A group of numbers and symbols is coded using letter codes as per the codes given below and the conditions that follow. Study the given codes and conditions and answer the question that follows.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Letter | F | T | E | P | A | U | X | R |
| Code | 7 | $ | @ | 9 | 2 | % | 6 | 4 |
Conditions:
1. If the 1st letter is a vowel and the last letter is a consonant, their codes are to be interchanged.
2. If the 2nd letter is a vowel and the last letter is a consonant, both are to be coded as 'W'.
3. If the 3rd and 4th letters are consonants, both are to be coded as the code for the 3rd letter.
4. If the 1st and 2nd letters are vowels, then both are to be coded as 'Q'.
What will be the code for the following group?
APUXR
The problem requires us to code a given group of letters (APUXR) based on a provided table of letter-to-code mappings and a set of conditional rules. We need to apply the conditions sequentially and only if a condition applies, modify the codes accordingly. If no condition applies, the direct codes from the table are used.
D) 4 9 % 6 2
The problem asks us to find a relationship between two numbers and then apply the same relationship to a third number to find its corresponding value. We are given two examples: 5 is related to 35, and 2 is related to 14. We need to find the number related to 9 using the same logic.
We need to find an operation that transforms 5 into 35. Common operations include multiplication, addition, subtraction, or a combination. Let's try multiplication:
\[ 5 \times X = 35 \]Dividing both sides by 5, we get:
\[ X = \frac{35}{5} = 7 \]So, the relationship could be multiplying the first number by 7.
If our logic (multiplying by 7) is correct, then \(2 \times 7\) should be 14.
\[ 2 \times 7 = 14 \]This matches the given relationship. Therefore, the logic is to multiply the given number by 7 to find the related number.
Using the established logic, we multiply 9 by 7:
\[ 9 \times 7 = 63 \]Thus, 9 is related to 63.
Correct Option: A) 63
This problem involves calculating the combined work rate of two pipes, one filling and one emptying, and then determining the time required to fill a specific fraction of the tank. We will find the individual filling/emptying rates, combine them to get the net filling rate, and then use this rate to calculate the time for the desired tank volume.
Calculate the filling rate of the first pipe:
The first pipe fills the tank in 8 minutes. So, in one minute, it fills \(\frac{1}{8}\) of the tank.
Calculate the emptying rate of the second pipe:
The second pipe empties the tank in 11 minutes. So, in one minute, it empties \(\frac{1}{11}\) of the tank.
Calculate the net filling rate when both pipes are open:
Since one pipe fills and the other empties, their effects are opposite. The net filling rate is the filling rate minus the emptying rate.
Calculate the time to fill the entire tank:
If \(\frac{3}{88}\) of the tank is filled in 1 minute, then the entire tank (1 unit) will be filled in \(\frac{88}{3}\) minutes.
Calculate the time to fill three-fourth of the tank:
We need to find the time to fill \(\frac{3}{4}\) of the tank. We multiply the time to fill the whole tank by \(\frac{3}{4}\).
A) 22 minutes is the time required to fill three-fourth of the tank.
This is a logical reasoning problem involving the arrangement of boxes. We need to deduce the exact order of the seven boxes (A, B, C, D, E, F, G) based on the given clues and then determine the number of boxes below A.
Clue 1: Only three boxes are kept above G.
This means G is at the 4th position from the top. Let's denote the positions from 1 (top) to 7 (bottom).
Position: 1 Position: 2 Position: 3 Position: 4: G Position: 5 Position: 6 Position: 7
Clue 2: Only one box is kept between F and G.
Since G is at position 4, F can be at position 2 (above G) or position 6 (below G).
Case 1: F is above G Position: 1 Position: 2: F Position: 3 Position: 4: G Position: 5 Position: 6 Position: 7 Case 2: F is below G Position: 1 Position: 2 Position: 3 Position: 4: G Position: 5 Position: 6: F Position: 7
Clue 3: Only three boxes are kept between F and B.
Considering Case 1 (F at position 2): If F is at position 2, then B must be at position 6 (2 + 3 + 1 = 6) or position 7 (if B is below F). If B is above F, it's not possible as F is at position 2 and there are only 7 boxes. If B is at position 6, there are 3 boxes (positions 3, 4, 5) between F and B.
Position: 1 Position: 2: F Position: 3 Position: 4: G Position: 5 Position: 6: B Position: 7
Considering Case 2 (F at position 6): If F is at position 6, then B must be at position 2 (6 - 3 - 1 = 2). There are 3 boxes (positions 3, 4, 5) between F and B.
Position: 1 Position: 2: B Position: 3 Position: 4: G Position: 5 Position: 6: F Position: 7
Clue 4: B is kept in some place above G.
This clue eliminates Case 1. In Case 1, B is at position 6, which is below G (at position 4). So, Case 1 is invalid. Case 2 is valid because B is at position 2, which is above G (at position 4).
The arrangement so far: Position: 1 Position: 2: B Position: 3 Position: 4: G Position: 5 Position: 6: F Position: 7
Clue 5: E is kept immediately below B.
Since B is at position 2, E must be at position 3.
Position: 1 Position: 2: B Position: 3: E Position: 4: G Position: 5 Position: 6: F Position: 7
Clue 6: A is kept in one of the places above D.
The remaining boxes are A, C, D. The remaining positions are 1, 5, 7. From this clue, A cannot be at position 7 because D would have to be below it, which is not possible. So, A can be at position 1 or 5. If A is at position 5, D must be at position 7.
Clue 7: C is not kept immediately above or below F.
F is at position 6. So, C cannot be at position 5 or position 7.
If C cannot be at position 5 or 7, and the remaining positions are 1, 5, 7, then C must be at position 1.
If C is at position 1, then the remaining positions are 5 and 7 for A and D. Since A is above D, A must be at position 5 and D at position 7.
Final arrangement: Position: 1: C Position: 2: B Position: 3: E Position: 4: G Position: 5: A Position: 6: F Position: 7: D
Question: How many boxes are kept below A?
A is at position 5. The boxes below A are F (position 6) and D (position 7). There are 2 boxes below A.
A) 2
The problem asks us to identify the highest and lowest numbers from a given set of three-digit numbers, then extract specific digits from them, and finally perform a subtraction operation to find the resultant value.
B) 1 — As calculated, the resultant value is 1.
The question asks to identify the tier of the Panchayati Raj system responsible for governing an entire district. This requires knowledge of the three-tier structure of Panchayati Raj institutions in India and their respective jurisdictions.
A) Zila Parishad is the correct answer because it is the district-level body in the three-tier Panchayati Raj system, responsible for governance and administration across the entire district.
This is a blood relation question where symbols represent relationships. We need to decode the given expression 'M – N × O ÷ P + Q' step-by-step to determine the relationship between M and Q.
A) Mother's Mother's Brother. This is consistent with our step-by-step deduction that M is the brother of Q's maternal grandmother (mother's mother).
Find the value of 3\(\sqrt{8a^2-4a+1}\) + 17a, when a = 2.
To find the value of the given expression, we need to substitute the value of 'a' into the expression and then simplify it following the order of operations (PEMDAS/BODMAS).
The given expression is \(3\sqrt{8a^2-4a+1} + 17a\).
We are given \(a = 2\). Substitute \(a=2\) into the expression:
\[ 3\sqrt{8(2)^2-4(2)+1} + 17(2) \]First, calculate \(2^2\):
\[ 2^2 = 4 \]Now substitute this back into the expression under the square root:
\[ 8(4) - 4(2) + 1 \]\[ 32 - 8 + 1 \]\[ 24 + 1 \]\[ 25 \]Now, find the square root of 25:
\[ \sqrt{25} = 5 \]The expression becomes:
\[ 3(5) + 17(2) \]Multiply the terms:
\[ 15 + 34 \]Add the final terms:
\[ 15 + 34 = 49 \]Thus, the value of the expression when \(a=2\) is 49.
Correct Option: B) 49
The question asks for the definition of "physiological density" in the context of population distribution. This is a standard geographical and demographic term. Understanding the different types of population densities is crucial for analyzing population pressure on resources.
A) unit of arable land — Physiological density is defined as the total population divided by the total amount of arable (farmable) land. It provides a more accurate picture of the pressure on agricultural resources than arithmetic density, especially in countries with significant non-arable land.
The problem presents a series of letter-number clusters. We need to identify the pattern in both the letters and the numbers to find the next cluster in the series. We will analyze the progression of each letter position and the numerical value separately.
D) GNP 27 is the correct option as it follows both the letter and number patterns identified.