This problem can be solved by using the empirical relationship between mean, median, and mode, which is commonly used for moderately skewed distributions. The formula states that Mode \(= 3 \times\) Median \(- 2 \times\) Mean. We are given a relationship between the median and mode, and we need to find the relationship between the median and mean.
Recall the Empirical Formula:
The empirical formula relating mean, median, and mode is:
Use the given information:
We are given that the median of the data is 45.98 less than its mode. This can be written as:
Rearrange the given information to express Mode in terms of Median:
From the above equation, we can write:
Substitute this into the empirical formula:
Substitute the expression for Mode into the empirical formula:
Rearrange the equation to find the relationship between Median and Mean:
We want to find by how much the median exceeds its mean, i.e., \(\text{Median} - \text{Mean}\). Let's rearrange the equation to isolate terms involving Median and Mean:
Solve for \(\text{Median} - \text{Mean}\):
\[ \text{Median} - \text{Mean} = \frac{45.98}{2} \]\[ \text{Median} - \text{Mean} = 22.99 \]Thus, the median of the data exceeds its mean by 22.99.
B) 22.99 is the correct answer, as calculated from the empirical formula and the given relationship.
The question asks to identify the state with the highest Scheduled Tribes (ST) sex ratio in 2011, according to the Census of India data. This requires knowledge of specific demographic data from the 2011 Census regarding ST populations.
B) Goa. As per the 2011 Census of India, Goa recorded the highest Scheduled Tribes (ST) sex ratio among the options provided, with 1046 females per 1000 males. This indicates a significantly higher number of females compared to males within the ST population of Goa.
An electric pump can fill a tank in 3 hours. Due to a leakage in the tank, it takes 5\( \frac{1}{4} \) hours to fill the tank. How much time will this leak take to empty the full tank if water does not get in or out of the tank through any other point during this period?
This problem can be solved by calculating the rates of filling and leaking. We'll determine the rate at which the pump fills the tank and the combined rate of the pump filling and the leak emptying. By subtracting these rates, we can find the rate at which the leak empties the tank alone, and then calculate the time it would take for the leak to empty a full tank.
Calculate the filling rate of the pump:
The pump fills the tank in 3 hours. So, in 1 hour, the pump fills \(\frac{1}{3}\) of the tank.
Calculate the combined rate (pump filling - leak emptying):
Due to the leak, the tank takes \(5\frac{1}{4}\) hours to fill. Convert this mixed fraction to an improper fraction:
So, in 1 hour, the pump and leak together fill \[\frac{1}{\frac{21}{4}}\] of the tank.
\[ \text{Combined rate} = \frac{4}{21} \text{ tank/hour} \]Calculate the leak's emptying rate:
The combined rate is the pump's filling rate minus the leak's emptying rate. Let \(R_L\) be the leak's emptying rate.
Now, solve for \(R_L\):
\[ R_L = \frac{1}{3} - \frac{4}{21} \]To subtract these fractions, find a common denominator, which is 21.
\[ R_L = \frac{1 \times 7}{3 \times 7} - \frac{4}{21} \]\[ R_L = \frac{7}{21} - \frac{4}{21} \]\[ R_L = \frac{7 - 4}{21} \]\[ R_L = \frac{3}{21} \]Simplify the fraction:
\[ R_L = \frac{1}{7} \text{ tank/hour} \]Calculate the time taken by the leak to empty the full tank:
If the leak empties \(\frac{1}{7}\) of the tank in 1 hour, then it will empty the full tank (1 unit) in the reciprocal of this rate.
Correct Option: B) 7 hours
The question asks to identify the island that is NOT part of the Andaman group. This requires knowledge of the geographical locations of various islands in India, specifically those in the Andaman and Nicobar Islands and Lakshadweep.
Correct Option: D) Minicoy is the southernmost island of the Lakshadweep archipelago, located in the Arabian Sea, whereas the Andaman group is in the Bay of Bengal.
The question asks us to identify the country where the United Nations Biodiversity Conference (COP16) concluded in February 2025. We need to distinguish between the country where COP16 originally began and the country where its resumed session concluded.
Understand COP16:
COP16 refers to the 16th meeting of the Conference of the Parties to the United Nations Convention on Biological Diversity (CBD).
The conference focuses on biodiversity conservation, sustainable use of biological resources and international cooperation to protect ecosystems and species.
Identify where COP16 originally began:
COP16 was originally held in Cali, Colombia, from 21 October to 1 November 2024.
However, the conference was suspended because several important negotiations, particularly those concerning biodiversity financing, remained unresolved.
Identify where the conference resumed:
The negotiations resumed in Rome, Italy, from 25 to 27 February 2025.
The resumed session successfully concluded on 27 February 2025, with countries reaching agreements on outstanding issues, including biodiversity financing.
Understand the distinction between Colombia and Italy:
Since the question specifically asks where COP16 concluded in February 2025, the correct country is Italy, not Colombia.
Determine the correct answer:
The resumed COP16 negotiations concluded in Rome, Italy, on 27 February 2025.
Therefore, Italy is the correct answer.
Correct Option: C) Italy — The United Nations Biodiversity Conference (COP16) began in Cali, Colombia, in October–November 2024 but was suspended before important negotiations could be completed. The talks resumed in Rome, Italy, in February 2025, where the conference concluded with agreements on biodiversity financing and other outstanding issues. Hence, Option C is the correct answer.
A) Germany: This is incorrect because Germany did not host the resumed COP16 negotiations that concluded in February 2025.
B) France: This is incorrect because France was not the country where the resumed COP16 session concluded.
D) Colombia: This is incorrect because Colombia hosted the original COP16 conference in Cali in October–November 2024. Although COP16 began there, it was suspended before the remaining negotiations were completed. The conference resumed and concluded in Rome, Italy, in February 2025.
This question tests knowledge of common shortcut keys in Microsoft PowerPoint 365, specifically for inserting a hyperlink. Understanding these shortcuts can significantly improve efficiency when working with presentation software.
In MS PowerPoint (and other Office applications like Word and Excel), the shortcut key combination to insert a hyperlink is Ctrl + K.
Correct Option: D) Ctrl + K
To find the shortest distance and direction to return to Point A, we need to determine Anuj's final position relative to Point A. We can do this by tracking his movements along the East-West and North-South axes separately.
D) 3 km to the south
This is a blood relations question. We need to establish the relationships between the given individuals step-by-step and then determine F's relation to J.
Correct Option: B) Father's father
The question asks for the command set that allows duplicating selected text without removing it from its original position. This is a fundamental operation in word processing, specifically related to copying and pasting content.
C) Copy → Paste: This sequence correctly achieves the goal. "Copy" places a duplicate of the selected text into the clipboard, leaving the original text in place. "Paste" then inserts the content from the clipboard at the cursor's current location, thus creating a duplicate without removing the original.
To find the dimensional formula of pressure, we need to recall its definition and the dimensional formulas of the fundamental quantities involved (mass, length, and time). Pressure is defined as force per unit area. We will first determine the dimensional formula for force and area, and then combine them to find the dimensional formula for pressure.
Pressure is defined as Force per unit Area.
\[ P = \frac{F}{A} \]According to Newton's second law, Force is Mass times Acceleration.
\[ F = m \times a \]The dimensional formula for Mass (m) is \([M]\).
Acceleration (a) is the rate of change of velocity, or Length per Time squared.
\[ a = \frac{\text{Length}}{(\text{Time})^2} = \frac{L}{T^2} = [L T^{-2}] \]So, the dimensional formula for Force (F) is:
\[ [F] = [M] \times [L T^{-2}] = [M L T^{-2}] \]Area is typically calculated as Length times Length.
\[ A = \text{Length} \times \text{Length} = L \times L = L^2 \]So, the dimensional formula for Area (A) is \([L^2]\).
Now, substitute the dimensional formulas of Force and Area into the pressure formula:
\[ [P] = \frac{[F]}{[A]} = \frac{[M L T^{-2}]}{[L^2]} \]Simplify the expression:
\[ [P] = [M L^{1-2} T^{-2}] = [M L^{-1} T^{-2}] \]Thus, the dimensional formula of pressure is \([M L^{-1} T^{-2}]\).
D) \([M L^{-1} T^{-2}]\) is the correct dimensional formula for pressure, derived from its definition as force per unit area.