The question asks about the founding period of the World Bank. To answer this, one needs to recall the historical context of its establishment, specifically the major global events surrounding its creation.
Correct Option: D) During the Second World War
This problem involves calculating equal annual payments to discharge a debt with compound interest. We need to find the present value of each annual payment such that their sum equals the total debt amount due today. The formula for the present value of an amount \(P\) due after \(n\) years at a compound interest rate \(r\) is given by \(P = A / (1 + r)^n\), where \(A\) is the future value. In this case, each annual payment acts as a future value, and we need to find the payment amount \(x\).
Let the annual payment be ₹\(x\).
The debt is ₹1,025 due in 2 years at 5% compound interest per annum. We need to find the annual payment \(x\) that will discharge this debt.
The present value of the first payment (made at the end of the first year) is:
\[ \text{PV}_1 = \frac{x}{\left(1 + \frac{5}{100}\right)^1} = \frac{x}{1.05} \]The present value of the second payment (made at the end of the second year) is:
\[ \text{PV}_2 = \frac{x}{\left(1 + \frac{5}{100}\right)^2} = \frac{x}{(1.05)^2} \]The sum of the present values of these two payments must be equal to the total debt amount, which is ₹1,025.
\[ 1025 = \frac{x}{1.05} + \frac{x}{(1.05)^2} \]Now, we solve for \(x\):
\[ 1025 = x \left( \frac{1}{1.05} + \frac{1}{(1.05)^2} \right) \]\[ 1025 = x \left( \frac{1}{1.05} + \frac{1}{1.1025} \right) \]Calculate the terms inside the parenthesis:
\[ \frac{1}{1.05} \approx 0.95238 \]\[ \frac{1}{1.1025} \approx 0.90703 \]Add these values:
\[ 0.95238 + 0.90703 = 1.85941 \]Substitute back into the equation:
\[ 1025 = x \times 1.85941 \]Solve for \(x\):
\[ x = \frac{1025}{1.85941} \]\[ x \approx 551.249 \]Rounding to two decimal places, the annual payment is ₹551.25.
The calculation shows that an annual payment of ₹551.25 is required to discharge a debt of ₹1,025 over 2 years at 5% compound interest.
This question asks us to determine the relationship between two given statements about price changes. We need to analyze if one statement causes the other, if they are both effects of a common cause, or if they are independent events.
B) Both the statements are effects of independent causes. This is the most appropriate explanation. The market dynamics, supply and demand factors, and technological advancements affecting motorcycles are largely independent of those affecting laptops. Therefore, the price changes observed for each product are effects stemming from their own distinct causes.
The given series is an alternating series with a pattern involving multiplication and a simple arithmetic progression. We need to identify the two interleaved sub-series to find the missing number.
Correct Option: D) 384
This problem can be solved using the concept of weighted averages or by setting up an algebraic equation based on the amount of orange juice in each mixture. We will use the algebraic method, focusing on the total amount of orange juice.
Identify the knowns:
Define the unknown:
Calculate the amount of orange juice from each source:
Calculate the total volume and total orange juice in the final mixture:
Set up the equation based on the desired percentage:
The total amount of orange juice in the mixture should be \(60\%\) of the total volume.
\[ 0.80x + 9 = 0.60 (x + 36) \]Solve the equation for \(x\):
First, distribute \(0.60\) on the right side:
\[ 0.80x + 9 = 0.60x + (0.60 \times 36) \] \[ 0.80x + 9 = 0.60x + 21.6 \]Subtract \(0.60x\) from both sides:
\[ 0.80x - 0.60x + 9 = 21.6 \] \[ 0.20x + 9 = 21.6 \]Subtract \(9\) from both sides:
\[ 0.20x = 21.6 - 9 \] \[ 0.20x = 12.6 \]Divide by \(0.20\):
\[ x = \frac{12.6}{0.20} \] \[ x = \frac{126}{2} \] \[ x = 63 \]So, \(63\) litres of the 80% orange juice drink must be mixed.
Correct Option: C) 63 litres
The question asks to identify the individual who succeeded Pahlaj Nihalani as the Chairperson of the Central Board of Film Certification (CBFC). This is a factual question related to appointments in government bodies, common in competitive exams.
Correct Option: D) Prasoon Joshi was appointed as the Chairperson of the Central Board of Film Certification (CBFC) in August 2017, succeeding Pahlaj Nihalani. He is a well-known lyricist, poet, and advertising executive.
Select the diagram that best represents the relationship between the given set of classes.
Mammals, Amphibians, Turtles
To determine the correct diagram representing the relationship between the classes Mammals, Amphibians, and Turtles, we need to understand their biological classification and relationships. These groups are distinct classes within the animal kingdom.
Correct Option: A) The diagram with three separate shapes correctly represents the distinct nature of Mammals, Amphibians, and Turtles.
The question asks for the headquarters of the Wildlife Crime Control Bureau (WCCB). To answer this, one needs to recall the administrative details of this statutory body.
A) New Delhi is the correct answer. The headquarters of the Wildlife Crime Control Bureau (WCCB) is located in New Delhi.
To find out how many ice cubes can fit into the ice compartment, we need to calculate the volume of the ice compartment and the volume of a single ice cube. Then, we divide the volume of the compartment by the volume of one ice cube.
Therefore, the ice compartment can hold 20 ice cubes.
Correct Option: C) 20
The problem can be solved by setting up an algebraic equation based on the given information. We need to find an unknown number such that when 40 is subtracted from it, the result is 60% of the original number.
Let the unknown number be \(x\).
According to the problem statement, "When 40 is subtracted from a number", this can be written as \(x - 40\).
The problem also states that this result "reduces to its 60%". This means \(x - 40\) is equal to 60% of \(x\).
Convert 60% to a decimal or fraction: \(60\% = \frac{60}{100} = 0.6\).
Formulate the equation:
\[ x - 40 = 0.6x \]Now, solve for \(x\). Subtract \(0.6x\) from both sides of the equation:
\[ x - 0.6x - 40 = 0 \]Combine the \(x\) terms:
\[ 0.4x - 40 = 0 \]Add 40 to both sides:
\[ 0.4x = 40 \]Divide by 0.4 to find \(x\):
\[ x = \frac{40}{0.4} \]\[ x = \frac{40}{\frac{4}{10}} \]\[ x = 40 \times \frac{10}{4} \]\[ x = 10 \times 10 \]\[ x = 100 \]Thus, the number is 100.
Correct Option: B) 100
