The question asks for the definition of a production function in economics. A production function describes the relationship between the inputs used in production and the maximum output that can be produced from those inputs.
Correct Option: B) inputs used and output produced
A production function is a fundamental concept in microeconomics that specifies the maximum output a firm can produce for each and every combination of inputs with a given technology. It illustrates how various inputs (like labor, capital, land, raw materials) are transformed into outputs (goods or services).
The problem presents a series of number pairs where the second number is related to the first number by a specific mathematical pattern. We need to identify this pattern and apply it to the third pair to find the missing number.
Correct Option: C) 121 — The pattern is to multiply the first number by 5 and then add 6 to the result. Applying this to 23 gives \( (23 \times 5) + 6 = 115 + 6 = 121 \).
The problem asks us to identify digits in a given sequence that satisfy two conditions simultaneously: they must be immediately preceded by an even number and immediately followed by an odd number. We will systematically scan the given number sequence and check each digit against these conditions.
Correct Option: C) Four
Select the option that represents the letters that, when placed from left to right in the same sequence in the blanks below, will complete the letter series:
B _ G K M _ T V _ C E _ L
This question is based on identifying a repetitive alphabetical pattern. The given letter series contains four blanks. We need to determine the sequence of alphabetical shifts and select the combination of letters that completes the series correctly.
B _ G K M _ T V _ C E _ L
There are four missing letters that must be filled from left to right.
Observe the first few known letters:
This suggests a repeating sequence of shifts:
+2, +3, +4
Starting from B, move 2 positions forward:
B → C → D
Therefore, the first missing letter is D.
Moving 3 positions forward from D gives G, confirming the pattern.
Continue the pattern:
Therefore, the second missing letter is P.
Continue applying the repeating shifts:
Therefore, the third missing letter is Y.
Continue the same pattern:
Therefore, the fourth missing letter is H.
The completed series is:
B D G K M P T V Y C E H L
Check the alphabetical shifts:
The repeating pattern is maintained throughout the entire series.
The four missing letters are:
Combining these letters gives DPYH.
Correct Option: B) DPYH
The letter series follows a repeating pattern of +2, +3, and +4 alphabetical shifts. Applying this pattern gives D, P, Y, and H as the missing letters. Therefore, the correct option is B) DPYH.
This is a logical reasoning problem involving ordering based on given clues. We need to deduce the birth year of each person by systematically placing them according to the conditions provided.
Correct Option: A) S
To find the ratio of heat produced by bulbs A and B, we need to use Joule's law of heating. Since the bulbs are connected in parallel, the voltage across them is the same. We can use the formula for heat produced in terms of voltage and resistance.
Correct Option: A) 3 : 1
This problem involves work and time, where the total work done is constant (building a wall). We need to find the individual work rate of a man and a woman to determine how long one woman would take to build the wall alone. We will set up a system of linear equations based on the given information and solve for the work rate of a woman.
Let \(M\) be the amount of work 1 man can do in 1 day, and \(W\) be the amount of work 1 woman can do in 1 day. The total work for building the wall is constant.
From the first statement: 8 men and 12 women can build a wall in 10 days. This means the total work done by them in 1 day is \(\frac{1}{10}\) of the wall. So, we can write the equation:
\[ 8M + 12W = \frac{1}{10} \quad \text{(Equation 1)} \]From the second statement: 6 men and 8 women can build the same wall in 14 days. This means the total work done by them in 1 day is \(\frac{1}{14}\) of the wall. So, we can write the equation:
\[ 6M + 8W = \frac{1}{14} \quad \text{(Equation 2)} \]Now we have a system of two linear equations. We need to solve for \(W\). Multiply Equation 1 by 3 and Equation 2 by 4 to eliminate \(M\):
Multiply Equation 1 by 3:
\[ 3 \times (8M + 12W) = 3 \times \frac{1}{10} \]\[ 24M + 36W = \frac{3}{10} \quad \text{(Equation 3)} \]Multiply Equation 2 by 4:
\[ 4 \times (6M + 8W) = 4 \times \frac{1}{14} \]\[ 24M + 32W = \frac{4}{14} = \frac{2}{7} \quad \text{(Equation 4)} \]Subtract Equation 4 from Equation 3:
\[ (24M + 36W) - (24M + 32W) = \frac{3}{10} - \frac{2}{7} \]\[ 4W = \frac{21 - 20}{70} \]\[ 4W = \frac{1}{70} \]Solve for \(W\):
\[ W = \frac{1}{70 \times 4} \]\[ W = \frac{1}{280} \]This means 1 woman can do \(\frac{1}{280}\) of the work in 1 day. Therefore, 1 woman will take 280 days to build the wall alone.
D) 280 Days is the correct answer. As calculated, one woman takes 280 days to complete the work alone.
Express 0.2\(\overline{7}\) in the form \( \frac{p}{q} \), where p and q are integers and q ≠ 0.
\( \frac{5}{18} \)
\( \frac{18}{7} \)
\( \frac{7}{18} \)
\( \frac{18}{5} \)
To express a repeating decimal in the form \(\frac{p}{q}\), we use an algebraic method. We set the given decimal equal to a variable, multiply it by powers of 10 to shift the decimal point, and then subtract the equations to eliminate the repeating part.
Let \(x\) be the given repeating decimal.
\[ x = 0.2\overline{7} \]The bar over '7' indicates that '7' is the repeating digit.
\[ x = 0.2777... \quad \text{(Equation 1)} \]Multiply Equation 1 by 10 to move the non-repeating digit '2' to the left of the decimal point.
\[ 10x = 2.777... \quad \text{(Equation 2)} \]Multiply Equation 1 by 100 to move one full cycle of the repeating digit '7' (along with the non-repeating '2') to the left of the decimal point.
\[ 100x = 27.777... \quad \text{(Equation 3)} \]Subtract Equation 2 from Equation 3 to eliminate the repeating part after the decimal point.
\[ 100x - 10x = 27.777... - 2.777... \]\[ 90x = 25 \]Divide both sides by 90 to find the value of \(x\).
\[ x = \frac{25}{90} \]Both the numerator and the denominator are divisible by 5.
\[ x = \frac{25 \div 5}{90 \div 5} \]\[ x = \frac{5}{18} \]A) \(\frac{5}{18}\) is the simplified fraction representing \(0.2\overline{7}\).
The angle of incidence is defined as the angle between the incident ray and the normal to the surface at the point of incidence. For a ray of light incident along the principal axis of a spherical mirror, we need to determine the direction of the normal at the point where the ray strikes the mirror.
Correct Option: A) The angle of incidence is defined as the angle between the incident ray and the normal to the surface at the point of incidence. For a ray incident along the principal axis of a spherical mirror, the ray itself travels along the normal to the mirror at the pole. Hence, the angle between the incident ray and the normal is \(0^\circ\).
The question asks about the harmful gas produced when coal and petroleum are burned in insufficient air (oxygen). This relates to the concept of incomplete combustion.
C) Carbon monoxide is produced during the incomplete combustion of carbon-based fuels like coal and petroleum when there is insufficient oxygen. It is a highly poisonous gas.