To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS. This means we perform operations in the following order: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Thus, the value of the expression is 40.
A) 40 is the correct answer, as derived by following the order of operations.
The problem asks us to find the principal sum given the difference between compound interest (CI) and simple interest (SI) for two years at a specific rate. We can use the standard formulas for CI and SI and their difference for two years to solve this.
Identify the given values:
Recall the formula for Simple Interest (SI):
\[ \text{SI} = \frac{P \times R \times T}{100} \]where \(P\) is the principal sum.
Substitute the given values:
\[ \text{SI} = \frac{P \times 5 \times 2}{100} = \frac{10P}{100} = \frac{P}{10} \]
Recall the formula for Compound Interest (CI):
\[ \text{CI} = P \left[ \left(1 + \frac{R}{100}\right)^T - 1 \right] \]
Substitute the given values:
\[ \text{CI} = P \left[ \left(1 + \frac{5}{100}\right)^2 - 1 \right] \]\[ \text{CI} = P \left[ \left(1 + \frac{1}{20}\right)^2 - 1 \right] \]\[ \text{CI} = P \left[ \left(\frac{21}{20}\right)^2 - 1 \right] \]\[ \text{CI} = P \left[ \frac{441}{400} - 1 \right] \]\[ \text{CI} = P \left[ \frac{441 - 400}{400} \right] \]\[ \text{CI} = P \left[ \frac{41}{400} \right] = \frac{41P}{400} \]
Calculate the difference between CI and SI:
We are given that \(\text{CI} - \text{SI} = 1\).
Substitute the expressions for CI and SI:
\[ \frac{41P}{400} - \frac{P}{10} = 1 \]
Find a common denominator (400):
\[ \frac{41P}{400} - \frac{40P}{400} = 1 \]\[ \frac{41P - 40P}{400} = 1 \]\[ \frac{P}{400} = 1 \]
Solve for P:
\[ P = 1 \times 400 \]\[ P = 400 \]
Alternative formula for CI - SI for 2 years:
For 2 years, the difference between CI and SI is given by:
\[ \text{CI} - \text{SI} = P \left( \frac{R}{100} \right)^2 \]
Substitute the given values:
\[ 1 = P \left( \frac{5}{100} \right)^2 \]\[ 1 = P \left( \frac{1}{20} \right)^2 \]\[ 1 = P \left( \frac{1}{400} \right) \]\[ P = 400 \]
C) ₹400 is the correct sum.
A and B both working together can finish a task in 10 days. B and C both working together can finish the same task in 15 days. A and C both working together can finish the task in 20 days. In how many days can A, B and C working together finish this task?
9 \( \frac{3}{13} \) days
9 \( \frac{4}{13} \) days
9 \( \frac{1}{13} \) days
9 \( \frac{2}{13} \) days
This problem involves calculating the combined work rate of individuals. We will use the concept that if a person or a group can complete a task in 'n' days, their one-day work rate is \( \frac{1}{n} \) of the task. We will set up equations for the given pairs, sum them up to find the combined rate of A, B, and C, and then calculate the total time taken.
Determine the one-day work rates for each pair:
Sum the one-day work rates of all pairs:
Add Equation 1, Equation 2, and Equation 3:
Calculate the combined one-day work rate of A, B, and C:
Divide the sum by 2 to find the one-day work rate of A, B, and C together:
Determine the total time taken by A, B, and C together:
If their one-day work rate is \( \frac{13}{120} \), then they can finish the task in the reciprocal of this rate:
Convert the improper fraction to a mixed fraction:
A) 9 \( \frac{3}{13} \) days is the correct answer, as calculated above.
The question asks to identify the committee or commission concerned with Centre-State relations in India. This requires knowledge of various committees and their primary areas of focus.
Correct Option: D) Sarkaria Commission
The Sarkaria Commission was set up in 1983 by the central government to examine the relationship and balance of power between the Centre and State governments in India. Its mandate was to review the working of the Indian Constitution and suggest changes to improve Centre-State relations. The Commission submitted its report in 1987, making 247 recommendations on various aspects of Centre-State relations, many of which were later implemented.
The task is to identify the word that is different from the other three. This usually involves finding a common category or relationship among three words and identifying the one that does not fit.
C) Movie — 'Movie' is the general term for a film, while 'Action', 'Romance', and 'Comedy' are specific genres or types of movies. Hence, 'Movie' is the odd one out.
To find the gain percentage, we first need to calculate the actual gain (profit) by subtracting the cost price from the selling price. Then, we divide the gain by the cost price and multiply by 100 to express it as a percentage.
Identify the Cost Price (CP) and Selling Price (SP):
Calculate the Gain (Profit):
Gain is the difference between the Selling Price and the Cost Price.
\[ \text{Gain} = \text{SP} - \text{CP} \] \[ \text{Gain} = \text{₹}1,200 - \text{₹}1,000 \] \[ \text{Gain} = \text{₹}200 \]Calculate the Gain Percentage:
The gain percentage is calculated by dividing the gain by the cost price and multiplying by 100.
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100\% \] \[ \text{Gain Percentage} = \left( \frac{\text{₹}200}{\text{₹}1,000} \right) \times 100\% \] \[ \text{Gain Percentage} = \left( \frac{1}{5} \right) \times 100\% \] \[ \text{Gain Percentage} = 0.2 \times 100\% \] \[ \text{Gain Percentage} = 20\% \]Correct Option: B) The gain percentage is 20%. This is calculated by finding the profit (₹200) and dividing it by the cost price (₹1,000), then multiplying by 100.
The question asks to identify the river on which the Indira Sagar Dam is constructed. This requires knowledge of major dams and their associated rivers in India, a common topic in Indian competitive exams under Geography or General Knowledge sections.
D) Narmada — The Indira Sagar Dam is indeed built on the Narmada River. It is one of the largest dams in India, playing a crucial role in irrigation, power generation, and water supply in Madhya Pradesh.
Select the option that is related to the third term in the same way as the second term is related to the first term.
Horse : Stable :: Rabbit : ?
This is an analogy question where we need to find the relationship between the first pair of words and apply the same relationship to the third word to find the fourth word. The relationship here is between an animal and its dwelling place.
C) Burrow: A burrow is a hole or tunnel dug by a small animal, especially a rabbit, as a dwelling.
The question asks to identify the author of the seminal scientific work 'The Origin of Species'. This is a direct recall question from the history of science, specifically biology.
Correct Option: D) Charles Darwin
Charles Darwin (1809-1882) was an English naturalist and biologist known for his theory of evolution by natural selection. His groundbreaking work, 'On the Origin of Species', published in 1859, laid the foundation for evolutionary biology and explained how life on Earth has evolved over millions of years through a process of natural selection.
The question asks for the full form of the acronym DOS. This is a fundamental concept in computer science, specifically related to operating systems. Recalling common computer terminology will help identify the correct expansion.
Correct Option: D) Disk Operating System
DOS stands for Disk Operating System. It was one of the earliest and most widely used operating systems for personal computers, particularly during the 1980s and early 1990s. Its primary function was to manage disk storage, files, and other hardware resources, often through a command-line interface.