The question asks to identify the international organization responsible for the formulation and implementation of global trade rules. We need to recall the primary functions of each listed organization.
D) WTO (World Trade Organization) is the only organization among the choices whose primary mandate is the formulation and implementation of global trade rules, including negotiating trade agreements and resolving trade disputes.
The question asks for the population threshold that defines a "Mega City" according to the Census of India, 2011. This is a factual question based on demographic classifications used in Indian census reports.
Correct Option: A) 10
As per the Census of India, 2011, Urban Agglomerations with more than 10 million population are known as Mega Cities.
The question asks for the year when India launched its first sounding rocket, the Nike-Apache. This is a factual question related to the history of India's space program.
Correct Option: C) 1963
India launched its first sounding rocket, a Nike-Apache, on November 21, 1963, from the Thumba Equatorial Rocket Launching Station (TERLS) near Thiruvananthapuram, Kerala. This event is considered the beginning of the Indian space program, which later evolved into ISRO.
This problem involves calculating distance, speed, and time. We are given the speeds of two women and the time difference between them to cover the same distance. We can use the formula \(\text{Distance} = \text{Speed} \times \text{Time}\) to set up an equation and solve for the unknown distance.
Let the distance be \(D\) km.
The speed of the first woman is \(S_1 = 6\) km/h. The time taken by the first woman is \[T_1 = \frac{D}{S_1} = \frac{D}{6}\] hours.
The speed of the second woman is \(S_2 = 8\) km/h. The time taken by the second woman is \[T_2 = \frac{D}{S_2} = \frac{D}{8}\] hours.
We are given that the first woman takes 40 minutes more than the second woman. First, convert 40 minutes to hours:
\[ 40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours} \]Set up the equation based on the time difference:
\[ T_1 - T_2 = \frac{2}{3} \]\[ \frac{D}{6} - \frac{D}{8} = \frac{2}{3} \]Find a common denominator for the fractions on the left side, which is 24:
\[ \frac{4D}{24} - \frac{3D}{24} = \frac{2}{3} \]\[ \frac{D}{24} = \frac{2}{3} \]Solve for \(D\):
\[ D = \frac{2}{3} \times 24 \]\[ D = 2 \times 8 \]\[ D = 16 \text{ km} \]B) 16 km
The question asks to identify the organization responsible for air traffic and aeronautical communication services in Indian airspace. This requires knowledge of the regulatory bodies governing civil aviation in India.
D) Airports Authority of India is the correct answer. The Airports Authority of India (AAI) is responsible for creating, upgrading, maintaining, and managing civil aviation infrastructure in India. This includes providing Air Traffic Management (ATM) services, which encompass air traffic control and aeronautical communication services, over Indian airspace and adjoining oceanic areas.
The question asks about the nature of water as a resource. To answer this, we need to understand the characteristics of different types of resources, particularly in the context of their renewability and how they behave in natural cycles.
C) Cyclic — Water is a cyclic resource because it continuously moves through the Earth's systems (atmosphere, land, oceans) in the hydrological cycle, being evaporated, condensed, precipitated, and collected, thus being naturally renewed and reused.
To find the area of a triangle, we use the standard formula that relates its base and corresponding height. The problem provides both the length of one side (which can be considered the base) and the height perpendicular to that side.
Correct Option: B) 45 cm² is the correct area of the triangle calculated using the given base and height.
Area of an equilateral triangle is 49\(\sqrt{3}\) cm². Find the side of the triangle.
To find the side of an equilateral triangle given its area, we use the formula for the area of an equilateral triangle, which relates the area to the square of its side. We will set up an equation and solve for the side length.
Recall the formula for the area of an equilateral triangle. If 'a' is the side length of an equilateral triangle, its area (A) is given by:
\[ A = \frac{\sqrt{3}}{4} a^2 \]We are given that the area of the equilateral triangle is \(49\sqrt{3}\) cm\(^2\). Substitute this value into the formula:
\[ 49\sqrt{3} = \frac{\sqrt{3}}{4} a^2 \]To solve for \(a^2\), we can first cancel out \(\sqrt{3}\) from both sides of the equation:
\[ 49 = \frac{1}{4} a^2 \]Now, multiply both sides by 4 to isolate \(a^2\):
\[ 49 \times 4 = a^2 \]\[ a^2 = 196 \]Take the square root of both sides to find the value of 'a':
\[ a = \sqrt{196} \]\[ a = 14 \text{ cm} \]Thus, the side of the equilateral triangle is 14 cm.
B) 14 cm is the correct side length calculated from the given area.
If \(\sqrt{2}\) sin(5x-5)° = tan 45°, then the value of x (in degrees) is:
The problem requires us to find the value of \(x\) given a trigonometric equation. We will use the known value of \(\tan 45^\circ\) and then solve the resulting sine equation for \(x\).
We know that \(\tan 45^\circ = 1\).
The given equation is \(\sqrt{2} \sin(5x-5)^\circ = \tan 45^\circ\).
Substituting \(\tan 45^\circ = 1\) into the equation, we get:
\[ \sqrt{2} \sin(5x-5)^\circ = 1 \]Divide both sides by \(\sqrt{2}\):
\[ \sin(5x-5)^\circ = \frac{1}{\sqrt{2}} \]We know that \(\sin 45^\circ = \frac{1}{\sqrt{2}}\).
Therefore, we can equate the angles:
\[ (5x-5)^\circ = 45^\circ \]Remove the degree symbol for calculation:
\[ 5x - 5 = 45 \]C) The value of \(x\) is 10 degrees.
The question asks to identify the state that contributed more than one-third of India's total sugar production in the 2019-2020 season. This requires knowledge of agricultural statistics related to sugar production in India.
B) Uttar Pradesh: In the 2019-2020 sugar season, Uttar Pradesh was indeed the leading sugar-producing state in India, contributing more than one-third of the total national production. Its share was around 35-40%, making it the correct answer.