SSC CGL Tier 1 2019 General Awareness Questions with Solutions

Explanation

For a period of 2 years, the difference between Compound Interest (CI) and Simple Interest (SI) is given by the formula: CI - SI = P · (ʳ⁄₁₀₀)²

Here, the difference is given as 9, the rate r is 15%, and the principal P is x. Substituting these values into the formula: 9 = x · (¹⁵⁄₁₀₀)²

Simplifying the fraction inside the square: 9 = x · (³⁄₂₀)² 9 = x · (⁹⁄₄₀₀)

To find x, rearrange the equation: x = (9 · 400)/(9) x = 400$

Explanation

When five cubes of edge a = 3 cm are joined end to end, the resulting solid is a cuboid. The dimensions of this cuboid are length l = 5 × 3 = 15 cm, breadth b = 3 cm, and height h = 3 cm. The total surface area of a cuboid is given by the formula 2(lb + bh + hl).

Substituting the values into the formula: Total Surface Area = 2(15 × 3 + 3 × 3 + 3 × 15) Total Surface Area = 2(45 + 9 + 45) Total Surface Area = 2(99) Total Surface Area = 198 cm²

Alternatively, each cube has 6 faces, making a total of 5 × 6 = 30 faces. When joined end to end, there are 4 contact points where two faces meet and are hidden from the surface. This removes 4 × 2 = 8 faces. The total surface area is the area of the remaining 30 - 8 = 22 faces. Since the area of one face is 3² = 9 cm², the total surface area is 22 × 9 = 198 cm².

Explanation

The expression is evaluated using the BODMAS rule, which dictates the order of operations as Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

First, perform the division operations in the expression 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5: 5.8 ÷ 2.9 = 2 2 ÷ 0.5 = 4

Substitute these values back into the expression: 15.2 + 2 × 2 - 3.5 × 4

Next, perform the multiplication operations: 2 × 2 = 4 3.5 × 4 = 14

Now, perform the addition and subtraction: 15.2 + 4 - 14 19.2 - 14 = 5.2

Explanation

The Khadi and Village Industries Commission (KVIC) is a statutory body established by the Government of India under the provisions of the Khadi and Village Industries Commission Act of 1956. Passed by the Parliament in 1956, this legislation provided the legal framework to create an apex organization for the development of khadi and village industries in rural areas. The commission officially began its operations in April 1957, taking over the functions of the erstwhile All India Khadi and Village Industries Board. It functions under the administrative ministry of Micro, Small and Medium Enterprises to promote employment opportunities in the rural non-farm sector.

Explanation

Mahe is a district of the Union Territory of Puducherry and is officially recognized as the smallest district in India by land area. According to the 2011 Census data, Mahe covers a total area of approximately 9 km². It is an enclave geographically located on the Malabar Coast, surrounded by the state of Kerala. As one of the four districts of Puducherry, its tiny size makes it the smallest administrative district in the country.

Explanation

Sushmita Sen was crowned Miss Universe in 1994, becoming the first Indian woman to win the prestigious title. The competition took place in Manila, Philippines, where she successfully competed against contestants from around the world to claim the crown. Her victory marked a historic milestone for India in international beauty pageants.

Explanation

Ghuar Mota, situated in the Kutch district of Gujarat, is the westernmost inhabited point of mainland India. It is located at approximately 68° 7' E longitude, near the Sir Creek and the Narayan Sarovar Sanctuary. This location marks the extreme longitudinal boundary of the Indian territory in the west, bordering the Arabian Sea.

Explanation

Diksha Dagar is a professional golfer from Haryana who was born with a hearing impairment. In March 2019, at the age of 18, she won the Investec South African Women’s Open held in Cape Town. This victory made her the second Indian woman to win a title on the Ladies European Tour (LET), following Aditi Ashok who first achieved the feat in 2016. Before turning professional in early 2019, Dagar had a distinguished amateur career, including winning a silver medal at the 2017 Deaflympics and representing India at the 2018 Asian Games.

Explanation

Wilson's disease is an autosomal recessive genetic disorder caused by mutations in the ATP7B gene. This gene provides instructions for making a protein that functions as a copper transporter, primarily in the liver. Under normal physiological conditions, the liver filters excess copper from the blood and releases it into bile for excretion from the body. In individuals with Wilson's disease, this transport mechanism is defective, preventing the elimination of copper. Consequently, the mineral builds up to toxic levels, damaging the liver and eventually overflowing into the bloodstream to accumulate in other vital organs, most notably the brain and the corneas of the eyes.

Explanation

The Kolkata Port is the oldest operating major port in India, having been established by the British East India Company. It was formally commissioned under the Calcutta Port Act of 1870, which created the Calcutta Port Commissioners to manage its operations. Located approximately 203 kilometers from the sea on the banks of the Hooghly River, it is the only major riverine port in the country. Throughout the 19th and 20th centuries, it served as the primary hub for the export of tea, jute, and coal, and it remained the most important commercial gateway for the British Empire in India for several decades.

Explanation

Indore was ranked as the cleanest city in India in the Swachh Survekshan 2019 awards, marking its third consecutive year at the top position after winning in 2017 and 2018. These annual awards are part of a nationwide survey conducted by the Ministry of Housing and Urban Affairs under the Swachh Bharat Abhiyan. The 2019 survey was one of the largest urban cleanliness surveys in the world, evaluating over 4,237 cities based on performance indicators such as waste collection and transportation, waste processing and disposal, sustainable sanitation, and citizen feedback. Indore's consistent top ranking is attributed to its highly efficient solid waste management systems, 100 percent door-to-door garbage collection, and robust waste processing infrastructure.

Explanation

The Pradhan Mantri Shram Yogi Maandhan (PM-SYM) is a voluntary and contributory pension scheme launched by the Ministry of Labour and Employment for workers in the unorganized sector. To ensure a sustainable contribution period before the pension payout begins at age 60, the scheme mandates an entry age window between 18 and 40 years. Since the maximum age for enrollment is capped at 40, any individual above this age limit is ineligible to join the scheme. This eligibility criterion ensures that subscribers contribute for a minimum of 20 years to the pension fund.

Explanation

Venus is the hottest planet in our solar system due to its exceptionally dense atmosphere, which consists of approximately 96.5 percent carbon dioxide. This high concentration of greenhouse gases triggers a runaway greenhouse effect, where solar heat is absorbed and trapped at the surface, preventing it from escaping back into space. The atmospheric pressure on the surface of Venus is about 92 times greater than that of Earth, and the planet is permanently shrouded by thick clouds of sulfuric acid. These factors combine to create a uniform surface temperature averaging about 462 degrees Celsius (864 degrees Fahrenheit), a temperature high enough to melt lead.

Explanation

The Pradhan Mantri Shram Yogi Maandhan (PM-SYM) is a voluntary and contributory pension scheme launched by the Ministry of Labour and Employment in February 2019. It is specifically designed to provide old age protection and social security for unorganised workers, including street vendors, mid-day meal workers, head loaders, brick kiln workers, cobblers, rag pickers, domestic workers, washermen, and rickshaw pullers. To qualify for the scheme, the worker must be in the age group of 18 to 40 years and have a monthly income of Rs 15,000 or less. Under the scheme, subscribers receive a minimum assured monthly pension of Rs 3,000 after attaining the age of 60 years. Eligible individuals must not be covered under other statutory social security schemes like the Employees Provident Fund (EPF), Employees State Insurance (ESI), or the National Pension System (NPS), and they must not be income tax payers.

Explanation

The Ayushman Bharat - Pradhan Mantri Jan Arogya Yojana (PM-JAY), launched in September 2018, is designed to provide a health cover of ₹5 lakh per family per year. This insurance coverage is specifically for secondary and tertiary care hospitalization across public and empanelled private hospitals in India. The scheme targets approximately 10.74 crore poor and vulnerable families, identified based on the deprivation and occupational criteria of the Socio-Economic Caste Census 2011. It provides cashless and paperless access to services for the beneficiary at the point of service, covering almost all secondary and many tertiary care procedures with no restriction on family size, age, or gender.

Explanation

The Char Dham Yatra in North India, commonly known as the Chota Char Dham, is a prominent pilgrimage circuit located in the Himalayan region of Uttarakhand. This circuit consists of four specific sites: Yamunotri, Gangotri, Kedarnath, and Badrinath. These shrines are dedicated to various deities, with Yamunotri and Gangotri marking the sources of the Yamuna and Ganga rivers respectively, Kedarnath being a primary Jyotirlinga of Lord Shiva, and Badrinath being a major seat of Lord Vishnu. Vaishno Devi is a significant holy cave temple dedicated to the Hindu Mother Goddess and is situated in the Trikuta Mountains in the union territory of Jammu and Kashmir. Therefore, it falls outside the geographic and traditional religious scope of the Uttarakhand Char Dham circuit.

Explanation

Vallabhbhai Patel led the Bardoli Satyagraha in 1928 to protest against the unjust 22 percent hike in land revenue imposed by the British colonial administration in the Bardoli Taluka of Gujarat. Under his leadership, the local farmers organized a non-violent movement and refused to pay the increased taxes despite the government seizing their property and livestock. The movement was a major success as the British government eventually formed the Maxwell-Broomfield Commission, which reduced the tax increase to approximately 6 percent and returned the confiscated lands to the farmers. It was during this struggle that the women of Bardoli bestowed the title of Sardar upon him in recognition of his efficient leadership and organizational skills.

Explanation

Captain William Hawkins reached the Mughal court at Agra in 1609, after arriving at the port of Surat in 1608 aboard the ship Hector. He served as a representative of the English East India Company and carried a letter from King James I of England addressed to Emperor Jahangir, who had succeeded to the throne in 1605. Hawkins was chosen for this mission because of his proficiency in the Turkish language, which allowed him to communicate directly with the Emperor without an interpreter. Jahangir welcomed him warmly, granting him a mansab of 400 and the title of English Khan. The primary objective of this mission was to secure formal permission for the English to establish a permanent trade factory at Surat, marking the first major diplomatic encounter between the British and the Mughal state.

Explanation

Pragjyotishpur was the ancient name of the modern city of Guwahati and served as the capital of the legendary Pragjyotisha Kingdom, which is extensively mentioned in Indian epics such as the Mahabharata and the Ramayana. The name is derived from the Sanskrit words Prag meaning eastern, Jyotisha meaning star or astrology, and Pur meaning city, together translating to the City of Eastern Astrology or City of Eastern Light. This designation highlights the city's historical importance as a premier center for astronomical and astrological studies in ancient India. It functioned as the seat of power for the Kamarupa kingdom under several prominent dynasties, including the Varman dynasty, and remains a site of immense historical and cultural significance in the Northeast region.

Explanation

The Portuguese rule in India officially came to an end on 19th December 1961 following the successful execution of Operation Vijay by the Indian Armed Forces. This military action was launched to liberate the territories of Goa, Daman, and Diu from Portuguese colonial control, which had lasted for approximately 451 years. After brief hostilities, the Portuguese Governor General Manuel Antonio Vassalo e Silva signed the Instrument of Surrender, handing over the administration of these territories to the Indian government. This historic event marked the final departure of European colonial powers from the Indian subcontinent. Since then, 19th December is observed annually as Goa Liberation Day to commemorate the integration of these regions into the Indian Union.

Explanation

India has been the leading milk-producing nation in the world since 1998. According to the data from the Department of Animal Husbandry and Dairying as well as the Economic Survey 2018-19, India's milk production reached approximately 176.3 million tonnes during the 2017-18 period. This volume of production represented a global market share of about 19%. The sustained growth in the dairy sector has been supported by various government schemes such as the National Dairy Plan and the National Programme for Bovine Breeding and Dairy Development, which aimed at increasing the productivity of milch animals and improving the collection and processing infrastructure across the country.

Explanation

Boeing showcased Microlattice in 2015 as a breakthrough material developed by HRL Laboratories, which is a joint venture between Boeing and General Motors. This synthetic porous material is a 3D open-cellular polymer structure composed of a network of interconnected hollow tubes. The walls of these tubes are extremely thin, approximately 100 nanometers, making the material 99.99 percent air by volume. Because of this unique architecture, Microlattice is exceptionally lightweight, famously demonstrated by its ability to rest atop a dandelion seed head without disturbing it. Despite its airy composition, the metallic microlattice structure possesses high energy absorption capabilities and a high strength-to-weight ratio, allowing it to withstand significant compression and recover its shape, which makes it a prime candidate for future aerospace applications.

Explanation

Sukumar Sen was a distinguished Indian civil servant who served as the first Chief Election Commissioner of India from 21 March 1950 to 19 December 1958. Under his leadership, the Election Commission of India successfully organized and conducted the first two general elections of independent India in 1951–52 and 1957. He is credited with establishing the foundational democratic machinery of the country, managing the complex task of enrolling millions of voters and ensuring a fair electoral process during a period when the nation was transitioning into a republic. Following his tenure in India, he also served as the first Chief Election Commissioner in Sudan.

Explanation

The Sun's diameter is approximately 1,392,700 kilometers, while the Earth's mean equatorial diameter is about 12,756 kilometers. The ratio between these two values is calculated as follows:

Ratio = (Diameter of the Sun)/(Diameter of the Earth)

Ratio = (1,392,700)/(12,756) ≈ 109.18

In astronomical contexts, this value is typically rounded to 109. This linear ratio means that approximately 109 Earths could be lined up across the face of the Sun. This massive difference in scale also implies that the Sun's volume is large enough to hold roughly 1.3 million Earths inside it.

Explanation

The festival of Sao Joao is celebrated in Goa on June 24th to honor St. John the Baptist. A central tradition of this monsoon festival involves the exchange of gifts between families, particularly from a mother-in-law to her son-in-law. These gift baskets, known as Dali, are traditionally filled with seasonal local fruits like pineapples, jackfruits, and mangoes. The presentation of these fruits represents a celebration of the harvest and the bounty of the rainy season, reinforcing communal and familial bonds during the festivities.

Explanation

To find the percentage by which the expenditure on Royalty is less than the expenditure on Printing, use the relative difference formula:

Percentage less = (Value of Printing - Value of Royalty)/(Value of Printing) × 100

From the table, the expenditure on Printing is 20% and the expenditure on Royalty is 15%. Substituting these values into the formula:

Percentage less = (20 - 15)/(20) × 100

Percentage less = ⁵⁄₂₀ × 100

Percentage less = ¼ × 100 = 25%

Thus, the expenditure on Royalty is 25% less than the expenditure on Printing.

Explanation

The distance covered by A before B starts is calculated using the formula D = Speed × Time. Since A has a head start of 4 hours at a speed of 4 km/h, the initial distance gap is 4 × 4 = 16 km.

The relative speed of B with respect to A, as they move in the same direction, is the difference of their speeds: Vᵣₑₗ = 10 km/h - 4 km/h = 6 km/h.

The time taken by B to catch up with A is given by Time = (Initial Distance Gap)/(Relative Speed). t = ¹⁶⁄₆ = ⁸⁄₃ hours.

The total distance from the starting point where B catches A is the distance B travels in this time at its own speed: Distance = Speed_B × t = 10 × ⁸⁄₃ = ⁸⁰⁄₃ km.

Converting this to a decimal, ⁸⁰⁄₃ ≈ 26.666... km, which rounded to two decimal places is 26.67 km.

Explanation

To calculate the average amount of interest on loans paid by the company from 1998 to 2002, sum the interest values provided for each year in the table and divide by the total number of years.

Total Interest = 23.4 + 32.5 + 41.6 + 36.4 + 49.4 = 183.3 Lakh Rupees

The number of years in the period from 1998 to 2002 is 5.

Average Interest = (Total Interest)/(Number of Years) = (183.3)/(5) = 36.66 Lakh Rupees

This mean value represents the annual average expenditure specifically for interest on loans over the five-year duration.

Explanation

To find the average marks obtained by all seven students in Physics, we first determine the sum of the marks obtained by each student. Since the values in the table represent percentages of the maximum marks (120), the marks obtained by each student are calculated by multiplying their percentage by the maximum marks.

Total Marks in Physics = (90 + 80 + 70 + 80 + 85 + 65 + 50)/(100) × 120

Sum of percentages = 520

Total Marks = ⁵²⁰⁄₁₀₀ × 120 = 5.2 × 120 = 624

The average marks for the seven students is the total marks divided by the number of students:

Average Marks = ⁶²⁴⁄₇ ≈ 89.142857

Rounding to two decimal places, the average marks obtained by the students in Physics is 89.14.

Explanation

To find the total sales of books from branches B1, B3, and B6 for both years combined, we sum the sales figures for these specific branches from the given data for both 2000 and 2001.

Sales of branch B1 for both years: 80 + 105 = 185 Sales of branch B3 for both years: 95 + 110 = 205 Sales of branch B6 for both years: 70 + 80 = 150

Total sales for B1, B3, and B6 = 185 + 205 + 150 = 540

Alternatively, calculating year-wise for the specified branches: Sales in 2000 (B1 + B3 + B6) = 80 + 95 + 70 = 245 Sales in 2001 (B1 + B3 + B6) = 105 + 110 + 80 = 295 Total sales = 245 + 295 = 540 (in thousands).

Explanation

Let the unknown number be x. In percentage terms, any number is equal to 100% of itself. According to the problem, when 85% of the number is added to 75, the result is the number itself (100%). This relationship can be expressed with the following equation:

85% of x + 75 = 100% of x

By rearranging the equation to group the percentage terms, we see that the constant value 75 must represent the difference between 100% and 85% of the number:

75 = 100% of x - 85% of x

75 = 15% of x

To find the value of x, we solve the linear equation:

0.15x = 75

x = (75)/(0.15)

x = ⁷⁵⁰⁰⁄₁₅

x = 500

Alternatively, if 15% of the number is 75, then 1% of the number is ⁷⁵⁄₁₅ = 5. Since the number itself is 100%, its value is 5 × 100 = 500. Thus, 85% of 500 is 425, and 425 + 75 = 500, which satisfies the given condition.

Explanation

In cyclic quadrilateral ABCD, the sum of opposite angles is 180°. Therefore, ∠ ADC + ∠ ABC = 180°. Given that ∠ ADC = 129°, we calculate ∠ ABC = 180° - 129° = 51°.

Since AB is the diameter of the circle circumscribing the quadrilateral, the angle subtended by the diameter at the circumference is always a right angle. Thus, ∠ ACB = 90°.

In triangle ABC, the sum of the interior angles is 180°. We have ∠ BAC + ∠ ABC + ∠ ACB = 180°. Substituting the known values, we get ∠ BAC + 51° + 90° = 180°. Solving for the required angle, ∠ BAC = 180° - 141° = 39°.

Explanation

The arithmetic mean of a set of numbers is calculated as the sum of the values divided by the total count of numbers. Given that the average of 27 numbers is 0, the sum of these numbers must be 27 × 0 = 0. To find the maximum number of values that can be greater than zero, we consider a scenario where as many numbers as possible are positive, and their combined sum is offset by the remaining numbers.

If we let 26 of the numbers be positive, their sum will be some positive value S. By setting the 27th number equal to -S, the total sum of all 27 numbers becomes S + (-S) = 0. This satisfies the condition that the average is zero while allowing 26 individual numbers to be greater than zero. Thus, for any set of n numbers with an average of zero, at most n-1 numbers can be positive.

Explanation

In a circle with center O, the radii OA and OB are perpendicular to the tangents PA and PB at the points of contact A and B, respectively. Therefore, ∠ OAP = 90° and ∠ OBP = 90°. In the quadrilateral OAPB, the sum of the interior angles is 360°. This implies ∠ AOB + ∠ APB + ∠ OAP + ∠ OBP = 360°, which simplifies to ∠ AOB + ∠ APB = 180°. Given that ∠ APB = 40°, we have ∠ AOB = 180° - 40° = 140°.

In △ OAB, the sides OA and OB are radii of the same circle, making it an isosceles triangle. Consequently, the base angles are equal, so ∠ OAB = ∠ OBA. Since the sum of angles in a triangle is 180°, we have ∠ OAB + ∠ OBA + ∠ AOB = 180°. Substituting the known values, 2 × ∠ OAB + 140° = 180°, which leads to 2 × ∠ OAB = 40°, and thus ∠ OAB = 20°. This result follows the general geometric property that ∠ OAB = ½ ∠ APB.

Explanation

Let M, W, and B represent the daily work efficiency of a man, a woman, and a boy respectively. According to the efficiency ratios provided, W = 3M and B = ½M.

The total work is the product of the combined efficiency and the time taken: Total Work = (3M + 4W + 6B) × 6

Substituting the efficiencies in terms of M: Total Work = (3M + 4(3M) + 6(½M)) × 6 Total Work = (3M + 12M + 3M) × 6 Total Work = 18M × 6 = 108M

To express this total work in terms of women's work capacity, we use M = ⅓W: Total Work = 108 × (⅓W) = 36W

Let n be the number of women required to complete 36W units of work in 4 days. The equation is: n × W × 4 = 36W 4n = 36 n = 9

Explanation

The equivalent discount for two successive discounts of x% and y% is calculated using the formula x + y - ˣʸ⁄₁₀₀. For successive discounts of 25% and 5%, the equivalent single discount is 25 + 5 - (25 × 5)/(100) = 30 - 1.25 = 28.75%.

The difference between the single discount of 30% and the effective successive discount of 28.75% is 30% - 28.75% = 1.25%. This difference can also be identified directly as the ˣʸ⁄₁₀₀ term when the sum of successive discounts equals the single discount. To find the monetary difference on a shopping amount of ₹2,000, we calculate 1.25% of the total:

Difference = (1.25)/(100) × 2000 = 1.25 × 20 = 25

Explanation

When a solid object is melted and recast into new shapes, the total volume remains constant. The volume V of a sphere is given by the formula V = ⁴⁄₃ π r³, where r is the radius. Let R be the radius of the large sphere and r be the radius of the smaller spheres. The number of smaller spheres n that can be formed is calculated by dividing the volume of the original large sphere by the volume of a single small sphere.

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

By substituting the given values R = 6 cm and r = 2 cm into the formula:

n = ( ⁶⁄₂ )³ = 3³ = 27

Explanation

In a compound interest system where interest is compounded annually, the amount at the end of any given year acts as the principal for the succeeding year. This means the difference between the amount at the end of the fifth year and the fourth year represents the interest earned on the fourth year's amount during the fifth year.

Let A₄ be the amount after 4 years and A₅ be the amount after 5 years. A₄ = 2,190 A₅ = 2,409

The interest earned during the fifth year is: I = A₅ - A₄ = 2,409 - 2,190 = 219

The annual rate of interest r is calculated by taking the interest earned as a percentage of the principal at the start of that period: r = A₅ - A₄{A₄} × 100 r = (219)/(2,190) × 100 r = ⅒ × 100 = 10%

This calculation follows from the standard compound interest formula A = P(1 + r/100)ⁿ. For consecutive years, the ratio of the amounts is Aₙ₊₁ / Aₙ = (1 + r/100). Substituting the given values, 2,409 / 2,190 = 1.1, which results in a rate of 10%.

Explanation

According to the property of remainders, if an integer n leaves a remainder r when divided by a divisor d, then the expression an + b will leave the same remainder as ar + b when divided by d. This can be expressed using modular arithmetic as: if n ≡ r d, then an + b ≡ ar + b d.

In this problem, n ≡ 3 8. We need to find the remainder of 6n - 1 when divided by 8. Substituting the remainder r = 3 into the expression gives: 6(3) - 1 = 18 - 1 = 17

Now, we divide 17 by 8 to find the final remainder. Using the division algorithm a = dq + r: 17 = 8 × 2 + 1

The remainder is 1. This can also be verified by substituting n = 8k + 3 into the expression: 6(8k + 3) - 1 = 48k + 18 - 1 = 48k + 17 48k + 17 = 8(6k) + 8(2) + 1 = 8(6k + 2) + 1 Since 8(6k + 2) is a multiple of 8, the remaining term 1 is the remainder.

Explanation

The equation 3cos²A + 7sin²A = 4 is solved by grouping terms to utilize the fundamental identity cos²A + sin²A = 1. By splitting 7sin²A into 3sin²A + 4sin²A, the expression becomes: 3(cos²A + sin²A) + 4sin²A = 4 3(1) + 4sin²A = 4 Subtracting 3 from both sides gives 4sin²A = 1, so sin²A = ¼. Since A is an acute angle, taking the positive square root gives sin A = ½, which identifies A as 30°. The required value is cot 30° = √3.

Explanation

The equation is of the form a³ + b³ + c³ = 3abc, where a = x - 5, b = x - 6, and c = x - 7. According to the algebraic identity, if a³ + b³ + c³ = 3abc, then either a + b + c = 0 or a = b = c.

In this case, x - 5 = x - 6 = x - 7 is not possible because it would imply 5 = 6 = 7. Therefore, we must use the condition a + b + c = 0:

(x - 5) + (x - 6) + (x - 7) = 0 3x - 18 = 0 3x = 18 x = 6

Explanation

The trigonometric identity relating tangent and cotangent functions states that tan θ = cot(90° - θ). This implies that if tan A = cot B, then the sum of the angles A + B = 90° for acute angles. Applying this to the given equation tan x = cot(45° + 2x), we set the sum of the angles equal to 90°:

x + (45° + 2x) = 90°

Simplifying the equation by combining the terms involving x gives:

3x + 45° = 90°

Subtracting 45° from both sides of the equation results in:

3x = 45°

Dividing both sides by 3 yields the value of x:

x = 15°

Explanation

Let CP represent the cost price of one article and SP represent the selling price of one article. The problem states that the selling price of 40 articles equals the cost price of 50 articles, which is expressed as 40 × SP = 50 × CP. Rearranging this equation gives the ratio of the selling price to the cost price as SP/CP = 50/40, which simplifies to 5/4. Since the selling price is greater than the cost price, the transaction results in a gain. The gain percentage is calculated using the formula Gain % = (SP - CP)/(CP) × 100. Substituting the values from the ratio, the calculation becomes (5 - 4)/(4) × 100 = ¼ × 100 = 25%.

Explanation

In an equilateral triangle, the circumradius R and the inradius r are related through the centroid, which divides the altitude in a 2:1 ratio. The circumradius R represents the distance from the vertex to the centroid, while the inradius r represents the distance from the centroid to the base. This geometric property yields the constant ratio R = 2r.

Given that the circumradius R is 8 cm, the inradius is calculated by substituting the value into the relationship: r = (R)/(2) r = ⁸⁄₂ r = 4 cm

This relationship can also be derived from the trigonometric properties of the triangle or from the formulas for R and r in terms of the side length a, where R = (a)/(√(3)) and r = (a)/(2√(3)). Dividing the expression for R by the expression for r confirms that the circumradius is exactly twice the inradius.

Explanation

Raj Babbar is a veteran actor-turned-politician who was a prominent member of the Indian National Congress during the May 2019 period. He served as the President of the Uttar Pradesh Congress Committee from 2016 until shortly after the 2019 Lok Sabha elections. During the 2019 general elections held in April and May, he contested as the Indian National Congress candidate from the Fatehpur Sikri constituency in Uttar Pradesh. Throughout this timeframe, he was one of the key leaders and star campaigners for the party.

Explanation

Piyush Goyal, the then Union Minister of Railways and Coal, was awarded the 4th Carnot Prize in 2018 by the Kleinman Center for Energy Policy at the University of Pennsylvania. The prize is named after French physicist Nicolas Sadi Carnot and recognizes distinguished contributions to energy policy. Goyal was honored for his leadership in transforming India's energy sector, specifically through the massive rural electrification drive and the successful implementation of the UJALA scheme, which promoted energy efficiency by distributing millions of LED bulbs across the country. His efforts significantly advanced sustainable energy solutions and moved India toward a cleaner energy future.

Explanation

Mihira Bhoja was the most powerful and illustrious ruler of the Gurjara-Pratihara dynasty, reigning from approximately 836 to 885 CE. He succeeded his father, Ramabhadra, and restored the prestige of his lineage by establishing Kannauj as his capital. Under his leadership, the Pratihara Empire reached its zenith, extending from the foothills of the Himalayas in the north to the Narmada River in the south, and from the borders of Bengal in the east to Sindh in the west. A devout follower of Lord Vishnu, he adopted the title Adivaraha, which is found inscribed on the silver coins issued during his reign. His era is significant for the successful defense of northern India against Arab incursions and for the cultural and architectural patronization that defined the Pratihara period in early medieval India.

Explanation

The 44th Amendment Act of 1978, enacted by the Janata Party government, removed the right to property from the list of Fundamental Rights in the Indian Constitution. It repealed Article 19(1)(f), which guaranteed the right to acquire, hold, and dispose of property, and Article 31, which related to the compulsory acquisition of property. Instead, the amendment inserted Article 300A into Part XII of the Constitution, which specifies that no person shall be deprived of his property save by authority of law. This change transformed the right to property from a Fundamental Right into a legal or constitutional right, meaning it is still protected by law but does not enjoy the same level of judicial protection as Fundamental Rights.

Explanation

Vidarbha won the 85th edition of the Ranji Trophy in February 2019 by defeating Saurashtra by 78 runs in the final held at the Vidarbha Cricket Association Stadium in Nagpur. Having won their maiden title in the 2017–18 season, Vidarbha entered the 2018–19 tournament as the defending champions and successfully retained the trophy. This victory made them only the sixth team in the history of the competition to win consecutive titles. Left-arm spinner Aditya Sarwate was named the man of the match for his match haul of 11 wickets and a crucial contribution with the bat, helping Vidarbha secure the championship under the leadership of captain Faiz Fazal.

Explanation

Agriculture remains the largest employer in the Indian economy, providing livelihoods to a significant portion of the workforce. According to data from the Periodic Labour Force Survey (PLFS) 2017-18 and contemporary economic reports, the agriculture and allied sectors employed approximately 44 percent of the total Indian workforce. While the sector's contribution to the Gross Value Added (GVA) has gradually decreased over time as the economy shifted toward services and industry, it continues to absorb the highest number of workers due to the labor-intensive nature of farming and the large rural population dependent on land-based activities for their primary income. This high level of employment is driven by both subsistence farming and commercial agriculture across rural India.