The pattern followed here is:

1. Middle arrow is rotated 45º in clockwise direction in every next figure.

2. Left bottom corner triangle is shifted towards right bottom corner of the next figure and rotated 90º degree in clockwise direction and turn into shaded portion, so on in the next figure.

3. Side half arrow is shifted one place to adjacent in the anti clockwise direction in every next figure.

Hence, the correct answer is "Option 1".

The correct order as per the dictionary is,

3) Moral

5) Morale

4) Morbid

2) More

1) Morning

Here, we can see that the word at the fourth position is More.

Hence, the correct answer is "More".

The logic followed here is:

Logic: 

Step 1: Positional value of the odd letter.

Step 2: Opposite positional value of even letter.

'INTERNAL' is coded as ' 91320221813115'

And,

'MOUNTAIN' is coded as '131221132026913'

Similarly,

'PAYMENTS' is coded as '?'

Hence, the correct answer is "16262514513208".

After interchanging × and -, the equations we get:

l. 11 + 6 - 8 × 8 ÷ 2 = 15

→ 11 + 6 - 8 × 4 = 15

→ 11 + 6 - 32 = 15

→ 17 - 32 = 15

→ - 15 ≠ 15

→ LHS ≠ RHS

II. 15 × 4 - 3 + 6 ÷ 1 = 63

→ 15 × 4 - 3 + 6 = 63

→ 60 - 3 + 6 = 63

→ 66 - 3 = 63

→ 63 = 63

→ LHS = RHS 

→ Here, we can see that only equation II is correct.

Hence, the correct answer is "Only II".

The logic followed here is:

Logic: Addition of +3 in first and second letter.

1. RTW

2) PSV

3) ADG

4) ILO

Clearly, RTW is different from others.

Hence, the correct answer is "RTW".

The logic followed here is:

Logic: The second word is an animal, and the first word is its shelter.

Den ∶ Lion

→ Lion lives in the Den.

Similarly,

Web ∶?

→ Spider lives in the web.

Hence, the correct answer is "Spider".

The pattern followed here is:

Logic: (Second number - First number) × 2 = Third number.

Given:

(286, 456, 340)

⇒ (456 - 286) × 2

⇒ 170 × 2 = 340

And,

(347, 592, 490)

⇒ (592 - 347) × 2

⇒ 245 × 2 = 490

Let's check each option one by one.

1) (456, 666, 400)

⇒ (666 - 456) × 2

⇒ 210 × 2 = 420 ≠ 400. (Incorrect)

2) (782, 907, 230)

⇒ (907 - 782) × 2

⇒ 125 × 2 = 250 ≠ 230. (Incorrect)

3) (198, 279, 162)

⇒ (279 - 198) × 2

⇒ 81 × 2 = 162 = 162. (Correct)

4) (324, 419, 210)

⇒ (419 - 324) × 2

⇒ 95 × 2 = 190 ≠ 210. (Incorrect)

Hence, the correct answer is "(198, 279, 162)".

The pattern followed here is:

Given:

Here, B is common in both the dice and rotated clockwise direction from the common face.

Opposite faces are:

⇒ C ⇔ E

⇒ A ⇔ D

Clearly, E is the opposite alphabet of C.

Hence, the correct answer is "E".

The number of cubes is as follow.

Cubes in first row = 6

Cubes in second row = 3

Cubes in third row = 1

⇒ 6 + 3 + 1 = 10

Hence, the correct answer is "10".

The pattern followed here is:

Given:

From dice number (1) and (2).

Here, @ is common in both the dice and rotated in clockwise direction from the common face.

Opposite faces:

⇒ # ⇔ 9

⇒ 8 ⇔ 7

Clearly, # is the opposite of 9.

Hence, the correct answer is "#".

The pattern followed here is:

Given:

Opposite face:

⇒ H ⇔ S

⇒ P ⇔ T

⇒ O ⇔ N

Clearly, S is opposite to H.

Hence, the correct answer is "S".

The logic followed here is:

Logic: The first word is a type of the second word. 

Scooter ∶ Vehicle

→ Scooter is a type of Vehicle.

Similarly,

Pencil ∶?

→ Pencil is a type of stationery.

Hence, the correct answer is "Stationery".

The least possible Venn diagram is given below according to the given information.

Conclusion:

I. No green is blue → Follow → (As no blue is green. So, No green is blue is definitely followed)

II. Some green are jungle → Follow ​→ (As some jungle are green. So, some green are jungle is definitely followed)

III. No jungle is blue → Does not follow  → (As some jungle are green and no blue is green. So no jungle is blue is not definitely followed)

So, Both conclusions I and II follows.

Hence, the correct answer is "Option 4".

The pattern followed here is: 

Logic: Addition of +249 in each number.

Given:

(413, 662, 911)

⇒ 413 + 249 = 662

⇒ 662 + 249 = 911

And,

(387, 636, 885)

⇒ 387 + 249 = 636

⇒ 636 + 249 = 885

Let's check each option one by one.

1) (287, 536, 785)

⇒ 287 + 249 = 536

⇒ 536 + 249 = 785. (Correct)

2) (403, 652, 907)

⇒ 403 + 249 = 652

⇒ 652 + 249 = 901 ≠ 907. (Incorrect)

3) (521, 770, 1009)

⇒ 521 + 249 = 770

⇒ 770 + 249 = 1019 ≠ 1009. (Incorrect)

4) (311, 560, 799)

⇒ 311 + 249 = 560

⇒ 560 + 249 = 809 ≠ 799. (Incorrect)

Hence, the correct answer is "(287, 536, 785)".

The pattern followed here is:

Given: H is the brother of I. G is the brother of H. I is the son of J. J is the sister of K.

Clearly, J is the mother of G.

Hence, the correct answer is "Mother".

When the paper is unfolded, the image we get is shown below:

Hence, the correct answer is "Option 3".

The correct venn diagram representing the relationship between Engineers, Lawyers and married people is:

Hence, the correct answer is "Option 3".

Hence, the correct answer is "AJX".

The pattern followed here is:

Logic: Each number is multiply by 3.

Given:

(17, 51, 153)

⇒ 17 × 3 = 51

⇒ 51 × 3 = 153

And,

(32, 96, 288)

⇒ 32 × 3 = 96

⇒ 96 × 3 = 288

Let's check each option one by one.

1. (73, 229, 657)

⇒ 73 × 3 = 219 ≠ 229

⇒ 229 × 3 = 687 ≠ 657. (Incorrect)

2. (81, 343, 729)

⇒ 81 × 3 = 243 ≠ 343

⇒ 343 × 3 = 1029 ≠ 729. (Incorrect)

3. (14, 48, 154)

⇒ 14 × 3 = 42 ≠ 48

⇒ 48 × 3 = 144 ≠ 154. (Incorrect)

4. (42, 126, 378)

⇒ 42 × 3 = 126

⇒ 126 × 3 = 387 (Correct)

Hence, the correct answer is "(42, 126, 378)".

The pattern followed here is.

Logic: Here 'A' is replace with '×'

Given:

1. 8 A 7

⇒ 8 × 7 = 56

And,

2. 9 A 11

⇒ 9 × 11 = 99

Similarly,

3. 16 A 15

⇒ 16 × 15 = 240

Hence, the correct answer is "240".

The logic followed here is:

Logic: 2 has been added in the letter's positional value to get the diagonally opposite terms.

DECENT: VPGEGF

ENERGY:?

Hence, the correct answer is "AITGPG".

The logic followed here is:

Logic: The second word is a sport, and the first word is the place where the sport is played.

Ring ∶ Boxing

→ Boxing is played in the Ring.

Rink ∶?

→ Skating is played in the Rink.

Hence, the correct answer is "Skating".

The logic followed here is:

Logic: The first word represents the field of study, and the second word represents the field.

Let's check each option as per the logic,

1) Physiology - Body

→ Physiology is the study of the functions of the body.

2) Pedology - Fishes

→ Pedology is the study of soils, not fishes. ⇒ Doesn't follow the logic.

3) Entomology - Insects

→ Entomology is the study of insects.

4) Selenography - Moon

→ Selenography is the study of the surface and physical features of the moon.

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

Hence, the correct answer is "Pedology - Fishes".

The logic followed here is:

Logic: Consecutive numbers starting from 2 has been added to the terms to get the next term of the series.

Hence, the correct answer is "22".

The pattern followed here is:

Logic: (First number × 16) = Second number.

1. 8 : 128

⇒ 8 × 16 = 128

And,

2. 16 : 256

⇒ 16 × 16 = 256

Similarly,

3. ? : 176

⇒ 176 ÷ 16 = 11

Hence, the correct answer is "11".

The correct answer is 943 females per 1000 males.

Key Points

• Sex Ratio:
• In the Population Census of 2011, it was revealed that the population ratio in India in 2011 is 943 females per 1000 males.
• The sex ratio is used to describe the number of females per 1000 males.
• Sex ratio is a valuable source for finding the population of women in India and what is the ratio of women to that of men in India.
• The Sex Ratio 2011 shows an upward trend from the census 2001 data.
• Census 2001 revealed that there were 933 females to that of 1000 males.
• For decades India has seen a decrease in the sex ratio, but since the last two decades, there has been a slight increase in the sex ratio.
• Over the last five decades, the sex ratio has been moving from around 930 females to that of 1000 males.

Additional Information

• Sex Ratio of Different Indian States:
• Kerala - 1084
• Puducherry - 1037
• Tamil Nadu - 996
• Andhra Pradesh - 993
• Chhattisgarh - 991
• Andaman and Nicobar Island - 876
• Delhi - 868
• Chandigarh - 818
• Dadra and Nagar Haveli - 774
• Daman and Diu - 618

The correct answer is Loo.

Key Points

• Permanent winds are those that persist throughout the year and are associated with the Earth's atmospheric circulation system.
• They help to distribute heat, moisture, and air masses across the planet, playing a crucial role in shaping global climate patterns.

​Loo

• Loo is not type of permanent wind.
• It is a strong, dry and hot afternoon wind from the west in the summer, blowing over the western Indo-Gangetic Plain region of North India and Pakistan.
• It is particularly strong in the months of May and June.
• Exposure to it also leads to lethal heat strokes because of its extremely high temperatures (45 °C–50 °C or 115 °F-120 °F).
• The technical words that signify the direction in which the wind is blowing are 'Windward' and 'leeward.'
• The direction upwind from the point of reference is windward.
• Loo has extended its reach and has now gripped more parts of Rajasthan, Gujarat, Maharashtra and even West Madhya Pradesh. Moreover, some parts of this region are also reeling under heat wave conditions.

Additional Information The example of permanent wind are Trade winds, Westerlies and Easterlies.

• Trade winds: These are consistent, prevailing winds that blow from the northeast in the Northern Hemisphere and the southeast in the Southern Hemisphere, found between approximately 30° latitude and the equator in both hemispheres.
• Westerlies: These winds blow from the southwest in the Northern Hemisphere and the northwest in the Southern Hemisphere, generally found between latitudes 30° and 60° in both hemispheres.
• Easterlies: Also known as polar easterlies, these winds blow from the east near the Earth's poles and are formed as cold air masses move away from the poles towards the lower latitudes..

The correct answer is Fourth Generation.

Key Points

• The GUI was first developed at Xerox PARC by Alan Kay, Douglas Engelbart, and a group of other researchers in 1981. Later, Apple introduced the Lisa computer with a GUI on January 19, 1983.
• Graphical User Interface (GUI) was developed during the Fourth Generation of computers.
• These graphical elements are sometimes enhanced with sounds or visual effects like transparency and drop shadows. Using these objects, a user can use the computer without having to know commands.

Additional Information

• A GUI (graphical user interface) is a system of interactive visual components for computer software.
• A GUI displays objects that convey information, and represent actions that can be taken by the user.
• A GUI includes GUI objects like icons, cursors, and buttons.
• The Icons are used to represent a specific operation. A settings bottom is represented by a gear icon.
• Menus contain the set of operations that can be performed on the following window. Menus mainly use drop-down drawers which contain multiple buttons.
• The graphs are also used to represent the data related to the system. Like the temperature of the motherboard is represented by the graphs.
• The command lines are not part of the graphical interface, but they work in the background.

The correct answer is SEBI.

Key Points 

• On 25^th July 2022, the Securities and Exchange Board of India (SEBI) incorporated new chapters relating to the Social Stock Exchange (SSE) by amending the SEBI (Issue of Capital and Disclosure Requirements) Regulations​1​. The Social Stock Exchange is a novel concept in India, intended to serve the private and non-profit sectors by channelling greater capital to them. The amendment provides a framework for the Social Stock Exchange, which mainly covers:
• Eligibility of organizations to raise funds through the SSE: Organizations eligible to raise funds through the Social Stock Exchange include Not for Profit Organizations seeking to get registered and/or raise funds through a Social Stock Exchange.
• A 'Not for Profit Organization' is defined as a social enterprise which can be a charitable trust registered under the Indian Trusts Act, 1882, a charitable trust registered under the public trust statute of the relevant state, a charitable society registered under the Societies Registration Act, 1860, a company incorporated under section 8 of the Companies Act, 2013, or any other entity as may be specified by the Board​2​. A 'For Profit Social Enterprise' is an entity involved in at least one of several specified activities aimed at social upliftment, such as eradicating hunger, promoting healthcare, promoting education, ensuring environmental sustainability, and others​.
• Targeting underserved or less privileged populations: The Social Enterprise should target underserved or less privileged population segments or regions recording lower performance in the development priorities of central or state governments​​.
• Provision of eligible activities to the target population: The Social Enterprise should have at least 67% of its activities, qualifying as eligible activities to the target population. This can be established through one or more of the following: at least 67% of the immediately preceding 3-year average of revenues comes from providing eligible activities to members of the target population, at least 67% of the immediately preceding 3-year average of expenditure has been incurred for providing eligible activities to members of the target population, members of the target population to whom the eligible activities have been provided constitute at least 67% of the immediately preceding 3-year average of the total customer base and/or total number of beneficiaries​​.
• Means through which Social enterprises can raise funds: A Social Enterprise can raise funds through a Not for Profit Organization

Additional Information 

The correct answer is Saint Ramanujacharya.

Key Points

Statue of Equality

• The world’s second tallest statue in a sitting position is made up of ‘panchaloha’, meaning a combination of five metals i.e. gold, copper, silver, brass and zinc.
• The inner sanctorum deity of Sri Ramanujacharya is built of 120 kilos of gold.
• It is located in Hyderabad, Telangana.
• This commemorates the 120 years the saint spent on earth.
• The project, worth Rs. 1,000 crores is funded by donations from global devotees and its foundation stone was laid in 2014.

Additional Information

 About the Sri Ramanuja Acharya    

• He was born in 1017 CE at Shriperumbudur village in Tamil Nadu. He was a great theologian philosopher and thinker of devotional Hinduism.
• He is the most respected Acharya in the philosophy of Sri Vaishnavism. Ramanuja is also known as Ramanujacharya.
• He is said to have liberated millions from social, cultural, gender, educational and economic discrimination with the foundational conviction that every human is equal regardless of nationality, gender, race, caste, or creed.

The correct answer is Lothal.

Key Points

• In Lothal Dockyard was found.
• List of Important sites with their features:

Additional Information

• The Indus Valley Civilization was spread from present-day North-East Afghanistan to Pakistan and North-West India.
• The civilization flourished in the river basins of the Ghaggar-Hakra river and the Indus.
• Indus valley civilization is one of the four oldest civilizations in the world.
• It is also known as Harappan Civilization and is well-known for its organized planning based on the grid system.

Important facts to be remembered.

• Social features:-
• Indus valley civilization is the first urbanization in India.
• It has a well-planned drainage system, grid pattern, and town planning.
• They have possessed equality in society.
• Religious Facts:-
• Matridevi or Shakti is the Mother goddess.
• Yoni worship and Nature worship existed.
• They worshipped trees like Peepal.
• They also worshipped Fire worship called Havan Kund.
• Pashupati Mahadeva is known as the lord of Animals.
• The people of Indus Valley Civilization worshipped Animal worship like Unicorn and ox.
• Economic facts:-
• Indus valley civilization is based on agriculture.
• Trade and commerce flourished in this period.
• A dockyard has been found at Lothal.
• There were export and import.
• Production of cotton was there.
• At Lothal, weights and measures of truth existed in Harappan culture was seen.
• The weights and were usually cubical in shape. and were made of limestone, steatite, etc

The correct answer is Capitalism.

Key Points

• Capitalism is an economic system in which private individuals or businesses own capital goods.
• Capitalism is an economic system that focuses on a free market to determine the most efficient allocation of resources and sets prices based on supply and demand.
• Socialism is often presented as the opposite of capitalism whereby there is no free market and the allocation of resources is determined by a central body.
• The essential feature of capitalism is the motive to make a profit.

Additional Information

• In a capitalist economy, capital assets—such as factories, mines, and railroads—can be privately owned and controlled, labor is purchased for money wages, capital gains accrue to private owners, and prices allocate capital and labor between competing uses.
• Socialist economy:
• This economic system acknowledges the three inquiries in a different way. In a socialist society, the government determines what products are to be manufactured in accordance with the requirements of the society.
• It is believed that the government understands what is appropriate for the citizens of the country.
• Therefore, the passions of individual buyers are not given much attention.
• Mixed economy:
• Mixed systems have characteristics of both the command and the market economic system.
• For this purpose, mixed economic systems are also known as dual economic systems.
• However, there is no sincere method to determine a mixed system.
• Sometimes, the word represents a market system beneath the strict administrative control in certain sections of the economy.

The correct answer is 18.

Key Points

• The maximum number of electrons that can be accommodated in the M shell of an atom is 18.
• The shell corresponds to the principal quantum numbers.
• For the M shell principle, the quantum number is 3.
• So, the maximum number of electrons present in the M shell is 18.
• The shell number is expressed by the formula 2n2, where n is the number of shells.
• The shells, values of n, and the total number of electrons can be accommodated.

Additional Information

• Each subshell is constrained to hold 4ℓ + 2 electrons at most, namely:
• Each s subshell holds at most 2 electrons
• Each p subshell holds at most 6 electrons
• Each d subshell holds at most 10 electrons
• Each f subshell holds at most 14 electrons
• Each g subshell holds at most 18 electrons

The correct answer is Indo-Islamic.

Key Points

• Qutub Minar (or Qutab Minar) is a minaret and "victory tower" that forms part of the Qutb complex.
• It is an example of Indo-Islamic architecture.
• It is a UNESCO World Heritage Site in the Mehrauli area of New Delhi, India.
• The height of Qutb Minar is 72.5 meters, making it the tallest minaret in the world built of bricks.
• The tower tapers, and has a 14.3 meters (47 feet) base diameter, reducing to 2.7 meters (9 feet) at the top of the peak. ​
• Between 1199 and 1503, Qutub-ud-Din Aibak and Shamsu'd-Din Iltutmish built a minar (minaret) near the southeast corner of the Quwwatu'l-Islam, drawing inspiration from their Ghurid homeland.

Additional Information

• The Nagara or North Indian temple style
• Became popular in northern India.
• The entire temple is generally built on a stone platform with steps leading to it.
• No grand boundary walls or gateways (unlike the Dravida style).
• Earlier temples had one shikhara whereas later temples had many.
• The garbhagriha is located directly beneath the tallest shikhara.
• Dravidian Style of Architecture – South Indian Style
• The temple is enclosed within a compound wall.
• Gopuram: The entrance gateway in the centre of the front wall.
• Vimana: The shape of the main temple tower. It is a stepped pyramid that rises up geometrically (unlike the Nagara style Shikhara that is curving).
• In the Dravida style, shikhara is the word used for the crowning element at the top of the temple (which is shaped like a stupika or octagonal cupola).
• At the entrance to the garbhagriha, there would be sculptures of fierce dvarapalas guarding the temple.
• Generally, there is a temple tank within the compound.
• Subsidiary shrines could be found wither within the main tower or beside the main tower.
• Example in the Sriranganathar Temple at Srirangam, Tiruchirappalli, there are 7 concentric rectangular enclosure walls each having gopurams. The tower in the centre has the garbhagriha.
• Famous temple towns of Tamil Nadu: Kanchipuram, Thanjavur (Tanjore), Madurai and Kumbakonam.
• In the 8^th to 12^th centuries – temples were not confined to being religious centres but became administrative centres as well with large swathes of land.
• The Vesara Style is a hybrid temple architecture. It has features of both the Nagara and Dravidian style of temple architecture.
• In particular, the shape of the superstructure over the sanctum is usually pyramidal in profile, and shorter than the northern shikhara tower.
• In plan, the walls and superstructure are broadly circular, or a straight-sided cone, though its geometry is based on rotating a square imposed on a circle.

The correct answer is July 4.

Key Points

• Swami Vivekananda
• He was born on 12^th January 1863.
• He attended the parliament of religions held in Chicago on 11^th September 1893.
• Swami Vivekananda is best known in the United States for his historic speech in the World’s Parliament of Religions held in 1893.
• A section of Michigan Avenue, that passes in front of the Art Institute was formally renamed "Swami Vivekananda Way" On 11 November 1995.
• Michigan Avenue is one of the most prominent streets in Chicago
• On 11 September 1995, Art Institute put up a bronze plaque to commemorate Swami Vivekananda's historic speech in 1893.
• The Art Institute of Chicago and the Republic of India reinstalled the plaque commemorating Vivekananda’s landmark speech in 2012.
• His birthday is celebrated as national youth day in India.
• The Ramakrishna Mission was founded by Swami Vivekananda.
• Narendranath Datta is the original name of Swami Vivekananda.
• He is considered the patriotic saint of India.
• "Go back to Gita" is a famous slogan raised by Swami Vivekananda.
• Every year, July 4 is observed as the death anniversary of Swami Vivekananda.

Additional Information

The correct answer is Forebrain.

• The front brain is associated with the feeling of the satisfaction of hunger.

Key Points

• The brain is the central information processing organ of our body, and acts as the 'command and control system'.
• It controls the voluntary movements, the balance of the body, functional of vital involuntary organs (e.g., lungs, heart, kidneys, etc.), thermoregulation, hunger and thirst, circadian (24-hour) rhythms of our body, activities of several endocrine glands, and human behaviour.
• There are four lobes in the human brain-
• Frontal lobe.
• Parietal lobe.
• Occipital lobe.
• Temporal lobe.
• Frontal lobe
• It is located at the front of each hemisphere (brain’s cerebral cortex) and largest lobe.
• The central sulcus frontal lobe is separated from the parietal lobe.
• The vital role of the frontal lobe is decision making including self-management, Speech, and language, Comparing objects, memories, understanding, and reacting to feelings, behaviour, attention, etc.

• The temporal lobe is located in the bottom section of the brain and sits close to the ear level within the skull.
• The vital functions are hearing, language recognization, speaking and understanding writing, memory acquisition, visual perception, etc.
• Therefore hearing is controlled by the temporal lobe.​

Additional Information

• Parietal lobe
• Located behind the frontal lobe.
• Receive and transmit sensory information from the body and it is also connected to other parts of the brain.
• Deals with many sensations including touch, pressure, pain, heat, cold, etc
• Occipital lobe
• It is the smallest of the lobes, located at the back portion of the brain and below the occipital bone.
• The primary visual cortex, which is located in the occipital lobe, receives and interprets information from the retinas of the eyes.
• The occipital lobe deals with aspects of vision, including face recognition, movement, object recognition, colour determination, distance, depth perception.

The correct answer is Only I.

Key Points

• India has won a total of 61 medals in the Commonwealth Games 2022.
• 22 gold,
• 16 silver, and
• 23 bronze
• In the 2018 Commonwealth Games, India won a total of 66 medals out of which 16 were in shooting.
• This time shooting was not included.
• India finished fourth in the medal tally.
• Australia took first place.
• England finished second and Canada third.
• New Zealand finished fifth.
• Ravi Kumar Dahiya won Gold for the country in Men's Freestyle 57kg Wrestling in Commonwealth Games 2022. Therefore 2^nd statement is incorrect.
• Avinash Sable win a silver medal in the 3000m steeplechase at the 2022 Commonwealth Games in Birmingham, clocking a time of 8:11.20. 1^st statement is correct.

Additional Information

• India took the total number of gold medals in the history of the Commonwealth Games (CWG 2022) to 203.
• Australia (1003 gold medals) is at the top in terms of the total number of gold medals in the Commonwealth Games, while England (773) is second and Canada (510) is in third place.
• India won its first gold in the Commonwealth Games in 1958 which was won by legendary sprinter Milkha Singh.
• India has won a gold medal in every Commonwealth Games since then (didn't participate in 1962 and 1986).
• The 2010 Commonwealth Games in Delhi has been the most successful for India in which it won 38 gold medals.

The correct answer is Amit Dave.

Key Points 

• Amit Dave is among four Indians honored with the prestigious Pulitzer Prize 2022 in the feature photography category.
• Siddiqui and his colleagues Adnan Abidi, Sanna Irshad Mattoo, and Amit Dave from the Reuters news agency have won the award.

Additional Information

• First awarded in 1917, the Pulitzer Prize recognizes excellence in journalism, literature, and musical composition.
• The categories include Public Service, Breaking News Reporting, Feature Writing, etc.
• Columbia University administers the award.
• These awards are being given annually in 21 categories.
• In 20 categories, each winner receives USD 15,000 and a certificate.
• A gold medal is awarded to the winner in the Public Service category of the award.

The correct answer is Both I and II.

Key PointsNational Income Calculation

• Intermediate goods are not included in the calculation of national income.
• Intermediate goods are products used in the production of final goods and services. Including them would result in double counting, as their value is already embedded in the value of final goods.

Hence, statement I is correct.

• Final goods are included in the calculation of national income.
• Final goods are products that have completed the production process and are available for consumption or investment. These goods are counted in national income because they reflect the actual value of production in the economy.

Hence, statement II is correct.

Additional Information

• National Income Overview
• National income is a measure of the total value of goods and services produced by a country within a specific period, typically one year.
• It is calculated using various methods, including the income method, production method, and expenditure method.
• Exclusion of Intermediate Goods
• Excluding intermediate goods prevents double counting and ensures that only the value of final products is considered, providing a more accurate measure of economic output.
• Inclusion of Final Goods
• Final goods are included in national income calculations because they represent the end product of economic activity, reflecting the actual value created in the economy.

Key facts about National income in India-

• The first attempt to calculate the national income of India was made by Dadabhai Naoroji.
• The first scientific method for calculating national income was made by Prof. V.K.R.V. Rao in 1931 but was not satisfactory.
• The first official attempt was made by National Income Committee headed by Prof. P.C. Mahalanobis in 1949.
• Central Statistical Organization (CSO) is responsible for calculating National income in India.

The correct answer is The size of the nucleus is very large as compared to the size of the atom.

Key Points

RUTHERFORD’S MODEL OF AN ATOM

• Ernest Rutherford was interested in knowing how the electrons are arranged within an atom.
• Rutherford designed an experiment for this. In this experiment, fast-moving alpha (α)-particles were made to fall on a thin gold foil.
• He selected a gold foil because he wanted as thin a layer as possible. This gold foil was about 1000 atoms thick.
• α-particles are doubly-charged helium ions. Since they have a mass of 4 u, the fast-moving α-particles have a considerable amount of energy.
• It was expected that α-particles would be deflected by the sub-atomic particles in the gold atoms. Since the α-particles were much heavier than the protons, he did not expect to see large deflections.
• But, the α-particle scattering experiment gave totally unexpected results.
• Observations 
• Most of the fast-moving α-particles passed straight through the gold foil.
• Some of the α-particles were deflected by the foil by small angles.
• Surprisingly one out of every 12000 particles appeared to rebound.
• Rutherford concluded from the α-particle scattering experiment that–
• Most of the space inside the atom is empty because most of the α-particles passed through the gold foil without getting deflected.
• Very few particles were deflected from their path, indicating that the positive charge of the atom occupies very little space.
• A very small fraction of α-particles were deflected by 180 Degrees, indicating that all the positive charge and mass of the gold atom were concentrated in a very small volume within the atom.
• From the data, he also calculated that the radius of the nucleus is about 105 times less than the radius of the atom.
• On the basis of his experiment, Rutherford put forward the nuclear model of an atom, which had the following features:
• There is a positively charged center in an atom called the nucleus. Nearly all the mass of an atom resides in the nucleus.
• The electrons revolve around the nucleus in circular paths.
• The size of the nucleus is very small as compared to the size of the atom.Therefore 1^st option is not correct regarding Rutherford's nuclear model of an atom.
• Drawbacks 
• The revolution of the electron in a circular orbit is not expected to be stable. Any particle in a circular orbit would undergo acceleration. During acceleration, charged particles would radiate energy.
• Thus, the revolving electron would lose energy and finally fall into the nucleus. If this were so, the atom should be highly unstable, and hence matter would not exist in the stable form.

The answer is Asiatic elephant

**Key Points:**Vulnerable Species: 

• Species whose population has declined to levels from where it is likely to move into the endangered category in the near future if the negative factors continue to operate.
• Examples:
• Blue sheep, Asiatic elephant, Gangetic dolphin

Endemic Species:

• Species that are only found in some particular areas usually isolated by natural or geographical barriers.
• Examples:
• Andaman teal, Nicobar pigeon, Andaman wild pig, Mithun in Arunachal Pradesh

Additional Information:

• Based on the International Union for Conservation of Nature and Natural Resources (IUCN), we can classify the plant and animal species as:

Normal Species:

• Species whose population levels are considered to be normal for their survival, such as cattle, sal, pine, rodents, etc.

Endangered Species:

• Species that are in danger of extinction.
• The survival of such species is difficult if the negative factors that have led to a decline in their population continue to operate.
• Examples:
• Blackbuck, Crocodile, Indian wild ass, Indian rhino, Lion-tailed macaque, Sangai (brow-antlered deer in Manipur)

Rare Species:

• Species with a small population may move into the endangered or vulnerable category if the negative factors affecting them continue to operate.
• Examples:
• Himalayan brown bear, Wild Asiatic buffalo, Desert fox and Hornbill

Extinct Species:

• Species that are not found after searches of known or likely areas where they may occur.
• A species may be extinct from a local area, region, country, continent or the entire earth.
• Examples:
• Asiatic cheetah, Pink head duck

The correct answer is Sunda

Key Points:

The correct answer is South Africa .

In News:

• In Women's Cricket, Australia lifted the ICC T20 World Cup Trophy for the sixth time.
• It was held in South Africa between 10 February and 26 February 2023.

Key Points:

• In the final match on 26 Feb 2023, they defeated South Africa by 19 runs at Newlands, Cricket Ground in Cape Town.
• Earlier, winning the toss and deciding to bat first, Australia posted 156 for 6 in their allotted 20 overs.
• Beth Mooneyc top-scored with unbeaten 74 runs for Australia.

**Additional Information:**Australia:

• Capital - Canberra
• Currency - Australian dollar
• Prime minister -  Anthony Albanese.
• National Sport - Australian Rules football.

Other Sports News:

• England Test captain Ben Stokes became the player to hit the most number of sixes in the history of Test cricket in the match against New Zealand on 18 February 2023.
• Jean-Eric Vergne of team DS Penske won the first-ever Formula E race held in Hyderabad on 11 February 2023.
• With his 36^th point against the Oklahoma City Thunder on February 7, 2023, LeBron James became the National Basketball Association's all-time leading scorer.
• Aditi Ashok clinched the Ladies European Tour Title with a nine-shot win, despite 1-over on final day, at the Magical Kenya Ladies Open on 5 February 2023.
• Prajnesh Gunneswaran won the final of the $25,000 ITF men’s tennis tournament in Al Zahra, Kuwait, on 29 January 2023.
• England captain Ben Stokes has been named the International Cricket Council Test Player of the Year for 2022$.

The correct answer is Precise

**Key Points:**The formatting options available in the 'Paragraph' setting window in MS Word 2016 are:

• Spacing.
• Indentation.
• Pagination under the option Line and Page breaks.
• Alignment.

​Paragraph formatting options are described as:

• Alignment
• Alignment or justification refers to the way in which the lines of a paragraph are aligned.
• There are four types of alignment, namely, left, center, right, and justified.
• Indentation
• The value in the Before text box specifies the width of the additional empty space that is inserted between the margin and the text on the left-hand side of a paragraph of left-to-right text.
• The value in the After text box specifies the width of the additional empty space that is inserted between the text and the margin on the right-hand side of a paragraph of left-to-right text.
• A negative value specifies the distance by which the text extends beyond the respective margin.
• Spacing
• The spacing between two paragraphs is determined by the spacing before one paragraph and the spacing after the preceding paragraph, which are displayed and can be modified in the Before and After boxes.
• Line spacing refers to the vertical distance between the lines within a paragraph.
• It determines the location of each line relative to the line above it.
• Line and Page Breaks tab (Pagination)
• The paragraph formatting options on the Line and Page Breaks tab under pagination of the Paragraph dialog box can help you control where automatic page breaks occur in your document.

Correct Answer Kathak

Key Points:

• Aditi Mangaldas is a leading dancer and choreographer in Kathak, a classical Indian dance form.
• She has received extensive training from renowned gurus Shrimati Kumudini Lakhia and Pandit Birju Maharaj.
• Aditi is recognized for her exceptional artistry, technique, and eloquence in every performance.
• Her characteristic energy sets her apart and adds a unique touch to her dance.
• Aditi Mangaldas is highly acclaimed and respected in the field of Kathak.

Additional InformationClassical dance

• Classical dances are performed by professional or highly trained dancers who have studied their form for many years.
• There are eight classical Dances in India.
• Classical dance expresses a story or theme and this form of art lies in the religious Hindu music theatre styles. It represents the culture.
• They are
• Kathak from North India,
• Sattriya of Assam,
• Bharatnatyam of Tamil Nadu,
• Kuchipudi of Andhra Pradesh,
• Kathakali and Mohiniaattam of Kerala,
• Manipuri of Northeast India, and
• Odissi of Odisha.
• It is the right way to connect with your feelings, coordinate and move the movement skills and build strength and stability in your body.

The correct answer is Calcutta

Key Points:

• The Calcutta High Court is the oldest High Court in India.
• It is located in B.B.D. Bagh, Kolkata, West Bengal.
• It has jurisdiction over the state of West Bengal and the Union Territory of the Andaman and Nicobar Islands. The High Court building's design is based on the Cloth Hall, Ypres, in Belgium.
• The high court was established on 1 July 1862.
• The current chief justice is T. S. Sivagnanam

Additional Information:

• The High Court of Karnataka is the High Court of the Indian state of Karnataka and thus its highest judicial authority. The court's principal bench is located in Bengaluru, the capital city of Karnataka, with additional benches in Hubballi-Dharwad and Kalaburagi. It was previously called the High Court of Mysore.
• Allahabad High Court, also known as the High Court of Judicature at Allahabad is the high court based in Prayagraj that has jurisdiction over the Indian state of Uttar Pradesh. It was established on 17 March 1866, making it one of the oldest high courts to be established in India
• The High Court of Delhi was established on 31 October 1966. The High Court of Delhi was established with four judges, including Chief Justice K. S. Hegde, Justice I. D. Dua, Justice H. R. Khanna, and Justice S. K. Kapur.

Correct Answer Attorney General of India

India's Attorney General (AG) is a member of the Union Executive.

Key Points:

• The Attorney General is the country's highest law enforcement official.
• Under Article 76 of the Constitution, ​the post of Attorney General of India is established.
• Attorney General appointed by the President of India after the advice of the Government of India.
• Constitution of India laid down eligibility conditions, he must be a citizen of India and must have served as a judge of a high court for five years or as an attorney of a high court for ten years, or as a prominent jurist.
• Attorney General can participate in the proceedings of both Houses of Parliament or their joint sitting and Parliamentary committee of which he may be named a member but cannot vote.
• The Constitution does not specify the length of the office's term.
• He serves at the pleasure of the President of India.

Therefore, Article 76 of the Indian Constitution deals with the Attorney General of India. 

Additional InformationResponsibilities of The Attorney General mentioned under the Indian Constitution are following:   

• To provide legal advice to the Government of India on subjects assigned to him by the President
• To represent the Government of India in all Supreme Court and High Court cases involving the Government of India.
• Under Article 143, To represent the Government of India in any Supreme Court referral made by the President.
• To carry out the duties entrusted to him by the Constitution or any other law.
• To carry out any additional legal responsibilities entrusted to him.

Correct Answer 23

Key Points:

• India won 23 Bronze medals in Commonwealth Games 2022.
• India won a total of 61 medals in the Commonwealth Games 2022.
• 22 gold,
• 16 silver, and
• 23 bronze
• In the 2018 Commonwealth Games, India won a total of 66 medals out of which 16 were in shooting.​
• This time shooting was not included.
• India finished fourth in the medal tally.
• Australia took first place.
• England finished second and Canada third.
• New Zealand finished fifth.

Additional Information

• India took the total number of gold medals in the history of Commonwealth Games (CWG 2022) to 203.
• Australia (1003 gold medals) is at the top in terms of the total number of gold medals in the Commonwealth Games, while England (773) is second and Canada (510) is in third place.
• India won its first gold in the Commonwealth Games in 1958 which was won by legendary sprinter Milkha Singh.
• India has won a gold medal in every Commonwealth Games since then (didn't participate in 1962 and 1986).
• The 2010 Commonwealth Games in Delhi has been the most successful for India in which it won 38 gold medals.

The correct answer is Rohit Sharma

Key Points:Rohit Sharma:

• Rohit Sharma was the captain of India in the ICC T20 World Cup 2022.
• Batsman Rohit Sharma completed 3000 T20 International runs and became the third cricketer in the world to achieve this feat.
• Rohit reached the 3000 run mark in a match against Namibia in the ICC men's T20 World Cup at Dubai International Cricket Stadium.
• Rohit Sharma is the only batsman to score five centuries in a single edition of the ICC World Cup.
• He achieved this milestone in the 2019 world cup.
• He scored centuries against South Africa, Pakistan, England Bangladesh and Sri Lanka.
• He is the only batsman in cricket history who has scored 3 double centuries in one-day international matches.

ICC T20 World Cup 2022:

• India squad for ICC T20 World Cup: Rohit Sharma (Captain), KL Rahul (vice-captain), Virat Kohli, Suryakumar Yadav, Deepak Hooda, Rishabh Pant (wicket-keeper), Dinesh Karthik (wicket-keeper), Hardik Pandya, R. Ashwin, Yuzvendra Chahal, Axar Patel, Jasprit Bumrah, Bhuvneshwar Kumar, Harshal Patel, Arshdeep Singh.
• The Eighth ICC Men's T20 World Cup tournament was held in 2022 at Australia.
• It was played from 16 October to 13 November 2022. In the final, England beat Pakistan by five wickets to win their second ICC Men's T20 World Cup title. 
• Sam Curran was named the Player of the Match and also the Player of the tournament.

Additional Information:

• The England and Wales Cricket Board is the national governing body of cricket in England and Wales.
• It was formed on 1 January 1997 as a single governing body to combine the roles formerly fulfilled by the Test and County Cricket Board, the National Cricket Association, and the Cricket Council.
• President: Giles Clarke
• Headquarters: London, United Kingdom
• Founded: 1 January 1997
• Chairman: Richard Thompson

The correct answer is 1784

Key Points:

• ​Pitt's India act of 1784 was passed to separate the commercial and political functions of the Company.
• Pitt’s India act of 1784 created a new body named the Board of control which manages the political affairs.
• Commercial affairs were managed by the Court of Directors.
• By this act, the British government was given supreme control over the company's affairs and its administration in India.
• The governor general council's strength was reduced to 3 members. One of the 3 would be Commander in chief of the British Crown's army in India.
• The Governor-General was given the right of veto.
• The Presidencies of Madras and Bombay became subordinate to the Bengal presidency
• Calcutta became the capital of British India till 1911.

Given:

PO = 27 cm

Concept Used:

The centroid of a triangle divides the medians into segments in the ratio of 2:1, where the centroid is closer to the midpoint of the side (where the median intersects the side).

Calculation:

The centroid of a triangle divides the medians into segments in the ratio of 2:1, where the centroid is closer to the midpoint of the side (where the median intersects the side).

Given that PO = 27 cm, if we let PM = x,

2/3 × x = 27

x = 27 × 3/2

x = 40.5 cm

So, the length of PM is 40.5 cm.

Given:

We need to find the sum of all three-digit numbers that are divisible by 20.

Formula Used:

Sum = (n/2)(first term + last term)

Calculation:

 The first term (a) is 100, the last term (l) is 980, and the common difference (d) is 20.

The number of terms (n) can be calculated using the formula:

n = (l - a)/d + 1

n = (980 - 100)/20 + 1

n = 45

Now, we can calculate the sum of the arithmetic series:

Sum = (n/2)(a + l)

Sum = (45/2)(100 + 980)

Sum = 22.5 × 1080

Sum = 24300

Therefore, the sum of all three-digit numbers divisible by 20 is 24,300.

Shortcut Trick

New Average = 42 kg, Old Average = 40 kg.

Increase in Average = 42 − 40 = 2 kg.

Total increase in weight for all 11 persons = 11 × 2 = 22 kg.

Weight of the new person = Old Average + Total Increase.

⇒ Weight = 40 + 22 = 62 kg.

∴ The correct answer is 62 kg.

Alternate Method

Given:

Average weight of 10 persons = 40 kg

Average weight of 11 persons (after new person joins) = 42 kg

Formula Used:

Sum of observations = Average × Number of observations

Initial Total Weight (10 persons)

400 kg

New Total Weight (11 persons)

400 kg

• 62 kg

Total: 462 kg

Calculations:

⇒ Total weight of initial 10 persons = 10 × 40 = 400 kg

⇒ Total weight of 11 persons = 11 × 42 = 462 kg

⇒ Weight of the new person = Total weight of 11 persons − Total weight of 10 persons

⇒ Weight of the new person = 462 − 400 = 62 kg

∴ The correct answer is 62 kg.

Additional Information

When a Person Leaves the Group

Value of the person leaving = Old Average + (Net Decrease in Average × Remaining Persons) OR Old Average − (Net Increase in Average × Remaining Persons).

Replacement in Average

When a new person replaces an existing one: Weight of new person = Weight of replaced person + (Net Change in Average × Total Number of Persons).

Combined Average

If two groups of sizes n₁ and n₂ have averages A₁ and A₂ respectively, then their Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Calculation:

cosec A (1 - cos A) (cosec A + cot  A)

⇒ (cosec A - cosec A . cos A) (cosec A + cot  A)

⇒ (cosec A - cot A) (cosec A + cot  A)

⇒ (cosec² A - cot² A) = 1                       [Trigonometry identity, 1 + cot² θ = cosec² θ]

∴ Option 2 is the correct answer.

Given:

Principal (P) = Rs. 12500

Final Amount (A) = Rs. 20000

Rate of interest (r) = 8% per annum

Concept:

Simple Interest = (Principal × Rate × Time)/100. We rearrange this formula to solve for Time.

Calculation:

Simple Interest = Final Amount - Principal

⇒ Rs. 20000 - Rs. 12500 = Rs. 7500

Time = (Simple Interest × 100) / (Principal × Rate)

⇒ (7500 × 100) / (12500 × 8) = 7.5 years

Hence, it will take 7.5 years for the sum to amount to Rs. 20000.

Given:

Total students = 414

Ratio of boys to girls = 5:4

Number of boys admitted = 46

Concept Used:

The new ratio is determined by the increased number of boys and the unchanged number of girls.

Calculation:

Total parts = 5 + 4 = 9

Boys initially = 5/9 × 414 = 230

Girls = 414 - 230 = 184

New total boys = 230 + 46 = 276

New ratio of boys to girls = 276:184 = 92 × 3 : 92 × 2 =  3:2

Hence, the new ratio of boys to girls is 3:2.

Given:

Radius (r) = 7 cm

Height (h) = 5 cm

Concept:

Total Surface Area of a cylinder = 2πr(h + r)

Calculation:

Total Surface Area = 2π × 7 × (5 + 7) = 2π × 7 × 12 = 528 cm²

Hence, the total surface area of the cylinder is 528 cm².

Given:

$\frac{\frac{3}{4} \div \frac{9}{64}+\frac{7}{11} \times \frac{121}{14}-\frac{9}{13} \times \frac{65}{36}}{\frac{1}{2} \div \frac{4}{5}+\frac{3}{4} \times \frac{16}{15}}$

Concept used:

Calculation:

$\frac{\frac{3}{4} \div \frac{9}{64}+\frac{7}{11} \times \frac{121}{14}-\frac{9}{13} \times \frac{65}{36}}{\frac{1}{2} \div \frac{4}{5}+\frac{3}{4} \times \frac{16}{15}}$

⇒ $\frac{\frac{3}{4} \times \frac{64}{9}+\frac{11}{2} -\frac{5}{4}}{\frac{1}{2} \times \frac{5}{4}+\frac{4}{5} }$

⇒ $\frac{\frac{16}{3}+\frac{17}{4}}{ \frac{5}{8}+\frac{4}{5} }$

⇒ $\frac{\frac{64 + 51}{12}}{ \frac{25 + 32}{40} }$

⇒ $\frac{\frac{115}{12}}{ \frac{57}{40} }$

⇒ $\frac{115 \times 40}{12 \times 57}$

⇒ $\frac{1150}{171}$

∴ Option 2 is the correct answer.

Given:

Tangent drawn from a point P, touches the circle at Q.

O is the centre of this circle.

PQ = 12 cm and OQ = 5 cm,

Concept used:

1. The radius and tangent of a circle at a point of contact is always perpendicular to each other. So the angle is 90°. 2. Pythagoras Theorem: Base² + Perpendicular² = Hypotenuse²

Calculation: 

According to the concept,

Since ∠OQP is 90°, ΔPQO is a right-angled triangle.

OP is the hypotenuse.

Now, OP

⇒ $\sqrt {OQ^2 + PQ^2}$

⇒ $\sqrt {5^2 + 12^2}$

⇒ $\sqrt {169}$ = 13 cm

∴ The value of OP is 13 cm.

Given:

The average of 5 consecutive even numbers is A

Calculation:

Let X is an even number.

So 5 five consecutive even numbers = X, X + 2, X + 4, X + 6 and X + 8

Avg = [5X + (2 + 4 + 6 + 8)] /5 = X + 4 = A

and if the next five even numbers X + 10, X + 12, X + 14, X + 16 and X + 18 are also included 

then Average will become = [10X + 2(1 + 2 + ... + 9)]/10

=  (10X + 90) / 10 = X + 9 = A + 5

Hence, A + 5 is the correct answer.

Given:

sin A = 6/7

Concept:

sin²A + cos²A = 1 and

sec A = 1/cos A

Calculation:

⇒ cos A = √(1 - sin² A)

⇒ √(1 - (6/7)²) = √(1 - 36/49)

⇒ √(13/49) = √(13)/7

⇒ sec A = 1/cos A = 7/√(13)

Hence, the value of sec A is 7/√(13).

Calculation:

I. The production of sugar by A in years J and K together is 7.69 percent more the production of sugar by B in year L and M together.

Production of sugar by A in years J and K together = 70 + 50 = 120

Production of sugar by B in year L and M together = 70 + 60 = 130

According to the question:

130 - 120 = 10

10/130 = 7.69%

The production of sugar by A in years J and K together is 7.69% less than the production of sugar by B in years L and M together.

Statement I is wrong.

II. The ratio of combined production of sugar by B in years M and N to the combined production of sugar by A in years K and L is 21 ∶ 16.

Production of sugar by B in years M and N = 60 + 45 = 105

Production of sugar by A in years K and L = 50 + 30 = 80

Ratio = 105 : 80 = 21 : 16

Statement II is correct.

∴ Option 1 is the correct answer.

Given:

Speed1 = 80 km/hr

Speed2 = 50 km/hr

Time difference between the two cases = 60 mins early + 48 mins late = 108 mins = 108/60 hrs

Concept:

In the equation Time = Distance/Speed, the difference in the times traveled at the two speeds will give the usual time taken to reach the office.

Calculation:

⇒ Let the usual time be 'T' hours, and the distance be 'D' kilometers.

⇒ D/80 = T - 1

⇒ D/50 = T + 48/60

⇒ Subtracting these two equations we get,

⇒ D/50 - D/80 = 1 + 4/5

⇒ D = 80 × 3

⇒ D = 240 km

⇒ Usual time =  D/T = 240/80 = T - 1

T = 4hr

Usual speed = 240/4 = 60km/hr

Hence, the speed of the scooter to reach on the usual time is 60 km/hr.

Given:

P = 420

Concept:

Using the given percentages, we can determine the values of Q and R from P.

Calculation:

P = 120% of Q

⇒ P = 1.2Q

⇒ Q = P/1.2 = 420/1.2 = 350

⇒ Q = 0.7R

⇒ R = Q / 0.7 = 350/0.7 = 500

Hence, the value of R is 500.

Given:

Selling Price (SP) = Rs. 1,260

Discount = 40%

Concept:

The marked price (MP) is calculated by dividing the Selling Price by (1 - Discount/100).

Calculation:

⇒ MP = SP / (1 - Discount/100)

⇒ MP = 1260 / (1 - 40/100) = Rs. 2100

Hence, the marked price of the article is Rs. 2100.

Shortcut Trick

Use the Substitution Method by testing the given options in the equation.

Substitute A = 45°: we know sin 45° = 1/√2 and cos 45° = 1/√2.

LHS = 2(1/√2)³ − (1/√2) = 2/(2√2) − 1/√2 = 1/√2 − 1/√2 = 0.

RHS = (1/√2) − 2(1/√2)³ = 1/√2 − 2/(2√2) = 1/√2 − 1/√2 = 0.

Since LHS = RHS for A = 45°, it is the correct value.

∴ The correct answer is 45°.

Alternate Method

Given: (2 cos³ A − cos A) = (sin A − 2 sin³ A)

Formula Used: cos 2A = 2 cos² A − 1 and cos 2A = 1 − 2 sin² A

⇒ cos A(2 cos² A − 1) = sin A(1 − 2 sin² A)

⇒ cos A × cos 2A = sin A × cos 2A

⇒ cos A × cos 2A − sin A × cos 2A = 0

⇒ cos 2A (cos A − sin A) = 0

⇒ If cos 2A = 0, then 2A = 90° ⇒ A = 45°

⇒ If cos A − sin A = 0, then sin A = cos A ⇒ tan A = 1 ⇒ A = 45°

∴ The correct answer is 45°.

Additional Information

Double Angle Identities

cos 2A can be expressed as cos² A − sin² A, 2 cos² A − 1, or 1 − 2 sin² A.

Triple Angle Identities

sin 3A = 3 sin A − 4 sin³ A and cos 3A = 4 cos³ A − 3 cos A.

Trigonometric Ratios at 45°

For A = 45°, sin A = cos A = 1/√2, which makes tan A = 1 and cot A = 1.

Calculation:

Loss on article P = 300 - 250 = 50

Loss on article Q = 400 - 375 = 25

Loss on article R = 350 - 250 = 100

Loss on article S = 500 - 350 = 150

⇒ Total loss = 50 + 25 + 100 + 150 = 325

⇒ Average loss = Total loss / Number of articles = 325 / 4 = 81.25

Hence, the average value of loss of all articles is Rs. 81.25.

Given:

A and B can complete the work in 20 days.

A is 20% more efficient than B.

Concept used:

Total Wok Done = Number of Days × Efficiency

Calculation:

The ratio of efficiency of A and B = 6 : 5

Let the efficiencies (work is done per day) of A, and B be 6x and 5x respectively.

Total Wok Done = Number of Days × Efficiency

⇒ 20 × (6x + 5x)

⇒ 20 × 11x

⇒ 220x

The time is taken by B alone to complete the work = 220x/5x

⇒ 44 days

∴ B can complete the whole work in 44 days.

Given:

$\frac{\mathrm{K}}{\mathrm{k}^2-2 \mathrm{~K}+1}=\frac{1}{6}$

Concept Used:

If x + 1/x = a, then

x³ + 1/x³ = a³ - 3a

Calculation:

 

$\frac{\mathrm{K}}{\mathrm{k}^2-2 \mathrm{~K}+1}=\frac{1}{6}$

Take K common from numerator and denominator

$\frac{\mathrm{1}}{\mathrm{K}-2 +\frac{1}{K}}=\frac{1}{6}$

${K}-2 +\frac{1}{K} = 6$

${K}+\frac{1}{K} = 8$

${K^3}+\frac{1}{K^3} = 8^3 - 3\times 8$

${K^3}+\frac{1}{K^3} = 512 - 24= 488$

∴ Option 4 is the correct answer.

Given:

ΔABC is similar to ΔPQR.

Length of sides in ΔABC: AB = 4 cm, BC = 8 cm, AC = 10 cm.

QR = 16 cm in ΔPQR.

Concept Used:

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Area of scalene triangle = √s(s - a)(s - b)(s - c), 

where s = semi perimeter = sum of sides/2,  and a, b, c are the sides of triangle.

Solution:

For ΔABC and ΔPQR, since ΔABC ~ ΔPQR, the ratio of corresponding sides QR/BC = 16/8 = 2.

The ratio of the areas of ΔABC and ΔPQR will be the square of the ratio of their corresponding sides.

⇒ Area(ΔPQR)/Area(ΔABC) = (QR/BC)² = 2² = 4.

Now the area of ΔABC

⇒ s = (4 + 8 + 10)/2 = 11 cm

⇒ Area of ΔABC = √11(11 - 4)(11 - 8)(11 - 10)

⇒ √11 × 7 × 3 × 1 = √231 cm²

Area of ΔPQR = 4 × Area of ΔABC = 4√231 cm2

∴ Option 2 is the correct answer.

Given:

The angle subtended by a chord on the major arc of a circle is 140 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, ∠POQ = 140° 

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

According to the concept,

∠POQ = 2 × ∠PRQ

⇒ ∠PRQ = 140°/2

⇒ ∠PRQ = 70°

∴  the angle subtended by the chord AB on the major arc of the circle is 70°.

Calculation:

Total number of passports issued in 6 consecutive years = 7000 + 9000 + 7500 + 9500 + 6500 + 8500 = 48000

Average = 48000/6 = 8000

∴ Option 3 is the correct answer.

Given:

(a + b) = 16

a³ + b³ = 1456

Concept used:

Use the formula a³ + b³ = (a+b)(a² + b² - ab)

(a + b)² = a² + b² + 2ab

Calculation:

Solving for ab :

⇒ (a + b)2 = a2 + b2 + 2ab

⇒ 162 = a2 + b2 + 2ab

⇒ a2 + b2 = 162 - 2ab

Now,

⇒ a³ + b³ = (a+b)(a2 + b2 - ab)

⇒ 1456 = 16(162 - 2ab - ab)

⇒ 1456/16 = (256 - 3ab)

⇒ 91 = (256 - 3ab)

⇒ 3ab = 256 - 91

⇒ ab = 165/3 = 55

Hence, the value of ab is 55.

Calculation:

Players have height less than 141 cm = 1 + 3 + 2 = 6 players

∴ Option 3 is the correct answer.

Given:

Cost Price (CP) = Rs. 4,000

Loss = 13%

Concept Used:

The Selling Price (SP) is found by subtracting the loss from the Cost Price.

Calculation:

Loss amount = Loss/100 ×  CP = 13/100 ×  4000 = Rs. 520

Selling Price = CP - Loss = 4000 - 520 = Rs. 3480

Hence, the selling price of the watch is Rs. 3480.

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

Key Points

• The word that means the same as "soar" is "fly."
• "Soar" is a verb that means to fly or rise high in the air, often rapidly and with ease.(उड़ना)
• It's often used to describe the flight of birds, airplanes, or other objects that can move through the air.
• "Fly" is the correct answer, as it also means to move through the air, often with the help of wings.(उड़ना)
• It can be a verb (as in the act of flying) or a noun (as in the insect).

Therefore, the correct answer is: 'Fly'.

Additional Information

• Now let's look at the other words:
• "Sweet" is an adjective that describes something with a pleasant taste that is similar to sugar.(मीठा)
• "Bitter" is an adjective used to describe a sharp, pungent taste that is often considered unpleasant. (कड़वा)
• "Sour" is an adjective that describes something with a taste like a lemon or vinegar, typically considered sharp or acidic.(खट्टा)

The correct answer is 'Option 2'.

Key Points

• The phrase "to miss the bus" is an idiom that means "to lose an opportunity."(एक अवसर खो देना)
• It implies that someone has failed to take advantage of a situation or a chance that could have benefitted them, much like missing a bus means you've lost your chance to travel with it.

Therefore, the correct answer is: 'To lose an opportunity'.

Additional Information

• Let's now look at the provided alternatives:
• "Short lived glory" refers to a success or accomplishment that lasts for only a brief period.(क्षणिक यश)
• "Escape by a thin margin" means to narrowly avoid a negative situation or outcome.(बाल-बाल बचना)
• "A problem in a situation" refers to a difficulty or obstacle that arises within a particular context or set of circumstances.(स्थिति में एक समस्या)

The correct answer is 'Option 3'.

Key Points

• The error is in the part "to meet society new needs."
• The correct phrase should be "to meet society's new needs."
• In English, when you want to indicate that something belongs to someone or something, you use the possessive form, which is often made by adding an apostrophe and an "s" at the end of the word.
• Here, "society's new needs" means "the new needs of society."

Therefore, the corrected sentence would be: "Workers and companies in all sectors can contribute their skills to meet society's new needs."

The correct answer is 'Option 2' i.e. 'Keep a'.

Key Points

• The correct improvement for the sentence "We keeps a horse, two cows, and six chickens." is "keep a."
• In English, the verb "to keep" means to own or have possession of something.
• When using it with plural subjects such as "we," "you," or "they," the form of the verb remains "keep."
• It only changes to "keeps" when the subject is third person singular, i.e., "he," "she," or "it."

Therefore, the corrected sentence would be: "We keep a horse, two cows, and six chickens."

The correct answer is 'Miranda told her teacher that she had been sick for a day'.

Key Points

• The correct indirect form of the sentence "Miranda said to her teacher, 'I was sick for a day.'" is "Miranda told her teacher that she had been sick for a day."
• When converting direct speech into indirect speech, the tense of the verbs usually shifts back (this is known as "backshifting").
• In this case, the past simple tense "was" changes to the past perfect tense "had been."
• This shift accurately conveys the timing of the events in the indirect speech.

Therefore, the correct sentence is: 'Miranda told her teacher that she had been sick for a day.'

Additional Information

• Let's look at the other options:
• "Miranda told her teacher that she has been sick for a day." - This is incorrect because the present perfect "has been" doesn't accurately convey the timing of past events in indirect speech.
• "Miranda told her teacher that she is sick for a day." - This is incorrect because the present tense "is" doesn't accurately represent the past events conveyed in the original direct speech.
• "Miranda told her teacher that she was sick for a day." - Although it might seem correct in some contexts, in proper English grammar, while changing from direct to indirect speech, the tense usually shifts back. Therefore, "was" should become "had been."

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

Key Points

• The word that is opposite in meaning to "fanatic" is "moderate."
• "Fanatic" is a noun that describes someone who has extreme and uncritical enthusiasm or zeal, especially in terms of religious or political beliefs.(कट्टर)
• It's often used to describe a person who is obsessively devoted to a cause and is unwilling to tolerate any differing views.
• "Moderate" -  A moderate is a person who holds views that are not extreme or radical, typically falling somewhere in the middle of the political or social spectrum. (संयमी)

Therefore, the correct answer is: 'Moderate'.

Additional Information

• Let's look at the other options:
• "Militant" - A militant is a person willing to take strong action, even use force, in support of their cause, often political or social. (योद्धा)
• "Sectarian" - A sectarian is a person who rigidly follows the doctrines of a particular sect or party, often with an inability to tolerate other perspectives. (संप्रदायिक)
• "Zealot" - A zealot is a person who is fanatically dedicated to a cause, much like a fanatic.(धर्मांध)

The correct answer is 'Option 2'.

Key Points

• The sentence with no spelling error is: "He seemed to be taller than him."
• Here's why:
• "He semed to be taller than him." - This sentence has a spelling error. The correct spelling of "semed" should be "seemed."
• "He seemed to be taller than him." - This sentence is spelled correctly. The verb "seemed" is spelled right, and so are the other words in the sentence.
• "He seemed to be taler than him." - This sentence has a spelling error. The correct spelling of "taler" should be "taller."
• "He seemed to bee taller then him." - This sentence has two spelling errors. "Bee" should be "be," and "then" should be "than." In this context, "than" is used as a conjunction to make a comparison between two things, while "then" is used to denote time or sequence.

Therefore, the correct sentence is: "He seemed to be taller than him."