The question asks to identify the incorrect statement about the modern periodic table. We need to evaluate each option based on the established structure and principles of the modern periodic table.
Based on the analysis, statement B is the incorrect one.
B) Period 1 has only one element — This statement is incorrect. Period 1 of the modern periodic table contains two elements: Hydrogen (H) and Helium (He).
The question asks about the effect of friction on screws, ball bearings, and shoe soles. We need to understand the nature of friction and its common consequences on materials that experience it.
Correct Option: D) Friction wears out these materials and damages them
To find the greatest number that divides 115, 149, and 183 leaving specific remainders (3, 5, and 7 respectively), we first subtract the remainders from the original numbers. The resulting numbers will be perfectly divisible by the required greatest number. Therefore, the problem reduces to finding the HCF (Highest Common Factor) of these new numbers.
D) 16 is the greatest number that divides 115, 149, and 183 leaving remainders 3, 5, and 7 respectively.
Convert into vulgar fraction: 4.1\(\overline{2}\)
\(\frac{371}{900}\)
\(\frac{299}{121}\)
4\( \frac{11}{90} \)
4\( \frac{11}{99} \)
To convert a recurring decimal into a vulgar fraction, we separate the non-recurring and recurring parts. We can express the given number as a sum of its integer part and its decimal part, and then convert the decimal part into a fraction using a standard method for recurring decimals.
The given number is \(4.1\overline{2}\). We can write this as:
\[ 4.1\overline{2} = 4 + 0.1\overline{2} \]Let \(x = 0.1\overline{2}\). This means \(x = 0.1222...\)
Multiply by 10 to move the non-recurring digit to the left of the decimal point:
\[ 10x = 1.222... \quad \text{(Equation 1)} \]Multiply by 100 to move one block of the recurring digits to the left of the decimal point:
\[ 100x = 12.222... \quad \text{(Equation 2)} \]Subtracting the two equations eliminates the recurring part:
\[ 100x - 10x = 12.222... - 1.222... \]\[ 90x = 11 \]Divide by 90 to find the fractional value of \(x\):
\[ x = \frac{11}{90} \]Now, substitute the value of \(x\) back into the expression from Step 1:
\[ 4.1\overline{2} = 4 + \frac{11}{90} \]\[ 4.1\overline{2} = 4\frac{11}{90} \]C) \(4\frac{11}{90}\) is the correct conversion of \(4.1\overline{2}\) into a mixed vulgar fraction.
To determine the number by which the product of four consecutive numbers is always divisible, we can use the properties of divisibility and factorials, or test with a few examples.
Thus, the product of four consecutive numbers is always divisible by 24.
Correct Option: A) 24 is the number by which the product of four consecutive numbers is always divisible.
The question asks to identify the award received by Virat Kohli and Mirabai Chanu in September 2018. This requires knowledge of major sports awards in India and their recipients in specific years.
Correct Option: B) Rajiv Gandhi Khel Ratna Award
Virat Kohli (Cricket) and Mirabai Chanu (Weightlifting) were jointly awarded the Rajiv Gandhi Khel Ratna Award in September 2018 for their outstanding achievements in their respective sports. This is India's highest sporting honor.
This is a coding-decoding problem where each letter is assigned a unique numerical code. We need to identify the pattern of coding from the given words and then apply it to the target word 'ASSIST'.
Correct Option: C) 466765
The problem asks us to evaluate two conclusions based on a given statement. We need to determine which conclusion(s) logically follow from the statement. The statement indicates a disparity between the increasing domestic demand for crude oil and the slower increase in indigenous production.
Analyze the Statement: The statement is: "Domestic demand has been increasing faster than the production of indigenous crude oil." This implies that the supply from indigenous production is not keeping pace with the domestic demand. In other words, there is a growing gap between demand and indigenous supply.
Evaluate Conclusion I: "Crude oil must be imported if the demand has to be met." If domestic production cannot meet the increasing demand, then to satisfy that demand, the deficit must be covered by an external source. Importing crude oil is the logical way to cover this deficit. Therefore, this conclusion logically follows from the statement.
Evaluate Conclusion II: "Domestic demand should be reduced." While reducing demand might be a possible solution to the problem of unmet demand, the statement itself only describes a situation (demand increasing faster than production). It does not provide any information or justification to conclude that demand *should* be reduced. This is a prescriptive statement (what *should* be done), whereas the original statement is descriptive. There might be other ways to address the gap, such as increasing indigenous production faster, or importing. The conclusion that demand *should* be reduced is an opinion or a policy suggestion, not a direct logical inference from the given factual statement. Therefore, this conclusion does not logically follow from the statement alone.
Combine the evaluations: Only Conclusion I logically follows from the given statement.
D) Only conclusion I follows
Conclusion I is a direct and necessary consequence of the statement. If demand is increasing faster than production, and the demand needs to be met, then the only way to bridge the gap is through imports.
A) Both conclusions I and II follow — This is incorrect because Conclusion II does not logically follow. Reducing demand is a potential solution, but not a logical necessity derived solely from the statement.
B) Only conclusion II follows — This is incorrect because Conclusion I logically follows, and Conclusion II does not.
C) Either conclusion I or II follows — This is incorrect. Conclusion I definitely follows, but Conclusion II does not. The word "either" implies that both are valid possibilities, which is not the case for Conclusion II.
Find the square root of \(\frac{x^2}{y^2}+\frac{y^2}{x^2}-2\)
\(\frac{x}{2y}+\frac{y}{2x}\)
\(\frac{x}{y}-\frac{y}{x}\)
\(\frac{x-y}{2}\)
\(\frac{x}{y}+\frac{y}{x}\)
The problem asks us to find the square root of a given algebraic expression. We can simplify the expression by recognizing it as a perfect square trinomial, specifically of the form \((a-b)^2 = a^2 - 2ab + b^2\).
Let the given expression be \(E\):
\[ E = \frac{x^2}{y^2} + \frac{y^2}{x^2} - 2 \]We can rewrite the terms in the expression to match the form \(a^2 + b^2 - 2ab\). Let \(a = \frac{x}{y}\) and \(b = \frac{y}{x}\).
Then, \[a^2 = \left(\frac{x}{y}\right)^2 = \frac{x^2}{y^2}\] and \[b^2 = \left(\frac{y}{x}\right)^2 = \frac{y^2}{x^2}\].
Now, let's calculate \(2ab\):
\[ 2ab = 2 \left(\frac{x}{y}\right) \left(\frac{y}{x}\right) = 2 \left(\frac{xy}{yx}\right) = 2(1) = 2 \]Substitute these back into the expression \(E\):
\[ E = \frac{x^2}{y^2} + \frac{y^2}{x^2} - 2 = \left(\frac{x}{y}\right)^2 + \left(\frac{y}{x}\right)^2 - 2 \left(\frac{x}{y}\right) \left(\frac{y}{x}\right) \]This is exactly the expansion of \((a-b)^2\), so we can write:
\[ E = \left(\frac{x}{y} - \frac{y}{x}\right)^2 \]The problem asks for the square root of this expression. Therefore, we need to find \(\sqrt{E}\):
\[ \sqrt{E} = \sqrt{\left(\frac{x}{y} - \frac{y}{x}\right)^2} \]The square root of a square is the absolute value of the term inside, i.e., \(\sqrt{k^2} = |k|\). However, in competitive exams, when not specified, the positive square root is generally implied, and the options usually provide the direct term. Thus, we take:
\[ \sqrt{E} = \frac{x}{y} - \frac{y}{x} \]B) \[\frac{x}{y}-\frac{y}{x}\] is the correct square root of the given expression, as derived by recognizing the perfect square trinomial.