The question asks to identify the Metro Rail Corporation that was the first in India to utilize power generated from a waste-to-energy plant. This requires knowledge of specific environmental initiatives undertaken by various metro systems in India.
C) Delhi Metro — The Delhi Metro Rail Corporation (DMRC) was the first metro system in India to draw power from a waste-to-energy plant, specifically from the one located in Ghazipur, starting in 2017. This initiative was part of DMRC's broader commitment to sustainable and green energy practices.
The question asks to identify the international organization for which Rajiv Mehrishi was elected as an external auditor for the period 2020 to 2023. This is a factual question related to current affairs and appointments in international bodies.
Correct Option: A) WHO
Rajiv Mehrishi, the former Comptroller and Auditor General (CAG) of India, was elected as the external auditor of the World Health Organization (WHO) for a four-year term from 2020 to 2023. This appointment was a significant recognition of India's auditing standards and expertise on the international stage.
The problem is a coding-decoding type question. We need to identify the pattern used to transform "ZEBRA" into "ZQADY" and then apply the same pattern to "HINTS" to find the coded word.
The pattern is a fixed shift for each position:
Applying this to HINTS:
Thus, HINTS is coded as HUMFQ.
A) HUMFQ is the correct code for HINTS based on the identified pattern of shifts for each letter's position.
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
| 48 | 64 | 80 |
| 24 | ? | 40 |
| 12 | 16 | 20 |
The problem presents a sequence of numbers arranged in three rows. We need to identify the pattern or relationship between the numbers in each column or row to find the missing number.
Let's write down the given numbers in a tabular format to better visualize the rows and columns:
| Column 1 | Column 2 | Column 3 |
|---|---|---|
| 48 | 64 | 80 |
| 24 | ? | 40 |
| 12 | 16 | 20 |
Observe the relationship between the numbers in the first column:
This suggests a division by 2 moving downwards in the first column.
Observe the relationship between the numbers in the third column:
This also suggests a division by 2 moving downwards in the third column.
Based on this consistent pattern, we can infer that the same rule applies to the second column. Let the missing number be \(x\).
Calculate the value of \(x\) using the first relationship:
\[ x = 64 \div 2 \]\[ x = 32 \]Verify this with the second relationship:
\[ 32 \div 2 = 16 \]Both relationships hold true for \(x = 32\).
B) 32 — The pattern observed is that each number in a row is half of the number directly above it in the same column. Applying this to the second column, \(64 \div 2 = 32\).
The problem asks us to find the value of \( \tan^2 \theta + \cot^2 \theta \) given the equation \( \tan \theta + \cot \theta = 6 \). We can solve this by squaring the given equation and using the algebraic identity \( (a+b)^2 = a^2 + b^2 + 2ab \) along with the trigonometric identity \( \tan \theta \cdot \cot \theta = 1 \).
We are given the equation:
\[ \tan \theta + \cot \theta = 6 \]Square both sides of the equation:
\[ (\tan \theta + \cot \theta)^2 = 6^2 \]Apply the algebraic identity \( (a+b)^2 = a^2 + b^2 + 2ab \) to the left side, where \( a = \tan \theta \) and \( b = \cot \theta \):
\[ \tan^2 \theta + \cot^2 \theta + 2 \tan \theta \cot \theta = 36 \]Recall the trigonometric identity \( \cot \theta = \frac{1}{\tan \theta} \). Therefore, \[\tan \theta \cdot \cot \theta = \tan \theta \cdot \frac{1}{\tan \theta} = 1\].
Substitute \( \tan \theta \cdot \cot \theta = 1 \) into the equation from Step 3:
\[ \tan^2 \theta + \cot^2 \theta + 2(1) = 36 \]Simplify the equation:
\[ \tan^2 \theta + \cot^2 \theta + 2 = 36 \]Subtract 2 from both sides to find the value of \( \tan^2 \theta + \cot^2 \theta \):
\[ \tan^2 \theta + \cot^2 \theta = 36 - 2 \]\[ \tan^2 \theta + \cot^2 \theta = 34 \]Correct Option: B) 34
The amount of paint required to paint a circular plate is directly proportional to its area. The area of a circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius. We need to find the ratio of the areas of the two circular plates to determine the amount of paint required for the larger plate.
The area of a circle is \( A = \pi r^2 \).
\[ A_1 = \pi (r_1)^2 = \pi (20 \text{ cm})^2 = 400\pi \text{ cm}^2 \]The ratio of the area of the second plate to the first plate is:
\[ \frac{A_2}{A_1} = \frac{6400\pi \text{ cm}^2}{400\pi \text{ cm}^2} = \frac{6400}{400} = 16 \]Since the paint required is directly proportional to the area, we can write:
\[ \frac{P_2}{P_1} = \frac{A_2}{A_1} \]\[ P_2 = P_1 \times \frac{A_2}{A_1} \]\[ P_2 = 30 \text{ ml} \times 16 \]\[ P_2 = 480 \text{ ml} \]B) 480 ml is the correct amount of paint required for the larger plate.
The question asks about the first time the Indian National Congress observed January 26 as Independence Day. This refers to a specific historical resolution and its immediate aftermath, predating India's actual independence.
Correct Option: A) 1930 — The Indian National Congress declared January 26, 1930, as 'Purna Swaraj Day' and observed it as Independence Day for the first time, following the Lahore Session resolution of December 1929.
The problem asks for the minimum possible HCF (Highest Common Factor) of any two even numbers. We need to understand the definition of even numbers and HCF, and then find the smallest common factor that all even numbers share.
Correct Option: D) 2
The HCF of any two even numbers must be at least 2 because every even number is a multiple of 2, and therefore 2 will always be a common factor. The smallest possible HCF occurs when the numbers themselves are small multiples of 2, such as 2 and 4, where HCF(2, 4) = 2.
The question asks to identify the incorrect statement regarding plant tissues, specifically xylem and phloem. We need to evaluate each option based on the known functions and characteristics of these vascular tissues.
Correct Option: D) Materials can move in both directions in xylem. This statement is incorrect because water and minerals are transported unidirectionally (upwards) in xylem, from the roots to the aerial parts of the plant.
The question asks to identify the two main organs in the human body where the magnetic field produced is significant. This relates to the bio-magnetic fields generated by electrical activity within the body.
D) Heart and brain
The heart and brain are the primary organs that produce significant and measurable magnetic fields due to their highly organized electrical activity. The heart's electrical impulses for contraction and the brain's neural activity are the strongest bioelectric sources in the body, leading to detectable biomagnetic fields.