The question asks about the authority responsible for the construction and maintenance of national highways in India. This falls under the jurisdiction of a specific level of government as per the Indian constitutional framework.
B) Central government is correct because national highways are a subject under the Union List, making the Central Government responsible for their construction and maintenance.
The question asks for the keyboard shortcut in Microsoft Word 2016 to remove paragraph formatting. This requires knowledge of common Word shortcuts.
In Microsoft Word, paragraph formatting includes attributes like indentation, line spacing, alignment, and space before/after paragraphs. To quickly revert these settings to their default or normal style, a specific shortcut is used.
B) Ctrl + Q is the correct shortcut to remove paragraph formatting in Microsoft Word 2016.
The question asks to identify the country where the Suez Canal, a vital waterway for global commerce, was constructed. This requires knowledge of world geography and significant historical infrastructure projects.
Correct Option: A) Egypt is the country where the Suez Canal was constructed and is located. It connects the Mediterranean Sea to the Red Sea, providing a vital shortcut for international maritime trade.
The problem involves arranging six persons in a row based on given conditions. We will use a step-by-step approach to deduce the seating arrangement and then identify the neighbours of O.
In both cases, the neighbours of O are D and E.
C) D and E — As determined in the step-by-step analysis, D and E are the persons sitting next to O.
The problem asks us to find the ratio \(a:b\) given a relationship between percentages of \(a\) and \(b\). We will convert the percentages into fractions and then rearrange the equation to express \(a/b\) as a single fraction, which directly gives us the ratio \(a:b\).
The problem states that "12% of a = 25% of b". We can write this mathematically as:
\[ 12\% \times a = 25\% \times b \]Recall that \(X\%\) can be written as \(\frac{X}{100}\). So, we convert the percentages:
\[ \frac{12}{100} \times a = \frac{25}{100} \times b \]We can multiply both sides of the equation by 100 to eliminate the denominators:
\[ 12a = 25b \]To find the ratio \(a:b\), we need to express \(\frac{a}{b}\). Divide both sides of the equation by \(b\) (assuming \(b \neq 0\)) and by 12:
\[ \frac{a}{b} = \frac{25}{12} \]The fraction \(\frac{25}{12}\) directly translates to the ratio \(25:12\).
Correct Option: C) 25 : 12
If 253.8 × 54.2 ÷ 56.4 = 25x, then the value of x is:
The problem involves simplifying an expression with exponents and then solving for an unknown variable \(x\). The key is to express all terms with the same base and then apply the rules of exponents: \(a^m \times a^n = a^{m+n}\) and \(a^m \div a^n = a^{m-n}\).
\[ (5^2)^{3.8} \times 5^{4.2} \div 5^{6.4} = (5^2)^x \]
\[ 5^{2 \times 3.8} \times 5^{4.2} \div 5^{6.4} = 5^{2x} \]
\[ 5^{7.6} \times 5^{4.2} \div 5^{6.4} = 5^{2x} \]
\[ 5^{7.6 + 4.2} \div 5^{6.4} = 5^{2x} \]
\[ 5^{11.8} \div 5^{6.4} = 5^{2x} \]
\[ 5^{11.8 - 6.4} = 5^{2x} \]
\[ 5^{5.4} = 5^{2x} \]
\[ 5.4 = 2x \]
\[ x = \frac{5.4}{2} \]
\[ x = 2.7 \]
A) 2.7 is the correct value for \(x\).
The problem asks us to identify the number that is different from the rest among a given set of four numbers. This type of question usually involves finding a common property or pattern shared by three of the numbers, while one number does not follow that pattern. Common patterns include prime/composite numbers, squares/cubes, even/odd numbers, divisibility rules, or sum of digits.
A) 81 — This is a composite number (\(9 \times 9\)), while the other three numbers (61, 83, 47) are prime numbers. This makes 81 the different number.
The question asks us to analyze two seemingly unrelated statements and determine if there's a cause-and-effect relationship, a common cause, or no relation between them. We need to evaluate each statement independently and then consider their potential connections.
C) Both the statements (I) and (II) are not related.
The question asks for the full form of the acronym GEO. This is a common acronym in the field of space technology and satellite communication, and knowing its full form is essential for competitive exams.
Correct Option: C) Geostationary Earth Orbit
GEO stands for Geostationary Earth Orbit. This is a specific type of high Earth orbit where a satellite moves in the same direction and at the same rate as the Earth's rotation, making it appear motionless relative to a fixed point on the ground. This characteristic makes GEO satellites ideal for communication, broadcasting, and meteorological applications.
This problem involves calculating the compound interest rate. We are given the principal amount, the final amount after a certain period, and the time duration. We will use the compound interest formula to find the annual interest rate.
The formula for the final amount \(A\) with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]Divide both sides by 10000:
\[ \frac{11025}{10000} = \left(1 + \frac{R}{100}\right)^2 \]\[ 1.1025 = \left(1 + \frac{R}{100}\right)^2 \]To find the value inside the parenthesis, take the square root of 1.1025:
\[ \sqrt{1.1025} = 1 + \frac{R}{100} \]\[ 1.05 = 1 + \frac{R}{100} \]Subtract 1 from both sides:
\[ 1.05 - 1 = \frac{R}{100} \]\[ 0.05 = \frac{R}{100} \]\[ R = 0.05 \times 100 \]\[ R = 5\% \]C) 5% — The calculated annual compound interest rate is 5%.