The logic followed here is:

Logic: (1st number)⁴ × 2nd number = 3rd number.

Now,

(3, 2, 162)

→ 3⁴ × 2 

→ 81 × 2 = 162.

(6, 3, 3888)

→ 64 × 3 

→ 1296 × 3 = 3888.

Similarly, (7, 2, 4802) 

→ 74 × 2 

→ 2401 × 2 = 4802.

Hence, the correct answer is "Option 4".

The logic followed here is:

‘SCREEN’ is coded as ‘LCCPAQ’,

Similarly, for 'SKILLS'

So, 'SKILLS' is coded as 'QJJGIQ'.

Hence, the correct answer is "Option 4".

The logic followed here is:

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

Now,

(18, 66, 48) 

→ 18 + 48 = 66.

(52, 144, 92)

→ 52 + 92 = 144.

Similarly, (24, 56, 32)

→ 24 + 32 = 56.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: The first unit measures or indicates the physical quantity in the second term.

Here,

Ohm : Electric Resistance → An Ohm measures or indicates electric resistance.

Similarly,

Newton : Force → A Newton measures or indicates force.

Hence, the correct answer is "Force".

Additional Information

The logic followed here is:

AMG : WIC

Similarly,

NZT : ? 

Hence, the correct answer is "Option 1".

The logic followed here is:

So, 'LBX' will complete the series.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: 4 has been subtracted to each letter's positional value to get the next letter of the cluster.

Let's check each option as per the logic:

1) EAW:

2) WSM:

3) HDZ:

4) YUQ:

Here, we can see that only Option 2 doesn't follow the logic.

Hence, the correct answer is " WSM ".

The correct mirror image of the given figure is shown below:

Hence, the correct answer is " Option 4 ".

BODMAS Table: 

Given equation I. 7 – 6 + 2 ÷ 1 × 9 = 2

Now, if '× and +' are interchanged, then:

⇒ 7 – 6 × 2 ÷ 1 + 9 = 2

⇒ 7 – 6 × 2 + 9 = 2

⇒ 7 – 12 + 9 = 2

⇒ 16 - 12 = 2

⇒ 4 ≠ 2

LHS ≠ RHS.

Given equation II: 16 + 4 – 9 × 1 ÷ 3 = 60

Now, if '× and +' are interchanged, then:

⇒ 16 × 4 – 9 + 1 ÷ 3 = 60

⇒ 16 × 4 – 9 + 0.33 = 60

⇒ 64 – 9 + 0.33 = 60

⇒ 64.33 - 9 = 60

⇒ 55.33 ≠ 60

LHS ≠ RHS.

Here, Both Equation I and II are the incorrect after interchanging the given symbol.

Hence, the correct answer is "Option 1".

The logic followed here is:

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

Now,

6 : 12

→ 6 × (6 ÷ 3)

→ 6 × 2 = 12.

15 : 75

→ 15 × (15 ÷ 3)

→ 15 × 5 = 75.

Similarly, 

18 : ?

→ 18 × (18 ÷ 3)

→ 18 × 6 = 108.

Hence, the correct answer is "Option 2".

The squares are:

So, there is '10' squares in the given figure.

Hence, the correct answer is "10".

The logic followed here is:

Logic: The first word represents the capital city of the respective state.

Let's check each option,

Here, we can see that only Option 1 doesn't follow the logic.

Hence, the correct answer is **"**Karnataka – Bengaluru".

Family Chart:

Given: 

M is the brother of N.

L is the father of M.

N is the sister of O.

O is the daughter of P.

So, P is mother of N.

Hence, the correct answer is "Option 1".

The logic followed here is:

‘GARMENTS’ is coded as ‘2019132214719’,

‘HYDROGEN’ is coded as ‘192523181272214’,

Similarly, for 'INVASIVE'

So, 'INVASIVE' is coded as '1814518955'.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: The circle and the arrow moves in clockwise direction in +2, +1 alternatively.

Hence, the correct answer is "Option 2".

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

Now, symbol '@' is given in Dice 2 and Dice 3, 

So, From Dice 2 and Dice 3,

→ @ is the common surface and &, #, ©, % is the adjacent surface.

So, the remaining 'O' will be the opposite face of '@'.

Hence, the correct answer is "O".

The logic followed here is:

Logic: The Second word is a type of First word.

Colour : Black

→ Black is a type of Colour.

Let's check each option:

1) Lily: Flower

→ Flower is not a type of Lily.

2) Eraser: Marker

→ Marker is not a type of Eraser.

3) Furniture: Table

→ Table is a type of Furniture. ⇒ Satisfies the logic.

4) Fruit: Onion

→ Onion is not a type of Fruit.

Here, we can see that only Option 3 follow the logic.

Hence, the correct answer is "Furniture: Table".

The Venn diagram representing the relationship between Pens, Pencils and Eraser is shown below:

Here, Pen, Pencil and Eraser all are different stationary item.

Hence, the correct answer is " Option 2 ".

The correct order as per the dictionary is shown below:

4. Dieldrin

5. Diestock

6. Diestrum

7. Diestrus

8. Dietetic

Here, we can see that the word at the Second position is Diestock.

Hence, the correct answer is " Diestock ".

The logic followed here:

Logic: Second Number = (1st Number) × 4 = 2nd number.

Let's check each option as per the logic:

1) 648 – 2592:

→ 2592 = 648 × 4

→ 2592 = 2592

→ LHS = RHS.

2) 378 – 1512:

→ 1512 = 378 × 4

→ 1512 = 1512

→ LHS = RHS.

3) 588 – 2352:

→ 2352 = 588 × 4

→ 2352 = 2352

→ LHS = RHS.

4) 278 – 1122:

→ 1122 = 278 × 4

→ 1122 ≠ 1112 

→ LHS ≠ RHS.

Here, we can see that only Option 4 doesn't follow the logic.

Hence, the correct answer is "278 – 1122".

The logic followed here is:

So, '166' is the missing term in the given series.

Hence, the correct answer is "Option 3".

The paper when unfolded will appear as shown below:

Hence, the correct answer is "Option 4".

The logic followed here is:

8 % 3 % 2 = 328

4 % 2 % 6 = 264

Similarly,

1 % 7 % 3 =?

Hence, the correct answer is "Option 4".

Given Statements:

I. All truck are car.

II. Some car are bike.

The least possible Venn diagram for the given statement is:

Conclusions:

I. No bike is truck - False (Because, no definite relation given between Bike and Truck, so it can be possible only).

II. Some truck are car - True (All truck are car, so some truck are also car).

III. Some bike are car - True (Some car are bike, so some bike is also car).

So, Both conclusions II and III follows.

Hence, the correct answer is "Option 4".

The correct mirror image of the given figure is shown below:

Hence, the correct answer is " Option 3 ".

The correct answer is Option 2. 

Key Points

• The East Coast of India lies between the Eastern Ghats mountain range and the Bay of Bengal.
• The Eastern Ghats, also known as the Mahendra Range, is a discontinuous mountain range that runs parallel to the East Coast of India.
• It stretches along the states of Odisha, Andhra Pradesh, Telangana, and Tamil Nadu.
• The East Coast plains, which lie between the Eastern Ghats and the Bay of Bengal, are relatively flat and fertile, making them suitable for agriculture.
• This region is home to several major cities and important ports along the coast.

Additional Information

• Between the Gulf of Cambay and Cape Comorin lies the western coast of India, also known as the West Coast of India.
• The West Coast of India is situated along the Arabian Sea and extends from the Gulf of Cambay (also known as the Gulf of Khambhat) in the north to Cape Comorin (also known as Kanyakumari) in the south.
• This coastal stretch includes the states of Gujarat, Maharashtra, Goa, Karnataka, and Kerala.
• The West Coast of India is known for its beautiful beaches, diverse culture, and important port cities such as Mumbai, Mangalore, Kochi, and Thiruvananthapuram.
• Between Maharashtra and Kerala lies the state of Karnataka.
• Karnataka is located on the southwestern part of India and shares its borders with Maharashtra to the north and Kerala to the south.
• The state capital of Karnataka is Bengaluru (Bangalore), which is known as the technology hub of India.
• Karnataka is known for its rich cultural heritage, historical sites, and natural beauty.
• It is also home to several important cities and tourist destinations, including Mysore, Hampi, Mangalore, and Coorg.
• ​Between Diu and Kerala lies the state of Gujarat and the Union Territory of Daman and Diu.
• Diu is a small island and town located off the southern coast of Gujarat, while Kerala is situated on the southwestern tip of India.
• To travel from Diu to Kerala, one would need to traverse the state of Gujarat, pass through Maharashtra, and then enter Kerala.
• The journey would involve traveling along the western coast of India.

The correct answer is Option 2. 

Key Points

• In a graphical diagram where ex ante aggregate demand (AD) and ex ante aggregate supply (AS) are plotted together, equilibrium is reached at the point where the two curves intersect.
• This intersection represents the level of real output and price level where the quantity of goods and services demanded (AD) is equal to the quantity supplied (AS).
• At this equilibrium point, there is no tendency for the economy to move away from it, as the quantity demanded matches the quantity supplied.
• The equilibrium point can be thought of as the point of balance in the economy, where there is no excess demand or excess supply.
• It is where buyers' and sellers' plans align, resulting in a stable state in which the economy is in equilibrium.

Additional Information

• In an economy, demand and supply refer to the forces that determine the quantity of goods and services exchanged in the market. 
• Demand: Demand represents the quantity of goods and services that buyers are willing and able to purchase at various price levels, during a specific period.
• Demand is influenced by factors such as price, consumer preferences, income levels, population, and the availability of substitutes.
• The relationship between price and quantity demanded is typically inverse, meaning that as the price increases, the quantity demanded tends to decrease, and vice versa.
• Demand is usually represented by a downward-sloping demand curve.
• Supply: Supply, on the other hand, represents the quantity of goods and services that sellers are willing and able to offer for sale at different price levels.
• The supply is influenced by factors such as production costs, technology, resource availability, government regulations, and expectations of future prices.
• The relationship between price and quantity supplied is usually positive, meaning that as the price increases, the quantity supplied tends to increase, and vice versa.
• Supply is often represented by an upward-sloping supply curve.
• The interaction of demand and supply determines the equilibrium price and quantity in a market.
• When the quantity demanded equals the quantity supplied, the market is said to be in equilibrium.
• Changes in demand or supply will shift the respective curves, leading to changes in the equilibrium price and quantity.
• For example, an increase in demand will shift the demand curve to the right, leading to a higher equilibrium price and quantity.
• Understanding the dynamics of demand and supply is crucial in analyzing market behavior, price fluctuations, and the allocation of resources in an economy.

The correct answer is Option 4. 

Key Points

• Bhavani Devi from Chennai became the first Indian athlete to represent India in the sport of fencing at the Olympics.
• Tokyo Olympics 2020 :Tokyo Olympics 2020 was an international multi-sport event held from 23 July to 8 August 2021 in Tokyo, Japan, with some preliminary events that began on 21 July.​
• India finished 48th on the medal tally in Tokyo, its highest ranking in over four decades..
• India marched at the 21st number with the boxer Mary Kom and men’s hockey captain Manpreet Singh as flag-bearers.
• The teams entered the stadium in alphabetical order according to the language selected by the organizing committee, generally the dominant language in the host city.
• The 2024 Summer Olympics will be held in Paris. And all the way out in 2028, Los Angeles will play host.

​

Additional Information

• PT Usha:
• Pilavullakandi Thekkeparambil Usha, commonly known as PT Usha, is an Indian former track and field athlete.
• She is often referred to as the "Payyoli Express."
• P.V. Sindhu:
• Pusarla Venkata Sindhu, commonly known as PV Sindhu, is an Indian professional badminton player.
• She has achieved great success in badminton, including winning a silver medal at the 2016 Rio Olympics and a bronze medal at the 2020 Tokyo Olympics in women's singles badminton.
• Aditi Ashok:
• Aditi Ashok is an Indian professional golfer.
• She represents India in golf tournaments and has achieved notable success in the sport.
• Bhavani Devi:
• Bhavani Devi, whose full name is C. A. Bhavani Devi, is an Indian sabre fencer.
• She made history by becoming the first Indian fencer to qualify and represent India in fencing at the Tokyo Olympics 2020 (held in 2021).

The correct answer is Option 3. 

Key Points

• Modhera in the state of Gujarat, India, has indeed become the first solar-powered village in the country.
• The solar project has provided renewable energy to the residents of Modhera, resulting in a surplus of power.
• The cost of the solar project was shared between the Indian government and the Government of Gujarat, amounting to $9.7 million.
• As a result of the solar power supply, residents of Modhera can save a significant portion of their power bills, ranging from 60 to 100 percent.
• This development aligns with the goal of promoting clean and sustainable energy sources, as highlighted by UN Secretary-General António Guterres.

The correct answer is Option 2. 

Key Points

• West Bengal has bagged the award for 'Best Destination For Culture' internationally.
• West Bengal receiving the International Travel Award 2023 for Best Destination for Culture is a significant achievement.
• The Pacific Area Travel Writers Association (PATWA) is an esteemed organization, and being accredited by them reflects the cultural richness and tourism potential of West Bengal.
• It's also noteworthy that the PATWA is an affiliate member of the United Nations World Tourism Organization (UNWTO), further enhancing the prestige of the award.

The correct answer is Option 1. 

Key Points

• The law that is also known as the law of inertia is Newton's First Law of Motion.
• It states that an object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an external force.
• This fundamental law of physics was formulated by Sir Isaac Newton and is one of the three laws that form the basis of classical mechanics.

Additional Information

• Newton's Second Law of Motion, also known as the law of acceleration, describes the relationship between the force acting on an object, the mass of the object, and the resulting acceleration.
• It is one of the fundamental principles of classical mechanics formulated by Sir Isaac Newton.
• Archimedes' principle states that when an object is placed in a fluid (like water), it experiences an upward force called buoyant force.
• This force is equal to the weight of the fluid that the object displaces (pushes aside).
• Example - when you put something in water, it feels a push from the water that tries to lift it up. The more water the object pushes away, the stronger the push (buoyant force) it feels. If the object is lighter than the water it displaces, it will float because the buoyant force is greater than the weight of the object. If the object is heavier, it will sink because the weight is greater than the buoyant force.
• Kepler's laws are a set of three fundamental principles that describe the motion of planets and other celestial objects around the Sun. Here's a simplified explanation of each law:
• Law of Orbits: Each planet in our solar system moves around the Sun in an elliptical orbit, with the Sun at one of the two foci of the ellipse. In simpler terms, the path of a planet is not a perfect circle but more like a stretched-out circle with the Sun slightly off-center.
• Law of Areas: An imaginary line connecting a planet to the Sun sweeps out equal areas in equal time intervals. In other words, as a planet moves in its elliptical orbit, it covers an equal area in space over equal periods of time. This means that a planet moves faster when it is closer to the Sun and slower when it is farther away.
• Law of Periods: The square of the time period of a planet's orbit is proportional to the cube of its average distance from the Sun. In simpler terms, the time it takes for a planet to complete one orbit around the Sun (its period) is related to its average distance from the Sun. The farther a planet is from the Sun, the longer its orbital period.

The Correct answer is Option 4. 

Key Points

• TOKYO OLYMPICS
• The 2020 Olympics was held in Tokyo from 23 July to 8 August 2021.
• The International Olympics Committee postponed the games due to Covid-19.
• This was the second time When Japan will host the Olympics. (First in 1964)
• Miraitowa is the official mascot of the 2020 Summer Olympics.
• The mascot is created by Japanese artist Ryo Taniguchi.
• The International Olympic Committee (IOC)
• IOC is a not-for-profit independent international organization.
• Created- 23 June 1894
• The first Olympic Games of the modern era were conducted in April 1896.
• The Olympic Charter is the codification of the Fundamental Principles of Olympism.
• President- Thomas Bach
• Olympic Motto- CITIUS – ALTIUS - FORTIUS meaning  (FASTER - HIGHER - STRONGER -COMMUNITER)
• The 138th session of the International Olympic Committee met between 20-21 July 2021.
• At this meeting, the International Olympic Committee decided to change the Olympic motto 'Citius, Altius, Fortius' to 'Citius, Altius, Fortius, Communiter'.

​

Additional Information

• Tokyo  Olympics 2020
• India won 7 medals at Tokyo Olympics 2020, which includes 1 Gold, 2 Silver, and 4 Bronze medals.
• Neeraj Chopra won a Gold medal in the Javelin Throw event.
• Ravi Kumar Dahiya won a Silver medal in Men's Wrestling 57KG category.
• Mirabai Chanu created history winning India’s first medal of the Tokyo Olympics when she clinched silver in women’s 49kg weightlifting event.
• P.V. Sindhu won a Bronze medal in Women's Singles Badminton.
• Lovlina Borgohain won a Bronze medal in the Women's Welterweight Boxing category.
• Indian Men's Hockey team won the Bronze medal.
• Bajrang Punia won a Bronze medal in Men's Wrestling 65 KG category.

The correct answer is Option 2. 

Key Points

• Sher Shah Suri defeated Humayun at the Battle of Kanauj in the year 1540.
• The battle took place near the city of Kanauj, located in present-day Uttar Pradesh, India.
• Sher Shah Suri's forces, under his leadership, emerged victorious in this battle, resulting in Humayun's temporary expulsion from the Indian subcontinent.
• Humayun was able to regain his empire later and reclaim Delhi in 1555.

Additional Information

• Sher Shah Suri was born in 1486 in Sasaram, present-day Bihar, India.
• He belonged to the Pashtun Sur tribe, hence the name "Suri."
• Sher Shah Suri initially served under the Delhi Sultanate and later joined the service of the Mughal emperor Humayun.
• ​Humayun, also known as Nasir-ud-Din Muhammad Humayun, was the second Mughal emperor who ruled over a significant portion of the Indian subcontinent.
• He was born on March 6, 1508, in Kabul, Afghanistan, and he ascended to the throne in 1530.
• Humayun was the eldest son of the first Mughal emperor, Babur.
• During his reign, he faced several challenges, including conflicts with regional rulers and internal power struggles.
• Humayun's reign was marked by ups and downs, as he lost and regained his empire multiple times.
  

The correct answer is Option 4. 

Key Points

• The most important festival of Assam is Bihu. Bihu is a series of three agricultural festivals celebrated with great enthusiasm and fervor throughout the state. These three Bihus are:
• Rongali Bihu (Bohag Bihu): It is the most popular and widely celebrated Bihu, which marks the arrival of the Assamese New Year in mid-April. It celebrates the onset of the spring season and the agricultural cycle. People indulge in traditional music, dance (Bihu dance), feasting, and various cultural activities.
• Kongali Bihu (Kati Bihu): Celebrated in mid-October, Kongali Bihu is dedicated to the worship of the household deities. This Bihu is more somber in nature and focuses on prayers and rituals for a bountiful harvest. People light oil lamps, offer prayers, and participate in community activities.
• Bhogali Bihu (Magh Bihu): Celebrated in mid-January, Bhogali Bihu is associated with the harvest and feasting. It is also known as the festival of food, where people enjoy various traditional delicacies, especially made from rice and sesame seeds. Bonfires are lit, and community feasts are organized during this Bihu.

Additional Information

• The Lumbini Festival is an important cultural festival celebrated in the state of Andhra Pradesh, India.
• It is organized annually to promote tourism and showcase the rich cultural heritage of the region.
• The festival takes place in Nagarjunasagar, a town located near the Nagarjuna Sagar Dam, which is a significant historical and tourist attraction.
• The Lumbini Festival is named after Lumbini, the birthplace of Gautama Buddha in Nepal.
• The festival aims to highlight the Buddhist connection and the influence of Buddhism in the region.
• It usually occurs in December and spans three days, featuring a variety of cultural events, exhibitions, performances, and competitions.
• ​The Hornbill Festival is one of the most important cultural festivals of Nagaland, a state located in Northeast India.
• It is named after the Indian Hornbill bird, which is deeply revered in Naga folklore.
• The festival takes place annually from December 1st to 10th in the Kisama Heritage Village, located near Kohima, the capital city of Nagaland.
• The Hornbill Festival aims to showcase and celebrate the rich cultural heritage and traditions of the Naga tribes.
• It provides a platform for the different tribes of Nagaland to come together, display their distinct customs, arts, crafts, music, dance, and culinary delights.
• The festival also promotes inter-tribal harmony and unity among the Naga people.
• Phool Dei is a traditional festival celebrated in the Kumaon region of Uttarakhand, a state in northern India.
• The festival marks the arrival of spring and is usually observed in the month of March.
• "Phool" means flowers, and "Dei" refers to an offering or gift. Therefore, Phool Dei can be translated as "the festival of flowers."
  

The correct answer is Option 1. 

Key Points

• The correct pairing of 'disease - duration' is:
• Acute - short time
• Chronic - long duration
• Acute diseases are characterized by a sudden onset and a relatively short duration. They typically resolve within a short period, ranging from a few days to a few weeks. Examples of acute diseases include the common cold, acute bronchitis, and acute appendicitis.
• On the other hand, chronic diseases are characterized by a long duration, typically lasting for months or years. They often develop slowly and persist over an extended period, sometimes for a person's lifetime. Examples of chronic diseases include diabetes, hypertension (high blood pressure), and rheumatoid arthritis.
• Therefore, the correct pairing would be "Acute - short time" and "Chronic - long duration."

The correct answer is Part III of the Constitution.

Key Points

• Fundamental Rights (FRs) are known as the base of the Indian constitution & mentioned in Part III of the constitution.
• They prohibit unreasonable interference of the state & prevent its executive & legislature to become authoritarian, hence put due limitations of state power.
• Observance of fundamental duties is required for having one’s FRs redressed in case of their violation.

Important Points

• FRs are not absolute but qualified rights.
• It is Subject to certain restrictions imposed by the state on the question of national security, interest & general welfare of the society.
• But restrictions are checked by SC & HCs, whether restrictions are reasonable or not.
• SC verdict in the Golaknath V/S state of Punjab (1967) - FRs have been given a transcendental position by constitution hence no authority functioning under the constitution including parliament has the power to amend FRs.
• In Keshavananda Bharati V/S state of Kerala, 1973, SC held that parliament has the power to amend any provision of the constitution including part III, however, parliament’s amending power subjects to the “Basic structure of the constitution".​

Additional Information

There are six Fundamental Rights-

The correct answer is Catalyzing New India's Techade.

Key Points

• Prime Minister Narendra Modi inaugurated Digital India Week 2022 in Gandhinagar in Gujarat on 4 July 2022.
• During the programme, he launched multiple digital initiatives aimed at enhancing the accessibility of technology, streamlining service delivery to ensure ease of living and giving a boost to startups.
• The theme for Digital India Week is Catalyzing New India’s Techade.​

Additional Information

• Mr Modi launched digital India Bhashini’ which enables easy access to the internet and digital services in Indian languages, including voice-based access and helps the creation of content in Indian languages.
• Prime Minister also launched ‘Digital India GENESIS’ - a National Deep-tech Startup Platform, to discover, support, grow and make successful startups in Tier-II and Tier-III cities of India.
• A total outlay of 750 crore rupees has been envisaged for the scheme.
• He launched ‘Indiastack.global’ - a global repository of key projects implemented under India Stack like Aadhaar, UPI, Digilocker, Cowin Vaccination Platform, Government e MarketPlace, DIKSHA Platform and Ayushman Bharat Digital Health Mission.
• Prime Minister dedicated to the citizens ‘MyScheme’ - a service discovery platform facilitating access to Government Schemes.
• It aims to offer a one-stop search and discovery portal where users can find schemes that they are eligible for.
• He also dedicates to the citizens ‘Meri Pehchaan’-  National Single Sign On for One Citizen Login.
• National Single Sign-On is a user authentication service in which a single set of credentials provide access to multiple online applications or services.
• Mr Modi announced the first cohort of 30 Institutions to be supported under the Chips to Startup Programme.
• The C2S Programme aims to train specialized manpower in the area of design of semiconductor chips at the Bachelor, Masters and Research levels.

The correct answer is Rajasthan.

Key Points

• Ghoomar is a traditional folk dance of the Bhil tribe performed to worship Goddess Sarasvati which was later embraced by other Rajasthani communities.
• Ghoomar became popular in the Indian state of Rajasthan during the reigns of Rajput kings and is typically performed by women during gatherings.
• Other Folk Dance from Rajasthan are:
• Chakri, Ganagor, Jhulan Leela, Jhuma, Suisini, Ghapal, and Kalbeliya.​

Additional Information

• List of the Folks Dances from the Different States:-

The correct answer is 7.

Key Points

• India Medal Tally Tokyo Olympics - 1 Gold, 2 Silver, 4 Bronze Medal. (Total-  7 Medal)
• India made a big comeback to beat Germany 5-4 and claim the bronze medal. It is their third Olympic bronze medal - after the 1968 and 1972 Games - and their 12th Olympic medal overall. It is India's fifth medal at Tokyo 2020.
• At Tokyo Olympics, India surpassed its previous best haul of six medals achieved in the 2012 London Games. Apart from Chopra's gold, India has won two silver and four bronze medals.

Additional Information

Tokyo Olympics 2020 India Medals List

The correct answer is Tahira Kashyap Khurrana.​

Key Points

• The 7 Sins of Being a Mother is a book by Tahira Kashyap Khurrana, an Indian writer, filmmaker, and wife of actor Ayushmann Khurrana.
• The book was published in October 2021 by Juggernaut Books.
• The book is a collection of essays in which Khurrana shares her experiences of motherhood, both the good and the bad.
• She writes about the joys of raising children, as well as the challenges and frustrations. She also talks about the guilt that many mothers feel, and how she has learned to overcome it.
• The book has been praised for its honesty and humor. Khurrana's writing is relatable and insightful, and she does not shy away from discussing the more difficult aspects of motherhood.

Additional Information

The correct answer is CTRL + M.

Key Points

• PowerPoint is a Microsoft software used to create presentations.
• CTRL + N is used to create a new presentation.
• CTRL + M is used to insert a new slide.
• CTRL + D is used to duplicate the slide.
• CTRL + K is used to insert a link.

Additional Information

• Other important MS PowerPoint shortcuts:

The correct answer is Japan.

Key Points

• It means that a law has been duly enacted by the competent body following the correct procedure. For example, the procedure mentioned in the constitution.
• The Doctrine of Procedure established by law has been taken from the Japanese Constitution.​

Additional Information

• The Indian constitution came into force on 26th January 1950.
• It was adopted by the Constituent Assembly on 26th November 1949.
• Some provisions of the Constitution pertaining to citizenship, elections, provisional parliament, and temporary and transitional provisions.
• And short title contained in Articles 5, 6, 7, 8, 9, 60, 324, 366, 367, 379, 380, 388, 391, 392 and 393 came into force on November 26, 1949,.
• The remaining provisions (the major part) of the Constitution came into force on January 26, 1950.
• This day is referred to in the Constitution as the date of its commencement and is celebrated as Republic Day.
• January 26 was specifically chosen as the date of commencement of the Constitution because of its historical importance.
• It was on this day in 1930 that Purna Swaraj day was celebrated, following the resolution of the Lahore Session (December 1929) of the INC.

Important Points

The other borrowed provisions from different countries and details of those are given in below:

The correct answer is Gateway.

Key Points

• A gateway serves as the entry and exit point of a network. It acts as a communication point or interface between different networks, allowing data to pass through it in order to use routing paths.
• Gateways are responsible for protocol translation, security enforcement, and network traffic management.
• They can connect networks that use different protocols, such as connecting a local area network (LAN) to the internet.

Additional Information 

• Network Interface: A gateway is equipped with multiple network interfaces to connect different networks. It can have connections to the internet, local area networks (LANs), wide area networks (WANs), or other networks.
• Protocol Translation: Gateways are responsible for translating protocols between different networks. They can convert data packets from one protocol to another, allowing communication between networks that use different standards or languages.
• Traffic Routing: When data enters a network, it must pass through the gateway. The gateway examines the packet's destination address and determines the best routing path for the data to reach its intended destination. It helps direct traffic efficiently within the network or between different networks.
• Network Address Translation (NAT): Gateways often perform Network Address Translation, which allows multiple devices on a LAN to share a single public IP address. It masks the private IP addresses of devices behind the gateway's public IP address, enhancing security and conserving IP addresses.

The Correct answer is: Parent rock

Key Points

• Parent Rock:
• This is the correct factor that determines the accumulation of soil.
• The parent rock provides the basic mineral composition of the soil.
• Its nature (hard, soft, coarse-grained, or fine-grained) influences the rate of weathering and the type of soil formed.
• Soils derived from granite are sandy, while basalt produces black cotton soil rich in clay.
• Fauna:
• Animals, insects, and microorganisms help in mixing organic matter and improving soil aeration.
• They aid in soil fertility but do not determine the accumulation of the soil itself.
• Flora:
• Plants add humus and organic matter to the soil.
• They enrich the soil but do not decide the fundamental accumulation of soil material.
• Relief:
• Relief (slope and altitude) influences drainage and erosion.
• It affects soil depth and moisture but is not the primary determinant of accumulation.

Additional Information

• Factors of Soil Formation:
• Parent rock – source of mineral matter.
• Climate – temperature and rainfall affect weathering and humus content.
• Organisms – flora and fauna add organic matter.
• Relief – slope and drainage determine soil depth and erosion.
• Time – longer duration allows mature soil profiles to develop.
• Example:
• Alluvial soils in India are deposited by rivers and depend on the parent rock material carried from the Himalayas.
• Black soil of the Deccan Plateau is derived from basaltic parent rock.

The correct answer is Assam.

Key Points

• Majuli is a large river island situated in the middle of the Brahmaputra River in Assam.
• Majuli is depicted as the largest river island in the world.
• This island has been formed over a period of time due to the change of direction and area of the Brahmaputra river and its tributaries especially the Lohit river.
• Majuli can also be called the 'cultural capital of Assam'.
• Majuli is located in the northern part of the Jorhat district and is separated from the mainland by the Brahmaputra river.

Additional Information 

• Brahmaputra River flows through Tibet, India and Bangladesh.
• The Brahmaputra rises in the north of the Himalayas near Lake Mansarovar in the Purang district of Tibet, where it is known as the Yarlung Tsangpo.
• Flowing in Tibet, this river enters the Indian state of Arunachal Pradesh.
• Flowing in the valley of Assam, it is called the Brahmaputra, and then it is called Jamuna as soon as it enters Bangladesh.​

The correct answer is Automatic Train Protection System.

Key Points

• Railway Minister Ashwini Vaishnaw has announced that the ‘Kavach’ System, the anti-collision test conducted by the Indian Railways to check the indigenous developed system to avoid rail accidents is successful.
• He held an on-site inspection near Secunderabad on 4 March 2022.

Additional Information

• The test involved two trains - one with the railway minister on board and the other with the Chairman of the Railway Board - hurtle towards each other at full speed.
• 'Kavach' automatically stopped the train before 380 metres of other Locomotive at the front.
• The indigenously developed Automatic Train Protection (ATP) system, Kavach, was designed to help the Railways achieve - zero accidents.
• The Kavach will be the world's cheapest automatic train collision protection system.
• The railway authorities informed that once implemented, it will cost 50 lakh rupees per kilometer to operate compared to about 2 crore rupees worldwide.

The correct answer is Only I.

Key Points

• Pampas
• Pampas grasslands are situated in Argentina.
• Found mostly in the interior of the continent.
• Temperature varies greatly in winter and summer.
• Rainfall can vary from 25-75cm
• It doesn't have much diversity in vegetation or animals.
• Mostly, horses are found here.
• steppes
• Grasslands (steppes) are temperate environments, with warm to hot summers and cool to very cold winters; temperatures are often extreme in these midcontinental areas.
• They are often located between temperate forests and deserts, and annual precipitation falls between the amounts characteristic of those zones.

Additional Information

• Temperate grasslands around the world-
• Pustaz - Hungary
• Prairies - North America
• Pampas - Argentina and Uruguay
• Veld - South Africa
• Downs - Australia
• Canterbury -  New Zealand
• Steppe - Russia

The correct answer is Satguru Ram Singh.

Key Points

• After the fall of the kingdom of Maharaja Ranjit Singh, there were several attempts to raise the old glory of the Khalsa.
• Several movements to reform the Sikhism were started.
• First, one being the Namdhari movement, which was started by Baba Ram Singh Namdhari after Anglo Sikh wars.
• He was a soldier in the Khalsa army.
• Like the Nirankari, this second reform movement known as the Namdhari, or Kuka, movement also had its origin in the north-west corner of the Sikh kingdom, away from the places of royal pomp and grandeur.
• It harked back to a way of life more in keeping with the spiritual tradition of the community.
• Its principal object was to spread the true spirit of Sikhism shorn of tawdry customs and mannerism, which had been growing on it since the beginning of the Sikh monarchy.

Additional Information

• In the midst of national pride born of military glory and political power, this movement extolled the religious obligation for pious and simple living.
• They were called "Kukas" because of their particular style to recite the Gurbani (Sayings of the Gurus).
• This style was in a high pitched voice, called Kook in Punjabi, and thus Namdhari Khalsa’s were named Kukas.
• In the post-1857 phase of the freedom struggle, the Namdhari movement occupies a very significant place in the annals of history.
• It was founded at a time when the socio-religious teachings of the great Gurus were slowly being shadowed by other considerations and the political life was at its lowest ebb.
• Namdhari movement was an offshoot of Sikhism.
• The Kuka Movement was launched on the Baisakhi day in April 1857 at Bhaini (sahib), in Ludhiana District of Punjab.
• The leader of the Namdhari movement Baba Ram Singh was inspired by Maharaj Singh’s struggle against aliens and worked for social reforms and gave a call for the political battle against the Britishers.

The correct answer is Distillation.

Key Points

• Distillation
• It Separates a mixture of two miscible liquids (Miscible liquids are one that together when mixed, form a homogenous mixture whose composition is the same throughout.)
• A liquid mixture's components are vaporized, condensed, and then separated here.
• As the mixture is heated, the volatile component vaporizes first.
• The vapour is deposited in a liquid state after passing through a condenser.
• EXAMPLE - separation of gasoline from crude oil, formation of freshwater from salt-water.

Additional Information

The correct answer is demand for a commodity and its price.

Key Points

• According to the law of demand
• ​​​​when the price of a commodity increase, its the quantity demanded decreases
• when the price of a commodity decreases, it’s the quantity demanded increases
• keeping other factors remains the same.
• The consumer’s demand for good must be inversely related to the price of the good.
• There is an inverse relationship between price and demand and due to this the demand curve always has a downward slope.
• Demand Curve is the relation between the quantity of the good chosen by a consumer and the price of the good.
• ​Assumptions for the Law of Demand
• ​​No change in the income of consumers
• No change is the taste and preference of the consumers
• No change in price related to other goods.

Given:

tanθ + cotθ = 8

Concept used:

cotθ = 1/tanθ

x² + 1/x²  = (x + 1/x)² - 2

Calculation:

tanθ + cotθ = 8

tanθ + 1/tanθ = 8

tan2θ + cot2θ 

We can write this as tan2θ + 1/tan²θ  using (cotθ = 1/tanθ)

By using the formula: x2 + 1/x2  = (x + 1/x)2 - 2

tan2θ + 1/tan2θ = (tanθ + 1/tanθ)² - 2

tan2θ + 1/tan2θ = (8)2 - 2

tan2θ + 1/tan2θ = 64 - 2

tan2θ + 1/tan2θ = 62

tan2θ + cot2θ = 62

∴ Option 4 is the correct answer.

Calculation:

Saving = Income - Expenditure.

Y1 Savings = 700 - 300 = 400

Y2 Savings = 500 -200 = 300

Y3 Savings = 400 - 300 = 100

Y4 Savings = 800 - 200 = 600

Y5 Savings = 300 - 150 = 150

Please note that the saving of Y3 is minimum.

∴ Option 2 is the correct answer.

Calculation:

Please note that at 1 pm the graph is at its highest point.

∴ Option 4 is the correct answer.

Given:

Loss on selling 18 pens = CP of 3 pens.

Concept used:

Loss = CP - SP

Calculation:

(C.P. of 18 pens) - (S.P. of 18 pens) = (C.P. of 3 pens)

⇒ CP of 15 pens = SP of 18 pens

⇒ CP (1 pen)/SP (1 pen) = 18/15 = 6/5

According to the question,

SP (1 pen) = 360/18 = 20

∴ CP of 1 pen = 6/5 × 20 = 24

∴ Option 3 is the correct answer.

Given:

Range of numbers: 23 to 43

Formula used:

A composite number is a number that has more than two factors

Solution:

The prime numbers between 23 and 43 are 23, 29, 31, 37, 41, and 43. Therefore, the composite numbers between 23 and 43 are 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, and 42

There are a total of 15 composite numbers between 23 and 43.

Given:

The angle subtended by a chord on the major arc of a circle is 65 degrees.

Concept used:

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Calculation:

Let O, R, and PQ be the centre, a point on the major arc, and the aforementioned chord respectively.

So, the major arc for the PQ chord is PRQ.

Hence, ∠PRQ = 65°

Here, ∠POQ is the angle subtended by the same chord, PQ on the centre of the circle.

According to the concept,

∠POQ = 2 × ∠PRQ

⇒ ∠POQ = 2 × 65°

⇒ ∠POQ = 130°

∴ The angle subtended by the same chord on the centre of the circle is 130°.

Shortcut Trick

In a right-angled triangle, the cotangent of an angle is the ratio of the adjacent side to the opposite side.

For ∠P, the side adjacent is PQ and the side opposite is QR.

Directly substitute the given values: cot P = PQ ÷ QR.

⇒ cot P = 9/11.

∴ The correct answer is (9)/(11).

Alternate Method

Given:

ΔPQR is a right-angled triangle where ∠Q = 90°.

The length of side PQ = 9 cm and the length of side QR = 11 cm.

Formula Used:

In a right triangle, for any acute angle θ:

cot θ = Adjacent Side / Opposite Side

Calculations:

⇒ For the angle at vertex P:

⇒ Adjacent side (Base for ∠P) = PQ = 9 cm

⇒ Opposite side (Perpendicular for ∠P) = QR = 11 cm

⇒ cot P = PQ / QR

⇒ cot P = 9/11

∴ The correct answer is (9)/(11).

Additional Information

Reciprocal Trigonometric Identities

The cotangent function is the reciprocal of the tangent function: cot θ = 1 / tan θ.

Complementary Angle Property

In a right-angled triangle, if ∠P + ∠R = 90°, then cot P = tan R and tan P = cot R.

Pythagoras Theorem

To find the hypotenuse PR, use PR = √(PQ² + QR²). Here, PR = √(9² + 11²) = √(81 + 121) = √202 cm.

Basic Ratios for ∠P

sin P = QR/PR, cos P = PQ/PR, and tan P = QR/PQ.

Given:

Distance between points P and Q: 130 km

Train stops for 30 minutes

Formula:

Speed = Distance/Time

Calculation:

Let's denote the speed of the car as '10x'.

The speed of the train is 30% more than the speed of the car, which can be expressed as 13x 

Now, let's calculate the time taken by the car and the train to travel from point P to Q.

Time is taken by the car: Distance/Speed of the car

Time taken by the train: Distance / Speed of the train + Time spent at the station

The time taken by the car and the train is the same, as mentioned in the question.

Therefore, we can write the equation:

130/10x = 130/(13x) + (30 minutes/60 minutes) [Converting 30 minutes to hours]

To simplify the equation, let's solve it step by step.

130/10x = 130/(13x)  + 1/2

13/x - 10/x = 1/2

x = 6

Speed of the train = 13 × 6 km/h = 78 km/h.

Hence, the speed of the train is 78 km/h.

Calculation:

Total sales of C2 for two years:

79 + 91 = 170

Total sales of C4 for two years:

66 + 86 = 152

The ratio will be:

170 : 152

85 : 76

∴ Option 4 is the correct answer.

Given:

a3 = b3 + 988

a - b = 4

Formula used:

a^3 - b^3 = (a - b)(a2 + ab + b2)

Solution:

From the equation a3 = b3 + 988, we can write

a3 - b3 = 988

(a - b)(a² + ab + b²) = 988

4(a2 + ab + b2) = 988

a2 + ab + b2 = 247

We can now substitute the value of a2 + ab + b2 into the equation 2a2 + 2ab + 2b2.

2(a2 + ab + b2 ) = 2(247)

 2a2 + 2ab + 2b2 = 494

Therefore, the value of  2a2 + 2ab + 2b2 is 494.

Given:

The radius of the incircle of an equilateral triangle = 9√3 cm

Concept Used:

In an equilateral triangle, the radius of the incircle is related to the side length (s) by the formula:

The radius of incircle = side / 2√3

Calculation:

Radius of incircle = side / 2√3

⇒ 9√3 = side / 2√3

⇒ side = 9√3 × 2√3 = 18 × 3 = 54 cm

So, Perimeter of an equilateral triangle = 3 × side = 3 × 54 = 162 cm

∴ The correct answer is option (2).

Shortcut Trick

Put A = 45° in the expression (sec A − tan A + 1)(sec A − tan A − 1).

⇒ (√2 − 1 + 1)(√2 − 1 − 1) = √2(√2 − 2) = 2 − 2√2

Checking Option 2 by substituting A = 45°:

⇒ 2 tan 45° (tan 45° − sec 45°) = 2 × 1 × (1 − √2) = 2 − 2√2

∴ The correct answer is 2 tan A (tan A − sec A).

Alternate Method

Given:

Expression: (sec A − tan A + 1)(sec A − tan A − 1)

Formula Used:

⇒ (a + b)(a − b) = a² − b²

⇒ sec² θ − 1 = tan² θ

Calculations:

⇒ Let a = (sec A − tan A)

⇒ The given expression is of the form (a + 1)(a − 1).

⇒ (a + 1)(a − 1) = a² − 1

⇒ Substituting the value of a: (sec A − tan A)² − 1

⇒ Expanding the square: sec² A + tan² A − 2 sec A tan A − 1

⇒ Rearranging terms: (sec² A − 1) + tan² A − 2 sec A tan A

⇒ Substituting (sec² A − 1) = tan² A

⇒ tan² A + tan² A − 2 sec A tan A

⇒ 2 tan² A − 2 sec A tan A

⇒ Taking 2 tan A common: 2 tan A (tan A − sec A)

∴ The correct answer is 2 tan A (tan A − sec A).

Additional Information

Trigonometric Identities

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

Difference of Squares

The algebraic identity (x + y)(x − y) = x² − y² helps in expanding product expressions quickly and efficiently.

Given :

5x + y = 17 and xy = 6

Formula used :

a3 + b3 = (a+b) (a2 + b2 - ab)

Calculation :

According to the question:

⇒ 5x + y = 17

Cubing both sides of the equation:

⇒ (5x + y)3 = (17)3

⇒ 125x3 + y3 + 3 × 5x × y × (5x + y) = 4913

⇒ 125x3 + y3 + 15xy × (17) = 4913

⇒ 125x3 + y3 + 90 × (17) = 4913

⇒ 125x3 + y3  = 4913 - 1530

⇒ 125x3 + y3  = 3383

∴ The answer is 3383.

Shortcut Trick

Apply MDH rule: Since the work is equal (half each), M₁D₁ = M₂D₂.

10 women × 20 days = M₂ women × 10 days

M₂ = 200 ÷ 10 = 20 women

Additional women = 20 − 10 = 10 women.

∴ The correct answer is 10 women.

Alternate Method

Given: Initial women (M₁) = 10, Days (D₁) = 20, Work (W₁) = 1/2. Remaining Work (W₂) = 1/2, Target Days (D₂) = 10.

Formula Used: (M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

⇒ (10 × 20) / (1/2) = (M₂ × 10) / (1/2)

⇒ 200 = 10 × M₂

⇒ M₂ = 200 ÷ 10 = 20 women

⇒ Additional women required = Total women required − Initial women

⇒ Additional women = 20 − 10 = 10

∴ The correct answer is 10 women.

Additional Information

General MDH Formula

The relation between Men (M), Days (D), Hours (H) and Work (W) is given by (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂.

Inverse Proportionality

For a constant amount of work, the number of people is inversely proportional to the time taken (M ∝ 1/D). If days are halved, the number of people must be doubled.

Work Efficiency

Total Work = Number of People × Time × Efficiency. If efficiency changes, it is multiplied in the numerator of the MDH formula.

Given:

 ∠POQ = 130 degree

Concept used:

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Calculation:

Let O, R, and PQ be the centre, a point on the major arc, and the aforementioned chord respectively.

So, the major arc for the PQ chord is PRQ.

Hence,  ∠POQ = 130 degree

Here, ∠POQ is the angle subtended by the same chord, PQ on the centre of the circle.

According to the concept,

∠POQ = 2 × ∠PRQ

⇒ 130° = 2 ×∠PRQ

⇒ ∠POQ = 65°

∴ The angle subtended by the same chord in the major segment of the circle is 65°.

Formula used:

Average = Sum of all the term/Number of term

Calculation:

6/5 = 1.2 (largest fraction)

11/15 = 0.73

4/7 = 0.57

5/13, the Denominator is more than twice the Numerator and is equal to 0.38, therefore this is the smallest fraction

So, The Largest and the Smallest Fraction is 6/5 + 5/13 = 103/65

∴ Option 3 is the correct answer

Shortcut Trick

Difference in percentage = 50% − 20% = 30%

Difference in marks = 25 (failed) + 20 (extra) = 45 marks

Since 30% corresponds to 45 marks, 1% = 45 ÷ 30 = 1.5 marks

Passing marks = 20% of total marks + 25 = (20 × 1.5) + 25 = 30 + 25 = 55

∴ The correct answer is 55.

Alternate Method

Given:

Rajiv's score 1 = 20%, Failure margin = 25 marks

Rajiv's score 2 = 50%, Surplus margin = 20 marks

Formula Used:

Passing Marks = (Percentage × Total Marks) ± Margin

Calculations:

⇒ Let the Total Marks be x.

⇒ 20% of x + 25 = 50% of x − 20

⇒ 50% of x − 20% of x = 25 + 20

⇒ 30% of x = 45

⇒ 0.30x = 45

⇒ x = 45 ÷ 0.30 = 150

⇒ Passing Marks = (20% of 150) + 25

⇒ Passing Marks = 30 + 25 = 55

∴ The correct answer is 55.

Additional Information

Maximum Marks

The 100% value represent the total marks of the examination, calculated as Total = (Mark Difference ÷ Percentage Difference) × 100.

Passing Percentage

It is the minimum percentage required to pass: Pass % = (Passing Marks ÷ Total Marks) × 100.

Percentage Base Change

When comparing two states of the same base (Total Marks), the numerical difference in marks is directly proportional to the difference in their percentage values.

Given:

The radius of the hemisphere: r

Radius of the sphere: 3r

Formula:

Volume of a hemisphere = (2/3)πr³

Volume of a sphere = (4/3)π(radius)³

Calculation:

Let's calculate the respective volumes of the hemisphere and the sphere.

Volume of the hemisphere = (2/3)πr3

Volume of the sphere = (4/3)π(3r)³

Simplifying the expressions:

Volume of the hemisphere = (2/3)πr3

Volume of the sphere = (4/3)π27r³

Now, let's calculate the ratio of the volumes.

The ratio of volumes = (Volume of the sphere) / (Volume of the hemisphere)

= [(4/3)π27r3]/[(2/3)πr3]

= 54

Therefore, the respective ratio of the volumes of the sphere and the hemisphere is 54:1.

Given:

P invested Rs. 4000 for one year.

Q joined him with an investment of Rs. 6000 after a few months.

At the end of one year, the ratio of profits of P and Q is 4 : 3.

Formula used:

Profit = (Investment × Time)

Solution:

Let x be the number of months after which Q joined.

The profit of P is 4x.

The profit of Q is 3x

(12*4000)/(12-x)*6000 = (4/3)

6 = 12 - x

x = 6

Therefore, Q joined after 6 months.

Given:

Principal amount lent to B = Rs. 12,000

Time period for B = 3 years

Principal amount lent to C = Rs. 10,000

Time period for C = 4 years

Total interest received = Rs. 6,080

Formula used:

Simple interest = (Principal amount × Time period × Rate of interest)/100

Solution:

The total interest received is the sum of the interest received from B and the interest received from C.

Interest received from B = (12,000 × 3 × R)/100

Interest received from C = (10,000 × 4 × R)/100

6,080 = (12,000 × 3 × R)/100 + (10,000 × 4 × R)/100

6,080 = 360R + 400R

6,080 = 760R

R = 6,080 / 760

R = 8%

Therefore, the annual rate of interest is 8%.

Formula used:

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

Calculation

By using the formula (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

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

∴ Option 4 is the correct answer.

Calculation:

J1 = The value of the average number of calculators sold by L in all the months.

(350 + 340 + 320 + 315 + 305)/5 = 326

J2 = The difference between the total number of calculators sold by L and M.

Total number of calculators sold by L = 350 + 340 + 320 + 315 + 305 = 1630

Total number of calculators sold by M = 305 + 310 + 360 + 330 + 325 = 1630

J2 = 1630 - 1630 = 0

so, J2/J1 = 0/326 = 0

∴ Option 3 is the correct answer.

Given:

The listed price of the cycle = Rs. 20,000

Selling price to the retailer = Rs. 14,000

Formula:

Percent discount = (Discount / Listed price) * 100

Calculation:

To calculate the percent discount, we need to find the discount first.

Discount = Listed price - Selling price

Substituting the given values:

Discount = Rs. 20,000 - Rs. 14,000

= Rs. 6,000

Now, we can calculate the percent discount:

Percent discount = (Discount / Listed price) * 100

= (6000 / 20000) * 100

= 30

Therefore, the percent discount given to the retailer is 30%.

Given:

Number of students = 132

Average marks of all students = 50

Average marks of passed students = 55

Average marks of failed students = 35

Formula:

Average marks = Total marks / Number of students

Solution:

By using the allegation method.

So the ratio is 15 : 5 or 3 : 1

The total marks of passed students = 3 × 55

The total marks of failed students =  35 × 1

The ratio is 

3 × 55 : 35 × 1

33 : 7

Therefore, the respective ratio of the total marks of passed students and the total marks of failed students is 33 : 7

Shortcut Trick

When two circles of equal radius (r) intersect such that each passes through the centre of the other, the distance between their centres is equal to the radius (d = r).

Length of the Common Chord = √3 × r

Given r = 20 cm

Length of common chord = 20 × √3 = 20√3 cm.

∴ The correct answer is 20√3 cm.

Alternate Method

Given:

Radius of both circles (r) = 20 cm

Distance between centres (O₁O₂) = 20 cm

Let O₁ and O₂ be the centres and AB be the common chord. Let M be the intersection of O₁O₂ and AB.

⇒ O₁O₂ = 20 cm

⇒ O₁M = M O₂ = 20 ÷ 2 = 10 cm (Line joining centres bisects the common chord at right angles)

⇒ In right-angled triangle ΔAMO₁:

⇒ AM² + O₁M² = O₁A²

⇒ AM² + 10² = 20²

⇒ AM² = 400 − 100 = 300

⇒ AM = √300 = 10√3 cm

⇒ Length of common chord AB = 2 × AM

⇒ AB = 2 × 10√3 = 20√3 cm

∴ The correct answer is 20√3 cm.

Additional Information

Common Chord Formula

Length of common chord L = 2√(r² − (d/2)²), where r is the radius and d is the distance between centres.

Angle in Semicircle

The angle subtended by a diameter at any point on the circumference of the circle is always 90°.

Perpendicular from Centre

The perpendicular from the centre of a circle to a chord bisects the chord.

The correct answer is 'Option 3' i.e. 'Eat'.

Key Points

• The word "famish" means to suffer from extreme hunger, to starve, or to be deprived of food.( भूखा होना)
• Eat means to consume food by chewing and swallowing it, satisfying one's hunger or appetite.(खाना)

Therefore, the correct answer is: 'Eat'.

Additional Information

• Meanings of the other given words:
• Abstain means to refrain or hold oneself back from doing something, usually from indulging in a particular behavior, such as eating, drinking, or participating in certain activities.(त्याग करना)
• Refrain: To refrain means to hold back or restrain oneself from doing something, often voluntarily or out of self-discipline.(सावधानी बरतना)
• Starve: Starve means to suffer from extreme hunger, to be deprived of food or nourishment for an extended period, leading to malnutrition or starvation.(भूखमरी करना)

The correct answer is 'Option 4' i.e. 'SPQR'.

Key Points

• S. were updated in 2012, and the new rule explicitly
• P. recognizes the growing risks to national
• Q. forests from climate change as well as expands
• R. opportunities for public input and engagement
• The rearranged sentence would be: Forest planning rules were updated in 2012, and the new rule explicitly recognizes the growing risks to national forests from climate change as well as expands opportunities for public input and engagement.

Therefore, the correct answer is: 'SPQR'

The correct answer is 'Option 1' i.e. 'Cateogry'.

Key Points

• The incorrectly spelled word is 'Cateogry'.
• The correct spelling is "Category."
• Category means a class or division of things that share common characteristics.(श्रेणी)

​Therefore, the correct answer is: 'Cateogry'. 

Additional InformationHindi and English meanings of the options:

Heap: A pile or collection of things (ढेर) 

Circle: A round or curved shape (वृत्त ) ,or a group of people or things with a shared interest or purpose.

Greed: An intense desire for wealth, possessions, or power(लोभ)

The correct answer is 'Option 2'.

Key Points

• To convert it into indirect speech, we need to make the necessary changes:
• Change the pronoun "you" to the appropriate pronoun based on the context.
• Since the professor said the statement, we can assume that the person being addressed is the person reporting the statement.
• Therefore, "you" changes to "I" in the indirect form.
• Change the verb form from "must" to a verb form that reflects indirect speech. In this case, "must" changes to "had to" in the indirect form.
• Add the conjunction "that" to introduce the reported statement.

Therefore, the correct sentence is: The professor said that I had to learn those words regularly.

The correct answer is 'Option 2'.

Key Points

• To transform an active sentence into the passive voice, the object of the active sentence becomes the subject in the passive form, and the verb is changed accordingly.
• In the given sentence, the object is "that lady," and the verb is "loved."
• To convert it into the passive voice, we change the verb to its past participle form ("loved") and introduce the subject ("that lady") as the receiver of the action.
• "That lady was loved by the president" accurately transforms the sentence into the passive voice.
• It maintains the past tense and correctly places the lady as the subject.

Therefore, the correct sentence is: 'That lady was loved by the president'.

The correct answer is 'Enmity'.

Key Points

• Enmity refers to a deep-seated hatred, hostility, or animosity between individuals or groups
• "hostility" refers to a state of antagonism, animosity, or opposition towards someone or something
• Therefore, the word that means the same as "hostility" is "enmity"

Therefore, the correct answer is: 'Enmity'

Additional Information

• Let's see the meaning of other given words.
• Authorize: To authorize means to give official permission or approval for something.(अधिकृत)
• Anchor: An anchor is a heavy object dropped by a vessel to hold it in place or a person who presents or hosts a television or radio program.(लंगर)
• Organize: To organize means to arrange or plan things systematically or in a structured manner.(आयोजित करना)

The correct answer is 'Option 1' i.e. 'Vandal'.

Key Points

• A "saboteur" is a person who engages in sabotage, which involves deliberate acts aimed at disrupting or damaging a system, organization, or plan.(विध्वंसक)
• "vandal" refers to a person who deliberately destroys, damages, or defaces public or private property.(उपद्रवी )
• So, the meaning of 'Vandal' is same as 'Saboteur'.

Therefore, the correct answer is: 'Vandal'.

Additional Information 

• Let's see the meaning of other given options.
• Associate: An associate is a person who is connected with another or involved in a group or organization. (सहयोगी)
• Mendicant: A mendicant is a beggar or someone who relies on alms or donations for their livelihood. (भिक्षुक)
• Sage: A sage refers to a wise and knowledgeable person, often associated with wisdom and deep understanding.(मुनि)

The correct answer is 'Motivational quotes will not help you.'

Key Points

• Motivational qoutes will not help you.
• The error in this option is the misspelling of the word "quotes" as "qoutes."
• Motivational quotes will not helpp you.
• The error in this option is the repetition of the letter "p" in the word "helpp." It should be spelled as "help."
• Motivatinal quotes will not help you.
• The error in this option is the misspelling of the word "Motivational" as "Motivatinal." The correct spelling should have an "i" after the "t."

Therefore, option 2) "Motivational quotes will not help you" is the correct sentence as it does not contain any spelling errors.

The correct answer is 'Option 1' i.e. 'illegible'.

Key Points

• The word "illegible" means difficult or impossible to read due to poor handwriting, faintness, or other factors that make the text unclear or indiscernible.(अस्पष्ट)
• Incapable of being read (पठनीय न होने योग्य)
• So, the correct word that can substitute the given group of words is 'illegible'.

Therefore, the correct answer is: 'Illegible'.

Additional Information

• Let's see the meaning of all other given words.
• Comprehensive: Comprehensive refers to something that is thorough, extensive, or inclusive, covering a wide range or including all aspects or details of a particular subject.(व्यापक)
• Decipherable: Decipherable means capable of being understood or interpreted, typically referring to the ability to decode or make sense of something that is difficult to comprehend.(समझने योग्य)
• Corrupt: Corrupt means morally or ethically dishonest, or having been altered or damaged in a way that affects its integrity or reliability.(भ्रष्ट)

The correct answer is 'Option 3' i.e. 'Holding'.

Key Points

• In the given sentence, the phrase "while holding" indicates that the subject (the speaker) is trying to retrieve the note from their pocket while simultaneously keeping the tray steady on their palm.
• So, option 3) "holding" is the correct answer as it accurately describes the physical action required in the sentence.

Therefore, the correct sentence is: 'I try to retrieve the note from my pocket while holding the tray steady on my palm'.

Additional Information

• Meanings of the other given options:
• Noting: "noting" refers to the act of observing or taking note of something, but it does not fit the context of the sentence.(ध्यान देना)
• Scolding: "scolding" means reprimanding or criticizing someone in a harsh or angry manner.(डांटना)
• Plotting: "plotting" refers to planning or scheming. (षड्यंत्र रचना)

The correct answer is 'Option 3' i.e. 'Ignorant'.

 Key Points

• The word "oblivious" means to be unaware or lacking knowledge or consciousness about something.
• It suggests a state of being oblivious or inattentive to one's surroundings or to important information.
• "Ignorant" means lacking knowledge or awareness about something, similar to "oblivious."
• It implies a lack of understanding or familiarity.
• So, according to explanation the word 'Oblivious' is same as 'Ignorant'.

Therefore, the correct answer is: 'Ignorant'.

Additional Information

• Let's see the meaning of all other options
• Suspecting: "Suspecting" means having doubts or being suspicious about something or someone.( संदेह करना)
• Aware: "Aware" means having knowledge or consciousness about something, being informed or conscious of one's surroundings.(जागरूक)
• Careful: "Careful" means taking precautions or being cautious, being attentive and aware of potential dangers or consequences.(सतर्क) 
  

The correct answer is 'Option 3' i.e. 'The five first girls'.

Key Points

• The error is in option 3) "The five first girls."
• The correct phrase should be "The first five girls."
• In English, when describing a specific group of people or objects in a particular order, the ordinal numbers (such as "first," "second," "third") typically come before the cardinal numbers (such as "five," "ten," "twenty").
• Therefore, the correct order is "first five" instead of "five first."

Therefore, the correct sentence is: "The first five girls will get the discount on our merchandise."

The correct answer is 'Option 3' i.e. 'To sleep soundly'.

Key Points

• The correct alternative that best expresses the meaning of the idiom "To sleep like a dog" is option 3) To sleep soundly.(गहरी नींद सोना)
• To be insomniac: This option means to have difficulty sleeping or to suffer from insomnia.(अनिद्रा होना)
• To make noise while sleeping: This option suggests that the person is making noise while sleeping,(सोते समय आवाज़ करना)
• To be less mindful: This option implies being less aware or attentive(कम सतर्क होना)

Therefore, the correct answer is: 'To sleep soundly'.

The correct answer is 'Option 2' i.e. 'Fugitive'.

Key Points

• The most appropriate one-word substitution for the given group of words "A person who has escaped from captivity or is in hiding" is option 2) Fugitive. (भगोड़ा)
• Farce: Farce refers to a humorous or absurd situation, often depicted in a play or performance.(तमाशा)
• Fastidious: Fastidious means being very attentive to detail or excessively concerned about cleanliness or accuracy.(अत्यंत सावधान)
• Fanatic: A fanatic is a person who is extremely enthusiastic or devoted to a particular cause or belief, often to an excessive or irrational degree.(प्रफुल्ल)

Therefore, the correct answer is: 'Fugitive'.

The correct answer is 'Option 4' i.e. 'Fully armed, having many weapons'.

Key Points

• The alternative that best expresses the meaning of the idiom "Armed to the teeth" is option 4) Fully armed, having many weapons.(पूरी तरह सशस्त्र धारी होना, कई हथियारों से लैस होना)
• Explanation of other options:
• Safeguard oneself in every possible way: हर संभव तरीके से अपनी सुरक्षा करना
• To have no weapon to fight: कोई हथियार नहीं होना
• Different attacking techniques: विभिन्न हमला करने की तकनीकें

Therefore, the correct answer is: 'Fully armed, having many weapons'.

The correct answer is 'Option 2' i.e. 'Smart phone age has lead'.

Key Points

• The part of the given sentence that has an error is**: 2) Smart phone age has lead**
• The correct form of the verb in this sentence should be "has led" instead of "has lead."
• The verb "lead" is an irregular verb, and its past participle form is "led" (pronounced like "leed").
• Therefore, in the present perfect tense, we use "has led" as the correct form.

Therefore, the correct sentence is: 'Smart phone age has led'.