Rajan can finish a certain task in 6 days. Bhavesh takes 8 days to complete the same task. Charan takes as long as Rajan and Bhavesh would take working together. How long will it take Bhavesh and Charan to complete the work together?
2\( \frac{2}{5} \) days
2\( \frac{7}{5} \) days
2\( \frac{3}{5} \) days
2\( \frac{4}{5} \) days
This problem involves work and time. We need to calculate the individual work rates of Rajan and Bhavesh, then find their combined work rate to determine Charan's work rate. Finally, we calculate the combined work rate of Bhavesh and Charan to find the time they take to complete the task together.
Rajan can finish the task in 6 days. So, in one day, Rajan completes:
\[ \text{Rajan's 1-day work} = \frac{1}{6} \text{ of the task} \]Bhavesh can finish the task in 8 days. So, in one day, Bhavesh completes:
\[ \text{Bhavesh's 1-day work} = \frac{1}{8} \text{ of the task} \]When Rajan and Bhavesh work together, their combined one-day work is:
\[ \text{Combined 1-day work (Rajan + Bhavesh)} = \frac{1}{6} + \frac{1}{8} \]To add these fractions, find a common denominator, which is 24:
\[ = \frac{4}{24} + \frac{3}{24} = \frac{4+3}{24} = \frac{7}{24} \text{ of the task} \]If they complete \(\frac{7}{24}\) of the task in one day, they will complete the whole task in:
\[ \text{Time (Rajan + Bhavesh)} = \frac{1}{\frac{7}{24}} = \frac{24}{7} \text{ days} \]Charan takes as long as Rajan and Bhavesh would take working together. So, Charan also takes \(\frac{24}{7}\) days to complete the task. Therefore, Charan's one-day work is:
\[ \text{Charan's 1-day work} = \frac{1}{\frac{24}{7}} = \frac{7}{24} \text{ of the task} \]Now, we need to find how long Bhavesh and Charan take together. Their combined one-day work is:
\[ \text{Combined 1-day work (Bhavesh + Charan)} = \text{Bhavesh's 1-day work} + \text{Charan's 1-day work} \] \[ = \frac{1}{8} + \frac{7}{24} \]Find a common denominator, which is 24:
\[ = \frac{3}{24} + \frac{7}{24} = \frac{3+7}{24} = \frac{10}{24} = \frac{5}{12} \text{ of the task} \]If they complete \(\frac{5}{12}\) of the task in one day, they will complete the whole task in:
\[ \text{Time (Bhavesh + Charan)} = \frac{1}{\frac{5}{12}} = \frac{12}{5} \text{ days} \]Convert this improper fraction to a mixed number:
\[ \frac{12}{5} = 2 \frac{2}{5} \text{ days} \]Correct Option: A) \(2 \frac{2}{5}\) days
The question asks to identify the Chief Minister of Sikkim as of August 2018. This requires knowledge of the political landscape and leadership in Indian states during that specific period.
Pawan Kumar Chamling served as the Chief Minister of Sikkim for a record 24 years, from 1994 to 2019. Therefore, in August 2018, he was indeed the Chief Minister of Sikkim.
Correct Option: B) Pawan Kumar Chamling was the Chief Minister of Sikkim as of August 2018. He held this position from 1994 to 2019, making him the longest-serving Chief Minister in India.
The question asks for the term that defines the rate of doing work or the rate of transfer of energy. This is a fundamental definition in physics related to energy and mechanics.
Based on this definition, the correct term is Power.
Correct Option: D) Power
The question asks to identify the CEO of iD Fresh Food Pvt Ltd who was invited to Harvard University in 2018. This is a factual recall question related to business personalities and current affairs (as of 2018).
Correct Option: C) P. C. Musthafa is the co-founder and CEO of iD Fresh Food Pvt Ltd. He was invited to address students at Harvard University in 2018, discussing his journey from a remote village to building a successful food enterprise.
The problem asks us to calculate the final position of an elevator after a certain time, given its rate of descent. We need to convert the time into minutes and then multiply it by the rate of descent. Since movement below the ground is represented by negative integers, the final position will be a negative value.
Since the rate is given in meters per minute, we need to convert the time from hours to minutes.
\[ 1 \text{ hour} = 60 \text{ minutes} \]The total distance descended is the product of the rate of descent and the total time in minutes.
\[ \text{Distance descended} = \text{Rate of descent} \times \text{Time} \] \[ \text{Distance descended} = 5 \text{ m/minute} \times 60 \text{ minutes} \] \[ \text{Distance descended} = 300 \text{ meters} \]The problem states that distance below the ground is represented by a negative integer. Since the elevator is descending into a mine shaft, its final position will be below the ground.
Therefore, the position after one hour will be \( -300 \) meters.
Correct Option: C) –300 m
The question asks for the definition of 1 Joule in terms of fundamental SI units. Joule is the SI unit of energy or work. We need to recall the formula for work done and identify the correct combination of units.
D) 1 N × 1 m is correct because 1 Joule is defined as the work done when a force of 1 Newton moves an object through a distance of 1 meter in the direction of the force.
This question tests your ability to identify implicit assumptions in a given statement. An assumption is something taken for granted or accepted as true without proof. When a government takes a decision based on a certain outcome, it implicitly assumes that the action will lead to that outcome.
A) Both I and II are implicit. Assumption I is directly implied because the government is taking action *to reduce accidents*, meaning it believes the action will achieve this. Assumption II is also implicit because a major infrastructure project like four-laning all major roads would only be undertaken for accident reduction if it were expected to have a significant impact, i.e., avoid most accidents.
Which of the two conclusions can be concluded on the basis of given statements?
Statement: Some Autos are Scooters. All the scooters are cycles.
Conclusions:
I. Some Autos are cycles
II. No scooter is Auto
Both (1) and (2) follow
Only (1) follows
Either (1) or (2) follows
Only (2) follows
This is a question based on syllogism. We need to draw Venn diagrams based on the given statements and then check which of the conclusions logically follow from these diagrams.
Based on the statements, we can draw the following Venn diagram:
Only Conclusion I follows from the given statements.
B) Only (1) follows
Which of the following is the smallest fraction?
\( \frac{3}{15} \), \( \frac{5}{20} \), \( \frac{25}{64} \), \( \frac{25}{1000} \)
\( \frac{3}{15} \)
\( \frac{5}{20} \)
\( \frac{25}{1000} \)
\( \frac{25}{64} \)
To find the smallest fraction among the given options, we can convert each fraction into its decimal equivalent or simplify them to a common denominator. Comparing decimal values is often the easiest method.
C) \( \frac{25}{1000} \) is the smallest fraction because its decimal value is \( 0.025 \), which is the smallest among all the given options.
The question asks us to identify the odd one out from a given list of words. This is a classification type of question where we need to find a common characteristic among three items and identify the one that does not share that characteristic.
Correct Option: A) Oxygen is the odd one out because it is a non-metal and a gas at room temperature, whereas Platinum, Silver, and Gold are all metals and solids at room temperature.