The question asks to identify which project is being implemented by C-DAC, Pune. This requires knowledge of various government projects and the agencies responsible for their implementation.
Correct Option: C) Project JATAN
Project JATAN (JATAN: Virtual Museum Builder) is a digital preservation project being implemented by C-DAC, Pune. It is a software developed for creating digital collections of museum artifacts and managing them. It aims to create a national digital repository for museums in India, allowing virtual access to cultural heritage.
Decimal expansion of \( \frac{109}{100} \) is:
1 + \( \frac{9}{10} \)
10 + \( \frac{9}{100} \)
1 + \( \frac{0}{10} \)+ \( \frac{9}{100} \)
100 + 9 +\( \frac{0}{100} \)
To find the decimal expansion of a fraction, we can either perform division or express the fraction as a sum of whole numbers and fractions with powers of 10 in the denominator. The given fraction is \( \frac{109}{100} \). We need to convert this improper fraction into a mixed number or a decimal and then match it with the given options.
The fraction is \( \frac{109}{100} \). We can divide 109 by 100.
\[ 109 \div 100 = 1 \text{ with a remainder of } 9 \]Therefore, the mixed number form is \( 1 \frac{9}{100} \).A mixed number \( 1 \frac{9}{100} \) can be written as the sum of its whole part and its fractional part:
\[ 1 + \frac{9}{100} \]In decimal expansion, the first digit after the decimal point represents tenths (\( \frac{1}{10} \)), the second digit represents hundredths (\( \frac{1}{100} \)), and so on.
The term \( \frac{9}{100} \) means there are 0 tenths and 9 hundredths.
So, \( \frac{9}{100} \) can be written as \[\frac{0}{10} + \frac{9}{100}\].
Substituting this back into our sum:
\[ 1 + \frac{0}{10} + \frac{9}{100} \]Directly converting \( \frac{109}{100} \) to a decimal gives \( 1.09 \).
In \( 1.09 \):
So, \[1.09 = 1 + \frac{0}{10} + \frac{9}{100}\].
C) \[1 + \frac{0}{10} + \frac{9}{100}\]
This option correctly represents the decimal expansion of \( \frac{109}{100} \) by breaking it down into its whole number part and the place values of its decimal part (tenths and hundredths).
This would be \( 1.9 \) or \( \frac{19}{10} \) or \( \frac{190}{100} \), which is not equal to \( \frac{109}{100} \).
This would be \( 10.09 \) or \( \frac{1009}{100} \), which is not equal to \( \frac{109}{100} \).
This would be \( 109 \), which is not equal to \( \frac{109}{100} \). The fraction \( \frac{0}{100} \) is simply 0.
The problem asks for the range of the function \(f(x) = x^2\) where \(x\) belongs to the set of real numbers (\(R\)). The range of a function is the set of all possible output values (\(f(x)\) values) that the function can produce.
B) non negative numbers. This is correct because the square of any real number is always greater than or equal to zero. It can be zero (when \(x=0\)) or any positive real number.
The question asks for the launch year of the Setu Bharatam Programme. This is a factual question related to government schemes and initiatives in India. Recalling the specific launch year of this program is key to answering correctly.
Correct Option: A) 2016
The Setu Bharatam Programme was launched on 4th March 2016 by Prime Minister Narendra Modi. The program aims to ensure safe and smooth travel on National Highways by building bridges and improving existing ones.
The question asks to identify one of the "nine gems" (Navaratnas) from the court of the Gupta emperor Chandragupta II. This requires knowledge of prominent figures associated with his reign.
D) Varahamihira — Varahamihira was a renowned astronomer, astrologer, and mathematician who was indeed one of the nine gems (Navaratnas) in the court of Chandragupta II (also known as Vikramaditya).
The coefficient of variation (CV) is a measure of relative variability. It expresses the standard deviation as a percentage of the mean. This allows for comparison of variability between data sets with different units or widely different means. The formula for the coefficient of variation is given by the ratio of the standard deviation to the mean, multiplied by 100 to express it as a percentage.
Correct Option: A) 20% is the correct coefficient of variation calculated using the given mean and standard deviation.
The question asks to identify the first island in India to operate seaplane service. This is a factual question related to Indian transportation and geography. Recalling key developments in regional connectivity initiatives helps answer this.
Correct Option: A) Andaman and Nicobar Island
The problem presents a number series: 1, 5, 29, ?. We need to identify the pattern in the given numbers and apply it to find the missing term. Often, such series involve powers, additions, or multiplications in a specific sequence.
Correct Option: B) 259 is the number that replaces the question mark.
Amit alone can complete a piece of work in 15 days and Balbir alone can do the same work in 10 days. If Amit alone works for 3 days after which Balbir joins him, then the work will be finished in how many days?
4 \( \frac{4}{5} \) days
\( \frac{1}{6} \) days
\( \frac{4}{5} \) days
7 \( \frac{4}{5} \) days
This problem involves work and time. We need to calculate the individual work rates of Amit and Balbir, determine the amount of work Amit completes alone, and then calculate the time taken for both to complete the remaining work.
Amit can complete the work in 15 days. So, in one day, Amit completes:
\[ \text{Amit's 1-day work} = \frac{1}{15} \text{ of the total work} \]Balbir can complete the work in 10 days. So, in one day, Balbir completes:
\[ \text{Balbir's 1-day work} = \frac{1}{10} \text{ of the total work} \]Amit works alone for 3 days. The work done by Amit in 3 days is:
\[ \text{Work done by Amit in 3 days} = 3 \times \frac{1}{15} = \frac{3}{15} = \frac{1}{5} \text{ of the total work} \]The total work is considered as 1 unit. After Amit works for 3 days, the remaining work is:
\[ \text{Remaining work} = 1 - \frac{1}{5} = \frac{4}{5} \text{ of the total work} \]When Amit and Balbir work together, their combined daily work rate is:
\[ \text{Combined 1-day work} = \frac{1}{15} + \frac{1}{10} \]\[ \text{Combined 1-day work} = \frac{2}{30} + \frac{3}{30} = \frac{5}{30} = \frac{1}{6} \text{ of the total work} \]Let \(D\) be the number of days taken by Amit and Balbir together to complete the remaining \( \frac{4}{5} \) of the work. If they complete \( \frac{1}{6} \) of the work in one day, then to complete \( \frac{4}{5} \) of the work, it will take:
\[ D = \frac{\text{Remaining work}}{\text{Combined 1-day work}} = \frac{\frac{4}{5}}{\frac{1}{6}} \]\[ D = \frac{4}{5} \times 6 = \frac{24}{5} \text{ days} \]\[ D = 4 \frac{4}{5} \text{ days} \]The total time is the sum of the days Amit worked alone and the days they worked together.
\[ \text{Total days} = 3 \text{ days (Amit alone)} + 4 \frac{4}{5} \text{ days (Amit and Balbir together)} \]\[ \text{Total days} = 3 + 4 + \frac{4}{5} = 7 \frac{4}{5} \text{ days} \]D) 7 \( \frac{4}{5} \) days — This is the total number of days required to complete the work, including the initial 3 days Amit worked alone and the subsequent \( 4 \frac{4}{5} \) days when they worked together.
The problem is a logical deduction question based on a given statement. We need to analyze the statement and determine which of the alternatives is a definite consequence of it. The statement is: "No newspaper is read by an illiterate." This implies a clear separation between newspapers and illiterates in the context of reading.
Correct Option: B) Only C & D