The question asks to identify the term that refers to a Buddhist monastery where monks reside. This requires knowledge of common architectural and religious terms associated with Buddhism in ancient India.
D) Viharas are Buddhist monasteries that served as residential quarters for monks and nuns. They were crucial centers for learning, meditation, and the propagation of Buddhist teachings.
The problem asks us to identify which assumptions are implicit in the given statement. An implicit assumption is something that must be true for the statement to make sense or be logically sound, even if it's not explicitly stated. We need to evaluate each assumption against the statement.
C) Only II is implicit
A can do a certain piece of work in 8 days, B can do the same work in 18 days and C can do the same work in 12 days. Find the number of days it will take to complete the same work, if they all work together.
\( \frac{19}{48} \)
\( \frac{72}{19} \)
\( \frac{48}{19} \)
\( \frac{19}{72} \)
To find the total time taken when A, B, and C work together, we first determine the individual work rates of A, B, and C. The work rate is the reciprocal of the time taken to complete the work. Then, we sum their individual work rates to find their combined work rate. Finally, the reciprocal of the combined work rate gives the total time taken to complete the work together.
Calculate individual work rates:
Calculate combined work rate:
When they work together, their 1-day work rates add up:
\[ \text{Combined 1-day work} = \frac{1}{8} + \frac{1}{18} + \frac{1}{12} \]Find a common denominator (LCM) for 8, 18, and 12:
The LCM of 8, 18, and 12 is 72.
Add the fractions:
\[ \text{Combined 1-day work} = \frac{1 \times 9}{8 \times 9} + \frac{1 \times 4}{18 \times 4} + \frac{1 \times 6}{12 \times 6} \]\[ = \frac{9}{72} + \frac{4}{72} + \frac{6}{72} \]\[ = \frac{9 + 4 + 6}{72} \]\[ = \frac{19}{72} \]Calculate the total time taken:
If their combined 1-day work is \( \frac{19}{72} \), then the total number of days to complete the work is the reciprocal of this fraction:
\[ \text{Total days} = \frac{1}{\text{Combined 1-day work}} = \frac{1}{\frac{19}{72}} = \frac{72}{19} \text{ days} \]Correct Option: B) \( \frac{72}{19} \)
The question asks about the definition of Constant Returns to Scale (CRS) in the context of a production function. We need to understand how output changes when all inputs are increased proportionally.
C) a proportional increase in all inputs results in an increase in output by the same proportion
This option perfectly matches the definition of Constant Returns to Scale (CRS). If you double all inputs, you double the output; if you triple all inputs, you triple the output, and so on.
Select the correct homologous series of alkanes.
CH4, C2H6, C3H8, C4H10
CH4, C2H4, C3H8, C4H10
CH4, C3H8, C2H6, C4H10
CH4, C2H4, C3H4, C4H10
To identify the correct homologous series of alkanes, we need to understand the definition of a homologous series and the general formula for alkanes. A homologous series is a series of organic compounds with the same functional group, similar chemical properties, and successive members differing by a \(-CH_2-\) group. Alkanes are saturated hydrocarbons with the general formula \(C_nH_{2n+2}\).
A) \(CH_4\), \(C_2H_6\), \(C_3H_8\), \(C_4H_{10}\)
All the compounds listed in this option are alkanes and follow the general formula \(C_nH_{2n+2}\). Each successive member differs by a \(-CH_2-\) group:
This perfectly fits the definition of a homologous series of alkanes.
To find the Highest Common Factor (HCF) of a set of numbers, we can use the prime factorization method. This involves finding the prime factors of each number and then multiplying the common prime factors raised to their lowest powers.
Correct Option: D) 4
The question asks about the qualifications required for the appointment of the Attorney-General for India, as specified in Article 76 of the Indian Constitution. To answer this, we need to recall the constitutional provisions related to this office.
Correct Option: B) appointed as Judge of the Supreme Court
Article 76(1) of the Indian Constitution clearly states that the President shall appoint a person who is qualified to be appointed a Judge of the Supreme Court to be the Attorney-General for India.
This problem involves solving a system of two equations with two variables. We are given the difference between two numbers and the difference between their squares. We can use algebraic identities to simplify the problem and find the values of the numbers.
A) 19 is the larger number, as calculated in our step-by-step solution.
This problem involves arranging six friends (A, B, C, D, E, F) based on their heights using a series of comparative statements. We need to deduce the height order and identify the shortest person.
C) A — Based on the step-by-step deduction, A is the shortest friend.
The question asks to identify the Indian badminton player who won the Women's Singles Title at the Singapore Open in 2022. This requires knowledge of recent sports achievements, specifically in badminton.
Correct Option: D) PV Sindhu