X varies inversely as Y and Y varies inversely as Z. In a particular case, X = \( \frac{1}{16} \) and Z = \( \frac{1}{32} \). What will be the value of X when Z = 3?
The problem describes inverse variation relationships between three variables, X, Y, and Z. We are given initial values for X and Z and asked to find the new value of X when Z changes. We need to establish the relationship between X and Z first, then use the given values to find the constant of proportionality, and finally calculate the new value of X.
X varies inversely as Y, which can be written as:
\[ X = \frac{k_1}{Y} \quad \text{or} \quad XY = k_1 \]where \(k_1\) is the constant of proportionality.
Y varies inversely as Z, which can be written as:
\[ Y = \frac{k_2}{Z} \quad \text{or} \quad YZ = k_2 \]where \(k_2\) is the constant of proportionality.
Substitute the expression for Y from the second equation into the first equation:
\[ X = \frac{k_1}{\left(\frac{k_2}{Z}\right)} \]\[ X = \frac{k_1 Z}{k_2} \]Let \( K = \frac{k_1}{k_2} \). Then the relationship simplifies to:
\[ X = KZ \]This means X varies directly as Z.
We are given \( X = \frac{1}{16} \) when \( Z = \frac{1}{32} \). Substitute these values into the direct variation equation:
\[ \frac{1}{16} = K \times \frac{1}{32} \]To find K, multiply both sides by 32:
\[ K = \frac{1}{16} \times 32 \]\[ K = 2 \]Now that we have the constant \( K = 2 \), use the relationship \( X = KZ \) with the new value of Z:
\[ X = 2 \times 3 \]\[ X = 6 \]Correct Option: A) 6
The question asks to identify the popular music of Bengal that represents spiritual folk song. This requires knowledge of traditional Bengali folk music forms and their characteristics.
Correct Option: B) Baul is the popular music of Bengal that represents spiritual folk song. Baul traditions are known for their unique blend of Sufism, Vaishnavism, and other spiritual philosophies, expressed through songs and dances.
The question asks to identify the correct statements regarding the PM Electric Drive Revolution in Innovative Vehicle Enhancement (PM E-DRIVE) Scheme launched in 2024. We need to evaluate each statement based on the known objectives and provisions of the scheme.
Statement 1: The scheme will remain in force until 31 March 2026.
Statement 2: One of the key aims of PM E-DRIVE is to provide direct subsidies to petrol and diesel vehicles to improve their fuel efficiency.
Statement 3: The scheme includes provisions to support the development of EV charging infrastructure.
Statement 4: PM E-DRIVE focuses exclusively on private vehicle ownership.
Based on the analysis, statements 1 and 3 are correct.
Correct Option: D) Only 1 and 3
The problem asks us to find the letter clusters that replace '#' and '%' based on a given analogy. We need to identify the pattern or relationship between the letters in the known pair (KRX and %) and apply the same logic to find '#' from MTZ.
D) # = HOU, % = PWC
This option correctly identifies the pattern where each letter in the first cluster is shifted forward by 5 positions in the alphabet to get the corresponding letter in the second cluster. Applying this to HOU gives MTZ, and applying it to KRX gives PWC.
The question asks about the duration for which the Kartarpur Corridor agreement was extended by India and Pakistan in October 2024. This is a factual question related to current affairs and international relations.
A) 5 — In October 2024, India and Pakistan agreed to extend the Kartarpur Corridor agreement for an additional five years, ensuring its continued operation for Sikh pilgrims.
The problem asks us to find the next number in a given series. To solve this, we need to identify the pattern or rule governing the sequence of numbers. We will calculate the differences between consecutive terms to find a common pattern.
Therefore, the number that should come in place of the question mark is 1372.
Correct Option: A) 1372 is the correct answer as it follows the identified pattern.
Where was the 67th Governing Body Meeting of the Asian Productivity Organization (APO) held in May 2025?
New Delhi, India
Bangkok, Thailand
Jakarta, Indonesia
Tokyo, Japan
The question asks for the venue of a specific international meeting, the 67th Governing Body Meeting of the Asian Productivity Organization (APO), scheduled for May 2025. This requires knowledge of current affairs and international organizational events.
C) Jakarta, Indonesia — The 67th Governing Body Meeting of the Asian Productivity Organization (APO) is indeed scheduled to be held in Jakarta, Indonesia, in May 2025. This information is typically available through APO's official communications and event calendars.
The question asks to identify the smallest inhabited island in the Union Territory of Lakshadweep. This requires knowledge of the geography and demographics of the Lakshadweep islands.
B) Bitra — Bitra is indeed the smallest inhabited island in the Lakshadweep archipelago. It has a very small land area, approximately \(0.105 \text{ km}^2\), and a population of around 271 people (as per the 2011 Census), making it the smallest in terms of both area and population among the inhabited islands.
To find the median of a set of observations, we first need to arrange the observations in ascending order. Once arranged, the median is the middle value if the number of observations is odd. If the number of observations is even, the median is the average of the two middle values.
Correct Option: C) 39
The question asks to identify a specific smartwatch-based metric discovered by Northwestern University researchers in March 2025 as a predictor of cardiovascular health risks. This requires knowledge of recent scientific findings, specifically related to wearable technology and health metrics.
A study published by Northwestern University researchers in March 2024 (the question likely has a typo and meant 2024, as 2025 is in the future) indeed identified "Daily Heart Rate Per Step" (DHRPS) as a significant predictor of cardiovascular disease risk. This metric is calculated by dividing a person's average daily heart rate by their average daily step count, providing insight into how efficiently the heart is working relative to physical activity.
D) Daily Heart Rate Per Step (DHRPS): This is the correct metric identified by Northwestern University researchers as a useful predictor of cardiovascular health risks. It reflects the heart's efficiency in relation to physical activity.