The question asks to identify the recipient of the Prime Minister's Award for outstanding contribution to the promotion and development of yoga in 2018. This requires specific knowledge of the awardees for that particular year.
Correct Option: D) Vishwas Mandlik was one of the recipients of the Prime Minister's Award for outstanding contribution to the promotion and development of yoga in 2018.
This problem involves the relationship between power, work, and time. Power is defined as the rate at which work is done or energy is transferred. We are given the power of an engine and the time for which it operates, and we need to find the total work done during that period.
Correct Option: B) 200 kJ
This is a work and time problem. We need to find the individual work rates of Arjun and Bharath to determine how long Arjun alone would take to complete the task. We will set up equations based on the given scenarios and solve for their individual work rates.
Let Arjun's one day's work be \(A\) and Bharath's one day's work be \(B\). The total work is 1 unit.
Scenario 1: Arjun worked for 2 days, then Bharath completed the rest in 9 days.
The work done by Arjun in 2 days is \(2A\). The work done by Bharath in 9 days is \(9B\). Together, they completed the full task.
\[ 2A + 9B = 1 \quad \text{(Equation 1)} \]Scenario 2: If Arjun had worked for 3 days, Bharath would have finished the remaining work in 6 days.
The work done by Arjun in 3 days is \(3A\). The work done by Bharath in 6 days is \(6B\). Together, they completed the full task.
\[ 3A + 6B = 1 \quad \text{(Equation 2)} \]Now we have a system of two linear equations with two variables:
Equation 1: \(2A + 9B = 1\)
Equation 2: \(3A + 6B = 1\)
To solve for \(A\) and \(B\), we can use the elimination method. Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of \(A\) equal:
Multiply Equation 1 by 3: \(3 \times (2A + 9B) = 3 \times 1 \implies 6A + 27B = 3 \quad \text{(Equation 3)}\)
Multiply Equation 2 by 2: \(2 \times (3A + 6B) = 2 \times 1 \implies 6A + 12B = 2 \quad \text{(Equation 4)}\)
Subtract Equation 4 from Equation 3:
\[ (6A + 27B) - (6A + 12B) = 3 - 2 \]\[ 15B = 1 \]\[ B = \frac{1}{15} \]So, Bharath's one day's work is \(\frac{1}{15}\) of the total work. This means Bharath alone can complete the task in 15 days.
Substitute the value of \(B\) into Equation 1 to find \(A\):
\[ 2A + 9 \left(\frac{1}{15}\right) = 1 \]\[ 2A + \frac{9}{15} = 1 \]\[ 2A + \frac{3}{5} = 1 \]\[ 2A = 1 - \frac{3}{5} \]\[ 2A = \frac{5 - 3}{5} \]\[ 2A = \frac{2}{5} \]\[ A = \frac{2}{5 \times 2} \]\[ A = \frac{1}{5} \]So, Arjun's one day's work is \(\frac{1}{5}\) of the total work. This means Arjun alone can complete the task in 5 days.
C) 5 days. Arjun's one day's work is \(\frac{1}{5}\), which means he can complete the task alone in 5 days.
The mean of the 6 smallest numbers from a group is 15 while the mean of all the 14 members of the group taken together is 17. What is the mean of the 8 largest numbers?
To find the mean of the 8 largest numbers, we will first calculate the sum of all 14 numbers and the sum of the 6 smallest numbers. Then, we will subtract the sum of the 6 smallest numbers from the total sum to get the sum of the 8 largest numbers. Finally, we will divide this sum by 8 to find their mean.
D) 18.50 is the correct mean of the 8 largest numbers.
To calculate the total time duration, we need to consider the number of full days and the difference in minutes between the start and end times. A crucial step is to correctly identify if the year 2024 is a leap year, as this affects the number of days.
D) 367 days 23 hours 51 minutes
The question asks us to analyze a given statement and determine which conclusions logically follow from it. The statement is a common idiom: "The grass is always greener on the other side of the fence." We need to interpret the meaning of this idiom and then evaluate each conclusion based on that interpretation.
A) Only conclusion I follows. This conclusion directly captures the essence of the idiom, which suggests that people are often dissatisfied with their own circumstances and believe others' situations are better.
The question asks to identify the first Pakistani cricketer to score a double century (200 runs or more) in One Day Internationals (ODIs). This requires knowledge of cricket records, specifically individual batting milestones in ODIs.
C) Fakhar Zaman — Fakhar Zaman holds the record for being the first Pakistani cricketer to score a double century in One Day Internationals. He achieved this milestone on July 20, 2018, against Zimbabwe, scoring an unbeaten 210 runs.
The question asks to identify a former or current Chief Minister of India who previously served as a temple priest. This requires knowledge of the personal background and religious affiliations of prominent Indian political figures.
A) Yogi Adityanath is the current Chief Minister of Uttar Pradesh. Before entering politics, he was the Mahant (head priest) of the Gorakhnath Math, a prominent Hindu monastery. His spiritual name is Yogi Adityanath, and he was known as Ajay Mohan Bisht before taking sanyas. He has been the head priest of the Gorakhnath Math since 1994, succeeding his spiritual father Mahant Avaidyanath.
The question asks about the primary agricultural product for which Pemba Island is famous. This requires knowledge of the geography and agricultural specializations of different regions.
D) Cloves — Pemba Island, along with Unguja (Zanzibar Island), is renowned globally for its extensive clove plantations. It has historically been one of the world's leading producers of cloves, which are dried flower buds used as a spice.
The question asks to identify the enzyme from pancreatic juice that converts proteins into amino acids. This requires knowledge of the digestive enzymes and their specific functions and origins.
C) Trypsin is a proteolytic enzyme secreted by the pancreas as inactive trypsinogen, which is then activated in the small intestine. It breaks down proteins and polypeptides into smaller peptides, contributing significantly to their digestion into amino acids.