The problem involves identifying a pattern in letter relationships based on their positions in the English alphabet. We need to find the numerical shift for each letter from the first word to the second word in the given pairs. Once the pattern is established, apply the same pattern to the third word to find its related word.
The pattern for the first pair is a uniform shift of +3 for each letter.
The pattern for the second pair is also a uniform shift of +3 for each letter.
Since both given pairs follow a +3 shift for each letter, we apply the same logic to SCHQ.
Therefore, SCHQ is related to VFKT.
Correct Option: C) VFKT
The mode of a set of observations is the value that appears most frequently in the data set. To find the mode, we need to count the occurrences of each distinct observation.
Correct Option: B) 32 is the mode because it occurs 5 times, which is the highest frequency among all the observations.
To solve this number series problem, we need to identify the pattern or rule governing the sequence of numbers. We will calculate the differences between consecutive terms to find a consistent arithmetic or geometric progression, or a pattern of differences.
C) 228 is the correct answer because it fits the established pattern where the differences between consecutive terms increase by 10 each time.
The question asks to identify the Indian bank that introduced "Embassy Deposits" specifically for diplomats and diplomatic missions. This is a factual question related to recent banking news or product launches.
Based on financial news and banking product launches, HDFC Bank has indeed introduced such a scheme.
A) HDFC Bank — HDFC Bank launched "Embassy Deposits" in March 2024 (the question mentions March 2025, which could be a forward-looking statement or a typo, but the product launch by HDFC Bank for this specific segment is a known fact from March 2024). This scheme is exclusively designed for foreign embassies, consulates, and their staff in India, offering tailored financial services.
The problem requires us to modify a given number based on specific rules for its odd and even digits. First, we need to identify each digit in the original number and determine if it's odd or even. Then, we apply the given operations (add 1 to odd digits, subtract 2 from even digits) to form a new set of digits. Finally, we find the highest and lowest digits in this new set and calculate their difference.
The difference between the highest and lowest digits in the number thus formed is 6.
D) 6 — As calculated, the highest digit in the new number is 8 and the lowest is 2, making their difference \(8 - 2 = 6\).
The question asks for the launch year of the Smart Cities Mission. This is a factual question related to government schemes in India. To answer correctly, one needs to recall the specific year this initiative was introduced.
A) 2015 — The Smart Cities Mission was launched on 25th June 2015 by the Prime Minister of India, Shri Narendra Modi. This mission aims to develop 100 cities across the country, making them citizen-friendly and sustainable.
We will use the basic formulas for profit and selling price. Let the initial cost price be \(C\), initial selling price be \(S_1\), and initial profit be \(P_1\). We are given conditions relating the new selling price and new profit to the initial values. We will set up equations based on these conditions and solve for the initial profit percentage.
Let the Cost Price (CP) of the bed be \(C\).
Let the initial Selling Price (SP) be \(S_1\).
Let the initial Profit be \(P_1\).
The formula for profit is: \[\text{Profit} = \text{Selling Price} - \text{Cost Price}\]
So, for the initial situation: \[P_1 = S_1 - C \quad \ldots (1)\]
According to the problem, the new selling price (\(S_2\)) is 2 times the initial selling price:
\[S_2 = 2 \times S_1\]The new profit (\(P_2\)) is 7 times the initial profit:
\[P_2 = 7 \times P_1\]Using the profit formula for the new situation:
\[P_2 = S_2 - C\]Substitute the expressions for \(S_2\) and \(P_2\):
\[7 P_1 = 2 S_1 - C \quad \ldots (2)\]Now we have a system of two equations:
From (1): \(S_1 = P_1 + C\)
Substitute \(S_1\) into equation (2):
\[7 P_1 = 2 (P_1 + C) - C\]\[7 P_1 = 2 P_1 + 2 C - C\]\[7 P_1 = 2 P_1 + C\]\[7 P_1 - 2 P_1 = C\]\[5 P_1 = C\]This means the Cost Price \(C\) is 5 times the initial Profit \(P_1\).
We need to find the initial profit percentage. The formula for profit percentage is:
\[\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\%\]Using the initial profit \(P_1\) and cost price \(C\):
\[\text{Initial Profit Percentage} = \frac{P_1}{C} \times 100\%\]Substitute \(C = 5 P_1\) into the profit percentage formula:
\[\text{Initial Profit Percentage} = \frac{P_1}{5 P_1} \times 100\%\]\[\text{Initial Profit Percentage} = \frac{1}{5} \times 100\%\]\[\text{Initial Profit Percentage} = 20\%\]B) 20
The question asks about a notable feature of the 'Tiger Triumph 2025' joint military exercise between India and the United States. To answer this, we need to recall specific details or unique aspects of this particular exercise, especially as it pertains to its evolution or new inclusions.
B) Inclusion of the United States Space Force for the first time. This is a significant and notable development for the 'Tiger Triumph 2025' exercise, indicating an expansion of cooperation into the space domain for HADR operations and overall strategic partnership.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others. We need to analyze the relationship between the two letter clusters in each option based on their positions in the English alphabetical order.
D) MN - PD is the letter-cluster pair that DOES NOT belong to the group. In options A, B, and C, the numerical position of each letter in the first cluster is exactly 5 more than the numerical position of the corresponding letter in the second cluster. For example, in A) IJ - DE, I (9) is 5 more than D (4), and J (10) is 5 more than E (5). This pattern is not observed in option D.
The problem involves finding two numbers based on their initial ratio and a modified ratio after specific operations. We will represent the numbers using a common multiple and set up an equation based on the given conditions to find the value of that multiple. Once the numbers are found, their sum can be calculated.
Represent the initial numbers:
Given that the ratio of the two numbers is \(7 : 11\), let the first number be \(7x\) and the second number be \(11x\), where \(x\) is a common multiple.
Apply the given operations:
The first number is increased by 10, so it becomes \(7x + 10\).
The second number is decreased by 20, so it becomes \(11x - 20\).
Formulate the equation based on the new ratio:
After these changes, the new ratio is \(2 : 3\). So, we can write the equation:
Solve the equation for \(x\):
Cross-multiply to solve for \(x\):
Isolate \(x\):
Subtract \(21x\) from both sides:
Find the value of \(x\):
Add 40 to both sides:
Calculate the original numbers:
First number \(= 7x = 7 \times 70 = 490\)
Second number \(= 11x = 11 \times 70 = 770\)
Calculate the sum of the original numbers:
Sum \(= 490 + 770 = 1260\)
C) 1260 is the sum of the original two numbers.