SSC CGL Tier 1 2019 General Awareness Questions with Solutions

Explanation

Afghanistan set a new world record for the highest T20 International total on February 23, 2019, during the second match of their series against Ireland. Playing at the Rajiv Gandhi International Cricket Stadium in Dehradun, which served as their adopted home ground, Afghanistan scored 278/3 in their allotted 20 overs. This massive total was fueled by an unbeaten 162 runs from Hazratullah Zazai and 73 runs from Usman Ghani, who together shared a record opening partnership of 236 runs. This performance surpassed the previous world record of 263/3 held by Australia.

Explanation

Article 39A of the Constitution of India directs the State to ensure that the operation of the legal system promotes justice on the basis of equal opportunity. It was inserted into the Directive Principles of State Policy by the 42nd Amendment Act of 1976. The article specifically mandates the State to provide free legal aid through suitable legislation or schemes to ensure that opportunities for securing justice are not denied to any citizen by reason of economic or other disabilities. This constitutional obligation led to the enactment of the Legal Services Authorities Act, 1987, and the establishment of the National Legal Services Authority (NALSA) to provide free and competent legal services to the weaker sections of society.

Explanation

The efficiency ratio of A, B, and C is given as 5 : 3 : 8. Let their daily work rates be 5x, 3x, and 8x respectively. When working together, their combined efficiency is 5x + 3x + 8x = 16x units per day. Since they complete the work in 30 days, the total work is 16x × 30 = 480x units.

A and B work together for 20 days. Their combined efficiency is 5x + 3x = 8x units per day. The work completed by them in 20 days is 8x × 20 = 160x units.

The remaining work is 480x - 160x = 320x units. This work is to be completed by C alone. With C's efficiency being 8x units per day, the time taken is calculated as: Time = (Remaining Work)/(Efficiency of C) = ³²⁰ˣ⁄₈ₓ = 40 days.

Explanation

In a triangle, the largest angle is always opposite the longest side. Given the side lengths of 6 cm, 7 cm, and 8 cm, the longest side is 8 cm. Therefore, the angle bisector of the largest angle divides the side of length 8 cm into two segments.

The Angle Bisector Theorem states that the internal bisector of an angle in a triangle divides the opposite side into segments that are proportional to the other two sides of the triangle. Let the segments of the side measuring 8 cm be x and y. According to the theorem, the ratio of these segments is equal to the ratio of the adjacent sides, which are 6 cm and 7 cm. Thus, (x)/(y) = ⁶⁄₇.

To find the length of the segments, we divide the total length of 8 cm in the ratio 6:7. The sum of the ratio parts is 6 + 7 = 13. The length of the first segment is ⁶⁄₁₃ × 8 = ⁴⁸⁄₁₃ cm, and the length of the second segment is ⁷⁄₁₃ × 8 = ⁵⁶⁄₁₃ cm. Comparing these two values, the shorter segment is ⁴⁸⁄₁₃ cm.

Explanation

When two objects move toward each other from two points, the time taken to meet is given by the formula t = (D)/(S₁ + S₂), where D is the initial distance and S₁, S₂ are their respective speeds.

Substituting the given values, t = (800)/(40 + 60) = ⁸⁰⁰⁄₁₀₀ = 8 hours.

The distance from station A where they cross is the distance covered by train X in this time. Using the formula Distance = Speed × Time, the distance from A is 40 × 8 = 320 km.

Explanation

The radius OR drawn to the point of contact R is perpendicular to the tangent line SR, meaning ∠ ORS = 90°. Since the line segment QR is the bisector of ∠ ORS, the measure of ∠ QRS is calculated as ½ × 90° = 45°.

According to the Alternate Segment Theorem, the angle formed between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alternate segment. In this configuration, the angle between the tangent SR and the chord QR is ∠ QRS. The angle subtended by the chord QR at the vertex P on the circumference is ∠ RPQ. Applying the theorem, we find that ∠ RPQ = ∠ QRS = 45°.

Explanation

Let R be the radius of the circle with centre O. Since points A, B, and C lie on the circle, the line segments OA, OB, and OC are all radii, so OA = OB = OC = R. In the parallelogram ACBO, opposite sides are equal, which means OA = BC and OB = AC. Given OA = OB = R, it follows that BC = R and AC = R.

Now consider the triangles △ OAC and △ OBC formed by the diagonal OC. In △ OAC, all three sides OA, AC, and OC are equal to R, making it an equilateral triangle. Therefore, ∠ AOC = 60°. Similarly, in △ OBC, all three sides OB, BC, and OC are equal to R, making it an equilateral triangle as well. Therefore, ∠ BOC = 60°. Since C is a point on the minor arc AB, the angle ∠ AOB is the sum of these two angles: ∠ AOB = ∠ AOC + ∠ BOC = 60° + 60° = 120°.

Explanation

In any parallelogram ABCD, the opposite sides are equal in length, so AB = DC. Because AD is parallel to BC, the perpendicular distance between these two parallel lines is constant at all points. This means that the lengths of the perpendiculars AE and DF dropped from vertices A and D to the line containing BC must be equal (AE = DF).

Now consider the right-angled triangles △ AEB and △ DFC. Both triangles have a right angle (∠ AEB = ∠ DFC = 90°), equal hypotenuses (AB = DC), and one pair of equal sides (AE = DF). According to the Right-Angle Hypotenuse Side (RHS) congruence criterion, △ AEB ≅ △ DFC. Since this congruence is a fundamental property derived from the nature of a parallelogram and its altitudes, it represents a true geometric relationship for the given figure.

Explanation

The total sum of the 12 numbers is 12 × 46 = 552. The sum of the first four numbers is 4 × 43 = 172, and the sum of the last five numbers is 5 × 49.4 = 247. To find the sum of the 5ᵗʰ, 6ᵗʰ, and 7ᵗʰ numbers, we subtract the sum of the first four and last five from the total sum: 552 - (172 + 247) = 552 - 419 = 133.

Let the 7ᵗʰ number be x. According to the problem, the 5ᵗʰ number is x + 4 and the 6ᵗʰ number is x + 6. We can set up the equation (x + 4) + (x + 6) + x = 133. Simplifying this gives 3x + 10 = 133, which leads to 3x = 123, so x = 41.

The 7ᵗʰ number is 41 and the 5ᵗʰ number is 41 + 4 = 45. The average of the 5ᵗʰ and 7ᵗʰ numbers is (45 + 41)/(2) = ⁸⁶⁄₂ = 43.

Explanation

To find two numbers x and y such that x + y = 12 and xy = 27, we test factors of 27. The pair (9, 3) satisfies both conditions since 9 + 3 = 12 and 9 × 3 = 27. Given the condition x > y, we have x = 9 and y = 3.

The value of x³ - y³ is calculated by substituting these values: x³ - y³ = 9³ - 3³ x³ - y³ = 729 - 27 = 702

Alternatively, using algebraic identities, we first find x - y using the relation (x - y)² = (x + y)² - 4xy: (x - y)² = 12² - 4(27) = 144 - 108 = 36 Since x > y, we have x - y = 6. Now, using the identity x³ - y³ = (x - y)³ + 3xy(x - y): x³ - y³ = 6³ + 3(27)(6) x³ - y³ = 216 + 486 = 702

Explanation

When the time period is a fraction, such as 2⁵⁄₇ years, the compound interest is calculated by applying the full interest rate for the complete years and a proportional rate for the fractional part. For the first 2 years, the successive interest rate is calculated as x + y + ˣʸ⁄₁₀₀. Here, 14 + 14 + (14 × 14)/(100) = 29.96%.

For the remaining ⁵⁄₇ of the year, the applicable interest rate is 14% × ⁵⁄₇ = 10%. The overall effective interest rate for the entire period is found by combining the 2-year rate of 29.96% with the 10% rate for the fractional part using the same successive formula: 29.96 + 10 + (29.96 × 10)/(100) = 39.96 + 2.996 = 42.956%.

To find the compound interest on ₹10,000, multiply the principal by the effective rate: 10000 × (42.956)/(100) = 4295.6. Rounding to the nearest rupee, the interest is ₹4,296.

Explanation

Let the cost prices of the two articles be CP₁ and CP₂. When the selling prices are equal for two items sold at a loss of L% and a profit of P%, the ratio of their cost prices is given by the inverse ratio of their selling price factors: CP₁ / CP₂ = (100 + P) / (100 - L). Substituting P = 14 and L = 14:

CP₁ / CP₂ = (100 + 14) / (100 - 14) = 114 / 86 = 57 / 43

The total cost price is represented by the sum of these ratio components: 57 + 43 = 100 units. Given that the total cost price is 624, one unit is equal to 624 / 100 = 6.24. The difference between the cost prices in ratio units is 57 - 43 = 14 units. The actual difference in rupees is calculated by multiplying these units by the value per unit: 14 × 6.24 = 87.36.

Explanation

The total production of type E cars in 2012 and 2013 is calculated by summing the values for those years: 47 + 43 = 90.

To find the average production of type A cars from 2012 to 2016, first calculate the total sum: 54 + 58 + 60 + 63 + 55 = 290. The average is this total divided by the number of years: 290 / 5 = 58.

The percentage by which the production of type E cars (90) exceeds the average production of type A cars (58) is determined using the formula: Percentage More = (Value - Reference)/(Reference) × 100 Percentage More = (90 - 58)/(58) × 100 = ³²⁄₅₈ × 100 = ¹⁶⁄₂₉ × 100 ≈ 55.17%

Rounding to one decimal place, we get 55.2.

Explanation

The pipe is a hollow cylinder. The volume of the metal used is the difference between the external and internal volumes, given by the formula V = π(R² - r²)h.

Given that the length h = 7.56 m = 756 cm, external radius R = 2.5 cm, and internal radius r = 1.5 cm, we substitute these values into the formula:

V = ²²⁄₇ × (2.5² - 1.5²) × 756

Using the identity a² - b² = (a+b)(a-b): R² - r² = (2.5 + 1.5)(2.5 - 1.5) = 4 × 1 = 4

V = ²²⁄₇ × 4 × 756 V = 22 × 4 × 108 V = 88 × 108 = 9504 cm³

The weight of the pipe is the product of its volume and the density of the metal: Weight = 9504 cm³ × 7.5 g/cm³ Weight = 71280 g

To convert the weight into kilograms: Weight in kg = ⁷¹²⁸⁰⁄₁₀₀₀ = 71.28 kg

Explanation

The total production of all types of cars except type B in 2012 is the sum of types A, C, D, and E for that year. Total (2012 excluding B) = 54 + 46 + 33 + 47 = 180 thousand.

The total production of all types of cars in 2016 is the sum of types A, B, C, D, and E for that year. Total (2016) = 55 + 67 + 77 + 49 + 52 = 300 thousand.

To find the percentage by which 180 is less than 300, we use the formula: Percentage Less = (Initial Value - Final Value)/(Initial Value) × 100 Percentage Less = (300 - 180)/(300) × 100 Percentage Less = ¹²⁰⁄₃₀₀ × 100 Percentage Less = 40%

Explanation

The total production of Type D cars over the period from 2012 to 2016 is calculated by summing the annual production figures provided in the table: 33 + 35 + 48 + 45 + 49 = 210 thousand units. In a pie chart, the entire circle represents the total production of 210 units, which corresponds to a total central angle of 360°. The central angle for a specific year is determined by the ratio of that year's production to the total production, multiplied by 360°. For the year 2013, the production of Type D cars was 35 thousand units. The central angle for 2013 is calculated as follows:

Central Angle = (Production in 2013 / Total Production) × 360° Central Angle = (35 / 210) × 360°

Simplifying the fraction, 35 / 210 = 1 / 6. Applying this to the angle calculation, we get (1 / 6) × 360° = 60°.

Explanation

The total production of type E cars in 2014 and type C cars in 2016 taken together is calculated by adding their respective values from the table: 53 + 77 = 130.

The total production of type B cars in 2014 and type D cars in 2013 taken together is calculated by adding their respective values from the table: 56 + 35 = 91.

To find the required ratio, we compare these two sums: Ratio = 130 : 91

Both numbers are divisible by 13. Dividing 130 by 13 gives 10, and dividing 91 by 13 gives 7. Ratio = 10 : 7

Explanation

The relationship between revenue, price, and sales is given by the formula: Revenue = Price × Sales. When two factors are multiplied to give a product, the net percentage change in the product can be calculated using the successive percentage change formula: Net Change = a + b + ᵃᵇ⁄₁₀₀, where a and b are the percentage changes in the two factors.

In this case, the change in price a = -20% (reduction), the change in sales b = x%, and the net change in revenue is 60%. Substituting these values into the formula:

60 = -20 + x + ⁽⁻²⁰⁾⁽ˣ⁾⁄₁₀₀

60 = -20 + x - 0.2x

80 = 0.8x

x = (80)/(0.8)

x = 100

Alternatively, using the ratio method, let the initial price be 100 and initial sales be 100, making initial revenue 10000. After a 20% reduction, the new price is 80. With a 60% increase in revenue, the new revenue becomes 16000. The new sales figure is ¹⁶⁰⁰⁰⁄₈₀ = 200. The increase in sales from 100 to 200 represents a 100% increase.

Explanation

Let the present ages of A and B be 8x and 9x respectively. According to the problem, after 9 years, their ages will be 8x + 9 and 9x + 9. The ratio is given as:

(8x + 9)/(9x + 9) = ¹⁹⁄₂₁

Cross-multiplying the terms: 21(8x + 9) = 19(9x + 9) 168x + 189 = 171x + 171 171x - 168x = 189 - 171 3x = 18 x = 6

B's present age is 9x = 9 × 6 = 54 years. Since C is 3 years younger than B, C's present age is 54 - 3 = 51 years.

Explanation

For a number to be divisible by 88, it must be divisible by both 8 and 11, as 8 and 11 are co-prime factors of 88.

According to the divisibility rule for 8, the last three digits of the number 5y2 must be divisible by 8. Testing the smallest possible values for y, we find that if y = 0, 502 is not divisible by 8. If y = 1, 512 / 8 = 64, which is a perfect division. Thus, the smallest possible value for y is 1.

The divisibility rule for 11 states that the difference between the sum of the digits at odd positions and the sum of the digits at even positions must be 0 or a multiple of 11. For the number 32x4115y2, the sum of digits at odd positions is 3 + x + 1 + 5 + 2 = 11 + x. The sum of digits at even positions is 2 + 4 + 1 + y = 7 + y.

The difference is (11 + x) - (7 + y) = 4 + x - y. Substituting the smallest value of y = 1, the difference becomes 4 + x - 1 = 3 + x. for the number to be divisible by 11, 3 + x must be 11 (since x is a single digit, it cannot be 22, and for the result to be 0, x would be negative). Solving 3 + x = 11 gives x = 8.

The required value is 4x - y. Substituting x = 8 and y = 1, we get 4(8) - 1 = 32 - 1 = 31.

Explanation

Let the total cost price of the goods be 100. Since the trader marks the goods 40% above the cost price, the marked price for the entire stock is 140.

The trader sells 70% of the goods at the marked price. The revenue from this portion is 0.70 × 140 = 98.

The remaining 30% of the goods are sold at a 40% discount on the marked price. The selling price for this portion is 140 × (1 - 0.40) = 140 × 0.60 = 84 per unit equivalent. The revenue from this remaining portion is 0.30 × 84 = 25.2.

Total revenue (Selling Price) is the sum of the two parts: Total SP = 98 + 25.2 = 123.2

The profit percentage is calculated as: Profit % = (Total SP - Total CP)/(Total CP) × 100 Profit % = (123.2 - 100)/(100) × 100 = 23.2%

Explanation

The Global Passport Index 2019, compiled by Arton Capital, ranked the Indian passport at the 67th position. This ranking is determined by the Mobility Score, which calculates the total number of countries that a passport holder can enter either visa-free or with a visa-on-arrival. In the 2019 report, India's rank improved as its citizens were granted increased travel freedom, reflecting the growing strength of Indian diplomatic relations and international mobility. The index specifically monitors the real-time visa requirements of 193 United Nations member countries and six territories to assign these global rankings.

Explanation

The Commission for Agricultural Costs and Prices (CACP) is an attached office of the Ministry of Agriculture and Farmers Welfare that is responsible for recommending the Minimum Support Price (MSP) for mandated crops. It performs a comprehensive analysis of various factors, such as the cost of production, changes in input prices, market price trends, demand and supply dynamics, and inter-crop price parity before submitting its recommendations. As of 2019, the CACP recommends MSPs for 23 commodities, including seven cereals, five pulses, seven oilseeds, and four commercial crops. These recommendations are sent to the Union Government, where the final decision on the price levels is taken by the Cabinet Committee on Economic Affairs (CCEA). The primary objective of this process is to ensure remunerative prices for farmers and encourage higher investment and production in the agricultural sector.

Explanation

Prime Minister Narendra Modi launched the Pradhan Mantri Shram Yogi Maandhan (PM-SYM) Yojana on March 5, 2019, during a public gathering at Vastral in Gandhinagar, Gujarat. The scheme is a voluntary and contributory pension program aimed at providing social security to unorganized sector workers, such as street vendors, rickshaw pullers, construction workers, and domestic helps. It ensures a minimum assured monthly pension of 3,000 rupees to the subscribers after they reach the age of 60. The central government provides a matching contribution to the monthly premium paid by the beneficiary, which varies depending on their entry age into the scheme.

Explanation

Rickets is a skeletal disorder primarily caused by a prolonged deficiency of Vitamin D in children. Vitamin D plays a crucial role in the body by facilitating the absorption of calcium and phosphorus from the gastrointestinal tract, minerals that are essential for the proper mineralization and hardening of bone tissue. When Vitamin D levels are insufficient, the bones becomes soft and weak, leading to structural deformities such as bowed legs, knock knees, and a thickened wrist or ankle. This deficiency prevents the growing skeleton from developing the necessary density and strength, often resulting in stunted growth and increased susceptibility to fractures. Sunlight exposure and specific dietary sources are the primary means of maintaining adequate Vitamin D levels to prevent the onset of this condition.

Explanation

Ghum railway station, situated in the Darjeeling district of West Bengal, holds the distinction of being the highest railway station in India. It is positioned at an elevation of 2,258 meters (7,407 feet) above sea level. The station is an integral part of the Darjeeling Himalayan Railway, a 2-foot narrow-gauge line that began operations in the late 19th century. Recognized for its unique engineering and scenic route, the Darjeeling Himalayan Railway was inscribed as a UNESCO World Heritage Site in 1999. Ghum serves as a prominent landmark for tourists visiting the region, offering a significant point of elevation on the climb from Siliguri to Darjeeling.

Explanation

Razia Begum, popularly known as Razia Sultan, was the daughter of the Mamluk Sultan Shamsuddin Iltutmish and ruled the Delhi Sultanate from 1236 to 1240. Iltutmish broke tradition by nominating her as his successor over his sons, whom he considered incompetent for the throne. She was a skilled administrator and a brave warrior who led her armies in battle. Despite the short duration of her reign, she holds a unique place in Indian history as the first and only woman to occupy the throne of the Delhi Sultanate, challenging the patriarchal norms of the 13th-century socio-political structure.

Explanation

Majuli is a river island located in the Brahmaputra River in Assam, India. In September 2016, it was officially recognized by the Guinness World Records as the world's largest river island, surpassing Marajó in Brazil. The island is formed by the Brahmaputra river to the south and the Kherkutia Xuti, an anabranch of the Brahmaputra, joined by the Subansiri River to the north. Apart from its geographical significance, Majuli is the first island in India to be designated as a district and serves as the principal center of Neo-Vaishnavite culture, housing many traditional monasteries known as Satras.

Explanation

Bariatric surgery is a medical procedure specifically designed to treat morbid obesity by making structural changes to the digestive system. These surgical interventions, which include procedures like gastric bypass and sleeve gastrectomy, involve reducing the functional size of the stomach to limit food intake or rerouting the small intestine to decrease the absorption of calories and nutrients. By altering the anatomy of the gastrointestinal tract, bariatric surgery also modifies the hormonal signals between the gut and the brain that regulate hunger and fullness, leading to long-term weight loss and improved metabolic function.

Explanation

Photosynthesis is the fundamental biochemical process by which green plants, algae, and certain bacteria convert light energy from the sun into chemical energy. Using chlorophyll to trap sunlight, plants transform carbon dioxide and water into glucose, which is a simple carbohydrate or monosaccharide. The overall chemical reaction is represented as 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂. This glucose serves as the primary energy source for the plant's growth and metabolic activities, while oxygen is released into the atmosphere as a byproduct. Any excess glucose produced is typically converted into starch for long-term energy storage.

Explanation

The World Happiness Report 2019, released by the United Nations Sustainable Development Solutions Network on March 20, 2019, ranked 156 countries based on several indicators of well-being. India was ranked at the 140th position, which was a drop of seven spots from its 133rd rank in the 2018 report. The index calculates rankings using a three-year average of data from the Gallup World Poll, focusing on six key variables: GDP per capita, social support, healthy life expectancy, freedom to make life choices, generosity, and absence of corruption. India's decline in the 2019 rankings reflected a downward trend in reported life evaluations and an increase in negative emotions among the surveyed population.

Explanation

The Royal Calcutta Golf Club (RCGC), established in 1829, is the oldest golf club in the world outside of the United Kingdom. Originally named the Calcutta Golf Club, it received the Royal title following a visit by King George V and Queen Mary in 1911. The club was instrumental in popularizing the sport in India and remains one of the most prestigious golfing institutions globally due to its historical significance and its status as the second oldest golf club in the world, surpassed only by the Royal and Ancient Golf Club of St Andrews in Scotland.

Explanation

Article 324 of the Indian Constitution establishes the Election Commission as an independent constitutional authority. It specifically vests the power of superintendence, direction, and control of the preparation of electoral rolls and the conduct of all elections to Parliament and to the Legislature of every State in the Election Commission. This mandate also extends to conducting elections for the offices of the President and the Vice-President of India, ensuring a centralized and autonomous body manages the electoral process to maintain democratic integrity.

Explanation

Akbar ascended the Mughal throne in 1556 following the accidental death of his father, Humayun, who died after falling from the stairs of his library in Delhi. At the time of his father's passing, the thirteen-year-old Akbar was in Kalanaur, Punjab, leading a military campaign against the Suri forces. He was formally crowned on February 14, 1556, at Kalanaur, with Bairam Khan serving as his regent and tutor. His reign began during a critical period, and shortly after his accession, he consolidated his authority by defeating the forces of Hemu at the Second Battle of Panipat in November 1556.

Explanation

Lal Krishna Advani, born on November 8, 1927, was the oldest member of the 16th Lok Sabha, which served from 2014 to 2019. He represented the Gandhinagar constituency in Gujarat during this term. As a founding member of the Bharatiya Janata Party and a veteran parliamentarian, his seniority in age surpassed all other elected representatives in the lower house during that specific legislative period.

Explanation

The Gandhi-Irwin Pact, signed on March 5, 1931, was a political agreement that aimed to end the Civil Disobedience Movement and ensure the participation of the Indian National Congress in the Second Round Table Conference. While the promotion of Khadi was a significant part of Mahatma Gandhi's broader socio-economic agenda and the nationalist struggle, the specific demand for the withdrawal of tax on Khadi production was not a provision of this pact. The agreement focused on the release of non-violent political prisoners, the withdrawal of emergency ordinances, and granting people in coastal areas the right to produce salt for personal use, but it did not address Khadi taxation.

Explanation

The Simon Commission, formally known as the Indian Statutory Commission, was established in November 1927 by the British government. It comprised seven Members of Parliament from the United Kingdom under the chairmanship of Sir John Simon. The primary mandate of the commission was to review the functioning of the Government of India Act 1919 and to suggest further constitutional reforms for British India. Because the commission did not include any Indian members, it was met with widespread protests and the slogan Simon Go Back upon its arrival in India in 1928. Its final report, published in 1930, served as a foundational document for the subsequent Round Table Conferences and the Government of India Act 1935.

Explanation

Pakhawaj is a traditional barrel-shaped, two-headed percussion instrument rather than a vocal form. It belongs to the category of Avanaddha Vadya or membranophones and serves as the primary rhythmic accompaniment for ancient vocal genres like Dhrupad and Dhamar. Historically evolved from the mridang, the Pakhawaj is played with the palms and fingers to produce deep, resonant tones. While it is essential to the performance of certain vocal styles, it remains a purely instrumental discipline involving specific rhythmic cycles and bols that are distinct from the melodic and lyrical structures of vocal music.

Explanation

The Khajuraho Group of Monuments is located in the Chhatarpur district of Madhya Pradesh. These temples were constructed between 950 and 1050 AD by the rulers of the Chandela dynasty. Renowned for their intricate Nagara-style architecture and expressive sculptures, the site originally comprised 85 temples, of which about 25 survive today. The complex includes both Hindu and Jain temples, symbolizing a tradition of religious acceptance. Due to their outstanding universal value, they were designated as a UNESCO World Heritage Site in 1986.

Explanation

According to Section 4(1) of the Micro, Small and Medium Enterprises Development (MSMED) Act, 2006, the National Board for Micro, Small and Medium Enterprises is required to meet at least once in every six months. In the provided options, which appear to follow a format where the second digit is the value, option D corresponds to the correct duration of 6 months.

Explanation

Varkala, Chowara, Chavakkad, and Nattika are all prominent coastal destinations located in the state of Kerala. Varkala Beach, also known as Papanasham Beach, is situated in the Thiruvananthapuram district and is unique for its towering tertiary sedimentary formation cliffs overlooking the Arabian Sea. Chowara Beach is another scenic spot located near Kovalam in the same district, characterized by its traditional fishing hamlets and golden sands. Chavakkad and Nattika beaches are both located in the Thrissur district. Chavakkad is famous for its estuary where the river meets the sea, while Nattika is a wide, tranquil beach often associated with traditional local lifestyles and film locations. These beaches form a significant part of the 580-kilometer coastline that defines the geography and tourism sector of Kerala.

Explanation

Justice Leila Seth was appointed as the first woman judge of the Delhi High Court on August 10, 1978. An accomplished jurist, she had earlier achieved the distinction of being the first woman to top the London Bar exam in 1958. Following her tenure at the Delhi High Court, she reached another historic milestone in 1991 when she was appointed as the Chief Justice of the Himachal Pradesh High Court, making her the first woman to serve as the Chief Justice of a state High Court in India. Throughout her career, she also contributed to significant legal reforms, including her work with the 15th Law Commission of India and the Justice Verma Committee.

Explanation

Malic acid is the predominant organic acid found in apples, accounting for approximately 90 percent of the fruit's total organic acid content. It is a dicarboxylic acid with the chemical formula C₄H₆O₅ and is responsible for providing apples with their characteristic tart and sour flavor. First isolated from apple juice by Carl Wilhelm Scheele in 1785, malic acid plays a crucial role in the fruit's metabolism and the Krebs cycle. The concentration of this acid typically decreases as the apple ripens and its sugar levels increase, leading to a sweeter taste.

Explanation

Wilson's disease is an inherited disorder that causes excessive amounts of copper to accumulate in the body, particularly in the liver, brain, and eyes. Night blindness is not a clinical manifestation of this condition. Instead, night blindness is typically caused by a deficiency of Vitamin A, which is necessary for the synthesis of rhodopsin in the retina, or by specific genetic retinal degenerations. While Wilson's disease does affect the eyes, it specifically causes the formation of Kayser-Fleischer rings, which are dark-colored deposits of copper in the cornea. These rings do not interfere with night vision. The primary symptoms of Wilson's disease are related to hepatic dysfunction, such as liver failure and fluid retention, and neurological or psychiatric issues resulting from copper toxicity in the central nervous system.

Explanation

Aditi Ashok created history in November 2016 by becoming the first Indian golfer to win a title on the Ladies European Tour. She achieved this feat by winning the Hero Women's Indian Open held at the DLF Golf and Country Club in Gurugram. Shortly after this victory, she won her second title of the season at the Qatar Ladies Open. Her remarkable debut season on the tour also earned her the Ladies European Tour Rookie of the Year award for 2016.

Explanation

The area of a circle is given by A = π r². For two concentric circles with radii R and r (where R > r), the area of the region between them is π(R² - r²). Since the radii are in the ratio 4:5:7, we can represent them as 4k, 5k, and 7k.

The area between the two inner circles is π((5k)² - (4k)²) = π(25k² - 16k²) = 9π k².

The area between the two outer circles is π((7k)² - (5k)²) = π(49k² - 25k²) = 24π k².

To find the required ratio, we divide the two areas: Ratio = (9π k²)/(24π k²) = ⁹⁄₂₄

Dividing both the numerator and the denominator by their greatest common divisor, 3, we get: Ratio = ⅜

Explanation

The given expression 3√3 x³ - 2√2 y³ can be rewritten using the algebraic identity a³ - b³ = (a - b)(a² + ab + b²).

Identifying the terms, we have a = √3x and b = √2y, since (√3x)³ = 3√3x³ and (√2y)³ = 2√2y³. Expanding the expression:

3√3 x³ - 2√2 y³ = (√3x - √2y)((√3x)² + (√3x)(√2y) + (√2y)²) = (√3x - √2y)(3x² + √6xy + 2y²)

Comparing this result with the given equation (√3 x - √2 y)(Ax² + By² + Cxy), we match the coefficients of the terms inside the second bracket: A = 3 B = 2 C = √6

Substitute these values into the required expression (A × B) ÷ C: (3 × 2) ÷ √6 = 6 ÷ √6 = (6)/(√(6)) = √6

Explanation

The total work is the product of the combined efficiency of all workers and the time taken to complete the task. Given the efficiency ratio of A, B, and C as 7:5:6, their combined efficiency is 7 + 5 + 6 = 18 units per day. Since they complete the work in 35 days, the total work is 18 × 35 = 630 units.

B and C work together for 21 days. Their combined efficiency is 5 + 6 = 11 units per day, so the work completed by them is 11 × 21 = 231 units. The remaining work to be done is 630 - 231 = 399 units. A completes this remaining work alone using an efficiency of 7 units per day. The time taken by A is calculated as ³⁹⁹⁄₇ = 57 days.

Explanation

In a circle, the perpendicular distance d from the center to a chord of length L is given by the formula d = √(R² - (L/2)²), where R is the radius. For the chord RS of length 12 cm and radius 10 cm, the distance d_R_S from the center O is √(10² - (12/2)²) = √(100 - 36) = √(64) = 8 cm.

Because the parallel chords PQ and RS are on opposite sides of the center O, the distance between them is the sum of their respective distances from the center. Let d_P_Q be the distance of chord PQ from the center. Given the total distance between the chords is 14 cm, we have d_P_Q + 8 = 14, which results in d_P_Q = 6 cm. The length of chord PQ, denoted as x, is calculated using the relation x = 2√(R² - d_P_Q₎_². Substituting the values gives x = 2√(10² - 6²) = 2√(100 - 36) = 2√(64) = 2 × 8 = 16 cm.

Explanation

In △ ACE and △ BDC, since BD ∥ AE, the two triangles are similar by the AA similarity criterion because ∠ C is a common angle and corresponding angles ∠ CBD = ∠ CAE are equal. A fundamental property of similar triangles is that the ratio of their areas is equal to the square of the ratio of their corresponding sides. The problem states that AE = ⁸⁄₃ BD, which can be rewritten to find the ratio of the corresponding sides as (BD)/(AE) = ⅜. Applying the area property, the ratio of the area of △ BDC to the area of △ AEC is ((BD)/(AE))² = (⅜)² = ⁹⁄₆₄.