We are given three numbers in a specific ratio and their Least Common Multiple (LCM). We need to find their Highest Common Factor (HCF). We can represent the numbers using a common factor, which will be their HCF, and then use the property of LCM for numbers expressed in terms of their HCF.
Let the HCF of the three numbers be \(x\).
Since the numbers are in the ratio \(1 : 5 : 6\), we can express the numbers as \(1x\), \(5x\), and \(6x\).
Now, we need to find the LCM of these three numbers: \(x\), \(5x\), and \(6x\).
To find the LCM, we can factor out the common factor \(x\):
\[ \text{LCM}(x, 5x, 6x) = x \times \text{LCM}(1, 5, 6) \]Calculate the LCM of \(1, 5, 6\):
The LCM of \(1, 5, 6\) is the product of the highest powers of all prime factors involved, which is \(1 \times 2 \times 3 \times 5 = 30\).
So, the LCM of the three numbers \(x, 5x, 6x\) is \(x \times 30 = 30x\).
We are given that the LCM of the three numbers is \(5250\).
Therefore, we can set up the equation:
\[ 30x = 5250 \]Solve for \(x\):
\[ x = \frac{5250}{30} \]\[ x = \frac{525}{3} \]\[ x = 175 \]Since \(x\) represents the HCF of the three numbers, their HCF is \(175\).
Correct Option: B) 175
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others. We need to find the relationship between the letters in each pair based on their positions in the English alphabet.
B) FA-KQ — In this option, the difference between the first and second letters of the first cluster (F and A) is \(6 - 1 = 5\). The difference between the first and second letters of the second cluster (K and Q) is \(17 - 11 = 6\). This makes the pattern (5, 6). The other options follow a (4, 6) pattern.
The surface area of a sphere is 4π cm². The volume of the sphere is:
\(\frac{2\pi}{3}\) cm³
\(\frac{5\pi}{3}\) cm³
\(\frac{13\pi}{3}\) cm³
\(\frac{4\pi}{3}\) cm³
To find the volume of the sphere, we first need to determine its radius. We can do this by using the given surface area of the sphere and the formula for the surface area of a sphere. Once the radius is found, we can then calculate the volume using the formula for the volume of a sphere.
Recall the formula for the surface area of a sphere:
The surface area (\(A\)) of a sphere with radius \(r\) is given by:
Use the given surface area to find the radius:
We are given that the surface area \(A = 4\pi \text{ cm}^2\). Substitute this into the formula:
Solve for \(r^2\):
Divide both sides by \(4\pi\):
Find the radius \(r\):
Take the square root of both sides:
Recall the formula for the volume of a sphere:
The volume (\(V\)) of a sphere with radius \(r\) is given by:
Substitute the value of \(r\) into the volume formula:
Substitute \(r = 1 \text{ cm}\) into the volume formula:
D) The calculated volume of the sphere is \(\frac{4\pi}{3}\) cm³, which matches option D.
To find the number of laptop bags to be bought and sold to earn a specific profit, we first need to determine the cost price and selling price per laptop bag. Then, we calculate the profit per bag. Finally, we divide the target profit by the profit per bag to find the required number of bags.
The vendor buys 44 laptop bags for ₹48,884.
\[ \text{CP per bag} = \frac{\text{Total Cost}}{\text{Number of bags bought}} = \frac{48884}{44} = \text{₹}1111 \]The vendor sells 28 laptop bags for ₹35,252.
\[ \text{SP per bag} = \frac{\text{Total Selling Price}}{\text{Number of bags sold}} = \frac{35252}{28} = \text{₹}1259 \]Profit per bag is the difference between the selling price per bag and the cost price per bag.
\[ \text{Profit per bag} = \text{SP per bag} - \text{CP per bag} = 1259 - 1111 = \text{₹}148 \]The target profit is ₹6,956. To find the number of bags, divide the target profit by the profit per bag.
\[ \text{Number of bags} = \frac{\text{Target Profit}}{\text{Profit per bag}} = \frac{6956}{148} = 47 \]C) 47 is the correct answer. To earn a profit of ₹6,956, the vendor needs to buy and sell 47 laptop bags.
The question asks to identify the bank that launched the 'Global Women NRE & NRO Savings Account' in March 2025. This is a factual question related to current affairs and banking news.
Correct Option: B) Bank of Baroda launched the 'Global Women NRE & NRO Savings Account' in March 2025. This account is designed to cater to the unique banking needs of Non-Resident Indian (NRI) women, offering features such as zero balance banking, free international debit cards, and preferential rates on remittances.
The problem asks us to find a relationship between two sets of letters based on their positions in the English alphabet. We need to identify the pattern in the given pairs (KUQC to MYSG and OCUK to QGWO) and then apply the same pattern to SKYS to find the corresponding set of letters.
The pattern observed is \(+2, +4, +2, +4\) for consecutive letters.
The pattern \(+2, +4, +2, +4\) is consistently followed.
Thus, SKYS is related to UOAW.
Correct Option: B) UOAW
The question asks to identify the specific government body responsible for managing disinvestment in India. Disinvestment proceeds are a significant component of the government's non-tax revenue. Understanding the roles of various financial and economic institutions in India is crucial for answering this question.
C) DIPAM (Department of Investment and Public Asset Management) is the nodal agency of the Government of India under the Ministry of Finance responsible for managing government investments in public sector enterprises and assets, including strategic disinvestment and equity restructuring.
The question asks to identify which of the given options is NOT one of the Ettuttokai (Eight Anthologies) of Sangam literature. To answer this, one needs to know the names of the eight anthologies.
Tolkappiyam is a foundational work on Tamil grammar and poetics, attributed to Tolkappiyar. While it is a significant work of the Sangam period, it is not one of the Ettuttokai (Eight Anthologies). It is a separate grammatical treatise.
The question asks to identify the statement that best describes the roles of RAM (Random Access Memory) and ROM (Read-Only Memory) in a computer system. Understanding the fundamental characteristics and functions of these two types of memory is crucial.
Based on the evaluation, Option B provides the most accurate description.
B) ROM is used to store system firmware, while RAM stores temporary data for active processes. This statement correctly identifies that ROM stores essential, permanent instructions (like BIOS/UEFI) needed to start the computer, and RAM provides fast, temporary storage for the operating system, applications, and data that the CPU is currently working with.