This is a coding-decoding problem where we need to find the code for a specific word by comparing common words and their codes across different statements.
The common word between 'guns and roses' and 'for the roses' is 'roses'.
The common code between 'li mh ca' and 'mh bo ph' is 'mh'.
Therefore, the code for 'roses' is 'mh'.
Let's find codes for other words to ensure consistency.
Now we have:
From Statement 1: 'guns and roses' = 'li mh ca'
Since 'guns' = 'ca' and 'roses' = 'mh', then 'and' must be 'li'.
From Statement 2: 'for the roses' = 'mh bo ph'
Since 'for' = 'bo' and 'roses' = 'mh', then 'the' must be 'ph'.
From Statement 3: 'guns for colours' = 'ca bo qu'
Since 'guns' = 'ca' and 'for' = 'bo', then 'colours' must be 'qu'.
All codes are consistent with 'roses' = 'mh'.
B) mh — By comparing the first two statements, 'roses' is the only common word and 'mh' is the only common code. Thus, 'roses' is coded as 'mh'.
The question asks why iron filings arrange themselves in a pattern around a bar magnet. This phenomenon is a classic demonstration of magnetic fields. We need to understand the fundamental forces at play when a magnet interacts with ferromagnetic materials like iron.
Therefore, the arrangement of iron filings is a direct visual representation of the magnetic field lines produced by the bar magnet.
Correct Option: C) Because of the magnetic field. This is the correct explanation. The magnetic field exerts a force on the iron filings, causing them to align along the field lines, thus revealing the pattern of the magnetic field.
To find the smallest 4-digit number that leaves a remainder of 9 when divided by 12, 16, and 20, we first need to find the Least Common Multiple (LCM) of 12, 16, and 20. Then, we find the smallest multiple of this LCM that is a 4-digit number and add the remainder to it.
Find the LCM of 12, 16, and 20:
First, find the prime factorization of each number:
The LCM is found by taking the highest power of all prime factors present:
\[ \text{LCM}(12, 16, 20) = 2^4 \times 3 \times 5 = 16 \times 3 \times 5 = 240 \]Find the smallest 4-digit multiple of the LCM:
The smallest 4-digit number is 1000. We need to find the smallest multiple of 240 that is greater than or equal to 1000.
Divide 1000 by 240:
\[ \frac{1000}{240} \approx 4.16 \]The smallest integer quotient greater than or equal to 4.16 is 5. So, the smallest multiple of 240 that is a 4-digit number is:
\[ 240 \times 5 = 1200 \]Add the remainder:
The problem states that the number should give a remainder of 9 when divided by 12, 16, and 20. Therefore, we add 9 to the smallest 4-digit multiple of the LCM:
\[ \text{Required number} = 1200 + 9 = 1209 \]A) 1209 is the smallest 4-digit number which, when divided by 12, 16, and 20, gives a remainder of 9.
The question asks to identify the first ruler of the Delhi Sultanate. This requires knowledge of the foundational history of the Delhi Sultanate and its early rulers.
B) Qutb-ud-din Aibak was the first ruler of the Delhi Sultanate, establishing the Mamluk Dynasty in 1206 CE.
The problem presents an analogy where a relationship exists between a pair of letter-clusters on the left side of '::' and the same relationship must hold for the pair on the right side. We need to find the missing letter-clusters, represented by '#' and '%', by identifying the pattern in the given pair.
A) # = EMI, % = JRN
The question asks to identify the correct statement about a substance with a pH of 11. This requires understanding the pH scale, the definitions of acidic, basic, and neutral substances, and their effects on litmus paper.
B) It is basic and can turn red litmus paper blue. A substance with a pH of 11 is basic. Bases are known to turn red litmus paper blue.
The given series is a numerical series. We need to identify the pattern or the difference between consecutive terms to find the missing number.
Correct Option: A) 54.8
This problem involves calculating time taken for travel under different modes (walking and driving) over the same distance. We can set up equations based on the given information about the total time taken for a walk-and-drive journey and a drive-both-ways journey. We need to find the time taken to walk both ways.
Let \(D\) be the distance to the viewpoint.
Let \(T_w\) be the time taken to walk the distance \(D\).
Let \(T_c\) be the time taken to drive the distance \(D\) by car.
The first condition states that the man walks to the viewpoint and returns by car, taking a total of 6 hours 45 minutes.
Convert 6 hours 45 minutes to hours:
\[ 6 \text{ hours } 45 \text{ minutes} = 6 + \frac{45}{60} \text{ hours} = 6 + \frac{3}{4} \text{ hours} = 6.75 \text{ hours} \]So, we have the equation:
\[ T_w + T_c = 6.75 \quad \text{(Equation 1)} \]The second condition states that he would have gained 2 hours by driving both ways. This means if he drove both ways, the total time would be \(6.75 - 2 = 4.75\) hours.
Driving both ways means driving the distance \(D\) to the viewpoint and driving the distance \(D\) back from the viewpoint. So, the time taken would be \(T_c + T_c = 2T_c\).
Thus, we have the equation:
\[ 2T_c = 4.75 \quad \text{(Equation 2)} \]From Equation 2, we can find \(T_c\):
\[ T_c = \frac{4.75}{2} = 2.375 \text{ hours} \]Now substitute the value of \(T_c\) into Equation 1 to find \(T_w\):
\[ T_w + 2.375 = 6.75 \]\[ T_w = 6.75 - 2.375 \]\[ T_w = 4.375 \text{ hours} \]The question asks for the time it would have taken for him to walk both ways. This means walking the distance \(D\) to the viewpoint and walking the distance \(D\) back from the viewpoint. The total time would be \(T_w + T_w = 2T_w\).
Calculate \(2T_w\):
\[ 2T_w = 2 \times 4.375 = 8.75 \text{ hours} \]Convert 8.75 hours back into hours and minutes:
\[ 8.75 \text{ hours} = 8 \text{ hours } + 0.75 \times 60 \text{ minutes} \]\[ 8.75 \text{ hours} = 8 \text{ hours } + 45 \text{ minutes} \]So, it would have taken him 8 hours 45 minutes to walk both ways.
D) 8 hours 45 minutes
This problem involves work and time. We can solve it by calculating the individual work rates of A and B. The work rate is the reciprocal of the time taken to complete the work. We are given the time A and B take together, and the time A takes alone. We need to find the time B takes alone.
Calculate the combined work rate of A and B:
If A and B together complete the work in 18 days, their combined work rate is:
\[ \text{Work rate of (A + B)} = \frac{1}{18} \text{ work per day} \]Calculate the work rate of A alone:
If A alone completes the work in 54 days, A's work rate is:
\[ \text{Work rate of A} = \frac{1}{54} \text{ work per day} \]Calculate the work rate of B alone:
The combined work rate of A and B is the sum of their individual work rates. So, we can find B's work rate by subtracting A's work rate from the combined work rate:
\[ \text{Work rate of B} = \text{Work rate of (A + B)} - \text{Work rate of A} \] \[ \text{Work rate of B} = \frac{1}{18} - \frac{1}{54} \]To subtract these fractions, find a common denominator, which is 54:
\[ \text{Work rate of B} = \frac{3}{54} - \frac{1}{54} \] \[ \text{Work rate of B} = \frac{3 - 1}{54} \] \[ \text{Work rate of B} = \frac{2}{54} \] \[ \text{Work rate of B} = \frac{1}{27} \text{ work per day} \]Calculate the time B alone takes to complete the work:
The time taken by B alone is the reciprocal of B's work rate:
\[ \text{Time taken by B} = \frac{1}{\text{Work rate of B}} \] \[ \text{Time taken by B} = \frac{1}{\frac{1}{27}} \] \[ \text{Time taken by B} = 27 \text{ days} \]Correct Option: B) 27
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the other three, based on English alphabetical order. We need to find the positional values of each letter and then analyze the relationship between the letters within each cluster and between the two clusters in a pair.
Correct Option: D) TR – XV
In this pair, the difference between the first letters of the clusters (T to X) is \(24 - 20 = 4\), and the difference between the second letters (R to V) is \(22 - 18 = 4\). This is different from the \(+3\) pattern found in the other options.