The question asks about the approximate percentage of carbon dioxide in the Earth's atmosphere. This is a factual recall question related to atmospheric composition. We need to identify the correct percentage from the given options.
Correct Option: C) 0.03% is the correct approximate percentage of carbon dioxide in the atmosphere.
Express 0.3\(\overline{59}\) in the form \( \frac{p}{q} \), where p and q are integers and q ≠ 0
\(\frac{178}{495}\)
\(\frac{359}{990}\)
\(\frac{119}{330}\)
\(\frac{179}{495}\)
To express a recurring decimal in the form \(\frac{p}{q}\), we use an algebraic method. We set the given decimal equal to a variable, multiply it by powers of 10 to align the repeating parts, and then subtract the equations to eliminate the repeating decimal, solving for the variable.
Correct Option: A) \(\frac{178}{495}\)
This question pertains to the Law of Variable Proportions (also known as the Law of Returns to a Factor), which describes the short-run production function. It explains how output changes when one input (variable factor) is increased while others (fixed factors) remain constant. The law is typically divided into three stages based on the behavior of marginal product (MP) and average product (AP).
Correct Option: A) Stage 1 is the stage where the marginal product of the variable input rises, signifying increasing returns to the factor. In this stage, total product increases at an increasing rate.
The question asks to identify the first chief guest at India's Republic Day celebration in 1950. This is a factual question related to India's history and international relations, specifically concerning the Republic Day tradition.
Correct Option: A) Sukarno
We are given two positive numbers with a difference and division relationship. We need to find the HCF of the greater of these two numbers and another given number. We will use the division algorithm (Dividend = Divisor × Quotient + Remainder) and properties of HCF to solve this problem.
Let the two positive numbers be \(A\) and \(B\), where \(A\) is the greater number and \(B\) is the smaller number.
From the problem statement, their difference is 3422:
\[ A - B = 3422 \quad \text{(Equation 1)} \]When the greater number (\(A\)) is divided by the smaller number (\(B\)), the quotient is 4 and the remainder is 290. Using the division algorithm:
\[ A = 4B + 290 \quad \text{(Equation 2)} \]Substitute Equation 2 into Equation 1:
\[ (4B + 290) - B = 3422 \]\[ 3B + 290 = 3422 \]\[ 3B = 3422 - 290 \]\[ 3B = 3132 \]\[ B = \frac{3132}{3} \]\[ B = 1044 \]Now, find the value of \(A\) using Equation 1:
\[ A = B + 3422 \]\[ A = 1044 + 3422 \]\[ A = 4466 \]The greater of the two numbers is \(A = 4466\). We need to find the HCF of 4466 and 4292.
We can use the Euclidean algorithm to find the HCF:
Divide 4466 by 4292:
\[ 4466 = 1 \times 4292 + 174 \]Now, divide 4292 by 174:
\[ 4292 = 24 \times 174 + 116 \]Now, divide 174 by 116:
\[ 174 = 1 \times 116 + 58 \]Now, divide 116 by 58:
\[ 116 = 2 \times 58 + 0 \]Since the remainder is 0, the HCF is the last non-zero divisor, which is 58.
Correct Option: D) The HCF of 4466 and 4292 is 58.
To find the next homologous member of a given compound, we need to understand the concept of a homologous series. A homologous series is a series of organic compounds with the same functional group but with each successive member differing by a \(-CH_2\) group. The general formula for a homologous series also changes systematically.
Starting with \(CH_3OH\):
\(CH_3OH + CH_2 \rightarrow C_2H_5OH\)
Alternatively, if \(CH_3OH\) corresponds to \(n=1\) in \(C_nH_{2n+1}OH\), then the next member will have \(n=2\):
\[ C_2H_{2(2)+1}OH = C_2H_5OH \]Correct Option: A) \(C_2H_5OH\)
The given compound is methanol (\(CH_3OH\)). The next homologous member will have one additional carbon atom and two additional hydrogen atoms (\(-CH_2\) unit). Adding a \(-CH_2\) group to \(CH_3OH\) gives \(C_2H_5OH\) (ethanol).
The question asks for the location where India's first fisheries business incubator was inaugurated. This is a factual recall question related to current affairs and government initiatives in the fisheries sector.
Correct Option: D) Gurugram is the correct answer because India's first fisheries business incubator was inaugurated there.
The diagram given below represents those students who study Physics, Chemistry and Math. Find the number of students who study Physics and Chemistry but not Math.
To find the number of students who study Physics and Chemistry but not Math, we need to analyze the Venn diagram provided. The diagram illustrates the distribution of students studying Physics, Chemistry, and Math.
Correct Option: B) 13
The question asks about the launch of the 'Stree Manoraksha' project and the Union Minister responsible for it in March 2022. This requires knowledge of recent government initiatives and the portfolios of Union Ministers.
Correct Option: C) Smriti Zubin Irani was the Union Minister for Women and Child Development when the 'Stree Manoraksha' project was launched in March 2022. The project was initiated by the Ministry of Women and Child Development in collaboration with NIMHANS, Bengaluru.