This problem involves work and time. We need to calculate the individual work rates of A and B, then determine how much work was done by A and B together and by B alone to find out when A left the task.
Calculate the work rate of A:
A alone can complete the work in 21 days. So, A's one day's work is:
Calculate the combined work rate of A and B:
A and B together can complete the work in 18 days. So, their combined one day's work is:
Calculate the work rate of B:
B's one day's work can be found by subtracting A's work rate from the combined work rate:
Determine the total work done:
The task was completed in 27 days in total. Let 'x' be the number of days A worked. This means B worked for all 27 days.
Formulate the equation for total work:
The total work done is the sum of work done by A and work done by B:
Solve for x (days A worked):
\[ \frac{x}{21} + \frac{27}{126} = 1 \]\[ \frac{x}{21} + \frac{3}{14} = 1 \]\[ \frac{x}{21} = 1 - \frac{3}{14} \]\[ \frac{x}{21} = \frac{14 - 3}{14} \]\[ \frac{x}{21} = \frac{11}{14} \]\[ x = \frac{11}{14} \times 21 \]\[ x = \frac{11 \times 3}{2} \]\[ x = \frac{33}{2} = 16.5 \text{ days} \]Calculate when A left:
A worked for 16.5 days. The total time taken to complete the task was 27 days. So, A left before the work got over by:
C) 10.5
The question asks about the factors that influence the kinetic energy of an object. We need to recall the definition and formula for kinetic energy to determine which physical quantity directly affects it.
Correct Option: B) Velocity β As per the formula \(KE = \frac{1}{2} m v^2\), kinetic energy is directly proportional to the square of the velocity. Therefore, an increase in velocity will lead to an increase in kinetic energy.
The question asks to identify the sport associated with Jasvir Singh. This requires general knowledge about prominent Indian sports personalities.
B) Kabaddi β Jasvir Singh is a celebrated Indian Kabaddi player, known for his raiding skills and his role in the Indian national Kabaddi team.
Leela has a terrace garden for which she buys supplies from a gardener on a monthly basis. Her expense pattern is as follows.
| Item | % Expense |
| New species of plants | 20 |
| Compost | 40 |
| Mud | 10 |
| Cowdung | 20 |
| Other supplies | 10 |
If she spends Rs. 750 on Compost, what will be her expected expense on new plants?
The problem provides the percentage of total expenses Leela spends on various items for her terrace garden and the actual amount spent on one specific item (Compost). We need to calculate the expected expense on another item (new plants) based on these percentages.
Since Rs. 750 represents 40% of the total expense, we can find the total expense using the formula:
\[ \text{Total Expense} = \frac{\text{Expense on Compost}}{\text{Percentage of Compost Expense}} \times 100 \]\[ \text{Total Expense} = \frac{750}{40} \times 100 \]\[ \text{Total Expense} = 18.75 \times 100 \]\[ \text{Total Expense} = \text{Rs. } 1875 \]Now that we have the total expense, we can find the expense on new plants, which is 20% of the total expense:
\[ \text{Expense on New Plants} = \text{Total Expense} \times \frac{\text{Percentage of New Plants Expense}}{100} \]\[ \text{Expense on New Plants} = 1875 \times \frac{20}{100} \]\[ \text{Expense on New Plants} = 1875 \times 0.20 \]\[ \text{Expense on New Plants} = \text{Rs. } 375 \]D) Rs. 375 is the correct answer. This is calculated by first finding the total expense based on the given compost expense and its percentage, and then calculating 20% of that total for new plants.
The question asks to identify a language spoken in the Bihar-Jharkhand region of eastern India that is also known as 'Magadhi'. This requires knowledge of the regional languages of India and their alternative names or historical connections.
Correct Option: A) Magahi is a language spoken primarily in the Magadh region of Bihar and also in parts of Jharkhand. It is a direct descendant of Magadhi Prakrit, an ancient Indo-Aryan language, and is therefore also known as 'Magadhi' due to its historical and linguistic roots.
To determine which assumption is implicit, we need to analyze the given statement and see what must be true for the statement to make sense. An implicit assumption is something that is not directly stated but is taken for granted or necessarily follows from the statement.
Correct Option: C) Only assumption I is implicit
The question asks about a specific diplomatic appointment made by India in 2018. This requires knowledge of current affairs and diplomatic postings during that period. The correct answer will be the individual who was appointed as India's Ambassador to Bolivia in 2018.
Correct Option: A) M. Subbarayudu was indeed appointed as the Ambassador of India to the Plurinational State of Bolivia in 2018. He was an Indian Foreign Service (IFS) officer of the 1994 batch.
The question asks to identify the political party of Mehbooba Mufti, a former Chief Minister of Jammu and Kashmir. This requires knowledge of prominent political figures and their affiliations in Indian politics, specifically concerning the Jammu and Kashmir region.
Correct Option: C) Jammu and Kashmir Peoples Democratic Party
The question asks about the language used in the Upanishads. To answer this, one needs to recall the historical context and linguistic evolution of ancient Indian texts, particularly those associated with the Vedic tradition.
Correct Option: C) Sanskrit
How many triangles are there in the following figure?
To find the total number of triangles in the given figure, we need to systematically count all possible triangles, considering various combinations of lines and intersections.
Therefore, the total number of triangles in the figure is 21.
Correct Option: C) 21