To find the time taken for two trains moving in opposite directions to cross each other completely, we need to calculate their relative speed and the total distance they need to cover. The total distance will be the sum of their lengths. The relative speed will be the sum of their individual speeds.
Identify the lengths of the trains:
Length of Train 1, \(L_1 = 250 \text{ m}\)
Length of Train 2, \(L_2 = 250 \text{ m}\)
Calculate the total distance to be covered:
When two trains cross each other completely, the total distance they cover is the sum of their lengths.
\[ \text{Total Distance} (D) = L_1 + L_2 = 250 \text{ m} + 250 \text{ m} = 500 \text{ m} \]Identify the speeds of the trains:
Speed of Train 1, \(S_1 = 90 \text{ km/h}\)
Speed of Train 2, \(S_2 = 60 \text{ km/h}\)
Calculate the relative speed:
Since the trains are running in opposite directions, their relative speed is the sum of their individual speeds.
\[ \text{Relative Speed} (S_{\text{rel}}) = S_1 + S_2 = 90 \text{ km/h} + 60 \text{ km/h} = 150 \text{ km/h} \]Convert the relative speed to meters per second (m/s):
To convert km/h to m/s, multiply by the conversion factor \(\frac{5}{18}\).
\[ S_{\text{rel}} = 150 \times \frac{5}{18} \text{ m/s} = \frac{750}{18} \text{ m/s} = \frac{125}{3} \text{ m/s} \]Calculate the time taken to cross each other:
Time is calculated using the formula: \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\).
\[ \text{Time} (T) = \frac{D}{S_{\text{rel}}} = \frac{500 \text{ m}}{\frac{125}{3} \text{ m/s}} \] \[ T = 500 \times \frac{3}{125} \text{ s} \] \[ T = \frac{1500}{125} \text{ s} \] \[ T = 12 \text{ s} \]Therefore, the trains will cross each other completely in 12 seconds.
D) 12 sec is the correct answer, as calculated above.
A) 15 sec — This would be incorrect if there was an error in calculation, for example, if the relative speed was calculated differently or if the conversion factor was misapplied.
B) 18 sec — This value would result from significant calculation errors, such as using incorrect distances or speeds, or conversion mistakes.
C) 10 sec — This would imply a higher relative speed or a shorter total distance than what is given in the problem.
The question asks about a specific event in May 2024 concerning DRDO and IIT Bhubaneswar. This is a factual recall question related to current affairs or general knowledge, specifically about defense technology transfers.
A) nine: In May 2024, the Defence Research and Development Organisation (DRDO) officially handed over nine defence technology projects to IIT Bhubaneswar. This collaboration is part of DRDO's efforts to engage academic institutions in advanced research for defence applications.
The problem requires us to find which two numbers, when interchanged, make the given equation correct. We will evaluate the original equation first to see if it's already correct. If not, we will test each option by swapping the specified numbers and then applying the order of operations (BODMAS/PEMDAS) to check if the equation holds true.
B) 19 and 17 — When 19 and 17 are interchanged, the equation becomes \(72 - 56 + (13 + 17) \times 2 - 95 \div 5 + 19\). Evaluating this expression gives \(72 - 56 + 30 \times 2 - 19 + 19 = 72 - 56 + 60 - 19 + 19 = 16 + 60 - 19 + 19 = 76 - 19 + 19 = 57 + 19 = 76\), which matches the right-hand side of the equation.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on the English alphabetical order. We need to analyze the positional differences between the letters within each cluster and between the clusters in each option.
Options A, B, and D follow a consistent pattern:
Option C deviates from this pattern:
C) AD – CG — This pair does not follow the same pattern as the others. The difference between the letters in the first cluster (A to D) is 3, and in the second cluster (C to G) is 4. Also, the second letters (D to G) have a difference of 3, unlike the other options where it is 2.
The problem involves decoding a word based on given codes for other words. This is a common type of coding-decoding question where letters are assigned specific numerical values. We need to identify the common letters and their corresponding codes to deduce the code for the letter 'U'.
Analyze the first given code:
'FEND' is coded as '9735'. This means:
Analyze the second given code:
'FEUD' is coded as '3769'. This means:
Compare the common letters and their codes:
We have two sets of codes. Let's look for consistency for common letters:
Re-evaluate the coding pattern:
Since 'F' and 'D' have different codes in the two words, the coding is not a direct substitution where each letter always corresponds to the same digit regardless of its position or the word it's in. However, the letter 'E' consistently maps to '7'. Let's re-examine the given codes carefully:
Notice that 'E' is the second letter in both words, and its code '7' is the second digit in both codes. This suggests a direct positional mapping for the letters within the words.
Find the code for 'U':
From the second word 'FEUD' coded as '3769', the letter 'U' is the third letter. The third digit in its code '3769' is '6'.
Therefore, the code for 'U' is 6.
B) 6 is the correct code for 'U' as derived from the positional mapping in 'FEUD' (3769).
The question asks why we observe a geometrical shadow when light falls on an opaque object. This phenomenon is a direct consequence of a fundamental property of light propagation.
Correct Option: C) light travelling in a straight line
This is a blood relation coding question. We need to decode the given expression step-by-step to determine the relationship between R and T. We will assign genders and relationships based on the given codes and then combine them to find the final relation.
Correct Option: B) Wife's mother
R is the mother of K, and K is the wife of T. Therefore, R is T's wife's mother, which is the mother-in-law. Option B states "Wife's mother", which is the correct relationship.
This is a direction and distance problem. We need to trace Nalin's path step-by-step, keeping track of his position relative to the starting point Y. We can use a coordinate system or draw a diagram to visualize the movements. Finally, we will calculate the shortest distance (straight line) and direction from the final point Z back to the starting point Y.
Therefore, Nalin should drive 37 km towards the West to reach Point Y again.
Correct Option: B) 37 km towards the west
The question asks to identify the plant hormone that is found in high concentrations in fruits and seeds. This requires knowledge of the primary functions and distribution of various plant hormones.
C) Cytokinin — Cytokinins are plant hormones that promote cell division (cytokinesis) and differentiation. They are found in high concentrations in actively dividing tissues, such as developing fruits and seeds. They play a crucial role in nutrient mobilization towards these developing organs, making fruits and seeds strong metabolic sinks. This high concentration supports the rapid cell proliferation and growth occurring during fruit and seed development.
The problem requires us to calculate the current number of girls in a school. We are given the number of boys last year, the percentage decrease in the number of boys this year, and the number of girls as a percentage of the current number of boys.
Correct Option: A) 854