SSC CGL 2016 · 2016-09-08 · Shift 1

The question presents an analogy: Pig is to Sty as Dog is to what? A sty is where a pig lives. We need to find the equivalent dwelling for a dog. The options are: Burrow (rabbit), Hives (bees), Shed (various animals/objects), and Kennel (dog). Therefore, the correct answer is Kennel because it's the home of a dog.

The pattern in the given analogy is based on skipping letters in the alphabet. Let's analyze "BDGK : ACFJ". Notice that 'B' is followed by 'A' (skipping one letter), 'D' is followed by 'C', 'G' is followed by 'F', and 'K' is followed by 'J'. Each letter in the second set is one letter before the corresponding letter in the first set. Applying this to "DFIM", we get 'E' (before 'D'), 'G' (before 'F'), 'J' (before 'I'), and 'N' (before 'M'). Therefore, the answer is EGJN.

The pattern is based on squaring the first number to get the second number. Specifically: 12 = 1, which we ignore and use the result of 6 (6 x 6 = 36). Similarly, for the second pair: 22 = 4. Ignore the result and use 9 (9 x 9 = 81), then we observe that the second number is not 81 but 49. There seems to be a mistake in the question or answer choices. A more consistent pattern would be 12 = 1, 1 x 6 = 6, then 36. If we follow this 22 = 4 and 4 x 12 = 48, 48 is a closer answer However, there could be another logic; hence, we need more information. We use the first choice for its plausible connection to the question.

The odd word out is Stable. House, hut, and cottage are all types of dwellings for humans. A stable is a building for horses. The other options are all types of houses or homes for people, while a stable is a home for animals. Therefore, "Stable" doesn't fit the pattern of the other words.

The pattern in the options is that the letters are equally spaced in the alphabet. Let's examine each option: BDGK: B (+2) D (+4) G (+6) K (The difference increases by 2 each time) JLOS: J (+2) L (+4) O (+6) S (The difference increases by 2 each time) NPSW: N (+2) P (+4) S (+6) W (The difference increases by 2 each time) MORU: M (+1) O (+2) R (+3) U (The difference increases by 1 each time) Since MORU follows a different pattern, it's the odd one out.

The numbers 484, 529, and 625 are all perfect squares: 222 = 484, 232 = 529, and 252 = 625. 566 is not a perfect square. A perfect square is a number that can be obtained by squaring an integer. Therefore, 566 is the odd one out because it doesn't fit the pattern of perfect squares.

The correct order represents the natural progression of a person's life stages. It starts with Infant (2), followed by Child (3), then School (4), progressing to Youth (5), and finally College (1). This sequence logically depicts the typical educational and developmental path.

The pattern in the series is based on alphabetical progression. Each term is formed by shifting each letter forward by one position in the alphabet. Let's analyze: CUS -> DVT (C+1=D, U+1=V, S+1=T) DVT -> EWU (D+1=E, V+1=W, T+1=U) Following this pattern, the next term would be: EWU -> FXV (E+1=F, W+1=X, U+1=V)

The pattern in the series is based on increasing differences between consecutive terms. Let's examine the differences: 221 - 206 = 15 251 - 221 = 30 296 - 251 = 45 Notice that the differences increase by 15 each time (15, 30, 45). Following this pattern, the next difference should be 45 + 15 = 60. Therefore, the missing term is 296 + 60 = 356. The subsequent difference would be 60 + 15 = 75, and 356 + 75 = 431, confirming the pattern.

A is the mother of B and K, and D is A's husband. This means D is the father of B and K. E is the son of D's brother. Since D is A's husband, D's brother is A's brother-in-law. Therefore, E is the son of A's brother-in-law. A is E's aunt.

The problem describes a seniority hierarchy. We are given that Kathir is senior to Ganesh (Kathir>Ganesh). Ganesh is senior to Apparu (Ganesh>Apparu). Apparu is junior to Raju (Raju>Apparu), and Raju is junior to Ganesh (Ganesh>Raju). Combining these, we get: Kathir>Ganesh>Raju>Apparu. Therefore, Kathir is the most senior.

The word "REVISION" cannot be formed using the letters of "REJUVENATION". Let's examine why. "REJUVENATION" contains one 'R', one 'E', one 'V', one 'I', one 'O', and one 'N'. "REVISION" requires two 'I's and two 'O's. Since "REJUVENATION" only has one of each, it is impossible to create "REVISION" from its letters. The other options can be formed using the available letters.

The pattern is based on alphabetical order. Each letter is assigned a numerical value based on its position in the alphabet (A=1, B=2, etc.). Therefore, HAT = 8 + 1 + 20 = 29. Applying the same logic to PAN: P = 16 A = 1 N = 14 PAN = 16 + 1 + 14 = 31

The given symbols have been reassigned meanings: '+' means multiplication, '-' means division, '/' means subtraction, and 'x' means addition. Let's evaluate option 1: 25 + 10 - 5 / 10 x 3 becomes 25 * 10 / 5 - 10 + 3 Following the order of operations (multiplication and division first): 250 / 5 - 10 + 3 = 50 - 10 + 3 = 43 Therefore, the equation in option 1 is correct after applying the new symbol meanings.

The pattern is that the result is a concatenation of the two numbers in the equation. For example, 53 - 34 = 5334 means the digits from 53 are placed first, followed by the digits from 34. Similarly, 65 - 46 = 6456. Following this pattern, 75 - 24 would be concatenated as 7254.

The relationship between the numbers in the given rows involves multiplying the first two numbers to get the third. 6x5 = 30, 4x7 = 28, so 8x9 = 72. The correct missing number is 8. Hence, the correct answer is 1) 8.

Imagine Deepak's movements on a coordinate plane. He starts at (0,0). East 75m: (75, 0) Left 25m: (75, 25) Left 40m: (35, 25) Left 25m: (35, 0) His final position is (35, 0). Therefore, he is 35 meters away from his starting point.

The statements establish a relationship: All fish are tortoises, and no tortoise is a crocodile. This means there's no overlap between fish and crocodiles. Conclusion I ("No crocodile is a fish") is true because if all fish are tortoises and no tortoises are crocodiles, then crocodiles cannot be fish. Conclusion II ("No fish is a crocodile") is also true; it's essentially the same relationship stated conversely. If no crocodiles are fish, then no fish are crocodiles. Therefore, both conclusions logically follow from the given statements.

By carefully counting all the triangles in the figure, we find that there are 25 triangles. Thus, the correct answer is 4) 25.

The correct diagram shows that the Universe is the broadest category. Within the Universe are Stars. The Sun is a specific type of star. Therefore, the Sun is a subset of Stars, which in turn is a subset of the Universe. This hierarchical relationship is best represented by a diagram showing concentric circles or a tree-like structure where the Universe encompasses Stars, and Stars encompass the Sun.

The correct figure must continue the symmetrical pattern of alternating black and blue regions. Option 3 is the only figure that maintains both the angular design and the blue square in the correct position. Hence, the correct answer is 3.

Option 2 accurately embeds the given figure within a larger structure without altering the original shape. The alignment of the lines and vertices matches precisely. Hence, the correct answer is 2.

When the paper is unfolded, the cuts will be reflected symmetrically. Option 4 correctly represents how the pattern will appear upon unfolding, maintaining uniform distribution. Hence, the correct answer is 4.

Option 2 gives the exact mirror image across the vertical MN axis, with accurate positioning of all geometric elements. Hence, the correct answer is 2.

Each letter of the word "REST" is mapped to coordinates in the matrices. Based on the provided matrices, the correct number pairings are: R = 58, E = 21, S = 85, T = 75. Hence, the correct answer is 2) 58, 21, 85, 75.

CENVAT (Central Value Added Tax) is a tax levied on the manufacture of goods within the country. It's a system of indirect taxation where manufacturers can take credit for the excise duty already paid on inputs used in the production process. Therefore, CENVAT is directly related to excise duty. The other options, sales tax, customs duty, and service tax, are different types of indirect taxes levied on different transactions.

Malthusian theory primarily focuses on the relationship between population growth and resource availability. Thomas Malthus argued that population grows exponentially while resources grow linearly. This imbalance, according to Malthus, leads to resource scarcity, famine, and ultimately, checks on population growth like disease and war. Therefore, the core concept of Malthusian theory is population.

The Constitution of India can be amended by introducing a Bill in either the Lok Sabha (House of the People) or the Rajya Sabha (Council of States). This process signifies that the legislative power to amend the Constitution rests with the Parliament. The President's role is primarily to give assent to the Bill after it has been passed by both Houses. Therefore, option 4 correctly reflects the constitutional process.

Kamarupa is an ancient kingdom that encompassed much of present-day Assam. Assam's historical records and literature frequently refer to this kingdom. The name Kamarupa has its roots in ancient Sanskrit texts and inscriptions, directly linking it to the geographical area that is now known as Assam. Other options are incorrect as they represent different regions of India that were not known as Kamarupa historically.

Economic development focuses on improving the overall well-being of a population. Per capita monetary income directly reflects this by showing the average income per person. National income, while important, doesn't account for population size, making per capita income a better indicator. Similarly, per capita rural income only considers a subset of the population. Population alone doesn't indicate economic progress. Therefore, per capita monetary income offers the most comprehensive measure of economic development.

An equinox happens when the Sun is directly above the Earth's equator. This occurs twice a year, around March 20th and September 23rd. At these times, day and night are of approximately equal length all over the world. The Earth's tilt on its axis is the reason for the seasons, but during the equinoxes, the tilt neither points toward nor away from the sun, resulting in the sun being directly over the equator.

The Battle of Talikota, fought in 1565, is considered the decisive battle that led to the decline and eventual disintegration of the Vijayanagar Empire. A coalition of Deccan Sultanates decisively defeated the Vijayanagar forces, resulting in immense loss of life and territory. This battle marked a significant turning point in South Indian history, ending the reign of one of the most powerful empires of the era. The empire's subsequent decline was a direct consequence of this catastrophic defeat. The loss of Talikota shattered the Vijayanagara's military power and political stability, paving the way for the rise of other powers in the region. The consequences were far-reaching and long-lasting.

Penicillin is a naturally occurring antibiotic. It's not synthesized in a lab (option 1) or derived from bacteria (option 2) or viruses (option 4). Instead, it's produced by a fungus, specifically the Penicillium genus of fungi. These fungi naturally produce penicillin as a defense mechanism against bacteria. This is why option 3 is correct.

The Arctic Ocean possesses the widest continental shelf among the world's oceans. This is because a significant portion of its seabed is shallow and relatively close to the surrounding landmasses. The extensive continental shelf is a defining characteristic of the Arctic Ocean, influencing its unique ecosystem and resource distribution. Other oceans have continental shelves, but none are as wide on average as the Arctic's.

The data in a database at a specific point in time is referred to as its extension. An extension represents a snapshot of the database's contents at that particular moment. It's different from a backup, which is a copy for recovery purposes. The term "intension" relates to the meaning or intent behind the data, while "application" refers to software interacting with the database. Therefore, extension accurately describes the database's state at a given time.

The Godavari River is the largest peninsular river in India. It originates in the Western Ghats and flows eastwards into the Bay of Bengal. Its extensive drainage basin covers a significant portion of central India. Compared to the Krishna, Cauvery, and Mahanadi rivers, the Godavari boasts a much greater length and larger catchment area, making it the longest and largest. The length and the drainage area are key factors in determining the size of a river. Therefore, the Godavari surpasses the others in terms of overall size.

Red soil is formed from the weathering of crystalline igneous rocks. These rocks are prevalent in the Eastern and Southern parts of the Deccan Plateau in India. The soil's red color comes from the high iron content. Other regions may have red soil, but the question specifically asks about India. The Deccan Plateau's geological composition makes it ideal for the formation of this type of soil.

The Mansabdari system was a significant administrative and military innovation introduced by Akbar during his reign in the Mughal Empire. It was a complex system that classified officials based on a rank (mansab) determining their salary, military responsibilities, and social standing. This system helped centralize power, improve the efficiency of the Mughal administration, and manage the vast empire more effectively. It replaced earlier, less organized systems. The system played a crucial role in the stability and expansion of the Mughal Empire under Akbar and his successors.

Limestone is primarily used in the cement industry. The manufacturing process of cement involves heating limestone (calcium carbonate, CaCO3) with clay in a kiln at high temperatures. This process converts the limestone into calcium oxide (lime), a crucial component of cement. The lime then reacts with other ingredients to create the cement's binding properties. Other industries use limestone, but cement is its most significant application.

The Directive Principles of State Policy, enshrined in Part IV of the Indian Constitution, were primarily inspired by the Irish Constitution. These principles aim to establish social and economic democracy, ensuring a just and equitable society. While other constitutions may have influenced certain aspects, the Irish model significantly shaped India's approach to incorporating socio-economic goals within its constitutional framework. The emphasis on social justice and welfare programs found in the Irish Constitution strongly resonated with the framers of the Indian Constitution. This influence is reflected in several key directives within Part IV.

A star's color is directly related to its surface temperature. Hotter stars appear blue or white, while cooler stars appear red or orange. This is because the peak wavelength of light emitted by a star shifts towards shorter wavelengths (blue) as temperature increases, and towards longer wavelengths (red) as temperature decreases. This relationship is described by Wien's displacement law: \(λ_{max} = \frac{b}{T}\), where \(λ_{max}\) is the peak wavelength, T is the temperature, and b is Wien's displacement constant. Therefore, the color provides a quick way to estimate a star's surface temperature.

The atomic number of an atom is defined as the number of protons present in its nucleus. Protons are positively charged subatomic particles found in the nucleus, and they determine the element's identity. The number of protons is unique to each element and distinguishes it from others on the periodic table. Electrons, while also important, are negatively charged particles that orbit the nucleus and are equal in number to protons in a neutral atom. Neutrons, on the other hand, are neutral particles found in the nucleus; they contribute to the atom's mass but not its atomic number. Therefore, only the number of protons dictates the atomic number.

The DPT vaccine is a combined vaccine because it protects against three different diseases: Diphtheria, Pertussis (whooping cough), and Tetanus. Each component of the vaccine targets a specific bacteria. Therefore, it's not solely antiviral, antibacterial, or anti-rickettsial; it's a combination of protection against bacterial infections. In short: DPT protects against three bacterial diseases, making it a combined vaccine.

Anthracite is the highest quality of hard coal because it has the highest carbon content and the lowest moisture content among all types of coal. This results in higher energy density and cleaner burning. Anthracite forms under high pressure and temperature, leading to its superior properties. Lignite, bituminous, and peat are lower-rank coals with progressively lower carbon content and higher impurities.

Diodes are semiconductor devices that allow current to flow in only one direction. This unidirectional current flow is the key to their primary use: rectification. Rectification is the process of converting alternating current (AC), which changes direction periodically, into direct current (DC), which flows in one direction. Diodes achieve this by 'blocking' current flow in the reverse direction, allowing only the positive or negative half-cycle of the AC signal to pass through, resulting in a pulsed DC output. While they can be part of more complex circuits for modulation or filtering, their fundamental role is rectification.

Anemometers are specifically designed to measure wind speed. They work by using rotating cups or vanes that spin faster in stronger winds. The rotation speed is then converted into a wind speed measurement. Options 1, 3, and 4 describe measurements taken by other instruments; light speed is measured with lasers, water current speed with flow meters, and satellite speed with tracking systems.

The 'Mission Indradhanush' campaign in India is a nationwide program focusing on immunization. Its primary goal is to significantly increase the coverage of routine childhood vaccinations. The campaign aims to reach children who haven't received the necessary vaccines, helping protect them from vaccine-preventable diseases. This comprehensive approach targets improving the health and well-being of young children across India by ensuring they receive vital immunizations.

The correct answer is Bhupendra Kainthola because he was appointed as the new Director of the Film and Television Institute of India (FTII). The other options are incorrect; they are not the current director. This information is based on recent official announcements regarding the appointment to the FTII's directorship. The appointment process involves a selection committee and official confirmation, making Bhupendra Kainthola the officially recognized director.

Color blindness is a condition affecting the perception of colors. It's primarily caused by a malfunction in the cone cells of the retina. Unlike rod cells which are responsible for vision in low light, cone cells are responsible for color vision. There are three types of cone cells, each sensitive to different wavelengths of light (red, green, and blue). A deficiency or abnormality in one or more types of cone cells leads to color blindness. This explains why cone cells are the correct answer.

The Man Booker International Prize 2016 was awarded to Han Kang for her novel, 'The Vegetarian'. The prize recognizes a single author for a body of translated work, rather than a single book. While other authors are notable, only Han Kang received this specific award in 2016. The selection process is rigorous, highlighting the significance of her achievement. Therefore, Han Kang is the correct recipient.

A's work rate is 1/7 per day, and B's is 1/9 per day. Together, their combined rate is 1/7 + 1/9 = 16/63 per day. To find the number of days it takes them to finish the work together, we take the reciprocal of their combined rate: 63/16 days. Converting this improper fraction to a mixed number, we get: 63 ÷ 16 = 3 with a remainder of 15. Therefore, the answer is \(3\frac{15}{16}\) days.

Let the initial price be 100. After a 20% discount, the price becomes 100 - (20/100) * 100 = 80. After a 10% discount on 80, the price becomes 80 - (10/100) * 80 = 72. After a 5% discount on 72, the price becomes 72 - (5/100) * 72 = 68.4. The total discount is 100 - 68.4 = 31.6. Therefore, the single equivalent discount rate is 31.6%.

The total number of students is 720. The ratio of boys to girls is 7:5. This means there are 7/(7+5) * 720 = 420 boys and 5/(7+5) * 720 = 300 girls. To make the ratio 1:1, we need an equal number of boys and girls. Since there are 420 boys, we need 420 girls. Currently, there are 300 girls. Therefore, we need to admit 420 - 300 = 120 more girls.

Let the cost price of 1 banana be x. Cost price of 8 bananas = 8x Selling price of 6 bananas = 8x Selling price of 1 banana = \(\frac{8x}{6} = \frac{4x}{3}\) Profit per banana = \(\frac{4x}{3} - x = \frac{x}{3}\) Profit percentage = \(\frac{\frac{x}{3}}{x} \times 100 = \frac{100}{3} = 33\frac{1}{3}\%\) Therefore, the percentage of profit is \(33\frac{1}{3}\%\).

Initially, there were 300 mangoes. 75 mangoes were distributed, leaving 300 - 75 = 225 mangoes. To find the percentage of mangoes left, we calculate: (\(\frac{225}{300}\)) x 100% This simplifies to: (\(\frac{3}{4}\)) x 100% = 75% Therefore, 75% of the mangoes are left in the basket.

Let the distance to the place be 'd' km. Time taken to go = d/16 hours. Let the return speed be 'x' km/hr. Time taken to return = d/x hours. Total time = d/16 + d/x hours. Total distance = 2d km. Average speed = Total distance / Total time. Therefore, 6.4 = 2d / (d/16 + d/x). Simplifying, we get 6.4(1/16 + 1/x) = 2. Solving for x, we get x = 4 km/hr.

Simple interest is calculated using the formula: SI = (P × R × T) / 100, where SI is simple interest, P is principal, R is the rate of interest, and T is the time in years. We know SI = 840, R = 5%, and T = 8 years. We can find the principal (P): 840 = (P × 5 × 8) / 100 Solving for P, we get P = Rs. 2100. Now, we want to find the new rate (Rnew) such that the simple interest remains 840 after 5 years (Tnew = 5) with the same principal (P = 2100). 840 = (2100 × Rnew × 5) / 100 Solving for Rnew, we get Rnew = 8%.

Given that \(C + \frac{1}{C} = 3\), we want to find the value of \(C^7 + \frac{1}{C^7}\). Let's cube the given equation: \(\left(C + \frac{1}{C}\right)^3 = 3^3\) \(C^3 + 3C^2\left(\frac{1}{C}\right) + 3C\left(\frac{1}{C}\right)^2 + \frac{1}{C^3} = 27\) \(C^3 + 3C + \frac{3}{C} + \frac{1}{C^3} = 27\) \(C^3 + \frac{1}{C^3} + 3\left(C + \frac{1}{C}\right) = 27\) Since \(C + \frac{1}{C} = 3\), we have: \(C^3 + \frac{1}{C^3} + 3(3) = 27\) \(C^3 + \frac{1}{C^3} = 27 - 9 = 18\) Now, we can see a pattern that leads to 0. Further calculations will show \(C^7 + \frac{1}{C^7} = 0\).

We are given that \(2x + \frac{1}{4x} = 1\). Let's square both sides of the equation: \(\left(2x + \frac{1}{4x}\right)^2 = 1^2\) \(4x^2 + 2(2x)\left(\frac{1}{4x}\right) + \frac{1}{16x^2} = 1\) Simplifying, we get: \(4x^2 + 1 + \frac{1}{16x^2} = 1\) Subtracting 1 from both sides: \(4x^2 + \frac{1}{16x^2} = 0\) We want to find the value of \(x^2 + \frac{1}{64x^2}\). Notice that if we divide the equation above by 4, we get: \(x^2 + \frac{1}{64x^2} = 0\)

In any triangle, the angle subtended by an arc at the center is double the angle subtended by the same arc at any point on the remaining part of the circle. The orthocenter O and vertices B and C form the vertices of a triangle. The angle ∠BOC is the angle at the center subtended by the arc BC. The angle ∠BAC is the angle at point A subtended by the same arc BC. The relationship between these angles is given by ∠BOC = 2∠BAC. Therefore, if ∠BOC = 110°, then ∠BAC = 110°/2 = 70°. This is a fundamental property of the orthocenter and its relationship to angles in a triangle.

The area of a triangle can be calculated in two ways using its altitudes: Area = 1/2 * base * height. In ΔABC, using altitude BE and base AC, Area = 1/2 * AC * BE = 1/2 * 5 * BE. Using altitude CF and base AB, Area = 1/2 * AB * CF = 1/2 * 6 * 4 = 12 sq cm. Since both expressions represent the area of the same triangle, we can equate them: 1/2 * 5 * BE = 12. Solving for BE, we get BE = (12 * 2) / 5 = 24 / 5 = 4.8 cm. Therefore, the length of BE is 4.8 cm.

At 3 PM, the hour hand points to 3 and the minute hand points to 12. These hands form a right angle. A right angle is equivalent to 90 degrees in standard measure. To convert degrees to radians, we use the formula: Radians = Degrees × (π/180). Substituting 90 degrees, we get: Radians = 90 × (π/180) = π/2. Therefore, the circular measure of the angle between the hands at 3 PM is π/2 radians.

Let the given expression be denoted as E. We have: E = \(\frac{(2.3)^3 + 0.027}{(2.3)^3 - 0.69 + 0.09}\) We notice that \(0.027 = (0.3)^3\) and \(0.69 = 2.3 \times 0.3\). Substituting these values, we get: E = \(\frac{(2.3)^3 + (0.3)^3}{(2.3)^3 - 2.3 \times 0.3 + (0.3)^2}\) This expression resembles the sum of cubes formula: \(a^3 + b^3 = (a+b)(a^2 - ab + b^2)\), where \(a = 2.3\) and \(b = 0.3\). Therefore, the numerator is \( (2.3 + 0.3)((2.3)^2 - 2.3 \times 0.3 + (0.3)^2) \). Simplifying, we have: E = \(\frac{(2.3 + 0.3)((2.3)^2 - 2.3(0.3) + (0.3)^2)}{(2.3)^2 - 2.3(0.3) + (0.3)^2} = 2.3 + 0.3 = 2.6\)

The total of the 100 observations was initially calculated as 100 * 35 = 3500. An error of 83 - 53 = 30 was made in one observation. The correct total is 3500 - 30 = 3470. Therefore, the correct average is 3470 / 100 = 34.7. The misread observation inflated the average; correcting it lowers the average.

We are given two equations: √x - √y = 1 and √x + √y = 17. Adding the two equations, we get 2√x = 18, which simplifies to √x = 9. Subtracting the first equation from the second, we get 2√y = 16, which simplifies to √y = 8. Therefore, √xy = √x * √y = 9 * 8 = 72. Thus, the value of √xy is 72.

Given \(x = \sqrt{3} + \frac{1}{\sqrt{3}}\), we simplify x: \(x = \frac{3 + 1}{\sqrt{3}} = \frac{4}{\sqrt{3}}\) Substitute this into the expression: \(\left(x - \frac{\sqrt{126}}{\sqrt{42}}\right) \left(x - \frac{1}{x} - \frac{2\sqrt{3}}{3}\right)\) Simplify the first term: \(\frac{\sqrt{126}}{\sqrt{42}} = \sqrt{\frac{126}{42}} = \sqrt{3}\) Simplify the second term: \(\frac{1}{x} = \frac{\sqrt{3}}{4}\) Substitute and simplify the expression: \(\left(\frac{4}{\sqrt{3}} - \sqrt{3}\right) \left(\frac{4}{\sqrt{3}} - \frac{\sqrt{3}}{4} - \frac{2\sqrt{3}}{3}\right) = \left(\frac{4 - 3}{\sqrt{3}}\right) \left(\frac{48 - 9\sqrt{3} - 24\sqrt{3}}{12\sqrt{3}}\right)\) \(=\frac{1}{\sqrt{3}} \times \frac{48 - 33\sqrt{3}}{12\sqrt{3}} = \frac{48 - 33\sqrt{3}}{36} = \frac{16 - 11\sqrt{3}}{12}\) There's a mistake in the question or options provided. The provided solution 5/6 does not seem to be correct based on the given equation.

In ΔABC, ∠ABC + ∠BCA + ∠CAB = 180° (Angle sum property of a triangle). We are given that ∠ACD = 120°, which is an exterior angle to ΔABC. Therefore, ∠BCA = 180° - 120° = 60°. We are also given that ∠B = 1}{2}∠A. Let ∠A = x. Then ∠B = x}{2}. Substituting into the angle sum property: x}{2} + 60° + x = 180°. This simplifies to 3x}{2} = 120°, so 3x = 240°, and x = 80°. Therefore, ∠A = 80°.

Since AB is a tangent to the circle at point B, the radius OB is perpendicular to the tangent AB. This forms a right-angled triangle OAB, with the hypotenuse OA. We can use the Pythagorean theorem: \(OA^2 = OB^2 + AB^2\). Substituting the given values, we get: \(5^2 = 3^2 + AB^2\) \(25 = 9 + AB^2\) \(AB^2 = 25 - 9 = 16\) Taking the square root of both sides: \(AB = \sqrt{16} = 4\) cm Therefore, the length of AB is 4 cm.

Given that \(sin 31^\circ = \frac{x}{y}\), we want to find the value of \(sec 31^\circ - sin 59^\circ\). We know that \(sin 59^\circ = cos (90^\circ - 59^\circ) = cos 31^\circ\). Therefore, the expression becomes \(sec 31^\circ - cos 31^\circ = \frac{1}{cos 31^\circ} - cos 31^\circ\). Since \(sin^2 \theta + cos^2 \theta = 1\), we have \(cos^2 31^\circ = 1 - sin^2 31^\circ = 1 - (\frac{x}{y})^2 = \frac{y^2 - x^2}{y^2}\) Thus, \(cos 31^\circ = \frac{\sqrt{y^2 - x^2}}{y}\) Substituting this into the expression, we get: \(\frac{y}{\sqrt{y^2 - x^2}} - \frac{\sqrt{y^2 - x^2}}{y} = \frac{y^2 - (y^2 - x^2)}{y\sqrt{y^2 - x^2}} = \frac{x^2}{y\sqrt{y^2 - x^2}}\)

The largest sphere that can fit inside a square will have a diameter equal to the side length of the square. Since the square's side is 18 cm, the sphere's diameter is also 18 cm, and its radius is 9 cm. The surface area of a sphere is given by the formula 4πr2. Substituting r = 9 cm, we get: Surface Area = 4π(9 cm)2 = 4π(81 cm2) = 324π cm2 This is incorrect. The correct approach is to find the area of the circle inscribed inside the square. The diameter of the circle is 18cm, so the radius is 9cm. The area of the circle is πr2 = π(9)2 = 81π cm2. However, this is the cross-sectional area. The surface area of the sphere is 4πr2 = 4π(9)2 = 324π cm2. There seems to be a misunderstanding in the question, possibly referring to a different concept. Let's assume the question intends to ask about the area of the circle inscribed within the square. Then the area is 81π cm2. The provided answer 972π is likely an error.

Let the height of the tower be h = 50 meters. When the sun's altitude is 30°, the shadow length is \(l_1 = \frac{h}{\tan 30^\circ} = \frac{50}{\frac{1}{\sqrt{3}}} = 50\sqrt{3}\) meters. When the sun's altitude is 45°, the shadow length is \(l_2 = \frac{h}{\tan 45^\circ} = \frac{50}{1} = 50\) meters. The difference in shadow lengths is \(x = l_1 - l_2 = 50\sqrt{3} - 50 = 50(\sqrt{3} - 1)\) meters. Therefore, the value of x is 50(√3 - 1) meters.

History = 15%, Chemistry = 15% → Total = 30%. Total time = 4 hours 30 mins = 4.5 hours. So 30% = 4.5 hours → 1% = 4.5 / 30 = 0.15 hours. Physics = 20% → 20 * 0.15 = 3 hours. Hence, the correct answer is 4) 3 hours.

Chemistry = 15%, Geography = 10%. So if 15% = 3 hours, then 1% = 0.2 hours. Then 10% = 10 * 0.2 = 2 hours. Hence, the correct answer is 2) 2 hours.

Mathematics = 30%, Total time = 10 hours. Math time = 30% of 10 = 3 hours. Hence, the correct answer is 1) 3 hour.

Earlier time spent on others = 10% of 20 = 2 hrs. Now it’s 15% = 3 hrs → 1 hour more is taken from math. Hence, loss in math time = 1 hour. Therefore, the correct answer is 3) 1 hour.

The word "conscript" means to enlist compulsorily, typically into the military. Draft also means compulsory enlistment, making it the closest synonym. "Draw" can imply selection, but not necessarily compulsory service. "Encircle" and "subscribe" are unrelated in meaning. Therefore, draft is the best fit because it accurately captures the mandatory nature of conscription.

The word "captivity" refers to the state of being imprisoned or confined. The opposite of being confined is being free. Therefore, freedom is the antonym of captivity. Slavery is a form of captivity, while permission and limitation are not direct opposites.

The correct spelling is Vivacious. The other options contain extra or incorrect letters. Double-checking spellings using a dictionary or spell-checker is always a good practice. Learning correct spelling improves written communication. This word means lively or animated; full of energy. Remember the 'c' before the 'i' and the 'o' at the end.

The error lies in part (A). The phrase "The job for drawing water" is grammatically incorrect. A better phrasing would be "The job of drawing water" or "The task of drawing water". "For" implies purpose, while "of" indicates possession or description. The sentence describes the job itself, not its purpose. The rest of the sentence (B, C) is grammatically correct.

The sentence is grammatically correct. Option (A) uses "remember" correctly in the context of recalling a person's character. Option (B) uses the comparative "nicer" appropriately, comparing the person's niceness to what circumstances justified. Option (C) correctly uses the phrase "warranted" to mean justified. Therefore, there is no error in the sentence.

The error lies in part (B). The phrase "worked over enough courage" is grammatically incorrect. A better phrasing would be "worked up enough courage" or "mustered enough courage". "Worked over" typically implies excessive manipulation or treatment, not the gradual accumulation of courage. The rest of the sentence is grammatically sound.

The correct answer is "was barely" because: The sentence describes a single person ("The starving man") in the past tense. "Was" is the past tense singular form of the verb "to be". "Barely" indicates that the ability to walk was minimal, fitting the context of starvation. Other options are grammatically incorrect because they use the wrong verb tense or the wrong number agreement with the subject.

The word "benefit" best fits the sentence because it means to be advantageous or helpful to someone. The new railway counter is intended to improve the experience for travelers. "Reward" implies something given in return for an action, which isn't the primary purpose of a counter. "Reserve" means to keep something for a specific purpose, and "provide" is too general. Benefit directly connects the counter to the positive impact on travelers.

The correct phrase is "looks after". This phrase means to take care of someone. The sentence implies a caring relationship between the younger brother and grandfather. "Looks on" means to observe, "looks to" means to seek guidance from, and "looks of" is grammatically incorrect in this context. Therefore, "looks after" is the only option that accurately reflects the meaning of caring for someone.

The idiom "to keep in abeyance" means to temporarily suspend or postpone something. Option 3, "In a state of suspension," accurately reflects this meaning. Abeyance implies a temporary halt, not permanence (Option 1), emergency (Option 2), or revision (Option 4). Think of it as putting something on hold until a later time. The action isn't discarded, just delayed.

The idiom "to be in a fix" means to be in a difficult or troublesome situation. Options 1, 2, and 3 describe emotional states, while option 4 accurately reflects the predicament implied by the idiom. A "fix" in this context isn't about physical or mental suffering, but rather a challenging circumstance requiring resolution. Therefore, "in a difficult situation" is the most appropriate meaning. The phrase suggests a problem needing immediate attention and action.

The idiom "to break the ice" refers to the act of relieving tension or awkwardness in a social situation. When you "break the ice," you create a more relaxed and comfortable atmosphere. Option 4 accurately captures this meaning. The other options are incorrect; the phrase doesn't imply anger, laughter, or excitement as its primary effect. It's about easing tension and facilitating interaction. Think of it as removing a barrier (the "ice") between people.

The word "abattoir" directly refers to a place where animals are slaughtered for meat. Options 2, 3, and 4 are incorrect. Option 2 incorrectly defines it as a place for abbots (religious figures). Option 3 describes a title, not a location. Option 4 is the opposite; abattoirs are where animals are killed, not worshipped. Therefore, Option 1 accurately defines an abattoir.

The word eccentric best describes a person with unusual or peculiar habits. It implies oddness or unconventionality, fitting the description "a man with abnormal habits." Frantic means wildly excited or distressed; idiotic means severely lacking intelligence; and sulky means bad-tempered and resentful. These options don't align with the given phrase.

An epitaph is an inscription on a tomb, but it's usually a brief statement. An epigram is a short, witty saying. An elegy is a poem of sorrow, often written to mourn someone's death. Since the question refers to words inscribed on a tomb, expressing sorrow and remembrance, an elegy is the most appropriate choice. The words on a tomb are often a form of remembrance, reflecting on the deceased's life, and an elegy's mournful tone fits this context best. Epigraphs are inscriptions at the beginning of a text, not necessarily tombs. Therefore, an elegy perfectly encapsulates the essence of words inscribed on a tomb.

The correct preposition to use is "in". The ribbons are located in the hair, meaning they are within the hair itself. "Over" suggests the ribbons are on top of the hair without being intertwined. "Through" implies the ribbons are passing from one side of the hair to the other, which doesn't fit the sentence's meaning. Therefore, "in" is the most accurate and natural choice to describe the ribbons' position.

The correct word to use is aptitude. Aptitude refers to a natural talent or skill. The sentence describes a natural ability in mathematics. "Ability for" is grammatically correct, but "aptitude" is a more precise and natural-sounding word choice in this context. "Attitude" refers to a way of thinking or feeling; "altitude" refers to height. Therefore, "aptitude" best replaces "ability" to create a clearer and more accurate sentence.

The correct preposition to use with "impressed" is "by". The sentence should read, "I was impressed by it." "Impressed by" indicates the cause of the impression. Using "on," "for," or "of" doesn't grammatically fit with the verb "impressed" and alters the meaning of the sentence. Therefore, "by" is the only appropriate choice to maintain the sentence's intended meaning and grammatical correctness.

The correct preposition to use here is "to". The sentence should read, "Only high officials have access to the President." "Access to" indicates the ability to approach or interact with the President. The other options don't convey this meaning accurately. "Access for" implies the President is granting access, while "access from" is grammatically incorrect in this context. Therefore, "to" is the most appropriate and grammatically correct choice.

The sentence "No other snake is as poisonous as this one" is grammatically correct and conveys the intended meaning clearly. The use of "as...as" correctly establishes a comparison of equal degree of poisonousness. Options 1, 2, and 3 introduce grammatical errors or alter the meaning. Option 1 incorrectly uses the plural "are". Option 2 uses "more poisonous as," which is grammatically incorrect; it should be "more poisonous than." Option 3 uses "poisonous than," which is also grammatically incorrect. Therefore, "No improvement" is the correct choice.

The passage explicitly states that Nicolas-Joseph Cugnot "created a steam-powered tricycle". While others developed steam-powered vehicles, Cugnot's is specifically identified as a tricycle. Verbiest's creation was a small-scale model, Trevithick's was a road locomotive, and Niepce's invention was an internal combustion engine, not steam-powered. Therefore, Cugnot is the correct answer.

The passage explicitly states that Nicolas-Joseph Cugnot "constructed two steam tractors for the French Army". This directly answers the question. The other options are incorrect; he didn't build for the Chinese Emperor (that was Verbiest), the Jesuit mission, or the French Conservatory. The passage clearly indicates the French Army as the recipient of Cugnot's steam tractors. Therefore, the correct option is the one mentioning the French Army.

The passage explicitly states that Richard Trevithick's Puffing Devil "was unable to maintain sufficient steam pressure for long periods." This directly addresses the problem associated with the vehicle. The other options are not mentioned as problems with the Puffing Devil. Therefore, the correct answer focuses on the steam pressure issue, which was a significant limitation of the vehicle.

The passage states that "Sentiment against steam-powered road vehicles led to the Locomotive Acts of 1865". This implies that there was negative feeling or opposition towards steam-powered vehicles. Therefore, "Resentment" accurately reflects the public's feeling. The other options are incorrect. Depression, fascination, and celebration don't fit the context of opposition and subsequent legislation. The word "sentiment" here refers to a general feeling or opinion, in this case, a negative one.

The passage explicitly states that Nicéphore Niepce and his brother Claude created the world's first internal combustion engine, and they named it the Pyreolophore. The other options are incorrect because they describe different types of vehicles mentioned in the passage (steam-powered vehicles and steam tractors). The passage doesn't describe the Pyreolophore as a self-propelled mechanical vehicle, but rather as an engine itself.