This is a coding-decoding problem based on letter positions and arithmetic operations. We need to identify the pattern in the given relationships and then apply it to the target term.
The problem requires us to evaluate a given mathematical expression after interchanging certain operators. We need to replace '+' with 'โ', 'โ' with '+', 'ร' with 'รท', and 'รท' with 'ร'. After performing these substitutions, we will evaluate the new expression following the order of operations (BODMAS/PEMDAS).
C) 629 is the correct answer. After interchanging the operators and following the order of operations, the value of the expression is 629.
The question asks to identify the country where a presidential runoff election was held on April 13, 2025, leading to the re-election of President Daniel Noboa. This requires knowledge of recent political events and leaders in South American countries.
President Daniel Noboa is the current President of Ecuador. He was elected in a snap election in October 2023. While the question mentions a future date (April 13, 2025) for a runoff and re-election, the key identifier is President Daniel Noboa and the country he governs. The question likely refers to a hypothetical or anticipated future election based on his current presidency in Ecuador.
Therefore, the country associated with President Daniel Noboa is Ecuador.
A) Ecuador is the country where Daniel Noboa is the current president. Although the specific date of April 13, 2025, for a runoff and re-election is a future event, the association of President Daniel Noboa with Ecuador makes this the correct answer.
To find the curved surface area of a cone, we need its radius and slant height. The problem provides the area of the base and the slant height. We can use the base area to find the radius, and then use the formula for the curved surface area.
The base of a right circular cone is a circle. The area of the base is given as \(3136 \pi \text{ cm}^2\).
The formula for the area of a circle is \(A = \pi r^2\), where \(r\) is the radius.
\[ \pi r^2 = 3136 \pi \]Divide both sides by \(\pi\):
\[ r^2 = 3136 \]\[ r = \sqrt{3136} \]To find \(\sqrt{3136}\), we can recognize that \(50^2 = 2500\) and \(60^2 = 3600\). The number ends in 6, so the unit digit of its square root must be 4 or 6. Let's try 56:
\[ 56 \times 56 = 3136 \]\[ r = 56 \text{ cm} \]The slant height (\(l\)) is given as \(65 \text{ cm}\).
The formula for the curved surface area (CSA) of a cone is \(CSA = \pi r l\).
Substitute the values of \(r\) and \(l\):
\[ CSA = \pi \times 56 \times 65 \]A) \(3640\pi\) is the calculated curved surface area of the cone.
The question asks to identify the head of the Kayastha community during ancient and early medieval India. This requires knowledge of administrative and social structures, particularly the roles and designations of various officials and community leaders during that period.
Correct Option: B) Prathamakayastha
The Prathamakayastha was the chief of the Kayastha community, who were primarily scribes, record-keepers, and administrators. This position held significant influence in local administration, especially in managing land records and official documents.
This question tests the fundamental properties of angles formed when a transversal line intersects two parallel lines. We need to recall the definitions and relationships between different types of angles, specifically corresponding angles.
Correct Option: C) equal
The question asks for the keyboard shortcut to open an existing MS PowerPoint file. This is a common function across many applications, and the shortcut keys are often standardized.
Correct Option: C) Ctrl + O is the standard shortcut used to open an existing file in most Microsoft Office applications, including MS PowerPoint.
This problem involves substituting given symbols with their corresponding mathematical operators and then evaluating the expression to find which one results in 182. We need to follow the order of operations (BODMAS/PEMDAS) while evaluating each option.
First, let's list the given substitutions:
Now, we will evaluate each option:
Substitute the symbols:
\[ 96 \times 16 + 112 - 48 \div 6 \]Following BODMAS:
So, the result for Option A is 1640.
Substitute the symbols:
\[ 96 + 16 \times 112 \div 48 - 6 \]Following BODMAS:
So, the result for Option B is approximately 127.33.
Substitute the symbols:
\[ 96 \div 16 - 112 + 48 \times 6 \]Following BODMAS:
So, the result for Option C is 182.
Substitute the symbols:
\[ 96 - 16 \div 112 \times 48 + 6 \]Following BODMAS:
So, the result for Option D is approximately 95.14.
C) 96 P 16 S 112 R 48 Q 6. When evaluated, this expression yields 182, which matches the target value.
To find the population after two years, we need to calculate the population increase for each year sequentially. First, calculate the population after the 5% increase in the first year. Then, use this new population as the base for calculating the 20% increase in the second year.
The initial population of the village is \(1,00,000\).
The population increased by 5% in the first year.
\[ \text{Increase in first year} = 5\% \text{ of } 1,00,000 = \frac{5}{100} \times 1,00,000 = 5,000 \]Population after the first year:
\[ \text{Population}_1 = 1,00,000 + 5,000 = 1,05,000 \]The population increased by 20% in the second year. This increase is calculated on the population at the end of the first year, which is \(1,05,000\).
\[ \text{Increase in second year} = 20\% \text{ of } 1,05,000 = \frac{20}{100} \times 1,05,000 = 21,000 \]Population after the second year:
\[ \text{Population}_2 = 1,05,000 + 21,000 = 1,26,000 \]Alternatively, we can use the multiplicative factor method:
Population after 1st year = Initial Population \(\times (1 + \text{percentage increase}/100)\)
Population after 2nd year = Population after 1st year \(\times (1 + \text{percentage increase}/100)\)
\[ \text{Population after 2 years} = 1,00,000 \times \left(1 + \frac{5}{100}\right) \times \left(1 + \frac{20}{100}\right) \] \[ = 1,00,000 \times \left(\frac{105}{100}\right) \times \left(\frac{120}{100}\right) \] \[ = 1,00,000 \times 1.05 \times 1.20 \] \[ = 1,00,000 \times 1.26 \] \[ = 1,26,000 \]Thus, the population after two years is \(1,26,000\).
Correct Option: A) 1,26,000
This problem can be solved by setting up a system of two linear equations based on the given information about the brother's and sister's ages. We will assign variables to their current ages and then solve the system of equations simultaneously to find their individual ages. Finally, we will calculate the difference between their ages.
Define variables:
Let \(B\) be the present age of the brother.
Let \(S\) be the present age of the sister.
Formulate the first equation:
The first statement says: "3 times the brother's present age is 25 years more than 5 times his sister's age."
This can be written as:
Formulate the second equation:
The second statement says: "5 times the sister's age is 5 years less than the brother's age."
This can be written as:
Solve the system of equations:
From Equation 2, we can express \(B\) in terms of \(S\):
Now, substitute this expression for \(B\) into Equation 1:
\[ 3(5S + 5) = 5S + 25 \]Distribute the 3:
\[ 15S + 15 = 5S + 25 \]Subtract \(5S\) from both sides:
\[ 10S + 15 = 25 \]Subtract 15 from both sides:
\[ 10S = 10 \]Divide by 10 to find \(S\):
\[ S = 1 \]Now substitute the value of \(S\) back into the expression for \(B\) (or Equation 2):
\[ B = 5(1) + 5 \] \[ B = 5 + 5 \] \[ B = 10 \]So, the brother's age is 10 years and the sister's age is 1 year.
Calculate the difference in ages:
The difference between their present ages is \(B - S\):
Correct Option: D) 9