The problem presents a coding pattern where a given word is transformed into a coded word. We need to identify the rule governing this transformation and then apply the same rule to a new word to find its coded form.
D) TNEDUTS is the correct code for STUDENT, as it is the reverse of the original word.
The question asks to identify the state with the highest per capita income for the fiscal year 2018-19, according to the Ministry of Statistics and Programme Implementation. This requires knowledge of economic statistics released by government bodies.
C) Goa had the highest per capita income among the given options for the financial year 2018-19, as per the Ministry of Statistics and Programme Implementation.
The problem provides the ratio of the sides of a rectangular field and its area. We need to find the actual length and breadth of the field. We can use the given ratio to express the sides in terms of a common multiple, then use the area formula for a rectangle to solve for that multiple.
Define the sides using the given ratio:
The ratio of the sides (length : breadth) is given as 3 : 4. Let the length be \(3x\) and the breadth be \(4x\), where \(x\) is a common multiple.
Use the area formula:
The area of a rectangle is given by the formula: \(\text{Area} = \text{Length} \times \text{Breadth}\).
We are given that the area is 300 m².
Set up the equation:
Substitute the expressions for length and breadth into the area formula:
Solve for \(x\):
Multiply the terms on the left side:
Divide both sides by 12:
\[ x^2 = \frac{300}{12} \]\[ x^2 = 25 \]Take the square root of both sides:
\[ x = \sqrt{25} \]\[ x = 5 \](Since length and breadth must be positive, we take the positive square root.)
Calculate the length and breadth:
Substitute the value of \(x\) back into the expressions for length and breadth:
Wait, the question states the ratio of sides is 3:4. Typically, length is greater than breadth. So, if the ratio is 3:4, it implies that one side is 3 units and the other is 4 units. If we assume length is \(4x\) and breadth is \(3x\), then:
Let's check the options. Option D has 20 m and 15 m. The ratio 20:15 simplifies to 4:3. The problem states the ratio of sides is 3:4. This means the smaller side is 3 parts and the larger side is 4 parts. So, the length should be 20 m and breadth 15 m, or vice-versa. The options usually list (length, breadth) in that order, or just the two dimensions. If we take the sides as \(3x\) and \(4x\), then the dimensions are 15 m and 20 m. Option D lists 20 m, 15 m. This matches our calculated dimensions.
Verify the area:
Area \( = 20 \text{ m} \times 15 \text{ m} = 300 \text{ m}^2\). This matches the given area.
Correct Option: D) 20 m, 15 m
The question asks to identify which of the given options is NOT a terrestrial planet. To answer this, we need to recall the classification of planets in our solar system, specifically distinguishing between terrestrial (rocky) planets and gas giants (Jovian planets).
B) Uranus is an ice giant, which is a type of gas giant (Jovian planet), not a terrestrial planet. Terrestrial planets are rocky, while gas/ice giants are primarily composed of gases and ices with no solid surface.
The question asks to identify the component within a CPU that is responsible for coordinating all computer functions. This requires knowledge of the basic architecture and roles of different CPU components.
C) Control unit. The Control Unit (CU) is a vital component of the CPU that directs and coordinates all operations within the computer system. It interprets instructions, manages data flow between the CPU and other components, and ensures that all parts of the computer work together harmoniously to execute programs.
The question asks for the year in which the Air (Prevention and Control of Pollution) Act was introduced in India. This is a factual question related to environmental legislation in India, which is a common topic in competitive exams.
A) 1981: The Air (Prevention and Control of Pollution) Act was enacted in India in 1981. It provides for the prevention, control, and abatement of air pollution and for the establishment of Boards at the Central and State levels with a view to carrying out the purposes of the Act.
To find the distance covered by the train, we need to calculate the total time taken for the journey and then use the formula: \(\text{Distance} = \text{Speed} \times \text{Time}\).
Correct Option: C) 810 km
To find the average speed when an object travels different distances at different speeds, we use the formula: Average Speed = (Total Distance) / (Total Time). In this problem, the distance is divided into two equal halves, each covered at a different speed. We will calculate the time taken for each half and then sum them up to find the total time.
Let the total distance be \(D\) km. Since the car travels the first half and the remaining half, each half distance will be \(\frac{D}{2}\) km.
Speed for the first half (\(v_1\)) = 30 km/h.
Distance for the first half (\(d_1\)) = \(\frac{D}{2}\) km.
Time taken for the first half (\(t_1\)) is given by:
\[ t_1 = \frac{d_1}{v_1} = \frac{\frac{D}{2}}{30} = \frac{D}{60} \text{ hours} \]Speed for the second half (\(v_2\)) = 50 km/h.
Distance for the second half (\(d_2\)) = \(\frac{D}{2}\) km.
Time taken for the second half (\(t_2\)) is given by:
\[ t_2 = \frac{d_2}{v_2} = \frac{\frac{D}{2}}{50} = \frac{D}{100} \text{ hours} \]Total distance covered = \(D\) km.
Total time taken (\(T\)) = \(t_1 + t_2\):
\[ T = \frac{D}{60} + \frac{D}{100} \]To add these fractions, find a common denominator, which is 300:
\[ T = \frac{5D}{300} + \frac{3D}{300} = \frac{8D}{300} = \frac{2D}{75} \text{ hours} \]Average speed (\(v_{avg}\)) is Total Distance / Total Time:
\[ v_{avg} = \frac{D}{\frac{2D}{75}} = D \times \frac{75}{2D} = \frac{75}{2} \text{ km/h} \] \[ v_{avg} = 37.5 \text{ km/h} \]Alternatively, for two equal distances covered at speeds \(v_1\) and \(v_2\), the average speed can be calculated using the harmonic mean formula:
\[ v_{avg} = \frac{2v_1 v_2}{v_1 + v_2} \]Substituting the given values:
\[ v_{avg} = \frac{2 \times 30 \times 50}{30 + 50} = \frac{2 \times 1500}{80} = \frac{3000}{80} = \frac{300}{8} = 37.5 \text{ km/h} \]Correct Option: A) 37.5 km/h
Solve the following.
\(\left(\frac{2}{7}\times-\frac{3}{5}-\frac{1}{12}-\frac{3}{5}\times\frac{4}{7}\right)\) × 7 = ?
-\( \frac{251}{420} \)
-\( \frac{251}{209} \)
-\( \frac{251}{60} \)
-\( \frac{251}{210} \)
To solve this problem, we need to simplify the expression inside the parentheses first, following the order of operations (PEMDAS/BODMAS). We will combine the terms by finding a common denominator, then multiply the result by 7.
Identify the expression:
\[ \left(\frac{2}{7}\times-\frac{3}{5}-\frac{1}{12}-\frac{3}{5}\times\frac{4}{7}\right) \times 7 \]Perform the multiplications inside the parentheses first:
\[ \frac{2}{7}\times-\frac{3}{5} = -\frac{2 \times 3}{7 \times 5} = -\frac{6}{35} \]\[ -\frac{3}{5}\times\frac{4}{7} = -\frac{3 \times 4}{5 \times 7} = -\frac{12}{35} \]Substitute these values back into the expression:
\[ \left(-\frac{6}{35}-\frac{1}{12}-\frac{12}{35}\right) \times 7 \]Combine the terms with the same denominator:
\[ \left(-\frac{6}{35}-\frac{12}{35}-\frac{1}{12}\right) \times 7 \]\[ \left(-\frac{6+12}{35}-\frac{1}{12}\right) \times 7 \]\[ \left(-\frac{18}{35}-\frac{1}{12}\right) \times 7 \]Find a common denominator for \(35\) and \(12\). The least common multiple (LCM) of \(35\) and \(12\) is \(420\).
Convert the fractions to have the common denominator:
\[ -\frac{18}{35} = -\frac{18 \times 12}{35 \times 12} = -\frac{216}{420} \]\[ -\frac{1}{12} = -\frac{1 \times 35}{12 \times 35} = -\frac{35}{420} \]Substitute these back into the expression and combine:
\[ \left(-\frac{216}{420}-\frac{35}{420}\right) \times 7 \]\[ \left(-\frac{216+35}{420}\right) \times 7 \]\[ \left(-\frac{251}{420}\right) \times 7 \]Finally, multiply by \(7\):
\[ -\frac{251}{420} \times 7 \]\[ -\frac{251 \times 7}{420} \]Simplify the fraction. Notice that \(420 = 60 \times 7\). So, we can cancel out \(7\):
\[ -\frac{251}{60} \]Correct Option: C) \( -\frac{251}{60} \)
The question asks to identify the nature of Goods and Services Tax (GST). To answer this, one needs to understand the fundamental classification of taxes into direct and indirect categories.
A) indirect tax — GST is an indirect tax because its burden can be shifted from the seller to the final consumer. The seller collects the tax from the buyer and remits it to the government.