The logic followed here is:

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

Now,

For, (7, 559, 6)

→ (7)³ + (6)3

⇒ 343 + 216 = 559.

For, (8, 637, 5)

→ (8)3 + (5)3

⇒ 512 + 125 = 637.

Similarly, for (9, 1241, 8)

→ (9)3 + (8)3

⇒ 729 + 512 = 1241.

Hence, the correct answer is "Option 1".

The correct order according to the English dictionary is:

To arrange the given words in the sequence in which they occur in the dictionary, we need to compare the first letters of each word.

The first letter of each word is in alphabetical order from H to H, so we move on to the second letter.

The second letter of "Head" is "e", which comes before "a" (the second letter of "Heal").

Therefore, "Head" comes before "Heal" in the dictionary order.

Next, we have "Health", which comes after "Head" and "Heal" since "a" comes before "l" and "t".

Then, we have "Heap", which comes after "Head", "Heal", and "Health" since "p" comes after "d" and "l".

Finally, we have "Heat", which comes after "Head", "Heal", "Health", and "Heap" since "t" comes after "p".

Therefore, the correct sequence of the given words in the dictionary order is:

 

1. Head
2. Heal
3. Health
4. Heap
5. Heat

The correct arrangement will be: '2,1,3,4,5.

Hence, the correct answer is "Option 4".

For find the opposite surface of '5', we need to compare the common surface in the given dices,

Now,

From the given Dice,

 

→ 1 is the common surface in both Dice, '6' is the opposite surface of '3' and '5' is the opposite surface of '2'.

Here, '2' is opposite to the face containing '5'.

Hence, the correct answer is "2".

The triangles are:

Here, there are '12' triangles in the given image.

Hence, the correct answer is "12".

The logic followed here is:

‘HAWK’ is coded as ‘8256’,

‘INKS’ is coded as ‘5497’,

‘GUNK’ is coded as ‘1935’,

‘HSGA’ is coded as ‘4326’

Here,

Code for 'G' is '3'.

Code for 'K' is '5'.

Code for 'N' is '9'.

Code for 'S' is '4'.

Code for 'H' and 'A' is either '2' or '6'.

So, Code for 'GK' is '35'

Here, According to the option '356' will be the code for 'GKA'. 

Hence, the correct answer is "356".

The logic followed here is:

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

Now,

For, (6, 121, 17)

→ (6 - 17)²

⇒ -11² = 121.

For, (38, 576, 14)

→ (38 - 14)2

⇒ 242 = 576.

Similarly, for (9, 81, 18)

→ (9 - 18)2

⇒ -92 = 81.

Hence, the correct answer is "Option 1".

The logic followed here is:

Here, '349' will complete the given series.

Hence, the correct answer is "349".

The mirror image of the question figure is shown below:

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: Last number is place on the 1st place.

For, 7 F 6 F 1

→ 761 after interchange 176.

For, 8 F 2 F 4 = 482

→ 824 after interchange 482.

Similarly, 3 F 1 F 8 = ?

→ 318 after interchange 831.

Hence, the correct answer is "831".

The logic followed here is:

1. Nest – Bird - A bird typically builds or finds a nest to live in and raise its young.
2. Palace – King - A king is a monarch who typically resides in a palace, which is a grand, impressive building.
3. Cottage – Peasant - A peasant is a member of a low social class who typically lives in a simple, rural dwelling like a cottage.
4. Lion – Den - Lions do live in dens, this word pair is different from the others because it doesn't involve a living being and their dwelling place, but rather a living being and their dwelling place. Here, the sequence of analogy is not followed.

So, 'Lion–Den' is odd among the given options.

Hence, the correct answer is "Option 4".

Venn diagram according to the given information is:

Mothers, Husbands and Males​​ 

All the husband are males so they will come inside the males circle.

But

Mothers is a different entity from them so it will come as a separate circle.

Hence, the correct answer is "Option 3".

The logic followed here is:

Step I: Letter 'H' has shifting a place in clockwise direction in next images, and lastly changed with Dotted Circle.

Step II: Letter 'O' has shifting a place in clockwise direction in next images, and changed with letter 'P'.

Step III: Symbol 'Rectangle' has shifting a place in clockwise direction in next images, and changed with letter 'C'.

Step IV: Symbol '=' has shifting a place in clockwise direction in next images, and changed with Shaded Triangle.

So, the complete series will be:

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

Hence, the correct answer is "Option 1".

Statement:

I. No P is Q.

II. All Q are R.

The least possible diagram for the given statements is as follows:

Conclusions:

I. Some R are Q - True (All Q are R, so Some R are also Q).

II. Some Q are P - False (Because No P is Q).

III. Some P are R - False (No definite relation given between P and R, so it can be possible only).

Here, Only conclusion I follows.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: The numbers given in the first sequence is written in reverse order in second sequence.

Option 1) 81962457 – 75426918

 

Option 2) 321645281 – 812546123

 

Option 3) 715623 – 326517

 

Option 4) 65428 – 82456

 

Hence, the correct answer is "Option 2".

Family Chart:

Given: Pointing towards a photo of a lady, Navneet said, “She is the sister of my sister’s mother”.

So, the Lady is the Maternal Aunt of the Navneet.

Hence, the correct answer is "Option 3".

The logic followed here is:

Law of Motion : Issac Newton → Issac Newton is the person who is known for his work on the Law of Motion.

Similarly,

Theory of Relativity : Albert Einstein → Albert Einstein is the person who is known for his work on the Theory of Relativity.

Therefore, the correct answer is "Option 4".

Additional InformationJames Chadwick is known for his discovery of the neutron, which helped to explain the structure of the atomic nucleus.

John Dalton is known for his work on atomic theory and the development of modern atomic theory.

J.J. Thomson is known for his discovery of the electron and his work on atomic structure.

The logic followed here is:

So, 'TKWJ' will replace the question mark in the given series.

Hence, the correct answer is "TKWJ".

The logic followed here is:

Logic: 1st number × 2 = 2nd number.

Now,

38 : 76

→ 38 × 2 = 76.

Similarly, for 42 ∶ 84

→ 42 × 2 = 84.

Hence, the correct answer is "Option 4".

The logic followed here is:

Option 1) XAEJ

Option 2) NQUZ

Option 3) DGKP

Option 4) GJNT

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

Hence, the correct answer is "Option 4".

The logic followed here is:

Ohm : Electric Resistance → Ohm is the unit of measurement for electric resistance.

Similarly,

Seconds : Time → Second is the unit of measurement for Time.

Hence, the correct answer is "Option 3".

Additional Information 

Option 1) Power : Watt → Watt is the unit of measurement for power.

Option 2) Volume : Litre → Litre is the unit of measurement for Volume.

Option 4) Pascal : Current → Pascal is the unit of measurement for Pressure not Current.

The logic followed here is:

Here,

AN : ER

Similarly, for BO : ?

Hence, the correct answer is "Option 4".

Given equation: 8 × 6 + 12 ÷ 2 - 4 = 14.

BODMAS Table: 

Let's check each option one by one.

Option 1) 8 and 6

Given: 8 × 6 + 12 ÷ 2 - 4 = 14

After interchanging the numbers we get;

⇒ 6 × 8 + 12 ÷ 2 - 4 = 14

⇒ 6 × 8 + 6 - 4 = 14

⇒ 48 + 6 - 4 = 14

⇒ 54 - 4 = 14

⇒ 50 ≠ 14

⇒ LHS ≠ RHS

Option 2) 2 and 4

Given: 8 × 6 + 12 ÷ 2 - 4 = 14

After interchanging the numbers we get;

⇒ 8 × 6 + 12 ÷ 4 - 2 = 14

⇒ 8 × 6 + 3  - 2 = 14

⇒ 48 + 3  - 2 = 14

⇒ 51 - 2 = 14

⇒ 49 ≠ 14

⇒ LHS ≠ RHS

Option 3) 2 and 6

Given: 8 × 6 + 12 ÷ 2 - 4 = 14

After interchanging the numbers we get;

⇒ 8 × 2 + 12 ÷ 6 - 4 = 14

⇒ 8 × 2 + 2 - 4 = 14

⇒ 16 + 2 - 4 = 14

⇒ 18 - 4 = 14

⇒ 14 = 14

⇒ LHS = RHS

Option 4) 12 and 14

Given: 8 × 6 + 12 ÷ 2 - 4 = 14

After interchanging the numbers we get;

⇒ 8 × 6 + 14 ÷ 2 - 4 = 12

⇒ 8 × 6 + 7 - 4 = 12

⇒ 48 + 7 - 4 = 12

⇒ 55 - 4 = 12

⇒ 51 ≠ 12

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 3".

The image embedded in given figure is as shown below:

Hence, "Option 3" is the correct answer.

The logic followed here is:

‘CHEWER’ is coded as ‘HAJPJK’,

Similarly, for 'HANDER'

So, 'HANDER' is coded as 'MTSWJK'.

Hence, the correct answer is "Option 2".

From the given open Dice:

A and @ is the opposite sides.

and Q is the opposite sides.

P and R is the opposite sides.

So, the face of '#' is opposite to the face showing 'Q'

Hence, the correct answer is "Option 2".

The correct answer is China.

Key Points

• The USSR (now Russia) Constitution served as a model for the Preamble's fundamental duties and the Ideals of justice (social, economic, and political).
• Federation with a strong Center, the vesting of residuary powers in the Center, the appointment of state governors by the Center, and advisory jurisdiction of the Supreme Court are characteristics of the Indian Constitution that are modelled after those of the Constitution of Canada.
• The South African Constitution served as a model for the Indian Constitution's amendment procedure and the election of Rajya Sabha members.
• These elements—parliamentary government, the rule of law, legislative process, single citizenship, the cabinet system, prerogative writs, parliamentary privileges, and bicameralism—are all taken directly from the UK Constitution.
• France:
• Ideals of Liberty, Equality, and Fraternity (from the French Revolution – included in the Preamble.
• Republic form of government
• No provision has been taken from China.

The correct answer is release of carbon dioxide.

• The carbon dioxide that is produced during human respiration reaches the empty spaces within the leaves and simultaneously photosynthesis is going on.

Key Points

• Due to this, carbon dioxide present in the air is used and consumed by the plants.
• Thus during the day, plants produce oxygen while consuming carbon dioxide but at the night the process of photosynthesis stops but respiration continues for plants.
• Meaning that oxygen is not produced by the plants at night.
• Because of this natural phenomenon, it is advised that at night if you sleep under the tree, you will not get oxygen, which can cause breathing problems, suffocation, etc.

The Correct Answer is 1784.

Key Points

• Pitts India Act 1784:
• It was named after the British prime minister William Pitt the Younger.
• The Pitt’s India Act, of 1784 also called the East India Company Act, 1784.
• Pitt’s India Act, of 1784 was passed to rectify the defects of the Regulating Act of 1773.
• It distinguished between the commercial and political functions of the company.
• It allowed the Court of Directors to manage commercial affairs but created a new body called the Board of Control to manage political affairs.
• It empowered the Board of Control to supervise and direct all operations of the civil and military government or revenues of the British possessions in India.
• The company's territories in India were for the first time called the 'British possessions in India'.
• The British Government was given supreme control over Company's affairs and its administration in India.

The correct answer is Untouchability.

Key Points

• Article 17- Abolition of Untouchability: 
• Untouchability is abolished and its practice in any form is forbidden.
• In fact, the enforcement of any disability arising out of untouchability shall be an offence punishable in accordance with the law.
• Abolition of untouchability has been included among the fundamental rights under article17.
• In fact, this is one of the few fundamental rights which is available against individuals.
• To make an untouchability law further strong, parliament passed an Untouchability (offences) Act in 1955.
• However, this act was further amended and also renamed in the year of 1976 as Protection of the Civil Rights Act, 1955.​

Additional Information

• Other important articles:

The correct answer is Sublimation.

Key Points

• Sublimation: It is the conversion of a solid directly into vapors.
• Sublimation takes place when the boiling point is less than the melting point.
• The heat required to change a unit mass of solid directly into vapors at a given temperature is called the heat of sublimation at that temperature.

Additional Information

• Condensation: The process by which water vapor in the air is changed into liquid water is called condensation. This caused the water vapor to condense, or turn into its liquid form.
• Condensation is crucial to the water cycle because it is responsible for the formation of clouds.
• Evaporation: The vaporization occurring from the free surface of a liquid is called evaporation.
• Evaporation is the escape of molecules from the surface of a liquid.
• This process takes place at all temperatures and increases with the increase of temperature.
• Evaporation leads to cooling because the faster molecules escape and, therefore, the average kinetic energy of the molecules of the liquid (and hence the temperature) decreases.
• Diffusion: It is the movement of a substance from an area of high concentration to an area of low concentration. 
• Diffusion happens in liquids and gases because their particles move randomly from place to place.

The correct answer is Share.

Key Points

• Collaboration and Accessibility: The "Share" feature in MS PowerPoint 365 allows Sam to collaborate with others and make the presentation accessible to a wider audience. He can easily share the presentation with multiple people, enabling them to view and collaborate on the same document simultaneously.
• Email Sharing: Within the "Share" feature, Sam can select the option to share the presentation via email. This allows him to send the presentation directly to the intended recipients' email addresses.
• Recipient Permissions: MS PowerPoint 365 provides options for specifying the level of permissions for recipients. Sam can choose whether recipients can simply view the presentation or have editing capabilities, depending on his requirements.
• Real-Time Updates: When Sam shares the presentation via email using MS PowerPoint 365, recipients can access and view the latest version of the presentation in real-time. Any changes made by Sam or other collaborators will be reflected immediately for all recipients.
• Collaboration Tools: The "Share" feature also includes collaboration tools that enable recipients to add comments, suggest edits, or make revisions directly within the presentation. This facilitates effective collaboration and feedback exchange among the larger audience.
• OneDrive Integration: MS PowerPoint 365 integrates with OneDrive, Microsoft's cloud storage service. When Sam shares the presentation via email, he can choose to store the file on OneDrive and provide recipients with a link to access it. This ensures that everyone has access to the most up-to-date version of the presentation.
• Security and Privacy: The "Share" feature in MS PowerPoint 365 includes various security measures to protect the presentation and ensure privacy. Sam can control who has access to the presentation, and he can also set passwords or expiration dates for the shared link to enhance security.
• Version History: MS PowerPoint 365 keeps a version history of the shared presentation. This means that Sam can easily revert to previous versions if needed or track the changes made by collaborators.
• Outlook Integration: If Sam uses Microsoft Outlook as his email client, the "Share" feature seamlessly integrates with it. He can share the presentation directly from within PowerPoint 365, leveraging the familiar email interface of Outlook.

Additional Information

The correct answer is Mahanadi river.

Key Points 

• River Mahanadi originates from Sihawa Mountain near a village in Raipur, Chhattisgarh.
• The Mahanadi River system is the third largest in peninsular India after Godavari and Krishna, and the largest river in Odisha state.
• The Mahanadi (“Great River”) follows a total course of 560 miles (900 km) and has an estimated drainage area of 51,000 square miles (132,100 square km).
• The catchment area of the river extends to Chhattisgarh, Madhya Pradesh, Odisha, Jharkhand, and Maharashtra.
• Tributaries
• Seonath, Hasdeo, Mand, and Ib join Mahanadi from the left whereas,
• Ong, Tel, and Jonk join it from the right.
• At Sambalpur, the Hirakud Dam on the river (the longest dam in India) has formed a man-made lake 35 miles (55 km) long; the dam has several hydroelectric generators.
• It enters the Odisha plains near Cuttack and enters the Bay of Bengal at False Point by several channels.

Additional Information

• Malwa plateau
• ​Indian plateau region known as the Malwa Plateau. It is bordered to the north by the Madhya Bharat Plateau and Bundelkhand Upland, to the east and south by the Vindhya Range, and to the west by the Gujarat Plains. The plateau, which is of volcanic origin, spans southeast Rajasthan state and central Madhya Pradesh state. The Sanskrit word malav is where the name Malwa comes from (part of the abode of Laksmi [goddess of wealth]). The Maurya, Gupta, and Paramara empires alternately dominated the plateau; during this time, numerous Buddhist temples and monuments (such as the stupas at Sanchi), known for their architecture and sculpture, were also constructed. In 1390 CE, the Muslims took control of the plateau, which then belonged to the Maratha empire. It was given to the British in 1817.
• The Malwa Plateau has an elevation range of 500 to 600 metres (about 1,650 to 2,000 feet). Sandstone hills and solitary mesas, as well as remnants of old lava flows, may be seen scattered throughout the plateau. The Mahi River drains the western portion of the area, the Chambal River the middle, and the Betwa River and the headwaters of the Dhasan and Ken rivers the eastern portion. Additionally, there are the Parbati, Sipra, Gambhir, and Choti Kali Sindh rivers, all of whose valleys are bordered by terraced hills. Savanna-style vegetation is present, with sporadic teak and sal (Shorea robusta) woods.

The correct answer is Tropical Deciduous Forests.

Key Points

Tropical Deciduous Forests:

• These are the most widespread forests out of all the types of forests in India
• Also, called Monsoon Forests.
• They are found in the regions having rainfall between 70-200cm.
• They shed their leaves for about six to eight weeks in dry summer.
• Tropical Deciduous Forests are further classified into two types of forests on the basis of rainfall- Tropical Moist Deciduous Forests and Tropical Dry Deciduous Forests.
• TROPICAL MOIST DECIDUOUS FORESTS:
• Present in the areas having rainfall between 100-200cm.
• Found in eastern slopes of Western Ghats, foothills of the Himalayas in the North-eastern States and Odisha.
• Main Species of Tropical Moist Deciduous Forests: Teak, Sal, Sheshum, amla, Kusum, mahua, Sandalwood, etc.
• TROPICAL DRY DECIDUOUS FORESTS.
• Found in the areas having rainfall between 70-100cm.
• Present in rainier areas of the peninsula and the plains of Uttar Pradesh and Bihar.
• During Dry seasons, Trees shed their leaves completely and the forest appears like a Grassland.
• Main species of Tropical Dry Deciduous Forests: Khair, Tendu, Palas, axlewood, bel, etc.

Additional Information

Tropical Evergreen Forests:

• These forests are restricted to heavy rainfall areas of the Western Ghats and the island groups of Lakshadweep, Andaman, and Nicobar, upper parts of Assam, and Tamil Nadu coast.
• They are at their best in areas having more than 200 cm of rainfall with a short dry season.
• The trees reach great heights up to 60 meters or even above.
• Since the region is warm and wet throughout the year, it has luxuriant vegetation of all kinds.
• The trees, shrubs, and creepers give it a multilayered structure.
• There is no definite time for trees to shed their leaves.
• As such, these forests appear green all the year-round

The correct answer is Madhya Pradesh.

Key Points

• ​Sanchi Stupa:
• Sanchi is about 50 km from Bhopal, the capital of Madhya Pradesh.
• Stupa at Sanchi is a world heritage site.
• It was built by Ashoka in the 3rd century BCE.
• It is the most prominent and the oldest and is believed to have the Buddha’s relics.
• Along with other relatively small stupas, there are three main stupas at Sanchi.

Additional Information

• • It is a religious place with historical and archaeological significance.
• Sanchi is famous in the world for stupas, monolithic Asokan pillar, temples, monasteries and sculptural wealth dating from 3rd century B.C. to 12th century A.D.
• During Sunga times, several edifices were raised at Sanchi and its surrounding hills.

The correct answer is Kareena Kapoor.

Key Points

• "The Pregnancy Bible" by Kareena Kapoor:
• It is a comprehensive guide to pregnancy, covering everything from conception to birth.
• It is written in a warm and engaging style and is full of personal anecdotes from Kareena's own pregnancies.
• It features contributions from experts in a variety of fields, including doctors, nutritionists, and fitness trainers.
• It is packed with information on everything from diet and exercise to labor and delivery.
• It is an essential resource for any woman who is pregnant or planning to become pregnant.

Additional Information

Here are some of the topics covered in the book:

• Pregnancy basics: This section covers everything from how to get pregnant to the first trimester.
• Diet and nutrition: This section provides guidance on how to eat a healthy diet during pregnancy.
• Exercise: This section provides advice on how to stay active during pregnancy.
• Labor and delivery: This section covers everything from the signs of labor to the different stages of delivery.
• Postpartum care: This section provides information on how to care for yourself and your baby after delivery.

The correct answer is Elena Rybakina.

Key Points

• Elena Rybakina won the women’s title at Wimbledon 2022 by beating Ons Jabeur of Tunisia. Rybakina is the first player representing Kazakhstan to win a Grand Slam singles title.
• She was born in Russia but switched nationalities to Kazakhstan in 2018 and she acquired Kazakh citizenship.
• The 23-year-old also became the youngest female player to win the title in Wimbledon since Petra Kvitova of Czech in 2011.
• The All England Lawn Tennis and Croquet Club is a private club founded on 23 July 1868, originally "The All England Croquet Club".
• In the spring of 1877, the club was renamed "The All England Croquet and Lawn Tennis Club".
• It is held every year at All England Lawn Tennis and Croquet Club in Wimbledon, London, the United Kingdom.
• Wimbledon is played on outdoor grass courts, with retractable roofs over the two main courts since 2019.
• During The Championships the height of the grass will be 8mm.
• There are four Grand Slam tennis tournaments:
• Wimbledon Open- 1877
• Us Open- 1881
• French Open- 1891
• Australian Open- 1905

Important Points 

• 135th Wimbledon Championship 2022 has 14 sponsors, a few are Slazenger (being the oldest sponsor), IBM, HSBC, OPPO, Rolex, etc. The new sponsor added this year to the event is Vodafone.
• Soft drinks company Robinsons has ended its 86 years-long partnership with Wimbledon. Now it will not sponsor Wimbledon.
• Wimbledon consists of five main events, four junior events, and seven invitation events.
• Wimbledon 2022 Winners:

The correct answer is Mamata Banerjee.

Key Points

• Mamata Banerjee founded the All India Trinamool Congress (AITC) in 1998, after separating from the Indian National Congress.
• She became the party's chairperson and has played a pivotal role in its growth and success in West Bengal, India.

Additional Information

The correct answer is Both I and II.

Key Points

• Syed Mushtaq Ali Trophy – T20:
• The Syed Mushtaq Ali Trophy is a domestic T20 cricket tournament in India organized by the Board of Control for Cricket in India (BCCI).
• Vijay Hazare Trophy – 50 overs:
• The Vijay Hazare Trophy is a domestic one-day (50 overs) cricket tournament in India, also organized by the BCCI.

Additional Information

• Syed Mushtaq Ali Trophy:
• Domestic T20 cricket tournament in India.
• Organized by the Board of Control for Cricket in India (BCCI).
• Inaugurated in the 2006-2007 season.
• Named after Syed Mushtaq Ali, an Indian cricketer known for his aggressive batting style.
• Features teams representing Indian states and cricket associations.
• Serves as a platform for budding cricketers to showcase their talent and earn opportunities in the Indian Premier League (IPL) and the Indian national team.
• Vijay Hazare Trophy:
• Domestic one-day (50 overs) cricket tournament in India.
• Organized by the Board of Control for Cricket in India (BCCI).
• Inaugurated in the 2002-2003 season.
• Named after Vijay Hazare, a legendary Indian cricketer and former Test captain.
• Features teams representing Indian states and cricket associations.
• Considered a prestigious competition for players to showcase their skills in the limited-overs format and gain selection for the Indian national team or the IPL.

The correct answer is Payment and Settlement Systems Act, 2007.

Key Points

• The National Payments Corporation of India (NPCI) was set up under the provisions of the Payment and Settlement Systems Act, of 2007.
• Payment and Settlement Systems Act, 2007:
• Regulates and supervises payment and settlement systems in India.
• Provides the Reserve Bank of India (RBI) with the authority to issue guidelines, set standards, and take action against payment system operators if needed.
• Ensures the safety, security, and efficiency of payment and settlement systems in the country.

Additional Information

• The SARFAESI Act, 2002:
• Stands for Securitization and Reconstruction of Financial Assets and Enforcement of Security Interest Act.
• Aims to address non-performing assets (NPAs) in the Indian banking system.
• Allows banks and financial institutions to recover loans by auctioning or selling borrowers' assets without intervention from the court.
• Government Securities Act, 2006:
• Governs the issuance, management, and trading of government securities in India.
• Streamlines procedures for the issuance of government securities and dematerialization of existing securities.
• Aims to protect the interests of investors and promote the development of a stable and efficient market for government securities.
• Companies Act, 2013:
• Governs the formation, regulation, and dissolution of companies in India.
• Replaces the Companies Act, of 1956, and introduces several new provisions to improve corporate governance and transparency.
• Provides guidelines for the functioning of companies, including rules for incorporation, management, fundraising, auditing, and the responsibilities of directors and other key personnel.

The correct answer is Both I and II.

Key Points

• In a socialist society or economy:
• The government decides what goods are to be produced.
• Central planning and public ownership of the means of production play a significant role in determining what goods and services are produced and in what quantities.
• The distribution of goods under socialism is supposed to be based on what people need.
• The aim is to ensure that everyone's basic needs are met, promoting a more equitable distribution of wealth and reducing income inequality.

Additional Information

The correct answer is I, II and III.

Key Points

• Natural Language Processing (NLP) is a subfield of artificial intelligence and computational linguistics.
• It focuses on the interaction between computers and humans through natural language.
• Understanding: NLP enables computers to comprehend human language as it is spoken or written.
• This involves understanding the semantics, syntax, and context of the language.
• Interpretation: NLP also involves the interpretation of human language by computers.
• This refers to the process of parsing the input, determining its meaning, and potentially transforming it into another format or language.
• Manipulation: Furthermore, NLP allows for the manipulation of human language.
• This could involve tasks like text generation, translation, summarization, and more.
• The combination of understanding, interpretation, and manipulation allows for a wide range of applications.
• These include chatbots, sentiment analysis, machine translation, voice recognition, and many more.
• Therefore, all three options (I, II, III) are correct. NLP involves the understanding, interpretation, and manipulation of human language by computers.
• The development and refinement of NLP technologies are continually evolving, making human-computer interactions more natural, intuitive, and effective.
• Overall, the goal of NLP is to make computers as proficient as possible at understanding and responding to human language, allowing for more natural and intuitive human-computer interaction.

The correct answer is Pakistan.

Key Points

• Sri Lanka defeated Pakistan by 23 runs to win the 6th Asia Cup.
• Sri Lanka, defending the target of 171 runs, bowled out Pakistan for 147 runs in 20 overs.
• Hasaranga won the Player of the Series award for his all-around performance in the entire Asia Cup 2022 in UAE.
• Haris Rauf bowled brilliantly against Sri Lanka in the final of the Asia Cup.
• He took three wickets for 29 runs in 4 overs.
• Pramod Madushan was a very unknown name on the Sri Lankan team before the tournament.
• But he performed brilliantly in the Asia Cup and caught everyone's attention, in the final match, he took 4 wickets for 34 runs in 4 overs.

Additional Information 

• Asia Cup
• The 2022 Asia Cup was the 15th edition of the Asia Cup cricket tournament, with matches played as Twenty20 Internationals (T20Is) during August and September 2022 in the United Arab Emirates.
• Host(s) - UAE
• Champions - Sri Lanka (6th title)
• Runners-up - Pakistan
• Participants - 6
• Matches - 13
• Player of the series -  Wanindu Hasaranga (Sri Lanka)
• Most runs - Pakistan Mohammad Rizwan (281)
• Most wickets - India Bhuvneshwar Kumar (11)

The correct answer is Miss Universe.

Key Points

• Harnaaz Kaur Sandhu has been crowned Miss Universe 2021 and is the third entrant from India to win Miss Universe.
• Sandhu became the first ever Sikh woman who won the title of Miss Universe.
• Sandhu has also crowned Femina Miss India Punjab in 2019.
• List of other Miss Universe from India:
• Sushmita Sen: 1994
• Lara Dutta: 2000

Important Points

• R'Bonney Gabriel from the US was named the winner of the 71st annual Miss Universe pageant on 15 January 2023.
• In second place was Miss Venezuela Amanda Dudamel, followed by Miss Dominican Republic Andreína Martínez.
• She is also the first Filipina American to win Miss USA.
• This year’s Miss Universe pageant allowed married women and mothers to compete for the first time in its 70-year history.

The correct answer is Option 2.

Key Points

• The height of the Western Ghats progressively decreases from north to south.
• In reality, the Western Ghats increase in height from north to south.
• The southern portion of the Western Ghats is generally higher than its northern counterpart, with some of the highest peaks found in the states of Kerala and Tamil Nadu.

Hence statement 2 is incorrect.

Additional Information

• Mahendragiri is the highest peak in the Eastern Ghats.
• Mahendragiri, located in the Gajapati district of Odisha, is the highest peak in the Eastern Ghats mountain range in India.
• It has an elevation of approximately 1,501 meters (4,925 feet) above sea level.
• The Eastern Ghats run roughly parallel to the east coast of India and are not as high or continuous as the Western Ghats.

Hence statement 1 is correct

• The Western Ghats cause orographic rain.
• Orographic rain occurs when moist air is forced to rise over a mountain range, cooling and condensing into clouds and eventually precipitation.
• The Western Ghats, a mountain range running parallel to the western coast of India, acts as a barrier to the moisture-laden winds coming from the Arabian Sea.
• When these winds encounter the Western Ghats, they are forced to rise, causing orographic rainfall on the windward side of the mountains.
• This results in high annual rainfall in the region and contributes to the lush greenery and biodiversity found in the Western Ghats.

Hence statement 3 is correct

• The Eastern Ghats stretch from the Mahanadi Valley to the Nilgiris in the south.
• The Eastern Ghats are a discontinuous mountain range that stretches along the eastern coast of India.
• They begin near the Mahanadi Valley in Odisha and extend through Andhra Pradesh and Tamil Nadu, eventually meeting the Western Ghats in the Nilgiri Hills.
• The Eastern Ghats are characterized by lower elevations, less precipitation, and more fragmented compared to the Western Ghats, which are more continuous and higher.

Hence statement 4 is correct

The correct answer is largest, largest.

Key Points

• India is the largest producer, importer and consumer of pulses in the world accounting for nearly 25% of global production, 15% of International trade and 27% of world consumption.
• Various types of pulses imported are Tur Whole (Pigeon Peas), Black Matpe (Urad), Green Moong, Chick Peas and Yellow Peas.
• India is the largest producer of Jute.
• India is the largest producer of Sugar (As of 2023).
• Gujarat is the largest producer of salt in the country.

Additional Information

The correct answer is Hemichordata.

Key Points

• Hemichordata is not a subgroup of the plant kingdom.
• Hemichordata is a phylum within the animal kingdom, which includes species like acorn worms and graptolites.
• Hemichordates are a group of marine invertebrates that are distantly related to echinoderms (such as starfish and sea urchins) and chordates (which include vertebrates like fish, birds, and mammals).
• Hemichordates are divided into two main groups: the acorn worms (Enteropneusta) and the colonial filter feeders (Pterobranchia).
• Acorn worms are typically solitary and burrow in sediment, while pterobranchs live in colonies attached to hard substrates.
• Hemichordates exhibit a range of body plans, from worm-like to more complex, colony-forming structures.
• They have a number of unique features, including a proboscis that can be used for feeding and respiration, and a structure called the stomochord that is thought to be homologous to the notochord in chordates.
• Hemichordates have been studied for their potential as model organisms in evolutionary and developmental biology, as well as for their ecological roles in marine ecosystems.
• Example:
• Acorn worms (Enteropneusta)
• Pterobranchs (Pterobranchia)
• Graptolites (Graptolithina)
• Cephalodiscus
• Xenoturbella

Additional Information

• Thallophyta:
• ​This group includes algae, which are simple, typically unicellular organisms that photosynthesize as plants do.
• Angiosperms:
• ​These are flowering plants, which produce seeds that are enclosed within a fruit. They are the most diverse group of land plants.
• Pteridophyta:
• ​This group includes ferns and their allies. They don't produce seeds or flowers; instead, they reproduce and disperse via spores.

The correct answer is 29th June.

Key Points

• Every year 29 June is celebrated as National Statistics Day in India.
• The day is celebrated in honour of the remarkable contribution of the famous Indian scientist and statistician PC Mahalanobis in the field of economic planning and statistical development.
• Professor Prasanta Chandra Mahalanobis is considered the father of Indian statistics.
• The National Statistics Day was first celebrated on 29th June 2007.
• The key contribution of PC Mahalanobis is known as "Mahalanobis distance'.
• The formula is used to find the distance between a point and a distribution, based on measurements in multiple dimensions.
• It is widely used in the field of cluster analysis and classification.

Additional Information

The correct answer is Ministry of Consumer Affairs, Food and Public Distribution.

Key Points

• The Bureau of Indian Standards is responsible for bringing services and products as a mandatory standard.
• It provides safe, reliable and quality goods and minimises the health hazard to the consumer.
• It Appoints the authority besides BIS to verify the reliability of the products and service
• The Bureau of Indian Standards is under the Ministry of Consumer Affairs, and it is a National Standard body.
• It was established under the Bureau of Indian Standard Act 1986.
• It was established on 23 December 1986.
• Headquarters is in Manek Bhawan New Delhi.

Important Points

• BIS is the national standards body of India.
• It develops & publishes Indian Standards, Implement Conformity Assessment Schemes,
• It Recognises & runs laboratories for Conformity Assessment and Implements Hallmarking.
• It Works for Consumer empowerment, Conducts capacity-building programs on quality assurance and represents the country in ISO & IEC.

The correct answer is Gupta.

Key Points

• The Iron Pillar at Mehrauli in Delhi is believed to record the achievements of Chandragupta II.
• The iron pillar at Mehrauli, Delhi, is a remarkable example of the skill of Indian crafts persons.
• It is made of iron, 7.2. m high, and weighs over 3 tonnes.
• It was made about 1500 years ago.
• We know the date because there is an inscription on the pillar mentioning a ruler named Chandra, who probably belonged to the Gupta dynasty.

Additional Information 

• Guptas established a small kingdom in Magadh at the beginning of the 4th century.
• Samudragupta was succeeded by his son Chandragupta II Vikramaditya during this period of time
• Pataliputra, an ancient city presently known as Patna, was the capital of the Gupta dynasty.
• The city was favored due to its central location which enabled easy trade and expansion of the empire.
• The Pallavas emerged as a formidable power in the South around the 4th century AD and were at the height of their power in the seventh century AD.
• They built great cities, centres of learning, temples, and sculptures and influenced a large part of Southeast Asia in culture.
• Narasimhavarman I was considered the greatest Pallava king who defeated and killed Pulakesin II the ruler of Badami Chalukya and captured Badami and was titled “Vatapikonda”.
• He was also known as Mamallan (great wrestler) and Mamallapuram was named after him where he built the famous rath temples (Sapt Pagoda).
• Aparajita Varman was the last ruler of the Pallava dynasty.
• The Pushyabhuti Dynasty (c. 500 CE - 647 CE) rose after the downfall of the Gupta Empire (3rd century CE - 6th century CE) in the 6th century CE in northern India.
• The core area of their kingdom was situated in what is now the state of Haryana in India with the capital at Sthanishvara or Thaneshvara.
• The most notable ruler of this dynasty was its last ruler, Emperor Harshavardhana, or Harsha (r. 606-647 CE).
• The capital of Harshavardhana's Empire was Kannuaj. He ruled from 606 AD to 647 AD.
• His Empire extended from Punjab to northern Orissa and from the Himalayas to the bank of the Narmada River.
• Nagabhata I was an Indian king who founded the imperial Gurjara Pratihara dynasty.
• He ruled the Avanti region in present-day Madhya Pradesh, from his capital at Ujjain.

The correct answer is Galdan Namchot.

Key Points

• The festival that marks the birthday of the great Tibetan Buddhist saint Je Tsongkhapa is Galdan Namchot.
• This festival also marks the start of the New Year celebrations in Ladakh, India.
• Je Tsongkhapa was a famous teacher of Tibetan Buddhism whose activities led to the formation of the Gelug school of Tibetan Buddhism.

Additional Information

• Sarhul: 
• Sarhul is a tribal festival celebrated by the ethnic groups in the Indian states of Jharkhand, Odisha, and Chhattisgarh.
• This festival is celebrated to mark the beginning of the new year and the arrival of spring.
• Sarhul is celebrated with traditional music and dance, the worship of village deities, and the sharing of a local drink made from fermented rice or salap.
• Losar:
• Losar is the Tibetan word for "New Year," and it is the most important holiday in Tibet and Tibetan border Indian states.
• It is celebrated for 15 days, with the main celebrations on the first three days.
• Losar involves ceremonies, rituals, prayers, and cultural performances, and it is a time to spend with family and friends, to exchange gifts, and to eat special foods.
• Tusu:
• Tusu is a harvest festival celebrated in the Indian states of Jharkhand, West Bengal, and Odisha.
• The festival is observed on Makar Sankranti, which usually falls on January 14th or 15th, marking the end of the winter season and the arrival of longer days.
• Tusu involves singing traditional songs, dancing, and offering prayers to Tusu, a folk deity, for a good harvest and prosperity in the coming year.

Calculation:

We know that sin(a + b) = sin a cos b + cos a sin b. Using this identity, we can rewrite the right-hand side of the given equation as:

sin x = cos 40°.sin 50° + sin 40°.cos 50°

= sin (40° + 50°) (since sin(a + b) = sin a cos b + cos a sin b)

= sin 90°

= 1

Therefore, we have:

sin x = 1

The only angle whose sine is 1 is 90°. Therefore, we have:

x = 90°

So the value of x is 90°.

Shortcut Trick

For any two acute angles, if tan X = cot Y, then X + Y = 90°.

Identify the angles from the given equation: X = 2A and Y = 46° − A.

Apply the sum property: 2A + (46° − A) = 90°.

⇒ A + 46° = 90° ⇒ A = 90° − 46° = 44°.

∴ The correct answer is 44 degree.

Alternate Method

Given: tan 2A = cot ( 46° − A )

Formula Used: cot θ = tan ( 90° − θ )

Calculations:

⇒ tan 2A = tan [ 90° − ( 46° − A ) ]

⇒ 2A = 90° − 46° + A

⇒ 2A − A = 44°

⇒ A = 44°

∴ The correct answer is 44 degree.

Additional Information

Complementary Trigonometric Ratios

Pairs such as sin/cos, tan/cot, and sec/cosec satisfy the identity ratio(θ) = co-ratio(90° − θ).

General Property of Tan and Cot

If tan α = cot β, then α + β = 90° (or π/2 radians) for acute angles.

Standard Values

At 45°, tan θ = cot θ = 1, which is a specific case of the complementary angle rule where 45° + 45° = 90°.

Given:

Two places B1 and B2 are 500 km.

The speed of Sonit is 80 km/hr more than the Robin.

They meet after 6 hours.

Concept Used:

Distance = Time × Speed

Calculation:

Let the speed of Robin is x km/hr.

And the distance travelled by Robin in 6 hrs y km.

Speed of Sonit = (x + 80) km/hr

The distance travelled by Sonit in 6 hrs = 500 + 500 - y = (1000 - y) km

Distance travelled by Robin in 6hrs = 6x km = y km    ...........(i)

Distance travelled by Sonit in 6hrs = 6(x + 80) km

According to the question,

(1000 - y) = 6(x + 80)

Put the value of y from eq (i)

1000 - 6x = 6x + 480

12x = 520

x = 130/3 km/hr

Speed of Robin = 130/3 km/hr

Distance travelled by Robin = (130/3) × 6 = 260 km

Distance travelled by Sonit = 1000 - 6x = 1000 - 6 × 130/3 = 740 km.

Statement I is wrong.

Speed of Robin = 130/3 km/hr

Statement II is wrong.

∴ Option 3 is the correct answer.

Given:

The radius of a circle = 50 cm

Distance of chord AB from the center of the circle = 14 cm

Formula used:

In a circle, the perpendicular bisector of a chord passes through the center of the circle.

If a perpendicular is drawn from the center of a circle to a chord, it bisects the chord.

In a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

Calculation:

Let's solve the question:

First, let's draw a rough diagram of the circle and chord AB:

Let O be the center of the circle, and let M be the midpoint of the chord AB. Draw OM, which is the perpendicular bisector of AB.

By the property of perpendicular bisectors, OM passes through the center O of the circle.

Since OM is perpendicular to AB, we can use the Pythagorean theorem to find the length of AM (or BM), which is half of the chord AB:

$AM^2 + OM^2 = OA^2\ AM^2 + 14^2 = 50^2\ AM^2 = 50^2 - 14^2\ AM = BM = √(50^2 - 14^2)\ AM = BM = √(2500 - 196)\ AM = BM = √2304\ AM = BM = 48$

Therefore, the length of the chord AB is:

AB = 2 × AM

= 2 × 48

= 96 cm

The diameter of the circle is twice the radius, so it is:

diameter = 2 × radius

= 2 × 50

= 100 cm

Therefore, the sum of the chord AB and the diameter of the circle is:

AB + diameter = 96 + 100

= 196 cm

Hence, the sum of chord AB and the diameter of this circle is 196 cm.

Calculation:

Average sales of branches A, B, and C in 2020 = (117 + 113 + 83)/3

⇒ 313/3

Average sales of branches C, D, and E in 2021 = (99 + 74 + 101)

⇒ 274/3

Percent = {(313/3)/(274/3)} × 100 = (313/274) × 100

⇒ 114.23%

∴ Option 3 is the correct answer.

Given:

x2 + 1/x2 = 51

Formula:

(x - 1/x)2 = x2 + 1/x2 - 2

| x | = x

| -x | = x

Calculation:

According to the formula

(x - 1/x)2 = x2 + 1/x2 - 2

⇒ (x - 1/x)2 = 51 - 2

⇒ (x - 1/x) = √49 

⇒ (x - 1/x) = 7

⇒ (x² - 1)/x = 7

∴ Option 2 is the correct answer.

Given:

Angle PQR = 90° and QS ⊥ PR.

PQ = 6 cm and PS = 4 cm

Concept Used:

In a right-angled triangle,

Hypotenuse² = Base² + Perpendicular²

Calculation:

In triangle PQR = 90° and QS ⊥ PR.

∴ QSP = 90° 

Apply Pythagoras in QSP

QS² + SP² = QP²

⇒ x² + 4² = 6²

⇒ x² = 36 - 16

⇒ x = √ 20

⇒ x = 2√ 5

∴ Option 1 is the correct answer.

Calculation:

Total Cost Price = 750 + 650 + 450 + 550 + 350 + 850 = 3600

Total Profit = 250 + 200 + 350 + 450 + 300 + 400 = 1950

P1 = 3600 - 1950 = 1650

The total cost price of A and B = 750 + 650 = 1400

The total selling price of E and F = 350 + 300 + 850 + 400 = 1900

P2 = 1900 - 1400 = 500

P1 - P2 = 1650 - 500 = 1150

∴ Option 3 is the correct answer.

Given:

Triangle PQR

∠P is the largest angle and ∠P = 80 degrees

Ratio of the angles is 4:3:2

To find: The smallest angle of triangle PQR

Formula:

The sum of the angles of a triangle is 180 degrees.

Solution:

Let the measures of the angles of triangle PQR be 4x, 3x, and 2x, where 4x is the largest angle and 2x is the smallest angle.

According to the question:

4x = 80

x = 20

So 2x = 2 × 20 = 40

Therefore, the smallest angle of triangle PQR is 40 degree.

Given:

Selling price of T.V. set = Rs. 68,000

Original price of T.V. set = Rs. 85,000

Formula used:

Percentage discount = [(List price - Sale price)/List price] × 100%

Calculation:

Let's solve the question:

The original price of the T.V. set is Rs. 85,000 and it is being sold for Rs. 68,000. We can use the formula for percentage discount to find out the discount percentage offered by the company:

Percentage discount = [(List price - Sale price) / List price] × 100%

In this case, the list price is Rs. 85,000 and the sale price is Rs. 68,000. Substituting these values in the formula, we get:

Percentage discount = [(85,000 - 68,000) / 85,000] × 100%

= (17,000 / 85,000) × 100%

 = 20%

Therefore, the percentage discount offered by the company is 20%.

Given:

The nine-digit number = 2x64y

Divisible by = 88

Concept used:

Divisibility rule of 8 - The last three digits of a number are divisible of 8

Divisibility rule of 11 - If the difference between the sum of the digits at odd places and even places equals 0 or divisible by 11 

Calculation:

We know that the last three digits of a number are divisible of 8

⇒ The number made from the last three digits without altering their position will be divisible by 8

⇒ Possible values of y = 8

Now, check the divisibility rule of 11

⇒ (2 + 6 + 8) - (x + 4) = 0 or 11

⇒ 12 - x =  0 or 11

Then, x = (12 – 11) = 1

Now,

⇒ (6x - 5y)

⇒ (6 × 1) - (5 × 8)

⇒ 6 - 40

⇒ - 34

∴ The required value is -34

Given:

S.I. for 5 years = 20% of Principal

Formula used:

S.I. = (P × R × T)/100

where P → Principal

R → Rate of interest

T → Time period

Calculation:

Let the principle be Rs. P

According to the question,

⇒ (P × 5 × rate)/100 = 20% of P

⇒ rate = 4%

Now, let in t years the simple interest will be equal to the principal

⇒ Simple interest = (P × 4 × t)/100

⇒ P = (P × t)/25

∴ t = 25 years

Shortcut TrickRatio of Principal to S.I. in 5 years = 100 : 20

Let the Principal be 100, so we are required to make S.I. = 100

⇒ S.I. of 20 = 5  years

⇒ S.I. of 100 = 5/20 × 100 = 25 years

Given:

Ratio of number of boys to girls in a college = 3:2

40 boys leave the college

40 girls join the college

New ratio of boys to girls after the change = 2:3

 

Formula:

If two quantities are in ratio a:b, then we can write them as a = ka' and b = kb', where k is a constant of proportionality and a' and b' are co-prime numbers.

The ratio of two quantities can be written as a fraction or a colon. For example, the ratio of a to b can be written as a/b or a:b.

Solution:

Let the initial number of boys in the college be 3x and the initial number of girls be 2x.

Using the formula, we can write:

Initial number of boys = 3x

Initial number of girls = 2x

After 40 boys leave, the number of boys becomes 3x - 40, and after 40 girls join, the number of girls becomes 2x + 40.

Using the new ratio, we can write:

(3x - 40)/(2x + 40) = 2/3

Cross-multiplying, we get:

9x - 120 = 4x + 80

Simplifying, we get:

5x = 200

Therefore, the initial number of boys in the college was 3x = 3(40) = 120.

Calculation:

The population of P in years M and N together:

M + N = 300 + 200 = 500

The population of Q in years K and L together

K + L = 500 + 350 = 850

According to the question:

(850 - 500)/850 × 100

(350)/850 × 100

41.17%

∴ Option 4 is the correct answer.

Given:

$\frac{(103^2-101^2)}{102}$

We can simplify it as follows:

$\frac{(103^2-101^2)}{102}$

⇒ $\frac{(103+101)(103-101)}{102}$

⇒ $\\frac{204 \times 2}{102}$

⇒ $\\frac{408}{102} = 4$

So, the expression evaluates to 4.

Given:

Average of 17 consecutive natural numbers = 41

Let the smallest number among these 17 consecutive natural numbers be x.

Formula:

The average of a set of numbers is equal to the sum of the numbers divided by the total number of numbers.

Solution:

Since there are 17 consecutive natural numbers, the largest number will be x + 16.

Using the formula, we can write:

Sum of the 17 numbers = Average x Total number of numbers

Sum of the 17 numbers = 41 x 17

Sum of the 17 numbers = 697

Since the numbers are consecutive, we can find the sum of the 17 numbers as:

Sum of the 17 numbers = (x + (x + 1) + (x + 2) + ... + (x + 16))

Sum of the 17 numbers = (17x + 136)

Equating the two expressions for the sum of the 17 numbers, we get:

17x + 136 = 697

17x = 561

x = 33

Therefore, the smallest number among the 17 consecutive natural numbers is 33.

Shortcut Trick

A completes 2/3 of the work in 60 days.

Time to complete Full Work (1 unit) = 60 × 3/2 = 90 days.

Time to complete 1/5 of the work = 90 × 1/5 = 18 days.

∴ The correct answer is 18 days.

Alternate Method

Given: A completes 2/3 work in 60 days.

Formula: (Work₁ / Time₁) = (Work₂ / Time₂)

⇒ (2/3) / 60 = (1/5) / T₂

⇒ 2 / (3 × 60) = 1 / (5 × T₂)

⇒ 2 / 180 = 1 / (5T₂)

⇒ 1 / 90 = 1 / (5T₂)

⇒ 5T₂ = 90

⇒ T₂ = 90 ÷ 5 = 18 days.

∴ The correct answer is 18 days.

Additional Information

Work-Time Relationship

Time taken to complete a certain fraction of work is directly proportional to the work fraction. Time ∝ Work (when efficiency is constant).

Total Work Formula

If 1/n part of a work is done in T days, then the whole work is done in n × T days.

Efficiency

Efficiency = Total Work ÷ Total Time. It represents the work done in a single unit of time (1 day, 1 hour, etc.).

The garden EFGH is shown in the figure. Where EF = 240 meters & EH = 80 meters.

The width of the path is 4 meters.

Now the area of the path leaving the four colored corners

= [2 × (240 × 4)] + [2 × (80 × 4)]

{∵2 is multiplied because, among the four parts of the path, two parts have dimension (100 × 10)& two parts have dimension (80 × 10)}

= (1920 + 640) square meter

= 2560 square meters

Now, the area of 4 square colored corners:

4 × (4 × 4)

{∵ Side of each square = 4 meter}

= 64 square meter

The total area of the path = the area of the path leaving the four colored corners + square colored corners

⇒ Total area of the path = 2560 + 64 = 2624 square meter

∴ Option 4 is the correct answer.

Given:

Two angles of a scalene triangle: 40° and 62°

Formula:

The sum of the interior angles of a triangle = 180°

Calculation:

To find the measure of the third angle, we need to subtract the measures of the two given angles from 180°:

Sum of the two given angles = 40° + 62°

= 102°

Third angle = 180° - Sum of the two given angles

= 180° - 102°

= 78°

So, the measure of the third angle is 78°.

Concept:

$\rm \rm cot (90^{\circ} - \theta ) = tan\ \theta$

Calculation:

tan 8x = cot (2x)

tan 8x = $\rm tan (90^{\circ} -2x)$

10x  = 90° 

x= 9° 

5x = 9 × 5 = 45° 

tan x = tan 45°  = 1

∴ Option 4 is the correct answer.

Calculation:

Total number of patients on Monday and Wednesday = 146 + 138 = 284

Total number of patients on Thursday = 152

The ratio will be:

284: 152

71: 38

∴ Option 3 is the correct answer.

Given:

p + r = 21 and pr = 38

Concept used:

x3 + y3 = (x + y)3 - 3xy(x + y)

x + y = a, then x - y = √a² - 4xy

Calculation:

p + r = 21........(1)

Using x - y = √a2 - 4xy,

⇒ p - r  = √21² - 4 × 38 

⇒ p - r  = √289

⇒ p - r  = 17........(2)

Solving equations (1) and (2),

We get p =19 and r = 2

⇒ p3 - r3

⇒ 19³ - 2³

⇒ 6859 - 8

⇒ 6851

∴​ The required answer is 6851.

Calculation:

Let Raj initially have Rs. 100x

Raj initially had Rs. 100x. After spending 10% of his money, he was left with 90x.

Out of this remaining amount, he spent 70%, which left him with 30% of the original 90x, which was equal to Rs. 2646.

30% of 90x = 2646

⇒ 27x = 2646

⇒ x = 98

So , 100x = 100 × 98 = 9800

∴ Option 4 is the correct answer.

Alternate Method

Let the sum of money be x

According to the question,

x × 9/10 × 3/10 = 2646

⇒ 27x/100 = 2646

⇒ x = 9800

Shortcut Trick

At 50% loss, Selling Price (SP₁) = 100% − 50% = 50% of CP.

At 40% profit, Selling Price (SP₂) = 100% + 40% = 140% of CP.

Ratio of SP₁ : SP₂ = 50 : 140 = 5 : 14.

Unitary method: 5 units = Rs. 4,270 ⇒ 1 unit = 4,270 ÷ 5 = 854.

14 units = 14 × 854 = Rs. 11,956.

∴ The correct answer is Rs. 11,956.

Alternate Method

Given: First Selling Price (SP₁) = Rs. 4,270, Loss% = 50%, New Profit% = 40%.

Formulas: CP = [SP × 100] ÷ [100 − Loss%], SP = [CP × (100 + Profit%)] ÷ 100.

⇒ Cost Price (CP) = (4,270 × 100) ÷ (100 − 50) = 4,27,000 ÷ 50 = Rs. 8,540.

⇒ New Selling Price (SP₂) = [8,540 × (100 + 40)] ÷ 100 = (8,540 × 140) ÷ 100.

⇒ SP₂ = 85.4 × 140 = Rs. 11,956.

∴ The correct answer is Rs. 11,956.

Additional Information

Direct Formula for New SP

When CP is constant, SP₂ = SP₁ × [(100 + Profit₂%) ÷ (100 − Loss₁%)].

Relationship between CP and SP

If the Profit% is given, SP is always greater than CP. If Loss% is given, SP is always less than CP.

Shortcut Trick

Prime factorization of 720 = 2⁴ × 3² × 5¹

Total factors = (4 + 1) × (2 + 1) × (1 + 1) = 5 × 3 × 2 = 30

Factors excluding 1 and 720 = 30 − 2 = 28

∴ The correct answer is 28.

Alternate Method

Given:

The number is 720.

Formula Used:

If N = p^a × q^b × r^c ..., where p, q, and r are prime numbers.

Total number of factors = (a + 1) × (b + 1) × (c + 1)...

Calculations:

⇒ Prime factorization of 720 = 72 × 10 = 8 × 9 × 2 × 5

⇒ 720 = 2³ × 3² × 2¹ × 5¹

⇒ 720 = 2⁴ × 3² × 5¹

⇒ Total number of factors = (4 + 1) × (2 + 1) × (1 + 1)

⇒ Total number of factors = 5 × 3 × 2 = 30

⇒ We need to find the number of factors except 1 and the number itself (720).

⇒ Required factors = Total factors − 2

⇒ Required factors = 30 − 2 = 28

∴ The correct answer is 28.

Additional Information

Sum of Factors

If N = p^a × q^b × r^c, the sum of its factors = [(p^a+1 − 1) ÷ (p − 1)] × [(q^b+1 − 1) ÷ (q − 1)] × [(r^c+1 − 1) ÷ (r − 1)]

Number of Odd Factors

To find the number of odd factors, ignore the power of 2 in the prime factorization and calculate the total factors using only the powers of the odd prime bases.

Number of Even Factors

Even factors can be found by subtracting the number of odd factors from the total number of factors, or by not adding 1 to the power of 2: a × (b + 1) × (c + 1).

Total Prime Factors

The total number of prime factors is simply the sum of the powers of all prime bases: a + b + c.

The correct answer is "Because of sentimental memories of the past."

Key Points

• The idiom "for old time's sake" means to do something or be nostalgic about something because of sentimental memories of the past.
• It is often used when people want to revisit a place or activity that they used to enjoy in the past.
• Example: He and his old friends from college went back to the bar for old times' sake.
• Option 1, "to consider the options," does not relate to the meaning of the idiom.
• Option 2, "deliberately stop someone," is not related to the idiom either.
• Option 3, "to be friends with an old person," is not the correct meaning of the idiom.
• Therefore, the correct answer is option 4, "Because of sentimental memories of the past."
• Grammatically, the idiom is a prepositional phrase consisting of the preposition "for," the adjective "old," the noun "time," and the noun's possessive form "sake."
• The phrase functions as an adverbial phrase modifying the verb in the sentence.
• In conclusion, the correct answer is Option 4.

The correct answer is "stabbed in broad."

Key Points

• The word "broad" is an adjective that modifies the noun "daylight," indicating that the stabbing occurred during the daytime.
• The correct phrase is "in broad daylight," which is an idiomatic expression meaning "in full view of the public."
• Example: Thieves had broken into the house **in broad daylight.**​
• In conclusion, the correct answer is "stabbed in broad," which correctly uses the idiomatic expression "in broad daylight" to describe the time of the stabbing.
• Thus, the correct answer is Option 4.

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Correct Sentence: A cloth merchant has been stabbed in broad daylight over a rupee.

The correct sentence with no spelling error is: Option 1: "Marinate your proteins ahead of time."

Key Points

• The grammatical rule involved in this sentence is the correct spelling of words.
• The word "marinate" is spelled correctly, as well as "proteins" and "ahead."
• Option 2, "Marinate your proteins aheade of time," has a spelling error in the word "ahead."
• Option 3, "Marinatte your proteins ahead of time," has a spelling error in the word "marinate."
• Option 4, "Marinate your protiens ahead of time," has a spelling error in the word "proteins."
• In conclusion, the correct sentence is option 1: "Marinate your proteins ahead of time."

Additional Information

• Marinate - (of food) undergo marination; soak (meat, fish, or other food) in a marinade.
• Protein - any of a class of nitrogenous organic compounds that have large molecules composed of one or more long chains of amino acids and are an essential part of all living organisms, especially as structural components of body tissues such as muscle, hair, etc., and as enzymes and antibodies.
• Ahead - further forward in space; in the line of one's forward motion.

The correct answer is "works."

Key Points

• "Deeds" and "brings" do not make sense in the context of a machine.
• "Clubs" is a verb that means to hit with a heavy object, so it also does not fit in this sentence.
• Grammatically, "works" is the correct verb to use when asking about how a machine operates.
• It is a present tense verb that agrees with the subject "machine."
• Conclusive line: The appropriate option to fill in the blank is "works."
• Thus, the correct answer is Option 3.

<br>

Correct Sentence: Have you ever wondered how this machine works?

The correct order is PSRQ.

Key Points

• P. "image gallery on your phone, or fast forward" - This part introduces the action of flicking through the image gallery on your phone, which implies quickly browsing or looking through.
• S. "through a previously watched movie, and notice" - This part introduces another action, which is watching a previously seen movie. It implies that while watching, one might notice something specific.
• R. "how the briefly presented images trigger memories" - This part explains the effect of the action. It discusses how the images that are briefly presented (likely during the flicking through) can trigger memories.
• Q. "with little or no effort on your part" - This part describes the ease with which the action can be performed. It explains that the activity of flicking through requires minimal effort.
• Therefore, the answer 2) PSRQ can be considered correct as it forms a coherent sentence.

Hinglish

• P. "image gallery on your phone, or fast forward" - इस भाग में फ़ोन पर इमेज गैलरी के माध्यम से झपकी झपकी से पार देखने की गतिविधि का परिचय दिया गया है।
• S. "through a previously watched movie, and notice" - यह भाग एक और क्रिया, जो एक पहले देखी गई फिल्म को फिर से देखने का परिचय देता है।
• R. "how the briefly presented images trigger memories" - इस भाग में क्रिया के प्रभाव की व्याख्या की गई है।
• Q. "with little or no effort on your part" - इस भाग में क्रिया को कितनी आसानी से किया जा सकता है, इसका वर्णन किया गया है।
• इसलिए, उत्तर "PSRQ" सही माना जा सकता है क्योंकि इससे सहज संदेश बनता है।

Here the correct answer is Idiosyncratic.

Key Points

• The word that means the same as "eccentric" is "idiosyncratic".
• As an adjective, "eccentric" describes someone or something that is unconventional, peculiar, or deviates from the normal or expected behavior. It often implies that the person or thing is unique or different in a somewhat strange or unusual way.
• Example: "John is known for his eccentric fashion sense. He always wears mismatched clothes and colorful accessories."
• Idiosyncratic means having peculiar or unique characteristics, which is synonymous with eccentric.
• Example: "Sarah has an idiosyncratic way of organizing her bookshelf. She arranges the books by color rather than by author or genre."
• Conclusion: The correct answer is "Idiosyncratic".

Additional Information

• Familiar means well-known or common, which is the opposite of eccentric.
• Garden refers to a piece of land where plants are grown, which is unrelated to eccentricity.
• Wonted means customary or habitual, which is also the opposite of eccentric.

Here the correct answer is Intensify.

Key Points

• The word "wane" means to decrease or diminish in size, strength, or intensity. It often refers to something gradually becoming weaker or fading away.
• Example: "As the moon began to wane, the night grew darker."
• In this example, "wane" is used to describe the moon's decreasing visibility or illumination as it moves through its lunar cycle.
• "Intensify" means to increase or become stronger or more intense, contrasting with the idea of decrease or fading associated with "wane."
• Example: The storm began to intensify as dark clouds rolled in, and the wind picked up speed.​
• Therefore, the correct answer is 1) Intensify because it represents the opposite meaning to "wane."

Additional Information

• Now let's analyze the other options:
• Evanesce: This word means to vanish or disappear gradually, similar to the concept of fading away. While it shares a similar idea of gradual disappearance with "wane," it is not an exact opposite. It is more synonymous with "diminish" or "fade."
• Example: "The morning mist began to evanesce as the sun rose higher in the sky."
• Diminish: This word means to make or become less or reduce in size, extent, or importance. It is somewhat synonymous with "wane" as both indicate a decrease or reduction, but it is not the exact opposite.
• Example: "The company's profits started to diminish after the economic downturn."
• Contract: This word means to become smaller or narrower or to decrease in size, extent, or quantity. While it shares the idea of decrease or reduction with "wane," it is not the opposite as it does not encompass the aspect of intensity or strength.
• Example: "The muscles contract during exercise."

The correct answer is 2) Fulfilment.

Key Points

• The word "delinquency" refers to the act of failing to fulfill one's obligations or responsibilities, especially in the context of legal or moral duties. It often connotes misconduct, negligence, or noncompliance. (कर्तव्य में चूक, अपराधवृत्ति)
• Example: "The delinquency of the student in completing assignments led to a significant drop in their grades."
• In this example, "delinquency" is used to describe the student's failure to fulfill their academic responsibilities, resulting in poor performance.
• "Fulfilment" signifies the act of meeting or completing obligations or responsibilities, which contrasts with the idea of failure or noncompliance associated with "delinquency." (लक्ष्‍य की प्राप्ति)
• Example: "The employee's prompt and efficient work ensured the fulfillment of all project deadlines."
• Therefore, the correct answer is 2) Fulfilment because it represents the opposite meaning of "delinquency."

Additional Information

• Now let's analyze the other options:
• Neglect: This word means to fail to care for or pay attention to something or someone, often resulting in the lack of proper maintenance or oversight. While there is a connection between neglect and delinquency, neglect is not the opposite. Neglect can contribute to delinquency but is not the exact opposite. (बिलकुल ध्यान न देना)
• Example: "The neglected garden became overgrown with weeds and was in a state of disarray."
• Tardiness: This word refers to the habit or act of being late or delayed in meeting obligations or appointments. While tardiness can be seen as a form of noncompliance, it is not the direct opposite of delinquency. (शिथिलता)
• Example: "Her constant tardiness to work led to disciplinary action from her employer."
• Default: This word typically refers to the failure to fulfill an obligation, especially in financial matters. While "default" shares some similarities with "delinquency," they are not precise antonyms. "Default" often specifically relates to a failure to meet financial obligations, whereas "delinquency" has a broader scope. (अभाव, गलती, दोष)
• Example: "The company went into default on their loan payments, leading to legal consequences."

The incorrectly spelt word is "Wropes".

Key Points

• The correct spelling is "Ropes".
• It refers to a thick cord made of twisted or braided strands.
• The other options are correctly spelled words.
• "Delible" means capable of being erased or removed.
• "Convince" means to persuade someone to believe or do something.
• "Rubber" is a material used for making various products, including tires and erasers.
• In conclusion, the incorrectly spelled word is "Wropes", and the correct spelling is "Ropes".
• Thus, the correct answer is Option 1.

Here the correct answer is QRSP.

Key Points

• Q. "After the initial development of glacial conditions, the Earth" - This part sets the context by stating that after the initial formation of glacial conditions, the Earth went through changes.
• R. "system alternated between two modes, one of cold" - This part explains that the Earth's system had two modes that alternated. One of the modes was characterized by cold conditions.
• S. "temperatures and growing glaciers and the other of" - This part describes one of the modes in the alternating pattern.
• P. "relatively warm temperatures and retreating glaciers" - This part describes the other system. It mentions relatively warm temperatures and retreating glaciers occurring during one phase.
• The correct order, therefore, is QRSP, which forms a coherent sentence explaining the alternating modes of the Earth's system after the initial development of glacial conditions.

Here the correct answer is divided on groups.

Key Points

• The error is in "divided on groups." It should be "divided into groups."
• The correct preposition to use with "divide" is "into," not "on."
• The word "into" is commonly used with the verb "divide" to indicate the separation or splitting of something into distinct parts or groups. Here are some examples:
• "The cake was divided into six equal slices."
• In this example, "into" is used to show how the cake was divided into specific portions or slices, with each slice being equal in size.
• "The team was divided into two groups for the competition."
• Here, "into" is used to indicate the division of the team into two distinct groups, possibly for different tasks or roles in the competition.
• Other options: - "The young learners were" is grammatically correct. - "According to their abilities" is also grammatically correct.

<br>

Correct Sentence: The young learners were divided into groups, according to their abilities.

The correct answer is "said, 'We plan to make the state a safer place for'".

Key Points

• 'That' is not used in direct speech after the verb 'said'.
• Thus, option 3 and 4 can be eliminated.
• The councillor said that they were planning to make the city safer from what it was.
• Thus, it is making a comparison between the situations of two different phases.
• Thus, a comparative degree should be used.
• The comparative degree of 'safe' is 'safer'.
• Thus, the correct answer is Option 2.

<br>

Correct Sentence: The councillor (said, “We plan to make the state a safer place for) everyone.”

The correct passive form of the given sentence is "Letters are sent by Megha."

Key Points

• In passive voice, the subject of the sentence becomes the receiver of the action, while the doer of the action is either omitted or introduced with the preposition "by."
• The position of the subject and the object is interchanged.
• The subject 'of the active voice is 'Megha' and the object is 'letters'.
• The given sentence is in simple present tense.
• 'sends' changes into 'are sent'.
• Option 1, "Letters is sent by Megha," is incorrect because "letters" is a plural noun and requires a plural verb form "are" instead of "is."
• Option 2, "Letters are being sent by Megha," is also grammatically correct, but it implies that the action is currently in progress, whereas the original sentence is in simple present tense.
• Option 3, "Letters were sent by Megha," is in the past tense and implies that the action has already been completed, but the given active voice is in present tense.
• Therefore, the correct answer is option 4, "Letters are sent by Megha," which is in the present tense and accurately conveys the passive voice of the original sentence.