To find the number of possible values of \(y\), we need to identify natural numbers \(y\) such that \(1 \le y \le 20\) and \(y\) is co-prime with 6. Two numbers are co-prime (or relatively prime) if their greatest common divisor (GCD) is 1.
\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\)
From the list above, cross out all numbers that are multiples of 2 or 3:
\(1, \cancel{2}, \cancel{3}, \cancel{4}, 5, \cancel{6}, 7, \cancel{8}, \cancel{9}, \cancel{10}, 11, \cancel{12}, 13, \cancel{14}, \cancel{15}, \cancel{16}, 17, \cancel{18}, 19, \cancel{20}\)
The numbers remaining are \(1, 5, 7, 11, 13, 17, 19\).
There are 7 such numbers.
B) 7. There are 7 values of \(y\) (1, 5, 7, 11, 13, 17, 19) that are co-prime with 6 and do not exceed 20.
The question asks for the full form of the acronym NBFC. This is a common term in the financial sector, particularly in India, and requires knowledge of financial terminology.
Correct Option: B) Non-Banking Financial Company
NBFC stands for Non-Banking Financial Company. These are financial institutions that do not have a full banking license but provide banking services such as loans, credit facilities, acquisition of shares/stocks/bonds/debentures, leasing, hire-purchase, insurance business, chit fund business, etc. They are regulated by the Reserve Bank of India (RBI).
To find the area of a parallelogram, we use the formula: Area = base × height. We are given the base and the corresponding height, so we can directly substitute these values into the formula.
The base of the parallelogram (\(b\)) is given as 10 cm.
The corresponding height of the parallelogram (\(h\)) is given as 6 cm.
The area of a parallelogram is calculated by multiplying its base by its corresponding height.
\[ \text{Area} = \text{base} \times \text{height} \]or
\[ A = b \times h \]Substitute \(b = 10 \text{ cm}\) and \(h = 6 \text{ cm}\) into the formula:
\[ A = 10 \text{ cm} \times 6 \text{ cm} \]Perform the multiplication:
\[ A = 60 \text{ cm}^2 \]D) 60
The calculated area of the parallelogram is 60 cm², which matches option D.
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 of numbers. This often involves looking at differences between consecutive terms, ratios, or combinations of arithmetic operations and powers.
Let the given series be \(S = \{4, 5, 13, 40, ?, 229, 445, 788, 1300\}\).
Calculate the differences between consecutive terms:
The differences are \(1, 8, 27\). These numbers are perfect cubes:
This suggests that the pattern for the differences is a sequence of consecutive cubes. If this pattern holds, the next difference should be \(4^3\).
Calculate the next term in the series using this pattern:
Verify the pattern for the subsequent terms using the calculated missing term \(104\):
Continue verifying:
And so on:
Finally:
Since the pattern of adding consecutive cubes (\(1^3, 2^3, 3^3, 4^3, 5^3, 6^3, 7^3, 8^3\)) holds true for the entire series, the missing number is \(104\).
D) 104 — The pattern in the series is that each subsequent term is obtained by adding the cube of consecutive natural numbers to the previous term. Starting with the first term \(a_1 = 4\), the terms are generated as follows:
Thus, the missing number is \(104\).
This is a syllogism problem. We need to analyze the given statements and determine which conclusions logically follow. We can use Venn diagrams or logical deduction to solve this. We will represent each category as a circle and show the relationships between them based on the statements.
From Statement 1 and 2, we can infer a nested structure:
Cars \(\subset\) Scooters \(\subset\) Trucks
From Statement 3, 'Helicopters' are completely separate from 'Trucks'.
From Statement 2, "All scooters are trucks." This implies that some trucks are scooters. Therefore, "No truck is scooter" is false.
Since all cars are scooters (Statement 1) and all scooters are trucks (Statement 2), it logically follows that all cars must be trucks. This conclusion is true.
Since all scooters are trucks (Statement 2), it means that the set of scooters is a subset of trucks. If all scooters are trucks, then it must be true that some trucks are scooters. This conclusion is true.
We know that all cars are trucks (from Conclusion II, which we established as true). We also know that no helicopter is truck (Statement 3). If no truck is a helicopter, and all cars are trucks, then no car can be a helicopter. This conclusion is true.
Conclusions II, III, and IV logically follow from the given statements.
C) Only conclusions II, III and IV follow
As determined in the step-by-step analysis, conclusions II, III, and IV are all logically derivable from the given statements.
When four numbers are in proportion, it means that the ratio of the first two numbers is equal to the ratio of the last two numbers. We will set up this relationship as an equation and solve for the unknown variable \(y\).
Understand the concept of proportion: If four numbers \(a, b, c,\) and \(d\) are in proportion, it means that the ratio \(a:b\) is equal to the ratio \(c:d\). This can be written as:
\[ \frac{a}{b} = \frac{c}{d} \]Apply to the given numbers: The given numbers are 5, 15, 20, and \(y\). So, we can write the proportion as:
\[ \frac{5}{15} = \frac{20}{y} \]Simplify the ratio (optional but helpful): The ratio \(\frac{5}{15}\) can be simplified by dividing both the numerator and the denominator by 5:
\[ \frac{5 \div 5}{15 \div 5} = \frac{1}{3} \]Rewrite the proportion with the simplified ratio:
\[ \frac{1}{3} = \frac{20}{y} \]Solve for \(y\): To solve for \(y\), we can cross-multiply:
\[ 1 \times y = 3 \times 20 \]\[ y = 60 \]C) 60 is the correct value for \(y\) because it satisfies the proportion \[\frac{5}{15} = \frac{20}{60}\], as both ratios simplify to \(\frac{1}{3}\).
The question asks to identify a greenhouse gas from the given options. We need to recall the definition of greenhouse gases and common examples.
Correct Option: A) Carbon dioxide is the most prominent example of a greenhouse gas among the given options. It is a major contributor to the greenhouse effect and global warming.
Refer to the following letter, number, symbol series and answer the question:
C @ B N M K J % F K L I & E W * P O S E A
How many such symbols are there in the above series which are immediately preceded and followed by a vowel?
The problem asks us to identify the number of symbols in the given series that are immediately preceded and followed by a vowel. We need to scan the series, identify symbols, and then check their preceding and succeeding characters to see if both are vowels.
B) One is the correct answer because only the symbol '&' in the series is immediately preceded by a vowel ('I') and immediately followed by a vowel ('E').
The question describes how the total value of final goods output is distributed among various factors of production. It asks for the term that describes what the entrepreneur appropriates after all other factor payments (wages, interest, rent) have been made, assuming no indirect taxes or subsidies.
Mathematically, if we consider the total value of output (Revenue) and subtract the payments to other factors:
\[ \text{Profit} = \text{Total Revenue} - (\text{Wages} + \text{Interest} + \text{Rent}) \]
This is precisely what the question describes as "whatever is left over is appropriated by the entrepreneur".
Correct Option: A) profit
Profit is the residual income that accrues to the entrepreneur after all other costs of production (wages, interest, rent) have been paid. It is the reward for risk-taking and organizing production.
To determine the percentage of a specific gamete type (tW) formed by a plant with genotype TtWw, we need to understand the principle of independent assortment during gamete formation. Each gene (T/t and W/w) segregates independently, meaning that the allele for one gene does not influence the allele for the other gene that ends up in the same gamete.
B) 25% is the correct percentage of tW gametes formed by a plant with genotype TtWw, based on the principles of independent assortment.