The problem asks for the positive value of Z given that 9 is the third proportional of 81 and Z. We need to understand the concept of a third proportional to solve this problem. If \(a\), \(b\), and \(c\) are in continued proportion, then \(a:b::b:c\), which means \[\frac{a}{b} = \frac{b}{c}\]. Here, \(c\) is the third proportional to \(a\) and \(b\).
The problem presents a series of letter-clusters. We need to identify the pattern in the series to find the missing cluster. We will analyze the progression of each letter's position in the alphabet across the clusters.
Based on the patterns, the next letter-cluster should be ZGD.
D) ZGD is the correct option because it follows the established patterns for all three positions in the letter-clusters.
The problem asks us to identify numbers in a given series that are immediately preceded by a symbol and immediately followed by a symbol. We need to scan the series from left to right and apply this condition.
(Left) & # 9 % 6 4 % © @ & 6 4 6 7 © 9 8 5 % 9 © 7 (Right)& # 9: Here, 9 is preceded by # (symbol) but followed by % (symbol). So, 9 fits the condition. (Count: 1)% 6 4: 6 is preceded by % (symbol) but followed by 4 (number). Does not fit.4 % ©: % is a symbol, not a number.% © @: © is a symbol, not a number.© @ &: @ is a symbol, not a number.@ & 6: & is a symbol, not a number.& 6 4: 6 is preceded by & (symbol) but followed by 4 (number). Does not fit.4 6 7: 6 is preceded by 4 (number). Does not fit.6 7 ©: 7 is preceded by 6 (number). Does not fit.7 © 9: Here, 9 is preceded by © (symbol) but followed by 8 (number). Does not fit.© 9 8: 9 is preceded by © (symbol) but followed by 8 (number). Does not fit.9 8 5: 8 is preceded by 9 (number). Does not fit.8 5 %: 5 is preceded by 8 (number). Does not fit.5 % 9: Here, 9 is preceded by % (symbol) but followed by © (symbol). So, 9 fits the condition. (Count: 2)% 9 ©: This is the same 9 we just counted.9 © 7: 7 is preceded by © (symbol) but followed by the end of the series. The condition requires it to be immediately followed by a symbol, which is not the case here.9 and the last 9.C) 2 is the correct answer because there are two numbers (the first '9' and the last '9') that satisfy the given condition of being immediately preceded by a symbol and immediately followed by a symbol.
The question asks to identify the regulatory authority established in 1997 to oversee India's telecom sector, which was a significant outcome of liberalisation. We need to recall the primary regulatory bodies in India and their respective sectors and establishment years.
Correct Option: A) TRAI
This is a blood relation problem. We need to establish the relationships between the individuals mentioned in the question and then determine how L is related to Q. We can use a family tree diagram or simply trace the relationships step-by-step.
Correct Option: B) Father's mother
To solve this problem, we need to track Fenil's movements and calculate his final position relative to his starting point Y. We can represent the movements on a 2D coordinate system or by separately tracking the net displacement in the East-West and North-South directions. Finally, we'll determine the shortest distance and direction from Point Z back to Point Y.
D) 45 km towards the east
Based on our step-by-step calculation, Fenil's final position (Point Z) is 45 km to the west of his starting point (Point Y). Therefore, to return to Point Y, he must drive 45 km towards the east.
We are given the average weight of M and three friends, and a relationship between M's weight and the average weight of his three friends. We need to find M's weight. We can set up equations based on the given information and solve for the unknown weights.
Correct Option: B) 71
The problem uses a direct letter-to-digit coding scheme. We need to identify the code for the letter 'H' by comparing the given coded words and their corresponding numerical codes.
Based on the direct mapping from 'HAVE' = '5723', the code for 'H' is '5'.
Correct Option: A) 5
The problem asks us to identify a pair of letter codes that follows the same pattern as two given pairs. We need to analyze the positional differences between the letters in the given pairs and apply the same logic to the options.
TRK : RQI
Let's check this pair against the \(-2, -1, -2\) pattern:
To find the principal, we use the formula for the difference between compound interest (CI) and simple interest (SI) for three years. The formula for CI - SI for 3 years is given by \[P \left( \frac{R}{100} \right)^2 \left( 3 + \frac{R}{100} \right)\]. We are given the difference, the rate, and the time, and we need to solve for the principal (P).
Identify the given values:
Recall the formula for the difference between CI and SI for 3 years:
The difference between compound interest and simple interest for 3 years is given by:
\[ \text{CI} - \text{SI} = P \left( \frac{R}{100} \right)^2 \left( 3 + \frac{R}{100} \right) \]Alternatively, we can derive this by:
Substitute the values into the formula:
\[ 228 = P \left( \frac{4}{100} \right)^2 \left( 3 + \frac{4}{100} \right) \] \[ 228 = P \left( \frac{1}{25} \right)^2 \left( 3 + \frac{1}{25} \right) \] \[ 228 = P \left( \frac{1}{625} \right) \left( \frac{75+1}{25} \right) \] \[ 228 = P \left( \frac{1}{625} \right) \left( \frac{76}{25} \right) \] \[ 228 = P \left( \frac{76}{625 \times 25} \right) \] \[ 228 = P \left( \frac{76}{15625} \right) \]Solve for P:
\[ P = \frac{228 \times 15625}{76} \]We can simplify the fraction:
\[ \frac{228}{76} = 3 \]So,
\[ P = 3 \times 15625 \] \[ P = 46875 \]The principal is ₹46,875.
Correct Option: D) 46,875