The problem asks us to identify the odd one out from a given list of words. This is a classification type of question where we need to find a common characteristic among three words and identify the one that does not share that characteristic.
Correct Option: A) Umpire is the odd one out because it refers to a person (an official) while Pitch, Ground, and Boundary are all physical parts of a cricket playing field.
The question asks about the specific committee constituted by the Government when the population of a particular area exceeds 3 lakh (300,000). This relates to the structure of urban local self-government in India, particularly the provisions for Ward Committees.
Correct Option: D) Ward Committee
Article 243S of the 74th Constitutional Amendment Act mandates the constitution of Ward Committees for municipalities with a population of 3 lakh or more. These committees are formed for one or more wards within the municipal area to facilitate local governance and citizen participation at a more granular level.
This problem can be solved by setting up a system of two linear equations based on the given information: the sum of two numbers and their difference. We can then solve these equations simultaneously to find the values of the two numbers and identify the larger one.
\[\begin{align*} x + y &= 33 \ \label{eq:1} x - y &= 13 \ \label{eq:2}\end{align*}\]
Correct Option: A) 23
The question asks about the places linked by National Highway 1 (NH1) according to the old numbering system in India. This requires knowledge of the historical routes of major National Highways.
C) Delhi-Atari
National Highway 1 (NH1), under the old numbering system, connected Delhi to Atari, a town near the Wagah border with Pakistan in Punjab. This route was historically a part of the Grand Trunk Road.
The positive value of \(\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}\) is:
This problem involves an infinite nested square root expression. The key to solving such problems is to recognize that the expression repeats itself. By setting the entire expression equal to a variable, we can substitute the variable back into the expression to form a quadratic equation.
Correct Option: C) 3
To find the volume of the largest sphere that can be cut from a solid cube, we need to determine the relationship between the cube's side length and the sphere's diameter. The largest sphere that can be cut from a cube will have a diameter equal to the side length of the cube. Once the diameter is known, the radius can be calculated, and then the volume of the sphere can be found using the standard formula.
C) \(36\pi \text{ cm}^3\)
The calculations show that the volume of the largest sphere is \(36\pi \text{ cm}^3\).
We need to find the marks obtained by Ravi and Rajesh based on two given conditions: Ravi scored 8 marks more than Rajesh, and Ravi's marks were 52% of the sum of their marks. We can set up a system of two linear equations with two variables and solve for the marks.
Let Ravi's marks be \(R\) and Rajesh's marks be \(J\).
From the first condition, "Ravi obtained 8 marks more than Rajesh", we can write the equation:
\[ R = J + 8 \quad \text{(Equation 1)} \]From the second condition, "his marks (Ravi's marks) were 52% of the sum of their marks", we can write the equation:
\[ R = 0.52 \times (R + J) \quad \text{(Equation 2)} \]Now, substitute Equation 1 into Equation 2:
\[ J + 8 = 0.52 \times ((J + 8) + J) \]\[ J + 8 = 0.52 \times (2J + 8) \]Distribute 0.52 on the right side:
\[ J + 8 = 1.04J + 0.52 \times 8 \]\[ J + 8 = 1.04J + 4.16 \]Rearrange the terms to solve for \(J\):
\[ 8 - 4.16 = 1.04J - J \]\[ 3.84 = 0.04J \]Calculate \(J\):
\[ J = \frac{3.84}{0.04} \]\[ J = 96 \]Now that we have Rajesh's marks (\(J = 96\)), substitute this value back into Equation 1 to find Ravi's marks (\(R\)):
\[ R = J + 8 \]\[ R = 96 + 8 \]\[ R = 104 \]So, Ravi's marks are 104 and Rajesh's marks are 96.
Correct Option: C) 104, 96
The value of \(\frac{3.6\times0.48\times2.50}{0.12\times0.09\times0.5}\) is:
To solve this problem, we need to simplify the given expression by performing the multiplication in the numerator and the denominator separately, and then dividing the results. A common strategy for such problems is to remove decimal points by multiplying by appropriate powers of 10, or by converting decimals to fractions, to make calculations easier.
We can rewrite each decimal as a fraction or multiply numerator and denominator by powers of 10 to eliminate decimals. Let's count the decimal places:
Since the total number of decimal places in the numerator and denominator are the same, we can simply remove the decimal points and divide the numbers as integers, then adjust if necessary. Or, more formally, multiply the numerator and denominator by \(10^5\):
\[ \frac{3.6 \times 0.48 \times 2.50}{0.12 \times 0.09 \times 0.5} = \frac{(3.6 \times 10) \times (0.48 \times 100) \times (2.50 \times 100)}{(0.12 \times 100) \times (0.09 \times 100) \times (0.5 \times 10)} \times \frac{10^5}{10^5} \]This simplifies to:
\[ \frac{36 \times 48 \times 250}{12 \times 9 \times 5} \]Now substitute these simplified terms back into the expression:
\[ 3 \times \frac{48}{9} \times 50 = 3 \times \frac{16 \times 3}{3 \times 3} \times 50 = 3 \times \frac{16}{3} \times 50 \]Now, cancel the \(3\) in the numerator with the \(3\) in the denominator:
\[ 16 \times 50 \]D) 800
The question asks to identify the Indian state to which Kalbelia folk songs and dances belong. This is a direct knowledge-based question related to Indian culture and geography.
Correct Option: C) Rajasthan
The question asks for the full form of the acronym FCCB in the financial field. This is a direct knowledge-based question related to financial instruments.
Correct Option: D) Foreign Currency Convertible Bond