This question is based on coding and decoding using alphabetical positions. The English alphabet is divided into two halves: A to M and N to Z. Letters belonging to the first half retain their normal alphabetical positions, while letters belonging to the second half are assigned their reverse alphabetical positions. We need to verify this rule using HONEY and then apply it to PATCH.
The English alphabet contains 26 letters, divided into two halves:
The coding rule is:
The reverse alphabetical position is calculated as:
\(\text{Reverse position}=27-\text{Normal position}\)
The word HONEY contains five letters: H, O, N, E, and Y.
Apply the coding rule to each letter:
Therefore:
HONEY β 8-12-13-5-2
This matches the given code and confirms the rule.
The word PATCH contains five letters: P, A, T, C, and H.
Identify the normal alphabetical position of each letter:
Therefore, the coded values are:
11 - 1 - 7 - 3 - 8
For HONEY:
H = 8, O = 12, N = 13, E = 5, Y = 2.
HONEY β 8-12-13-5-2
For PATCH:
P = 11, A = 1, T = 7, C = 3, H = 8.
PATCH β 11-1-7-3-8
Both words follow the same coding rule. Therefore, option D is correct.
Correct Option: D) 11-1-7-3-8
The letters A to M retain their normal alphabetical positions, while the letters N to Z are assigned their reverse alphabetical positions. In PATCH, P = 11, A = 1, T = 7, C = 3, and H = 8. Therefore, PATCH is coded as 11-1-7-3-8, making option D correct.
This problem involves calculating the time a train stops per hour given its speed with and without stoppages. The key idea is to determine the distance the train would have covered in one hour without stoppages and compare it to the distance it actually covers when stoppages are included. The difference in distance can then be used to find the time lost due to stoppages.
Identify the given speeds:
Calculate the distance covered in 1 hour with stoppages:
If the train travels at an average speed of \(45 \text{ km/h}\) including stoppages, then in 1 hour, it covers a distance of:
Determine the time it would take to cover this distance without stoppages:
If the train were traveling at its actual speed of \(60 \text{ km/h}\) without any stoppages, the time taken to cover \(45 \text{ km}\) would be:
Calculate the time lost due to stoppages:
In 1 hour of travel (including stoppages), the train effectively travels for only \(\frac{3}{4}\) of an hour. The difference is the time it stopped.
Convert the time stopped to minutes:
Since \(1 \text{ hour} = 60 \text{ minutes}\), we convert \(\frac{1}{4}\) hour to minutes:
Thus, the train stops for 15 minutes per hour.
D) 15 min is the correct answer. The calculation shows that the train loses 15 minutes of travel time per hour due to stoppages.
The question asks to identify the odd one out from a list of four cities. This type of question usually requires finding a common characteristic among three items and identifying the one that does not share that characteristic. We need to analyze the nature and significance of each city.
Correct Option: D) Kanpur is the odd one out because it is not a state capital, whereas Bhopal, Chandigarh, and Gandhinagar are all capital cities.
The question asks for the term describing the direct exchange of goods or services without the use of any form of currency or tokens. This is a fundamental concept in economics, particularly related to early forms of trade.
B) Barter β Barter is the system of exchange by which goods or services are directly exchanged for other goods or services without the use of money, credit, or any other medium of exchange. This directly matches the definition provided in the question.
The problem involves solving a proportion. A proportion states that two ratios are equal. We are given the proportion \(0.75 : x :: 2.5 : 8\), which can be written as a fraction equality. We will use the property that the product of the means equals the product of the extremes to find the value of \(x\).
Understand the proportion notation: The notation \(a : b :: c : d\) means that the ratio \(a\) to \(b\) is equal to the ratio \(c\) to \(d\). This can be written as:
\[ \frac{a}{b} = \frac{c}{d} \]Apply to the given problem: Given the proportion \(0.75 : x :: 2.5 : 8\), we can write it as:
\[ \frac{0.75}{x} = \frac{2.5}{8} \]Cross-multiply: To solve for \(x\), we cross-multiply the terms:
\[ 0.75 \times 8 = x \times 2.5 \]Calculate the product on the left side:
\[ 0.75 \times 8 = 6 \]Substitute the value back into the equation:
\[ 6 = 2.5x \]Solve for \(x\): Divide both sides by \(2.5\):
\[ x = \frac{6}{2.5} \]Simplify the fraction: To remove the decimal from the denominator, multiply both the numerator and the denominator by \(10\):
\[ x = \frac{6 \times 10}{2.5 \times 10} = \frac{60}{25} \]Perform the division:
\[ x = 2.4 \]D) 2.4 β As calculated, the value of \(x\) is \(2.4\).
To find the total cost of 15.2 kg of rice, we need to multiply the quantity of rice by the cost per kilogram.
The total cost will be the product of the quantity of rice and the cost per kg.
\[ \text{Total Cost} = \text{Quantity of rice} \times \text{Cost per kg} \]Substitute the given values into the formula:
\[ \text{Total Cost} = 15.2 \text{ kg} \times \text{βΉ}45/\text{kg} \]\[ \text{Total Cost} = 15.2 \times 45 \]Multiply 15.2 by 45:
\[ 15.2 \times 45 = 684.0 \]The total cost of 15.2 kg of rice is βΉ684.
Correct Option: A) 684
The question asks to identify the first large-scale iron and steel plant in India. This requires knowledge of the history of industrial development in India, specifically the establishment dates of major steel plants.
Comparing these dates, TISCO is clearly the earliest large-scale iron and steel plant.
Correct Option: D) TISCO (Tata Iron and Steel Company) was established in 1907 and began production in 1911, making it the first large-scale iron and steel plant in India.
Which of the following fractions is greater than \( \frac{8}{5} \) and less than \( \frac{7}{4} \)?
\( \frac{2}{7} \)
\( \frac{8}{3} \)
\( \frac{19}{11} \)
\( \frac{1}{4} \)
To find the fraction that lies between two given fractions, we can convert all fractions (the given ones and the options) into decimal form. This makes comparison straightforward. Alternatively, we can find a common denominator for all fractions, but decimal conversion is often quicker for multiple comparisons.
First, convert the two boundary fractions to decimals:
\[ \frac{8}{5} = 1.6 \]\[ \frac{7}{4} = 1.75 \]We are looking for a fraction \(x\) such that \(1.6 < x < 1.75\).
Only option C satisfies the given condition.
C) \( \frac{19}{11} \) is approximately \(1.7272\), which lies between \(1.6\) and \(1.75\).
The question asks to identify the book written by Megasthenes from the given options. This requires knowledge of ancient Indian history and literature, specifically the authors of prominent historical and literary works.
Correct Option: C) Indica is the famous work written by Megasthenes. It provides valuable insights into the administration, society, and geography of Mauryan India, based on his observations during his stay as an ambassador to Chandragupta Maurya's court.