The problem presents a number series and asks us to find the missing term that continues the pattern. We need to analyze the relationship between consecutive numbers to identify the underlying rule.
Thus, the missing term is 27.
Correct Option: B) 27 is the correct alternative that continues the given pattern. The pattern alternates between multiplying by 2 and adding a power of 3 (specifically, \(3^0, 3^1, 3^2, \dots\)).
The problem asks us to identify the pattern in the given sequence of numbers and then find the next number that continues this pattern. We will analyze the differences between consecutive terms to find a consistent rule.
The differences are \(1, 4, 9, 16\). These numbers are perfect squares:
This indicates that the difference between consecutive terms is increasing by the square of the term's position in the difference sequence.
Following the pattern, the next difference should be \(5^2\).
\[ 5^2 = 25 \]To find the next term after 34, we add the calculated difference (25) to 34.
\[ 34 + 25 = 59 \]D) 59 — The pattern of differences between consecutive terms is \(1^2, 2^2, 3^2, 4^2, \dots\). The next difference is \(5^2 = 25\). Adding this to the last term \(34\) gives \(34 + 25 = 59\).
The problem presents a number series and asks us to find the next term that continues the established pattern. We need to analyze the relationship between consecutive numbers to identify the rule governing the series.
C) 8 — The pattern is that each subsequent number is the product of the digits of the previous number. Following this rule, for the number 18, the next number is \(1 \times 8 = 8\).
The given sequence is an alternating series where the numbers follow two different patterns. We need to identify these patterns and apply them to find the missing term.
D) 72
The given sequence is a number series where each term is related to the preceding terms by a specific pattern. We need to identify this pattern to find the missing term.
Therefore, the next term in the sequence is 50.
C) 50 — This option correctly follows the identified pattern where each term is the sum of the three preceding terms.
The problem presents a number series and asks us to find the missing term. We need to identify the pattern or rule governing the sequence by examining the differences between consecutive terms.
C) 26 is the correct answer because it fits the established pattern of differences (2, 4, 4, 8, 8, 16, 16).
The problem asks to calculate the demand factor of a consumer given their connected load and maximum demand. The demand factor is a ratio that indicates how much of the total connected load is actually used at the time of maximum demand.
The demand factor is defined as the ratio of the maximum demand on a power station or system to the total connected load of the consumer.
\[ \text{Demand Factor} = \frac{\text{Maximum Demand}}{\text{Connected Load}} \]Correct Option: A) 0.75
The question asks to identify the type of electric current that periodically changes its direction. We need to recall the definitions of different types of electric currents.
C) Alternating current is defined as the electric current that periodically reverses its direction. This reversal happens at regular, fixed intervals of time, typically many times per second (e.g., 50 Hz or 60 Hz in power grids).
The question asks about the primary function of sheaths in electrical cables. We need to understand the construction of a cable and the role of each layer to identify the correct function of the sheath.
C) prevent ingress of moisture. The metallic sheath in cables, typically made of lead or aluminum, forms a waterproof barrier. This barrier is crucial for preventing moisture, gases, and other liquids from penetrating the insulation, which would otherwise reduce its dielectric strength and lead to electrical breakdown.