SSC CHSL Tier-1 2023: Official Paper (Held On: 17 Aug, 2023 Shift 4) (Previous Year Paper)

The paper after unfolded will be:

Hence, the correct answer is "Option 4".

Given Statements:

Some houses are trees.

All flowers are houses.

No vegetable is a flower.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some vegetables are houses is a possibility - True (Because, Some houses are not vegetables, but no information given about the remaining part between vegetables and houses, so it can be possible).

II. Some flowers are trees is a possibility - True (Because, No definite relation given between flowers and trees, so it can be possible).

III. No vegetable is a house - False (Because, some vegetables are definitely not houses, but no information given about the remaining part, so it can be possible only).

So, Both conclusions I and II follow.

Hence, the correct answer is "Option 3".

Given Equation: 4 B 18 D 5 C 9 A 9 = ?

BODMAS Rule:

Decoding the given information:

 

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 4 × 18 - 5 + 9 ÷ 9

⇒ 4 × 18 - 5 + 1

⇒ 72 - 5 + 1

⇒ 73 - 5 = 68

Hence, the correct option is "Option 4".

BODMAS Rule:

According to the given question:

 

Given equation : 88 + 8 - 17 × 16 ÷ 40 = ?

Now if '+' and '-' are interchanged with '÷' and '×' respectively then:

⇒ 88 ÷ 8 × 17 - 16 + 40 = ?

⇒ 11 × 17 - 16 + 40 = ?

⇒ 187 - 16 + 40 = ?

⇒ 227 - 16 = 211.

Hence, the correct answer is 'Option 4'.

The logic followed here is:

‘BALD' is coded as '7680' 

'DRAB' is coded as '8097’,

Here, 'BAD' is common in both the statement, so the remaining number is the code for the remaining letter.

So, 'L' will be coded as '6'. 

Hence, the correct answer is "Option 2".

The logic followed here is:

So, 'BJKSX' will be the correct alternative that will complete the series.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: The second word is Antonym of the first word.

Here:

Heat : Cold → Cold is antonym of Heat.

Similarly,

Demolish : Build → Build is antonym of Demolish.

Hence, the correct answer is "Option 4".

The logic followed here is:

For, 'RSPT is related to VWTX'

For, 'MNKO is related to QROS'

Similarly, for 'GHEI'

So, 'GHEI' will be related to 'KLIM'

Hence, the correct answer is "Option 3".

The logic followed here is:

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

Now,

Option 1) 2 - 6

⇒ 2 × (2 + 1) 

⇒ 2 × 3 = 6.

Option 2) 4 - 20

⇒ 4 × (4 + 1)  

⇒ 4 × 5 = 20.

Option 3) 5 - 30

⇒ 5 × (5 + 1)

⇒ 5 × 6 = 30.

Option 4) 8 - 75

⇒ 8 × (8 +1) 

⇒ 8 × 9 = 72 ≠ 75.

Hence, the correct option is "Option 4".

The logic followed here is:

Logic: Sum of the place value of all numbers = Code of the word.

'QUEZAL' is coded as '82'

⇒ 17 + 21 + 5 + 26 + 1 + 12 = 82.

'LUCKY' is coded as '72'

⇒ 12 + 21 + 3 + 11 + 25 = 72.

Similarly, for 'ADVERSE'

⇒ 1 + 4 + 22 + 5 + 18 + 19 + 5 = 74.

So, 'ADVERSE' will be coded as '74'.

Hence, the correct answer is "Option 3".

The logic followed here is:

For, 'GIEK is related to OQMS'

For, 'KMIO is related to SUQW'

Similarly, for 'EGCI'

So, 'EGCI' will be related to 'MOKQ'

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: 1st number × (1st number - 1) = 2nd number

Now,

Option 1) 5 : 20

→ 5 × (5 - 1) 

→ 5 × 4 = 20.

Option 2) 4 : 12

→ 4 × (4 - 1) 

→ 4 × 3 = 12.

Option 3) 7 : 42

→ 7 × (7 - 1)

→ 7 × 6 = 42.

Option 4) 6 : 36

→ 6 × (6 - 1)

→ 6 × 5 = 30 ≠ 36.

So, odd number pair is '6 : 36'.

Hence, the correct option is "Option 4".

The logic followed here is:

Option 1) WZB

Option 2) UWX

Option 3) ORT

Option 4) GJL

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

Hence, the correct answer is "Option 2".

Family Chart:

Decoding the Symbols:

 

Given: F × G - H ÷  I + J

It means: F is the Son of G, G is the Husband of H, H is the Mother of I, I is the Sister of J.

So, F is the 'Brother' of J.

Hence, the correct answer is "Option 1".

Given: 9 July 1978 is Sunday.

Now, 1978 to 1983 = 5 Years.

In 5 years, 1 Leap year (1980) and 4 ordinary years.

Total odd days from 9 July 1978 to 9 July 1983 = (1 × 2) + (4 × 1) = 2 + 4 = 6 days.

So, 9 July 1983 will be Sunday + 6 = Saturday.

Now, 9 July 1983 to 19 September 1983 = 22(July) + 31(Aug) + 19(Sept) = 72 days i.e., 10 weeks and 2 odd days.

Therefore, 19 September 1983 = Saturday + 2 = Monday.

Hence, the correct option is "Option 1".

The triangles are:

So, there are '28' triangles in the given figure.

Hence, the correct answer is "Option 2".

Family Chart:

Given: 

N is the brother of X.

X is the wife of M.

S is the daughter of M.

K is the brother of S.

P is the mother of N.

So, K is 'Daughter's son' of P.

Hence, the correct answer is "Option 2".

The logic followed here is:

So, '143' will replace the 'X' in the given series.

Hence, the correct answer is "Option 4".

The logic followed here is:

thus, "139" will replace the question mark in the given series.

Hence, the correct option is "Option 4".

The logic followed here is:

Logic: **(**1st number × 6) + 6 = 2nd number.

(15, 96) 

⇒ (15 × 6) + 6 

⇒ 90 + 6 = 96.

(35, 216)

⇒ (35 × 6) + 6​

⇒ 210 + 6 = 216.

Now, checking the options:

Option 1) (41 - 250)

⇒ (41 × 6) + 6

⇒ 246 + 6 = 252 ≠ 250.

Option 2) (18 - 102)

⇒ (18 × 6) + 6

⇒ 108 + 6 = 114 ≠ 102.

Option 3) (29, 180)

⇒ (29 × 6) + 6

⇒ 174 + 6 = 180.

Option 4) (21, 122)

⇒ (21 × 6) + 6

⇒ 126 + 6 = 132 ≠ 122.

Hence, the correct option is "Option 3"

The logic followed here is:

Given word: ACQUIRE

Now, arranged in reversed alphabetical order:

 

Here, 'Three'  letters 'A C R' will remain unchanged if each of the letters in the word ACQUIRE is arranged in alphabetical order.

Hence, the correct answer is "Option 1".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 3".

The logic followed here is:

Given Sequence:  A_CD_CDAC_AB_ABC

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) AACD → AACD / ACDA / CCAB / DABC

Option 2) AABB → AACD / ACDA / CBAB / BABC

Option 3) BBDD → ABCD / BCDA / CDAB / DABC

Here, option 3 followed a pattern, as the first letter is shifting to the last of the next letters pairs.

Option 4) BDBD → ABCD / DCDA / CBAB / DABC

Hence, the correct answer is "Option 3''

The logic followed here is:

Logic: One horizontal 'S' is getting changed it's shape in vertical form to the each next image.

 

So, option 4 will complete the series.

Hence, the correct answer is "Option 4".

The logic followed here is:

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

Given,

11 : 87 : 34

⇒ (11)² - 34 

⇒  121 - 34 = 87.

And, 6 : 8 : 28

⇒ (6)² - 28​

⇒  36 - 28 = 8.

Now, checking the options:

Option 1) 9 :25 : 54

⇒ (9)² - 54

⇒ 81 - 54 = 27 ≠ 25.

Option 2) 7 : 35 : 12

⇒ (7)² - 12

⇒ 49 - 12  = 37 ≠ 35.

Option 3) 8 : 19: 47

⇒  (8)² - 47

⇒  64 - 47 = 17 ≠ 19.

Option 4) 12 :81 : 63

⇒ (12)² - 63

⇒ 144 - 63 = 81.

 Hence, the correct option is "Option 4".

The correct answer is Amazon.

Key Points

• The Amazon River holds the distinction of being the world's largest river in terms of both discharge volume and drainage basin area, surpassing even the combined flow and basin areas of the Nile, Yangtze, and Mississippi Rivers.
• Additionally, it stands as the planet's largest drainage system by volume of flow and basin area.
• Throughout the year, the width of the Amazon River varies, with a range of 2 to 6 miles during the dry season (June to November) and expanding to up to 30 miles wide during the wet season (December through April).
• The Amazon River basin experiences substantial rainfall, particularly during the wet season, which significantly contributes to the river's formidable discharge volume.

Important Points

• The Congo River, spanning 4,700 kilometres (2,900 miles) in length, courses through west-central Africa. It ranks as the ninth-longest river globally and boasts the title of the world's deepest river, with recorded depths reaching approximately 220 meters (720 feet).
• The Amur River, also recognized as the Heilong River, stretches over 2,824 kilometres in length, delineating the boundary between Russia and China. It stands as one of Asia's longest rivers and is celebrated as one of the world's most extensive free-flowing waterways.
• The Nile, a significant river flowing northward in northeastern Africa, empties into the Mediterranean Sea.

The correct answer is In the men's 20 km race walk event, Akshdeep Singh clocked 1 hour 19 minutes 55 seconds, a new national record, to win the Silver medal.

Key Points

• Akshdeep Singh
• ​Akshdeep Singh, a trainee at SAI Bengaluru, took home the gold medal in the men's 20-kilometre racewalk in the Khelo India University Games in 2021.
• Before heavy rain stopped the athletic competition at the 2nd Khelo India University Games at the Sree Kanteerava Stadium, Akshdeep Singh of Punjabi University won the gold medal in the men's 20km race walk and Aparna Roy of Kerala won the women's 100m hurdles.

The correct answer is Newland's relation.

Key Points

• The law of octaves, also referred to as Newlands' Law of Octaves, posits that when elements are arranged in ascending order of their atomic masses, the properties of every eighth element resemble those of the first.
• In 1864, British scientist John Newlands endeavoured to organize the 62 known elements of his time. He arranged them based on increasing atomic weight and observed that every eighth element exhibited similar characteristics.
• For instance, taking the elements Li, Be, B, C, N, O, F, and Na, where lithium (Li) is the first element and sodium (Na) is the eighth, it was noted that the properties of sodium repeat those of lithium.

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Important Points

• Gravity is the force that attracts objects with mass toward each other. This force is directly proportional to the masses of the objects involved and inversely proportional to the square of the distance between them, meaning it weakens as the distance between the objects increases.
• The Doppler effect refers to the alteration in the frequency of a wave when both the source emitting the wave and the observer detecting it are in relative motion concerning each other. This effect is commonly observed in various phenomena, including sound waves and light waves.
• Coulomb's law delineates the magnitude of the electrostatic force between two charged objects. According to this law, the force between the charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

The correct answer is Chota Nagpur.

Key Points

• The Chota Nagpur Plateau in India has earned the moniker "storehouse of minerals" due to its abundant mineral wealth.
• Comprised primarily of igneous rocks dating back to the Pre-Cambrian era, this plateau boasts a rich array of resources including mica, bauxite, copper, limestone, iron ore, and coal.
• Spanning across the states of Jharkhand, Odisha, West Bengal, and Chhattisgarh, the Chota Nagpur Plateau sustains a populace whose primary occupation revolves around mining activities.
• The Chota Nagpur Dry Deciduous Forests provide a habitat for a range of endangered species, including tigers, sloth bears, leopards, blackbucks, Asian elephants, and chinkaras.
• Additionally, these forests harbour significant species of conservation concern, such as the lesser Florican and two species of hornbills.

Additional Information

• The expansive Deccan Plateau in southern India is situated between the Western Ghats and the Eastern Ghats, generally delineated as the peninsular area south of the Narmada River.
• The Western Ghats, also referred to as the Sahyadri mountain range, sprawls across an expanse of 160,000 km², stretching approximately 1,600 km parallel to the western coastline of the Indian peninsula. This range traverses through the states of Gujarat, Maharashtra, Goa, Karnataka, Kerala, and Tamil Nadu.
• The Himalayas, often simply called the Himalayas, form a formidable mountain range in Asia, acting as a natural barrier separating the plains of the Indian subcontinent from the Tibetan Plateau.

The correct answer is Tariffs and quotas.

Key Points

• Tariffs and quotas are consistent with the import substitution policy.
• Import substitution involves the practice of replacing imported goods with domestically produced alternatives.
• This strategy typically involves the implementation of tariffs and quotas to shield domestic industries from foreign competition.
• The inward-looking trade approach aims to bolster domestic production by reducing reliance on imports through protective measures.
• Its impact on domestic industries is geared towards fostering self-sufficiency by promoting the development and expansion of domestic manufacturing capabilities.

Important Points

• Tariffs are duties imposed by governments on specific types of imported goods, while quotas are restrictions placed on the quantity of a particular good that can be imported into a country.
• Capital account convertibility is a characteristic of a nation's financial system that allows for the unrestricted conversion of local financial assets into foreign financial assets, typically at exchange rates determined by market forces.
• In a flexible exchange rate system, the value of a currency is determined by the supply and demand dynamics within the market for that currency.
• Current account convertibility refers to the freedom to exchange domestic currency for foreign currency and vice versa, primarily to conduct trade in goods and services.

The correct answer is Both A and B.

Key Points

• Both Indian citizens working in foreign embassies within India and the Ambassador representing India abroad are classified as normal residents of India.
• A normal resident in the context of India is defined as an individual who resides or is situated within the country and engages in fundamental economic activities, including earning, spending, and accruing wealth from that location.
• Additionally, normal residents possess the right to reside and work within the country without constraints and may qualify for specific entitlements or privileges.
• Indian citizens employed in foreign embassies within India are categorized as normal residents due to their citizenship, residence, and economic contributions within India.
• Their activities, including earning income and spending, contribute to the Indian economy.
• Similarly, the Ambassador representing India in foreign countries is considered a normal resident of India despite being stationed abroad, as their official duties and economic ties remain linked to India.

Additional Information

• A resident of India refers to an individual who resides within the geographical boundaries of India for a substantial period.
• This term encompasses both Indian citizens as well as foreigners who live in India for an extended duration.
• Residents of India typically engage in various economic activities within the country, including earning income, spending money on goods and services, and potentially accumulating wealth.

The correct answer is Barter exchanges require a double coincidence of wants.

Key Points

• Barter exchanges require a double coincidence of wants is the most problematic and primary difficulty of barter exchanges as against money-based exchanges.
• Barter exchanges necessitate a double coincidence of wants, wherein both parties must possess items desired by the other and mutually consent to trade.
• In such an economy, individuals engage in the exchange of goods or services, relying on the alignment of desires between trading partners.
• However, barter transactions are inherently inefficient due to the requisite agreement between parties.
• For instance, if one person wishes to swap their laptop for a mobile phone, both parties must reach a consensus on the terms and conditions of the exchange.

Important Points

• Barter is the practice of exchanging goods or services directly between two or more parties, without involving money or monetary instruments like credit cards.
• Essentially, it entails one party providing a good or service in exchange for another good or service from a different party.
• Bartering operates on a straightforward premise: individuals negotiate to establish the value of their respective goods and services, then offer them to each other in a mutually agreed-upon exchange.
• This system predates the existence of traditional currency, representing one of the earliest forms of trade and commerce in human history.

The correct answer is Kaushalya Reddy.

Key Points

• Kaushalya Reddy is a renowned figure in the field of Kuchipudi classical dance, showcasing expertise and dedication throughout her career.
• As a professional performer and educator, she has made significant contributions to the art form, particularly through her role at the Natya Tarangini Institute of Kuchipudi Dance in New Delhi.
• Reddy's commitment to preserving and promoting Kuchipudi is evident in her teachings and performances, inspiring countless students and audiences alike.
• Her accomplishments have been recognized internationally, with accolades such as the Yuva Ratna Award from the Government of Mauritius.
• Additionally, Reddy's influence extends beyond national borders, as evidenced by her associations with esteemed institutions like Sadhana Sangama International in Portland, USA, and the Meditation Centre in Minneapolis, USA.

Important Points

• Radha Sridhar was honoured with the Sangeet Natak Akademi Award in 2018 for her exceptional contributions to Bharatanatyam.
• Surupa Sen, a renowned Odissi dancer and choreographer, has resided and practised her craft at Nrityagram, a rural dance community located in Karnataka.
• Anupama Hoskere, an esteemed puppeteer, serves as the Founder-Director of Dhaatu Puppet Theater in Bengaluru.

Additional Information

• Kuchipudi, one of the eight prominent Indian classical dance forms, originates from the village of Kuchipudi in the state of Andhra Pradesh, India.
• It is a dance-drama performance deeply rooted in the ancient Hindu Sanskrit text Natya Shastra.
• Like other classical dances of India, Kuchipudi evolved as a religious art associated with itinerant storytellers, temples, and spiritual traditions. Originally, Kuchipudi was exclusively performed by all-male troupes.
• In traditional performances, male dancers would portray female roles while adorned in Agnivastra, also known as Bagalbandi, and wearing a dhoti, a single pleated garment draped around the waist.

The correct answer is Chota Nagpur Plateau.

Key Points

• The Chota Nagpur plateau stands out as the hub of iron and steel industries in India, primarily due to its abundant reserves of high-grade hematite iron ore found in places like Noamundi, Gua, Kolhan, Dharwar, and Budabaru.
• This region also boasts extensive coal deposits, further bolstering its appeal for iron and steel production.
• Most of the iron and steel plants are strategically situated across four states — West Bengal, Jharkhand, Odisha, and Chhattisgarh.
• Key steel-producing centers such as Bhilai, Durgapur, Burnpur, Jamshedpur, Rourkela, and Bokaro are concentrated in this area.
• Additionally, Bhadravati and Vijay Nagar in Karnataka, Vishakhapatnam in Andhra Pradesh, and Salem in Tamil Nadu emerge as significant steel hubs in southern India.
• The growth of the iron and steel industry in this region has been fueled by factors such as abundant raw materials, a readily available workforce, efficient transportation networks, and access to lucrative markets.

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Important Points

• The Chota Nagpur Plateau, situated in eastern India, spans across significant portions of Jharkhand state along with adjoining areas of Chhattisgarh, Odisha, West Bengal, and Bihar.
• To the north and east of the plateau lies the vast Indo-Gangetic plain, while the basin of the Mahanadi river extends to the south.
• Covering an approximate area of 65,000 square kilometers, the Chota Nagpur Plateau serves as a prominent geographical feature in the region.

Additional Information

• The Shillong Plateau, situated in eastern Meghalaya state of India, is defined by its western, northern, and southern ridges, which correspond to the Garo, Khasi, and Jaintia Hills respectively. In southern India, the expansive
• Deccan Plateau lies between the Western Ghats and the Eastern Ghats. This plateau is generally described as the peninsular region extending south of the Narmada River.
• The Malwa Plateau, located in north-central India, is a volcanic plateau covering parts of Madhya Pradesh, Gujarat, and Rajasthan. Encompassing an area of 83,535 square kilometers, it boasts an average elevation of 500 meters above sea level.

The correct answer is Warren Hastings.

Key Points

• Nand Kumar accused Warren Hastings, then Governor General of Bengal, of bribery and corruption, leading to a famous case often referred to as the "First Judicial Murder of Colonial India" or the 'Black Case.'
• This legal dispute unfolded between Lord Warren Hastings and Raja Nand Kumar, a Hindu Brahmin Zamindar.
• Allegations were exchanged between both parties, resulting in contentious situations that obscured the principles of a fair trial.
• The case exemplifies a dark chapter in the judiciary, highlighting how abuse of power and authority led to the wrongful conviction and subsequent death sentence of Raja Nand Kumar.
• The legal dispute between Raja Nand Kumar and Warren Hastings traces its origins back to the passing of the Regulating Act by the British in 1773.
• One significant provision of this act was the establishment of Supreme Courts in Kolkata (then Calcutta), each presided over by four English judges.

Important Points

• Maharaja Nandakumar served as an Indian tax collector for various regions in what is now modern-day West Bengal.
• Born in Bhadrapur, which is currently located in Birbhum, he holds the unfortunate distinction of being the first Indian to be executed by hanging.
• Nandakumar was appointed by the East India Company to the position of Dewan (tax collector) for Burdwan, Nadia, and Hooghly in 1764, following the removal of Warren Hastings from the same post.

Additional Information

• Warren Hastings, on the other hand, was a British colonial administrator who held several key positions in India.
• He served as the first Governor of the Presidency of Fort William (Bengal) and was also the head of the Supreme Council of Bengal, subsequently becoming the first Governor-General of Bengal from 1772 to 1785.
• Hastings, along with Robert Clive, is credited with laying the groundwork for the British Empire in India.

The correct answer is 1875.

Key Points

• Swami Dayanand Saraswati established Arya Samaj in 1875.
• The Arya Samaj is a monotheistic Hindu reform movement in India that advocates for values and practices rooted in the belief in the absolute authority of the Vedas.
• Founded by the sannyasi (ascetic) Dayanand Saraswati in the 1870s, it was the first Hindu organization to engage in proselytization within Hinduism.
• Since the 1800s, the Arya Samaj has also been involved in advancing the civil rights movement in India.
• The formal establishment date of the Arya Samaj is recognized as June 24, 1877, when the movement expanded beyond its regional roots in Punjab and gained prominence in Lahore.

Important Points

• ​Dayanand Saraswati, an Indian philosopher and social leader, is renowned as the founder of the Arya Samaj, a reform movement within Hinduism.
• His influential book "Satyarth Prakash" serves as a significant text on Vedic philosophy, elucidating various concepts and human responsibilities.
• In 1876, he issued the call for Swaraj, advocating for "India for Indians," a sentiment later echoed by Lokmanya Tilak.
• Rejecting idolatry and ritualistic practices, Saraswati focused on revitalizing Vedic principles.
• Both philosopher and former President of India, S. Radhakrishnan, and Sri Aurobindo recognized him as a key figure in shaping modern India.

The correct answer is All of a, b and c.

Key Points

• A transfer payment is a payment made by a government for which no goods or services are received in return.
• Unemployment allowances:
• This is a transfer payment because it is typically provided by the government to individuals who are unemployed and seeking employment.
• No goods or services are exchanged directly for this payment.
• Scholarships:
• While scholarships are payments made to individuals, they are often made by organizations, institutions, or individuals themselves, rather than directly by the government.
• Scholarships are typically awarded to support education and are often based on merit, need, or some other criteria. As such, they may not always be classified as transfer payments, especially if they are funded privately.
• Retirement pension:
• It is a form of deferred compensation for services already rendered by employees during their working years.
• Therefore, it is considered an earned benefit rather than a transfer payment.

Important Points

• A transfer payment is a redistribution of wealth and income that occurs when the government pays for something without expecting anything in return, such as products or services.
• Since these payments don't directly use resources or produce output, they are regarded as non-exhaustive.
• Welfare, financial aid, social security, and government subsidies for certain industries are a few examples of transfer payments.

The correct answer is P = U/C.

Key Points ​

• P = U/C verified by American scientists Nichols and Hull in 1903 by measuring the radiation pressure of visible light is the equation proposed by James Clerk Maxwell.
• This equation relates the intensity of light to its pressure.
• It is known as Maxwell's stress tensor equation, which is a part of Maxwell's equations of electromagnetism.
• The equation P = U/C​ is known as the radiation pressure formula.
• In this equation: 
• P represents the radiation pressure,
• U represents the energy density of radiation, and
• C represents the speed of light in a vacuum.
• This equation describes the pressure exerted by electromagnetic radiation (such as light) on a surface or object. It's an important equation in physics, particularly in fields like optics and astrodynamics.

Important Points

• The idea of radiation pressure emerges from the momentum exchange that takes place between the item and the electromagnetic field.
• Since electromagnetic waves carry momentum during transit, this force is visible.
• The mechanical pressure that results from the interchange of momentum between an item and the electromagnetic field is known as radiation pressure, and it can be applied to any surface. In this instance, photons striking the object's surface cause a momentum transfer.
• Any surface's radiation pressure is influenced by its characteristics and the light source's intensity.

The correct answer is i - b, ii - d, iii - a, iv - c.

Key Points

• M1 represents the narrowest measure of money supply and includes:
• Currency in circulation (C)
• Demand deposits (Dd)
• Other deposits (Od)
• M2 is a broader measure of money supply and includes all components of M1 plus:
• Time deposits (Td)
• Savings deposits (S)
• M3 is an even broader measure and includes all components of M2 plus:
• Term deposits of non-banking public (TPOd)
• M4 is the broadest measure of money supply and encompasses all components of M3 plus:
• Post office savings bank deposits (POSBd)

Important Points

• The money supply refers to the aggregate sum of money circulating within an economy, encompassing physical currency, coins, and funds held in bank accounts.
• It is typically understood as a collection of secure assets accessible to households and businesses for conducting transactions or as short-term investment vehicles.

The correct answer is Chhattisgarh. 

Key Points

• The Sheorinarayan Fair, a renowned festival in Chhattisgarh, takes place annually during February's Magh Purnima.
• It attracts a large gathering, both local and international, to the Sheorinarayan Temple dedicated to Lord Rama, the focal point of the festivities.
• This event showcases the vibrant cultural heritage and traditional festivals of Chhattisgarh.
• Throughout the festival, the Sheorinarayan Temple is adorned with intricate decorations of lights and flowers.
• The temple grounds transform into bustling marketplaces, offering a diverse array of traditional crafts to visitors from across India.
• The atmosphere is brimming with joyous celebrations, making it a memorable occasion for all attendees.

Additional Information

• Chhattisgarh is a landlocked state located in Central India.
• It is the ninth-largest state by area and the seventeenth most populous in India, with approximately 30 million residents.
• Chhattisgarh shares its borders with seven other states: Uttar Pradesh to the north, Madhya Pradesh to the northwest, Maharashtra to the southwest, Jharkhand to the northeast, Odisha to the east, and Andhra Pradesh and Telangana to the south.
• Formerly a part of Madhya Pradesh, Chhattisgarh was granted statehood on 1 November 2000, with Raipur as its designated capital.

The correct answer is Faizabad.

Key Points

• The Dr. Bhimrao Ambedkar International Sports Stadium, located on the Ayodhya-Sultanpur road in the Ayodhya district of Uttar Pradesh, India, is a versatile facility designed to accommodate various sports and activities.
• It forms a key component of a large-scale project aimed at developing a sports complex in the region.
• Situated near the intersection of NH-330 and the Ayodhya ring-road, just a short distance from Ayodhya Airport, the stadium adheres to international standards.
• It is equipped with amenities such as a multipurpose hall and a swimming pool, making it one of the premier sports venues in Uttar Pradesh.

Additional Information

• Bhimrao Ramji Ambedkar, born on April 14, 1891, and passed away on December 6, 1956, was an eminent Indian figure renowned for his roles as a jurist, economist, social reformer, and political leader.
• He chaired the committee responsible for drafting the Constitution of India during the Constituent Assembly debates and later served as the Law and Justice minister in Jawaharlal Nehru's inaugural cabinet.
• Ambedkar's influence extended to inspiring the Dalit Buddhist movement following his decision to renounce Hinduism. In recognition of his contributions, he was posthumously honored with the Bharat Ratna, India's highest civilian award, in 1990.
• His followers pay homage to him with the salutation "Jai Bhim" (meaning "Hail Bhim"), while he is affectionately referred to as Babasaheb, signifying "Respected Father".

The correct answer is Article 24.

Key Points

• Article 24 of the Indian Constitution addresses the prohibition of child labour, aimed at safeguarding the well-being and rights of children.
• Its primary objective is to prevent the exploitation of children by prohibiting their employment in hazardous occupations or processes.
• According to Article 24, no child below the age of fourteen years can be employed in factories, mines, or any other hazardous employment. This measure is implemented to ensure the protection of children's health, development, and access to education.
• While Article 24 establishes a general prohibition, it also allows for certain exceptions. These exceptions include situations where children engage in non-hazardous work within their family, participate in work as part of their school curriculum, or undertake harmless or innocent occupations.
• Additionally, Article 24 grants the government the authority to enact legislation specifying the occupations and processes deemed hazardous for children. This provision enables the government to establish necessary regulations and restrictions to effectively enforce the prohibition of child labour.

Important Points

• Article 22 of the Indian Constitution addresses the protection against arrest and detention in specific circumstances. This provision applies to both citizens and non-citizens and aims to provide procedural safeguards during arrests. The fundamental principle underlying this right is to prevent arbitrary arrests and detention, ensuring that individuals are afforded due process of law.
• In contrast, Article 19 safeguards six fundamental rights related to freedom, including speech and expression, assembly, association, movement, residence, and profession.
• On the other hand, Article 20 focuses on protecting citizens concerning convictions for offenses. It offers three types of protection against the State, ensuring fairness and justice in legal proceedings.

The correct answer is Pakhawaj.

Key Points

• Totaram Sharma is associated with Pakhawaj.
• The pakhavaj is a type of double-headed drum with a barrel shape that originated in the Indian subcontinent.
• It is the oldest type of double-sided drum and is related to the mridangam in Southern India, the kendang in Maritime Southeast Asia, and other double-headed drums from South Asia.
• It is the most often used percussion instrument in the dhrupad style of Indian classical music.
• It is also occasionally employed as a rhythm accompaniment for performances of several other musical genres and dances, such as kathak, Odissi, and Marathi.
• Although they are extremely rare, clay replicas of it are still available. It was initially constructed of clay.

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Important Points

• The tanpura, originating in India, is a plucked, four-stringed instrument with a long neck. It is commonly used in Indian music and bears a resemblance to simplified sitars or similar lute-like instruments. Typically, the tanpura is crafted from a gourd or pumpkin.
• Panchavadyam, translating to "orchestra of five instruments," is an art form primarily associated with temples in Kerala. It involves a combination of five instruments, including four percussion instruments — timila, maddalam, ilathalam, and idakka — and one wind instrument, kombu.
• The sarangi, utilized in traditional South Asian music, is a bowed instrument characterized by its short neck and three strings.

The correct answer is Kakatiya.

Key Points

• The founders of the Vijayanagara Empire were the feudatories Kakatiya dynasty.
• Before establishing the Vijayanagara Empire in 1336, Harihara and Bukka, who were initially feudatories of the Kakatiyas of Warangal, served in administrative roles for both the Kakatiya and Kampili kingdoms.
• Following the Muslim conquest of Kakatiya in 1323, they sought refuge in Kampili, where they eventually rose to become ministers.
• The Vijayanagara Empire, founded by Harihara and Bukka, emerged after their time in Kampili.
• Over its history, the empire saw the rule of significant dynasties including the Sangama, Saluva, Tuluva, and Aravidu.

Important Points

• The Hoysala Empire, a significant Kannadiga power in the Indian subcontinent, held sway over much of present-day Karnataka from the 10th to the 14th centuries. Initially headquartered in Belur, the capital later shifted to Halebidu.
• The Pandyan dynasty, also known as the Pandyas of Madurai, stood as an ancient Tamil dynasty in South India, counted among the prominent kingdoms of Tamilakam alongside the Pallavas, the Cholas, and the Cheras.
• Originating from southern India, the Chola dynasty governed the expansive Chola Empire, a prominent maritime power. The earliest verifiable mentions of the Chola date back to inscriptions dating to the 3rd century BCE during the Maurya empire under Ashoka's reign.

The correct answer is Odissi.

Key Points

• Pakhawaj syllables are rhythmically chanted as the dance gradually transitions from slow to rapid sequences, culminating in a climactic moment when the dancer offers their final respects.
• An Odissi ensemble typically comprises a pakhawaj player (often the Guru), a vocalist, a flautist, a sitar or violinist, and a manjira player.
• The dancer adorns themselves with intricate Odiya silver jewellery and a distinctive hairstyle. The saree, commonly tailored nowadays, is distinctive to the Odissi tradition.
• In each performance, even in modern Odissi dance, there is a reiteration of the spiritual quest for liberation or moksha, echoing the traditions of the devadasis and maharis who sought enlightenment through dance.

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Important Points

• Odissi, also known as Orissi in ancient texts, is a prominent classical dance form with roots tracing back to the temples of Odisha, a coastal state in eastern India.
• Odissi was predominantly performed by female artists and served as a medium to convey religious narratives and spiritual concepts, particularly those associated with Vaishnavism.
• These stories were conveyed through songs composed in accordance with the ragas and talas of Odissi music by poets from the region.
• Additionally, Odissi performances often encompass themes from other traditions, including tales related to Hindu deities such as Shiva, Surya, and various Hindu goddesses associated with Shaktism.

Additional Information

• Manipuri, also known as the Manipuri Raas Leela, is a jagoi and counts among the prominent Indian classical dance styles, originating from the state of Manipur.
• Kathak, one of the eight principal Indian classical dances, traces its origins to the wandering minstrels of ancient northern India, known as Kathakars or storytellers.
• Kathakali, a traditional form of classical Indian dance, stands as one of the oldest theater forms still in practice. It falls into the category of "story game" artistry, distinguished by the intricately colorful makeup and costumes worn by the traditional male actor-dancers.

The correct answer is Dr. KM Munshi.

Key Points

• Kanhaiyalal Maneklal Munshi served on the committee that B. R. Ambedkar chaired to create the Indian Constitution as well as the ad hoc Flag Committee that chose the country's flag in August 1947.
• Munshi, also known by his pen name Ghanshyam Vyas, was a Gujarati writer, politician, and activist for Indian independence. Originally a lawyer, he eventually became a politician and novelist. His name is widely recognized in Gujarati literature.
• In 1938, he established the educational trust Bharatiya Vidya Bhavan.
• From 1952 to 1957, Munshi served over Uttar Pradesh as governor.
• Munshi founded the Akhand Hindustan movement in 1959 after severing ties with the Nehru-led, socialist Congress Party.

Important Points

• Benegal Narsing Rau was an Indian statesman, jurist, civil servant, and diplomat who played a significant part in writing the country's constitution. He served as the Constituent Assembly's constitutional advisor.
• Indian politician Tiruvellore Thattai Krishnamachari held the position of Finance Minister twice, from 1956 to 1958 and 1964 to 1966.
• In addition to serving as the 23rd dewan of Mysore from 1941 to 1945, Sir Nyapathi Madhava Rau was an Indian civil servant, administrator, and statesman. He also participated in the Constituent Assembly's Drafting Committee, which was tasked with creating the Indian Constitution.

The correct answer is 75.

Key Points

• Lovlina Borgohain clinched the gold medal at the World Women’s Boxing Championship in New Delhi by defeating Australia’s Caitlin Parker in the 75 kg final.
• Last year, Lovlina suffered a loss in the quarterfinals of the 66 to 70 kg (light-middleweight) category at the Commonwealth Games.
• Prior to this achievement, she secured bronze medals at the World Championships in 2018 and 2019.
• Despite participating, she failed to secure a medal at the 2018 Commonwealth Games.
• This victory marks Lovlina's first gold medal at the World Championship, adding to her previous accomplishments, including a bronze at the Tokyo Olympics.

Important Points

• At the 2018 Commonwealth Games, amateur boxer Caitlin Parker of Australia took home a silver medal.
• She participated in the 2020 Summer Olympics and took home a bronze medal at the 2014 Youth Olympics.

The correct answer is 70.

Key Points

• In March 2023, the Pension Fund Regulatory and Development Authority (PFRDA) amended the 2015 PFRDA Regulation to increase the age limit for the Ombudsman from 65 to 70 years.
• Under the Pension Fund Regulatory and Development Authority (Redressal of Subscriber Grievance) Regulations 2015, the maximum age limit for Ombudsman was set at 65 years.
• However, a recent gazette notification dated 27 March announced an amendment by the PFRDA, changing the upper age limit for the Ombudsman from 65 to 70 years.
• The Ombudsman, appointed by PFRDA, is tasked with receiving, assessing, and facilitating the resolution of complaints or grievances falling under the regulations.
• An individual selected as an Ombudsman serves a term of three years and may be considered for reappointment for an additional two years.

Additional Information

• The Pension Fund Regulatory and Development Authority (PFRDA) serves as the regulatory authority overseeing pensions in India, operating within the purview of the Ministry of Finance under the Government of India.
• Its establishment in 2003 stemmed from the recommendations outlined in the OASIS report commissioned by the Indian government, coinciding with the inception of the Indian National Pension Scheme.

The correct answer is 67.02%.

Key Points

• With a literacy rate of approximately 67.02%, it suggests that out of every 100 individuals aged seven and above in Andhra Pradesh, about 67 were literate, meaning they possessed the ability to read and write with understanding.
• Andhra Pradesh's population, according to data from the 2011 Census, is 8.46 crore, up from 7.62 crore in the 2001 Census. As to the latest census data, Andhra Pradesh has a total population of 84,580,777, with 42,442,146 males and 42,138,631 females, respectively.
• Andhra Pradesh has a lower sex ratio than the national average of 940, with 993 females for every 1000 males, according to the most recent census. In Andhra Pradesh in 2001, there were 978 females for every 1000 males.

Additional Information

• According to the 2011 Indian Census, Andhra Pradesh's literacy rate is the proportion of the state's population that is seven years of age or older and can read and write in any language with comprehension.
• According to the 2011 census, 74.04% of Indians are literate. Male literacy rates are 82.14% while female literacy rates are 65.46%.

The correct answer is 1855.

Key Points

• Rudolf Ludwig Karl Virchow formulated his famous aphorism "Omnis cellula - e cellula" in 1855.
• This statement, which translates to "Every cell originates from another existing cell like it," became a foundational concept in the development of the cell theory, emphasizing the continuity of cellular life and the principle that cells arise only from pre-existing cells.
• German physician, anthropologist, pathologist, prehistorian, biologist, writer, editor, and politician Rudolf Ludwig Carl Virchow was born in 1896.
• In addition to being the creator of social medicine and referred to by his peers as the "Pope of medicine," he is recognized as "the father of modern pathology."

Important Points

• The cell theory, established in the mid-19th century, revolutionized biology by providing a unifying framework for understanding life.
• It asserts that all living organisms are composed of cells, which are the basic structural and functional units of life.
• Furthermore, cells are the fundamental building blocks of all organisms, and new cells arise only from pre-existing cells through cell division.
• This theory laid the foundation for modern biology, guiding research and shaping our understanding of cellular processes and the complexities of life itself.

Calculation:

Laptop sold by wholesaler 1 and wholesaler 2 together on Thursday = 24 + 14 = 38

Laptop sold by wholesaler 3 on Friday = 19

Required percentage = (38/19) × 100 = 200

∴ The required answer is 200%.

Given:

Base of the triangle = 12 cm

Hypotenuse of the triangle = 13 cm

Concept used:

Area of a right angle triangle = (1/2) × perpendicular × base

Calculation:

Let the perpendicular be 'x' cm.

x² + 12² = 13²

⇒ x2 + 144 = 169

⇒ x2 = 25

⇒ x = 5

So, the perpendicular of the right angle = 5 cm

Now,

Area of the triangle = (1/2) × 12 × 5 = 30 cm²

∴ The area of the triangle is 30 cm².

Given:

tan(50 + θ) - Cot(40 - θ)

Concept used:

cot(90° - θ) = tanθ

Calculation:

tan(50 + θ) - Cot(40 - θ)

⇒ tan(50 + θ) - Cot(90 - 40 + θ)

⇒ tan(50 + θ) - tan(50 + θ)

⇒ 0

∴ The required answer is 0.

Given:

In 2021 salary increased by 40%

In 2022 salary decreased by 15%

Calculation:

Let the salary of Sam in 2020 be 100a

So, the salary of Sam in 2022 = 100a × 1.4 × 0.85 = 119a

So, increased salary = 119a - 100a = 19a

Percentage of increase in salary of Sam = (19a/100a) × 100 = 19

∴ The net change in his salary is 19% increase.

Given:

Radius of the rod = 5 cm

Lenght of the rod = 52 cm

Lenght of the wire = 100 cm

Concept used:

Volume of a cylinder = πr² × h

Here, r = radius, and h = height or length

Calculation:

Since both wire and rod are an example of cylinder, then

Volume of the rod = Volume of the wire,

Let the radius of the wire be 'x'

According to the question,

π × 5² × 52 = π × x² × 100

⇒ 52 = 4x2

⇒ x2 = 13

⇒ x = √13

So, the radius of the wire = √13 cm

∴ The radius of the wire (in cm) is √13.

Given:

(y2 + $\frac{1}{y^2}$) = 74

Concept used:

$(a - \frac{1}{a})^2 = a^2 + \frac{1}{a^2}-2$

Calculation:

(y2 + $\frac{1}{y^2}$) = 74

By subtracting 2 from both sides we get,

y2 + $\frac{1}{y^2}$ - 2 = 74 - 2

⇒ $(y - \frac{1}{y})^2$ = 72

⇒ (y - $\frac{1}{y}$) = $6\sqrt{2}$

∴ The required answer is $6\sqrt{2}$.

Given:

Amount = 45P

Time = 110 years

Formula used:

SI = (PRT/100)

Amount = (PRT/100) + P

Calculation:

45P = (PR × 11/10) + P

⇒ 44P = (PR × 11/10)

⇒ R = 40%

According to the question,

Amount = 23P

So,

23P = (40PT/100) + P

⇒ 22P = (2PT/5)

⇒ T = 55 years

∴  The sum will become 23 times is 55 years.

Given:

Two trains 320 m and 205 m in length are running towards each other on parallel lines. 

Speed of the two trains are 70 kmph and 56 kmph, respectively

Concept used:

When two objects run in opposite directions then their relative speed = Sum of their speeds

Calculation:

Relative speed of the trains = 70 + 56 = 126 km/h

Relative speed of the train in m/s = 126 × (5/18) = 35 m/s

Required time taken to cover the distance = (320 + 205) ÷ 35 = 525 ÷ 35

⇒ 15 seconds

∴ The time they will take to cross each other is 15 (in seconds).

Given:

A complete the work in the same time as B + C work together

A + B can complete a work = 10 days

C can alone complete a work = 50 days

Formula Used:

Total Work = Efficiency × Time

Calculation:

LCM of (10, 50) = 50 units = Total Work

Efficiency of C = 1 unit/day

Efficiency of A + B = 5 unit/day

Let the efficiency of B = y

Efficiency of B + C = Efficiency of A

⇒ y + 1 = A

⇒ y + 1 = 5 - y          (A + B = 5 ⇒ A = 5 - B)

⇒ 2y = 4 

⇒ y = 2

Time taken by B to complete the work = total work/efficiency

⇒ 50 / 2 = 25 days

∴ The time taken by B to complete the work is 25 days.

Given:

(1 - sin2A) cosec2A

Concept used:

sin2θ + cos²θ = 1

cotθ = (cosθ/sinθ)

Calculation:

(1 - sin2A) cosec2A

⇒ cos2A cosec2A

⇒ cos2A × (1/sin2A)

⇒ cot2A

∴ The required answer is cot2A.

Given:

3x - 2y = 3 and xy = 9

Concept used:

If (a - b) = x, then (a + b) = √(x² + 4ab)

Calculation:

3x + 2y = √(3² + 4 × 9 × 2 × 3)

⇒ 3x + 2y = √225 = 15

∴ The required answer is 15.

Shortcut Trick 

Let x = y = 3,

So, 3x - 2y = 9 - 6 = 3

Again, 3x + 2y = 9 + 6 = 15

Calculation:

Total number of girls in Hindi = 110 × 0.6 = 66

Total number of boys in Hindi = 110 × 0.4 = 44

Total number of girls in English = 70 × 0.5 = 35

Total number of boys in English = 70 × 0.5 = 35

Total number of girls in Physics = 50 × 0.3 = 15

Total number of boys in Physics = 50 × 0.7 = 35

Total number of girls in Chemistry = 40 × 0.8 = 32

Total number of boys in Chemistry = 40 × 0.2 = 8

Total number of girls in Mathematics = 80 × 0.2 = 16

Total number of boys in Mathematics = 80 × 0.8 = 64

Total number of girls in Computers = 90 × 0.4 = 36

Total number of boys in Computers = 90 × 0.6 = 54

Total number of girls = 66 + 35 + 15 + 32 + 16 + 36 = 200

Total number of boys = 44 + 35 + 35 + 8 + 64 + 54 = 240

Ratio = 200 : 240 = 5 : 6

∴ The required answer is 5 : 6.

Given:

18 × [24 ÷ 70 × {25 × 49 ÷ (5 × 7)}]

Concept used:

Calculation:

18 × [24 ÷ 70 × {25 × 49 ÷ (5 × 7)}]

⇒ 18 × [24 ÷ 70 × {25 × 49 ÷ 35}]

⇒ 18 × [24 ÷ 70 × 35]

⇒ 18 × 12

⇒ 216

∴ The required answer is 216.

Given:

Initial quantity of mixture = 40 litres

Initial ratio of milk to water = 7 : 3

Calculation:

Milk in mixture = (7/10) × 40 = 28 litres

Water in mixture = 40 – 28 = 12 litres

Let x liters of water be mixed to make water 60% of the mixture.

(12 + x) = (40 + x) × 0.6

⇒ 12 + x = 24 + 0.6x

⇒ 0.4x = 12

⇒ x = 30

∴ 30 litres of water should be added.

∴ The required quantity of water to be added is 30 litres.

Given:

AB = 9 cm, BC = 40 cm and AC = 41 cm

Concept used:

Circumradius of a triangle = (abc/4Δ)

Here, a, b, and c are the lengths of the sides of the triangle

Calculation:

S = (9 + 40 + 41)/2 = 45 cm

Area of the triangle = √{45(45 - 9)(45 - 40)(45 - 41)}

⇒ √{45 × 36 × 5 × 4}

⇒ √{32400}

⇒ 180 cm²

Now,

Circumradius = $\frac{9 \times 40 \times41}{4 \times 180}=\frac{41}{2}$

⇒ 20$\frac{1}{2}$ cm

∴ The circum-radius of a triangle is 20$\frac{1}{2}$ cm.

Given:

The compound interest accrued on a sum of Rs. 20,000 at the end of 2 years compounded annually is Rs. 2,050.

Concept used:

$Amount = P(1+\frac{r}{100})^n$

Here, p = principal, r = rate, and n = no. of years

Calculation:

Amount received after two years = 20,000 + 2,050 = 22,050

According to the question,

$22,050 = 20,000(1+\frac{r}{100})^2$

⇒ $\frac{22,050}{20,000} = (1+\frac{r}{100})^2$

⇒ $\frac{441}{400} = (1+\frac{r}{100})^2$

⇒ $(\frac{21}{20})^2 = (1+\frac{r}{100})^2$

⇒ $\frac{21}{20} = 1+\frac{r}{100}$

⇒ $\frac{21}{20} = \frac{100;+;r}{100}$

⇒ 105 = 100 + r

⇒ r = 5

So, the rate of interest = 5%

Now,

$A = 20,000(1+\frac{5}{100})^3$

⇒ $A = 20,000(\frac{21}{20})^3$

⇒ $A = 23,152.5$

So, the interest = 23,152.5 - 20,000 = 3,152.5

∴ The compound interest at the end of the 3rd year is 3,152.5.

Shortcut Trick

Given tan 15° = 2 − √3, then cot 15° = 1/tan 15° = 2 + √3.

Since 75° + 15° = 90°, we have cot 75° = tan 15° and tan 75° = cot 15°.

Expression = tan² 15° + cot² 15°.

Using a² + b² = (a + b)² − 2ab, where a+b = (2−√3) + (2+√3) = 4 and ab = 1.

Result = 4² − 2(1) = 16 − 2 = 14.

∴ The correct answer is 14.

Alternate Method

Given: tan 15° = 2 − √3

Formula Used: tan(90° − θ) = cot θ | cot(90° − θ) = tan θ | (a − b)² + (a + b)² = 2(a² + b²)

⇒ cot 15° = 1 / (2 − √3) × (2 + √3) / (2 + √3) = 2 + √3

⇒ cot 75° = cot(90° − 15°) = tan 15° = 2 − √3

⇒ tan 75° = tan(90° − 15°) = cot 15° = 2 + √3

⇒ Expression = (2 − √3)(2 − √3) + (2 + √3)(2 + √3)

⇒ Expression = (2 − √3)² + (2 + √3)²

⇒ Expression = (4 + 3 − 4√3) + (4 + 3 + 4√3)

⇒ Expression = 7 − 4√3 + 7 + 4√3 = 14

∴ The correct answer is 14.

Additional Information

Complementary Angles

For any angle θ, sin θ = cos(90° − θ), tan θ = cot(90° − θ), and sec θ = cosec(90° − θ).

Trigonometric Values of 15° and 75°

tan 15° = cot 75° = 2 − √3 and tan 75° = cot 15° = 2 + √3.

Algebraic Identity

(a + b)² + (a − b)² = 2(a² + b²). In this case, 2(2² + (√3)²) = 2(4 + 3) = 14.

Given:

A certain sum was to be divided between A and B in the ratio 8 ∶ 5

Actual ration of share of A and B = 5 : 8

Calculation:

Let the actual sum should be divided between A and B be 8a and 5a

Let the sum get by A and B be 5b, and 8b

According to the question,

8a + 5a = 5b + 8b

⇒ 13a = 13b

⇒ (a/b) = 1

So, 8a - 5b = 300

⇒ 8 - 5 = 300

⇒ 3 = 300

⇒ 1 = 100

So, total sum was divided between them = 100 × 13 = ₹1,300

∴ The required answer is ₹1,300.

Given:

Akash sold a motorcycle to Navin at a profit of 10%.

Navin sold it to Vinay at a profit of 20%.

Vinay sold it to Vishal at a loss of 5%.

Vishal paid Rs. 62,700 for the motorcycle

Calculation:

Let the cost price of the motorcycle for Akash be 100a.

According to the question,

100a × 1.1 × 1.2 × 0.95 = 62,700

⇒ 125.4a = 62,700

⇒ a = 500

⇒ 100a = 50,000

So, the cost price of the motorcycle for Akash = Rs. 50,000

∴ The cost of the motorcycle (in Rs.) for Akash 50,000.

Given:

ΔXYZ ∼ ΔPQR 

Perimeter of ΔXYZ = 62 cm

Perimeter of ΔPQR = 42 cm

PQ = 21 cm

Concept used:

If ΔXYZ ~ ΔPQR 

then, Perimeter of (ΔXYZ/ΔPQR) = XY/PQ = YZ/QR = ZX/PR 

Calculation:

According to the question,

we have ΔXYZ ∼ ΔPQR 

Perimeter of (ΔXYZ/ΔPQR) = XY/PQ 

⇒ 62/42 = XY/21 

⇒ XY = (62 × 21)/42 

⇒ XY = 31

∴ The length of XY is 31 cm.

Shortcut Trick

Here, there are 4 variables but only 2 equations.

So, lets put p = q = 1

px + qy = 1

⇒ 1.x + 1.y = 1

⇒ x + y = 1   ----(1)

qx + py = $\frac{2 p q}{p^2+q^2}$

⇒ 1.x + 1.y = $\frac{2× 1× 1}{1^2+1^2}$

⇒ x + y = 2/2

⇒ x + y = 1   ----(2)

Here, again 2 variables but only one equation,

So, put x = 1/2, then y = 1/2

i.e. p = 1, q = 1, x = 1/2, y = 1/2

Now,

(x2 + y2) (p2 + q2)

⇒ (1/2² + 1/2²)(12 + 12)

⇒ (1/4 + 1/4) (1 + 1)

⇒ 1/2 × 2 = 1

∴ The correct answer is 1.

 Alternate Method

Given:

$px + qy = 1$

$qx + py = \frac{2pq}{p^2+q^2}$

Formula Used:

To find the value of $(x^2 + y^2) (p^2 + q^2)$, we use the formulas for solving simultaneous linear equations and properties of squares.

Calculation:

Multiplying the first equation by $p$ and the second by $q$ and adding them:

$⇒ p(px + qy) + q(qx + py) = p × 1 + q × \frac{2pq}{p^2+q^2}$

$⇒ p^2x + pqy + q^2x + pqy = p + \frac{2pq^2}{p^2+q^2}$

$⇒ (p^2 + q^2)(x + y) = p + \frac{2pq^2}{p^2+q^2}$

Multiplying the first equation by $q$ and the second by $p$ and subtracting them:

$⇒ q(px + qy) - p(qx + py) = q × 1 - p × \frac{2pq}{p^2+q^2}$

$⇒ qpx + q^2y - pqx - p^2y = q - \frac{2p^2q}{p^2+q^2}$

$⇒ (q^2 - p^2)(y - x) = q - \frac{2p^2q}{p^2+q^2}$

Squaring and adding the above results eliminates $x + y$ and $y - x$, allowing us to solve for $x^2 + y^2$:

$(x + y)^2 = x^2 + 2xy + y^2$

$(y - x)^2 = y^2 - 2xy + x^2$

$x^2 + y^2 = \frac{(x + y)^2 + (y - x)^2}{2}$

Substituting back into our first results, we get:

$(x^2 + y^2)(p^2 + q^2) = \frac{1}{2}\left(\left(\frac{p + \frac{2pq^2}{p^2+q^2}}{p^2 + q^2}\right)^2 + \left(\frac{q - \frac{2p^2q}{p^2+q^2}}{p^2 + q^2}\right)^2\right) × (p^2 + q^2)$

After simplifying, this leads to:

$(x^2 + y^2)(p^2 + q^2) = 1$

The value of $(x^2 + y^2) (p^2 + q^2)$ is 1.

Given:

The radii of two circles are 9 cm and 4 cm, the distance between their centres is 13 cm

Concept used:

Length of direct common tangent= $√{(distance;between;centers)^2 −(difference;of ;radii)^2}$ ​

Calculation:

Length of direct common tangent = √{13² − (9 − 4)²}

⇒ √{(169 − 25)}

⇒ √144

⇒ 12 cm

∴ The length of the direct common tangent is 12 cm.

Given:

Ravi got a reduction of Rs. 260.39.

Discount percentage = 13

Calculation:

Let the electricity bill of Ravi be '100a'

100a × 13% = 260.39

⇒ 13a = 260.39

⇒ a = 20.03

⇒ 100a = 2003

So, the electricity bill of Ravi = Rs. 2,003

∴ The amount of his electricity bill (in Rs.) was 2,003.

Given:

A salesman marks his goods 30% above the cost and gives a discount of 10% on them.

Calculation:

Let the cost price of the goods be 100x

So, the marked price of the goods = 100x × 1.3 = 130x

Selling price of the goods = 130x × 0.9 = 117x

So, profit = 117x - 100x = 17x

Profit % = $\frac{17x}{100x} \times 100$ = 17

∴ The required answer is 17% gain.

Calculation:

Total percentage of teachers in English, Sanskrit, and Hindi = 20 + 10 + 10 = 40%

Total percentage of teachers in Mathematics, Biology, and Social Studies = 20 + 20 + 20 = 60%

Required ratio = 40 : 60 = 2 : 3

∴ The required answer is 2 : 3.

The correct answer is: Energetic.

Key Points

• The word "Dynamic" means characterized by constant change, activity, or progress. It refers to something or someone that is full of energy and new ideas. (गतिशील)
• Example: The dynamic speaker captured the audience's attention with his energetic presentation.
• "Energetic" refers to showing or involving great activity or vitality. It is synonymous with being dynamic as it implies being active and vigorous. (सक्रिय)
• Example: Despite her long day at work, she remained energetic and completed her evening workout.
• Therefore, we can infer that the most appropriate synonym for 'Dynamic' is 'Energetic'.

Therefore, the correct answer is: Energetic.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Famous (प्रसिद्ध): Well known by many people.
• Example: She became famous after her novel won a prestigious award.
• Halt (रुकावट): Bring or come to an abrupt stop.
• Example: All activities came to a halt during the power outage.
• Innate (जन्मजात): Inborn; natural.
• Example: Her innate sense of rhythm makes her an exceptional dancer.

The correct answer is: Option 4.

Key Points

• The word "archive" refers to a collection of historical documents or records providing information about a place, institution, or group of people. It can include manuscripts, documents, letters, and other items that are preserved because of their historical importance. (संग्रहणालय)
• Example: The national archive houses all the important documents related to the country's history.
• The sentence mentions finding "valuable artifacts such as ancient manuscripts" in the museum’s archive, which aligns with the definition of an archive as a collection of historical documents or records. (ऐतिहासिक दस्तावेज़ या रिकॉर्ड)
• Example: The archive contained rare manuscripts dating back to the 15th century.
• Hence, we can infer that the correct meaning of "archive" in the given context is a collection of historical documents or records.

Therefore, the correct answer is: Option 4.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• A collection of essays (निबंधों का संग्रह): This refers to a compilation of essays, which are short pieces of writing on a particular subject.
• Example: She published a collection of essays on modern art.
• A room to store lots of books (पुस्तकों को संग्रहित करने के लिए एक कमरा): This typically refers to a library or a storage room specifically for books.
• Example: The old mansion had a large room dedicated to storing the family's extensive book collection.
• A room to store important official documents (महत्वपूर्ण आधिकारिक दस्तावेज़ों को संग्रहित करने के लिए एक कमरा): This can refer to a specific area within an archive or a records room in an organization where official documents are kept.
• Example: The company's records room contains all the contracts and legal documents.

The correct answer is: Honesty.

Key Points

• The word "Guile" means the use of clever but usually dishonest methods to achieve something; it involves cunning or deceit. (छल)
• Example: The salesman used all his guile to close the deal, misleading the customer about the product's true capabilities.
• "Honesty" refers to the quality of being fair and truthful; the state of being honest. It implies a refusal to lie, steal, or deceive in any way. (ईमानदारी)
• Example: Her honesty earned her the respect and trust of her colleagues, as she always spoke the truth, even when it was difficult.
• Hence, we can infer that the opposite of 'Guile' is 'Honesty'.

Therefore, the correct answer is: Honesty.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Deceit (धोखा): The action or practice of deceiving someone by concealing or misrepresenting the truth.
• Example: The deceit involved in the scheme was eventually uncovered, leading to legal action.
• Treachery (विश्वासघात ): Betrayal of trust; deceptive action or nature.
• Example: His treachery was revealed when his plot against the king came to light.
• Terseness (संक्षिप्तता): The quality of being brief and to the point; conciseness.
• Example: Her terseness in communication sometimes came off as abrupt or rude, though she was just being efficient.

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

Key Points

• The word "hoard" means to accumulate for future use; stash away.
• It correctly fills the blank, implying that ants collect and save food for the winter.
• Homophones are words that sound the same but have different meanings and/or spellings.
• "Hoard" and "horde" are homophones, but only "hoard" is appropriate in this context.

Therefore, the correct answer is- Option 2.

Additional Information

• Horde: A large group of people.
• Heard: Past tense of hear, meaning to have perceived with the ear.
• Herd: A large group of animals, especially hoofed mammals, that live, feed, or migrate together or are kept together as livestock.