This problem involves analyzing syllogistic statements and drawing logical conclusions. We can use Venn diagrams or the rules of syllogism to determine which conclusions logically follow from the given statements.
Short Run Average Cost is equal to ____________.
Average Variable Cost + Average Fixed Cost
Average Variable Cost × Average Fixed Cost
\( \frac{\text{Average Variable Cost}}{\text{Average Fixed Cost}} \)
Average Variable Cost – Average Fixed Cost
To determine the Short Run Average Cost, we need to understand its components. Total Cost (TC) in the short run is composed of Total Fixed Cost (TFC) and Total Variable Cost (TVC). Average Cost (AC) is derived by dividing Total Cost by the quantity of output (Q). Similarly, Average Fixed Cost (AFC) and Average Variable Cost (AVC) are derived from TFC and TVC, respectively.
Correct Option: A) Average Variable Cost + Average Fixed Cost
As on 4th February 2022, which one of the following schemes caters to primary needs of women in difficult circumstances – women and girls rendered homeless due to family discord, crime, violence, mental stress, social ostracism or are being forced into prostitution and are in moral danger?
Ujjawala Scheme
Swadhar Greh Scheme
One Stop Centres (OSCs)
National Social Assistance Programme (NSAP)
The question asks to identify the scheme that caters to the primary needs of women in difficult circumstances, specifically those rendered homeless due to various adversities like family discord, violence, mental stress, social ostracism, or forced prostitution. We need to evaluate each given option against this specific objective.
B) Swadhar Greh Scheme is the correct answer. The Swadhar Greh Scheme specifically targets women in difficult circumstances, including those rendered homeless due to family discord, crime, violence, mental stress, social ostracism, or forced into prostitution, by providing them with shelter, food, clothing, medical care, and rehabilitation services.
Refer to the following five 3-letter words and answer the question.
MAY JUG PEN FOR FAN
If in each of the words, each letter is changed to the immediate previous letter in the English alphabetical order, how many words thus formed will have at least one vowel? (Note – A is changed to Z)
The problem asks us to modify a given set of five 3-letter words by changing each letter to its immediate previous letter in the English alphabetical order (with 'A' changing to 'Z'). After this transformation, we need to count how many of the newly formed words contain at least one vowel (A, E, I, O, U).
B) 4
The question asks about the structure enclosed by Bowman's capsule. This requires knowledge of the basic anatomy of the nephron, which is the functional unit of the kidney.
A) the glomerulus — Bowman's capsule is a double-walled cup-like structure that surrounds the glomerulus, forming the renal corpuscle. This arrangement is crucial for the ultrafiltration of blood in the kidneys.
The question asks to identify the FALSE statement regarding Compressed Natural Gas (CNG) and Liquefied Petroleum Gas (LPG). We need to evaluate each option based on the properties and uses of CNG and LPG.
Based on the analysis, Option A appears to be the false statement because while natural gas (PNG) is piped to homes, CNG itself is not typically piped to individual homes in the same manner, and LPG is usually delivered in cylinders.
A) CNG and LPG can be piped to homes. This statement is FALSE. While natural gas (in the form of PNG - Piped Natural Gas) is piped to homes for cooking and heating, CNG (Compressed Natural Gas) is stored under high pressure and is primarily used as a vehicle fuel. LPG (Liquefied Petroleum Gas) is typically supplied to homes in cylinders, not through a pipeline network like PNG. Therefore, stating that both CNG and LPG can be piped to homes is incorrect.
In ΔABC, \(\overline{DE}\) is parallel to \(\overline{BC}\), where D is a point on \(\overline{AB}\) and E is a point on \(\overline{AC}\), and m(\(\overline{AD}\)) : m(\(\overline{DB}\)) = 2 : 5. If m(\(\overline{AC}\)) is 8.4 cm, find m(\(\overline{AE}\)).
The problem involves a triangle with a line segment parallel to one of its sides. This situation can be solved using the Basic Proportionality Theorem (also known as Thales Theorem or Thales's Theorem) or its converse. The theorem states that if a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
Given that in \(\Delta ABC\), \(\overline{DE}\) is parallel to \(\overline{BC}\), where D is on \(\overline{AB}\) and E is on \(\overline{AC}\).
According to the Basic Proportionality Theorem (BPT), if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio. Therefore, we have:
\[ \frac{m(\overline{AD})}{m(\overline{DB})} = \frac{m(\overline{AE})}{m(\overline{EC})} \]We are given the ratio \(m(\overline{AD}) : m(\overline{DB}) = 2 : 5\). So, we can write:
\[ \frac{m(\overline{AD})}{m(\overline{DB})} = \frac{2}{5} \]From steps 2 and 3, we get:
\[ \frac{m(\overline{AE})}{m(\overline{EC})} = \frac{2}{5} \]This implies that \(m(\overline{AE}) = 2k\) and \(m(\overline{EC}) = 5k\) for some constant \(k\).
We know that \(m(\overline{AC}) = m(\overline{AE}) + m(\overline{EC})\).
Substitute the values: \(8.4 = 2k + 5k\).
Simplify the equation: \(8.4 = 7k\).
Solve for \(k\):
\[ k = \frac{8.4}{7} = 1.2 \]Now, find \(m(\overline{AE})\):
\[ m(\overline{AE}) = 2k = 2 \times 1.2 = 2.4 \text{ cm} \]B) 2.4 cm is the correct answer, as calculated above.
If the surface area of a sphere is 1144 cm², then find its diameter (in cm). (Use π = \( \frac{22}{7} \))
To find the diameter of a sphere given its surface area, we first need to use the formula for the surface area of a sphere to calculate its radius. Once the radius is known, the diameter can be found by doubling the radius.
The surface area (\(A\)) of a sphere with radius (\(r\)) is given by:
\[ A = 4 \pi r^2 \]We are given \(A = 1144 \text{ cm}^2\) and \(\pi = \frac{22}{7}\). Substituting these values:
\[ 1144 = 4 \times \frac{22}{7} \times r^2 \]First, simplify the constants:
\[ 1144 = \frac{88}{7} r^2 \]Now, isolate \(r^2\):
\[ r^2 = \frac{1144 \times 7}{88} \]Perform the division:
\[ r^2 = \frac{1144}{88} \times 7 \]We can simplify \(\frac{1144}{88}\). \(1144 \div 88 = 13\).
\[ r^2 = 13 \times 7 \] \[ r^2 = 91 \]Now, find \(r\):
\[ r = \sqrt{91} \text{ cm} \]The diameter (\(D\)) is twice the radius:
\[ D = 2r \] \[ D = 2 \times \sqrt{91} \text{ cm} \] \[ D = 2\sqrt{91} \text{ cm} \]Correct Option: C) \(2\sqrt{91}\)
The question asks about the significance of the Easter festival for Christians. To answer this, one needs to recall the core beliefs and events associated with major Christian festivals.
Correct Option: C) It marks the resurrection of Jesus Christ from the dead.
Easter is the celebration of Jesus Christ's resurrection from the dead, which occurred on the third day after his crucifixion. This event is fundamental to Christian belief, signifying victory over sin and death and offering hope of eternal life to believers.
The problem requires us to modify a given set of three-digit numbers by adding 2 to their second digit. Then, for each modified number, we need to check if its new second digit is exactly divisible by its third digit. Finally, we count how many numbers satisfy this condition.
Correct Option: B) Three