The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others. We need to find a common rule or relationship between the letters in each pair based on their positions in the English alphabet.
Now, let's observe the pattern:
Therefore, option A does not follow the same pattern as the other three.
A) ZI-UD is the odd one out. In this pair, the difference between the alphabetical positions of the letters in both clusters (ZI and UD) is 17 (\(26-9=17\) and \(21-4=17\)). In the other options, the differences are 9 and 17 (or 17 and 9).
To find the number of sides of a regular polygon given the number of its diagonals, we use the standard formula for the number of diagonals in an n-sided polygon. We will set up an equation and solve for 'n'.
Recall the formula for the number of diagonals:
The number of diagonals, \(D\), in a polygon with \(n\) sides is given by the formula:
Substitute the given information into the formula:
We are given that the polygon has 20 diagonals. So, \(D = 20\).
Solve the equation for \(n\):
First, multiply both sides by 2:
Rearrange the equation into a standard quadratic form:
\[ n^2 - 3n - 40 = 0 \]Solve the quadratic equation:
We can solve this by factoring. We need two numbers that multiply to -40 and add to -3. These numbers are -8 and 5.
Find the possible values for \(n\):
From the factored form, we get two possible solutions for \(n\):
Choose the valid solution:
Since the number of sides of a polygon cannot be negative, we discard \(n = -5\). Therefore, the number of sides of the polygon is 8.
Correct Option: C) 8
The question asks to identify the statement that does NOT represent a property of suspensions. We need to recall the characteristics of suspensions and evaluate each given option against these properties.
Correct Option: C) The particles of a suspension cannot be seen by the naked eyes. This statement is incorrect because the particles in a suspension are large enough to be seen with the naked eye.
This problem involves applying a set of given symbol transformations to a mathematical expression and then evaluating the new expression using the order of operations (BODMAS/PEMDAS).
+ means -- means ×× means ÷÷ means +The original equation is: \(22 - 5 \div 3 + 12 \times 3 = ?\)
Applying the transformations:
- becomes ×÷ becomes ++ becomes -× becomes ÷So, the new equation is: \(22 \times 5 + 3 - 12 \div 3 = ?\)
BODMAS/PEMDAS stands for Brackets, Orders (powers/roots), Division/Multiplication (from left to right), Addition/Subtraction (from left to right).
First, perform Division and Multiplication from left to right:
Substitute these values back into the equation:
\[ 110 + 3 - 4 = ? \]So, \(? = 109\).
B) 109 is the correct answer after applying the given symbol transformations and following the order of operations.
The question asks to identify the field in which Shailesh Nayak received the Padma Shri award in 2024. This requires knowledge of recent Padma Awards recipients and their respective fields of contribution.
Correct Option: A) Science and Engineering — Shailesh Nayak, a renowned scientist and former Secretary of the Ministry of Earth Sciences, was awarded the Padma Shri in 2024 for his significant contributions to the field of Science and Engineering, particularly in oceanography and remote sensing.
This is a coding-decoding problem. We need to find the code for the word 'tree' by comparing the given coded statements and identifying common words and their corresponding codes.
Therefore, the code for 'tree' is 'cx'.
Correct Option: B) cx
The question asks to identify the type of reaction where there is an exchange of ions between reactants. We will examine the definition and characteristics of each given reaction type to determine which one fits this description.
Here, \(\text{Ag}^+\) ions swap with \(\text{Na}^+\) ions, and \(\text{NO}_3^-\) ions swap with \(\text{Cl}^-\) ions.
C) Double displacement reaction — In a double displacement reaction, the constituent ions of two reactant compounds swap places to form two new products. This is the defining characteristic of this type of reaction.
The question asks to identify another system, besides the nervous system, that is responsible for control and coordination in the human body. This requires knowledge of the major organ systems and their primary functions, particularly those involved in regulating bodily processes.
Correct Option: B) The endocrine system works in conjunction with the nervous system to control and coordinate various bodily functions. It uses hormones as chemical messengers to regulate processes like growth, metabolism, and reproduction, providing slower but often longer-lasting effects than the nervous system.
To solve this problem, we first need to calculate the initial speed of the car using the given distance and time. Then, we will reduce the speed as specified in the problem to find the new speed. Finally, we will use this new speed to calculate the time required to cover the new distance.
The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]Given:
So, the initial speed is:
\[ \text{Initial Speed} = \frac{275 \text{ km}}{5 \text{ hours}} = 55 \text{ km/hr} \]The problem states that the speed is reduced by \(5 \text{ km/hr}\).
\[ \text{New Speed} = \text{Initial Speed} - 5 \text{ km/hr} \]\[ \text{New Speed} = 55 \text{ km/hr} - 5 \text{ km/hr} = 50 \text{ km/hr} \]The formula for time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]Given:
So, the time taken is:
\[ \text{Time} = \frac{250 \text{ km}}{50 \text{ km/hr}} = 5 \text{ hours} \]D) 5 hr is the correct answer. The car will take 5 hours to cover a distance of 250 km at the reduced speed.
A diver rowing at the speed of 3 km/h in still water takes double the time going 50 km upstream compared to going 50 km downstream. The speed of the diver against the stream is:
\( \frac{4}{3} \) km/h
1 km/h
\( \frac{7}{3} \) km/h
2 km/h
This problem involves the concept of speed, time, and distance in the context of boats and streams. We are given the speed of the diver in still water and a relationship between the time taken to travel upstream and downstream. We need to find the speed of the diver against the stream (upstream speed).
Let the speed of the diver in still water be \(v_d\) and the speed of the stream be \(v_s\).
Given: \(v_d = 3 \text{ km/h}\)
The speed of the diver downstream (with the stream) is \(v_{down} = v_d + v_s\).
The speed of the diver upstream (against the stream) is \(v_{up} = v_d - v_s\).
The distance to be covered is \(D = 50 \text{ km}\).
The time taken to go downstream is \[T_{down} = \frac{D}{v_{down}} = \frac{50}{v_d + v_s}\].
The time taken to go upstream is \[T_{up} = \frac{D}{v_{up}} = \frac{50}{v_d - v_s}\].
According to the problem statement, the diver takes double the time going upstream compared to going downstream:
\[ T_{up} = 2 \times T_{down} \]Substitute the expressions for \(T_{up}\) and \(T_{down}\):
\[ \frac{50}{v_d - v_s} = 2 \times \frac{50}{v_d + v_s} \]Cancel out 50 from both sides:
\[ \frac{1}{v_d - v_s} = \frac{2}{v_d + v_s} \]Cross-multiply:
\[ v_d + v_s = 2(v_d - v_s) \]\[ v_d + v_s = 2v_d - 2v_s \]Rearrange the terms to solve for \(v_s\):
\[ v_s + 2v_s = 2v_d - v_d \]\[ 3v_s = v_d \]Substitute the given value of \(v_d = 3 \text{ km/h}\):
\[ 3v_s = 3 \]\[ v_s = 1 \text{ km/h} \]The question asks for the speed of the diver against the stream, which is \(v_{up} = v_d - v_s\).
\[ v_{up} = 3 - 1 \]\[ v_{up} = 2 \text{ km/h} \]D) 2 km/h is the speed of the diver against the stream, calculated as \(v_d - v_s = 3 - 1 = 2 \text{ km/h}\).