q _ m _ t _ r

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

m l t q r / m l t q r / m l t q r / m l t q r

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

Option (4) l, t, r, l, l, r, q

m _ t q _ m l _ q r m _ t q _ m _ t _ r

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

m l t q t / m l r q r / m l t q l / m r t q r

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

Hence, ‘l, r, t, l, r, l, q’ is the correct answer.

Given:

1) Alekhya is six years old at present.

So, Alekhys age = 6 year

2) Alekhya’s father twenty-five years older than Alekhya.

So, Alekhya’s father age = 25 + 6 = 31 years

3) Alekhya’s father is two years older than Alekhya’s mother.

So, Alekhya’s mother age = 31 - 2 = 29 years

4) Alekhya was born a year after her mother's marriage.

So, mother's marriage before = 6 + 1 = 7 years

5) Age of Alekhya’s mother at married.

29 – 7 = 22

Hence,  Alekhya’s mother age at married is “22”.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except ‘GDAW’.

Hence, “GDAW” is the odd one.

According to BODMAS rule:

Given equation 221 * 17 * 12 * 130 * 24 * 50

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

221 ÷ 17 - 12 × 130 = 24 + 50

By BODMAS rule

13 - 12 × 130 = 24 + 50

13 - 1560 = 24 + 50

13 - 1560 = 74

-1547 = 74 (LHS ≠ RHS)

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

221 × 17 ÷ 12 - 130 + 24 = 50

221 × 1.417 - 130 + 24 = 50

313 - 130 + 24 = 50

337 – 130 = 50

207 = 50 (LHS ≠ RHS)

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

221 ÷ 17 × 12 - 130 + 24 = 50

13 × 12 - 130 + 24 = 50

156 - 130 + 24 = 50

180 - 130 = 50

50 = 50 (LHS = RHS)

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

221 ÷ 17 × 12 - 130 = 24 + 50

13 × 12 - 130 = 24 + 50

156 - 130 = 24 + 50

26 = 74 (LHS ≠ RHS)

Hence, the answer is “÷, ×, -, +, =”.

The correct answer is Protozoa.

Key Points

• Kala-azar is a parasitic protozoan belonging to the class Mastigophora or flagellata caused by Leishmania donovani.
• Leishmania donovani is a human parasite that is dimorphic (i.e. shows two forms)& digenetic in nature.
• It causes the disease Kala-azar or Dumdum fever by sand fly (phelobotomus).

Additional Information

• This disease is spread by the bite of infected sand-fly, It can affect the Skin (Cutaneous Leishmaniasis), the mucous membrane of the mouth, throat, and nose (Mucocutaneous Leishmaniasis), Liver, lymph nodes, spleen, and bone marrow (Visceral Leishmaniasis).
• Symptoms include Cutaneous Leishmaniasis - Skin ulcers.
• Mucocutaneous Leishmaniasis - Ulcers in mouth, throat, and nose, Nosebleed, Difficulty in breathing.
• Visceral Leishmaniasis - Weakness, weight loss, loss of appetite, enlarged spleen, liver, lymph nodes, a decrease in the production of blood cells.

The correct answer is Sidhu Manjihi.

Key Points

• Santhal Rebellion took place during Lord Dalhousie (1848-1856) tenure at Rajmahal hills (in Jharkhand) led by Sidhu Manjhi.
• Santhal uprising took place during 1855-56.
• The tyrannical British revenue system, usury practices, and the zamindari system in India made Santhal peoples annoyed, and two Santhal brothers Sidhu and Kanhu Murmu organized 10,000 Santhals and proclaimed a rebellion against the British.
• The Santhals are the largest tribal group in India found in Jharkhand, WestBengal, and Odisha.
• Santhal Rebellion:
• It was a rebellion against both the British colonial authority and zamindars by the Santhal people.
• Leaders: Sidhu, Kahnu, Chand, and Bhairav.
• Location: Jharkhand.
• The rebellion was suppressed and largely shadowed by other rebellions.
• To quell rebellion British created Santhal Pargana and special laws were

passed protecting them.

Additional Information

• Britishers invited the Santhals to come and settle in Jharkhand promising land and economic amenities.
• Thus Santhals from different states came to settle in today's Jharkhand.
• Later zamindars dominated these areas as they collected taxes and lent money at very high rates which the people could not generally pay and their lands were forcibly taken.
• This became the roots of the Santhal rebellion.
• In a fierce encounter, Santhals were defeated as they were fighting with bows and arrows while Britishers had modern weapons.
• Sidhu was caught in August 1855 and was hanged on a banyan tree at a place called Panchkathia.

The correct answer is China.

Key Points

• Nathu La is one of the highest motorable roads in the world. It is situated on the Indo-Tibetan border 14450 ft. above sea level.
• It is one of the most important Himalayan passes in the country. Nathu means 'listening ears', and La means 'pass'.
• It is one of the three open trading border posts between India and China and is famous for its picturesque beauty and beautiful environment.
• Nathu La is located on the Old Silk Route. It is a mountain pass in the Himalayas in the East Sikkim district.
• It connects Sikkim to China's Tibet Autonomous Region. It was sealed for almost 4 decades after the People's Republic of China suppressed a Tibetan uprising in 1959.
• The Nathu La Pass was reopened in 2006 and since then, it has served as an official Border Personnel Meeting(BPM) Point.

Additional Information

Other important passes: 

The  correct answer is Goa.

Key Points

• The Sao Joao festival is celebrated in Goa to pay tribute to St. John the Baptist.
• During the Sao Joao festivities, Goans present fruits to each other.
• It is held at the beginning of monsoon, on June 24.
• St. John was the relative of Mother Mary.

The correct answer is Axis Bank.

Key Points

• Axis Bank has launched a range of wearable contactless payment devices under the brand Wear ‘N’ Pay.
• The devices comprise different forms of wearables like a band, key chain, and watch loop.
• The wearables function like a regular debit card and are directly linked to the bank account of an Axis Bank customer.

Additional Information

• Workability:
• These wearable devices can be worn easily to carry out contactless transactions on the go, Users do not need to carry their smartphones and wallet for payments anymore.
• Customers can use these devices at any merchant that accepts contactless transactions. Users need to wave the device at a POS machine for transactions up to Rs 5,000 and for more than Rs 5,000; a PIN is required.

The correct answer is Bihar.

Key Points

• The Son Bhandhar Caves are located in Rajgir in the state of Bihar.
• As per an inscription written in the Gupta language/characters on a rock at the entrance, bhandhar caves were constructed by a Jain muni, meaning named Vairadeva, which makes them structures belonging from 4^th century BC.
• The Son Bhandar caves, also Sonebhandar, are two artificial caves located in Rajgir in the state of Bihar in India.
• They belonged to the Jains.

Additional Information

• Some other important caves:
• Elephanta Caves:
• Location: Elephanta Islands in Mumbai.
• Developed between A.D. 600 to 1000.
• Developed under the patronage of the Rashtrakuta kings.
• Status: UNESCO World Heritage Site (1987).
• The caves are carved from solid basalt rock.
• It is a conglomeration of seven caves, out of which the most important is the Mahesa-murti cave.
• Ajanta Caves:
• Location: The Sahyadri ranges (Western Ghats) near Aurangabad (Maharashtra).
• They were developed between 200 B.C. to 650 A.D.
• They are older than Ellora caves.
• Status: UNESCO World Heritage Site (1983).
• It comprises about 29 rock-cut Buddhist cave monuments.
• 25 were used as Viharas while 4 were used as Chaitya.
• Famous fresco paintings of Ajanta are dying princess, flying apsara and preaching Buddha.
• Travellers like Fa Hien & Hieun Tsang has mentioned the Ajanta caves in their respective books.
• The paintings in this cave were generally themed around Buddhism – the life of Buddha and Jataka stories.
• Ellora Caves:
• Location: In the Sahyadri range of Maharashtra.
• Locally known as ‘Verul Leni’.
• They were developed between the 5^th & 11^th centuries A.D.
• Status: UNESCO World Heritage site (1983).
• It is a group of 34 caves out of which 17 are Brahmanical, 12 are Buddhist & 5 are Jain.
• Guilds from Vidarbha, Karnataka and Tamil Nadu made these caves.
• The rock paintings of Ellora were done in two series;
• 1^st series: It is focused on Lord Vishnu & Goddess Laxmi.
• 2^nd series: It is focused on Shaiva, apsaras.
• It is famous for the largest monolithic excavation in the world- the great Kailasa.

The correct answer is Germany.

Key Points

• The 11^th session of the Petersberg Climate Dialogue with 30 countries including India took place on April 28, 2020, through a video conference.
• The dialogue was conducted to discuss the ways of tackling the societies and economies after COVID-19.
• The Union Minister for Environment, Forest and Climate Change, Prakash Javedekar attended the Dialogue.
• The Dialogue was hosted by Germany.
• Germany: Capital - Berlin.
• Currency - Euro.

The correct answer is Protein.

Key Points

• Collagens are available in large quantities the human body. They are found in skins, bones muscles, and tendons.
• Collagen is the main structural protein in the various connective tissues in the body. They are a primary structural component of connective tissues, such as skin and cartilage.
• Foods that are high in Collagen protein are- Chicken, fish, egg whites, citrus foods, etc.

Additional Information

• Carbohydrate
• It is a biomolecule consisting of Carbon, Hydrogen and Oxygen atoms. Carbohydrates are found in a wide array of foods-bread, beans, milk, popcorn, potatoes, cookies.
• Fat
• It usually means any ester of fatty acids. The following food are good sources of fat - avocados, tofu, nuts, seeds, fish, peanut butter, boiled and eggs.
• Vitamin
• Vitamin means 'vital for life'. It is an organic non-protein substance.
• Vitamins are compounds necessary for the healthy functioning of our bodies.
• We need vitamins to help us grow, to see correctly, as well as to help us battle infections.
• It is required by an organism for normal metabolic function but cannot be synthesized in sufficient quantity by that organism.
• They are also required in small quantities to prevent deficiency diseases.

The correct answer is Dadabhai Naoroji.

Key Points

• First Indian elected to the British House of Commons, Dadabhai Naoroji contested on the ticket of Liberal Party.
• Dadabhai Naoroji was also known as the "Grand Old Man of India" and "Unofficial Ambassador of India".
• He was an Indian political leader, merchant, scholar and writer who was a Liberal Party Member of Parliament in the United Kingdom House of Commons between 1892 and 1895.
• Naoroji is honoured for his work in the Indian National Congress, of which he was one of the founding members and thrice - in 1886,1893, and 1906 - elected president.
• His authored book Poverty and Un-British Rule in India brought attention to his theory of the Indian "wealth drain" into Britain.
• India Post showing Naoroji on stamps in **1963, 1997 and 2017.**​

Additional Information

• Liberal Party:
• Liberal Party, a British political party that emerged in the mid-19^th century as the successor to the historic Whig Party.
• It was the major party in opposition to the Conservatives until 1918, after which it was supplanted by the Labour Party.
• The Liberals continued as a minor party until 1988 when they merged with the Social Democratic Party to form what is now called the Liberal Democratic Party.
• Through its long history, the Liberal Party included various schools of thought, but all Liberals were united by the conviction that the source of progress lay in the free exercise of individual energy.
• Labour Party:
• Labour Party, a British political party whose historic links with trade unions have led it to promote an active role for the state in the creation of economic prosperity and in the provision of social services.
• In opposition to the Conservative Party, it has been the major democratic socialist party in Britain since the early 20^th century.
• In 1900 the Trade Union Congress (the national federation of British trade unions) cooperated with the Independent Labour Party(founded in 1893) to establish a Labour Representation Committee, which took the name Labour Party in 1906.
• Conservative Party:
• Conservative Party, byname Tories, in the United Kingdom, a political party whose guiding principles include the promotion of private property and enterprise, the maintenance of a strong military, and the preservation of traditional cultural values and institutions.
• Since World War I the Conservative Party and its principal opponent, the Labour Party, have dominated British political life.
• The name Conservative was first used as a description of the party by John Wilson Croker writing in the Quarterly Review in 1830.
• Communist Party:
• The Communist Party of Britain (CPB) is a communist political party in Great Britain idealized to Marxist-Leninist theory.
• The party came out from a dispute between Eurocommunists and Marxist-Leninists in the Communist Party of Great Britain in 1988.
• Ex-members included General Secretaries of three organisations:
• Bob Crow of the RMT union, Ken Gill of the Manufacturing.
• Science and Finance (MSF) union and member of the TUC General Council.
• Kate Hudson of the Campaign for Nuclear Disarmament (CND).

The correct answer is Shashi Tharoor.

Key Points

• Shashi Tharoor is an Indian politician, writer, and former international diplomat.
• Inglorious Empire arose from a speech given by Dr Shashi Tharoor in May 2015 at the Oxford Union in support of the motion Britain Owes Reparations to Her Former Colonies, focusing on British exploitation of India.
• He 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 contested for the post of Secretary-General in 2006.
• He has also written hundreds of columns in many famous publications like
• The New York Times
• The Washington Post.
• In 2019, Dr. Shashi Tharoor got the Sahitya Academy Award for his book "An Era of Darkness' in a non-fiction category in the English language.
• His books provide an insight into the Indian culture, its position in modern society, and how it evolved into one of the largest democracies in the world.

The correct answer is Viktor Axelsen.

• The Toyota Thailand Open was a badminton tournament that took place at the Impact Arena in Thailand from 19 to 24 January 2021.
• Viktor Axelsen won the men’s singles title at the Toyota Thailand Open badminton tournament in January 2021.

Additional Information

• Viktor Axelsen of Denmark took the gold medal in the men's singles badminton at the Tokyo 2020 Olympic Games.
• He is the 2017 World Champion and the gold medalist at the 2020 Summer Olympics.
• He becomes the first non-Asian man to claim the singles title since 1996.
• He beat China's defending champion Chen Long.

The correct answer is Gujarat.

Key Points

• Saurashtra is the south-western part of Gujarat which includes districts like Junagadh, Porbandar, Surendranagar etc.
• Kathiawar peninsula is surrounded by the Gulf of Kutch and by the Gulf of Khambhat.
• It is made of the Deccan Lava and there are tertiary rocks in the Kutch area, the Gir Range is located in the southern part of the Kathiawar peninsula.
• Kathiawar peninsula is an example of emerged shoreline Telangana, Mysore and Kerala are situated on the Deccan Plateau.

The correct answer is Aam Aadmi Party.

Key Points

• In April 2011, a civil society movement was born in the backdrop of big-ticket corruption scandals that came to light during the Congress-led UPA regime.
• The birth of the AAP on 2^nd October 2012 was a watershed moment in India's political history.

Additional Information

• Criteria for State Party:
• If it secures 6% of the valid votes polled in the state at a general election to the legislative assembly of the state concerned and in addition, it wins 2 seats in the assembly of the state concerned.
• If it secures 6% of the valid votes polled in the state at a general election to the Lok Sabha from the state concerned and in addition, it wins 1 seat in the Lok Sabha from the state concerned or If it wins 3% of seats in the legislative assembly at a general election to the legislative assembly of the state concerned or 3 seats in the assembly, whichever is more.
• If it wins 1 seat in the Lok Sabha for every 25 seats or any fraction thereof allotted to the state at a general election to the Lok Sabha from the state concerned.
• If it secures 8% of the total valid votes polled in the state at a General Election to the Lok Sabha from the state or to the legislative assembly of the state. This condition was added in 2011.

The correct answer is 1784.

Key Points

• The Asiatic Society was established in Calcutta by Sir William Jones in the year 1784.
• It is located at Kolkata.
• It was a unique institution having served as a fountainhead of all literary and scientific activities.
• It was visualized as a centre for Asian studies including everything concerning man and nature within the geographical limits of the continent.
• **Warren Hasting had set up the Bengal Asiatic Society.**​

Additional Information

• Sir William Jones was a British Orientalist and jurist. He established the Asiatic Society of Bengal in 1784.
• It was formed to encourage Oriental studies in India. The formation of the Asiatic Society was supported by the then governor-general of British India Warren Hastings.
• The headquarters of the Asiatic Society of Bengal was in Kolkata. Indians were first admitted as members of the Asiatic Society of Bengal in 1829.

The correct answer is Gujarat.

Key Points

• Bharat Heavy Electricals Limited (BHEL) and LIBCOIN will build India's first 1GWh lithium-ion battery plant.
• The plant's capacity will be scaled up to 30GWh in due course.
• This project will bring energy independence by replacing oil imports with abundant renewable energy.
• It will also create an integrated manufacturing ecosystem resulting in self-reliance and lower cost.

The correct answer is Arya Rajendran.

Key Points

• Mayor is the First Citizen of the City.
• In December 2020 Arya Rajendran become the youngest mayor of India (21 years) in the Thiruvananthapuram city of Kerala.
• She secured 54 votes in the 100-member Council in the election held on December 28.
• The head of the **Municipal Corporation of the respective city elected by the public is called Mayor.**​

Additional Information

The correct answer is  Mr. Narendra Modi.

Key Points

• "Abode of Love" is written by the Indian Prime Minister Mr. Narendra Modi.
• It was published in 2018.
• Narendra Modi is the 14^th and current Prime Minister of India. He is the first prime minister born in independent India.
• He is the second prime minister to visit the Siachin glacier.
• His administration revoked the special status of Jammu and Kashmir in 2019.
• He was honored with the "Order of the Distinguished Rule of Izzuddin"(The highest honor of the Maldives awarded to foreign dignitaries) in 2019.

Additional Information

• Notable works of Narendra Modi are:
• Exam Warriors.
• Social Harmony.
• Letters to Mother.
• Abode of Love.
• Convenient Action: Continuity for Change.
• Sakshi Bhaav.
• Notable work of Shankar Dayal Sharma
• Sanskriti aur Siksha.
• Vikas aur Virasat.
• Manavta ki humari virasat.
• Bhartiyata ke adhar.
• Notable work of APJ Abdul Kalam
• Wings of fire.
• Ignited minds.
• You are born to blossom.
• Turning points.
• India 2020.
• Notable work of Manmohan Singh
• Changing India.
• Demonetisation : The Economists.
• India's economic reforms and development.
• Collateral and financial plumbing.

The correct answer is Wants are satiable.

Key Points

• Human wants are unlimited; There is no limit to man's wants so any particular want is satiable.
• Want is often thought of as a psychological desire which makes life just a little more enjoyable, but which is not physiological necessary to life.
• You need oxygen, but you want a hot fudge sundae.
• Satisfaction is achieved by fulfilling wants.
• Wants are the form taken by human needs when shaped by culture and individual personality.
• When backed by buying power wants become demands companies address needs by putting forth a value proposition, a set of benefits that they promise to consumers to satisfy their needs.

The correct answer is Alexander Cunningham.

Key Points

• Alexander Cunningham is known as the father of the Archaeological Survey of India.
• Cunningham was the first to excavate Sarnath (Varanasi).

Additional Information

The correct answer is Goa.

Key Points

• Goa became the first 'Har Ghar Jal State' in India with 100% tap water connections in October 2020.
• Goa has become the first state in India to provide 100 percent tap water connections in the rural areas covering 2.30 lakh households.
• The Jal Jeevan Mission of the Central Government aims to provide piped water to all the rural households by 2024.
• Two districts-South Goa with 98,000 households in 191, gram-panchayats and North Goa with one lakh 65 thousand rural households have been fully saturated with assured water supply through the tap connections.
• Goa to strengthen the water testing facilities is also in the process of getting 14 water quality testing laboratories that are accredited by the National Accreditation Board for Testing and Calibration Laboratories (NABL).
• Under Jal Jeevan Mission, it is mandatory that 5 persons in every village, especially women, must be trained in using field test kits to test the water.
• Currently, **Gajendra Singh Shekhawat is a Union Jal Shakti Minister.**​

Additional Information

• Goa is a state in western India with coastlines stretching along the Arabian Sea.
• Its long history as a Portuguese colony prior to 1961 is evident in its preserved 17^th-century churches and the area's tropical spice plantations.
• Goa is also known for its beaches.

The correct answer is Overloading.

Key Points

• An electric fuse is a safety device used to limit the current in an electric circuit which melts and breaks the circuit whenever there is an excess flow of current through the circuit.
• A fuse is usually a short piece of wire and is installed in a circuit to stop the flow of excessive current.
• The material of the fuse has high resistivity and a low melting point.

Additional Information

• Functions of Electric Fuse:
• It acts as a barrier between an electric circuit and the human body.
• It prevents any damage to the electric device by restricting excess current flow.
• It prevents overloading of current.
• It prevents the damage caused by the mismatch of the load.
• It prevents blackouts.

The correct answer is 'Haryana'

Key Points

• Haryana:
• Delhi, the capital of India, shares its border with the state of Haryana.
• Haryana surrounds Delhi on three sides: in the west, north, and south.
• Major cities in Haryana such as Gurugram, Faridabad, and Sonipat are in close proximity to Delhi, making these areas part of the National Capital Region (NCR).
• The extensive connectivity between Delhi and these nearby regions in Haryana facilitates a significant socio-economic interaction.

Additional Information

• Punjab:
• Punjab does not share a border with Delhi.
• It is located to the northwest of Haryana and has distinct geopolitical boundaries separated from Delhi by the state of Haryana.
• Punjab is renowned for its rich agricultural land, history, and Punjabi culture, but it does not have direct geographical adjacency to Delhi.
• Himachal Pradesh:
• Himachal Pradesh is a northern state known for its mountainous terrain and does not share a border with Delhi.
• The state's boundaries are adjacent to Punjab, Haryana, and Jammu and Kashmir, but it lies further to the north compared to Delhi.
• Himachal Pradesh's geographical separation from Delhi is significant enough that it does not influence Delhi's immediate socioeconomic dynamics.
• Jammu and Kashmir:
• Jammu and Kashmir, comprising the northernmost part of India, does not share a boundary with Delhi.
• It is separated from Delhi by a considerable distance, with the states of Punjab and Himachal Pradesh lying in between.
• Jammu and Kashmir's proximity to the western Himalayan range marks its distinct geographical and cultural landscape, separate from Delhi's border dynamics.

Important Points

• Delhi also shares its border with the state of Uttar Pradesh apart from Haryana.
• Uttar Pradesh lies to the east of Delhi and includes important nearby cities such as Noida and Ghaziabad, which are also part of the NCR.
• The National Capital Territory (NCT) of Delhi is a significant area for India's administration, geography, and urban planning, influencing multiple surrounding states.

The correct answer is Pancreas.

Key Points

• The pancreas is a compound (both exocrine and endocrine) elongated organ situated between the limbs of the 'C' shaped duodenum,99% part of the pancreas is exocrine while only 1% part is endocrine.
• The exocrine portion (acini cells) secretes an alkaline pancreatic juice containing enzymes and the endocrine portion (islets of Langerhans) secretes hormones - insulin, glucagon & Somatostatin.
• The islets of Langerhans has 3 types of cells A cells, B cells, and the 8-cells.
• The cells surround the B cells.
• Insulin is secreted by the B cells.
• Glucagon is secreted by the A cells.
• The hormone somatostatin is secreted by the 6-cells (Delta Cells).

Additional Information

• The hormones insulin & glucagon are very important for sugar metabolism.
• Insulin is released into the bloodstream to lower down blood sugar levels and prevent hyperglycemia.
• Glucagon is released into the bloodstream to prevent blood sugar levels from dropping too low (hypoglycemia).
• Somatostatin is a growth-inhibiting hormone, it inhibits the secretion of several other hormones.

The correct answer is Rahul Dravid.

Key Points

• Rahul Dravid
• He holds the record for most catches in Test cricket by a non-wicket-keeper and also the record for highest scoring partnership in Test cricket with Sachin Tendulkar.
• He is a former Indian cricketer who is often called 'Mr. Dependable and 'The Great Wall'.
• He made his international ODI debut on 3 April 1996 against Sri Lanka and his test debut on 20 June 1996 against England.
• He has been felicitated with national awards like Arjuna Award, Padma Shri, and Padma Bhushan awards and was inducted into the ICC Hall of Fame in 2018.

Additional Information

• ​Ajay Jadeja
• He made his debut in the international ODI on 28 February 1992 against Sri Lanka and his debut in the international test cricket on13 November 1992 against South Africa.
• He holds the record of the longest one-day partnership with Mohammed Azharuddin in matches against Zimbabwe and Sri Lanka.
• Saurav Ganguly
• He is a former national cricket team captain of India.
• Nickname: God of the Off Side.
• Currently serving as the president of the Board of Control for Cricket in India.
• Mohammad Azharuddin
• Mohammad Azharuddin is an Indian politician and a former international cricketer.
• He is the Working President of the Telangana Pradesh Congress Committee and was the Member of Parliament for Moradabad.

The correct answer is 56^th Amendment Act.

Key Points

• 56^th Constitution Amendment
• Under this amendment, on 30 May 1987, Goa was given the status of a separate state.
• Goa became the 25^th state of India.

Additional Information

Given:

Cost price is Rs. 1680.

Desired profit to earn is 25%

Discount given is 16%

Concept Used:

S.P = C.P + Profit

S.P = M.P - Discount

Calculation:

S.P of the bag = 1680 + 1680 × 1/4

⇒ 1680 + 420

⇒ 2100

Let the Marked Price (M.P) of the bag be Rs. M.

According to the question,

M - M × 16% = 2100

⇒ M - M × 0.16 = 2100

⇒ M (1 - 0.16) = 2100

⇒ M × 0.84 = 2100

⇒ M = 2500

So, MP = Rs. 2500

∴ Radha should mark the bag as Rs. 2500.

Shortcut TrickLet the marked price of the bag be A.

According to the question,

A × 0.84 = 1680 × 1.25

⇒ A = 2500

∴ Radha should mark the bag as Rs. 2500.

Given:

2 cos2 θ - 5 cos θ + 2 = 0

0° < θ < 90°

Concept used:

Middle Term Factor Method

Tanα = Sinα/Cosα 

Calculation:

Let Cosθ be P

Now putting Cos θ = P in the given expression,

2 P²- 5 P + 2 = 0

⇒ (2p - 1) (P - 2) = 0

Now, We can't take (P - 2) = 0 because Cos θ is always less than 1.

Now, (2p - 1) = 0

⇒ P = 1/2

⇒ Cos θ = Cos 60°

⇒ θ = 60°

Now, sec 60° = 2

So, tan 60° = sin60°/cos60° = √3

Now, (sec θ + tan θ) = (sec 60° + tan 60°) 

⇒ (2 + √ 3)

∴ The required value of (sec θ + tan θ) is (2 + √ 3).

Given:

15 ÷ 3 of 2 × 4 + 9 ÷ 18 of 2 × 3 - 4 ÷ 8 × 2

Concept used:

Calculation:

15 ÷ 3 of 2 × 4 + 9 ÷ 18 of 2 × 3 - 4 ÷ 8 × 2

⇒ 15 ÷ 6 × 4 + 9 ÷ 36 × 3 - 4 ÷ 8 × 2

⇒ 5/2 × 4 + 1/4 × 3 - 1/2 × 2

⇒ 10 + 3/4 - 1

⇒ (40 + 3 - 4)/4

⇒ 39/4

⇒ $9\frac{3}{4}$

**∴ Required answer is $9\frac{3}{4}$**​​​​​​

Given:

Points A, D, C, B, and E are concyclic

∠AEC = 50°

∠ABD = 30°

Concept used:

Angles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points.  

Calculation:

AD & AC are joined.

Now,

∠AEC = 50° and ∠AEC = ∠ABC = 50°

∠ABD = 30°

Now,

∠ABC = ∠ABD + ∠CBD

⇒ 50° = 30° + ∠CBD

⇒ ∠CBD = 50° - 30°

⇒ ∠CBD = 20°

∴ The measure of ∠CBD is 20°.

Given:

$\frac{x}{y}+\frac{y}{x}=2$

Concept used:

(x - y)² = (x2 - 2xy + y2)

Calculation:

x/y + y/x = 2

⇒ {(x × x) + (y × y)}/(x × y) = 2

⇒ (x² + y²)/xy = 2

⇒ (x2 + y2) = 2xy      ----(1)

Now,

(x - y)

⇒ √(x - y)²

⇒ √(x2 - 2xy + y2)

⇒ √(x2 + y2 - 2xy)

⇒ √(2xy - 2xy)      (From (1))

⇒ 0

∴ The required value of (x - y) is 0.

Shortcut Trick

${x \over y} + {y \over x}=2$

${x^2+ y^2 \over xy}=2$ ⇒ ${x^2+ y^2 }-2xy=0$

$(x- y)^2=0$ ⇒ x - y = 0

Given:

Pipe A fills the empty tank in 10 hours

Pipe B fills the empty tank in 16 hours

Concept Used:

Total work = LCM of time taken by each pipe

Calculation:

LCM of 16 and 10 = 80

Let total work be 80 units

Pipe A does = 80/10 = 8 units per hour

Pipe B does = 80/16 = 5 units per hour

Now,

Pipe B & A fill the tank in two hour

⇒ (5 + 8) units

⇒ 13 units

Now,

Each B & A will keep filling the tank for = (80/13) ≈ 6 hours 

After (6 × 2) = 12 hours, the tank will be filled by (13 × 6) = 78 units. 

2 units are yet to be filled

On, 13^th hour B will be opened. 

It will take 2/5 hour for B to fill the remaining tank entirely.

Total time = 12 + 2/5 = $12\frac{2}{5}$ hours 

∴ The empty tank will be filled in $12\frac{2}{5}$ hours.

Given:

Profit on 1^st item = 20%

Loss on second item = 10%

Concept Used:

S.P = C.P × (1 + profit percentage)

S.P = C.P × (1 -  loss percentage)

Calculation:

Let the cost price (C.P) of the first item be Rs. 100x.

Now,

S.P of the first item = 100x × 1.2 = Rs. 120x

C.P of the second item = Rs. 120x

S.P of the second item = 120x × 0.9 = Rs. 108x

C.P of both items = (100x + 120x) = Rs. 220x

S.P of both items = (120x + 108x) = Rs. 228x

Overall profit at the end of both transaction = (228x - 220x) = Rs. 8x

Profit percentage = (8x/220x) × 100% = $3\frac{7}{11}$%

∴ The overall profit percentage is $3\frac{7}{11}$%

Shortcut Trick Let's SP of first item is 100 

then CP of second item is 100 

CP of first item = 100× ${100 \over 120}$ = $1000 \over 12$

SP of second item = 100 × ${90 \over 100}$ = 90 

Profit = 190 - $({1000 \over 12} + 100)$ 

${80 \over 12}$

Profit % = ${{ 80\over 12} \over { 2200\over 12}} (\times 100 )$ 

 $3 {7 \over 11}$%

Given:

Numbers are 5, 35, 39 and 65

Concept used:

The smallest number that is divisible by a series of numbers is their LCM.

Calculation:

LCM (5, 35, 39, 65) = 1365

Largest five-digit number = 99999

The approximate quotient when 99999 is divided by 1365

⇒ 99999 ÷ 1365 ≈ 73

The largest five-digit number which is divisible by 1365

⇒ 73 × 1365

⇒ 99645

So, the largest five-digit number which is divisible by 5, 35, 39 & 65 is 99645

Now,

The sum of digits of 99645 = 9 + 9 + 6 + 4 + 5 = 33

∴ The sum of the digits of the largest five digit number which is divisible by 5, 35, 39 and 65 is 33.

Given:

The angles of a Triangle are in AP

the smallest angle is 50° less than that of the largest angle

Concept used:

All three angles of a triangle sum up to 180°

Three elements of arithmetic progression can be supposed as (a - d), a, (a + d) where a is the first term and d is the common difference

Calculation:

Let the smallest angle of the triangle be (A - D)°

Now,

The second-largest angle of the triangle = A°

The largest angle of the triangle = (A + D)°

According to the question,

(A + D)° - 50°  = (A - D)°

⇒ (A + D)° - (A - D)° = 50°

⇒ 2D = 50°

⇒ D = 25°

Now,

(A - D)° + A° + (A + D)° = 180° 

⇒ 3A° = 180° 

⇒ A° = 60° 

The largest angle of the triangle = (A + D)° = (60 + 25) = 85°

∴ The largest angle of the triangle is 85°.

Given:

(56√7x3 - 2√2y3) ÷ (2√7x - √2y) = Ax2 + By2 - Cxy

Concept used:

(a3 – b3) = (a – b)(a2 + b2 + ab)

Calculation:

(56√7x3 - 2√2y3) ÷ (2√7x - √2y)

⇒ {(2√7x)³ - (√2y)³} ÷ (2√7x - √2y)

⇒ {(2√7x - √2y) × (2√7x)2 + 2√7x × √2y + (√2y)2} ÷ (2√7x - √2y)

⇒ {(2√7x - √2y) × (28x² + 2√14xy + 2y²)} ÷ (2√7x - √2y)

⇒ (28x2 + 2√14xy + 2y2)

According to the question,

(56√7x3 - 2√2y3) ÷ (2√7x - √2y) = Ax2 + By2 - Cxy

⇒ (28x2 + 2√14xy + 2y2) = Ax2 - Cxy+ By2 

Now comparing both side we get,

A = 28

B = 2

C = (- 2√14)

Now,

A + B - √14C

⇒ 28 + 2 - {√14 × (- 2√14)}

⇒ 28 + 2 + 28

⇒ 58

∴ The required value of (A + B - √14C) is 58.

Given: 

The present population of the village is 15280

Male population increases by 25% i.e. 1/4

Female population increases by 15% i.e. 3/20

Population become after increment 18428

Concept used:

The Elimination Method for solving linear equations

Calculation:

Let the present male & female population be M & F respectively.

According to the question,

M + F = 15280      ....(1)

Then,

After increment male population = M + M × 1/4 = 5M/4

After increment Female population = F + F × 3/20 = 23F/20

According to the question,

(5M/4) + (23F/20) = 18428      ....(2)

Now, solving (1) & (2), we get M = 8560 & F = 6720.

Now, the difference between the present male & female population = M - F = 8560 - 6720 = 1840.

∴ The difference between the present population of males and females in the village is 1840.

Given:

The ratio of monthly incomes of A and B is 4 ∶ 5

The ratio of monthly expenditures is 3 ∶ 8

The income of A is equal to the expenditure of B

Concept used:

Savings = Income - Expenditure

Calculation:

Let the common ratio of monthly incomes & expenditures be P & Q respectively.

Now,

Monthly income of A = 4P

Monthly income of B = 5P

Now,

Monthly expenditures of A = 3Q

Monthly expenditures of B = 8Q

According to the question,

4P = 8Q

⇒ P = 2Q

Now,

Monthly income of A = 4 × 2Q = 8Q

Monthly income of B = 5 × 2Q = 10Q

Now,

Monthly savings of A = (8Q - 3Q) = 5Q

Monthly savings of B = (10Q - 8Q) = 2Q

Ratio of the savings of A & B = 5Q : 2Q = 5 : 2

∴ The ratio of the savings of A & B is 5 : 2.

Anuj scored in subject A = 80% × 75 = 60

Anuj scored in subject B = 55% × 80 = 44

Anuj scored in subject C = 68% × 100 = 68

Anuj scored in subject D = 66% × 50 = 33

Anuj scored in subject E = 84% × 150 = 126

Total marks obtained by Anuj = (60 + 44 + 68 + 33 + 126) = 331

∴ The total marks obtained by Anuj in all the five subjects are 331.

Mistake Points In the table, marks are not given. The percentage of each student in each subject is given.

So before calculating the sum, we need to find the individual marks obtained in each subject by each student as explained in the solution.

Given:

The radius of the bigger circle = 18 cm

The radius of the smaller circle = 16 cm

Length of the common chord = 20 cm

Concept used:

If two circles intersect in two points, prove that the line through their centers is a perpendicular bisector of the common chord.

Calculation:

Here,

AB is the common chord and C1C2 is the distance between the centres of the circles.

AB is being perpendicularly bisected at point D by C₁C₂.

ΔAC₁D & ΔAC₂​D are right-angled triangles.

AC1 = 18 cm

AC2 = 16 cm

AB = 20 cm

AD = 20/2 = 10 cm

From ΔAC1D,

(AC₁)² = (C1​D)² + (AD)²

⇒ 18² = (C1​D)2 + 10²

⇒ (C1​D)2 = 324 - 100

⇒ (C1​D)2 = 224

⇒ (C1​D)2 = 14 × 16

⇒ C₁D = 4√14

From ΔAC2D,

(AC2)2 = (C2​D)2 + (AD)2

⇒ 162 = (C2​D)2 + 102

⇒ (C2​D)2 = 256 - 100

⇒ (C2​D)2 = 156

⇒ (C2​D)2  = 4 × 39

⇒ C2​D = 2√39

Now, the distance two centres of the intersecting circles = C1C2 = C1D + C2​D = (4√14 + 2√39) cm

∴ The distance between their centres is (4√14 + 2√39) cm.

Shortcut Trick

Simplify the expression using the identity (1 − cos² θ) = sin² θ and (1 − sin² θ) = cos² θ.

Expression = [2(1 − cos θ)(1 + cos θ)] ÷ [2(1 − sin θ)(1 + sin θ)] = (1 − cos² θ) ÷ (1 − sin² θ).

This simplifies directly to sin² θ ÷ cos² θ = tan² θ.

Since cot θ = 15/8, then tan θ = 8/15.

Result = (8/15)² = 64/225.

∴ The correct answer is 64/225.

Alternate Method

Given: cot θ = 15/8, where θ is an acute angle.

In a right-angled triangle, cot θ = Base / Perpendicular.

Using Pythagoras Theorem: H² = P² + B² ⇒ H² = 8² + 15² = 64 + 225 = 289 ⇒ H = 17.

Formula Used: (a − b)(a + b) = a² − b²

Expression = ((1 − cos θ)(2 + 2 cos θ)) / ((2 − 2 sin θ)(1 + sin θ))

⇒ [2 × (1 − cos θ)(1 + cos θ)] / [2 × (1 − sin θ)(1 + sin θ)]

⇒ (1 − cos² θ) / (1 − sin² θ)

By trigonometric identities: 1 − cos² θ = sin² θ and 1 − sin² θ = cos² θ

⇒ sin² θ / cos² θ = tan² θ

⇒ (1 / cot θ)²

⇒ (1 / (15/8))² = (8/15)²

⇒ 64 / 225

∴ The correct answer is 64/225.

Additional Information

Fundamental Trigonometric Identities

1. sin² θ + cos² θ = 1 | 2. 1 + tan² θ = sec² θ | 3. 1 + cot² θ = cosec² θ.

Reciprocal Relations

tan θ = 1 / cot θ, sec θ = 1 / cos θ, and cosec θ = 1 / sin θ.

Pythagorean Triplet

For a right-angled triangle with sides (8, 15, 17), the square of the largest side equals the sum of the squares of the other two sides (17² = 8² + 15²).

Given:

The volume of the wall is 51.2m³

Height = 10 × Width

Length = 8 × Height

Concept used:

Volume = Length × Width × Height

Surface area of one side of a wall = Height × Length

Cost of painting = Painting Cost per m² × Surface area

Calculation:

Let the width of the wall = A meter

Now,

the measure of height = 10 × A = 10A meter

the measure of length = 8 × 10A = 80A meter

Now,

The volume of the wall = A × 10A × 80A = 800A³ m³

According to the question,

800A3​ = 51.2

⇒ 8000 × A³ = 512

⇒ 8000 × A3 = 8 × 64

⇒ 1000 × A3 = 64

⇒ 10 × A = 4

⇒ A = 0.4

Now,

The width of the wall = 0.4m

The height of the wall = (0.4 × 10) = 4m

The length of the wall = (4 × 8) = 32m

Now, the surface area of one side of the wall

⇒ (4 × 32) m²

= 128 m²

Now,

The cost of painting the wall on one side

⇒ Rs. (128 × 100)

⇒ Rs. 12800

∴ The cost of painting the wall on one side at the rate of Rs. 100/m2 is Rs. 12800.

Number of students studying Science in Institute C = 36

Number of students studying Science in Institute D = 48

Total number of students studying Science in Institute C & D = (36 + 48) = 84

Number of students studying Computer Science in Institute A = 57

Number of students studying Computer Science in Institute E = 55

Number of students studying Computer Science in Institute A & E = (57 + 55) = 112

Now,

The ratio of number of students studying Science in institutes C and D taken together to the number of students studying Computer Science in institutes A and E taken together

⇒ 84 : 112

⇒ 3 : 4

∴ The ratio of the number of students studying Science in institutes C and D taken together to the number of students studying Computer Science in institutes A and E taken together is 3 : 4.

Persons who earn less than Rs. 200 = 12

Persons who earn Rs. 200 or more but less Rs. 250 = (26 - 12) = 14

Persons who earn Rs. 250 or more but less Rs. 300 = (34 - 26) = 8

Persons who earn Rs. 300 or more but less Rs. 350 = (40 - 34) = 6

Persons who earn Rs. 350 or more but less Rs. 400 = (50 - 40) = 10

Total number of people = 12 + 14 + 8 + 6 + 10 = 50

The number of persons who earn more than Rs. 250 = 8 + 6 + 10 = 24

Now,

The percentage persons earning Rs. 250 or more = 24/50 × 100% = 48%

∴ The percentage persons earning Rs. 250 or more is 48%.

Given:

The boat takes 45 mins to go 5 km upstream and 7.5 km downstream.

The boat takes 25 mins to go 5 km downstream and 2.5 km upstream

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. 

Distance =  Time × Speed

Elimination method for solving linear equations

Calculation:

Let the speed of the boat and the flow of the riven be B & R respectively. (in Kilometer per hours i.e. kmph)

Now,

Upstream speed = B - R = 1/P (suppose)

Downstream speed = B + R = 1/Q (suppose)

45 mins = 3/4 hour

25 mins = 5/12 hour

According to the question,

5/(B - R) + 7.5/(B + R) = 3/4

⇒ 5P + 7.5Q = 3/4      ....(1)

According to the question,

2.5/(B - R) + 5/(B + R) = 5/12

⇒ 2.5P + 5Q = 5/12      ....(2)

Solving (1) & (2) we get,

Q = 1/30 i.e. 1/(B + R) = 30

Now,

B + R = 30

The net speed during downstream = 30kmph

Now,

Time taken to cover 6km downstream

⇒ 6/30 hour

⇒ 1/5 hour

⇒ 1/5 × 60 mins

⇒ 12 mins

∴ 12 mins will it take to go 6 km downstream.

Given:

cos (2θ + 54°) = sin θ

 0° < (2θ + 54°) < 90°

Concept used:

Sin(90° - θ) = cosθ

Cos (90° - θ) = Sinθ

Calculation:

cos (2θ + 54°) = sin θ

⇒ sin(90° - (2θ + 54°) = sinθ

⇒ 90° - 2θ - 54° = θ

⇒ 36° = θ + 2θ

⇒ 36° = 3θ

⇒ θ = 12°

Now,

5θ = 5 × 12° = 60°

Now,

Sec (5θ/2)

⇒ Sec (60°/2)

⇒ Sec 30°

⇒ 2/√3

Now,

Cot 5θ 

⇒ Cot (5 × 12°)

⇒ Cot 60°

⇒ 1/√3

Now,

Cot 5θ + Sec (5θ/2)

⇒ 2/√3 + 1/√3

⇒ 3/√3

Now,

1/(Cot 5θ + Sec 5θ/2)

⇒ 1 / (3/√3)

⇒ √3/3

∴ The required value of 1/(Cot 5θ + Sec 5θ/2) is √3/3.

Given: 

$√{x}-\frac{1}{√{x}}=√{7}$

Concept used:

(A + B)² = A² + 2AB + B²

(A - B)² = A² - 2AB + B²

Calculation:

$√{x}-\frac{1}{√{x}}=√{7}$

⇒ (√x - 1/√x)² = (√7)² (Squaring both side)

⇒ (√x)² - (2 × √x × 1/√x) + (1/√x)² = 7

⇒ (√x)2 - (2 × 1) + (1/√x)2 = 7

⇒ (x + 1/x)  = 7 + 2

⇒ (x + 1/x)  = 9

⇒ (x + 1/x)² = 9²  (Squaring both side)

⇒ (x)²+ (2 × x × 1/x) + (1/x)2 = 92

⇒ (x)2 + (1/x)2 = 81 - 2

⇒ (x)2 + (1/x)2 = 79

∴ The required value of (x)2 + (1/x)2 is 79.

Amit scored in subject A = 64% × 75 = 48 

Amit scored in subject B = 65% × 80 = 52

Amit scored in subject C = 80% × 100 = 80

Total marks obtained by Amit in A,B, & C = (48 + 52 + 80) = 180

Vikram scored in subject B = 70% × 80 = 56

Vikram scored in subject C = 73% × 100 = 73

Vikram scored in subject D = 84% × 50 = 42

Vikram scored in subject E = 86% × 150 = 129

Total marks obtained by Vikram in B,C,D & E = (56 + 73 + 42 + 129) = 300

Amit scored less than Vikram = (300 - 180) = 120 marks

Amit scored less than Vikram by = 120/300 × 100% = 40%

∴ The total marks obtained by Amit in subjects A, B and C is 40% less than the total marks obtained by Vikram in subjects B C, D and E.

Given:

Principle (P) = Rs. 30000

Rate = 15% per annum

Time = ​$2\frac{2}{3}$ years ​​

Concept Used:

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:

Interest rate for first 2 years = 15%

Interest rate for 2/3 years = 15 × 2/3 = 10%

Now,

A = P × (1 + r/100)³

⇒ A = 30,000 × (115/100) × (115/100) × (110/100)

⇒ A = 30,000 × (23/20) × (23/20) × (11/10)

⇒ A = 43642.5

Now,

C.I = 43642.5 - 30000

⇒  13642.5

∴ The interest to be paid is Rs. 13642.5.

Shortcut Trick Amount become after $2\frac{2}{3}$ years = 30000 × 1.15 × 1.15 × 1.1

⇒ Rs. 43642.5

C.I = 43642.5 - 30000

⇒  13642.5

∴ The interest to be paid is Rs. 13642.5.

Given:

The average monthly salary of 60 employees of a factory is Rs. 29900

Concept used:

Total = Number of entities × Average

Calculation:

The total salary of 60 employees = Rs.(29900 × 60)

⇒ Rs. 1794000

The total salary of two officers = Rs. (90000 × 2)

⇒ Rs. 180000

The total salary of 8 supervisors

⇒ Rs. (65000 × 8)

⇒ Rs. 520000

The total salary of the remaining employees

⇒ Rs. (1794000 - 180000 - 520000)

⇒ Rs. 1094000

Number of remaining employees

⇒ 60 - 2 - 8

⇒ 50

The average salary of the remaining employees

⇒ Rs. (1094000 ÷ 50)

⇒ Rs. 21880

∴ The average salary of the remaining employees is Rs. 21880.

Shortcut Trick 

In any right angled triange like above 

a = √(b² + c² - d²)

In the question, we have b = 11, c = 8 and d = 13

So, a = √(112 + 82 - 132) 

⇒ a = √16 = 4 cm

∴ PQ = 4 cm.

Alternate Method

Given:

ΔABC is a right-angled triangle at ∠B.

AQ = 11cm

PC = 8cm

AC = 13cm

Concept used: 

Pythagorean theorem states that the sum of the squares on the other two sides of a right-angled triangle is equal to the square on the hypotenuse (the side opposite the right angle)

Calculation:

Let the length of AB, BC, BQ & PB be T, S, x & y respectively.

Now,

ΔABC, ΔABQ, ΔBPC and ΔPBQ are all right-angled triangles. 

From ΔABC,

⇒ S² + T² = 13²      ....(1)

From ΔABQ,

⇒ x² + T2 = 112      ....(2)

From ΔBPC,

⇒ y² + S2 = 82      ....(3)

From ΔPBQ,

⇒ x2 + y2 = PQ2      ....(4)

Adding (2) & (3),

x2 + T2 + y2 + S2 = 112 + 82

⇒ x2 + y2 + (S2 + T2) = 185

⇒ x2 + y2 = 185 - (S2 + T2) 

⇒ x2 + y2 = 185 - 169

⇒ x2 + y2 = 16

⇒ x2 + y2 = 4²

⇒ PQ² = 4² (From 4)

⇒ PQ = 4 (∵ Negative value can't be consider for length)

∴ The length of PQ is 4cm.

The correct answer is 'Invigilator.'

Key Points

• Let's see the meanings of the given words-
• Inspector - an official employed to ensure that official regulations are obeyed, especially in public services. (स्‍कूलों, कारख़ानों आदि में नियमों के पालन आदि की जाँच करने वाला अधिकारी; निरीक्षक, इंस्‍पेक्‍टर)
• Manager - a man or woman who controls an organization or part of an organization. (प्रबंधक, पुरुष या महिला संचालक; मैनेजर)
• Invigilator - a person who supervises in an examination hall. (एक व्यक्ति जो एक परीक्षा हॉल में पर्यवेक्षण करता है; निरीक्षक)
• Verifier - someone who vouches for another or for the correctness of a statement. (जाँचकर्ता, सत्यापक)

​

Hence, the correct answer is option 3.

The correct answer is 'Applause.'

Key Points

• The given word 'Censure' means to tell somebody, in a strong and formal way, that he or she has done something wrong. (अनुचित काम करने के लिए किसी की भर्त्सना करना; घोर निंदा, भर्त्सना)
• Example: The parent was notified that her son received a censure from the principal for misbehaving.
• ​Let's see the meaning of other given options:-
• 'Contempt' means the feeling that somebody/something does not deserve any respect or is without value. (यह भावना कि कोई व्यक्ति सम्मान का हक़दार नहीं है तथा उसका कोई महत्व नहीं है; तिरस्‍कार, अवज्ञा)
• Example: She was arrested for contempt of court.
• 'Applause' means approval or praise expressed by clapping. (सराहना, शाबाशी, वाहवाही)
• Example: His speech drew enthusiastic applause.
• 'Blunder' means a stupid mistake. (भद्दी या मूर्खतापूर्ण भूल)
• Example: A last-minute blunder cost them the match.
• 'Fault' means something wrong or not perfect in a person’s character or in a thing. (व्‍यक्ति के चरित्र या किसी वस्‍तु में दोष)
• Example: Her main fault is laziness.

Hence, the correct answer is option 2.

Additional Information

• The antonyms of the word 'Censure' are "applause, praise, acclamation".
• The synonyms of the word 'Censure' are "criticism, scolding, condemnation".

The correct answer is 'The herd is grazing.'

Key Points

• In the underlined segment, the plural form of the verb ''are'' is incorrect.
• The subject 'The herd' in the given sentence is a singular subject.
• The singular form of the verb 'is' should be used with the singular subject 'The herd'.
• Therefore, the singular form of the verb ''is'' should be used in place of the plural form 'are'.

Hence, the correct answer is option 4.

Correct sentence: The herd is grazing in the fields far away from the farmer’s hut.

Additional Information

• Subjects and verbs must agree with one another in number (singular or plural). (विषय और क्रिया एक दूसरे के साथ संख्या (एकवचन या बहुवचन) में सहमत होना चाहिए)
• Thus, if a subject is singular, its verb must also be singular; if the subject is plural, its verb must also be plural. (इस प्रकार, यदि कोई विषय एकवचन है , तो उसकी क्रिया भी एकवचन होनी चाहिए ; यदि विषय बहुवचन है , तो उसकी क्रिया भी बहुवचन होनी चाहिए)

Hinglish

• रेखांकित खंड में क्रिया 'are' का बहुवचन रूप गलत है ।
• दिए गए वाक्य में subject 'The herd' एक एकवचन subject है।
• क्रिया का एकवचन रूप 'is', एकवचन subject 'The herd' के साथ प्रयोग किया जाना चाहिए।
• इसलिए बहुवचन क्रिया 'are' के स्थान पर एकवचन क्रिया 'is' का प्रयोग किया जाना चाहिए।

अत: सही उत्तर विकल्प 4 है।

सही वाक्य: The herd is grazing in the fields far away from the farmer’s hut.