To find the amount Shenoy has to pay at the end of 2 years when interest is compounded annually, we use the compound interest formula. The formula for the amount \(A\) is given by \(A = P \left(1 + \frac{R}{100}\right)^N\), where \(P\) is the principal amount, \(R\) is the rate of interest per annum, and \(N\) is the number of years.
The formula for the amount \(A\) is:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]The amount Shenoy has to pay at the end of 2 years is Rs 4,96,125.
C) Rs 4,96,125 is the correct amount calculated using the compound interest formula.
To find the total surface area of a cube, we need to know the formula for the surface area of a cube and the length of its side. A cube has 6 identical square faces. The area of one square face is the square of its side length. The total surface area is 6 times the area of one face.
The side length of the cube (\(a\)) is 5 cm.
The total surface area (\(TSA\)) of a cube with side length \(a\) is given by:
\[ TSA = 6a^2 \]Substitute \(a = 5 \text{ cm}\) into the formula:
\[ TSA = 6 \times (5 \text{ cm})^2 \]Thus, the total surface area of the cube is 150 cm².
Correct Option: C) 150
To solve this problem, we need to perform two main steps: first, reverse the letters of each given word, and second, arrange these newly formed words/clusters alphabetically (as per dictionary arrangement). The word that appears in the middle of this sorted list will be our answer.
TSOL, KLAT, KLAW, MLAK, WAHS
To arrange them alphabetically, we compare them letter by letter from left to right.
Comparing KLAT and KLAW: Both start with 'KL'. The third letter for KLAT is 'A' and for KLAW is 'A'. The fourth letter for KLAT is 'T' and for KLAW is 'W'. Since 'T' comes before 'W', KLAT comes before KLAW.
So the sorted list is:
There are 5 words in the sorted list. The middle word is the 3rd word.
The 3rd word in the sorted list is MLAK.
MLAK was formed by reversing the letters of KALM.
C) KALM is the original word corresponding to MLAK, which is the middle word in the alphabetically arranged list of reversed words.
The following table shows the population (in lakhs) of four cities (A, B, C and D) over the past four years. Study the table and answer the question.
| City's Name | 2018-19 (In lakhs) | 2020-21 (In lakhs) |
| A | 78 | 92 |
| B | 61 | 84 |
| C | 71 | 92 |
| D | 72 | 95 |
Which city has registered the highest percentage of population growth from 2018–19 to 2020–21?
To find the city with the highest percentage of population growth, we need to calculate the percentage growth for each city. The formula for percentage growth is:
\[ \text{Percentage Growth} = \frac{\text{Final Population} - \text{Initial Population}}{\text{Initial Population}} \times 100 \]
We will apply this formula to each city using the population data from 2018-19 (initial) and 2020-21 (final).
Initial Population (2018-19) = 78 lakhs
Final Population (2020-21) = 92 lakhs
\[ \text{Percentage Growth (A)} = \frac{92 - 78}{78} \times 100 = \frac{14}{78} \times 100 \approx 0.1795 \times 100 \approx 17.95\% \]
Initial Population (2018-19) = 61 lakhs
Final Population (2020-21) = 84 lakhs
\[ \text{Percentage Growth (B)} = \frac{84 - 61}{61} \times 100 = \frac{23}{61} \times 100 \approx 0.3770 \times 100 \approx 37.70\% \]
Initial Population (2018-19) = 71 lakhs
Final Population (2020-21) = 92 lakhs
\[ \text{Percentage Growth (C)} = \frac{92 - 71}{71} \times 100 = \frac{21}{71} \times 100 \approx 0.2958 \times 100 \approx 29.58\% \]
Initial Population (2018-19) = 72 lakhs
Final Population (2020-21) = 95 lakhs
\[ \text{Percentage Growth (D)} = \frac{95 - 72}{72} \times 100 = \frac{23}{72} \times 100 \approx 0.3194 \times 100 \approx 31.94\% \]
City B has the highest percentage growth.
Correct Option: B) City B has the highest percentage population growth of approximately \(37.70\%\).
Which of the following is a renewable source of energy?
Nuclear energy
Fossil fuel energy
Oil–coal energy
Biomass energy
The question asks to identify a renewable source of energy from the given options. We need to understand the definition of renewable and non-renewable energy sources and classify each option accordingly.
Correct Option: D) Biomass energy is derived from organic materials like plants and animal waste, which can be continuously replenished, making it a renewable source of energy.
The question asks about the tenure of a Panchayat as stipulated in Article 243 E of the Indian Constitution. This requires knowledge of the constitutional provisions related to Panchayati Raj institutions.
Correct Option: D) five
To find the third proportional to two numbers, say 'a' and 'b', we assume the third proportional is 'x'. The relationship for a third proportional is that 'a', 'b', and 'x' are in continuous proportion, meaning the ratio of the first to the second is equal to the ratio of the second to the third. This can be written as \(a : b :: b : x\), or \[\frac{a}{b} = \frac{b}{x}\].
Let the given numbers be \(a = 60\) and \(b = 90\).
Let the third proportional be \(x\).
According to the definition of a third proportional, the numbers \(a, b, x\) are in continuous proportion. This means:
\[ \frac{a}{b} = \frac{b}{x} \]Substitute the given values of \(a\) and \(b\) into the proportion:
\[ \frac{60}{90} = \frac{90}{x} \]Now, solve for \(x\). Cross-multiply the terms:
\[ 60 \times x = 90 \times 90 \]Calculate the product on the right side:
\[ 60x = 8100 \]Divide both sides by 60 to find \(x\):
\[ x = \frac{8100}{60} \]\[ x = \frac{810}{6} \]\[ x = 135 \]Thus, the third proportional to 60 and 90 is 135.
Correct Option: D) 135
The question asks for the headquarters of the State Bank of India (SBI). This is a factual question related to general knowledge about major Indian financial institutions. Knowing the headquarters of prominent banks and organizations is crucial for competitive exams.
Correct Option: D) Mumbai
The headquarters of the State Bank of India (SBI), India's largest public sector bank, is located in Mumbai, Maharashtra. Mumbai is often referred to as the financial capital of India, and many major banks, financial institutions, and the Bombay Stock Exchange (BSE) and National Stock Exchange (NSE) are based there.
The question describes a scenario where a point source of light produces a parallel beam after passing through an optical system. We need to identify which optical system (mirror or lens) can achieve this. This involves understanding the focusing and diverging properties of different optical elements, especially their behavior with light originating from their focal points.
Correct Option: C) either a concave mirror or a convex lens
To determine if an assumption is implicit, we must check if it is a necessary consequence or a direct underlying premise of the given statement. The statement only provides information about traffic diversion due to roadwork. We should not infer beyond what is directly stated or logically required for the statement to be true.
Neither assumption is a necessary condition or a direct logical consequence of the statement.
Correct Option: C) Neither assumption I nor II is implicit