When light passes from a denser medium (water) to a rarer medium (air), it bends away from the normal. This phenomenon, known as refraction, causes objects submerged in water to appear shallower than they actually are. The relationship between the real depth, apparent depth, and refractive index of the medium is given by a specific formula.
The apparent depth (\(h_{\text{apparent}}\)) is related to the real depth (\(h_{\text{real}}\)) and the refractive index (\(n\)) of the medium by the formula:
\[ n = \frac{h_{\text{real}}}{h_{\text{apparent}}} \]Rounding to one decimal place, the apparent depth is approximately 22.6 cm.
D) 22.6 cm is the calculated apparent depth, which matches the result from applying the formula for refraction.
The question asks about the number of seats won by the Aam Aadmi Party (AAP) in the Punjab Assembly Election 2022. This is a factual question related to recent political events in India. To answer this, one needs to recall the results of the said election.
Correct Option: C) 92
This problem involves understanding relative directions and how they change when positions are exchanged. We will first establish the initial positions of P, D, A, and J based on the given statements. Then, we will perform the position exchange between P and A. Finally, we will determine the direction of J with respect to the new position of P.
Let's place D as a reference point.
Now, place A relative to D:
Finally, place J relative to A:
So, the initial relative positions are:
North | West--East | South D --- A | | P J
P exchanges his position with A. This means P moves to A's original position, and A moves to P's original position.
The new arrangement looks like this:
D --- P (P is now where A was) | | A J (A is now where P was)
The question asks for the direction of J with respect to the new position of P. From the new arrangement, P is at the top-right position (where A used to be), and J is directly below P.
Therefore, J is to the South of the new position of P.
A) South - After P exchanges position with A, P is now at the location where A was. Since J was to the south of A, J is now to the south of P's new position.
To determine Shalika's final position relative to her house, we need to track her movements in the north-south and east-west directions separately. We can represent her house as the origin (0,0) on a coordinate plane.
A) North-west is the correct direction because her final position is 5 km west and 10 km north of her starting point (house).
Refer to the given number, symbol series and answer the question that follows.
(Left) ¥ 1 λ 2 5 $ 2 # 1 & 2 3 € 1 5 6 % ¥ 2 @ 6 (Right)
How many such symbols are there, each of which is immediately preceded by a symbol and also immediately followed by a number?
The problem asks us to identify the number of symbols in the given series that satisfy two conditions: they must be immediately preceded by another symbol and immediately followed by a number. We will scan the series from left to right, applying these conditions to each symbol we encounter.
¥ 1 λ 2 5 $ 2 # 1 & 2 3 € 1 5 6 % ¥ 2 @ 6
D) 1 — As identified in the step-by-step analysis, only one symbol (¥) satisfies both conditions: being immediately preceded by a symbol (%) and immediately followed by a number (2).
This problem involves analyzing inequalities. We are given a statement with several inequalities and need to determine which of the given conclusions logically follows from the statement. We will combine the given inequalities to establish relationships between the variables and then check each option.
D) A > E
This is a circular seating arrangement problem. We need to place six friends (P, Q, R, S, T, U) around a circular table based on the given clues and then identify the immediate neighbours of R.
Correct Option: A) U and T
The given series is a number series where we need to find the pattern or rule governing the sequence of numbers. Once the pattern is identified, we can apply it to find the missing number.
Therefore, the number that replaces the question mark is 45.
Correct Option: A) 45
To simplify the given algebraic expression, we will use the distributive property to expand the products, then combine like terms by adding or subtracting their coefficients.
Correct Option: A) The simplified expression is \(-2x^2 + 21x + 7\).
The problem asks for the product of the Least Common Multiple (LCM) and the Highest Common Factor (HCF) of two numbers, 18 and 25. A fundamental property of numbers states that for any two positive integers, the product of their LCM and HCF is equal to the product of the numbers themselves.
Identify the given numbers: The two numbers are 18 and 25.
Recall the property of LCM and HCF: For any two positive integers \(a\) and \(b\), the following relationship holds:
\[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \]Apply the property to the given numbers: Here, \(a = 18\) and \(b = 25\). So, the product of their LCM and HCF will be equal to the product of 18 and 25.
\[ \text{Product} = 18 \times 25 \]Calculate the product:
\[ 18 \times 25 = 450 \]Alternatively, one could calculate LCM and HCF separately:
Prime factorization of 18: \(18 = 2 \times 3^2\)
Prime factorization of 25: \(25 = 5^2\)
Calculate HCF: Since there are no common prime factors between 18 and 25, their HCF is 1.
\[ \text{HCF}(18, 25) = 1 \]Calculate LCM: The LCM is the product of the highest powers of all prime factors present in either number.
\[ \text{LCM}(18, 25) = 2 \times 3^2 \times 5^2 = 2 \times 9 \times 25 = 18 \times 25 = 450 \]Calculate the product of LCM and HCF:
\[ \text{LCM}(18, 25) \times \text{HCF}(18, 25) = 450 \times 1 = 450 \]C) 450. The product of the LCM and HCF of 18 and 25 is 450, which matches the product of the numbers themselves.