The question asks to identify the Chairman of the Indigo Commission. This requires knowledge of key figures associated with significant historical commissions during British rule in India, specifically the Indigo Commission.
A) WS Seton-Karr was indeed the Chairman of the Indigo Commission, which was established in 1860 to inquire into the indigo cultivation system in Bengal following the Indigo Revolt.
The problem presents a series of letter-clusters and asks us to find the next cluster in the sequence. We need to identify the pattern in how the letters change from one cluster to the next.
D) SATZ is the correct option because it follows the identified patterns for each position in the letter-clusters.
The problem provides the product of two integers and asks for the product of two decimal numbers derived from these integers. We can solve this by understanding how decimal places affect multiplication. The key is to count the total number of decimal places in the numbers being multiplied and apply that to the given product.
We are given that \(331 \times 226 = 74806\).
We need to find the value of \(3.31 \times 0.226\).
The total number of decimal places in the product will be the sum of the decimal places in the numbers being multiplied:
\[ \text{Total decimal places} = 2 + 3 = 5 \]Since \(331 \times 226 = 74806\), the product \(3.31 \times 0.226\) will have the same digits but with 5 decimal places.
Starting from the right of \(74806\), we move the decimal point 5 places to the left:
\[ 74806 \rightarrow 0.74806 \]Correct Option: D) 0.74806
The question asks for the specific date on which World Tuberculosis (TB) Day is observed annually. This is a factual question related to important international observances.
Correct Option: B) 24 March is the correct date for World Tuberculosis (TB) Day.
The question asks to identify the incorrect statement about the Bureau of Indian Standards (BIS). We need to evaluate each option based on factual knowledge about BIS.
Based on the evaluation, statement C is the incorrect one.
Correct Option: C) BIS was established in the year 2010.
How much does one have to subtract from \( \frac{8}{5} \) to obtain \( \frac{5}{8} \)?
\( \frac{39}{64} \)
\( \frac{39}{40} \)
\( \frac{31}{40} \)
\( \frac{25}{64} \)
To find out how much needs to be subtracted from one fraction to obtain another, we need to set up an equation. Let the unknown quantity to be subtracted be \(x\). Then, we can write the equation as: (First fraction) - \(x\) = (Second fraction). We then solve for \(x\).
Let the quantity to be subtracted be \(x\).
According to the problem statement, if we subtract \(x\) from \( \frac{8}{5} \), we should obtain \( \frac{5}{8} \). This can be written as an equation:
\[ \frac{8}{5} - x = \frac{5}{8} \]To solve for \(x\), we can rearrange the equation:
\[ x = \frac{8}{5} - \frac{5}{8} \]To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 5 and 8 is 40.
Convert each fraction to an equivalent fraction with a denominator of 40:
\[ \frac{8}{5} = \frac{8 \times 8}{5 \times 8} = \frac{64}{40} \]\[ \frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40} \]Now, substitute these equivalent fractions back into the equation for \(x\):
\[ x = \frac{64}{40} - \frac{25}{40} \]Perform the subtraction:
\[ x = \frac{64 - 25}{40} \]\[ x = \frac{39}{40} \]Thus, \( \frac{39}{40} \) must be subtracted from \( \frac{8}{5} \) to obtain \( \frac{5}{8} \).
B) \( \frac{39}{40} \) is the correct answer, as calculated above.
If \( \frac{3}{5} \) of a bottle is filled, what is the ratio of the filled part to the empty part of the bottle?
The problem asks for the ratio of the filled part to the empty part of a bottle, given that a certain fraction of the bottle is filled. We need to determine the fraction of the bottle that is empty and then form the ratio.
Understand the given information: The bottle is \( \frac{3}{5} \) filled.
Determine the total parts: The denominator of the fraction \( \frac{3}{5} \) indicates that the bottle can be considered to have 5 equal parts in total.
Identify the filled parts: The numerator of the fraction \( \frac{3}{5} \) indicates that 3 out of these 5 parts are filled.
Calculate the empty parts: If the total parts are 5 and the filled parts are 3, then the empty parts can be found by subtracting the filled parts from the total parts:
\[ \text{Empty parts} = \text{Total parts} - \text{Filled parts} \]\[ \text{Empty parts} = 5 - 3 = 2 \]Form the ratio: The question asks for the ratio of the filled part to the empty part. This can be written as:
\[ \text{Ratio} = \text{Filled parts} : \text{Empty parts} \]\[ \text{Ratio} = 3 : 2 \]Correct Option: A) 3 : 2 is the correct ratio of the filled part to the empty part.
The problem requires us to evaluate an expression involving multiple division operations. When multiple divisions are present in an expression without parentheses, we perform the operations from left to right. This is in accordance with the order of operations (PEMDAS/BODMAS), where multiplication and division have equal precedence and are performed from left to right.
Let's calculate step-by-step:
So, \(243 \div 3 \div 3 \div 3 \div 3 = 3\).
D) 3 is the correct answer, as derived from the step-by-step calculation.
We are given the ratio of two numbers and their Highest Common Factor (HCF). We need to find their Least Common Multiple (LCM). We can use the property that if two numbers are \(A\) and \(B\), and their ratio is \(a:b\), then the numbers can be expressed as \(H \times a\) and \(H \times b\), where \(H\) is their HCF. Once the numbers are found, their LCM can be calculated, or we can use the direct relationship between HCF, LCM, and the numbers.
Let the two numbers be \(N_1\) and \(N_2\). Since their ratio is \(3:7\) and their HCF is \(3\), we can write the numbers as:
\[ N_1 = 3 \times \text{HCF} = 3 \times 3 = 9 \] \[ N_2 = 7 \times \text{HCF} = 7 \times 3 = 21 \]Now we need to find the LCM of \(9\) and \(21\).
The least common multiple is \(63\).
We know that for any two numbers \(N_1\) and \(N_2\):
\[ N_1 \times N_2 = \text{HCF}(N_1, N_2) \times \text{LCM}(N_1, N_2) \]We have \(N_1 = 9\), \(N_2 = 21\), and \(\text{HCF} = 3\).
\[ 9 \times 21 = 3 \times \text{LCM} \] \[ 189 = 3 \times \text{LCM} \] \[ \text{LCM} = \frac{189}{3} \] \[ \text{LCM} = 63 \]The question asks to identify the recipient of the Nobel Prize in Literature in the year 2020. This requires knowledge of recent Nobel laureates, a common topic in general awareness sections of competitive exams.
In 2020, the Nobel Prize in Literature was awarded to American poet Louise Glück "for her unmistakable poetic voice that with austere beauty makes individual existence universal."
C) Louise Gluck — Louise Gluck was indeed awarded the Nobel Prize in Literature in 2020 for her distinctive poetic voice.