SSC CGL Tier 1 2019 General Awareness Questions with Solutions

Explanation

Dolly was a female Finn-Dorset sheep and the first mammal to be successfully cloned from an adult somatic cell in 1996 at the Roslin Institute. She was created using the process of somatic cell nuclear transfer and lived for six years.

Explanation

Vedangi Kulkarni, a 20-year-old cyclist from Pune, became the fastest Asian woman to cycle around the globe in December 2018. She completed the grueling 29,000-kilometer journey in 159 days, starting and ending her expedition in Perth, Australia. During her journey, she cycled through 14 countries including Australia, New Zealand, Canada, Iceland, Portugal, Spain, France, Germany, Denmark, Sweden, and Finland. To meet the requirements for a global circumnavigation record, she covered the necessary distance and passed through two antipodal points. Her achievement was marked by enduring extreme weather conditions ranging from sub-zero temperatures to intense heat across four continents.

Explanation

Vinayak Damodar Savarkar, popularly known as Veer Savarkar, founded the Mitra Mela in 1900 at Nasik along with his brother Ganesh Savarkar. It was established as a secret revolutionary society with the objective of achieving absolute political independence for India through armed resistance against British colonial rule. The organization focused on spreading revolutionary ideology, physical training, and promoting the spirit of nationalism among Indian youth. In 1904, after a meeting of about 200 members from various parts of Maharashtra, Savarkar rebranded and expanded this organization into the Abhinav Bharat Society, modeled after Giuseppe Mazzinis Young Italy.

Explanation

Preeti Saran, a senior Indian diplomat and retired officer of the Indian Foreign Service, was elected to the United Nations Committee on Economic, Social and Cultural Rights (CESCR) in December 2018. She was elected unopposed to represent the Asia-Pacific region on this 18-member body of independent experts. Her four-year tenure on the committee began on January 1, 2019. The CESCR is a technical body under the Economic and Social Council (ECOSOC) that monitors the implementation of the International Covenant on Economic, Social and Cultural Rights by its member states. Saran brought extensive diplomatic experience to the role, having previously served as the Secretary (East) in India's Ministry of External Affairs and as India's Ambassador to Vietnam.

Explanation

The Indian Premier League (IPL) was established by the Board of Control for Cricket in India (BCCI) in 2007, and its first season was conducted in 2008. The league was conceptualized as a professional Twenty20 cricket competition featuring eight franchise teams representing different Indian cities. The opening match of the inaugural season was held on April 18, 2008, at the M. Chinnaswamy Stadium in Bengaluru. The season concluded with the Rajasthan Royals winning the title after defeating the Chennai Super Kings in the final. This inaugural edition set the foundation for the league's global popularity and commercial success in the following years.

Explanation

Article 331 of the Constitution of India provides the specific provision for the representation of the Anglo-Indian community in the Lok Sabha. It stipulates that if the President is of the opinion that the Anglo-Indian community is not adequately represented in the House of the People, he may nominate not more than two members of that community to the House. This provision was incorporated into the Constitution to safeguard the interests and ensure the political participation of a small, distinct minority group whose members were scattered across the country and might not otherwise secure representation through general elections.

Explanation

Burma, officially known today as Myanmar, attained its status as an independent sovereign republic on January 4, 1948. This transition followed the signing of the Nu-Attlee Agreement in October 1947 between the Burmese leader U Nu and British Prime Minister Clement Attlee. Under the terms of the Burma Independence Act 1947, the country formally exited the British Empire. Notably, unlike many other former British colonies, Burma chose not to join the Commonwealth of Nations upon gaining its independence, establishing itself immediately as a fully independent republic outside the Commonwealth framework.

Explanation

Catriona Gray was crowned Miss Universe 2018 at the 67th Miss Universe pageant held on December 17, 2018, in Bangkok, Thailand. Representing the Philippines, she became the fourth Filipina to win the prestigious title, following Gloria Diaz, Margie Moran, and Pia Wurtzbach. Gray gained international recognition for her signature lava walk and her red gown inspired by the Mayon Volcano. Her platform during the competition focused on providing education to children living in impoverished areas, such as the slums of Tondo, Manila, through her work with various non-government organizations.

Explanation

Muhammad Ali Jinnah is widely known by the honorific title Quaid-i-Azam, which translates from Urdu as Great Leader. This title was popularized and famously used by Mahatma Gandhi in 1944 during their correspondence and negotiations regarding the future of the Indian subcontinent. It was bestowed upon him by his followers and the public in recognition of his role as the pre-eminent leader of the All-India Muslim League and the founder of Pakistan. Jinnah's leadership was central to the Pakistan Movement, and he eventually served as the first Governor-General of the independent nation of Pakistan in 1947.

Explanation

The total production of cars of type A in 2015 and type C in 2013 is calculated as: Sum = A(2015) + C(2013) = 48 + 52 = 100

The total production of cars of type D over the five-year period is: Σ D = 50 + 42 + 45 + 46 + 47 = 230

The required percentage is determined by the formula: Percentage = (Sum of A(2015) and C(2013))/(Total sum of D) × 100 Percentage = ¹⁰⁰⁄₂₃₀ × 100 = ¹⁰⁰⁰⁄₂₃

Performing the division: 1000 ÷ 23 ≈ 43.478

Rounding to one decimal place, the production is approximately 43.5 percent.

Explanation

Jamdani is a fine muslin textile of Bengali origin, traditionally produced in the Dhaka district of present-day Bangladesh. It is considered one of the most time-intensive and advanced forms of handloom weaving, characterized by intricate floral and geometric patterns created using a supplementary weft technique. Historically known as Dhakai Jamdani, the craft flourished under Mughal patronage and remains a significant cultural symbol. In 2013, UNESCO recognized the traditional art of weaving Jamdani by inscribing it on the Representative List of the Intangible Cultural Heritage of Humanity.

Explanation

The area of a triangle is proportional to its base when the triangles share the same altitude. In △ ABC, point P lies on BC such that BP:PC = 3:4. This implies the length of the base BC is 3 + 4 = 7 units relative to the segments. Since △ ABP and △ ABC share the same altitude from vertex A to the line BC, their areas are in the ratio of their bases. Thus, ar(△ ABP) = ³⁄₇ × ar(△ ABC).

Furthermore, Q is the midpoint of segment AP. In △ ABP, the segment BQ is the median from vertex B to the side AP. A median divides a triangle into two smaller triangles of equal area. Therefore, the area of △ ABQ is half the area of △ ABP. By substitution, ar(△ ABQ) = ½ × ar(△ ABP) = ½ × ( ³⁄₇ × ar(△ ABC) ) = ³⁄₁₄ × ar(△ ABC). This results in the ratio ar(△ ABQ) : ar(△ ABC) = 3:14.

Explanation

The volume V of a frustum of a cone is given by the formula V = ⅓ π h (R² + r² + Rr), where h is the height, R is the radius of the larger base, and r is the radius of the smaller base.

Substituting the given values h = 10.5 cm, R = 5 cm, and r = 3 cm into the formula:

V = ⅓ × ²²⁄₇ × 10.5 × (5² + 3² + 5 × 3)

First, calculate the term in the parentheses: 5² + 3² + 5 × 3 = 25 + 9 + 15 = 49

Now, substitute this back into the volume equation and simplify the constants: V = ²²⁄₂₁ × 10.5 × 49

Since 10.5 = ²¹⁄₂, the expression simplifies as follows: V = ²²⁄₂₁ × ²¹⁄₂ × 49 V = 11 × 49 V = 539

The volume of the frustum is 539 cm³.

Explanation

The average production of rice in state A is calculated using the formula for arithmetic mean:

Average = (Sum of production over all years)/(Total number of years)

From the table, the production values for state A from 2011 to 2016 are 5.2, 5.4, 5.8, 6.2, 6.5, and 6.9 million tonnes respectively.

Sum = 5.2 + 5.4 + 5.8 + 6.2 + 6.5 + 6.9 = 36.0 million tonnes

Total number of years = 6

Average = (36.0)/(6) = 6 million tonnes

Explanation

The total selling price (SP) of the two articles is 4800 + 4800 = 9600. To find the overall gain or loss, first calculate the total cost price (CP). For the first article sold at a 22% gain, CP₁ = (SP)/(1 + gain){100} = (4800)/(1.22) = ²⁴⁰⁰⁰⁰⁄₆₁. For the second article sold at a 20% loss, CP₂ = (SP)/(1 - loss){100} = (4800)/(0.80) = 6000.

Total CP = ²⁴⁰⁰⁰⁰⁄₆₁ + 6000 = (240000 + 366000)/(61) = ⁶⁰⁶⁰⁰⁰⁄₆₁ ≈ 9934.43. Since the total CP is greater than the total SP, there is an overall loss. The loss percentage is calculated using the formula Loss % = (Total CP - Total SP)/(Total CP) × 100. Substituting the values: Loss % = (606000)/(61) - 9600{⁶⁰⁶⁰⁰⁰⁄₆₁} × 100 = (606000 - 585600)/(606000) × 100 = ²⁰⁴⁰⁰⁄₆₀₆₀₀₀ × 100 = ²⁰⁴⁰⁄₆₀₆ ≈ 3.366%. Rounding to the nearest one decimal place, the overall loss is 3.4%.

Explanation

A perpendicular drawn from the center of a circle to a chord bisects that chord. This creates a right-angled triangle where the radius of the circle (r) is the hypotenuse, the distance of the chord from the center (d) is one leg, and half the length of the chord ((L)/(2)) is the other leg. According to the Pythagorean theorem:

r² = d² + ((L)/(2))²

Given that the radius r = 13cm and the distance d = 5cm, we substitute these values into the formula:

13² = 5² + ((L)/(2))² 169 = 25 + ((L)/(2))² ((L)/(2))² = 169 - 25 ((L)/(2))² = 144 (L)/(2) = √(144) = 12cm

Since (L)/(2) represents half the length of the chord, the full length L is calculated as:

L = 2 × 12 = 24cm

This result follows the standard Pythagorean triple (5, 12, 13), where the half-chord length is 12cm.

Explanation

The efficiencies of A, B, and C are given in the ratio 2:3:5. Let their respective daily work units be 2x, 3x, and 5x. The total efficiency of the group working together is the sum of their individual efficiencies:

Total Efficiency = 2x + 3x + 5x = 10x units/day

Since they complete the task in 6 days, the total work is calculated as:

Total Work = Total Efficiency × Time = 10x × 6 = 60x units

The problem asks for the time taken by A to complete 20% of this task. The specific amount of work to be done by A is:

Work for A = 20% of 60x = 0.20 × 60x = 12x units

The time taken by A alone to complete this portion is the work divided by A's efficiency:

Time taken by A = ¹²ˣ⁄₂ₓ = 6 days

Explanation

The line joining the centers of two intersecting circles is the perpendicular bisector of their common chord. Let the centers of the circles be O₁ and O₂, and let M be the intersection point of the line O₁O₂ and the common chord PQ. Since PQ = 12 cm, the length of PM is 6 cm.

In the right-angled triangle Δ O₁MP where the radius O₁P = 10 cm: O₁M = √(O₁P² - PM²) = √(10² - 6²) = √(64) = 8 cm

In the right-angled triangle Δ O₂MP where the radius O₂P = 8 cm: O₂M = √(O₂P² - PM²) = √(8² - 6²) = √(28) ≈ 5.2915 cm

The distance between the centers x is the sum of these segments: x = O₁M + O₂M = 8 + 5.2915... = 13.2915... cm

Correct to one decimal place, the value of x is 13.3.

Explanation

For a seven digit number like 6913x08 to be divisible by 88, it must satisfy the divisibility rules for both 8 and 11, as 88 is the product of these coprime numbers. According to the divisibility rule for 11, the difference between the sum of digits at odd positions and the sum of digits at even positions must be 0 or a multiple of 11. Summing the digits from the left, the digits at odd positions are 6, 1, x, and 8, which sum to 6 + 1 + x + 8 = 15 + x. The digits at even positions are 9, 3, and 0, which sum to 9 + 3 + 0 = 12. The difference is (15 + x) - 12 = x + 3. For this difference to be a multiple of 11, we set x + 3 = 11, which gives x = 8. Furthermore, a number is divisible by 8 if its last three digits are divisible by 8. Substituting x = 8 into the last three digits x08 yields 808. Since 808 / 8 = 101, the condition for divisibility by 8 is also satisfied.

Explanation

The relationship between the marked price (MP) and the selling price (SP) after successive discounts is given by the formula SP = MP × (1 - d₁/100) × (1 - d₂/100), where d₁ and d₂ are the discount percentages.

Given SP = 612, d₁ = 25%, and d₂ = 15%, we can substitute these values into the equation: 612 = MP × (1 - 25/100) × (1 - 15/100) 612 = MP × (75/100) × (85/100) 612 = MP × (3/4) × (17/20) 612 = MP × (51/80)

Solving for MP: MP = (612 × 80) / 51 MP = 12 × 80 MP = 960

Thus, the marked price of the article is ₹ 960.

Explanation

For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Given △ ABC ∼ △ RQP, the side AB in the first triangle corresponds to the side RQ in the second triangle based on the order of vertices in the similarity statement. The relationship is expressed as:

(ar(△ ABC))/(ar(△ RQP)) = ( (AB)/(RQ) )²

Substituting the given values where ar(△ ABC) : ar(△ RQP) = ⁴⁄₉ and QR = RQ = 12 cm:

⁴⁄₉ = ( (AB)/(12) )²

Taking the square root of both sides to find the ratio of the corresponding sides:

√(⁴⁄₉) = (AB)/(12)

⅔ = (AB)/(12)

Solving for AB:

AB = ⅔ × 12

AB = 8 cm

Explanation

Distance is constant, which means speed and time are inversely proportional (v ∝ 1/t). When the person walks at 3/4 of his usual speed, the time taken is 4/3 of his usual time. Let the usual time be t. The delay is the difference between the new time and the usual time, expressed as ⁴⁄₃t - t = 18 minutes. Simplifying this gives ⅓t = 18. Solving for t, we find the usual time is 18 × 3 = 54 minutes.

Using the ratio method, if the speed ratio is 3:4 (new speed to usual speed), the time ratio is 4:3 (new time to usual time). The difference in the time ratio is 4 - 3 = 1 unit. Since this 1 unit represents the 18-minute delay, the usual time (3 units) is calculated as 3 × 18 = 54 minutes. This can also be solved using the direct formula for usual time when speed is x/y of usual speed and delay is L: Usual Time = (x × L)/(y - x). Substituting the values x=3, y=4, and L=18 yields (3 × 18)/(4 - 3) = 54 minutes.

Explanation

Given the ratio a:b = 2:3, we can let a = 2k and b = 3k. Since the expression (5a + 3b):(6a - 2b) is a ratio of linear homogeneous functions, we can directly substitute a = 2 and b = 3 to find the value.

Substituting these values into the given expression: Numerator = 5a + 3b = 5(2) + 3(3) = 10 + 9 = 19 Denominator = 6a - 2b = 6(2) - 2(3) = 12 - 6 = 6

The resulting ratio is 19:6.

Explanation

To find the central angle of the sector representing the production in 2014, we first calculate the total production for each year and then the grand total for all six years.

Total production in 2011 = 5.2 + 3.8 + 4.5 = 13.5 Total production in 2012 = 5.4 + 4.1 + 5.2 = 14.7 Total production in 2013 = 5.8 + 4.4 + 5.8 = 16.0 Total production in 2014 = 6.2 + 4.8 + 6.4 = 17.4 Total production in 2015 = 6.5 + 5.2 + 6.7 = 18.4 Total production in 2016 = 6.9 + 5.7 + 7.4 = 20.0

The grand total production for all three states over all six years is the sum of these annual totals: Grand Total = 13.5 + 14.7 + 16.0 + 17.4 + 18.4 + 20.0 = 100.0 million tonnes.

The central angle in a pie chart is determined by the ratio of the specific value to the total value, multiplied by 360°. For the year 2014, the production is 17.4 million tonnes.

Central Angle for 2014 = (Production in 2014)/(Grand Total) × 360° Central Angle for 2014 = (17.4)/(100) × 360° Central Angle for 2014 = 0.174 × 360° = 62.64°

Rounding 62.64° to the nearest whole number gives 63°.

Explanation

The trigonometric identity for complementary angles states that csc A = sec B when A + B = 90°, as csc A = sec(90° - A). Applying this property to the given equation csc 3θ = sec(20° + 2θ), we can set the sum of the two angles to 90°:

3θ + (20° + 2θ) = 90°

5θ + 20° = 90°

5θ = 70°

θ = (70°)/(5) = 14°

Explanation

The percentage increase in the production of rice for state B from 2014 to 2016 is calculated using the formula: Percentage Increase = (Value in 2016 - Value in 2014)/(Value in 2014) × 100

From the table, the production for state B in 2014 was 4.8 million tonnes and in 2016 was 5.7 million tonnes. Substituting these values into the formula: Percentage Increase = (5.7 - 4.8)/(4.8) × 100 Percentage Increase = (0.9)/(4.8) × 100 Percentage Increase = ⁹⁄₄₈ × 100

Dividing both the numerator and the denominator by 3, the fraction becomes ³⁄₁₆. Multiplying ³⁄₁₆ by 100 gives 3 × 6.25 = 18.75. Thus, the percentage increase is 18.75%.

Explanation

The total production of rice in all three states in the year 2014 is the sum of the production in states A, B, and C for that year. Total production (2014) = 6.2 + 4.8 + 6.4 = 17.4 million tonnes.

The total production of rice in all three states in the year 2016 is the sum of the production in states A, B, and C for that year. Total production (2016) = 6.9 + 5.7 + 7.4 = 20.0 million tonnes.

The required ratio is 17.4 : 20.0. Multiplying both sides by 10 to remove the decimals gives 174 : 200. Dividing both terms by their greatest common divisor, which is 2, simplifies the ratio to 87 : 100.

Explanation

To evaluate the expression 7.5 + (5.4 ÷ 4.5 × 2) - 8 × 4 ÷ 3.2, follow the BODMAS rule, which specifies the order of operations: Brackets, Orders, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).

Start by calculating the value inside the parentheses: (5.4 ÷ 4.5 × 2). Moving from left to right, divide 5.4 by 4.5 to get 1.2. Then, multiply 1.2 by 2 to get 2.4. The expression now becomes 7.5 + 2.4 - 8 × 4 ÷ 3.2.

Next, evaluate the multiplication and division terms from left to right: 8 × 4 ÷ 3.2. First, multiply 8 by 4 to get 32. Then, divide 32 by 3.2 to get 10. The expression is now simplified to 7.5 + 2.4 - 10.

Finally, perform addition and subtraction from left to right. Adding 7.5 and 2.4 results in 9.9. Subtracting 10 from 9.9 results in 9.9 - 10 = -0.1.

Explanation

The total efficiency of A, B, and C is the sum of their individual efficiency ratios: 4 + 5 + 3 = 12 units per day. Given that they complete the work in 25 days, the total work can be calculated using the formula Work = Efficiency × Time: Total Work = 12 × 25 = 300 units.

The task is to find the time taken by A and C to complete 35% of this total work. First, calculate the required work: Required Work = 35% of 300 = ³⁵⁄₁₀₀ × 300 = 105 units.

Next, find the combined efficiency of A and C, which is 4 + 3 = 7 units per day. The time taken by A and C to finish the required work is: Time = (Required Work)/(Efficiency of (A + C)) = ¹⁰⁵⁄₇ = 15 days.

Explanation

The angle subtended by the arc AC at the center O is ∠ AOC = 132°. According to the circle theorem, the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. Let D be a point on the major arc of the circle. Then, the angle at the circumference is ∠ ADC = ½ ∠ AOC = (132°)/(2) = 66°.

Since the points A, B, C, and D lie on the circle, ABCD forms a cyclic quadrilateral. A property of cyclic quadrilaterals is that the exterior angle formed by extending one side is equal to the interior opposite angle. When the chord AB is extended to point P, the exterior angle ∠ CBP is equal to the interior opposite angle ∠ ADC. Therefore, ∠ CBP = 66°.

Explanation

The difference between compound interest and simple interest for a period of 2 years is calculated using the formula D = P × (ʳ⁄₁₀₀)², where D represents the difference, P is the principal, and r is the rate of interest per annum. Given that D = 48, r = 8, and P = x, the formula becomes:

48 = x × (⁸⁄₁₀₀)² 48 = x × ⁶⁴⁄₁₀₀₀₀

To solve for x, rearrange the equation: x = (48 × 10000)/(64)

Simplifying the fraction by dividing both 48 and 64 by 16: x = (3 × 10000)/(4) x = 3 × 2500 x = 7500

Explanation

The algebraic identity relating the given terms is a³ + b³ + c³ - 3abc = (a + b + c)[(a + b + c)² - 3(ab + bc + ca)]. By substituting the given values a + b + c = 6 and a³ + b³ + c³ - 3abc = 126 into this formula, we get the equation 126 = 6 × [6² - 3(ab + bc + ca)].

Dividing both sides of the equation by 6 results in 21 = 36 - 3(ab + bc + ca). Rearranging the equation to solve for the unknown term, we get 3(ab + bc + ca) = 36 - 21, which simplifies to 3(ab + bc + ca) = 15. Finally, dividing by 3 gives ab + bc + ca = 5.

Explanation

The percentage reduction in consumption required to limit the increase in expenditure is calculated using the relationship Expenditure = Price × Consumption . By assuming initial price and consumption to be 100 units each, the initial expenditure is 10,000 .

With a 24% increase, the new price becomes 124 . The person wants to increase expenditure by only 15% , making the new target expenditure 115% of the original, which is 11,500 . The new consumption level is found by dividing the new expenditure by the new price: New Consumption = 11500 / 124 ≈ 92.7419

The reduction in consumption is the difference between the original consumption (100) and the new consumption level: Reduction = 100 - 92.7419 = 7.2581

To find the percentage reduction, we divide the reduction by the original consumption: Percentage Reduction = (7.2581 / 100) × 100 = 7.2581%

Rounding the result to one decimal place yields 7.3% .

Explanation

The cost price (CP) can be determined using the relation between the selling price (SP) and the loss percentage: CP = (SP × 100)/(100 - Loss%). Substituting the given values, where SP = 288 and Loss% = 4, we get CP = (288 × 100)/(100 - 4) = (288 × 100)/(96) = 3 × 100 = ₹300.

The marked price (MP) is ₹315. The markup value represents how much the marked price exceeds the cost price, which is MP - CP = 315 - 300 = ₹15. To find the percentage by which the article is marked above the cost price, we use the formula Markup% = (MP - CP)/(CP) × 100. Calculating this gives ¹⁵⁄₃₀₀ × 100 = ¹⁵⁄₃ = 5%.

Explanation

The angle between the altitude AD and the diameter AK from the same vertex A in a triangle ABC is determined by the formula: ∠ DAK = |∠ B - ∠ C|

Given the measures ∠ B = 80° and ∠ C = 64°, substitute these into the relation: ∠ DAK = |80° - 64°| = 16°

This property arises because in the right-angled triangle ABD, ∠ BAD = 90° - ∠ B = 90° - 80° = 10°. In the right-angled triangle ABK (where ∠ ABK = 90° as it is inscribed in a semicircle), ∠ BAK = 90° - ∠ AKB. Since ∠ AKB and ∠ C both subtend the arc AB, ∠ AKB = ∠ C = 64°, making ∠ BAK = 90° - 64° = 26°. The difference ∠ BAK - ∠ BAD yields 26° - 10° = 16°.

Explanation

In △ ADC and △ BEC, we have ∠ ADC = ∠ BEC = 90°. Both triangles share ∠ C. Therefore, the third angles must be equal: ∠ DAC = 90° - ∠ C and ∠ EBC = 90° - ∠ C. This gives ∠ DAC = ∠ FBD.

Now consider △ BDF and △ ADC. Both are right-angled triangles since AD ⊥ BC. We have ∠ BDF = ∠ ADC = 90°, ∠ FBD = ∠ DAC as derived above, and the hypotenuses are equal as given: BF = AC. By the AAS (Angle-Angle-Side) congruence criterion, △ BDF ≅ △ ADC.

From the congruence of these triangles, the corresponding sides BD and AD must be equal. In △ ABD, we have AD ⊥ BD and BD = AD. Since two sides are equal in this right-angled triangle, it is an isosceles right triangle. The base angles must be equal, so ∠ ABD = ∠ BAD = (180° - 90°) / 2 = 45°. Since ∠ ABD is the same as ∠ ABC, the measure of ∠ ABC is 45°.

Explanation

The given equation 16x² + 9y² + 4z² = 24(x - y + z) - 61 can be rearranged by bringing all terms to one side: 16x² - 24x + 9y² + 24y + 4z² - 24z + 61 = 0

We group the terms to form perfect squares of the form (ax ± b)² = a²x² ± 2abx + b²: For x: 16x² - 24x + 9 = (4x - 3)² For y: 9y² + 24y + 16 = (3y + 4)² For z: 4z² - 24z + 36 = (2z - 6)²

Summing these constants gives 9 + 16 + 36 = 61, which matches the constant in the equation. Thus, the equation simplifies to: (4x - 3)² + (3y + 4)² + (2z - 6)² = 0

For the sum of squares of real numbers to be zero, each individual term must be zero: 4x - 3 = 0 ⟹ x = ¾ 3y + 4 = 0 ⟹ y = -⁴⁄₃ 2z - 6 = 0 ⟹ z = 3

Substituting these values into the required expression (xy + 2z): xy + 2z = (¾)(-⁴⁄₃) + 2(3) xy + 2z = -1 + 6 = 5

Explanation

The Battle of Suvali, also known as the Battle of Swally, occurred on November 29-30, 1612, off the coast of a village near Surat, Gujarat. A small fleet of the English East India Company, led by Captain Thomas Best, successfully defeated a Portuguese naval force. This engagement was historically significant because it effectively ended the Portuguese monopoly over sea trade in the Indian Ocean and challenged their naval supremacy. The English victory impressed the Mughal Emperor Jahangir, leading him to grant the British a royal farman to establish their first permanent factory at Surat in 1613. This event marked the beginning of the British East India Company's rise as a dominant commercial and political power in India.

Explanation

The Chinese zodiac follows a repetitive twelve-year cycle, with each year represented by one of twelve animal signs in a specific order: Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, and Pig. The year 2019 followed the Year of the Dog (2018), making it the Year of the Pig. According to the Chinese lunar calendar, this specific year began on 5 February 2019 and concluded on 24 January 2020. The Pig is the twelfth and final animal in the zodiac sequence, symbolizing the end of the twelve-year rotational cycle before it begins again with the Year of the Rat.

Explanation

Chennai Super Kings secured their third Indian Premier League title by defeating Sunrisers Hyderabad in the 2018 final held at the Wankhede Stadium in Mumbai. In the final, Chennai Super Kings successfully chased a target of 179 runs in 18.3 overs, winning the match by eight wickets. Shane Watson played a pivotal role by scoring an unbeaten 117 runs off 57 balls. This victory was notable as it marked a successful return for the franchise after being suspended from the tournament for the previous two seasons.

Explanation

To find the required ratio, first calculate the total production for the first group. The production of type C cars in 2013 is 52 and type E cars in 2013 is 36. Sum 1 = 52 + 36 = 88

Next, calculate the total production for the second group. The production of type D cars in 2014 is 42 and in 2016 is 46. The production of type E cars in 2017 is 55. Sum 2 = 42 + 46 + 55 = 143

The ratio is determined by comparing these two totals: Ratio = 88 : 143

To simplify the ratio, divide both terms by their greatest common divisor, which is 11: 88 / 11 = 8 143 / 11 = 13

The simplified ratio is 8 : 13.

Explanation

Greenhouse gases are atmospheric constituents that possess the ability to absorb and emit radiant energy within the thermal infrared range. When solar radiation reaches the Earth, the surface absorbs energy and re-radiates it as long-wave infrared radiation. Greenhouse gases, such as carbon dioxide (CO₂), methane (CH₄), and water vapor, trap this outgoing heat rather than allowing it to escape into space. This process, known as the greenhouse effect, maintains the planet's temperature at a level capable of supporting life. However, an increase in the concentration of these gases due to human activities intensifies the effect, leading to a rise in the Earth's average surface temperature, a phenomenon referred to as global warming.

Explanation

Hemoglobin and myoglobin are specialized oxygen-binding proteins that both utilize a prosthetic group known as heme. The core of every heme group is a central iron atom in the ferrous state (Fe²⁺), which is coordinated within a porphyrin ring. This iron atom is the functional site that binds reversibly with molecular oxygen. Hemoglobin, found in red blood cells, consists of four subunits each containing a heme group, while myoglobin, found in muscle tissues, consists of a single polypeptide chain with one heme group. Therefore, iron is a structural and functional requirement for the synthesis of both proteins to enable their oxygen-carrying and storage capabilities.

Explanation

Mo Yan was awarded the Nobel Prize in Literature in 2012, becoming the first Chinese national and citizen to receive this honor. The Swedish Academy recognized him for his hallucinatory realism that merges folk tales, history, and the contemporary. His writing, particularly in works like Red Sorghum and Frog, explores the complexities of Chinese history and society through a unique narrative style. His achievement is distinguished as the first time a writer holding Chinese citizenship and residing in mainland China was recognized with the Nobel Prize in Literature, marking a major milestone in the international recognition of Chinese letters.

Explanation

India secured the 2019 South Asian Football Federation (SAFF) Women's Championship title by winning the final match held in Biratnagar, Nepal. The Indian team defeated Nepal with a score of 3–1, with goals scored by Dalima Chhibber, Grace Dangmei, and Anju Tamang. This victory represented India's fifth successive championship win, as the team has won every edition of the tournament since its debut in 2010. The 2019 win further established India's status as the most successful nation in South Asian women's football.

Explanation

The Opium Wars were two mid-19th-century military conflicts fought between the British Empire and the Qing dynasty of China. The First Opium War (1839–1842) was triggered by the Chinese government's crackdown on the illegal opium trade, which British merchants were using to reverse a trade deficit. The British deployed their superior naval power to force China to open its markets. The Second Opium War (1856–1860), also known as the Arrow War, involved both British and French forces against China to secure further commercial concessions and legal immunity for foreigners. These conflicts resulted in the Treaties of Nanjing and Tientsin, which led to the opening of treaty ports, the legalization of the opium trade, and the cession of Hong Kong to Great Britain.

Explanation

Vikram Seth is the author of the non-fiction book Two Lives, published in 2005. The book is a deeply personal memoir and biography that chronicles the lives of his great-uncle, Shanti Behari Seth, and his German-Jewish great-aunt, Hennerle Gerda Caro, known as Henny. It traces their journey from pre-war Berlin through the horrors of World War II and the Holocaust, eventually following their lives together in London. Seth reconstructed their story using a collection of letters and personal documents he discovered, blending family history with broader historical events of the twentieth century.

Explanation

A greenfield project is a form of foreign direct investment where a parent company starts a new venture in a foreign country by constructing new operational facilities from the ground up. This approach provides the firm with a clean slate, meaning it is not restricted by the existing organizational structures, cultural issues, or physical limitations of a pre-existing company. By building from scratch, the firm can implement its own specific management systems, choose its own staff, and install the latest technology and production processes that align perfectly with its global strategic objectives without having to modify or accommodate inherited legacy practices.

Explanation

Volleyball was officially declared the national sport of Sri Lanka in 1991. The sport was first introduced to the country in 1916 by Walter Camack, who was the Director of Physical Education at the Colombo YMCA. It gained rapid popularity across the island, particularly in rural areas, because it requires minimal equipment and space. This widespread grassroots participation and its integration into the local culture led the Ministry of Sports to formally recognize it as the national sport.

Explanation

The algebraic identity for the sum of cubes minus the triple product is given by the formula x³ + y³ + z³ - 3xyz = (x + y + z)((x + y + z)² - 3(xy + yz + zx)). By substituting the given values x + y + z = 19 and xy + yz + zx = 114 into this equation, we can calculate the value inside the square root:

x³ + y³ + z³ - 3xyz = 19 × (19² - 3 × 114) x³ + y³ + z³ - 3xyz = 19 × (361 - 342) x³ + y³ + z³ - 3xyz = 19 × 19 = 361

The question asks for the square root of this value: √(x³ + y³ + z³ - 3xyz) = √(361) = 19