SSC CGL Tier 1 2019 General Awareness Questions with Solutions

Explanation

The Chham dance is a traditional ritualistic mask dance performed by Buddhist monks in the monasteries of Himachal Pradesh, particularly in the Lahaul, Spiti, and Kinnaur districts. It is a significant part of Tibetan Buddhism and is performed during religious festivals to ward off evil spirits and negative energy while promoting peace and prosperity. The performers wear elaborate costumes and large, colorful masks that often represent various deities or protector spirits. Accompanied by traditional instruments such as drums, cymbals, and long horns, the rhythmic movements of the Chham are intended to offer spiritual cleansing and demonstrate the victory of good over evil.

Explanation

The Krishna River, originating in the Western Ghats near Mahabaleshwar, is one of the longest rivers in India and the second-largest east-flowing peninsular river. The Bhima River is its longest tributary, flowing through Maharashtra, Karnataka, and Telangana before joining the Krishna. The Musi River is a major left-bank tributary that originates in the Ananthagiri Hills of Telangana and is notable for flowing through the city of Hyderabad before its confluence with the Krishna in the Nalgonda district. Together, these tributaries form a significant part of the Krishna river basin's drainage system across the Deccan Plateau.

Explanation

The Justice V.S. Malimath Committee was constituted by the Ministry of Home Affairs in 2000 to suggest fundamental changes to the Indian Criminal Justice System. Submitted in 2003, the report proposed 158 recommendations aimed at balancing the rights of the accused with the rights of the victims and the interests of society. It specifically focused on the Code of Criminal Procedure (CrPC), the Indian Penal Code (IPC), and the Indian Evidence Act. Key suggestions included introducing an inquisitorial element to the existing adversarial system, improving witness protection through a dedicated scheme, and redefining the standard of proof required for conviction to ensure the system is more effective in delivering justice.

Explanation

Mahmud of Ghazni, the ruler of the Ghaznavid Empire, conducted seventeen raids into the Indian subcontinent between 1000 and 1027 AD. His most significant and sixteenth expedition took place in 1025–1026 AD, specifically targeting the wealthy Somnath temple located on the coast of Saurashtra in Gujarat. During this raid, he defeated the local forces led by the Chalukya (Solanki) ruler Bhima I. Mahmud looted the temple of its immense riches, including gold, precious stones, and the sacred lingam, which he destroyed. These raids were primarily motivated by the desire to accumulate wealth to fund his military campaigns in Central Asia and to establish his prestige through the destruction of prominent religious structures.

Explanation

France was the first country in the world to implement the Goods and Services Tax (GST), introducing the system in 1954. The tax was designed to replace a complex web of multiple indirect taxes with a streamlined value-added system. This move aimed to reduce tax evasion and eliminate the cascading effect of taxes, where tax is levied on tax at different stages of production and distribution. Since France's pioneering implementation, more than 160 countries have adopted similar GST or Value Added Tax (VAT) models to modernize their fiscal structures and improve revenue collection efficiency.

Explanation

The Badampahar mines, located in the Mayurbhanj district of Odisha, are a major source of high-grade hematite iron ore. This region is part of the Gorumahisani-Badampahar-Sulaipat iron ore belt, which is characterized by extensive deposits of hematite found within the Banded Iron Formations of the Precambrian era. The ore extracted from Badampahar is known for its high iron content and is historically significant as it was one of the primary sources of raw material for the establishment and operation of the Tata Iron and Steel Company (TISCO) in Jamshedpur. This mining belt remains a critical component of India's mineral wealth and supports the domestic steel industry.

Explanation

Sundari (Heritiera fomes) is a significant species of mangrove tree that thrives in the brackish water and tidal environments of the Sundarbans. The Sundarbans, located in the delta of the Ganges, Brahmaputra, and Meghna rivers across India and Bangladesh, is the largest mangrove forest in the world and derives its name from these trees. As a mangrove species, the Sundari tree is highly adapted to saline conditions and periodic flooding, often featuring specialized roots and salt-tolerant physiology. Its timber is valued for being hard and durable, making it useful for boat building and various construction purposes in coastal communities.

Explanation

The Tata Iron and Steel Company (TISCO) was founded by Jamsetji Nusserwanji Tata and established by his son, Sir Dorabji Tata, on August 26, 1907. The company was set up at Sakchi in Jharkhand, a location chosen for its proximity to iron ore, coal, and manganese deposits, as well as its access to water from the Subarnarekha and Kharkai rivers. This venture represented a pioneering step in the industrialization of India, becoming the first integrated steel plant in Asia. While the incorporation took place in 1907, the plant began producing pig iron in 1911 and steel in 1912.

Explanation

Sundari Nanda, a 1988-batch Indian Police Service (IPS) officer of the AGMUT (Arunachal Pradesh-Goa-Mizoram and Union Territory) cadre, was appointed as the Director General of Police (DGP) of Puducherry in July 2018. Her appointment was historic as she became the first woman to head the police force in the Union Territory. Before taking over this prestigious role, she served in several high-profile positions, including as the Special Commissioner of Police (Vigilance) in Delhi. Her tenure in Puducherry focused on improving law and order and enhancing the efficiency of the police administration.

Explanation

Silicon is a chemical element with the symbol Si and atomic number 14. It is classified as a metalloid because it possesses physical and chemical properties that are intermediate between those of metals and non-metals. For instance, while it has a metallic luster, it is brittle rather than malleable. Its most significant metalloid characteristic is its semiconductor behavior, where its electrical conductivity is between that of a conductor and an insulator. This property allows silicon to be used as the foundational material for modern electronic devices and integrated circuits. In the periodic table, silicon is positioned along the diagonal stair-step line that separates the metals on the left from the non-metals on the right.

Explanation

Isomers are compounds that possess the same molecular formula but different structural arrangements of atoms. Methyl propane, commonly known as isobutane, has a parent propane chain (three carbon atoms) with a methyl group attached to the second carbon, giving it a total of four carbon atoms and ten hydrogen atoms. Its molecular formula is C₄H₁₀. Similarly, n-butane is a straight-chain alkane consisting of four carbon atoms and ten hydrogen atoms, also resulting in the molecular formula C₄H₁₀. Since both molecules share the same chemical formula but differ in the connectivity of their carbon skeletons, methyl propane is a structural isomer (specifically a chain isomer) of n-butane.

Explanation

The Economist Intelligence Unit (EIU) Worldwide Cost of Living Survey 2019 identified the cheapest cities globally by comparing the prices of over 160 items across 133 cities. In the 2019 report, three Indian cities were featured in the list of the ten cheapest cities in the world: Bengaluru, Chennai, and New Delhi. These cities maintained low costs due to low wages and high subsidies on certain goods. Mumbai, while appearing in similar lists in previous years, was not ranked among the three cheapest Indian cities in the 2019 edition of the report.

Explanation

The Wadiyar dynasty, also known as the Wodeyar dynasty, was an Indian royal house that ruled the Kingdom of Mysore from 1399 until 1950. Founded by Yaduraya Wodeyar, the dynasty initially served as feudatories to the Vijayanagara Empire before becoming an independent kingdom in the 16th century. Throughout their long tenure, the Wadiyars significantly shaped the cultural and economic landscape of the Mysore region. Even after a period of displacement by the military commanders Hyder Ali and Tipu Sultan in the late 18th century, the British restored the Wadiyar lineage to power in 1799 following the Fourth Anglo-Mysore War. The kingdom remained a prominent princely state under British paramountcy, known for its administrative reforms and patronage of the arts, until it acceded to the Union of India after independence.

Explanation

Justice V. Ramaswami was the first judge of the Supreme Court of India against whom impeachment proceedings were initiated in the Parliament. The motion was moved in the Lok Sabha in 1991, based on allegations of financial irregularities and gross abuse of office during his previous tenure as the Chief Justice of the Punjab and Haryana High Court. An investigative committee constituted under the Judges (Inquiry) Act, 1968, found him guilty of several charges of misconduct. The impeachment motion was subsequently taken up for voting in the Lok Sabha in May 1993. Although the motion received a majority of those voting, it failed to achieve the constitutionally mandated two-thirds majority of members present and voting because the members of the ruling Congress party abstained from the vote.

Explanation

Pramod Sawant was sworn in as the 13th Chief Minister of Goa on March 19, 2019. His appointment followed the death of the incumbent Chief Minister, Manohar Parrikar, who passed away on March 17, 2019. Before becoming the Chief Minister, Sawant served as the Speaker of the Goa Legislative Assembly and represented the Sanquelim constituency as a member of the Bharatiya Janata Party. He was administered the oath of office by Governor Mridula Sinha at a ceremony held at Raj Bhavan.

Explanation

J.J. Thomson was awarded the Nobel Prize in Physics in 1906 in recognition of his theoretical and experimental investigations on the conduction of electricity by gases. His most celebrated achievement was the discovery of the electron in 1897 through experiments with cathode rays. By applying electric and magnetic fields to cathode rays, he demonstrated that they consisted of negatively charged particles with a mass much smaller than that of a hydrogen atom. He calculated the specific charge, or charge-to-mass ratio (e/m), of these particles, proving that they were fundamental subatomic constituents of all atoms. This work fundamentally changed the understanding of atomic structure and marked the beginning of modern particle physics.

Explanation

Rani Durgavati was the ruling Queen of Gondwana from 1550 to 1564, governing the kingdom of Garha Katanga as regent for her son Vir Narayan. In 1564, the Mughal Emperor Akbar's general Asaf Khan attacked the kingdom, attracted by its wealth and strategic importance. Rani Durgavati chose to lead her army in person to defend her territory against the invading forces. During the fierce battle at Narrai, she sustained heavy injuries from Mughal arrows. To avoid the disgrace of being captured by the enemy, she preferred death over dishonor and killed herself with a dagger on June 24, 1564. Her resistance remains a significant symbol of bravery in the history of the Gond dynasty.

Explanation

Dry ice is the solid form of carbon dioxide (CO₂). It is called dry ice because it undergoes sublimation, a process where a substance transitions directly from a solid state to a gaseous state without passing through a liquid phase at standard atmospheric pressure. This occurs because the triple point of carbon dioxide is at a pressure of 5.11 atmospheres and a temperature of -56.4°C, meaning that at normal sea-level pressure, it cannot exist as a liquid. In its solid form, it maintains a very low temperature of approximately -78.5°C (-109.3°F), making it an effective cooling agent for transporting perishable goods like food and medical supplies without leaving any moisture or residue behind.

Explanation

The Olympic Council of Asia (OCA) General Assembly, meeting in Bangkok in March 2019, officially decided to reintroduce cricket into the sports program for the 2022 Asian Games in Hangzhou, China. Cricket was previously included as a medal sport in the 2010 Guangzhou and 2014 Incheon Asian Games but was subsequently dropped from the 2018 edition held in Jakarta and Palembang. The reintroduction was intended to enhance the profile of the sport in Asia and provide another major international platform for the Twenty20 format.

Explanation

Catenation is the unique ability of an element to form long chains, branched structures, or rings by bonding with its own atoms. Carbon shows the most predominant catenation property because of its small atomic radius and high C-C bond energy, which is approximately 348 kJ/mol. This high bond enthalpy makes the linkages extremely stable. Carbon's tetravalency and the absence of significant electronic repulsion between its small atoms facilitate the formation of these strong covalent networks, providing the structural basis for the vast diversity of organic compounds.

Explanation

Thoda is a traditional martial art form and sport dance native to the state of Himachal Pradesh, particularly prevalent in the districts of Shimla, Sirmaur, and Solan. This performance-based sport traces its origins to the era of the Mahabharata, where it is believed to have originated from the archery skills of the Pandavas and Kauravas. Conducted during the Baisakhi festival, the game involves two teams known as the Saathi and the Pashi, who are considered descendants of the legendary warriors. Participants use wooden bows and arrows to aim at the opponent's legs below the knee, specifically targeting the calf area. The dance combines physical agility, precision in archery, and cultural storytelling, making it a significant part of the Himalayan folk heritage.

Explanation

Kavinder Singh Bisht secured the lone gold medal for India at the 38th GeeBee Boxing Tournament held in Helsinki, Finland, in March 2019. Competing in the 56kg bantamweight category, he emerged victorious in the final to claim the top spot on the podium. His gold medal was the highlight of the Indian boxing contingent performance at the tournament, where the team overall secured eight medals, including four silver and three bronze medals.

Explanation

The 33ʳᵈ edition of the India-Indonesia Coordinated Patrol (IND-INDO CORPAT) was conducted from 19ᵗʰ March to 4ᵗʰ April 2019. The exercise commenced with the opening ceremony at Port Blair, Andaman and Nicobar Islands, and concluded with a closing ceremony at Belawan, Indonesia. Since its inception in 2002, this bilateral maritime exercise has been held twice a year to enhance mutual understanding and interoperability between the two navies. The 33ʳᵈ iteration involved the participation of INS Kulish and a Dornier maritime patrol aircraft from the Indian Navy, alongside Indonesian naval assets, to monitor and secure the International Maritime Boundary Line (IMBL) against illegal activities such as maritime terrorism, piracy, and smuggling.

Explanation

Mark Zuckerberg co-founded Facebook on February 4, 2004, while studying at Harvard University. Working with fellow students Eduardo Saverin, Andrew McCollum, Dustin Moskovitz, and Chris Hughes, he developed the platform originally known as thefacebook.com. Zuckerberg has served as the Chairman and Chief Executive Officer since the company's inception, overseeing its expansion from a university-based network into a global social media platform with billions of users. Under his leadership, the company acquired other major platforms like Instagram and WhatsApp, cementing his role as the primary founder and driving force behind the organization's development.

Explanation

The Indian National Association, also known as the Indian Association of Calcutta, was founded on July 26, 1876, by Anand Mohan Bose and Surendranath Banerjee. It was established as a premier nationalist organization to represent the interests of the educated middle class and to promote the unification of Indians on a common political program. Anand Mohan Bose served as its first secretary and played a vital role in organizing its activities. The association focused on creating a strong public opinion on various issues of national importance, such as the reduction of the age limit for Civil Service examinations, and it served as a significant precursor to the Indian National Congress.

Explanation

The geometric property of tangents states that the lengths of two tangents drawn from an external point to a circle are equal. In triangle ABC, the vertices A, B, and C serve as external points to the inscribed circle.

From vertex A, the tangents are AQ and AR, meaning AR = AQ = 4.5 cm. From vertex B, the tangents are BR and BP, meaning BP = BR = 6 cm. From vertex C, the tangents are CP and CQ, meaning CQ = PC = 5.5 cm.

The perimeter of triangle ABC is the sum of the lengths of its three sides: AB, BC, and AC. Side AB = AR + RB = 4.5 + 6 = 10.5 cm. Side BC = BP + PC = 6 + 5.5 = 11.5 cm. Side AC = AQ + QC = 4.5 + 5.5 = 10 cm.

Summing these gives the perimeter: 10.5 + 11.5 + 10 = 32 cm. This can also be calculated using the formula for the perimeter of a triangle with an incircle: Perimeter = 2(AQ + PC + BR) = 2(4.5 + 5.5 + 6) = 2(16) = 32 cm.

Explanation

To find the central angle of a sector in a pie chart, the formula used is: Central Angle = (Value of the specific category)/(Total value of all categories) × 360°

First, calculate the total production of cars of type E from 2012 to 2016: Total Production (Type E) = 20 + 42 + 40 + 35 + 43 = 180

The production of type E cars in the year 2013 is 42. Substituting these values into the formula: Central Angle for 2013 = ⁴²⁄₁₈₀ × 360°

Central Angle for 2013 = 42 × 2° = 84°

Explanation

The relationship between distance, speed, and time is defined by the formula t = ᵈ⁄ₛ. Let the original speed of the truck be s km/h. According to the given condition, decreasing the speed by 16 km/h increases the travel time by 2 hours for a distance of 384 km. This can be expressed as:

(384)/(s - 16) - ³⁸⁴⁄ₛ = 2

Dividing the entire equation by 2:

(192)/(s - 16) - ¹⁹²⁄ₛ = 1

(192s - 192(s - 16))/(s(s - 16)) = 1

192s - 192s + 3072 = s² - 16s

s² - 16s - 3072 = 0

To solve this quadratic equation, we find factors of 3072 that have a difference of 16. These factors are 64 and 48:

s² - 64s + 48s - 3072 = 0

(s - 64)(s + 48) = 0

Since speed must be a positive value, s = 64 km/h. The question asks for 75% of this original speed:

75% of 64 = ¾ × 64 = 3 × 16 = 48

Explanation

Let the ages of A and B four years ago be 4x and 5x respectively. The time gap between four years ago and eight years from now is 4 + 8 = 12 years. According to the given condition, the ratio eight years from now will be:

(4x + 12)/(5x + 12) = ¹¹⁄₁₃

Cross-multiplying the terms: 13(4x + 12) = 11(5x + 12) 52x + 156 = 55x + 132 55x - 52x = 156 - 132 3x = 24 x = 8

The ages of A and B four years ago were 4(8) = 32 years and 5(8) = 40 years. Their present ages are: A = 32 + 4 = 36 years B = 40 + 4 = 44 years

The sum of their present ages is 36 + 44 = 80 years.

Alternatively, using the ratio difference method, the ratio 4 years ago is 4:5 (difference 1) and 8 years later is 11:13 (difference 2). To equalize the age difference, multiply the first ratio by 2 to get 8:10. The change in units is 11 - 8 = 3 units, which corresponds to the 12-year interval. Thus, 1 unit equals 4 years. The sum of their ages 4 years ago was (8 + 10) × 4 = 72 years. Adding 8 years (4 for each person) to reach the present gives 72 + 8 = 80 years.

Explanation

Since FE ∥ BC, △ AFE is similar to △ ABC. In similar triangles, the ratio of the areas is equal to the square of the ratio of their corresponding altitudes. Let AG be the altitude of △ AFE and AD be the altitude of △ ABC.

Given that FE divides △ ABC into two parts of equal area, we have Area(△ AFE) = Area(FEBC). Since Area(△ ABC) = Area(△ AFE) + Area(FEBC), it follows that Area(△ ABC) = 2 × Area(△ AFE).

The ratio of the areas is: (Area(△ AFE))/(Area(△ ABC)) = ½

Using the property of similar triangles: ((AG)/(AD))² = ½ (AG)/(AD) = (1)/(√(2)) AD = √2 · AG

Since D lies on BC and G lies on FE along the same altitude line AD, we have AD = AG + GD. Substituting the value of AD: AG + GD = √2 · AG GD = √2 · AG - AG GD = AG(√2 - 1)

Rearranging to find the required ratio: (GD)/(AG) = √2 - 1{1}

Thus, GD : AG = (√2 - 1) : 1.

Explanation

The total production of cars of type A in 2014 and type C in 2013 taken together is 48 + 36 = 84 thousand. The total production of cars of type B in 2016 and type E in 2015 taken together is 56 + 35 = 91 thousand.

The required ratio is determined by the formula:

Ratio = (Production of (A in 2014 + C in 2013))/(Production of (B in 2016 + E in 2015))

Ratio = ⁸⁴⁄₉₁

Both 84 and 91 are divisible by 7. Simplifying the fraction gives:

(84 ÷ 7)/(91 ÷ 7) = ¹²⁄₁₃

Thus, the ratio is 12:13.

Explanation

To find the value of x, equate the results of the two percentage operations given in the problem: 120 × (1 - ˣ⁄₁₀₀) = 40 × (1 + ˣ⁄₁₀₀)

Divide both sides by 40 to simplify: 3(1 - ˣ⁄₁₀₀) = 1 + ˣ⁄₁₀₀ 3 - ³ˣ⁄₁₀₀ = 1 + ˣ⁄₁₀₀ 3 - 1 = ˣ⁄₁₀₀ + ³ˣ⁄₁₀₀ 2 = ⁴ˣ⁄₁₀₀ x = ²⁰⁰⁄₄ = 50

Now, calculate the values for the comparison: First value: x% of 210 = 50% of 210 = 0.5 × 210 = 105 Second value: (x + 20)% of 180 = (50 + 20)% of 180 = 70% of 180 = 0.7 × 180 = 126

To find what percent 105 is less than 126, calculate the difference and divide it by the base value (126): Percentage less = (126 - 105)/(126) × 100 Percentage less = ²¹⁄₁₂₆ × 100 = ⅙ × 100 ¹⁰⁰⁄₆ = 16⅔%

Explanation

For a number to be divisible by 72, it must be coprime factors 8 and 9. According to the divisibility rule of 8, the last three digits of the number, which are 78y, must be divisible by 8. By testing the last three digits, we find that 784 ÷ 8 = 98, which means the value of y is 4.

According to the divisibility rule of 9, the sum of all the digits of the number must be divisible by 9. The sum of the digits in the number 985x36784 is 9 + 8 + 5 + x + 3 + 6 + 7 + 8 + 4 = 50 + x. For 50 + x to be a multiple of 9, the nearest multiple greater than 50 is 54. Solving 50 + x = 54 gives x = 4.

Substituting the values x = 4 and y = 4 into the given expression (4x - 3y), we get 4(4) - 3(4) = 16 - 12 = 4.

Explanation

Total efficiency of A, B, and C is 2 + 5 + 3 = 10. Total work is calculated as Total efficiency × Total days, which is 10 × 27 = 270 units.

The part of the work to be completed by B and C is ⁴⁄₉ of the total work. Work to be done = 270 × ⁴⁄₉ = 120 units.

The combined efficiency of B and C is 5 + 3 = 8. Time taken by B and C = (Work to be done)/(Combined efficiency of B and C) = ¹²⁰⁄₈ = 15 days.

Explanation

The sum of all twelve numbers is 12 × 42 = 504. The sum of the first four numbers is 4 × 44 = 176 and the sum of the last five numbers is 5 × 40 = 200. Therefore, the sum of the 5ᵗʰ, 6ᵗʰ, and 7ᵗʰ numbers is 504 - (176 + 200) = 128.

Let the 6ᵗʰ number be x. According to the problem, the 5ᵗʰ number is x + 6 and the 7ᵗʰ number is x + 5. Combining these, the sum of these three numbers is (x + 6) + x + (x + 5) = 128. Solving for x gives 3x + 11 = 128, which simplifies to 3x = 117, resulting in x = 39.

The 5ᵗʰ number is 39 + 6 = 45 and the 7ᵗʰ number is 39 + 5 = 44. The average of the 5ᵗʰ and 7ᵗʰ numbers is calculated as (45 + 44)/(2) = ⁸⁹⁄₂ = 44.5.

Explanation

In a circle with center O and radius 10 cm, PQ and PR are chords of equal length 12 cm. In △ POQ and △ POR, OQ = OR = 10 cm (radii), PQ = PR = 12 cm, and PO is a common side. Thus, the triangles are congruent by SSS criteria, and PO acts as the perpendicular bisector of the chord QR at point S.

Let OS = x. Since OP is the radius, OP = 10 cm, which makes PS = OP - OS = 10 - x. In the right-angled triangle OQS, by Pythagoras theorem: QS² = OQ² - OS² QS² = 10² - x² = 100 - x²

In the right-angled triangle PQS, by Pythagoras theorem: QS² = PQ² - PS² QS² = 12² - (10 - x)² = 144 - (100 - 20x + x²) QS² = 44 + 20x - x²

Equating the two expressions for QS²: 100 - x² = 44 + 20x - x² 100 = 44 + 20x 20x = 56 x = 56 / 20 = 2.8 cm

Explanation

In compound interest, if a sum P amounts to A₁ in n years and to A₂ in 2n years, the constant multiplier for n years is k = (A₂)/(A₁). The principal can then be calculated using the relation P = (A₁)/(k) or P = (A₁²)/(A₂).

Given A₁ = 8028 at t = 3 years and A₂ = 12042 at t = 6 years, the time interval is doubled. First, find the ratio of the amounts:

k = (A₂)/(A₁) = ¹²⁰⁴²⁄₈₀₂₈

Dividing both by 4014:

k = ³⁄₂ = 1.5

This means the amount increases by a factor of 1.5 every 3 years. Therefore, the principal P multiplied by 1.5 must equal the amount after the first 3 years:

P × ³⁄₂ = 8028

P = (8028 × 2)/(3)

P = 2676 × 2 = 5352

Explanation

The selling price (SP) is obtained by subtracting the total discount from the marked price (MP). SP = 720 - 259.2 = 460.8

The formula for the final selling price after two equal successive discounts of x% is: SP = MP × (1 - ˣ⁄₁₀₀)²

Substituting the given values into the formula: 460.8 = 720 × (1 - ˣ⁄₁₀₀)²

Rearranging to solve for the discount factor: (1 - ˣ⁄₁₀₀)² = (460.8)/(720) (1 - ˣ⁄₁₀₀)² = ⁴⁶⁰⁸⁄₇₂₀₀ (1 - ˣ⁄₁₀₀)² = ⁶⁴⁄₁₀₀ = 0.64

Taking the square root of both sides of the equation: 1 - ˣ⁄₁₀₀ = √(0.64) 1 - ˣ⁄₁₀₀ = 0.8

Solving for x: ˣ⁄₁₀₀ = 1 - 0.8 ˣ⁄₁₀₀ = 0.2 x = 20

Explanation

The volume of a cube is given by the formula V = s³, where s is the side length. Let A be the side length of the original cube and a be the side length of the smaller cube. The problem states the original cube is cut into 8 cubes of equal volume, which means the volume of each small cube v is one-eighth of the original volume V: v = (V)/(8) a³ = (A³)/(8) Taking the cube root of both sides gives: a = (A)/(2) or A = 2a

The surface area of a cube is calculated as 6s². Therefore, the surface area of the original cube is Sₒᵣᵢ_gᵢₙₐₗ = 6A². The sum of the surface areas of three smaller cubes is Sₜₕᵣₑₑ = 3 × 6a² = 18a².

The ratio of the surface area of the original cube to the sum of the surface areas of three smaller cubes is: Ratio = (6A²)/(18a²) = (A²)/(3a²)

By substituting the relation A = 2a into the ratio: Ratio = ((2a)²)/(3a²) = (4a²)/(3a²) = ⁴⁄₃

Explanation

Total production of type B cars in the years 2012, 2014, and 2015 is calculated by summing the values from the table: 42 + 40 + 38 = 120. Total production of type A cars in the years 2013 and 2016 is 35 + 56 = 91. To find how much percent more the production of type B is compared to type A, use the formula for percentage increase:

Percentage Increase = (Production of B - Production of A)/(Production of A) × 100

Substituting the values into the formula: (120 - 91)/(91) × 100 = ²⁹⁄₉₁ × 100

By performing the division, we get: 2900 ÷ 91 ≈ 31.868

Rounding this value to one decimal place yields 31.9%.

Explanation

The average production of type D cars over the five-year period is calculated by summing the production values for each year and dividing by the total number of years: Average of D = (51 + 24 + 30 + 46 + 54)/(5) = ²⁰⁵⁄₅ = 41 The production figures for type B cars from 2012 to 2016 are 42, 48, 40, 38, and 56 respectively. To find the number of years where type B production is less than the average of type D, compare each year's production of B to 41. In 2012 (42 > 41), in 2013 (48 > 41), in 2014 (40 < 41), in 2015 (38 < 41), and in 2016 (56 > 41). The years 2014 and 2015 are the only instances where the production of type B cars is less than 41, totaling 2 years.

Explanation

Let the Cost Price (CP) of the article be 100%. The difference between a loss of 15% and a gain of 9% represents a total change of 9% - (-15%) = 24% in the selling price.

According to the problem, this 24% difference corresponds to ₹30.60.

24% of CP = 30.60

1% of CP = (30.60)/(24) = 1.275

To achieve a gain of 10%, the article must be sold at 110% of its Cost Price.

Selling Price = 110 × 1.275

110 × 1.275 = 11 × 12.75 = 140.25

The person should have sold the article for ₹140.25 to obtain a 10% gain.

Explanation

Given the equation x⁴ + (1)/(x⁴) = 194, we can determine the value of x² + (1)/(x²) by using the algebraic identity a² + b² = (a+b)² - 2ab. Adding 2 to both sides of the equation yields: x⁴ + (1)/(x⁴) + 2 = 194 + 2 (x² + (1)/(x²))² = 196 Since x > 0, taking the square root gives x² + (1)/(x²) = 14.

Next, we find the value of x + ¹⁄ₓ by again adding 2 to both sides: x² + (1)/(x²) + 2 = 14 + 2 (x + ¹⁄ₓ)² = 16 Taking the square root gives x + ¹⁄ₓ = 4.

Rearranging this linear equation results in: x² + 1 = 4x x² - 4x = -1

The expression to be evaluated is (x - 2)². Expanding this square gives: (x - 2)² = x² - 4x + 4

By substituting the value x² - 4x = -1 into this expanded form, we get: -1 + 4 = 3

Explanation

Gobind Behari Lal was a pioneering Indian-American journalist and independence activist who became the first person of Indian origin to win the Pulitzer Prize. In 1937, he was awarded the Pulitzer Prize for Reporting for his exceptional coverage of science during the Harvard University tercentenary celebration. Serving as a science editor for the Hearst Newspapers, he was honored for his ability to translate complex scientific advancements into accessible and engaging reports for the general public. His achievement established him as the earliest Indian-origin recipient of this prestigious award, marking a significant milestone for the Indian diaspora in the field of international journalism.

Explanation

The Gamocha is an indispensable part of the socio-cultural life in Assam, serving as a symbol of Assamese identity and heritage. It is a handwoven rectangular cotton cloth, typically white with red borders and intricate floral or geometric motifs at the ends. While the name literally translates to a cloth for wiping the body, its significance is far more profound. It is used to honor guests, offered to elders as a mark of respect during festivals like Bihu, and placed on the altar in prayer halls. The Gamocha reflects the state's rich weaving tradition and acts as a traditional token of love and hospitality across all sections of Assamese society.

Explanation

The Parliament of Sri Lanka is a unicameral legislature that consists of 225 members according to the provisions of the 1978 Constitution. The membership is divided into two categories: 196 members are elected from 22 multi-member electoral districts through a proportional representation system using an open list method, while the remaining 29 members are appointed from a National List. The National List seats are allocated to political parties and independent groups in proportion to their share of the total national vote polled. All members serve a term of five years.

Explanation

Viyahula Giddha is a traditional folk dance of Punjab, specifically performed by women during wedding celebrations. The term Viyahula is derived from Viyah, which means marriage in the Punjabi language. This dance is a vibrant expression of joy where women form a circle, clap rhythmically, and perform to the accompaniment of bolis, which are short traditional couplets. These songs often capture the various emotions, teasing, and social dynamics associated with matrimonial ceremonies, making it an integral part of the cultural and festive heritage of the Punjabi people.

Explanation

Ramanathan Krishnan was a trailblazer for Indian tennis in the years following the nation's independence. Among the players listed, he was the first to compete at the Wimbledon Championships, making his senior debut in 1953. He achieved a significant milestone for Indian sports by winning the Junior Wimbledon title in 1954, making him the first Asian to achieve this feat. Krishnan further distinguished himself by reaching the semi-finals of the men's singles at Wimbledon in both 1960 and 1961. His performances during the 1950s and 1960s set a high standard for Indian tennis on the international stage during the early decades of the Republic of India.

Explanation

Combustion is a chemical process in which a substance reacts rapidly with oxygen or an oxidizing agent to release energy in the form of heat and light. The explosion of crackers is a specific type of rapid combustion known as explosive combustion. When a cracker is ignited, the chemical constituents—typically a fuel like sulfur or charcoal and an oxidizer like potassium nitrate—undergo a sudden, large-scale chemical reaction. This reaction produces an enormous amount of heat, light, and sound, along with a rapid evolution of gases, which creates the pressure necessary for the explosion.

Explanation

Global Recycling Day was first established in 2018 by the Bureau of International Recycling and is observed annually on March 18th. The initiative aims to raise awareness of the importance of recycling as a key component of the circular economy and to encourage the world to look at waste as a resource rather than trash. In 2019, the second annual event focused on the theme of Recycling into the Future, emphasizing the role of youth, education, and innovation in ensuring the sustainability of the planet. By designating recycling as the seventh resource alongside water, air, oil, natural gas, coal, and minerals, the day promotes global action to preserve primary resources and reduce carbon emissions.