The problem asks us to find what percentage of 2500 is equal to 50% of 500. We can solve this by first calculating 50% of 500, and then determining what percentage this result is of 2500.
To find a percentage of a number, we convert the percentage to a decimal or a fraction and multiply it by the number.
\[ 50\% \text{ of } 500 = \frac{50}{100} \times 500 \] \[ = 0.50 \times 500 \] \[ = 250 \]Let the unknown percentage be \(x\%\). We are looking for \(x\%\) of 2500 that equals 250.
\[ x\% \text{ of } 2500 = 250 \] \[ \frac{x}{100} \times 2500 = 250 \]Simplify the equation and solve for \(x\).
\[ 25x = 250 \] \[ x = \frac{250}{25} \] \[ x = 10 \]So, 250 is 10% of 2500.
Correct Option: D) 10%
The question asks to identify which of the given options is NOT a cause of a tsunami. We need to evaluate each option to determine if it can generate a tsunami.
Correct Option: B) Soil Erosion is NOT a cause of a tsunami. While soil erosion can contribute to landslides, it does not directly cause the massive displacement of ocean water necessary to generate a tsunami.
To identify the number that does not belong to the series, we need to find the pattern or rule governing the sequence of numbers. This typically involves looking at the differences between consecutive terms, or other mathematical relationships.
A) 42 — The number 42 disrupts the pattern of differences being consecutive prime numbers. If 42 were replaced by 41, the series would follow the rule of adding consecutive prime numbers (5, 7, 11, 13, 17, 19) to the previous term.
The question asks to identify the Viceroy of India at the time of the Indian National Congress's (INC) foundation. This requires knowledge of key dates in Indian history, specifically the founding year of the INC and the tenures of various Viceroys.
Correct Option: A) Lord Dufferin
This problem can be solved using the concept of work and time. We calculate the individual work rates of Ram and Shyam and then combine them to find their combined work rate. The reciprocal of the combined work rate gives the total time taken to finish the task together.
Ram can finish the task in 20 days. So, in one day, Ram completes \(\frac{1}{20}\) of the task.
Shyam can finish the task in 30 days. So, in one day, Shyam completes \(\frac{1}{30}\) of the task.
When they work together, their one-day work is the sum of their individual one-day works.
\[ \text{Combined one-day work} = \text{Ram's one-day work} + \text{Shyam's one-day work} \]\[ = \frac{1}{20} + \frac{1}{30} \]The least common multiple (LCM) of 20 and 30 is 60.
\[ \frac{1}{20} + \frac{1}{30} = \frac{3}{60} + \frac{2}{60} \]\[ = \frac{3+2}{60} = \frac{5}{60} \]\[ = \frac{1}{12} \]If they complete \(\frac{1}{12}\) of the task in one day, then they will take 12 days to complete the entire task.
\[ \text{Total days} = \frac{1}{\text{Combined one-day work}} = \frac{1}{\frac{1}{12}} = 12 \text{ days} \]Correct Option: D) 12
The question asks to identify the geographical location of the Great Indian Desert within India. This requires knowledge of India's physical geography.
Correct Option: D) The Great Indian Desert, also known as the Thar Desert, is primarily located in the state of Rajasthan, which is situated in the western part of India. It extends into parts of Gujarat, Punjab, and Haryana, all of which are in the western or northwestern regions of the country.
To find the ratio of the areas, we will first define the side length of the original square. Then, we will calculate the side length of the new square when the original side is tripled. After that, we will calculate the areas of both squares and finally determine their ratio.
Let the side of the original square be \(s\).
The area of the original square, \(A_{\text{original}}\), is given by the formula for the area of a square:
\[ A_{\text{original}} = s^2 \]According to the problem, the side of the square is tripled. So, the side of the resulting square, \(s_{\text{new}}\), will be:
\[ s_{\text{new}} = 3s \]The area of the resulting square, \(A_{\text{new}}\), will be:
\[ A_{\text{new}} = (s_{\text{new}})^2 = (3s)^2 = 9s^2 \]Now, we need to find the ratio of the area of the resulting square to that of the original square. This can be written as:
\[ \text{Ratio} = \frac{A_{\text{new}}}{A_{\text{original}}} \]Substitute the expressions for \(A_{\text{new}}\) and \(A_{\text{original}}\) into the ratio:
\[ \text{Ratio} = \frac{9s^2}{s^2} \]Cancel out \(s^2\) from the numerator and the denominator:
\[ \text{Ratio} = \frac{9}{1} \]This ratio can be expressed as \(9:1\).
Correct Option: C) 9 : 1
The ratio of the area of the resulting square to that of the original square is \(9:1\).
The question asks to identify the temple built by Raja Raja Chola. This requires knowledge of the history of prominent South Indian temples and their patrons.
Correct Option: C) Brihadisvara Temple. The Brihadisvara Temple, located in Thanjavur, Tamil Nadu, is a magnificent example of Chola architecture and a UNESCO World Heritage Site. It was built by Raja Raja Chola I between 1003 and 1010 CE and is dedicated to Lord Shiva. Its construction marked a high point in Dravidian architecture.
The question asks to identify the person who was NOT a recipient of the Bharat Ratna in 2019. To answer this, one needs to recall the individuals who were awarded India's highest civilian honor in that year.
Correct Option: C) Rajeshwar Acharya is the correct answer because he was not among the recipients of the Bharat Ratna in 2019. Rajeshwar Acharya is a renowned Indian classical singer and musicologist, but he has not been awarded the Bharat Ratna.
The question asks to identify which option is NOT a division of the National Sample Survey Organisation (NSSO). To answer this, one needs to know the organizational structure and key divisions of the NSSO.
Correct Option: D) National Development Agenda is NOT a division of the National Sample Survey Organisation.