The question asks for the symbol representing the constant of gravitation. This is a fundamental constant in physics, specifically in Newton's Law of Universal Gravitation. We need to recall the standard notation used for this constant.
Correct Option: A) G is the universally accepted symbol for the Universal Gravitational Constant, as derived from Newton's Law of Universal Gravitation.
The problem asks us to find the area of a rectangle given the area of a semicircle inscribed within it. The key information is that the diameter of the semicircle coincides with the length of the rectangle. We will use the formula for the area of a semicircle to find its radius, then relate this radius to the dimensions of the rectangle, and finally calculate the rectangle's area.
The diameter of the semicircle is equal to the length of the rectangle. The radius of the semicircle will be half of the length of the rectangle. The height of the semicircle (from its diameter to its arc) is equal to its radius. This height will also be the width of the rectangle.
The area of a semicircle is given by the formula:
\[ \text{Area of semicircle} = \frac{1}{2} \pi r^2 \]We are given that the area of the semicircle is \(50\pi\) square units. So,
\[ 50\pi = \frac{1}{2} \pi r^2 \]Divide both sides by \(\pi\):
\[ 50 = \frac{1}{2} r^2 \]Multiply both sides by 2:
\[ 100 = r^2 \]Take the square root of both sides:
\[ r = \sqrt{100} \] \[ r = 10 \text{ units} \]As established in step 1:
The area of a rectangle is given by the formula:
\[ \text{Area of rectangle} = \text{Length} \times \text{Width} \]Substitute the values we found:
\[ \text{Area of rectangle} = 20 \times 10 \] \[ \text{Area of rectangle} = 200 \text{ sq units} \]Correct Option: A) 200 sq units
The question asks to identify the founder of a micro-enterprise named after her and the Ekta Sakhi Producer Company. This requires specific knowledge about prominent women entrepreneurs and their ventures, particularly in the context of micro-enterprises in India.
Correct Option: C) Kamal Kumbhar is a renowned social entrepreneur from Maharashtra, India. She started her journey with a small loan and built a successful micro-enterprise focused on animal husbandry, which she named after herself. She is also instrumental in establishing the Ekta Sakhi Producer Company, which aims to empower women by collectivizing their efforts in various economic activities.
The question asks to identify the statement that is NOT true about White Blood Cells (WBCs), also known as leukocytes. We need to evaluate each option based on the known characteristics of WBCs.
A) Size – 18–25 μm. The typical size range for WBCs is generally smaller than 18-25 μm, with most types falling between 7-20 μm. While monocytes can be up to 20 μm, stating 18-25 μm as a general size is inaccurate and on the higher side for the majority of WBCs. Therefore, this statement is NOT true.
This problem involves work and time. We will calculate the total work required and then determine how much work is completed in different phases with varying numbers of workers. Finally, we will find the remaining work and the time needed to complete it with the final number of workers.
Calculate Total Work:
The total work is the product of the number of persons and the number of days initially planned.
\[ \text{Total Work} = \text{Persons} \times \text{Days} = 15 \times 20 = 300 \text{ units} \]Work done in the first 10 days:
15 persons worked for 10 days.
\[ \text{Work done (1st phase)} = 15 \times 10 = 150 \text{ units} \]Remaining work after 10 days:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work done (1st phase)} = 300 - 150 = 150 \text{ units} \]Number of persons after 10 days:
5 persons left, so the number of persons remaining is:
\[ \text{Persons remaining} = 15 - 5 = 10 \text{ persons} \]Work done in the next 5 days:
10 persons worked for 5 days.
\[ \text{Work done (2nd phase)} = 10 \times 5 = 50 \text{ units} \]Remaining work after 15 days (10 + 5 days):
\[ \text{Remaining Work} = 150 - 50 = 100 \text{ units} \]Number of persons after 15 days:
Another 5 persons left, so the number of persons remaining is:
\[ \text{Persons remaining} = 10 - 5 = 5 \text{ persons} \]Days required to complete the remaining work:
The remaining 100 units of work will be done by 5 persons.
\[ \text{Days required} = \frac{\text{Remaining Work}}{\text{Persons}} = \frac{100}{5} = 20 \text{ days} \]Total days after the first 5 persons left:
The question asks for the number of days after the first 5 persons left. This means we need to sum the days from the second phase onwards.
Days in 2nd phase (when 10 persons worked) = 5 days
Days in 3rd phase (when 5 persons worked) = 20 days
\[ \text{Total days after first 5 left} = 5 + 20 = 25 \text{ days} \]Correct Option: C) 25
We need to find the cost price (CP) of the textbook. We are given two scenarios involving selling prices (SP) and their corresponding profit/loss percentages. We can set up equations based on these scenarios and solve for the cost price.
Let the Cost Price (CP) of the textbook be \( \text{Rs } x \).
First scenario: Ankitha sold the textbook for a loss of 15%.
The Selling Price (\( \text{SP}_1 \)) in this case can be calculated as:
\[ \text{SP}_1 = \text{CP} - (15\% \text{ of CP}) \]\[ \text{SP}_1 = x - \frac{15}{100}x = \frac{85}{100}x \]Second scenario: If she would have sold the textbook for an increased price of Rs 150, there would have been a gain of 10%.
This means the new selling price (\( \text{SP}_2 \)) is \( \text{SP}_1 + 150 \). Also, \( \text{SP}_2 \) results in a 10% gain on the CP.
So, \( \text{SP}_2 \) can also be calculated as:
\[ \text{SP}_2 = \text{CP} + (10\% \text{ of CP}) \]\[ \text{SP}_2 = x + \frac{10}{100}x = \frac{110}{100}x \]Now, we can set up the equation relating \( \text{SP}_1 \) and \( \text{SP}_2 \):
\[ \text{SP}_2 = \text{SP}_1 + 150 \]\[ \frac{110}{100}x = \frac{85}{100}x + 150 \]Solve the equation for \( x \):
\[ \frac{110}{100}x - \frac{85}{100}x = 150 \]\[ \frac{(110 - 85)}{100}x = 150 \]\[ \frac{25}{100}x = 150 \]\[ \frac{1}{4}x = 150 \]\[ x = 150 \times 4 \]\[ x = 600 \]Therefore, the cost price of the textbook was Rs 600.
Correct Option: D) Rs 600
The question asks about the relationship between Panchasheel (five precepts) and a fundamental Buddhist path. To answer this, one needs to recall the core teachings of Buddhism, specifically the Noble Eightfold Path and its connection to ethical conduct.
Correct Option: A) eight-fold path
The question asks to identify the person who does not belong to the group. This implies that three of the given options share a common characteristic, while one does not. We need to identify this common characteristic and then find the outlier.
Correct Option: D) Pullela Gopichand is a famous Indian badminton player and coach, while the other three options are famous Indian cricketers.
The question asks to identify the representation of alkenes among the given options. Alkenes are hydrocarbons that contain at least one carbon-carbon double bond. Understanding the basic structural features of different types of hydrocarbons (alkanes, alkenes, alkynes) is key to answering this question.
Correct Option: A) -C = C- represents an alkene because it shows a carbon-carbon double bond, which is the defining functional group for this class of hydrocarbons.
This is a statement and conclusion type of question. We need to analyze the given statement and determine which of the conclusions logically follow from it, without introducing any outside information or assumptions.
Correct Option: D) Both the conclusions follow