To find the odd one out, we need to identify a common property or pattern shared by three of the given numbers, and then find the number that does not fit this pattern.
Based on these observations, the most distinct property that sets one number apart from the others is that 25 is a perfect square, while 60, 30, and 15 are not. Also, 60, 30, and 15 are all multiples of 15, whereas 25 is not.
A) 25 is the odd one out. It is the only perfect square among the given options (\(5 \times 5 = 25\)). The other numbers (60, 30, 15) are not perfect squares. Additionally, 60, 30, and 15 are all multiples of 15, while 25 is not.
This is a question based on Syllogism. We need to analyze the given statements and determine which of the conclusions logically follow. We can use Venn diagrams to represent the statements and check the validity of the conclusions.
A) Neither conclusion I nor II follows. Both conclusions are not logically derivable from the given statements.
To determine the net result of the sale, we need to calculate the selling price (SP) based on the cost price (CP) after applying both the markup and the discount. We can assume a base cost price (e.g., โน100) for easier calculation and then find the percentage change.
Let the Cost Price (CP) of the article be โน100.
The article is marked 20% above the cost price.
\[ \text{Marked Price (MP)} = \text{CP} + (20\% \text{ of CP}) \]\[ \text{MP} = 100 + \left(\frac{20}{100} \times 100\right) \]\[ \text{MP} = 100 + 20 = โน120 \]A discount of 20% is given on the Marked Price.
\[ \text{Selling Price (SP)} = \text{MP} - (20\% \text{ of MP}) \]\[ \text{SP} = 120 - \left(\frac{20}{100} \times 120\right) \]\[ \text{SP} = 120 - 24 = โน96 \]Now, compare the Selling Price (SP) with the Cost Price (CP).
\[ \text{CP} = โน100 \]\[ \text{SP} = โน96 \]Since \(\text{SP} < \text{CP}\), there is a loss.Loss = \(\text{CP} - \text{SP} = 100 - 96 = โน4\)
Loss Percentage = \(\frac{\text{Loss}}{\text{CP}} \times 100\)
\[ \text{Loss Percentage} = \frac{4}{100} \times 100 = 4\% \]Correct Option: D) 4% loss
This is an analogy question where we need to identify the relationship between the first pair of words and then apply the same relationship to the second pair to find the missing word.
Correct Option: A) Cut
This problem involves the concept of boats and streams. We are given the speed of the boat upstream and downstream, and we need to find the speed of the boat in still water. We can use the standard formulas relating upstream speed, downstream speed, speed of the boat in still water, and speed of the stream.
Let \(u\) be the speed of the boat in still water and \(v\) be the speed of the stream.
The speed of the boat upstream is given by \(u - v\). From the problem, this is 36 km/h.
\[ u - v = 36 \quad \text{(Equation 1)} \]The speed of the boat downstream is given by \(u + v\). From the problem, this is 40 km/h.
\[ u + v = 40 \quad \text{(Equation 2)} \]To find the speed of the boat in still water (\(u\)), we can add Equation 1 and Equation 2:
\[ (u - v) + (u + v) = 36 + 40 \]\[ 2u = 76 \]Now, solve for \(u\):
\[ u = \frac{76}{2} \]\[ u = 38 \text{ km/h} \]The information about the distance covered in each trip being the same is important because it implies that the speeds given are average speeds for those legs of the journey, which is consistent with the standard definitions of upstream and downstream speeds.
Correct Option: C) 38 km/h โ The speed of the boat in still water is found by averaging the upstream and downstream speeds, which gives 38 km/h.
Find the LCM of \( \frac{2}{3} \) and \( \frac{6}{7} \).
\( \frac{6}{21} \)
\( \frac{12}{21} \)
\( \frac{2}{21} \)
6
To find the Least Common Multiple (LCM) of fractions, we use a specific formula: the LCM of fractions is equal to the LCM of their numerators divided by the HCF (Highest Common Factor) of their denominators.
We need to find LCM(2, 6).
The smallest common multiple is 6. So, LCM(2, 6) = 6.
We need to find HCF(3, 7).
The highest common factor is 1. So, HCF(3, 7) = 1.
The formula is:
\[ \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} \]Substitute the calculated values:
\[ \text{LCM}\left( \frac{2}{3}, \frac{6}{7} \right) = \frac{\text{LCM}(2, 6)}{\text{HCF}(3, 7)} = \frac{6}{1} = 6 \]D) 6 is the correct LCM of the given fractions.
The question asks to identify the Greek letter commonly used to denote wavelength in physics and related fields. This is a fundamental concept in wave mechanics.
D) Lambda (\(\lambda\)) โ The Greek letter lambda (\(\lambda\)) is the standard symbol for wavelength in physics and engineering.
The question asks to identify the individual who took charge as the MD & CEO of Yes Bank in March 2019. This is a factual question related to appointments in the banking sector, which is a common topic in competitive exams.
In March 2019, Ravneet Gill took over as the Managing Director and Chief Executive Officer of Yes Bank. He succeeded Rana Kapoor, whose term was not extended by the Reserve Bank of India.
A) Ravneet Gill took charge as the MD & CEO of Yes Bank in March 2019. He was previously the CEO of Deutsche Bank India.
To determine the factors affecting electrical energy consumption, we need to recall the fundamental formula for electrical energy. Electrical energy is the product of power and time. We will then analyze how power itself is defined and how these quantities relate to the options provided.
A) The power rating of the appliance and the time for which it is used. This is correct because electrical energy (\(E\)) is defined as the product of power (\(P\)) and time (\(t\)), i.e., \(E = P \times t\). The power rating specifies the rate at which an appliance consumes energy, and the time specifies the duration of consumption.
This problem can be solved using the concept of work and time. We need to determine the individual work rates of P and Q, and then combine them to find their combined work rate. The time taken to complete the work is the reciprocal of the combined work rate.
Determine Q's work rate:
Q alone can complete the work in 12 days. This means Q's work rate is \(\frac{1}{12}\) of the work per day.
\[ \text{Q's work rate} = \frac{1}{\text{Time taken by Q}} = \frac{1}{12} \text{ work/day} \]Determine P's work rate:
P works twice as fast as Q. So, P's work rate will be twice Q's work rate.
\[ \text{P's work rate} = 2 \times \text{Q's work rate} = 2 \times \frac{1}{12} = \frac{2}{12} = \frac{1}{6} \text{ work/day} \]Calculate the combined work rate of P and Q:
When P and Q work together, their work rates add up.
\[ \text{Combined work rate} = \text{P's work rate} + \text{Q's work rate} \]\[ \text{Combined work rate} = \frac{1}{6} + \frac{1}{12} \]To add these fractions, find a common denominator, which is 12.
\[ \text{Combined work rate} = \frac{2}{12} + \frac{1}{12} = \frac{2+1}{12} = \frac{3}{12} = \frac{1}{4} \text{ work/day} \]Calculate the time taken to complete the work together:
The time taken to complete the work is the reciprocal of the combined work rate.
\[ \text{Time taken together} = \frac{1}{\text{Combined work rate}} = \frac{1}{\frac{1}{4}} = 4 \text{ days} \]Correct Option: B) 4 days