To find the smallest number which, when increased by 3, is divisible by 27, 35, 25, and 21, we first need to find the Least Common Multiple (LCM) of these four numbers. The LCM will be the smallest number that is perfectly divisible by all of them. Once we have the LCM, the required number will be LCM - 3.
To find the LCM, we take the highest power of all prime factors present in the numbers.
\[ \text{LCM}(27, 35, 25, 21) = 3^3 \times 5^2 \times 7^1 \]\[ \text{LCM} = 27 \times 25 \times 7 \]\[ \text{LCM} = 675 \times 7 \]\[ \text{LCM} = 4725 \]The question states that when the required number is increased by 3, it becomes divisible by 27, 35, 25, and 21. This means that the required number plus 3 is equal to the LCM.
\[ \text{Required Number} + 3 = \text{LCM} \]\[ \text{Required Number} + 3 = 4725 \]\[ \text{Required Number} = 4725 - 3 \]\[ \text{Required Number} = 4722 \]Correct Option: D) 4722
When 4722 is increased by 3, it becomes 4725, which is the LCM of 27, 35, 25, and 21, and is therefore divisible by all of them.
The question asks for the full form of DHCP in a networking system. This is a direct recall question related to common networking protocols. Understanding the purpose of DHCP can help in identifying its full form.
Correct Option: A) Dynamic Host Configuration Protocol
DHCP stands for Dynamic Host Configuration Protocol. It is a network management protocol used on Internet Protocol (IP) networks for automatically assigning IP addresses and other communication parameters to devices connected to the network. This automation simplifies network administration by eliminating the need for manual IP address configuration for each device.
The Coefficient of Variation (C.V.) is a measure of relative variability. It expresses the standard deviation as a percentage of the mean. This allows for comparison of variability between different data sets, even if they have different units or vastly different means.
Mean \((\bar{x})\) = 40
Standard Deviation \((\sigma)\) = 5
The formula to calculate the Coefficient of Variation is:
\[ \text{C.V.} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100\% \]D) 12.5% is the correct answer, as calculated by dividing the standard deviation by the mean and multiplying by 100%.
The question asks to identify India's longest road-cum-rail bridge that connects Assam and Arunachal Pradesh. This requires knowledge of major infrastructure projects in India.
The Bogibeel Bridge is a significant infrastructure project in India, known for being the longest rail-cum-road bridge in the country. It spans the Brahmaputra River and connects the Dibrugarh district in Assam to Dhemaji district in Arunachal Pradesh.
D) Bogibeel Bridge — The Bogibeel Bridge is indeed India's longest road-cum-rail bridge, spanning 4.94 km over the Brahmaputra River. It connects Dibrugarh in Assam to Dhemaji in Arunachal Pradesh, significantly reducing travel time and distance between the two states.
This is a blood relation question. We need to establish the relationships between the individuals mentioned and then determine how D is related to C. We can use a family tree or symbolic representation to visualize the relationships.
Correct Option: B) Aunt. D is the wife of A, and A is the brother of B, who is the father of C. Therefore, A is C's uncle, and D, being A's wife, is C's aunt.
The problem asks us to find the letter-cluster that has the same relationship with "GHIJ" as "ZYXW" has with "ABCD". This is a letter-analogy question where we need to identify the pattern or rule connecting the first pair of letter-clusters and then apply that same rule to the third letter-cluster to find the fourth one.
Correct Option: A) TSRQ is the letter-cluster that follows the same pattern.
When two items are sold at the same price, and one is sold at a certain percentage gain while the other is sold at the same percentage loss, there is always a net loss. The percentage loss can be calculated using a specific formula or by finding the cost price and total cost/selling price.
Identify given values:
Calculate the Cost Price (CP) of the first toy:
Let \( \text{CP}_1 \) be the cost price of the first toy.
Since there is a 10% gain:
\[ \text{SP}_1 = \text{CP}_1 + 0.10 \times \text{CP}_1 = 1.10 \times \text{CP}_1 \] \[ 990 = 1.10 \times \text{CP}_1 \] \[ \text{CP}_1 = \frac{990}{1.10} = \frac{9900}{11} = 900 \]So, the cost price of the first toy is ₹900.
Calculate the Cost Price (CP) of the second toy:
Let \( \text{CP}_2 \) be the cost price of the second toy.
Since there is a 10% loss:
\[ \text{SP}_2 = \text{CP}_2 - 0.10 \times \text{CP}_2 = 0.90 \times \text{CP}_2 \] \[ 990 = 0.90 \times \text{CP}_2 \] \[ \text{CP}_2 = \frac{990}{0.90} = \frac{9900}{9} = 1100 \]So, the cost price of the second toy is ₹1100.
Calculate the Total Selling Price (Total SP):
\[ \text{Total SP} = \text{SP}_1 + \text{SP}_2 = 990 + 990 = 1980 \]Calculate the Total Cost Price (Total CP):
\[ \text{Total CP} = \text{CP}_1 + \text{CP}_2 = 900 + 1100 = 2000 \]Determine the total gain or loss:
Since Total CP (₹2000) > Total SP (₹1980), there is a loss.
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 2000 - 1980 = 20 \]Calculate the percentage loss:
\[ \text{Percentage Loss} = \frac{\text{Loss}}{\text{Total CP}} \times 100 \] \[ \text{Percentage Loss} = \frac{20}{2000} \times 100 = \frac{1}{100} \times 100 = 1\% \]Alternatively, for cases where selling price is the same and percentage gain/loss is equal, the overall percentage loss can be found using the formula:
\[ \text{Percentage Loss} = \left(\frac{\text{Common Percentage}}{10}\right)^2 \]Here, the common percentage is 10%.
\[ \text{Percentage Loss} = \left(\frac{10}{10}\right)^2 = (1)^2 = 1\% \]B) 1% Loss
The question asks to identify the welfare scheme whose achievements have been recognized by the Guinness World Records. This requires knowledge of the specific accomplishments of various government schemes.
A) Pradhan Mantri Jan Dhan Yojana. This scheme holds a Guinness World Record for opening the most bank accounts in one week as part of a financial inclusion campaign.
This question tests knowledge about the geographical locations of various National Parks and Wildlife Sanctuaries in India. To answer correctly, one must identify which of the given protected areas is located in Jammu and Kashmir.
Correct Option: A) Dachigam National Park is situated in Jammu and Kashmir.