SSC CHSL Tier-1 2022: Official Paper (Held On: 16 March, 2023 Shift 1) (Previous Year Paper)

Logic is "Shape : Number of sides".

Square : Four ⇒ A square is a shape that has four sides.

Similarily,

Rectangle : Four ⇒ A rectangle is a shape that also has four sides.

Therefore, "Rectangle : Four" follows the same relationship.

As for the other options:

• "Six : Hexagon" and "Five : Pentagon" also relate their number of sides to shape, So, these two options are wrong as they follow a reverse relationship.
• "Triangle : Five" is incorrect because a triangle has three sides, not five.

Hence, the correct answer is "Rectangle : Four".

In the given pair, "Arena : Wrestling", an arena is the place where the sport of wrestling typically takes place. So the relationship here is "Place : Sport".

Following this logic, a pitch is the place where the sport of cricket typically takes place. Therefore, "Pitch : Cricket" is the correct answer, following the same relationship.

While a pitch can also refer to the playing field in other sports (like hockey), it is most commonly associated with cricket. The other options, chess and skating, don't have a 'pitch' as their standard playing areas.

Hence, the correct answer is "Cricket".

Family Chart:

Given: 

Bharti is the sister of Chavi.

Avni is the mother of Bharti.

Chavi is the wife of Dhruv.

Dhruv is the father of Esha.

So, Avni is the maternal grandmother of Esha.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: Images are placed same in alternate places.

So, 'Option 1' will replace the question mark.

Hence, the correct answer is "Option 1".

According to the given Venn diagram:

The shaded area shows the "total number of wrappers are not pens".

So, the total number of 'wrappers are not pens' = 6 + 12 = 18.

Hence, the correct answer is "18".

The logic followed here is:

Option 1) JJG

Option 2) FFC

Option 3) XXT

Option 4) PPM

Here, 'XXT' is odd among the given options.

Hence, the correct answer is "Option 3".

The pattern followed here is,

(1) 225 – 5733  → 

15² = 225, 15³ = 3375 reverse order 5733

(2) 169 – 7912  →  

13² = 169, 13³ = 2197 reverse order 7912

(3) 361 – 9786  → 

19² = 361, 19³ = 6859 reverse order 9586 ≠ 9786

(4) 289 – 3194 →

172 = 289, 173 = 4913 reverse order 3194

Hence, "361 – 9786" is odd from the given alternatives.

Given equation: 9 ÷ 3 + 7 × 4 – 5 = 20.

BODMAS Table: 

Let's check each option one by one.

Option 1) ÷ and –, 5 and 4

Given: 9 ÷ 3 + 7 × 4 – 5 = 20

After interchanging the numbers and signs we get;

⇒ 9 - 3 + 7 × 5 ÷ 4 = 20

⇒ 9 - 3 + 7 × 1.25 = 20

⇒ 9 - 3 + 8.75 = 20

⇒ 17.75 - 3 = 20

⇒ - 14.75 ≠ 20

⇒ LHS ≠ RHS

Option 2) × and –, 3 and 5

Given: 9 ÷ 3 + 7 × 4 – 5 = 20

After interchanging the numbers and signs we get;

⇒ 9 ÷ 5 + 7 - 4 × 3 = 20

⇒ 1.8 + 7 - 4 × 3 = 20

⇒ 1.8 + 7 - 12 = 20

⇒ 8.8 - 12 = 20

⇒ - 3.2 ≠ 20

⇒ LHS ≠ RHS

Option 3) + and ×, 9 and 7

Given: 9 ÷ 3 + 7 × 4 – 5 = 20

After interchanging the numbers and signs we get;

⇒ 7 ÷ 3 × 9 + 4 – 5 = 20

⇒ 21 + 4 – 5 = 20

⇒ 25 - 5 = 20

⇒ 20 = 20

⇒ LHS = RHS

Option 4) ÷ and –, 7 and 5

Given: 9 ÷ 3 + 7 × 4 – 5 = 20

After interchanging the numbers and signs we get;

⇒ 9 - 3 + 7 × 4 ÷ 5 = 20

⇒ 9 - 3 + 7 × 0.8 = 20

⇒ 9 - 3 + 5.6 = 20

⇒ 14.6 - 3 = 20

⇒ 11.6 ≠ 20

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 3".

The first three items - Mobile, Laptop, and Computer - are all computing devices. They can process information, run software programs, connect to the internet, and perform multiple complex tasks.

On the other hand, a bulb, while it's an electrical device, does not have computing capabilities. Its primary function is to provide light. Therefore, it is different from the other three and is the correct answer.

Hence, the correct answer is "Bulb".

The  logic followed here is:

Consider '3' as '3 times',

Now,

7 @ 3 = 343

→ 7³ ⇒ 7 × 7 × 7 = 343.

9 @ 3 = 729

→ 93 ⇒ 9 × 9 × 9 = 729.

Similarly, for 6 @ 3 = ?

→ 63 ⇒ 6 × 6 × 6 = 216.

Hence, the correct answer is "216".

The logic followed here is:

Logic: (Sum of the Opposite value of all letters) × 3 = Code of the word.

‘YEAH’ is coded as ‘207’.

'YEAH' opposite 'BVZS'

⇒ (2 + 22 + 26 + 19) × 3

⇒ 69 × 3 = 207.

‘BULK’ is coded as ‘186’.

'BULK' opposite 'YFOP'

⇒ (25 + 6 + 15 + 16) × 3

⇒ 62 × 3 = 186.

Similarly, for 'CORD'

'CORD' opposite 'XLIW'

⇒ (24 + 12 + 9 + 23) × 3

⇒ 68 × 3 = 204.

So, 'CORD' will be written as '204'.

Hence, the correct answer is "204".

The image embedded in given figure is as shown below:

Hence, "Option 3" is the correct answer.

The image embedded in given figure is as shown below:

Hence, "Option 1" is the correct answer.

The correct dictionary order for the give words are:

3. Maternal
4. Maternity
5. Mother
6. Motor
7. Mundane

So, the correct sequence is '3, 1, 5, 4, 2'.

Hence, the correct answer is "Option 3".

Given Statements:

I. No R is T.

II. All T are H.

The least possible Venn diagram for the given statement is:

Conclusions:

I. No T is R - True (No R is T, so No T will be R).

II. No H is T - False (Because, All T are H).

III. No R is H - False (Because, No definite relation given between R and H, so it can be possible only).

So, Only conclusion I follows.

Hence, the correct answer is "Option 1".

The logic followed here is:

'SHOWER' is coded as 'SEXOIS',

Similarly, for 'TOPICS'

So, 'TOPICS' is coded as 'TCJPPT'.

Hence, the correct answer is "Option 3".

Logic: The relationship that is established in the given example is "tool : user".

In the given pair "Axe : Woodcutter", an Axe is the tool that a Woodcutter uses in their profession.

Following this logic, from the given options, a Spade is the tool that a Labourer (particularly one working in fields like construction or agriculture) uses in their profession.

Thus, "Spade : Labourer" follows the same relationship.

Hence, the correct answer is "Option 3".

The triangles are:

So, there are '14' triangles in the given figure.

Hence, the correct answer is "14".

The pattern followed here is,

(1) 6666 – 3333  → 6666 is divided by 2 = 3333.

(2) 8888 – 4444 →  8888 is divided by 2  = 4444.

(3) 4444 – 2222 → 4444 is divided by 2  = 2222.

(4**) 3333 – 1111→ 3333 is divided by 3  = 1111.**

Hence, "3333 – 1111" is odd from the given alternatives.

The logic followed here is:

Here, '80' will complete the given series.

Hence, the correct answer is "80".

The logic followed here is:

Logic: (1st number + 1)3 = 2nd number.

Now,

For, 7 : 512

→ (7 + 1)3

⇒ 83 = 512.

For, 11 : 1728

→ (11 + 1)3

⇒ 123 = 1728.

Similarly, for 10 : ?

→ (10 + 1)3

⇒ 113 = 1331.

Hence, the correct answer is "Option 1".

The logic followed here is

Hence, the correct answer is "Option 3".

The image embedded in given figure is as shown below:

 

Hence, "Option 2" is the correct answer.

The logic followed here is:

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (1st number + 3rd number) ÷ 2 = 2nd number.

Now,

For, (28, 53, 78)

→ (28 + 78) ÷ 2

⇒ 106 ÷ 2 = 53.

For, (34, 49, 64)

→ (34 + 64) ÷ 2

⇒ 98 ÷ 2 = 49.

Similarly, for (38, 40, 42)

→ (38 + 42) ÷ 2

⇒ 80 ÷ 2 = 40.

Hence, the correct answer is "Option 3".

The correct answer is Mandovi.

Key PointsMandovi River-

• It originates from a cluster of 30 springs at Bhimgad in the Western Ghats in the Belagavi district of Karnataka.
• The river has a total catchment area of 2032 sq km, of which 1580 sq km lies in Goa.
• Panaji is situated on the banks of the river Mandovi.
• Dudhsagar Falls in Goa are also formed by this river.
• The river passes through Karnataka and Goa before it empties into the Arabian Sea.

Additional InformationNarmada River-

• Narmada originates from Amarkantak in the Anupur district of Madhya Pradesh.
• Narmada is the longest river in MP and the 5th largest river in the country.
• Narmada is also the largest west-flowing river in India.
• The total length of Narmada is 1312 km and its total length in Madhya Pradesh is 1077 km.
• Narmada does not form a delta, it forms an estuary.

Luni River-

• Luni River originates from Nag Pahar or Naga hills in the Ajmer district of Rajasthan.
• Luni originates in the Pushkar valley of the Aravalli Range, near Ajmer, and passes through the southeastern portion of the Thar Desert.
• It ends in the marshy lands of Rann of Kutch in Gujarat.
• Jaswant Sagar Dam was built in 1892 by Maharaja Jaswant Singh. It is one of the largest artificial lakes in India.

Banas River-

• Banas River originates from Khamnor Hills of Aravalli Range, near Kumbhalgarh in Rajsamand, Rajasthan.
• Banas River is a tributary of the Chambal River and it is approximately 512 kilometers in length.
• This river is also called ‘Van Ki Asha‘.

The correct answer is Aluminium.

Key Points

• Out of the following, the speed of sound is maximum in Aluminium.
• Speed of sound in Aluminium at 25 deg Celsius is around 6420 m/s.
• Sound is a mechanical wave and needs a material medium for its propagation. It cannot travel through a vacuum.
• Sound travels at different speeds depending on what it is traveling through.
• Of the three mediums (gas, liquid, and solid) sound waves travel the slowest through gases, faster through liquids, and fastest through solids.
• Temperature also affects the speed of sound.
• For Example, at 0º Celcius, sound travels through air at 331 meters per second, but, at 20ºC, at room temperature, sound travels at 343 meters per second.

Important Points

The correct answer is rapid industrialization.

Key Points

• The second five-year plan's main focus was on the rapid industrial development of the country.
• It was made from 1956 to 1961, under the leadership of Jawaharlal Nehru.
• The Second Five Year Plan was based on Mahalanobis Model.
• P. C. Mahalanobis was a famous Indian statistician who founded the Indian Statistical Institute.
• This plan lags behind its target growth rate of 4.5% and achieved a growth rate of 4.27%.

Additional Information

The correct answer is National Bank for Agriculture and Rural Development.

Key PointsNABARD- 

• National Bank for Agriculture and Rural Development is the full form of NABARD.
• The National Bank for Agriculture and Rural Development was established on 12 July 1982.
• It is under the jurisdiction of the Ministry of Finance, Government of India.
• The bank has been entrusted with "matters concerning policy, planning, and operations in the field of credit for agriculture and other economic activities in rural areas in India".
• NABARD is active in developing and implementing financial inclusion.
• NABARD operates at 32 Regional Offices in the country.
• Headquarters of NABARD is located in Mumbai.

Additional InformationSEBI-

• SEBI stands for Securities and Exchange Board of India.
• The SEBI is the regulator of the securities and commodity market in the country owned by the Indian Government.
• SEBI was established on 12 April 1988 and its headquarters are located in Mumbai.
• On 30 January 1992, Statutory powers given were to it through the SEBI Act, 1992.
• The regional offices of SEBI are located in Ahmadabad, Kolkata, Chennai, and Delhi.

SIDBI-

• Small Industries Development Bank of India (SIDBI) is a development financial institution in India.
• It was established on April 2, 1990.
• It is headquartered in Lucknow.
• Its purpose is to provide refinance facilities and short-term lending to industries and serves as the principal financial institution in the Micro, Small, and Medium Enterprises (MSME) sector.

RBI-

• Reserve of India (RBI) was established in India on 1st April, in Kolkata in 1935 under the Reserve Bank Of India Act, 1934.
• It was set up on the recommendation of the Hilton Young Commission.
• RBI is the central bank of India and is responsible for the issue and supply of Indian currency,
• RBI is the regulatory body of the Indian Banking system and it is also managing a country's Payment system.

The correct answer is Mumbai City FC.

Key Points

• The Durand Cup is one of the oldest football tournaments in the world and the oldest in India.
• It's named after its founder, Sir Mortimer Durand, who started the tournament in 1888.
• In the 2022 Durand Cup, Bengaluru FC emerged as the winner and the runners-up is Mumbai City FC.

Important PointsDurand Cup -

• Founded- 1888
• Number of teams: 20
• Organizing body: Durand Football Tournament Society, and AIFF

Additional InformationOther tournaments related to Football are:-

• Senior NFC (Santosh Trophy)
• B.C. Roy Trophy
• Senior Women's National Football Championship
• Junior Girl's National Football Championship
• Sub–Junior Girl's National Football Championship

The correct answer is Maharashtra.

Key Points

• Kalsubai Peak, the highest point of the Sahyadri Mountains, is situated in the Ahmednagar district of Maharashtra, India.
• Standing at an impressive height of 5,400 feet (1,646 meters), it is often referred to as the 'Everest of Maharashtra'.
• The mountain range is part of the Western Ghats, a UNESCO World Heritage site renowned for its biodiversity.

Additional InformationOther state's highest peak-

The correct answer is 28.

Key Points

• Currently India has a total of 28 states and 8 Union Territories.
• With effect from October 31st, 2019 the state of Jammu and Kashmir has been officially bifurcated into the Union Territories of Jammu & Kashmir and Ladakh.
• Currently 8 Union Territories are

1. Andaman and Nicobar Islands
2. Chandigarh
3. Dadra Nagar Haveli & Daman and Diu
4. Delhi
5. Jammu & Kashmir
6. Ladakh
7. Puducherry
8. Lakshadweep

Important Points

• With the States Reorganisation Act, of 1956 and, the 7th Constitutional Amendment Act 1956, the distinction between Part A, and Part B states was done away with, and Part C states were abolished.
• On 1 November 1956, 14 states and 6 union territories were created.
• Andhra Pradesh was the first state of independent India formed on a linguistic basis it was formed on October 1, 1953.

The correct answer is Sardar Udham.

Key Points

• The 67th Filmfare Awards were given out on 30 August 2022 at Jio World Centre, Mumbai.
• The 67th edition of the awards honored the films released in 2021.
• Sardar Udham won the best film (critics) award at the 67th Filmfare Awards.
• Director of Sardar Udham Singh's movie is Shoojit Sircar.

Important Points68th Filmfare Awards- 

• Best Film- Gangubai Kathiawadi
• Best Film (Critics') - Badhaai Do
• Best Actor (Male) - Rajkummar Rao for Badhaai Do
• Best Actor (Female) - Alia Bhatt for Gangubai Kathiawadi

The correct answer is COVAXIN.

Key Points

• COVAXIN India's first indigenous vaccine against COVID-19.
• Hyderabad-based Bharat Biotech has developed Covaxin.
• It is done in collaboration with the Indian Council of Medical Research (ICMR) and the National Institute of Virology (NIV).

Important PointsCOVID-19

• COVID-19 stands for Corona Virus disease of 2019.
• Coronavirus disease (COVID-19) is an infectious disease caused by the SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) virus.

Additional InformationOther vaccines of COVID-19-

The correct answer is Web Browser.

Key Points

• Web Browser is a software application used to access information on the WWW (World Wide Web).
• When a user requests some information, the web browser fetches the data from a web server and then displays the webpage on the user’s screen.
• Visiting any website can be done using a web browser. When a URL (Uniform Resource Locator) is entered in a browser, the web server takes us to that website.
• Example of Web Browser- Google Chrome, Firefox, Safari, Opera Mini, Microsoft edge, etc.

Additional InformationHyperlink-

• A hyperlink is a text or an icon that you can click on to get to another website.
• Hyperlinks are found on virtually every webpage to help navigate readers to other pages and websites.
• The default formatting for a hyperlink on a webpage or in a document is blue, underlined text.

World Wide Web-

• The World Wide Web (WWW) is a network of online content that is formatted in HTML (Hypertext Markup Language) and accessed via HTTP (Hypertext Transfer Protocol).
• Tim Berners Lee invented the World Wide Web in 1989.

Joystick-

• A joystick is an input device that can be used for controlling the movement of the cursor or a pointer in a computer device.
• A joystick is also known as the control column.
• The joystick is used for gaming purposes.

The correct answer is Golconda Fort.

Key Points

• Golconda Fort:-​
• The Golconda Fort was built by the Qutubshahi of the Qutub Shahi Dynasty.
• Golconda Fort is a fortified citadel.
• It was the capital city of the Qutb Shahi dynasty.
• It is located in Hyderabad, Telangana.
• It was originally known as Mankal and built on a hilltop in 1143.
• It has thick walls and tall heavy gates with sharp iron spokes.
• In some places, a part of the wall comes out in a round shape.
• These are called bastions (Burj).
• These bastions have small holes in them to attack enemies while being hidden.
• These are even higher than the wall.
• The outer wall of this fort has 87 bastions.
• The Golconda Fort was made strong and big to protect it from any outside enemy attack.
• In 1200, this fort was made of mud and different rulers lived here.

Additional Information

• Red Fort (Lal Qila):- 
• It is a monument built in 1638 that rises 33 meters (108 ft) above Old Delhi.
• It was built by the Mughal Emperor Shah Jahan in the mid-17th century. The fort is located in what is now the center of Delhi, India.
• Red Fort massive, 2.5-km-long enclosing walls are made of red sandstone and that's where the monument got its name from.
• A few parts of the fort are also made of red stone while the remaining structure is built using marble.
• Rajgad Fort:-​
• ​​It is a fort situated in the Pune district of Maharastra.
• It was also known as Murumdev.
• It served as the capital of the Maratha Empire under the rule of Chatrapati Shivaji Maharaj.
• Chiktan Fort:-
• ​Chiktan Fort is located in Chiktan village of Kargil district by the river Indus.
• The fort was built in the 16th century and had nine stories.
• Balti craftsmen constructed the castle in the 16th century which served as a royal residence for centuries.

The correct answer is offences for armed assembly.

Key Points

• Right to Freedom
• The objective of the Indian Constitution is to ensure freedom of thought, expression, belief, religion, and worship. Therefore, the Right to Freedom has been mentioned in the Indian Constitution from Articles 19 to 22.
• In these, provisions have been given keeping in mind all the sections of the people of the country, so that any person can do any work of his mind, but that work should not be illegal and unconstitutional, nor should that work be done by any other person such that the fundamental rights should be violated.
• Article 19 of the Indian Constitution is most important in this regard. Article 19 of the Indian Constitution at present describes only 6 freedoms for the citizens of the country, which are as follows
• Freedom of thought and expression
• Freedom of arms and peaceful assembly.
• Community and freedom of association
• Freedom of travel
• Freedom of residence
• Freedom of trade (Hence option 1 is correct)
• Article 20 offers protection in respect of conviction for offences. (Hence option 4 is correct)
• Article 21 offers protection of life and personal liberty. (Hence option 2 is correct)
• Article 22 offers protection against arrest and detention in certain cases.

The correct answer is September 16.

Key Points 

• Ozone Layer:-
• International Day for the Preservation of the Ozone Layer or World Ozone Day is observed on September 16, every year.
• It is celebrated to spread awareness among people about the depletion of the Ozone Layer and search for possible solutions to preserve it.
• On December 19, 1994, the United Nations General Assembly proclaimed September 16 the International Day for the Preservation of the Ozone Layer.
• On September 16, 1987, the United Nations and 45 other countries signed the Montreal Protocol, on substances that deplete the Ozone layer.
• The purpose of the Montreal Protocol is to protect the Ozone layer by reducing the production of substances that are supposed to be responsible for Ozone layer depletion.
• In 1985, the world’s governments adopted the Vienna Convention for the Protection of the Ozone Layer.

Additional Information

• Other Important Days of September:-

The correct answer is Kashi.

Key Points

• Saint Kabir Das:-​
• Kabir believed in a formless Supreme God and preached that the only path to salvation was through bhakti or devotion.
• The language of his poetry was a form of spoken Hindi widely understood by ordinary people.
• His great writing, Bijak, has a huge collection of poems.
• Some of these were later collected and preserved in the Guru Granth Sahib, Panch Vani and Bijak.
• We get to know of his ideas from a vast collection of verses called sakhis and pads said to have been composed by him and sung by wandering Bhajan singers.
• He was brought up in a family of Muslim julahas or weavers settled in or near the city of Benares (Varanasi).
• He was an Indian mystic poet, whose writings influenced the Bhakti movement.
• He lived in the fifteenth-sixteenth centuries and was one of the most influential saints.
• Kashi:-  
• ​It is one of the oldest cities in the world.​
• ​It is located on the left bank of the Ganges (Ganga) River and is one of the seven sacred cities of Hinduism

Additional Information

• Amritsar:-
• ​The famous Golden Temple is situated the Amritsar city of Punjab state of India.
• Somanth:-
• ​It is famous for the Somanth Temple of Gujrat.
• Agra:-
• ​The city of Agra is famous for various World Heritage Sites including Taj Mahal, Agra Fort.

The correct answer is Venus.

Key Points

• Venus:-
• Venus is sometimes called Earth's twin because Venus and Earth are almost the same size, have about the same mass (they weigh about the same), and have a very similar composition (are made of the same material).
• They are also neighboring planets.
• However, Venus and Earth are also very different.
• Venus has an atmosphere that is about 100 times thicker than Earth's and has surface temperatures that are extremely hot.
• Venus does not have life or water oceans like Earth does.
• Venus also rotates backward compared to Earth and the other planets.

Additional Information

• Neptune:-
• It was discovered on the basis of the law of gravitation.
• It is the farthest known planet from the Sun in the Solar System.
• Its revolution period is 164 years and the rotation period is 16 hours and 7 minutes.
• Neptune and Uranus are the only two planets discovered with the help of a telescope.
• Uranus:-
• It is the seventh planet from the Sun and has the third-largest diameter in our solar system.
• It was the first planet found with the aid of a telescope, Uranus was discovered in 1781 by astronomer William Herschel, although he originally thought it was either a comet or a star.
• Mars:-​
• Mars is called Red Planet.
• It has two satellites - Phobos and Deimos.
• Mars is the fourth planet in the solar system.
• It is the second smallest planet in the solar system.
• In English Mars carries the name of the Roman God of War.

The correct answer is 1765.

Key Points

• East India Company:- 
• It was a privately owned company that was established to create profitable trade with countries in the region of Asia called the "East Indies".
• It was granted a Royal Charter by Queen Elizabeth in 1600.
• The company was formed to own a stake in the East Indian spice business.
• That trade was a monopoly of Spain and Portugal until the defeat of the Spanish Armada (1588) by England gave the British a chance to break the monopoly.
• By 1612 the company made separate trips, subscribing separately.
• There were temporary joint stocks until 1657 when a permanent joint stock was raised.
• On 12 August 1765 the Mughal emperor appointed the East India Company as the Diwan of Bengal.

The correct answer is Lawn Bowls.

Key Points

• Lawn Bowls:-
• ​In this game, a ball (known as a bowl) is rolled toward a smaller stationary ball, called a jack.
• Bowls is generally played on a flat lawn, about 40–42 yards (37–38 meters) square, and surrounded by a shallow ditch and grass banks beyond.
• Lovely Choubey:-
• She is a female international lawn bowler
• ​She won a silver medal in the singles as well as the pairs events at the 2014 Asian Lawn Bowls Championship.
• In 2023, she won the fours gold medal at the 14th Asian Lawn Bowls Championship in Kuala Lumpur.

The correct answer is 31.

Key Points

• Article 31:-
• Article 31 which contained the right to property was abolished.
• It is still a constitutional right but not a Fundamental Right.
• Constitution of India:-
• It took 2 years, 11months, 18 days to be written.
  

It is the lengthtiest written constitution in the world.

• Dr. B. R. Ambedkar is known as the Father of the Indian Constitution.

Additional Information

• Article 31 A of the Constitution of India, speaks about the acquisition of estates.
• Article 31B states that the acts which are present in the ninth schedule and are inconsistent with the provisions laid down by the constitution or resist any decree or order will be left on the competent legislature to amend, revoke, or to let it be in force.
• Article 31 D mentioned about Saving of laws in respect of anti-national activities.

The correct answer is Rhinoceros

Key Points

• Rhinoceros:- 
• ​​They are found in the Indian subcontinent.
• It is listed as Vulnerable on the IUCN Red List.
• 90% are found in Kaziranga National Park.
• There are 2,640 rhinoceros in four protected areas in Assam.
• They are mainly found in Assam, West Bengal, and Uttar Pradesh.
• The one-horned rhinoceros (Indian rhinoceros) are the largest of the rhino species.
• The National Rhino Conservation Strategy was launched in the year 2019 for the conservation of big-horned rhinos.
• Indian Rhino Vision 2020 was launched in 2005, it is an ambitious effort to attain a wild population of at least 3,000 greater one-horned rhinos spread over seven protected areas in the Indian state of Assam by the year 2020.
• Kaziranga National Park:-
• Kaziranga National Park’s 430 sq. km. area sprinkled with dense forests
• This is home to more than 2200 Indian one-horned rhinoceros, approximately 2/3rd of their total world population.
• It was formed in 1908 on the recommendation of Mary Curzon, the park is located on the edge of the Eastern Himalayan biodiversity hotspots – Golaghat and Nagaon districts.
• Kaziranga national park present in Assam is famous for conserving Rhinoceros (Rhinoceros unicorns).
• It is basically a reserve of natural, semi-natural, or developed land that a sovereign state declares or owns.
• Kaziranga National Park is a national park in the Golaghat and Nagaon districts of the state of Assam, India.
• Kaziranga National Park also shelters about 15 species of India’s threatened mammals.

Additional Information

• Hippopotamus:-
• Hippopotamuses are large, semiaquatic mammals native to sub-Saharan Africa.
• Although their name comes from the Greek for “river horse”—because of the time they spend in the water—their closest living relatives are whales, dolphins, and pigs.
• They can’t swim, breathe underwater, or even float—but they have developed a tactic that lets them nap underwater.
• Langur:-
• The general name given to numerous species of Asian monkeys belonging to the subfamily Colobinae.
• The head and body are about 40 to 80 cm (16 to 31 inches) long and the tail about 50 to 110 cm;
• weight varies from 5.5 kg to 19 kg.
• Gibbon:-
• A species of small apes found in the tropical forests of Southeast Asia.

The correct answer is Calcium hydroxide

Key Points

• Calcium hydroxide:-
• It is used to neutralize excess acidity.
• For example, lakes and soils are affected by acid rain.
• Calcium hydroxide dissolves in water to produce limewater, which is used to test carbon dioxide.
• The pH value of Calcium hydroxide is ranging from 9 to 11.5.

Additional Information

• Potassium hydroxide:-​
• ​Potassium hydroxide is an inorganic compound with the components KOH and is generally referred to as caustic potash.
• KOH is noteworthy as the precursor to maximum smooth and liquid soaps, as well as numerous potassium-containing chemicals.
• Even at high temperatures, solid KOH does not dehydrate without difficulty.
• Magnesium hydroxide:-​
• It is a white-colored substance, slightly soluble in water.
• A suspension of Mg(OH)2 in water is called Milk of magnesia.
• It is used as an antacid, as a laxative, and for neutralizing acid wastewater.
• It is also used in the treatment of scalp dandruff.
• Ammonium hydroxide:-​
• The chemical formula for ammonium hydroxide is NH4OH.
• Ammonium hydroxide is a colorless liquid with a strong, pungent odor.
• It is made by dissolving ammonia gas in water, and the resulting solution contains around 30-35% ammonia by weight.

The correct answer is Bal Gangadhar Tilak.

Key Points

• The slogan "Swaraj is my birthright and I shall have it" was famously spoken by Bal Gangadhar Tilak.
• He was one of the prominent leaders of the Indian independence movement.
• Tilak was an influential figure in the late 19th and early 20th centuries and played a crucial role in mobilizing people against British colonial rule in India.
• His slogan became a rallying cry for India's struggle for self-rule and was widely embraced by freedom fighters and nationalists during that era.

Additional Information

• Bhagat Singh
• Bhagat Singh was a revolutionary and freedom fighter who played a significant role in India's struggle for independence from British rule.
• He was born on September 28, 1907, in Punjab, India, and became a prominent member of the Hindustan Socialist Republican Association (HSRA).
• He is remembered for his acts of resistance against British rule, including his involvement in the Lahore Conspiracy Case and the assembly bomb incident.
• Bhagat Singh was an advocate of socialist ideals and believed in the power of armed struggle to achieve freedom and justice for the Indian masses.
• Mahatma Gandhi
• Mahatma Gandhi, also known as the Father of the Nation, was a prominent leader and the guiding force behind India's nonviolent struggle for independence.
• He was born on October 2, 1869, in Gujarat, India, and led various movements such as the Non-Cooperation Movement and the Salt March.
• One of his famous quotes is "Be the change that you wish to see in the world."
• He promoted nonviolent civil disobedience as a means to achieve political and social change, emphasizing the principles of truth (Satya) and nonviolence (Ahimsa).
• Ambika Charan Majumdar
• Ambika Charan Majumdar was also an Indian revolutionary who actively participated in the freedom struggle against British colonial rule.
• He was born on November 13, 1888, in Bengal, India, and was associated with organizations like Anushilan Samiti and Jugantar.
• Majumdar's quote "I am prepared to make the supreme sacrifice, but I will not beg for mercy." also sparked the struggle for freedom among the revolutionaries.
• He assassinated a British district judge, Kingsford, in retaliation for his brutal suppression of freedom fighters.
• His dedication and fearlessness in the face of adversity made him an iconic figure in India's revolutionary movement during the early 20th century.

The correct answer is F7.

Key Points

• In MS-Word 365, the shortcut key to display the Editor task pane and check spelling and grammar in the document or selected text is F7.
• It provides a fast way to open the Editor task pane for spell and grammar checking in MS-Word 365.
• The Editor task pane examines spelling, grammar, style, and more, offering suggestions for improvements.
• We can also customize settings in the Editor task pane to ignore specific errors or modify language preferences.

Additional Information

• F10
• Pressing F10 activates the "KeyTips" feature.
• KeyTips are keyboard shortcuts that allow you to navigate and access various commands and options in the Ribbon interface.
• Pressing F10 displays KeyTips on the Ribbon, enabling you to use the keyboard to access different tabs, commands, and options.
• F1
• Pressing F1 in Microsoft Word opens the Help pane.
• It provides access to the Word Help feature, where you can find assistance, tutorials, and information on using different features and functions within the application.
• We can search for specific topics or browse through the available help resources.
• F2
• Pressing F2 allows you to edit the selected text directly.
• It activates the editing mode and places the cursor at the location of the selected text, enabling you to make changes or modifications easily.
• This can be helpful for quickly editing or updating content within your document.

The correct answer is Novak Djokovic.

Key Points

• Novak Djokovic won the Men’s Single title at Wimbledon 2022.
• He defeated Nick Kyrgios and earned his seventh Wimbledon title.
• He has won a total of 93 singles titles in total till date.
• He is a Serbian professional tennis player and one of the most successful athletes in the sport.

Additional Information

• Nick Kyrgios
• He is a professional tennis player from Australia.
• He has won seven ATP (Association of Tennis Professionals) singles titles, including the 2019 and 2022 Washington Open.
• In doubles, he has won four titles, including a major doubles title at the Australian Open in 2022.
• ​Rafael Nadal
• He is a professional tennis player from Spain.
• He has won a joint-record 22 Grand Slam men’s singles titles, including a record 14 French Open titles.
• He has also won 92 ATP singles titles.
• Rafael Nadal is one of only two men to complete the Career Golden Slam in singles.
• ​Daniil Medvedev
• He is a professional tennis player from Russia.
• He has won 20 ATP Tour singles titles, including the 2021 US Open and 2020 ATP Finals.
• He has also won six Masters titles, and contested four major finals and nine Masters finals in all.

Important Points

• Women’s Single Title at Wimbledon 2022
• Elena Rybakina won the Women’s Single title at Wimbledon 2022.
• She defeated Ons Jabeur in the final to win the Women’s’ singles tennis title at the 2022 Wimbledon Championships.
• This was her first Grand Slam title and the first for Kazakhstan.
• Rybakina was born in Russia but switched nationalities in 2018.

The correct answer is 1936.

Key Points

• Godaan is a Hindi novel written by Munshi Premchand, published in the year 1936.
• It was first published in 1936 and is considered one of Premchand's most renowned works.
• Munshi Premchand, whose real name was Dhanpat Rai Srivastava, was born on July 31, 1880, in Lamhi, near Varanasi.
• His literary contributions earned him the title of "Upanyas Samrat" (Emperor of Novels).
• Some of his famous novels are **Nirmala, Rangbhoomi, Gaban, Kafan etc.**​

Additional Information

• Rangbhoomi
• It was published in 1924 and is considered one of Munshi Premchand's significant works.
• This novel explores various social issues prevalent in Indian society during the colonial era, such as corruption, exploitation, and the struggle for justice.
• It revolves around the world of theatre, highlighting the challenges and complexities faced by artists, their conflicts, and their efforts to bring about social change through their art.
• Gaban
• It was published in 1931 and is considered one of Munshi Premchand's notable works.
• The novel delves into themes of greed, social hypocrisy, and the consequences of materialism in Indian society.
• The story revolves around Ramanath, the main character, who succumbs to his desires for wealth and social status. The novel follows his journey as he becomes entangled in a web of deceit and faces the consequences of his actions.
• Kafan
• It depicts the bleak and tragic life of a poor peasant named Gheesu and his son Madhav, who struggle with extreme poverty and societal indifference.
• The story explores themes of poverty, social inequality, and the dehumanizing effects of a rigid caste system prevalent in rural Indian society.
• "Kafan" serves as a sharp critique of the oppressive social conditions and the apathy of the privileged classes towards the suffering of the poor.

The correct answer is AVGAS 100 LL.

Key Points

• AVGAS 100 LL is the f indigenously developed special aviation fuel by the Indian Oil Corporation in 2022.
• AVGAS 100 LL stands for Aviation Gasoline 100 Low Lead.
• It is a special aviation fuel meant for piston-engine aircraft and unmanned aerial vehicles.
• It was produced at **IOCL's Gujarat refinery.**​

Additional Information

• Indian Oil Corporation Limited (IOCL)
• It is an Indian central public sector undertaking under the ownership of the Ministry of Petroleum and Natural Gas, Government of India.
• It is headquartered in New Delhi, India.
• Indian Oil is ranked 142nd on the Fortune Global 500 list of the world’s biggest corporations as of 2022.
• It is the largest government-owned oil producer in the country, with a net profit of $6.1 billion for the financial year 2020-21.

Shortcut Trick

By the property of circles, a chord subtends a 90° angle at the circumference if and only if it is the diameter of the circle.

Given diameter = 44 cm.

∴ The length of chord MN = 44 cm.

∴ The correct answer is 44 cm.

Alternate Method

Given:

Diameter of the circle = 44 cm

Angle subtended by chord MN at the circumference = 90°

Formula Used:

Angle in a semi-circle: The angle subtended by the diameter of a circle at any point on its circumference is always 90°.

Calculations:

⇒ Let P be any point on the circumference of the circle.

⇒ Given that ∠MPN = 90°.

⇒ According to Thales’ Theorem, if an angle subtended by a chord at the circumference is a right angle, then that chord must be the diameter of the circle.

⇒ Chord MN = Diameter of the circle

⇒ MN = 44 cm

∴ The correct answer is 44 cm.

Additional Information

Thales' Theorem

It states that if M, N, and P are points on a circle where the line MN is a diameter, then the angle ∠MPN is a right angle (90°).

Chord and Central Angle

The central angle subtended by the diameter is 180°. Since the angle at the circumference is half the angle at the center, 180° ÷ 2 = 90°.

Longest Chord

The diameter is the longest possible chord in any circle and its length is twice the radius (D = 2 × r).

Given:

cos Θ + sin Θ = √2

Formula:

sec Θ = 1/cos Θ

cosec Θ = 1/sin Θ

Solution:

$((cos Θ + sin Θ)^2 = (√2)^2$

$cos^2 Θ + 2cos Θ sin Θ + sin^2 Θ = 2$

$(cos^2 Θ + sin^2 Θ) + 2cos Θ sin Θ = 2$

1 + 2cos Θ sin Θ = 2

2cos Θ sin Θ = 1

2 = 1/cos Θ sin Θ

sec Θ cosec Θ = 2

Therefore, the value of sec Θ cosec Θ is 2.

Given:

Ratio of the marked price(MP) of a trouser and a jacket = 1 : 3

Discount on trouser = 20%

Total discount on both of them = 30%

Formula used:

Discount% = (Discount/MP) × 100

Calculation:

Let the MP of trouser and jacket be x and 3x

Discount on trouser = 0.2 × x = 0.2x

Total discount on both = 0.3 × (x + 3x) = 1.2x

⇒ Discount on jacket = 1.2x - 0.2x = x

Discount% on jacket = (x/3x) × 100 = 33.33

Shortcut TrickLet the discount on the jacket is x.

 3x - 90 = 10

3x = 100

x = 33.33%

∴ Discount on jacket = 33.33%

Calculation:

J1 = The value of average GDP of countries L and M in year Y1 = (205 + 315)/2 = 520/2 = 260

J2 =The value of average GDP of countries L and M in year Y4 = (105 + 115)/2 = 220/2 = 110

The value of (J1/J2) = 260/110 = 2.36

∴ Option 2 is the correct answer.

Given:

The radii of two concentric circles are 34 cm and 50 cm.

ABCD is a straight line and BC = 32 cm.

A and D are the points on larger circle and B and C are points on smaller circle.

Concept Used:

Pythagoras theorem

Hypotenuse² = Perpendicular² + Base²

Perpendicular drawn from the centre to the chord divide the chord into two equal parts.

Calculation:

<br>

BC = 32 cm

BP = 32/2 = 16 cm

In triangle OBP

Apply Pythagoras Theorem

OB² = BP² + OP²

34² = OP² + 16²

OP² = 1156 - 256

OP² = 900

OP = 30 cm

In triangle OPD

OD² = OP² + PD²

50² = 30² + PD²

PD² = 2500 - 900

PD² = 1600

PD = 40 cm

AD = 2 × PD = 2 × 40 = 80 cm

The length of AD is 80 cm.

∴ Option 2 is the correct answer.

Given:

P ∶ Q = 3 ∶ 5 and P ∶ R = 2 ∶ 3

Calculation:

P ∶ Q = 3 ∶ 5

P ∶ R = 2 ∶ 3 

Make P equal

P ∶ Q = 6 ∶ 10

P ∶ R = 6 ∶ 9 

So, P : Q : R = 6 : 10 : 9

Hence, P = 6k, Q = 10k and R = 9k (k = constant)

Now, 3P ∶ 4Q ∶ 3R

⇒ 3 × 6k : 4 × 10k : 3 × 9k

⇒ 18 : 40 : 27

∴ 3P ∶ 4Q ∶ 3R equals 18 : 40 : 27.

∴ Option 2 is the correct answer.

Given:

x + y = 12

y + z = 17

z + x = 19

Calculation:

Add all the given equation,

2(x + y + z) = 12 + 17 + 19

x + y + z = 48/2 = 24

Average of x, y and z = 24/3 = 8

∴ Option 2 is the correct answer.

Given:

Principal = Rs. 7500

Rate = 7%

Time = 2 years

Concept Used:

Simple Interest = PRT/100

Amount = Principal + Simple Interest

Calculation:

Simple Interest = PRT/100

Simple Interest = (7500 × 7 × 2)/100

Simple Interest = Rs. 1050

Amount = Principal + Simple Interest

Amount = 7500 + 1050

Amount = Rs. 8550

∴ Option 2 is the correct answer.

Given:

∠YXZ = 50 degree

XR = PR, ZR = QR 

∠RQZ = 80 degree

Concept Used:

If two sides of the triangle are equal then the triangle is isosceles triangle. The two angles opposite to the equal sides are congruent to each other.

Calculation:

<br>

In Δ XPR,

∠PXR = 50° 

PR = XR

∴ Triangle is isosceles

∠XPR = ∠PXR = 50° 

∠XRP = 180° - 50° - 50° 

∠XRP = 80°

Similarly,

∠RQZ = ∠RZQ = 80° 

∠QRZ = 180° - 80° - 80° 

∠QRZ = 20° 

Now,

∠PRQ = 180° - 20° - 80° = 80° 

∴ Option 1 is the correct answer.

Shortcut Trick

In a circle, the radius, distance from center, and half-chord length form a right-angled triangle.

Radius (r) = 50 ÷ 2 = 25 cm. Distance (d) = 7 cm.

Using the Pythagorean triplet (7, 24, 25):

Half-chord length = 24 cm.

Length of chord JK = 2 × 24 = 48 cm.

∴ The correct answer is 48 cm.

Alternate Method

Given:

Diameter of the circle = 50 cm

Distance of chord JK from centre (O) = 7 cm

Formula Used:

Radius (r) = Diameter ÷ 2

In ▵OMJ (Right-angled), OJ² = OM² + MJ² (Pythagoras Theorem)

Chord length JK = 2 × MJ (Perpendicular from center bisects the chord)

Calculations:

⇒ Radius (r) = 50 ÷ 2 = 25 cm

⇒ In right ▵OMJ, OJ = 25 cm and OM = 7 cm

⇒ MJ² = OJ² − OM²

⇒ MJ² = 25² − 7²

⇒ MJ² = 625 − 49 = 576

⇒ MJ = √576 = 24 cm

⇒ Total length of chord JK = 2 × MJ

⇒ JK = 2 × 24 = 48 cm

∴ The correct answer is 48 cm.

Additional Information

Perpendicular Bisector Property

A perpendicular drawn from the center of a circle to a chord always bisects the chord into two equal segments.

Pythagorean Triplets

Sets of three integers that satisfy a² + b² = c², such as (3, 4, 5), (5, 12, 13), (7, 24, 25), and (8, 15, 17), are extremely useful for quick circle calculations.

Chord Distance Relation

Chords that are equidistant from the center of a circle are equal in length, and longer chords are closer to the center.

Given:

$\frac{8\times5\div25}{7\div14\times 2}-\frac{14\div7-5}{7\div14-25}$

$\frac{8\times1/5}{1/2\times 2}-\frac{2-5}{1/2-25}$

$\frac{8}{5}-\frac{-3}{-49/2}$

$\frac{8}{5}-\frac{6}{49}$

$\frac{392 - 30}{245}$

$\frac{362}{245}$

∴ Option 1 is the correct answer.

Given:

The range of numbers is between 501 and 701.

We are looking for numbers divisible by 10 but not divisible by 3.

Formula:

 A number is divisible by 10 if its last digit is 0.

A number is divisible by 3 if the sum of its digits is divisible by 3.

Solution:

The smallest number greater than 501 and divisible by 10 is 510

The largest number smaller than 701 and divisible by 10 is 700.

(700 - 510)/10 + 1 = 190/10 + 1 = 19 + 1 = 20

So, there are 20 numbers between 501 and 701 inclusive that are divisible by 10.

Next, we need to subtract those that are also divisible by 3.

A number is divisible by 30 if it is divisible by both 3 and 10, so we need to find numbers divisible by 30 between 501 and 701.

The smallest number greater than 501 and divisible by 30 is 510.

The largest number smaller than 701 and divisible by 30 is 690.

To find the count of such numbers, we calculate:

(690 - 510)/30 + 1 = 180/30 + 1 = 6 + 1 = 7

We subtract these 7 from the 20 we found earlier:

20 - 7 = 13

Therefore, there are 13 numbers between 501 and 701 which are divisible by 10 but are not divisible by 3.

Given:

 

Solution:

Sum of time invested in 'teaching and reading' = 8 hours + 6 hours = 14 hours

Sum of time invested in 'sleep and play' = 7 hours + 1 hour = 8 hours

Ratio = 14 hours : 8 hours

Ratio = 7 : 4

Therefore, the ratio between the sum of time invested in 'teaching and reading' and 'sleep and play' is 7 : 4.

Calculation:

Income of company A = 300 + 100 = 400

Income of company B = 800 + 400 = 1200

Income of company C = 600 + 300 = 900

Income of company D = 300 + 200 = 500

Income of company E = 1000 + 400 = 1400

Sequence is correct about the income of company A, B, C, D and E is E > B > C > D > A.

∴ Option 2 is the correct answer.

Shortcut Trick

The side of a rhombus is the hypotenuse of a right triangle formed by half of its diagonals.

Side = √((d₁ ÷ 2)² + (d₂ ÷ 2)²)

⇒ Side = √(12² + 5²) = √(144 + 25) = √169 = 13 cm

Perimeter = 4 × Side = 4 × 13 = 52 cm

∴ The correct answer is 52 cm.

Alternate Method

Given:

Length of first diagonal (AC) = 24 cm

Length of second diagonal (BD) = 10 cm

Formula Used:

The diagonals of a rhombus bisect each other at right angles (90°).

By Pythagoras theorem: Hypotenuse² = Perpendicular² + Base²

Perimeter of a rhombus = 4 × side

Calculations:

⇒ Half of diagonal AC (OA) = 24 ÷ 2 = 12 cm

⇒ Half of diagonal BD (OB) = 10 ÷ 2 = 5 cm

⇒ In right-angled ΔAOB, the intersection at center O forms a 90° angle.

⇒ Applying Pythagoras theorem in ΔAOB:

⇒ AB² = OA² + OB²

⇒ a² = 12² + 5²

⇒ a² = 144 + 25

⇒ a² = 169

⇒ a = √169 = 13 cm

⇒ The perimeter of the rhombus = 4 × a

⇒ Perimeter = 4 × 13 = 52 cm

∴ The correct answer is 52 cm.

Additional Information

Direct Formula for Perimeter

The perimeter of a rhombus can be calculated directly from its diagonals using the formula: P = 2 × √(d₁² + d₂²).

Area of Rhombus

The area of a rhombus is half the product of the lengths of its diagonals: Area = (1/2) × d₁ × d₂.

Properties of Rhombus

All four sides of a rhombus are equal in length, and opposite sides are parallel. Its diagonals bisect interior angles and are perpendicular bisectors of each other.

Given:

Manoj bought two TVs for Rs. 2,280.

One TV was sold at a loss of 20% and the other at a profit of 10%.

Calculation:

CP₁ = Cost price of the first TV (the one sold at a loss).

CP₂ = Cost price of the second TV (the one sold at a profit).

We know from the given conditions that:

CP₁ + CP₂ = Rs. 2,280 (since Manoj bought two TVs for this amount).

Each TV was sold for the same price, which means:

The price at which the first TV was sold (with a loss of 20%) equals the price at which the second TV was sold (with a profit of 10%).

So, CP₁ - 20% of CP₁ = CP₂ + 10% of CP₂.

Simplifying that, we get 0.8 × CP₁ = 1.1 × CP₂.

0.8 × CP₁ = 1.1 × (2,280 - CP₁)

Solving this gives:

0.8 × CP₁ = 2,508 - 1.1 × CP₁

1.9 × CP₁ = 2,508

CP₁ = Rs. 1,320

So, the cost price of the TV which was sold at a loss is Rs. 1,320.

Alternate Method 1st article at loss = 20% = 1/5

2nd article at profit = 10% = 1/10

 

But both articles sold at the same SP.

 

Now, 95 unit = 2280 (Manoj bought two TVs for this amount)

⇒ 55 unit = 2280/95 × 55 = Rs. 1320

∴ The cost price of the TV which was sold at a loss is Rs. 1,320.

Given:

a2 + b2 + c2 = 62

a + b + c = 12

Formula used:

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

Calculation:

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

12² = 62 + 2(ab + bc + ca)

144 = 62 + 2(ab + bc + ca)

82 = 2(ab + bc + ca)

41 = ab + bc + ca

The value we want to find is 4 times this, so:

4ab + 4bc + 4ca = 4 × 41 = 164

So, 4ab + 4bc + 4ca = 164.

Given:

The average of 15 numbers is 53.

The average of 14 numbers is 55.

Calculation:

Let's denote:

N = the number that was removed.

The sum of the initial 15 numbers can be calculated as 15 × Average = 15 × 53 = 795.

The sum of the 14 remaining numbers can be calculated as 14 × Average = 14 × 55 = 770.

The number removed is the difference between these two sums:

N = 795 - 770 = 25

So, the number that was removed is 25.

Given:

$\rm x+\frac{1}{x}=\frac{K}{2}$

Concept Used:

$\rm x+\frac{1}{x}=a$, then

$\rm x^2+\frac{1}{x^2}=a^2 - 2$

$\rm x^4+\frac{1}{x^4}=[x^2-\frac{1}{x^2}]^2 - 2$

Calculation:

$\rm x+\frac{1}{x}=\frac{K}{2}$

⇒ $\rm x^2+\frac{1}{x^2}=\frac{K^2}{4} - 2$

⇒ $\rm x^2+\frac{1}{x^2}=\frac{K^2 - 8}{4}$

⇒ $\rm x^4+\frac{1}{x^4}=[\frac{K^2 - 8}{4}]^2 - 2$

⇒ $\rm x^4+\frac{1}{x^4}=[\frac{K^4 + 64 - 16K^2}{16}] - 2$

⇒ $\rm x^4+\frac{1}{x^4}=[\frac{K^4 + 32 - 16K^2}{16}]$

∴ Option 1 is the correct answer.

Shortcut Trick

Equating total work: (4M + 7W) × 8 = (7M + 4W) × 5

⇒ 32M + 56W = 35M + 20W ⇒ 3M = 36W ⇒ M = 12W

Total Work = (4 × 12W + 7W) × 8 = 440W units

Time for 8 women = 440W ÷ 8W = 55 days

∴ The correct answer is 55 Days.

Alternate Method

Given:

4 men and 7 women complete the work in 8 days.

7 men and 4 women complete the work in 5 days.

Calculations:

Let the efficiency of 1 man be M and 1 woman be W.

⇒ 4M + 7W = 5     . . . . (1)

⇒ 7M + 4W = 8     . . . . (2)

Multiplying equation (1) by 7 and equation (2) by 4:

⇒ 28M + 49W = 35

⇒ 28M + 16W = 32

Subtracting the two equations:

⇒ 33W = 3

⇒ W = 1/11

Efficiency of 8 women = 8 × (1/11) = 8/11

Time taken by 8 women = Total Work ÷ Efficiency of 8 women

⇒ Time taken = 40 ÷ (8/11)

⇒ Time taken = (40 × 11) ÷ 8 = 55 days

∴ The correct answer is 55 Days.

Additional Information

Total Work Concept

Total Work is assumed as the LCM of the days taken by different groups to simplify calculation of individual efficiencies, keeping fractions to a minimum until the final steps.

MDH Formula

(M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂, where M is number of workers, D is days, H is hours per day, and W is the total work done.

Pipes & Cisterns Analogy

Follows the exact same efficiency principles as Time & Work, where an inlet pipe represents positive work (filling) and an outlet pipe represents negative work (emptying).

Calculation:

Number of mobiles in 2015 = 23

Number of Tablet in 2018 = 23

23 : 23

1 : 1

∴ Option 4 is the correct answer.

Given:

sin C = 9/10

Formula used:

sin² C + cos² C = 1

Calculation:

sin2 C + cos2 C = 1

(9/10)² + cos2 C = 1

 cos2 C = 1 - (9/10)2 

 cos2 C = 19/100

∴ Option 1 is the correct answer.

Calculation:

Let;

Total Distance = x km

Speeds S1, S2, and S3 are 10 km/h, 15 km/h, and 20 km/h respectively.

Time taken is T1, T2, and T3 respectively.

According to the question;

Time = Distance/Speed

T1 = (x/3)/S1 = x/30 hr

T2 = (x/4)/S2 = x/60 hr

Remaining Distance = x - (x/3) - (x/4) = 5x/12

So, T3 = (5x/12)/S3 = x/48 hr

Total time = T1 + T2 + T3

= (x/30) + (x/60) + (x/48)

= 17x/240

Average Speed = Total Distance/Total Time

= x/(17x/240)

= 240/17 km/hr

Hence, 240/17 km/h is the correct answer.

Given:

Price of 15 chairs is 20% more than the price of 8 tables.

Price of 2 tables is Rs. 2400.

Calculation:

Let's denote:

P_C = Price of 15 chairs.

P_T = Price of 8 tables.

We know from the given conditions:

P_C = 1.2 × P_T

P_T = 4 × Price of 2 tables (since 2 × 4 = 8)

Substitute the given value of the price of 2 tables into the second equation:

P_T = 4 × 2400 = Rs. 9600

Substitute this into the first equation to get the price of 15 chairs:

P_C = 1.2 × 9600 = Rs. 11,520

So, the price of 15 chairs is Rs. 11,520.

Calculation:

$\rm \frac{1+\tan A}{cosec A}+\frac{1+\cot A}{\sec A}$

⇒ $\rm \frac{1+\frac{sin A}{cos A}}{\frac{1}{sin A}}+\rm \frac{1+\frac{cos A}{sin A}}{\frac{1}{cos A}}$

⇒ $\rm \frac{\frac{cos A+sin A}{cos A}}{\frac{1}{sin A}}+\rm \frac{\frac{sin A +cos A}{sin A}}{\frac{1}{cos A}}$

⇒ $\frac{sin A(cos A+sin A)}{cos A}+{\frac{cos A(sin A +cos A)}{sin A}}$

⇒ $(cos A+sin A)[\frac{sin A}{cos A}+{\frac{cos A}{sin A}}]$

⇒ $(cos A+sin A)[\frac{sin^2 A + cos ^2}{sin Acos A}]$

⇒ $[\frac{(cos A+sin A)}{sin Acos A}]$

⇒ sec A + cosec A

∴ Option 2 is the correct answer.

The correct answer is 'Option 2' i.e. "Apostate".

Key Points

• An "Apostate" is a person who renounces a religious or political belief or principle. (धर्मत्यागी)
• This word comes from the Greek term "apostasia", meaning defection or revolt.
• It is often used in religious contexts, but can also be applied in political or other ideological settings.

Therefore, the correct answer is: 'Apostate'.

Additional Information

• Now, let's look at the meanings of the other words:
• Arsonist: An arsonist is a person who intentionally sets fire to property, either out of malice or for some criminal purpose.(आगज़नी करने वाला)
• Anarchist: An anarchist is a person who believes in or tries to bring about anarchy, which is a state of society without government or law.(अराजकतावादी)
• Agnostic: An agnostic is a person who believes that nothing is known or can be known of the existence or nature of God or of anything beyond material phenomena.(अज्ञेयवादी)