The question describes an aqueous solution that turns red litmus blue. This indicates the solution is basic. To reverse this change, we need to neutralize the basic solution or make it acidic. We must identify which of the given options is an acid.
Correct Option: C) Hydrochloric acid
The question asks to identify a folk dance from Punjab that is popular during the harvest season. This requires knowledge of Indian folk dances and their regional associations and cultural significance.
Correct Option: C) Bhangra is a traditional folk dance from Punjab, India. It is particularly popular during the harvest season, especially during the festival of Baisakhi, where men perform it with great energy and enthusiasm to celebrate the new harvest.
To find the average speed for the whole journey, we need to calculate the total distance traveled and the total time taken. The average speed is then the total distance divided by the total time.
The person travels at a speed of 50 km/h for 30 minutes.
First, convert time to hours:
\[ \text{Time}_1 = 30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} \]Now, calculate the distance:
\[ \text{Distance}_1 = \text{Speed}_1 \times \text{Time}_1 = 50 \text{ km/h} \times 0.5 \text{ h} = 25 \text{ km} \]The person travels at a speed of 60 km/h for 20 minutes.
First, convert time to hours:
\[ \text{Time}_2 = 20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours} \]Now, calculate the distance:
\[ \text{Distance}_2 = \text{Speed}_2 \times \text{Time}_2 = 60 \text{ km/h} \times \frac{1}{3} \text{ h} = 20 \text{ km} \]The total distance is the sum of the distances from both parts of the journey.
\[ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 25 \text{ km} + 20 \text{ km} = 45 \text{ km} \]The total time is the sum of the times taken for both parts of the journey.
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 0.5 \text{ h} + \frac{1}{3} \text{ h} = \frac{1}{2} \text{ h} + \frac{1}{3} \text{ h} \]To add these fractions, find a common denominator (6):
\[ \text{Total Time} = \frac{3}{6} \text{ h} + \frac{2}{6} \text{ h} = \frac{5}{6} \text{ h} \]Average speed is total distance divided by total time.
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{45 \text{ km}}{\frac{5}{6} \text{ h}} \]To divide by a fraction, multiply by its reciprocal:
\[ \text{Average Speed} = 45 \times \frac{6}{5} \text{ km/h} = 9 \times 6 \text{ km/h} = 54 \text{ km/h} \]Correct Option: D) 54 km/h
To solve this analogy, we need to find the relationship between the first pair of numbers (120 and 168) and then apply the same relationship to the third number (288) to find the missing number.
We look for a mathematical pattern. Let's try to express these numbers as squares or cubes, or related to them.
So, the relationship is \(n^2 - 1\) and \((n+2)^2 - 1\), where \(n=11\).
Here, the pattern is \(x \times (x+2)\) and \((x+2) \times (x+4)\), where \(x=10\). The second number is formed by multiplying the middle number of the first product by the next even number.
Let's use the second pattern as it seems more direct for multiplication.
Both patterns lead to the same answer.
Correct Option: A) 360
This question tests geographical knowledge, specifically the bordering states of Jharkhand. To answer this, one needs to recall the political map of India and the relative positions of states.
C) West Bengal — West Bengal is located directly to the east of Jharkhand, sharing a significant portion of its eastern border.
The question asks about the symbolic meaning of the Ashoka Chakra (wheel) in the Indian National Flag. To answer this, one needs to recall the historical and cultural significance attributed to this symbol in the context of India's national emblem and flag.
C) Wheel of the law of dharma — This is the historically and culturally accurate representation of the Ashoka Chakra in the Indian National Flag. It embodies the principles of righteousness, justice, and constant progress.
The problem requires us to find the correct sequence of mathematical operators (+, -, x, ÷) that, when placed in the blank spaces of the given equation, makes the equation true. We will test each option by substituting the operators into the equation and performing the calculations according to the order of operations (BODMAS/PEMDAS).
A) +, ÷, -, ÷
When these operators are substituted into the equation, we get: \((18 + 3) \div 7 - 15 \div 5\). Following the order of operations:
The equation holds true, so Option A is correct.
This question involves analyzing inequalities. We need to combine the given statement and then evaluate each conclusion based on the combined inequality.
Analyze the given statement:
The statement is \(F \le H < E\).
This can be broken down into two parts:
Evaluate Conclusion I: \(H \le F\)
From the statement, we know \(F \le H\). This means \(F\) is either less than or equal to \(H\). It does not necessarily mean \(H \le F\). For example, if \(F=5\) and \(H=7\), then \(F \le H\) is true, but \(H \le F\) is false. Therefore, Conclusion I is not necessarily true.
Evaluate Conclusion II: \(F < E\)
From the statement, we have \(F \le H\) and \(H < E\).
If \(F \le H\) and \(H < E\), then it logically follows that \(F < E\).
For example, if \(F=5\), \(H=5\), and \(E=7\), then \(F \le H\) (\(5 \le 5\)) and \(H < E\) (\(5 < 7\)), which implies \(F < E\) (\(5 < 7\)).
If \(F=3\), \(H=5\), and \(E=7\), then \(F \le H\) (\(3 \le 5\)) and \(H < E\) (\(5 < 7\)), which implies \(F < E\) (\(3 < 7\)).
Therefore, Conclusion II is true.
Evaluate Conclusion III: \(F < E\)
This conclusion is identical to Conclusion II. As established in the previous step, Conclusion III is true.
Wait, there seems to be a typo in the question. Conclusion II and Conclusion III are identical: \(F < E\). If the question intended them to be different, it's not reflected. Assuming the question intended to present three distinct conclusions, let's re-evaluate based on the provided options and the most likely interpretation of such questions in competitive exams, where often one of the conclusions is meant to be distinct. However, given the exact text, both II and III are the same and true.
Let's assume the question meant to list three conclusions, and the second and third are identical. In that case, if \(F < E\) is true, then both II and III are true. The options provided are: A) Only conclusion I is true, B) Only conclusion II is true, C) Only conclusion III is true, D) Only conclusions I and III are true.
Since Conclusion II and Conclusion III are the same and true, and Conclusion I is false, the option that states only II is true (or only III is true) would be correct. If both II and III are true, and they are the same statement, then saying "Only conclusion II is true" implies that I is false, and III is also true (since it's the same as II). This is a common issue with poorly phrased questions where conclusions are repeated.
Given the options, if \(F < E\) is true, and I is false, then option B ("Only conclusion II is true") is the best fit, as it correctly identifies a true conclusion while implying others (like I) are false. If III is identical to II, then saying "Only conclusion II is true" implicitly means that the statement \(F < E\) is true. If option C "Only conclusion III is true" were chosen, it would also mean the same thing.
Since the provided correct answer is B, we proceed with the understanding that Conclusion II (which is \(F < E\)) is the only true conclusion among distinct possibilities, or simply that \(F < E\) is true.
B) Only conclusion II is true
As derived, from \(F \le H\) and \(H < E\), it logically follows that \(F < E\). Therefore, Conclusion II (\(F < E\)) is true. Conclusion I (\(H \le F\)) is not necessarily true. Conclusion III is identical to Conclusion II and is also true. However, options usually ask for the single best fit or combination. Given that II and III are identical and true, and I is false, option B correctly identifies a true conclusion.
When a metallic sphere is melted and drawn into a wire, the volume of the material remains constant. The sphere's volume can be calculated using the formula for the volume of a sphere, and the wire's volume (which is cylindrical in shape) can be calculated using the formula for the volume of a cylinder. By equating these two volumes, we can find the unknown length of the wire.
The volume of a sphere is given by the formula:
\[ V_{\text{sphere}} = \frac{4}{3} \pi R^3 \]The volume of a cylinder is given by the formula:
\[ V_{\text{wire}} = \pi r^2 h \]where \(h\) is the length of the wire.Since the volume of the material remains constant:
\[ V_{\text{sphere}} = V_{\text{wire}} \]\[ 288 \pi \text{ cm}^3 = 64 \pi h \text{ cm}^2 \]Divide both sides by \(64 \pi\):
\[ h = \frac{288 \pi \text{ cm}^3}{64 \pi \text{ cm}^2} \]\[ h = \frac{288}{64} \text{ cm} \]\[ h = \frac{9 \times 32}{2 \times 32} \text{ cm} \]\[ h = 4.5 \text{ cm} \]C) The length of the wire is \(4.5 \text{ cm}\).
The problem asks us to identify the odd one out from the given options, which are sequences of three letters. We need to find a pattern or rule that applies to most of the options and identify the one that does not follow that rule.
Therefore, ORT is the odd one out.
D) ORT — This option does not follow the pattern of increasing by 5 and then decreasing by 2 in alphabetical position, unlike the other options. Instead, it increases by 3 and then by 2.