The question asks about the region associated with the Takht-i-Bahi inscription. This requires knowledge of ancient Indian history and geography, specifically the locations of significant archaeological sites and inscriptions.
A) Gandhara — The Takht-i-Bahi monastic complex, where the inscription was found, is located in the historical Gandhara region, which was a prominent center of Buddhist culture and art in ancient times.
The question asks to identify the Windows OS tool used for changing the system date and time. We need to evaluate the function of each given option to determine the correct one.
Correct Option: C) Control Panel is the primary Windows OS tool that allows users to change various system settings, including the date and time.
The question asks about a specific provision introduced by the Sixty-fifth Amendment Act of 1990 concerning the welfare of Scheduled Castes (SCs) and Scheduled Tribes (STs). To answer this, one needs to recall the key changes brought about by this constitutional amendment.
A) A multi-member National Commission. The 65th Constitutional Amendment Act of 1990 amended Article 338 of the Constitution to replace the single Special Officer for Scheduled Castes and Scheduled Tribes with a multi-member National Commission for Scheduled Castes and Scheduled Tribes. This commission was tasked with investigating all matters relating to the safeguards provided for SCs and STs under the Constitution and reporting to the President.
The question asks for a key feature of the Broadcasting Services (Regulation) Bill, 2024. We need to identify the correct provision among the given options based on the known details of this bill.
D) Mandatory registration of digital news broadcasters and content creators
This is a key feature of the Broadcasting Services (Regulation) Bill, 2024. The bill seeks to expand the regulatory ambit to include digital news and current affairs content providers, as well as Over-The-Top (OTT) content platforms, requiring them to register with the government. This aims to create a unified regulatory framework and ensure content accountability.
The problem asks us to identify the letter-cluster that does not follow the same pattern as the others, based on the English alphabetical order. We need to find a common rule or relationship between the letters in three of the clusters and then identify the one that deviates from this rule. The hint states that the odd one out is not based on the number of consonants/vowels or their position.
Observation:
A) PXR
The pattern observed in options B, C, and D is that the second letter is 8 positions ahead of the first letter, and the third letter is 5 positions behind the second letter. Let the letters be \(L_1, L_2, L_3\). The rule is \(L_2 = L_1 + 8\) and \(L_3 = L_2 - 5\).
For PXR:
Therefore, PXR does not follow the pattern of the third letter being 5 positions behind the second letter.
The problem involves calculating the profit share of individuals based on their investment ratio and then finding the difference between the shares of two individuals. We will first find the total sum of the ratios, then determine the value of one ratio unit, and finally calculate the individual shares and their difference.
The difference between the share of Y and Z is ₹620.
B) ₹620 is the correct answer, calculated by finding the difference in ratio units and multiplying it by the value of one ratio unit.
The question asks to identify the Indian city most influenced by retreating monsoon rainfall. This requires understanding the geography of India's monsoon patterns, specifically the Northeast Monsoon (also known as the retreating monsoon).
B) Chennai is located on the Coromandel Coast of Tamil Nadu, which receives substantial rainfall from the Northeast Monsoon (retreating monsoon) as the winds pick up moisture from the Bay of Bengal before hitting the coast.
The problem asks us to identify a set of numbers that follows the same relationship as the given example sets. We need to find a mathematical operation or pattern that connects the three numbers in each set. Let the three numbers in a set be \(A\), \(B\), and \(C\).
C) (20, 34, 14)
To find the missing number in the series, we need to identify the pattern of differences between consecutive terms. This often involves looking at the first-order differences, and if necessary, the second-order differences.
Thus, the missing number in the series is 115.
Correct Option: B) 115
If x + \( \frac{1}{x} \) = 15, then the value of x³ + \( \frac{1}{x^3} \) is:
The problem asks us to find the value of \(x^3 + \frac{1}{x^3}\) given the equation \(x + \frac{1}{x} = 15\). We can solve this by cubing both sides of the given equation and using the algebraic identity for the cube of a sum: \((a+b)^3 = a^3 + b^3 + 3ab(a+b)\).
We are given the equation:
\[ x + \frac{1}{x} = 15 \]Cube both sides of the equation:
\[ \left(x + \frac{1}{x}\right)^3 = (15)^3 \]Apply the algebraic identity \((a+b)^3 = a^3 + b^3 + 3ab(a+b)\). Here, \(a=x\) and \(b=\frac{1}{x}\):
\[ x^3 + \left(\frac{1}{x}\right)^3 + 3 \cdot x \cdot \frac{1}{x} \left(x + \frac{1}{x}\right) = (15)^3 \]Simplify the terms:
Substitute these simplified values back into the equation:
\[ x^3 + \frac{1}{x^3} + 3(15) = 3375 \]Calculate \(3 \times 15\):
\[ x^3 + \frac{1}{x^3} + 45 = 3375 \]Isolate \(x^3 + \frac{1}{x^3}\) by subtracting 45 from both sides:
\[ x^3 + \frac{1}{x^3} = 3375 - 45 \]Perform the subtraction:
\[ x^3 + \frac{1}{x^3} = 3330 \]Correct Option: B) 3330