A group of numbers and symbols is coded using letter codes as per the codes given below and the conditions that follow. Study the given codes and conditions and answer the question that follows.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Number/Symbol | 3 | 9 | @ | & | 2 | 7 | 5 | % | 1 | 8 | Δ | 4 | 6 |
| Code | L | C | Z | M | D | W | A | P | R | T | F | B | K |
Conditions:
(i) If the first element is a symbol and the last a number, the codes for these two (the first and the last elements) are to be interchanged.
(ii) If the first element is an odd number and the last an even number, the first and last elements are to be coded as ©.
(iii) If both second and third elements are perfect squares, the third element is to be coded as the code for the second element.
What will be the code for the following group?
@ 9 3 8 5
The problem requires us to code a given group of numbers and symbols based on a provided table and a set of conditions. We need to apply the conditions in the given order and then use the direct codes if no condition applies or after a condition has been applied.
D) A C L T Z is the correct code for the group @ 9 3 8 5 after applying condition (i).
The question asks to identify the recipient of the Padma Shri award in 2025 in the 'Others–Spiritualism' category, awarded posthumously. This requires knowledge of recent Padma Awards announcements.
C) Lama Lobzang received the Padma Shri award in 2025 posthumously in the category of 'Others–Spiritualism'. He was a prominent Buddhist spiritual leader and social worker from Ladakh, known for his efforts in preserving Buddhist culture and promoting education.
What is the mean of the following distribution?
| Marks | 19 | 36 | 60 | 69 | 85 |
| No. of Students | 63 | 62 | 59 | 17 | 70 |
To find the mean of a distribution given marks and the number of students (frequency), we use the formula for the weighted mean (or mean of grouped data). The mean is calculated as the sum of the product of each mark and its corresponding number of students, divided by the total number of students.
The mean of the distribution is approximately 52.
Correct Option: D) 52
On 26 March 2025, where was the 8th State Level Coordination Committee (SLCC) meeting conducted by the Reserve Bank of India (RBI)?
The question asks for the location of the 8th State Level Coordination Committee (SLCC) meeting conducted by the Reserve Bank of India (RBI) on 26 March 2025. This is a factual question requiring knowledge of recent events related to financial regulatory bodies in India.
B) Gangtok — The 8th State Level Coordination Committee (SLCC) meeting, convened by the Reserve Bank of India (RBI), was held in Gangtok, Sikkim, on March 26, 2025. This meeting focused on discussing various issues related to financial sector coordination and regulation in the state.
Two pipes, A and B, can fill a tank of 7800 litres in 12 hours and 10 hours, respectively. If they are opened together, how many hours will they take to fill an empty tank of 8800 litres?
\( \frac{70}{13} \) hours
\( \frac{89}{13} \) hours
\( \frac{88}{13} \) hours
\( \frac{80}{13} \) hours
To solve this problem, we first need to determine the filling rate of each pipe. Then, we calculate their combined filling rate. Finally, we use the combined rate to find the time taken to fill the new tank capacity.
Correct Option: D) \( \frac{80}{13} \) hours
The question asks to identify the individual recognized by the 2025 TIME Earth Awards for environmental justice advocacy, specifically for marginalised communities. This requires knowledge of recent environmental awards and the recipients' specific areas of work.
Catherine Coleman Flowers is widely recognized for her work on environmental justice, particularly addressing the lack of adequate sanitation infrastructure in rural, impoverished communities in the United States, which disproportionately affects marginalised populations. Her efforts align directly with the criteria of the TIME Earth Awards for environmental justice advocacy.
A) Catherine Coleman Flowers — Catherine Coleman Flowers is a prominent environmental justice advocate known for her work on wastewater and sanitation issues in rural Alabama, particularly among low-income and minority communities. Her advocacy highlights how environmental degradation disproportionately affects marginalised populations, making her a fitting recipient for an award recognizing environmental justice.
This problem involves relative speed. We can solve it by considering the distance covered by the cabs and the man in the given time intervals. The key idea is that the distance between two consecutive cabs is constant, and this distance is covered by the man and the cab in relative motion.
The cabs start at an interval of 29 minutes at a speed of 54 km/hr. In 29 minutes, the first cab covers a certain distance, and the second cab starts. This distance represents the separation between two consecutive cabs.
\[ \text{Distance between cabs} = \text{Speed of cab} \times \text{Time interval} \]First, convert the time interval to hours:
\[ \text{Time interval} = 29 \text{ minutes} = \frac{29}{60} \text{ hours} \]Now, calculate the distance:
\[ \text{Distance between cabs} = 54 \text{ km/hr} \times \frac{29}{60} \text{ hr} = \frac{54 \times 29}{60} \text{ km} = \frac{9 \times 29}{10} \text{ km} = 26.1 \text{ km} \]A man is coming in the opposite direction. He meets the cabs at an interval of 12 minutes. This means that in 12 minutes, the man and the cab (which is also moving) together cover the distance between two cabs.
Let the speed of the man be \(V_m\) km/hr.
Since the man and the cab are moving in opposite directions, their relative speed is the sum of their individual speeds:
\[ \text{Relative speed} = \text{Speed of cab} + \text{Speed of man} = (54 + V_m) \text{ km/hr} \]The time taken for the man to meet the next cab is 12 minutes. Convert this to hours:
\[ \text{Time} = 12 \text{ minutes} = \frac{12}{60} \text{ hours} = \frac{1}{5} \text{ hours} \]The distance covered by the man and the cab (relative distance) in 12 minutes is equal to the distance between two cabs.
\[ \text{Distance between cabs} = \text{Relative speed} \times \text{Time} \]Substitute the values:
\[ 26.1 = (54 + V_m) \times \frac{1}{5} \]Multiply both sides by 5:
\[ 26.1 \times 5 = 54 + V_m \]\[ 130.5 = 54 + V_m \]
Solve for \(V_m\):
\[ V_m = 130.5 - 54 \]\[ V_m = 76.5 \text{ km/hr} \]
Correct Option: C) 76.5 km/hr
We are given a scenario where the selling price changes, leading to a change in profit. We need to find the initial profit percentage. We will use the basic formulas for profit and profit percentage, setting up equations based on the given conditions to solve for the unknown variables.
Let the initial Cost Price (CP) of the bed be \(C\).
Let the initial Selling Price (SP) of the bed be \(S\).
Let the initial Profit be \(P\). The formula for profit is:
\[ P = S - C \]According to the problem, if the selling price is 2-times the initial selling price, the new selling price \(S'\) is:
\[ S' = 2S \]The problem states that if the selling price is 2-times the initial, then the profit is 10-times the initial. The new profit \(P'\) is:
\[ P' = 10P \]The cost price \(C\) remains constant. So, the new profit can also be expressed as:
\[ P' = S' - C \]Substitute the expressions for \(S'\) and \(P'\) into the new profit equation:
\[ 10P = 2S - C \]We have two equations:
Equation (1): \(P = S - C\)
Equation (2): \(10P = 2S - C\)
From Equation (1), we can express \(C\) as \(C = S - P\). Substitute this into Equation (2):
\[ 10P = 2S - (S - P) \]\[ 10P = 2S - S + P \]\[ 10P = S + P \]\[ 9P = S \]Now we have a relationship between the initial selling price \(S\) and the initial profit \(P\). We can substitute \(S = 9P\) back into Equation (1) to find the cost price \(C\):
\[ P = 9P - C \]\[ C = 9P - P \]\[ C = 8P \]The initial profit percentage is calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100\% \]Substitute \(P\) for Profit and \(8P\) for Cost Price:
\[ \text{Profit Percentage} = \left( \frac{P}{8P} \right) \times 100\% \]\[ \text{Profit Percentage} = \left( \frac{1}{8} \right) \times 100\% \]\[ \text{Profit Percentage} = 12.5\% \]Correct Option: C) 12.5
The problem asks us to identify numbers in a given series that satisfy two conditions: they must be immediately preceded by a number and immediately followed by a symbol. We will scan the series from left to right, checking each number against these conditions.
D) 2 — As determined in the step-by-step analysis, there are exactly two numbers (4 and 2) that satisfy the given conditions.
If the ratio of two numbers is 17 : 6 and the product of their LCM and their HCF is 102, then the sum of the reciprocals of the LCM and the HCF is:
\( \frac{103}{109} \)
\( \frac{103}{105} \)
\( \frac{103}{102} \)
\( \frac{103}{132} \)
The problem involves two numbers whose ratio is given, along with the product of their LCM and HCF. We need to find the sum of the reciprocals of their LCM and HCF. We will use the fundamental property that for any two positive integers, the product of the numbers is equal to the product of their LCM and HCF.
Let the two numbers be \(A\) and \(B\). The ratio of the two numbers is given as \(17:6\).
So, we can write \(A = 17x\) and \(B = 6x\) for some common factor \(x\).
We are given that the product of their LCM and HCF is 102.
We know the property: \(\text{Product of two numbers} = \text{LCM} \times \text{HCF}\).
Therefore, \(A \times B = 102\).
Substitute the expressions for \(A\) and \(B\) into the equation:
\[ (17x) \times (6x) = 102 \]\[ 102x^2 = 102 \]Solve for \(x\):
\[ x^2 = \frac{102}{102} \]\[ x^2 = 1 \]\[ x = 1 \quad (\text{since numbers are positive}) \]Now, find the two numbers:
\(A = 17x = 17 \times 1 = 17\)
\(B = 6x = 6 \times 1 = 6\)
Calculate the HCF and LCM of 17 and 6.
Since 17 is a prime number and 6 is not a multiple of 17, 17 and 6 are coprime. Therefore, their HCF is 1.
\(\text{HCF}(17, 6) = 1\)
The LCM of two coprime numbers is their product.
\(\text{LCM}(17, 6) = 17 \times 6 = 102\)
Alternatively, we know \(\text{LCM} \times \text{HCF} = 102\). Since \(\text{HCF} = 1\), then \(\text{LCM} = 102\).
We need to find the sum of the reciprocals of the LCM and the HCF.
\[\frac{1}{\text{LCM}} + \frac{1}{\text{HCF}} = \frac{1}{102} + \frac{1}{1}\]
Calculate the sum:
\[ \frac{1}{102} + \frac{1}{1} = \frac{1}{102} + \frac{102}{102} = \frac{1 + 102}{102} = \frac{103}{102} \]Correct Option: C) \( \frac{103}{102} \)