The problem is an analogy question where we need to find the relationship between the first pair of words and apply the same relationship to the second pair to find the missing term.
B) Chair — A chair is a distinct item of furniture that is commonly used in conjunction with a table, just as a shirt and trousers are distinct items of clothing commonly worn together.
This problem involves the concept of work and time, specifically how the number of workers affects the time taken to complete a task. We will calculate the total work units, the work done by the initial group, and then the time required for the expanded group to complete the remaining work.
If 10 men can complete a task in 18 days, the total work can be expressed in 'man-days'.
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]\[ \text{Total Work} = 10 \text{ men} \times 18 \text{ days} = 180 \text{ man-days} \]For the first 6 days, 10 men worked.
\[ \text{Work done in 6 days} = 10 \text{ men} \times 6 \text{ days} = 60 \text{ man-days} \]Subtract the work done from the total work to find the remaining work.
\[ \text{Remaining Work} = \text{Total Work} - \text{Work done in 6 days} \]\[ \text{Remaining Work} = 180 \text{ man-days} - 60 \text{ man-days} = 120 \text{ man-days} \]After 6 days, 5 more men join the original 10 men.
\[ \text{New Number of Men} = 10 + 5 = 15 \text{ men} \]Now, 15 men need to complete 120 man-days of work.
\[ \text{Days to complete remaining work} = \frac{\text{Remaining Work}}{\text{New Number of Men}} \]\[ \text{Days to complete remaining work} = \frac{120 \text{ man-days}}{15 \text{ men}} = 8 \text{ days} \]D) The remaining work will be completed in 8 days.
The given series is 2, 10, 30, 68, ?, 222. We need to identify the pattern in the series to find the missing number. This type of series often involves operations like addition, subtraction, multiplication, division, squares, cubes, or combinations of these.
Let's examine the differences between consecutive terms:
The differences are 8, 20, 38. This doesn't immediately reveal a simple arithmetic or geometric progression.
Let's look at the differences of these differences (second-order differences):
The second-order differences are 12, 18. This suggests a pattern where the difference increases by 6 each time.
Following this pattern, the next second-order difference should be \(18 + 6 = 24\).
Now, we can find the next first-order difference. The last known first-order difference was 38. Adding 24 to it gives the next first-order difference:
\[ 38 + 24 = 62 \]Finally, to find the missing term, we add this new first-order difference (62) to the last known term in the original series (68):
\[ 68 + 62 = 130 \]Let's verify the pattern with the last term, 222. The next second-order difference after 24 would be \(24 + 6 = 30\). The next first-order difference after 62 would be \(62 + 30 = 92\). Adding this to 130 should give 222:
\[ 130 + 92 = 222 \]This confirms our pattern and the calculated missing number.
Alternatively, consider the pattern as \(n^3 + n\):
This pattern perfectly matches all the given terms and confirms that the missing number is 130.
Correct Option: C) 130
The question asks to identify the country with the highest number of operational nuclear reactors as of 2021. This requires knowledge of global nuclear energy statistics.
According to data from the World Nuclear Association and the International Atomic Energy Agency (IAEA) for 2021:
Therefore, the United States had the most operational nuclear reactors in 2021.
D) United States: As of 2021, the United States had the largest number of operational nuclear reactors globally, with approximately 93-94 reactors.
To find the odd one out among the given letter-clusters, we need to identify the pattern or relationship between the letters in each cluster. This usually involves checking the positional values of the letters in the English alphabet.
Correct Option: D) ADG
The question asks to identify the traditional theatre form of Kerala that involves the performance of eight plays over eight days. We need to recall the characteristics of each given option to determine the correct answer.
Correct Option: C) Krishnanattam is a temple art form from Kerala, consisting of a cycle of eight plays performed over eight consecutive days, narrating the story of Lord Krishna.
The question asks to identify the scientist who proposed the atomic model where electrons are embedded in a positive sphere. This refers to a specific early model of the atom.
Correct Option: A) J.J. Thomson proposed the "plum pudding" model of the atom, where electrons are embedded in a uniformly distributed sphere of positive charge.
The question asks to identify a region located on the western coast of India from the given options. This requires knowledge of the geographical divisions of India's coastal plains.
D) The Malabar Region: The Malabar Coast is a long and narrow coastal plain on the southwestern shoreline of the mainland Indian subcontinent, stretching from the south of Goa to Kanyakumari, the southernmost tip of India. It is part of the Western Coastal Plain.
To find the area of a triangle, we use the standard formula involving its base and corresponding altitude (height). The formula for the area of a triangle is half the product of its base and height.
The base of the triangle (\(b\)) is given as 12 m.
The altitude (height, \(h\)) on this base is given as 6 m.
The area of a triangle (\(A\)) is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]\[ A = \frac{1}{2} \times b \times h \]Substitute \(b = 12 \text{ m}\) and \(h = 6 \text{ m}\) into the formula:
\[ A = \frac{1}{2} \times 12 \text{ m} \times 6 \text{ m} \]Perform the multiplication:
\[ A = \frac{1}{2} \times 72 \text{ m}^2 \]\[ A = 36 \text{ m}^2 \]Correct Option: A) The area of the triangle is \(36 \text{ m}^2\).
To find the Least Common Multiple (LCM) of a set of numbers, we can use the prime factorization method. This involves finding the prime factors of each number and then taking the highest power of each prime factor present in any of the numbers.
The unique prime factors are 2, 3, and 11.
Correct Option: C) 528 is the Least Common Multiple of 22, 24, 48, and 16.