The question asks to identify the Indian state where the 'Moatsu' festival is celebrated. This requires knowledge of major festivals and their associated regions in India.
Correct Option: B) Nagaland
This problem involves calculating the annual rate of increase when production grows over a period, compounded annually. This is analogous to compound interest problems. We can use the compound interest formula to find the rate of increase.
The formula for compound interest (or growth compounded annually) is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]Divide both numerator and denominator by common factors. Both are divisible by 6:
\[ \frac{7986 \div 6}{6600 \div 6} = \frac{1331}{1100} \]So,
\[ \frac{1331}{1100} = \left(1 + \frac{R}{100}\right)^2 \]Wait, let's recheck the division. \(7986/6600 = 1.21\). This is a more direct approach.
\[ 1.21 = \left(1 + \frac{R}{100}\right)^2 \]Correct Option: C) 10%
To find the length of the sides of the square room, we first need to calculate the total area of the floor. This can be done by multiplying the number of tiles by the area of a single tile. Since the room is square, its area is the square of its side length. We will then take the square root of the total area to find the side length of the room. It's crucial to maintain consistent units throughout the calculation, converting centimeters to meters as needed.
Each tile is a square with a side of 50 cm.
\[ \text{Side of tile} = 50 \text{ cm} \]\[ \text{Area of one tile} = (\text{Side of tile})^2 = (50 \text{ cm})^2 = 2500 \text{ cm}^2 \]There are 784 such tiles.
\[ \text{Total area of floor} = \text{Number of tiles} \times \text{Area of one tile} \]\[ \text{Total area of floor} = 784 \times 2500 \text{ cm}^2 = 1,960,000 \text{ cm}^2 \]Since \(1 \text{ m} = 100 \text{ cm}\), then \(1 \text{ m}^2 = (100 \text{ cm})^2 = 10,000 \text{ cm}^2\).
\[ \text{Total area of floor in m}^2 = \frac{1,960,000 \text{ cm}^2}{10,000 \text{ cm}^2/\text{m}^2} = 196 \text{ m}^2 \]The room is square, so its area is \((\text{Side of room})^2\).
\[ (\text{Side of room})^2 = 196 \text{ m}^2 \]\[ \text{Side of room} = \sqrt{196 \text{ m}^2} = 14 \text{ m} \]Correct Option: B) 14 m
The question asks for the launch year of the Nano Mission (Mission on Nano Science and Technology) in India. This is a factual question related to government initiatives in science and technology. Recalling the specific year of its inception is key to answering this question.
Correct Option: A) The Nano Mission, a significant initiative by the Government of India to foster research and development in Nanoscience and Nanotechnology, was indeed launched in 2007. This program has been instrumental in positioning India among the top nations in nanoscience research.
This problem involves two trains moving towards each other. We can use the concept of relative speed or analyze the distance covered by each train over the same time period until they meet. Since one train travels 80 km more than the other, we can set up an equation based on the difference in distances covered and solve for the time taken to meet, and then calculate the total distance.
Let the speed of the first train be \(S_1 = 20 \text{ km/h}\).
Let the speed of the second train be \(S_2 = 25 \text{ km/h}\).
Let \(T\) be the time in hours until the two trains meet. Since they start at the same time and meet at a certain point, they travel for the same duration \(T\).
The distance covered by the first train in time \(T\) is \(D_1 = S_1 \times T = 20T \text{ km}\).
The distance covered by the second train in time \(T\) is \(D_2 = S_2 \times T = 25T \text{ km}\).
We are given that one train has travelled 80 km more than the other. Since \(S_2 > S_1\), the second train travels more distance than the first train. So, the difference in distances is:
\[ D_2 - D_1 = 80 \text{ km} \]Substitute the expressions for \(D_1\) and \(D_2\) into the equation:
\[ 25T - 20T = 80 \] \[ 5T = 80 \]Solve for \(T\):
\[ T = \frac{80}{5} \] \[ T = 16 \text{ hours} \]The total distance between the two stations is the sum of the distances covered by both trains until they meet:
\[ \text{Total Distance} = D_1 + D_2 \] \[ \text{Total Distance} = 20T + 25T \] \[ \text{Total Distance} = 45T \]Substitute the value of \(T = 16\) hours into the total distance equation:
\[ \text{Total Distance} = 45 \times 16 \] \[ \text{Total Distance} = 720 \text{ km} \]The question asks to identify the discoverer of the dwarf planet Pluto. This is a factual question related to astronomical discoveries. We need to recall the names of prominent astronomers and their contributions.
Correct Option: B) Clyde Tombaugh discovered Pluto in 1930. His discovery was a significant event in astronomy, though Pluto was later reclassified as a dwarf planet.
The problem asks us to find the value of an algebraic expression given the values of \(a\), \(b\), and \(c\) in terms of \(x\) and \(y\). The given expression \(a^{2} + b^{2} + c^{2} - 2ab + 2ac - 2bc\) resembles the expansion of a trinomial square. We will substitute the given values of \(a\), \(b\), and \(c\) into the expression and simplify it. Alternatively, we can recognize the pattern of the trinomial square formula.
Given:
\[ a = x + y \]\[ b = x - y \]\[ c = 2x - 1 \]We need to evaluate \( (a - b + c)^2 \). Substitute the given values into \( (a - b + c) \):\[ a - b + c = (x + y) - (x - y) + (2x - 1) \]B) \( (2x + 2y - 1)^{2} \)
As derived in the step-by-step solution, the given expression simplifies to \( (2x + 2y - 1)^{2} \).
This problem can be solved using the Pythagorean theorem. We are given the distance between the feet of two poles, the distance between their tops, and the height of the smaller pole. We need to find the height of the larger pole. We can visualize this as a right-angled triangle where the horizontal distance between the poles forms one leg, and the difference in their heights forms the other leg, with the distance between their tops as the hypotenuse.
Let the height of the small pole be \(h_1\) and the height of the big pole be \(h_2\).
Given:
Imagine a right-angled triangle formed by:
Apply the Pythagorean theorem:
\[ (\text{Difference in heights})^2 + (\text{Horizontal distance})^2 = (\text{Distance between tops})^2 \]\[ (h_2 - h_1)^2 + d^2 = L^2 \]
Substitute the given values into the equation:
\[ (h_2 - 10)^2 + (48)^2 = (50)^2 \]
Calculate the squares:
\[ (h_2 - 10)^2 + 2304 = 2500 \]
Isolate the term with the unknown height:
\[ (h_2 - 10)^2 = 2500 - 2304 \]
\[ (h_2 - 10)^2 = 196 \]
Take the square root of both sides:
\[ h_2 - 10 = \sqrt{196} \]
\[ h_2 - 10 = 14 \]
Solve for \(h_2\):
\[ h_2 = 14 + 10 \]
\[ h_2 = 24 \text{ m} \]
D) 24 m — The height of the big pole is found to be 24 m using the Pythagorean theorem, which correctly relates the horizontal distance, the difference in heights, and the distance between the tops of the poles.
The problem describes a scenario where an arithmetic operation was performed incorrectly, leading to a given result. We need to find the original number based on the incorrect operation and then calculate what the result should have been if the correct operation were performed.
Therefore, the actual answer should be 8.
C) 8 is the correct answer because the original number was 4, and multiplying 4 by 2 gives 8.
The question asks to identify the scientific field dedicated to the study of earthquakes. We need to recall the definitions of the given options to find the correct match.
Correct Option: D) Seismology is the scientific study of earthquakes and seismic waves.