The problem involves decoding a word based on a given coding pattern. We need to identify the numerical code assigned to each letter in the word "REMEMBER" and then apply the same pattern to decode "MEMBER". This is a direct coding problem where each letter corresponds to a specific digit.
The word "REMEMBER" is coded as "12323421".
Let's map each letter to its corresponding digit:
From this mapping, we can establish the unique codes for each letter present:
Now, we need to find the code for the word "MEMBER" using the established mapping:
Putting these digits together in order, the code for "MEMBER" is 323421.
D) 323421 — This matches the code derived from the established pattern where M=3, E=2, B=4, R=1.
This problem involves finding the Least Common Multiple (LCM) of two numbers given their ratio and their Highest Common Factor (HCF). We will use the fundamental relationship between two numbers, their HCF, and their LCM: the product of two numbers is equal to the product of their HCF and LCM.
Let the two numbers be \(A\) and \(B\).
Given that the ratio of the two numbers is 5 : 6, we can write them as:
\[ A = 5x \]\[ B = 6x \]We are also given that their HCF (Highest Common Factor) is 6. The HCF of \(5x\) and \(6x\) is \(x\), because 5 and 6 are coprime (their only common factor is 1).
Therefore, we can set \(x\) equal to the given HCF:
\[ x = 6 \]Now, substitute the value of \(x\) back into the expressions for \(A\) and \(B\) to find the actual numbers:
\[ A = 5 \times 6 = 30 \]\[ B = 6 \times 6 = 36 \]We need to find the LCM (Least Common Multiple) of these two numbers, 30 and 36.
We can use the formula that relates two numbers, their HCF, and their LCM:
\[ A \times B = \text{HCF}(A, B) \times \text{LCM}(A, B) \]Substitute the values we have:
\[ 30 \times 36 = 6 \times \text{LCM}(30, 36) \]Now, solve for LCM:
\[ \text{LCM}(30, 36) = \frac{30 \times 36}{6} \]\[ \text{LCM}(30, 36) = 5 \times 36 \]\[ \text{LCM}(30, 36) = 180 \]Alternatively, we can find the LCM directly from the numbers 30 and 36 by listing multiples or prime factorization:
Prime factorization of 30: \(2 \times 3 \times 5\)
Prime factorization of 36: \(2^2 \times 3^2\)
LCM is the product of the highest powers of all prime factors:
\[ \text{LCM}(30, 36) = 2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 36 \times 5 = 180 \]Correct Option: C) 180
The question asks for the chemical composition of ruby. This requires knowledge of common gemstones and their chemical formulas.
Correct Option: B) Aluminium oxide
To find the letter in the center after arranging the letters of a given word in alphabetical order, we first need to list all the letters in the word, count them, arrange them alphabetically, and then identify the middle letter. If there's an even number of letters, there will be two middle letters; if odd, there will be one.
C) N — The 7th letter in the alphabetically arranged sequence is N.
The question asks for the founding year of the Shanghai Cooperation Organisation (SCO). This requires knowledge of international organizations and their historical timelines.
Correct Option: C) 2001 is the correct year when the Shanghai Cooperation Organisation was officially founded with the signing of its charter.
How many seats were won by the Bhartiya Janata Party (BJP) in the 17th Lok Sabha General Elections (2019)?
The question asks about the number of seats won by the Bhartiya Janata Party (BJP) in the 17th Lok Sabha General Elections held in 2019. This is a factual question related to Indian political history and election results.
Correct Option: C) 303
This question is based on coding and decoding using reverse alphabetical positions. In the given code language, NAMAN is written as 92. We need to identify the mathematical relationship between the letters and their numerical code and apply the same rule to CARPET. The coding rule is to assign each letter its reverse alphabetical position and add all the values.
The English alphabet contains 26 letters.
In reverse alphabetical coding, the letters are assigned values as follows:
The reverse alphabetical position of a letter is calculated using:
\(\text{Reverse position}=27-\text{Normal position}\)
The given word is NAMAN.
Its letters and normal alphabetical positions are:
Apply the reverse alphabetical position formula to each letter:
Add these values:
\(13+26+14+26+13=92\)
Therefore:
NAMAN → 92
This matches the given code and confirms the rule.
The word CARPET contains six letters:
C - A - R - P - E - T
Their normal alphabetical positions are:
Using the same rule:
Add the reverse alphabetical positions:
\(24+26+9+11+22+7\)
\(=50+20+29\)
\(=99\)
Therefore:
CARPET → 99
The same reverse alphabetical position rule works for both words.
Therefore, option A is correct.
Correct Option: A) 99
Each letter is assigned its reverse alphabetical position, and the values are added. For CARPET, the values are C = 24, A = 26, R = 9, P = 11, E = 22, and T = 7. Their sum is \(24+26+9+11+22+7=99\). Therefore, option A is correct.
The question asks to identify what 'Patna Kalam' refers to. This is a knowledge-based question related to Indian art and culture. Recalling the historical art forms associated with the region of Patna (Bihar) will help in answering this question.
Correct Option: A) a style of painting
The question asks to identify which of the given air pollutants is commonly known as soot. Soot is a black, powdery substance resulting from incomplete combustion of organic matter. We need to evaluate each option based on this definition.
C) Particulate matter. Soot is essentially fine carbonaceous particulate matter formed from incomplete combustion. It falls under the broader category of particulate matter.
The question asks about the primary focus of the organization CRY. To answer this, one needs to know the full form or the mission of CRY (Child Rights and You).
Correct Option: A) protection of child rights. CRY (Child Rights and You) is a well-known Indian non-governmental organization (NGO) that works extensively for the protection and promotion of child rights, focusing on issues like education, health, and protection from child labor and abuse.