The question asks to identify which of the given rivers originates in the Western Ghats. To answer this, we need to recall the origin points of each river listed in the options.
Correct Option: A) Krishna
The question asks for the location of the Leadership Summit 2024, a corporate-academia event focused on 'Grooming Young Talents'. This is a factual question requiring knowledge of recent events, specifically those related to prominent educational institutions in India.
D) Indian Institute of Technology Guwahati: The Leadership Summit 2024, a two-day corporate-academia event with the theme 'Grooming Young Talents', was hosted by IIT Guwahati in collaboration with CII and YI Guwahati Chapter.
The problem asks us to identify the lowest and highest numbers from a given set of three-digit numbers, then extract their first digits, and finally subtract the first digit of the lowest number from the first digit of the highest number.
The resultant value is 7.
Correct Option: A) 7 is the correct answer.
The problem involves similar triangles and their areas. When two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides. We will use this property to find the ratio of the area of \(\Delta BDE\) to the area of \(\Delta BAC\), and then use this to find the ratio of the area of \(\Delta BDE\) to the area of the trapezium ADEC.
Identify similar triangles: Given that \(DE \parallel AC\), we can conclude that \(\Delta BDE\) is similar to \(\Delta BAC\).
This is because:
Therefore, by AAA similarity criterion, \(\Delta BDE \sim \Delta BAC\).
Determine the ratio of corresponding sides: We are given \(BD = 17 \text{ cm}\) and \(AD = 14 \text{ cm}\).
The side \(AB\) of \(\Delta BAC\) is \(AB = AD + BD = 14 + 17 = 31 \text{ cm}\).
The ratio of corresponding sides is \[\frac{BD}{AB} = \frac{17}{31}\].
Calculate the ratio of areas of similar triangles: For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
\[ \frac{\text{Area}(\Delta BDE)}{\text{Area}(\Delta BAC)} = \left(\frac{BD}{AB}\right)^2 \]
\[ \frac{\text{Area}(\Delta BDE)}{\text{Area}(\Delta BAC)} = \left(\frac{17}{31}\right)^2 = \frac{17^2}{31^2} = \frac{289}{961} \]
Find the area of the trapezium ADEC: The area of the trapezium ADEC can be found by subtracting the area of \(\Delta BDE\) from the area of \(\Delta BAC\).
\[ \text{Area}(\text{trapezium ADEC}) = \text{Area}(\Delta BAC) - \text{Area}(\Delta BDE) \]
Let \(\text{Area}(\Delta BDE) = 289k\) and \(\text{Area}(\Delta BAC) = 961k\) for some constant \(k\).
\[ \text{Area}(\text{trapezium ADEC}) = 961k - 289k = 672k \]
Determine the required ratio: We need to find the ratio of the area of \(\Delta BDE\) to that of the trapezium ADEC.
\[ \frac{\text{Area}(\Delta BDE)}{\text{Area}(\text{trapezium ADEC})} = \frac{289k}{672k} = \frac{289}{672} \]
B) 289 : 672
This is a linear arrangement puzzle. We need to deduce the exact seating order of the seven friends (A, B, C, D, E, F, O) based on the given clues. We will place the friends one by one, starting with the most restrictive clues, and then use the remaining clues to fill in the gaps and confirm the arrangement.
The question asks about the size of the special economic and comprehensive package announced by the Central Government of India to combat the COVID-19 pandemic. This is a factual question related to government policy and economic measures taken during a specific period.
Correct Option: D) The Central Government launched a special economic and comprehensive package of ₹20 lakh crore (approximately 10% of India's GDP at that time) to fight the COVID-19 pandemic. This package was announced on May 12, 2020, as part of the Atmanirbhar Bharat Abhiyan.
The problem presents a series of three-letter codes and asks us to find the next code in the sequence. We need to identify the pattern by analyzing the position of each letter in the English alphabet.
The next code in the series is UIF.
D) UIF is the correct answer as derived from the pattern of adding 10 to the alphabetical position of each letter, cycling back from A after Z.
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 (SUZD to ZBGK and UWBF to BDIM) and then apply the same pattern to PRWA to find the related set of letters.
Correct Option: D) WYDH
The question asks to identify the winner of the women's singles title at the Indian Open 2025 Professional Squash Association (PSA) Copper event. This requires knowledge of recent squash tournament results, specifically for the Indian Open 2025.
Correct Option: B) Anahat Singh won the women's singles title at the Indian Open 2025 Professional Squash Association (PSA) Copper event. She is a rising star in Indian squash.
Taran ranked 28th from the top and 64th from the bottom in his class. How many students are there in his class?
This problem involves calculating the total number of students in a class given a person's rank from both the top and the bottom. The key is to understand that the person whose rank is given is counted twice when summing the ranks from both ends. Therefore, we need to subtract 1 from the sum of the ranks to get the total number of students.
Therefore, there are 91 students in the class.
D) 91 — This is the correct answer because when Taran's rank from the top (28) and his rank from the bottom (64) are added, Taran himself is counted twice. Subtracting 1 corrects this double-counting, giving the total number of unique students as \(28 + 64 - 1 = 91\).