The problem involves a letter-shifting cipher, specifically a Caesar cipher variant. Each letter is shifted three places forward in the alphabet. This operation is performed four times in total. We need to find the letter at the fourth position of the final word after all four operations.
A) O is the correct answer because after a total shift of 12 positions from 'C', the resulting letter is 'O'.
When three cubes are arranged next to each other, they form a cuboid. We need to determine the dimensions of this resulting cuboid and then calculate its total surface area using the formula for the surface area of a cuboid.
Correct Option: A) 350 cm²
This is a syllogism problem. We need to determine which conclusions logically follow from the given statements. We can use Venn diagrams to visualize the relationships between the categories mentioned in the statements.
A) Only conclusion I follows.
Which of the following options is the closest approximate value which will come in place of the question mark (?) in the following equation?
(\(\sqrt{785}\) + 72 ÷ 4 × 3 − \(\sqrt{120}\)) × 2 =?
To find the approximate value, we need to simplify the given expression by first approximating the square roots and then following the order of operations (BODMAS/PEMDAS).
A) 142 is the closest approximate value.
A dishonest dealer sells goods at a 6\( \frac{1}{4} \)% loss on cost price but actually gives 14 gm of goods for every 16 gm that is mentioned on the weight. His gain or loss percent is:
7\( \frac{1}{3} \)%
6\( \frac{1}{7} \)%
7\( \frac{1}{7} \)%
6\( \frac{1}{7} \)%
This problem involves a dishonest dealer who claims to sell at a loss but uses a false weight, which actually results in a gain. We need to calculate the overall gain or loss percentage by considering both the stated loss on cost price and the profit from using a false weight.
Calculate the stated loss percentage:
The dealer claims to sell at a loss of \(6\frac{1}{4}\)%. Convert this mixed fraction to an improper fraction:
\[ 6\frac{1}{4}\% = \frac{25}{4}\% \]Calculate the profit from false weight:
The dealer gives 14 gm for every 16 gm mentioned. This means for every 16 gm the customer thinks they are getting, they only receive 14 gm. The profit in terms of weight is \(16 - 14 = 2\) gm.
The profit percentage due to false weight is calculated on the actual weight given:
\[ \text{Profit \% (false weight)} = \frac{\text{Error}}{\text{True Value}} \times 100 \]\[ \text{Profit \% (false weight)} = \frac{(16 - 14)}{14} \times 100 = \frac{2}{14} \times 100 = \frac{1}{7} \times 100 = \frac{100}{7}\% \]Combine the two effects using successive percentage change:
Let the cost price of 1 gm be Re. 1. So, the cost price of 16 gm is Rs. 16.
First, the dealer sells at a loss of \(6\frac{1}{4}\)% on the cost price. This means the selling price (SP) for 16 gm, based on the stated loss, would be:
\[ \text{SP}_{\text{stated}} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]\[ \text{SP}_{\text{stated}} = 16 \times \left(1 - \frac{25/4}{100}\right) = 16 \times \left(1 - \frac{25}{400}\right) = 16 \times \left(1 - \frac{1}{16}\right) \]\[ \text{SP}_{\text{stated}} = 16 \times \frac{15}{16} = 15 \]So, the dealer sells 16 gm for Rs. 15, according to his stated loss.However, the dealer only gives 14 gm instead of 16 gm. The cost price for the dealer for the actual quantity given (14 gm) is Rs. 14.
The effective selling price for the 14 gm he actually gives is Rs. 15 (as calculated above, this is what he charges for the '16 gm').
Now, calculate the actual gain or loss percentage:
\[ \text{Gain/Loss \%} = \frac{\text{Effective SP} - \text{Effective CP}}{\text{Effective CP}} \times 100 \]\[ \text{Gain/Loss \%} = \frac{15 - 14}{14} \times 100 = \frac{1}{14} \times 100 = \frac{100}{14}\% \]\[ \text{Gain/Loss \%} = \frac{50}{7}\% \]Convert the result to a mixed fraction:
\[ \frac{50}{7}\% = 7\frac{1}{7}\% \]Since the result is positive, it's a gain.Correct Option: C) \(7\frac{1}{7}\)%
The question asks about the number of Deputy Governors of the Reserve Bank of India (RBI) as of June 2022. This is a factual question related to the organizational structure of the RBI.
Correct Option: A) The Reserve Bank of India Act, 1934, allows for a maximum of four Deputy Governors. The RBI typically operates with one Governor and four Deputy Governors. As of June 2022, this structure was in place.
This problem can be solved by applying Ohm's Law, which states the relationship between voltage, current, and resistance in an electrical circuit. Ohm's Law is given by the formula \(V = IR\), where \(V\) is the potential difference (voltage), \(I\) is the current, and \(R\) is the resistance.
The problem provides the following information:
Ohm's Law is expressed as:
\[ V = IR \]To find the resistance, we need to isolate \(R\):
\[ R = \frac{V}{I} \]Plug in the values of \(V\) and \(I\):
\[ R = \frac{3 \text{ V}}{0.1 \text{ A}} \]Perform the division:
\[ R = 30 \text{ } \Omega \]D) 30 Ω is the correct answer. By applying Ohm's Law \(R = V/I\) with the given values \(V = 3 \text{ V}\) and \(I = 0.1 \text{ A}\), the resistance is calculated as \(3 \text{ V} / 0.1 \text{ A} = 30 \text{ } \Omega\).
The question asks about the fundamental concept represented by an indifference map in economics. An indifference map is a graphical tool used in consumer theory to show consumer preferences. Understanding what each indifference curve and the collection of them (the map) signifies is key to answering this question.
Correct Option: B) satisfaction — An indifference map is a collection of indifference curves, where each curve represents a specific level of satisfaction or utility. Curves further from the origin indicate higher levels of satisfaction, while curves closer to the origin indicate lower levels of satisfaction. Thus, the map as a whole represents different levels of satisfaction.
30 cricketers are standing in a straight row facing the north. Amar is standing 10th from the right end while Dinesh is standing 5th from the left end. How many cricketers are standing between Amar and Dinesh?
To find the number of cricketers between Amar and Dinesh, we first need to determine their positions from a common reference point (either the left end or the right end). Once we have their positions from the same end, we can subtract the smaller position from the larger position and then subtract 1 (because we are looking for the number of people *between* them, not including them).
If Amar is 10th from the right end in a row of 30, his position from the left end can be calculated as:
\[ \text{Amar's position from left} = \text{Total cricketers} - \text{Amar's position from right} + 1 \]\[ \text{Amar's position from left} = 30 - 10 + 1 = 21 \]So, Amar is 21st from the left end.We now have Dinesh at 5th from the left end and Amar at 21st from the left end. Both positions are from the same reference point (left end).
The number of people between them is the difference in their positions minus 1.
\[ \text{Cricketers between Amar and Dinesh} = \text{Amar's position from left} - \text{Dinesh's position from left} - 1 \]\[ \text{Cricketers between Amar and Dinesh} = 21 - 5 - 1 \]\[ \text{Cricketers between Amar and Dinesh} = 16 - 1 = 15 \]C) 15 is the correct answer. There are 15 cricketers standing between Amar and Dinesh.
The question describes a specific configuration of angles formed when a transversal line intersects two other straight lines. We need to identify the correct term for such a pair of angles based on their relative positions.
C) corresponding. This term perfectly fits the description: angles on the same side of the transversal and in the same relative position (both above or both below) with respect to the two intersected lines.