To solve this problem, we will use the formula for average speed, which is total distance divided by total time. We will define the distances and speeds for each segment of the journey, calculate the time taken for each segment, and then set up an equation using the given average speed to find the unknown return speed.
Average Speed = \[\frac{\text{Total Distance}}{\text{Total Time}}\]
Given average speed = 56 km/hr.
\[ 56 = \frac{6D}{D \left( \frac{1}{52} + \frac{2}{39} + \frac{3}{x} \right)} \] Cancel \(D\) from numerator and denominator: \[ 56 = \frac{6}{\frac{1}{52} + \frac{2}{39} + \frac{3}{x}} \]Correct Option: B) 81.9
This is a circular seating arrangement puzzle. We need to deduce the positions of seven people (Prabhat, Dinesh, Yug, Monu, Sakshi, Amit, Shipra) sitting around a circular table, facing the centre, based on the given clues. We will place individuals one by one based on the definite information and then use the remaining clues to fill the gaps.
Correct Option: A) Shipra
The question asks for the initial location where the 2024 United Nations Biodiversity Convention (COP16) was planned to be held. This requires knowledge of recent international environmental conference host cities.
A) Cali, Colombia — Cali, Colombia, was indeed the initial host city chosen for the 2024 United Nations Biodiversity Convention (COP16). Colombia was confirmed as the host country, and Cali was the city initially designated. Later, the venue was changed to Cartagena, but the question asks for the initial location.
Who among the following is the political head of the municipal council in India?
Mayor
Chairman
Chief Municipal Officer
Municipal Commissioner
The question asks to identify the political head of a municipal council in India. Understanding the structure of urban local bodies in India, as established by the 74th Constitutional Amendment Act, is crucial to answer this question.
Correct Option: B) Chairman. The Chairman is the elected political head of a Municipal Council in India, responsible for presiding over its meetings and representing the council.
To find the greatest number that divides two given numbers leaving specific remainders, we first subtract the respective remainders from the numbers. The problem then reduces to finding the HCF (Highest Common Factor) of these new numbers. The HCF will be the greatest number that divides the original numbers with the given remainders.
When a number \(N\) divides 48 leaving a remainder of 9, it means that \(48 - 9\) must be perfectly divisible by \(N\).
\[ 48 - 9 = 39 \]Similarly, when \(N\) divides 46 leaving a remainder of 7, it means that \(46 - 7\) must be perfectly divisible by \(N\).
\[ 46 - 7 = 39 \]We need to find the greatest number that divides both 39 and 39. The HCF of a number with itself is the number itself.
\[ \text{HCF}(39, 39) = 39 \]Both conditions are satisfied.
Correct Option: D) 39
To find a single equivalent discount for consecutive discounts, we can assume an initial price (e.g., 100 units) and calculate the price after each discount. The total discount will then be the difference between the initial price and the final price, expressed as a percentage of the initial price.
Assume an initial price: Let the original price of the item be \(P = 100\).
Apply the first discount (26%):
Price after first discount \(P_1 = P - (0.26 \times P) = P(1 - 0.26) = 100 \times 0.74 = 74\).
Apply the second discount (29% on the new price):
Price after second discount \(P_2 = P_1 - (0.29 \times P_1) = P_1(1 - 0.29) = 74 \times 0.71 = 52.54\).
Apply the third discount (2% on the further reduced price):
Price after third discount \(P_3 = P_2 - (0.02 \times P_2) = P_2(1 - 0.02) = 52.54 \times 0.98 = 51.4892\).
Calculate the total discount:
Total discount amount \(D = P - P_3 = 100 - 51.4892 = 48.5108\).
Express as a single percentage discount:
Since the initial price was 100, the total discount percentage is \(48.5108\%\).
Round up to two decimal places:
Rounding \(48.5108\%\) up to two decimal places gives \(48.51\%\).
C) 48.51% is the single equivalent discount when rounded up to two decimal places.
The question asks about the key objective of the Jan Vishwas (Amendment of Provisions) Act, 2023, which was notified in October 2024. We need to identify the primary purpose of this legislation among the given options.
Correct Option: C) To convert minor offenses under various laws from criminal to civil penalties
The Jan Vishwas (Amendment of Provisions) Act, 2023, is a landmark legislation that seeks to decriminalize minor offenses across 42 Central Acts administered by 19 ministries. Its primary objective is to convert imprisonment penalties for minor offenses into monetary penalties, thereby reducing the burden on the judicial system, promoting ease of doing business, and fostering trust-based governance. The notification in October 2024 operationalized these rules.
This question tests general knowledge about significant international events and their locations. Candidates need to recall or be aware of major summits related to critical global issues like energy security.
Correct Option: D) London, United Kingdom is the correct answer. The International Summit on the Future of Energy Security is scheduled to take place in London in April 2025.
This problem involves decoding a set of symbolic operations and then applying them to a given mathematical expression. We need to replace the given operators with their new meanings and then solve the expression following the order of operations (BODMAS/PEMDAS).
The original equation is: \(109 \div 76 \times 4 - 5 + 18 = ?\)
Applying the new meanings, the equation becomes:
\[ 109 + 76 \div 4 \times 5 - 18 = ? \]First, perform division:
\[ 109 + (76 \div 4) \times 5 - 18 \]\[ 109 + 19 \times 5 - 18 \]Next, perform multiplication:
\[ 109 + (19 \times 5) - 18 \]\[ 109 + 95 - 18 \]Finally, perform addition and subtraction from left to right:
\[ (109 + 95) - 18 \]\[ 204 - 18 \]\[ 186 \]So, the value of the expression is \(186\).
Correct Option: B) 186
The question asks to identify the term used for tanks or ponds in Gupta records. This requires knowledge of specific terminology from ancient Indian history, particularly related to the Gupta period's administrative and geographical terms.
Correct Option: D) Tadaga was the term used for tanks or ponds in Gupta records. This term is frequently found in inscriptions and literary sources of the period to refer to artificial reservoirs built for irrigation and other purposes.