SSC CGL Tier 1 2019 General Awareness Questions with Solutions

Explanation

Rule 193 of the Rules of Procedure and Conduct of Business in Lok Sabha provides for Short Duration Discussions on matters of urgent public importance. Under this rule, a member can raise a discussion by giving notice in writing to the Secretary-General, which must be supported by the signatures of at least two other members. The primary characteristic of a discussion under Rule 193 is that it does not involve a formal motion being moved before the House. As there is no substantive or formal motion for the House to adopt or reject, the procedure concludes without any voting. The member who provides the notice makes a short statement, followed by other members who wish to speak on the subject, and finally, the Minister concerned provides a reply to the points raised during the debate.

Explanation

Nitrous oxide, represented by the chemical formula N₂O, is widely known as laughing gas. It is a colorless, non-flammable gas with a slightly sweet odor and taste. When inhaled, it induces a state of euphoria, relaxation, and sometimes uncontrollable laughter, which led to its popular name. In medical and dental practices, it is frequently utilized as a safe and effective sedative agent to manage pain and anxiety during minor procedures. It functions by interacting with the central nervous system to provide analgesic and anesthetic effects while the patient remains conscious. The gas was first synthesized by Joseph Priestley in 1772, and its physiological properties were extensively studied by Humphry Davy in the late 18th century.

Explanation

Bihar Diwas is celebrated every year on 22nd March to mark the formation of the state of Bihar. On this day in 1912, the British government carved out the province of Bihar from the Bengal Presidency, which also included the territory of present-day Jharkhand and Odisha at that time. The state government of Bihar officially started celebrating this day annually to commemorate the state's distinct identity and to showcase its rich cultural heritage. It is observed as a public holiday across the state, featuring various cultural programs and events organized by the government.

Explanation

The cost price of the first article is calculated as CP₁ = (SP)/(1 + gain%){100} = (975)/(1.3) = 750. The cost price of the second article is calculated as CP₂ = (SP)/(1 - loss%){100} = (975)/(0.75) = 1300.

Total cost price CPₜₒₜₐₗ = CP₁ + CP₂ = 750 + 1300 = 2050. Total selling price SPₜₒₜₐₗ = 975 + 975 = 1950.

Since the total cost price is greater than the total selling price, there is an overall loss. Overall Loss = 2050 - 1950 = 100. Overall Loss percentage = (Loss)/(CPₜₒₜₐₗ₎ × 100 = ¹⁰⁰⁄₂₀₅₀ × 100 = ¹⁰⁰⁰⁄₂₀₅ = ²⁰⁰⁄₄₁ ≈ 4.878%.

Rounding to one decimal place, the overall loss is 4.9%.

Explanation

The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the remaining part of the circle. Let D be a point on the circle such that ABCD forms a cyclic quadrilateral. Since arc ABC subtends an angle of 140° at the center O, the angle subtended at point D is ∠ ADC = ½ × 140° = 70°.

In a cyclic quadrilateral, the exterior angle produced by extending one side is equal to the interior opposite angle. When the chord AB is produced to point P, the angle ∠ CBP is the exterior angle at vertex B. The interior opposite angle to ∠ CBP is ∠ ADC. Therefore, ∠ CBP = ∠ ADC = 70°.

Explanation

The algebraic identity for the given expression is: a³ + b³ + c³ - 3abc = (a + b + c)[(a + b + c)² - 3(ab + bc + ca)]

By substituting the given values a + b + c = 7 and ab + bc + ca = 1 into this formula, we get: a³ + b³ + c³ - 3abc = 7 × [7² - 3(1)] a³ + b³ + c³ - 3abc = 7 × [49 - 3] a³ + b³ + c³ - 3abc = 7 × 46 a³ + b³ + c³ - 3abc = 322

Explanation

In △ ABC, the triangles ABQ and ACB share the same vertex A and their bases BQ and BC lie on the same straight line BC. Therefore, the height h from vertex A to the line BC is the same for both triangles. The area of a triangle is given by the formula Area = ½ × base × height. Since the height is constant, the ratio of the areas of these triangles is equal to the ratio of their bases.

Given the ratio BP:PC = 4:3, let BP = 4x and PC = 3x. The total length of the base BC is BP + PC = 4x + 3x = 7x. Q is the midpoint of BP, so the length of BQ is ½ × BP = ½ × 4x = 2x.

The ratio of the areas is: (ar(ABQ))/(ar(ACB)) = (1)/(2) × BQ × h{½ × BC × h} = (BQ)/(BC) = ²ˣ⁄₇ₓ = ²⁄₇

Explanation

The relationship between expenditure, price, and consumption is governed by the formula Expenditure = Price × Consumption. Let the initial price be 100 and initial consumption be 100, resulting in an initial expenditure of 10000.

After the price increases by 24%, the new price becomes 124. The person wants to increase the total expenditure by only 18%, making the new expenditure 11800. The new consumption can be calculated as New Consumption = (New Expenditure)/(New Price) = ¹¹⁸⁰⁰⁄₁₂₄.

Simplifying this fraction, we get ¹¹⁸⁰⁰⁄₁₂₄ ≈ 95.16. The percentage decrease in consumption is the reduction from the original 100 units, which is 100 - 95.16 = 4.84%. Rounding to the nearest decimal, the required decrease is approximately 4.8%.

Explanation

To evaluate the expression 108 ÷ 36 × 4 + 2.5 × 4 ÷ 0.5 - 10, apply the BODMAS rule which dictates the order of operations as Division, Multiplication, Addition, and Subtraction. Begin with the divisions: 108 ÷ 36 = 3 and 4 ÷ 0.5 = 8. The expression simplifies to 3 × 4 + 2.5 × 8 - 10. Next, perform the multiplication steps: 3 × 4 = 12 and 2.5 × 8 = 20. Substituting these values gives 12 + 20 - 10. Finally, calculate the addition and subtraction to reach the result: 32 - 10 = 22.

Explanation

The percentage increase in the number of students passing out of college B from 2016 to 2017 can be calculated using the pass percentages provided, as the base number of students appearing (200) remains constant for both years.

Pass percentage of college B in 2016 = 68% Pass percentage of college B in 2017 = 77%

Number of students passed in 2016 = 68% of 200 = 136 Number of students passed in 2017 = 77% of 200 = 154

The percentage increase in the number of students passing is: Percentage Increase = (Passed in 2017 - Passed in 2016)/(Passed in 2016) × 100 Percentage Increase = (154 - 136)/(136) × 100 = ¹⁸⁄₁₃₆ × 100 Percentage Increase = ⁹⁄₆₈ × 100 ≈ 13.235%

Rounding to one decimal place, we get 13.2%.

Explanation

When a solid object is melted and recast into smaller objects, the total volume remains constant. The volume of a sphere is given by the formula V = ⁴⁄₃ π r³. Let R be the radius of the original large sphere and r be the radius of each smaller sphere. The number of smaller spheres n is the ratio of the volume of the large sphere to the volume of one small sphere:

n = (4)/(3) π R³{⁴⁄₃ π r³} = (R³)/(r³) = ((R)/(r))³

Substituting the given values R = 4 cm and r = 2 cm:

n = (⁴⁄₂)³ = 2³ = 8

The volume of the large sphere is 64 × ⁴⁄₃π and the volume of each small sphere is 8 × ⁴⁄₃π, resulting in exactly 8 spheres.

Explanation

For a constant distance, speed is inversely proportional to time (v ∝ 1/t). If a person walks at 3/5 of his usual speed, the time taken will be 5/3 of his usual time.

Let the usual time be t minutes. The new time taken is ⁵⁄₃t. According to the problem, the difference between the new time and the usual time is 20 minutes:

⁵⁄₃t - t = 20

⅔t = 20

2t = 60

t = 30

The usual time taken by the person to reach his office is 30 minutes.

Explanation

The average marks for the entire class can be determined using the weighted average formula. Given that 60% of the students are girls, the remaining 40% are boys. This establishes a ratio of girls to boys as 60:40, which simplifies to 3:2.

Using the weighted average formula A = (n₁ a₁ + n₂ a₂)/(n₁ + n₂), where n represents the weights (ratios) and a represents the average marks of each group:

A = ((3 × 72) + (2 × 54))/(3 + 2)

Calculating the values in the numerator: 3 × 72 = 216 2 × 54 = 108 216 + 108 = 324

Dividing by the total weight: A = ³²⁴⁄₅ = 64.8

Alternatively, calculating with the actual number of students yields the same result. In a class of 40, there are 24 girls (60%) and 16 boys (40%). The total marks are (24 × 72) + (16 × 54) = 1728 + 864 = 2592. The class average is 2592 ÷ 40 = 64.8.

Explanation

The combined efficiency of A, B, and C is 2 + 5 + 3 = 10 units per day. Since they complete the task in 9 days, the total work is calculated using the formula Total Work = Combined Efficiency × Time, which gives 10 × 9 = 90 units. The specific task for C is 40% of this total work, calculated as 0.4 × 90 = 36 units. Given that the efficiency of C is 3 units per day, the time taken by C alone to complete 36 units of work is Time = Work / Efficiency = 36 / 3 = 12 days.

Explanation

To determine the ratio a:b:c, we must equalize the value of the common variable b in the given ratios. We are given a:b = 2:5 and c:b = 3:4, which can be expressed as b:c = 4:3. In the first ratio, b is represented by 5, and in the second, it is represented by 4. The least common multiple of 5 and 4 is 20.

By multiplying the first ratio a:b by 4, we get a:b = (2 × 4) : (5 × 4) = 8:20. By multiplying the second ratio b:c by 5, we get b:c = (4 × 5) : (3 × 5) = 20:15. Since the value of b is now 20 in both expressions, the combined ratio is found to be a:b:c = 8:20:15.

Explanation

To find the college with the least average passing percentage, we calculate the total sum of percentages for each college over the three years. Since the number of students (200) is identical for every college and every year, the college with the lowest sum will also have the lowest average. For College B, the sum of the passing percentages is 65 + 68 + 77 = 210. Dividing this sum by the three years gives an average passing percentage of 210 / 3 = 70%. This total of 210 is lower than the totals for College A (214), College C (260), College D (285), and College E (220).

Explanation

The trigonometric identity for complementary angles states that csc A = sec B if A + B = 90°. Applying this to the given equation csc 4θ = sec (60° - 2θ), we set the sum of the angles to 90°:

4θ + (60° - 2θ) = 90°

Simplifying the equation:

2θ + 60° = 90°

2θ = 90° - 60°

2θ = 30°

θ = 15°

Explanation

Sachin Tendulkar holds the record for the highest number of runs scored in the history of the ICC Cricket World Cup. Over a career spanning six tournament editions from 1992 to 2011, he accumulated a total of 2,278 runs in 45 matches. This record includes 6 centuries and 15 half-centuries at an average of 56.95. His most prolific tournament performance occurred during the 2003 World Cup, where he scored 673 runs, which remains the record for the most runs scored by an individual in a single edition of the tournament.

Explanation

The Tesla (symbol: T) is the SI derived unit of magnetic flux density, which represents the strength of a magnetic field. It is named in honor of the physicist and inventor Nikola Tesla. One Tesla is defined as the amount of magnetic flux through a square meter area when a magnetic field of one Tesla is perpendicular to that area. In terms of mechanical force, it is the field intensity that exerts a force of 1 Newton on a conductor of 1 meter length carrying a current of 1 Ampere. This is expressed by the formula B = F / (I · L), where B is the magnetic field, F is force, I is current, and L is length. Consequently, 1 T = 1 N · A⁻¹ · m⁻¹.

Explanation

Productivity measures the efficiency with which inputs like labor and capital are converted into goods and services. At the firm level, an increase in productivity means that more output is generated for every unit of input used. According to the aggregate production function Y = A · f(K, L), where Y represents total output or Gross Domestic Product, A represents total factor productivity, K is capital, and L is labor, any improvement in productivity A directly leads to an expansion of total output Y. When firms across an economy become more productive through technological advancement, better management, or improved worker skills, the cumulative effect is a rise in the nation's total production of goods and services. This expansion of the economy's productive capacity facilitates higher real incomes and sustained economic growth, resulting in a measurable increase in Gross Domestic Product.

Explanation

Sarojini Naidu, an eminent Indian independence activist and celebrated poet, authored the collection titled The Bird of Time: Songs of Life, Death and the Spring, published in 1912. This work is one of her most significant literary contributions and features a series of lyrical poems that explore themes of Indian folklore, nature, and the cycle of life. The book includes some of her most famous pieces, such as In the Bazaars of Hyderabad. Known as the Nightingale of India, Naidu used her poetry to weave together traditional Indian imagery with rhythmic English verse, establishing herself as a major figure in Indian English literature long before her political career as the first female Governor of an Indian state.

Explanation

The Orion constellation is named after a figure from Greek mythology who was a legendary giant hunter. It is one of the most recognizable constellations in the night sky, situated on the celestial equator and visible throughout the world. The stars are arranged in a pattern that resembles a human figure holding a bow or shield and a sword, with three prominent stars forming the waistline known as Orion's Belt. Due to this mythological depiction and its distinctive shape, the constellation is universally referred to as The Hunter.

Explanation

Vaporisation is the physical process by which a substance undergoes a phase transition from the liquid state to the gaseous state. This occurs when the atoms or molecules of the liquid gain sufficient thermal energy to overcome the intermolecular attractive forces that keep them in the liquid phase. Vaporisation encompasses two distinct phenomena: evaporation, which is a surface phenomenon occurring at temperatures below the boiling point, and boiling, which is a bulk phenomenon occurring when the vapor pressure of the liquid equals the external environmental pressure. In both instances, the substance absorbs latent heat to facilitate the change in state.

Explanation

The 2019 Special Olympics World Summer Games were hosted in Abu Dhabi, United Arab Emirates, from March 14 to March 21, 2019. This event marked the first time the Special Olympics World Games were held in the Middle East and North Africa region since the movement's inception. More than 7,500 athletes from over 190 countries participated in 24 different Olympic-style sports. The games were centered on the theme of inclusion and empowerment for people with intellectual disabilities, with the opening ceremony held at the Zayed Sports City Stadium.

Explanation

Lusei, also known as Lushai, is the primary dialect of the Mizo people and serves as the foundation for the modern Mizo language. It is predominantly spoken in the state of Mizoram, where it functions as the lingua franca among various ethnic groups. Historically, the region was administered as the Lushai Hills District during the British Raj, a name derived from the Lusei tribe who were the most influential group in the area, establishing the dialect's dominance in the state's linguistic and cultural landscape.

Explanation

Under Article 110(3) of the Constitution of India, if any question arises whether a Bill is a Money Bill or not, the decision of the Speaker of the Lok Sabha is final. This constitutional mandate grants the Speaker the exclusive authority to certify the status of such legislation. Furthermore, Article 110(4) requires that when a Money Bill is transmitted to the Rajya Sabha for recommendations or presented to the President for assent, it must carry an endorsement by the Speaker of the Lok Sabha certifying that it is indeed a Money Bill. This decision is conclusive and cannot be questioned in any court of law, in either House of Parliament, or by the President.

Explanation

The Rehuke khim is a distinctive traditional textile of the Yimkhiung Naga tribe, one of the major ethnic groups in Nagaland. Often referred to as the cowrie shawl, it is characterized by its elaborate decoration using rows of white cowrie shells stitched onto a hand-woven base. In Naga culture, shawls are not merely garments but are profound symbols of a person's social standing, achievements, or tribal identity. The Rehuke khim specifically represents the heritage of the Yimkhiung people, showcasing the intricate weaving techniques and symbolic ornamentation that define the indigenous craftsmanship of Nagaland. Traditionally, the patterns and embellishments on such shawls indicate the status of the wearer within the community.

Explanation

Zero Hour is an informal parliamentary device that allows Members of Parliament to raise matters of urgent public importance without any prior notice. It is a unique Indian innovation in the field of parliamentary procedures and has been in existence since 1962. This period starts immediately after the Question Hour and lasts until the regular business of the House, as listed in the agenda, is taken up. Since it typically begins at 12 noon, it is popularly referred to as the Zero Hour. Unlike the Question Hour, Zero Hour is not mentioned in the Rules of Procedure of the House.

Explanation

The Gandikota Canyon, located in the Kadapa district of Andhra Pradesh, is known as the Grand Canyon of India. This geological marvel was formed by the Pennar River cutting through the Erramala hills, resulting in a massive gorge characterized by steep, layered rock walls of red sandstone. The deep valley and the unique rock formations created by the erosion of the river over millions of years closely mirror the landscape of the Grand Canyon in Arizona, USA, leading to its popular designation. The site also features the historic Gandikota Fort, which sits majestically on the edge of the canyon cliffs.

Explanation

The Battle of Kanauj, also known as the Battle of Bilgram, was fought on May 17, 1540. It was a decisive encounter between the Mughal Emperor Humayun and the Afghan ruler Sher Shah Suri. Following his victory at the Battle of Chausa in 1539, Sher Shah Suri consolidated his power and met Humayun's forces again at Kanauj. The Mughal army was soundly defeated, leading to the complete collapse of Humayun's authority in India. This battle forced Humayun into exile for fifteen years and allowed Sher Shah Suri to establish the Sur Dynasty, making him the sovereign ruler of Delhi and Agra.

Explanation

Period. End of Sentence. won the Academy Award for Best Documentary Short Subject at the 91st Oscars in 2019. Directed by Rayka Zehtabchi and co-produced by Indian filmmaker Guneet Monga, the film is set in the village of Kathikhera in Hapur, Uttar Pradesh. It documents the lives of local women who fight the deep-rooted social stigma surrounding menstruation by installing a low-cost sanitary pad machine. The documentary highlights their journey toward economic empowerment and improved menstrual hygiene as they manufacture and sell their own pads under the brand name Fly, inspired by the real-life work of Arunachalam Muruganantham.

Explanation

Substitute goods are products that can be used in place of each other to satisfy the same consumer need. In economic theory, there is a positive relationship between the price of a substitute and the demand for the original good. When the price of a substitute product increases, consumers find the original product relatively more affordable and switch their consumption toward it. This increase in demand occurs independently of the original product's own price changes. Consequently, at every given price point, a higher quantity is demanded, which results in a rightward or outward shift of the entire demand curve.

Explanation

Kibithu is the easternmost inhabited point of India, located in the Anjaw district of Arunachal Pradesh. It is situated on the banks of the Lohit River at an altitude of approximately 1,300 meters above sea level. Geographically, it lies near the tri-junction of India, China, and Myanmar. India's longitudinal extent reaches its eastern limit at approximately 97 degree 25 minute E, and Kibithu is the most prominent settlement representing this extreme geographical boundary. It serves as an important administrative and military outpost along the Line of Actual Control.

Explanation

Oxygen is the most abundant element in the Earth's crust by mass, accounting for approximately 46.6 percent of the crust's total weight. It occurs predominantly in combination with other elements, forming silicate and oxide minerals that make up the majority of the rocks found in the continental and oceanic crust. Because the vast majority of crustal minerals are silicates, oxygen atoms are present in vast quantities, outperforming all other chemical elements in terms of total weight percentage.

Explanation

The Sahyadri Mountains, also known as the Western Ghats, are a massive mountain range that runs parallel to the western coast of the Indian peninsula. This range originates in the western state of Gujarat, specifically south of the Tapti River near the border of Maharashtra. It spans approximately 1,600 kilometers through the states of Maharashtra, Goa, Karnataka, Kerala, and Tamil Nadu, finally concluding at Kanyakumari, the southernmost tip of mainland India. The northern part of the range situated in Maharashtra and Gujarat is traditionally referred to as the Sahyadri.

Explanation

The Aligarh Movement was established by Sir Syed Ahmed Khan in the late 19th century to promote modern education and social reform among the Muslim community in India. He was the founder of the Muhammadan Anglo-Oriental College, which later became the Aligarh Muslim University.

Explanation

In cricket, the phrase bend your back is a common idiom used to describe a fast bowler putting in extra physical effort to generate more pace and bounce from the pitch. It refers to the physical exertion involved when a bowler uses their torso and back muscles more aggressively during the delivery stride to hit the deck harder. This is typically done on flat or unresponsive surfaces where the bowler needs to work harder than usual to extract any advantage from the conditions.

Explanation

Rabindranath Tagore was the primary inspiration behind the founding of Dartington Hall School through his partnership with the British idealist Leonard Elmhirst. Elmhirst had served as the first director of the Institute of Rural Reconstruction at Sriniketan under Tagore's guidance, where they experimented with progressive educational and social reforms. When Leonard and Dorothy Elmhirst established Dartington Hall in 1926, they modeled its curriculum and communal structure on Tagore's ideals of freedom, creativity, and the harmony between nature and education. The school was designed to implement the pedagogical innovations practiced at Shantiniketan, emphasizing the development of the whole person through arts, crafts, and academic study. Tagore's influence was so significant that the school is often considered the Western counterpart to his educational experiments in India.

Explanation

The National War Memorial is located in New Delhi, situated within the India Gate complex at the C-Hexagon. It was inaugurated on February 25, 2019, to honor the personnel of the Indian Armed Forces who have sacrificed their lives in the line of duty since India's independence in 1947. The memorial complex is spread over 40 acres and features four concentric circles—Amar Chakra, Veerta Chakra, Tyag Chakra, and Rakshak Chakra—which represent the cycle of birth, the bravery of soldiers, the sacrifice of life, and the protection provided by the forces. The names of the fallen soldiers are inscribed in golden letters on the walls of the Tyag Chakra.

Explanation

The Indian Association was established on July 26, 1876, in Calcutta by Surendranath Banerjee and Ananda Mohan Bose. It was the first declared nationalist organization founded in British India and served as a precursor to the Indian National Congress. The association was formed to represent the views of the educated middle class and to create a strong body of public opinion on political matters. It focused on promoting the political, intellectual, and material advancement of the people and played a pivotal role in organizing national-level agitations, such as the protest against the reduction of the age limit for the Indian Civil Service examinations and the opposition to the Vernacular Press Act. Its objective of unifying Indians on a common political platform significantly contributed to the growth of the national movement.

Explanation

Hydra is the largest of the 88 modern constellations recognized by the International Astronomical Union (IAU), covering an area of approximately 1303 square degrees. It is an elongated constellation that stretches across more than 100 degrees of the celestial sphere, with its head located south of Cancer and its tail extending as far as Libra and Centaurus. Despite its immense size, which accounts for about 3.16 percent of the sky, it is not particularly prominent as it contains only one moderately bright star, Alphard. Its vast scale makes it the longest constellation in the night sky.

Explanation

Let the marked price be M. The selling price after successive discounts of d₁% and d₂% is determined by the relation SP = M × (1 - (d₁)/(100)) × (1 - (d₂)/(100)). Substituting the given values:

288 = M × (1 - ²⁰⁄₁₀₀) × (1 - ²⁵⁄₁₀₀) 288 = M × ⁸⁰⁄₁₀₀ × ⁷⁵⁄₁₀₀ 288 = M × ⅘ × ¾

Simplifying the equation: 288 = M × ⅗ M = (288 × 5)/(3) M = 96 × 5 = 480

Alternatively, the equivalent single discount for successive discounts x% and y% is calculated as x + y - ˣʸ⁄₁₀₀. For discounts of 20% and 25%, the equivalent discount is 20 + 25 - (20 × 25)/(100) = 45 - 5 = 40%. Since the total discount is 40%, the selling price of ₹ 288 represents 60% of the marked price. Therefore, 0.6M = 288, which results in M = 480.

Explanation

In a circle, the perpendicular distance from the centre to a chord bisects the chord, forming a right-angled triangle. In this triangle, the radius of the circle acts as the hypotenuse (r = 17 cm), the distance from the centre is the altitude (d = 15 cm), and half the length of the chord is the base (b).

Using the Pythagorean theorem: r² = d² + b² 17² = 15² + b² 289 = 225 + b² b² = 289 - 225 = 64 b = √(64) = 8 cm

Since b represents half the length of the chord, the full length of the chord is 2 × 8 = 16 cm. This calculation follows the standard Pythagorean triple (8, 15, 17).

Explanation

Given the ratio a : b = 5 : 7, we can substitute a = 5 and b = 7 directly into the expression because the terms in the ratio (5a - 3b) : (4a - 2b) are homogeneous, meaning each term is of the same degree. This ensures that any common constant multiplier k (where a = 5k and b = 7k) would cancel out during the calculation.

Substituting these values into the expression: Numerator: 5a - 3b = 5(5) - 3(7) = 25 - 21 = 4 Denominator: 4a - 2b = 4(5) - 2(7) = 20 - 14 = 6

The resulting ratio is 4 : 6. By simplifying this ratio through division by the common factor of 2, we obtain 2 : 3.

Explanation

The expression is simplified by following the BODMAS rule, which establishes the order of operations as Division, Multiplication, Addition, and then Subtraction. First, the division components are calculated: 21.6 ÷ 3.6 = 6 and 16 ÷ 4 = 4. Substituting these results into the original equation gives 6 × 2 + 0.25 × 4 - 6. Next, the multiplication steps are performed: 6 × 2 = 12 and 0.25 × 4 = 1. The expression now simplifies to 12 + 1 - 6. Following the order for addition and subtraction, we calculate 13 - 6, which results in 7.

Explanation

The trigonometric identity for complementary angles states that sin A = cos (90° - A), which implies that if sin A = cos B, then A + B = 90°. Applying this relation to the equation sin 3θ = cos (20° - θ), we substitute the given expressions for A and B into the formula: 3θ + (20° - θ) = 90° 2θ + 20° = 90° 2θ = 70° θ = 35°

Explanation

The total work is calculated by multiplying the combined efficiency of A, B, and C by the number of days they work together. Given the ratio of efficiencies as 2:5:3, the combined efficiency is 2 + 5 + 3 = 10 units per day. Since they complete the task in 12 days, the total work is 10 × 12 = 120 units.

The task A needs to perform is 30% of this total work, which is 0.30 × 120 = 36 units. The efficiency of A is 2 units per day. Therefore, the time taken by A alone to complete this portion of the task is calculated as 36 / 2 = 18 days.

Explanation

The relationship between price, consumption, and expenditure is given by the formula Expenditure = Price × Consumption. Let the initial price of petrol be 100 and the initial consumption be 100 units, making the initial expenditure 100 × 100 = 10000.

With a 28% increase in price, the new price becomes 128. The person wants the expenditure to increase by only 22%, so the new expenditure should be 10000 × 1.22 = 12200.

Let the new consumption be x. According to the formula: 128 × x = 12200 x = ¹²²⁰⁰⁄₁₂₈ = ³⁰⁵⁰⁄₃₂ = 95.3125

The percentage decrease in consumption is calculated as: Percentage decrease = Initial Consumption - New Consumption Percentage decrease = 100 - 95.3125 = 4.6875%

Alternatively, the reduction can be calculated directly using the change relative to the new price base: Percentage reduction = (Percentage Price Increase - Percentage Expenditure Increase)/(100 + Percentage Price Increase) × 100 Percentage reduction = (28 - 22)/(100 + 28) × 100 = ⁶⁄₁₂₈ × 100 = 4.6875%

Rounding 4.6875% to the nearest tenth gives approximately 4.7%.

Explanation

The average marks of the entire class can be calculated using the weighted average formula based on the ratio of boys to girls. Since 60% of the students are boys, the remaining 40% are girls, establishing a ratio of 3:2.

Average of class = ((Ratio of Boys × Average of Boys) + (Ratio of Girls × Average of Girls))/(Sum of Ratios)

Substituting the given values into the formula: Average = ((3 × 62) + (2 × 68))/(3 + 2) Average = (186 + 136)/(5) Average = ³²²⁄₅ = 64.4

Alternatively, using the deviation method, if we take 62 as the base average, the girls average 6 marks more than the boys. Since girls represent 40% of the class, they contribute an additional 0.4 × 6 = 2.4 marks to the total average. Adding this to the base average results in 62 + 2.4 = 64.4.

Explanation

To find the average number of students who play cricket across all four schools, we first determine the total number of cricket players by summing the values provided for each school in the Cricket row of the table.

Total number of students playing cricket = 125 (A) + 250 (B) + 150 (C) + 175 (D) = 700

The average is then calculated by dividing this total sum by the total number of observations, which in this case corresponds to the four schools being surveyed.

Average = (Sum of students)/(Number of schools) = ⁷⁰⁰⁄₄ = 175

This calculation follows the standard arithmetic mean formula x = (Σ xᵢ)/(n) to arrive at the mean value for the cricket category across the specified group of schools.