The question asks to identify which of the given options is NOT a part of the Local Government in India. This requires knowledge of the structure and components of local self-governance institutions in both rural and urban areas as defined by the Indian Constitution.
C) Development Authority: Development Authorities (e.g., Delhi Development Authority, Bangalore Development Authority) are statutory bodies created under specific state laws, primarily for planning, regulating, and promoting urban development in specific areas. While they perform functions related to urban planning and infrastructure, they are not part of the constitutionally mandated three-tier structure of local self-government (Panchayats or Municipalities). They operate alongside, but distinct from, the regular urban local bodies.
The question asks to identify which of the given options is NOT a hardware component of a computer. We need to understand the basic definitions of hardware and software in the context of a computer system.
Correct Option: C) Operating system is not a hardware component; it is a type of system software.
The question asks to identify the country that used Kuna as its currency as of 2021. This requires knowledge of international currencies and their respective countries.
Correct Option: B) Croatia
The Croatian Kuna (HRK) was the currency of Croatia from 1994 until January 1, 2023, when it was replaced by the Euro. Therefore, as of 2021, Kuna was indeed the currency of Croatia.
Find the value of sin 15°.
\(\frac{\sqrt{3}+1}{2\sqrt{2}}\)
\(\frac{\sqrt{3}-1}{2\sqrt{2}}\)
\(\frac{\sqrt{3}+1}{\sqrt{2}}\)
\(\frac{\sqrt{3}-1}{\sqrt{2}}\)
To find the value of \(\sin 15^{\circ}\), we can use the trigonometric identity for the sine of the difference of two angles: \(\sin(A - B) = \sin A \cos B - \cos A \sin B\). We need to choose angles A and B whose difference is \(15^{\circ}\) and for which we know the exact sine and cosine values. Common choices are \(45^{\circ}\) and \(30^{\circ}\).
B) \(\frac{\sqrt{3}-1}{2\sqrt{2}}\) is the correct value obtained from the calculation.
To solve this series, we need to identify the pattern in both the alphabetic and numeric parts of each cluster. We will analyze the progression of letters and numbers separately.
Correct Option: D) r25
This question tests knowledge of the constitutional powers of various high-ranking officials in the Indian political system, specifically concerning the Parliament. We need to identify which office holds the power to summon and prorogue the Houses of Parliament.
Correct Option: A) The President is vested with the constitutional power to summon and prorogue either house of the Indian Parliament as per Article 85(1) of the Constitution.
This problem involves work and time. We are given the relationship between the efficiencies of two individuals, Mohan and Kamlesh, and the time they take to complete a task together. We need to find the time Mohan takes to complete the task alone. We can solve this by expressing their individual work rates and then using the combined work rate formula.
Define work rates:
Let Mohan's one day's work be \(M\) and Kamlesh's one day's work be \(K\).
The problem states that Mohan is twice as good as Kamlesh. This means Mohan's work rate is twice Kamlesh's work rate.
Combined work rate:
Together, they finish the task in 22 days. This means their combined one day's work is \(\frac{1}{22}\) of the total task.
Substitute and solve for K:
Substitute \(M = 2K\) into the combined work rate equation:
Calculate Mohan's work rate (M):
Since \(M = 2K\):
Determine time taken by Mohan alone:
Mohan's one day's work is \(\frac{1}{33}\) of the task. This means Mohan alone can finish the task in 33 days.
C) 33 days. Based on our calculations, Mohan's one day's work is \(\frac{1}{33}\), so he can complete the task alone in 33 days.
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 second pair to find the missing word.
C) Education — A college is an institution primarily dedicated to providing education. Just as a court provides justice, a college provides education. This establishes the same functional relationship.
The question asks for the actual reason behind Lord Curzon's Partition of Bengal. This requires knowledge of British colonial policies and the political climate in India during the early 20th century, specifically Lord Curzon's tenure as Viceroy.
Correct Option: B) Divide and Rule Policy of the British.
The diameter of circle whose perimeter is 8.8 cm is ______. (π = \( \frac{22}{7} \))
The problem asks us to find the diameter of a circle given its perimeter (circumference). We will use the formula for the perimeter of a circle, which relates it to the radius, and then use the relationship between the radius and the diameter to find the diameter.
The perimeter (circumference) of a circle is given by the formula:
\[ P = 2 \pi r \]where \(P\) is the perimeter and \(r\) is the radius of the circle.
We are given that the perimeter \(P = 8.8 \text{ cm}\) and \( \pi = \frac{22}{7} \). Substitute these values into the formula:
\[ 8.8 = 2 \times \frac{22}{7} \times r \]First, simplify the right side:
\[ 8.8 = \frac{44}{7} \times r \]Now, isolate \(r\):
\[ r = 8.8 \times \frac{7}{44} \]Convert 8.8 to a fraction or decimal for calculation:
\[ r = \frac{88}{10} \times \frac{7}{44} \]Simplify the expression:
\[ r = \frac{2 \times 44}{10} \times \frac{7}{44} \]Cancel out 44:
\[ r = \frac{2 \times 7}{10} \]\[ r = \frac{14}{10} \]\[ r = 1.4 \text{ cm} \]The diameter of a circle is twice its radius:
\[ D = 2r \]Substitute the value of \(r\) we just found:
\[ D = 2 \times 1.4 \]\[ D = 2.8 \text{ cm} \]A) 2.8 cm is the calculated diameter of the circle.