To find the maximum value of 'p' for which the given eight-digit number is divisible by 6, we need to apply the divisibility rules for 6. A number is divisible by 6 if it is divisible by both 2 and 3. We will first use the divisibility rule for 2 to determine possible values for 'p', and then use the divisibility rule for 3 to narrow down the options and find the maximum value.
Correct Option: C) 7
If \(p=7\), the number becomes \(59044722\). The sum of its digits is \(5+9+0+4+4+7+2+2 = 33\), which is divisible by 3. The last digit is 2, so it's divisible by 2. Since it's divisible by both 2 and 3, it is divisible by 6. This is the maximum possible value for 'p'.
This is a syllogism problem. We need to evaluate the given conclusions based on the provided statements. We can use Venn diagrams or logical deduction to determine which conclusions logically follow.
C) Both conclusions (I) and (II) follow
This problem involves calculating the combined work rate of multiple taps filling and emptying a cistern. We will determine the individual rates of each tap and then combine them to find the net filling rate. The time taken to fill the cistern will be the reciprocal of this net rate.
Calculate the filling rate of the first tap:
The first tap fills the cistern in 2 hours. So, in 1 hour, it fills \(\frac{1}{2}\) of the cistern.
Calculate the filling rate of the second tap:
The second tap fills the cistern in 81 hours. So, in 1 hour, it fills \(\frac{1}{81}\) of the cistern.
Calculate the emptying rate of the third tap:
The third tap empties the cistern in 81 hours. So, in 1 hour, it empties \(\frac{1}{81}\) of the cistern. Since it's emptying, its contribution to filling is negative.
Calculate the net filling rate when all three taps are opened together:
The net rate is the sum of the filling rates minus the emptying rate.
Simplify the net filling rate:
The terms \(\frac{1}{81}\) and \(-\frac{1}{81}\) cancel each other out.
Calculate the total time to fill the cistern:
If the cistern fills \(\frac{1}{2}\) in 1 hour, then the total time to fill the entire cistern (which is 1 unit) is the reciprocal of the net filling rate.
D) 2
As calculated, the net filling rate is \(\frac{1}{2}\) of the cistern per hour, which means it will take 2 hours to fill the entire cistern.
The question asks to identify the state to which the folk dance 'Paika' belongs. This requires knowledge of Indian folk dances and their associated states.
Correct Option: B) Jharkhand. Paika is a famous martial folk dance of Jharkhand, where dancers use shields and swords, representing the bravery of warriors.
The question asks to identify the winner of the 2025 Pulitzer Prize for Poetry for the collection "New and Selected Poems". This requires knowledge of recent literary awards, specifically the Pulitzer Prize winners in the poetry category.
The Pulitzer Prizes are announced annually, typically in April, for works published in the preceding calendar year. For the 2025 awards, the prizes would be given for works published in 2024. However, it's important to note that the question might be hypothetical or refer to a future event, as the 2025 Pulitzer Prizes have not yet been announced as of the current date (late 2024).
Assuming the question refers to a hypothetical future award or a common knowledge fact about a poet's significant work:
Marie Howe is a highly acclaimed poet whose collection "New and Selected Poems" has garnered significant recognition. While the 2025 Pulitzer Prizes are in the future, Marie Howe's "New and Selected Poems" (published in 2023) was a finalist for the 2024 Pulitzer Prize for Poetry. This makes her a strong candidate for such an award in the future or a past award if the year is a typo. Given the options, Marie Howe is the most plausible choice associated with a "New and Selected Poems" collection receiving a major award.
Correct Option: C) Marie Howe
The question asks for an alternative name for "representative elements." This requires knowledge of the classification of elements in the periodic table.
Correct Option: C) Main group elements
The question asks about the official membership date of Algeria in the New Development Bank (NDB). This is a factual question requiring knowledge of recent international financial institution developments.
Correct Option: B) May 2025 is the officially announced date for Algeria's membership in the New Development Bank to become effective.
To evaluate the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform operations in the following order: Brackets (Parentheses), Orders (Exponents), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). We will start from the innermost brackets and work our way outwards.
First, evaluate the innermost parentheses: \((30 - 30 \times 4)\).
According to BODMAS, multiplication comes before subtraction.
\[ 30 \times 4 = 120 \]\[ 30 - 120 = -90 \]Substitute this value back into the expression:
\[ 30 - [30 - \{30 - (-90)\}] \]Next, evaluate the curly braces: \(\{30 - (-90)\}\).
Subtracting a negative number is equivalent to adding the positive number.
\[ 30 - (-90) = 30 + 90 = 120 \]Substitute this value back into the expression:
\[ 30 - [30 - 120] \]Now, evaluate the square brackets: \([30 - 120]\).
\[ 30 - 120 = -90 \]Finally, substitute this value back into the expression and perform the last subtraction:
\[ 30 - (-90) \]\[ 30 + 90 = 120 \]Thus, the value of the expression is 120.
C) 120 is the correct answer, as derived by following the order of operations.
The question asks to identify the Windows feature used for recovering accidentally deleted files. We need to evaluate each option based on its primary function in the Windows operating system.
Correct Option: A) Recycle Bin
The Recycle Bin is a temporary storage area for files and folders that have been deleted from the hard drive. When you delete a file, it is moved to the Recycle Bin, allowing you to restore it to its original location if needed. Files remain in the Recycle Bin until it is emptied manually or automatically when its size limit is reached.
Find the value of \(\sqrt{385+\sqrt{213+\sqrt{144}}}\).
To solve this problem, we need to evaluate the expression by simplifying it from the innermost square root outwards. This involves calculating the square root of perfect squares step-by-step.
The innermost term is \(\sqrt{144}\).
\[ \sqrt{144} = 12 \]Now substitute this value back into the expression:
\[ \sqrt{213+\sqrt{144}} = \sqrt{213+12} \] \[ = \sqrt{225} \]Now, calculate \(\sqrt{225}\):
\[ \sqrt{225} = 15 \]Finally, substitute this value back into the original expression:
\[ \sqrt{385+\sqrt{213+\sqrt{144}}} = \sqrt{385+15} \] \[ = \sqrt{400} \]Calculate \(\sqrt{400}\):
\[ \sqrt{400} = 20 \]Thus, the value of the given expression is 20.
Correct Option: B) 20