The question asks about the normal tenure of the Comptroller and Auditor General (CAG) of India. This is a factual question related to the Indian Constitution and the powers/tenure of constitutional bodies. To answer this, one needs to recall the specific provisions regarding the CAG's term of office.
A) six — The normal tenure of the Comptroller and Auditor General (CAG) of India is six years, or until they attain the age of 65 years, whichever is earlier, as per the CAG's (Duties, Powers and Conditions of Service) Act, 1971.
The question asks about the poverty lines recommended by the C. Rangarajan Committee in 2014 for India. This committee was constituted to review the methodology for poverty estimation. We need to identify the correct monthly per capita consumption expenditure (MPCE) thresholds for rural and urban areas as per its recommendations.
D) A person who has a monthly per capita consumption expenditure of less than ₹1,407 living in the urban areas should be considered poor.
This statement correctly reflects the urban poverty line recommended by the Rangarajan Committee in 2014, which was ₹1,407 per month per person.
If \(\sqrt{x}\) ÷ \(\sqrt{6.25}\) = 2, then the value of x is:
The problem requires us to find the value of \(x\) given an equation involving square roots. We will first simplify the square root of the known number, then isolate \(\sqrt{x}\), and finally square both sides to find \(x\).
The given equation is:
\[ \sqrt{x} \div \sqrt{6.25} = 2 \]This can be written as:
\[ \frac{\sqrt{x}}{\sqrt{6.25}} = 2 \]First, calculate the value of \(\sqrt{6.25}\). We know that \(6.25 = \frac{625}{100}\).
\[ \sqrt{6.25} = \sqrt{\frac{625}{100}} = \frac{\sqrt{625}}{\sqrt{100}} \]Since \(25^2 = 625\) and \(10^2 = 100\), we have:
\[ \sqrt{6.25} = \frac{25}{10} = 2.5 \]Substitute this value back into the original equation:
\[ \frac{\sqrt{x}}{2.5} = 2 \]To isolate \(\sqrt{x}\), multiply both sides of the equation by \(2.5\):
\[ \sqrt{x} = 2 \times 2.5 \]This simplifies to:
\[ \sqrt{x} = 5 \]To find \(x\), square both sides of the equation:
\[ (\sqrt{x})^2 = 5^2 \]This gives:
\[ x = 25 \]D) 25 — The step-by-step calculation shows that \(x = 25\).
The problem asks us to identify the odd one out from a given set of words. This type of question usually requires us to find a common characteristic among three of the words and identify the one that does not share that characteristic. In this case, the words are related to chemistry, specifically types of substances.
Therefore, Amalgam is different from the other three.
Correct Option: B) Amalgam
The standard equation of a circle with center \((h, k)\) and radius \(r\) is given by \((x - h)^2 + (y - k)^2 = r^2\). We will substitute the given center coordinates and radius into this formula and then expand the equation to match the general form presented in the options.
Identify the given values:
Write the standard equation of a circle:
The standard equation of a circle is:
\[ (x - h)^2 + (y - k)^2 = r^2 \]Substitute the given values into the standard equation:
\[ (x - (-2))^2 + (y - 3)^2 = 4^2 \] \[ (x + 2)^2 + (y - 3)^2 = 16 \]Expand the squared terms:
Recall the algebraic identities: \((a+b)^2 = a^2 + 2ab + b^2\) and \((a-b)^2 = a^2 - 2ab + b^2\).
For \((x + 2)^2\):
\[ x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4 \]For \((y - 3)^2\):
\[ y^2 - 2(y)(3) + 3^2 = y^2 - 6y + 9 \]Combine the expanded terms and simplify:
\[ (x^2 + 4x + 4) + (y^2 - 6y + 9) = 16 \] \[ x^2 + y^2 + 4x - 6y + 4 + 9 = 16 \] \[ x^2 + y^2 + 4x - 6y + 13 = 16 \]Rearrange the equation to set it equal to zero:
\[ x^2 + y^2 + 4x - 6y + 13 - 16 = 0 \] \[ x^2 + y^2 + 4x - 6y - 3 = 0 \]Correct Option: B) \( x^{2} + y^{2} + 4x - 6y - 3 = 0 \)
The theme of the United Nations Day Concert 2020 was:
Health for All – Everyone, Everywhere
Potential in Diversity
The Future We Want
Reimagine, Rebalance, Restart: Recovering Together for Our Shared Humanity
The question asks for the theme of the United Nations Day Concert in 2020. This is a factual question related to current events and UN observances, requiring knowledge of specific themes for particular years.
D) Reimagine, Rebalance, Restart: Recovering Together for Our Shared Humanity — This was the official theme for the United Nations Day Concert in 2020. The concert, performed by the Republic of Korea, was dedicated to multilateralism and global solidarity in the face of the COVID-19 pandemic.
This problem involves a two-step transaction with profit and loss percentages. We need to work backward from the final selling price to find the original cost price. First, we'll find the cost price for the friend, and then use that to find the original cost price for the man.
Let the original cost price of the car for the man be \(C_M\).
The man sells the car to his friend at a loss of 20%. So, the selling price for the man (which is the cost price for the friend, \(C_F\)) is:
\[ C_F = C_M - 20\% \text{ of } C_M \]\[ C_F = C_M \left(1 - \frac{20}{100}\right) \]\[ C_F = C_M \left(\frac{80}{100}\right) \]\[ C_F = 0.8 C_M \]The friend then sells the car for ₹58,000 at a profit of 30%. Let the selling price for the friend be \(S_F\).
\[ S_F = C_F + 30\% \text{ of } C_F \]\[ S_F = C_F \left(1 + \frac{30}{100}\right) \]\[ S_F = C_F \left(\frac{130}{100}\right) \]\[ S_F = 1.3 C_F \]We are given that \(S_F = \text{₹}58,000\). Substitute this into the equation from step 3:
\[ 58,000 = 1.3 C_F \]Now, calculate \(C_F\):
\[ C_F = \frac{58,000}{1.3} \]\[ C_F = 44,615.3846... \]Now, substitute the value of \(C_F\) back into the equation from step 2 to find \(C_M\):
\[ C_F = 0.8 C_M \]\[ 44,615.3846... = 0.8 C_M \]Calculate \(C_M\):
\[ C_M = \frac{44,615.3846...}{0.8} \]\[ C_M = 55,769.2307... \]Rounding to the nearest integral value, the original cost price of the car was ₹55,769.
C) ₹55,769 is the correct original cost price when rounded to the nearest integral value.
The question asks to identify the type of cyclone 'Fani'. This requires knowledge of recent major cyclones and their classification.
Correct Option: D) tropical cyclone
To find the gain percentage, we first need to calculate the cost price (CP) and selling price (SP) of the articles. Then, we can determine the profit and use the formula for percentage gain.
The man buys 20 articles for ₹16.
\[ \text{CP per article} = \frac{\text{Total Cost}}{\text{Number of articles}} = \frac{\text{₹}16}{20 \text{ articles}} = \text{₹}0.80 \text{ per article} \]The man sells them at the rate of ₹1.50 per article.
\[ \text{SP per article} = \text{₹}1.50 \]Profit is the difference between the selling price and the cost price.
\[ \text{Profit per article} = \text{SP} - \text{CP} = \text{₹}1.50 - \text{₹}0.80 = \text{₹}0.70 \]The gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\% \]\[ \text{Gain Percentage} = \left( \frac{\text{₹}0.70}{\text{₹}0.80} \right) \times 100\% \]\[ \text{Gain Percentage} = \left( \frac{7}{8} \right) \times 100\% \]\[ \text{Gain Percentage} = 0.875 \times 100\% = 87.5\% \]Correct Option: C) 87.5%
The question asks to identify the Central Nodal Agency responsible for channeling subsidies under the Pradhan Mantri Awas Yojana (Urban) scheme. This requires knowledge of the institutional framework of major government housing schemes in India.
B) NHB — The National Housing Bank (NHB) has been identified as a Central Nodal Agency (CNA) to channelize the subsidy under the Credit Linked Subsidy Scheme (CLSS) component of Pradhan Mantri Awas Yojana (Urban). It plays a crucial role in regulating and financing housing finance institutions and facilitating the flow of subsidies to eligible beneficiaries.