This is a syllogism problem. We need to analyze the given statements and determine which conclusions logically follow. We can use Venn diagrams to visualize the relationships between the categories mentioned in the statements.
C) Neither conclusion (I) nor (II) follows
As determined in the step-by-step analysis, neither conclusion (I) nor conclusion (II) can be logically derived from the given statements.
The problem can be solved by translating the given word statement into a mathematical equation. We need to calculate 1800% of 10 first, then subtract 10 from it. This result will be equal to 25% of k. Finally, we can solve for k.
Calculate 1800% of 10:
To find a percentage of a number, convert the percentage to a decimal or fraction and multiply it by the number.
\[ 1800\% \text{ of } 10 = \frac{1800}{100} \times 10 \]\[ = 18 \times 10 \]\[ = 180 \]Determine the value that is 10 less than 1800% of 10:
The problem states "10 less than 1800% of 10". So, we subtract 10 from the value calculated in step 1.
\[ 180 - 10 = 170 \]Formulate the equation:
The problem states "25% of k is 10 less than 1800% of 10". From step 2, we know that "10 less than 1800% of 10" is 170. So, we can write the equation:
\[ 25\% \text{ of } k = 170 \]Solve for k:
Convert 25% to a fraction or decimal and solve for k.
\[ \frac{25}{100} \times k = 170 \]\[ \frac{1}{4} \times k = 170 \]\[ k = 170 \times 4 \]\[ k = 680 \]B) 680 is the correct value for k, as derived from the step-by-step calculation.
The question asks for the main advantage of saving an MS PowerPoint presentation as a .pdf file. We need to evaluate each option based on the characteristics of PDF files and their common uses, especially in comparison to native PowerPoint files.
Based on these points, we can assess the given options.
B) It reduces file size and prevents unwanted editing. This is the main advantage. PDFs are often smaller than their original PowerPoint counterparts due to efficient compression. More importantly, they are designed to preserve the document's appearance and prevent easy modification, making them ideal for sharing final versions where content integrity is crucial.
The problem asks us to find the positive value of Z given that the third proportional of 36 and Z is 4. We will use the definition of the third proportional to set up an equation and solve for Z.
Understand the concept of third proportional: If \(a\), \(b\), and \(c\) are in continued proportion, then \(a:b::b:c\). Here, \(c\) is called the third proportional to \(a\) and \(b\).
Formulate the proportion: According to the definition, if 4 is the third proportional of 36 and Z, then the numbers 36, Z, and 4 are in continued proportion. This can be written as:
\[ 36 : Z :: Z : 4 \]Convert the proportion to an equation: The ratio \(a:b::b:c\) can be written as \[\frac{a}{b} = \frac{b}{c}\]. Applying this to our problem:
\[ \frac{36}{Z} = \frac{Z}{4} \]Solve for Z: Cross-multiply the terms in the equation:
\[ Z \times Z = 36 \times 4 \] \[ Z^2 = 144 \]Find the value of Z: Take the square root of both sides:
\[ Z = \pm\sqrt{144} \] \[ Z = \pm 12 \]Select the positive value: The question asks for the positive value of Z. Therefore,
\[ Z = 12 \]Correct Option: D) 12
The problem asks us to find a triad of letter pairs that follows the same pattern as the two given triads: OL-QN-SU and LI-NK-PR. We need to analyze the positional differences between the letters within each pair and between consecutive pairs in the given triads.
Let's consider the pattern for each letter's position independently:
This pattern is not uniform for the second letters. Let's re-examine the differences within each pair and the jump from the second letter of a pair to the first letter of the next pair.
The pattern for differences within pairs is \(-3, -3, +2\).
So, the pattern is: (First letter, First letter - 3), then jump +5 from the second letter of the first pair to the first letter of the second pair, then (First letter, First letter - 3), then jump +5 from the second letter of the second pair to the first letter of the third pair, then (First letter, First letter + 2).
This matches the \(-3, -3, +2\) pattern for differences within pairs.
This also matches the \(+5\) jump pattern. Thus, the established pattern is:
All parts of the pattern match for option B.
With reference to the 40th Amendment Act, 1976, which category of maritime zones came under the legislative jurisdiction of the Parliament?
Groundwater reserves
Territorial waters and EEZ
Inter-state river waters
Inland rivers and lakes
The question asks about the specific categories of maritime zones that came under the legislative jurisdiction of the Indian Parliament through the 40th Amendment Act of 1976. This requires knowledge of the constitutional amendments related to India's maritime boundaries and resources.
B) Territorial waters and EEZ. The 40th Amendment Act, 1976, specifically empowered the Parliament to legislate on matters concerning the limits of India's territorial waters, continental shelf, exclusive economic zone (EEZ), and other maritime zones, thereby bringing these areas under its legislative jurisdiction.
To calculate the compound interest when compounded quarterly, we need to adjust the annual interest rate and the time period. The annual rate is divided by 4 (since there are 4 quarters in a year), and the number of years is multiplied by 4 to get the total number of compounding periods. Then, we use the compound interest formula to find the total amount and subtract the principal to get the interest earned.
B) Rs.1,11,384 is the compound interest earned.
The problem requires us to evaluate a mathematical expression after interchanging certain operators. We need to apply the BODMAS/PEMDAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction) after performing the operator interchanges.
B) 51 is the correct answer. After interchanging the operators and following the BODMAS rule, the value of the expression is 51.
The question asks to identify the bank that launched a verified WhatsApp channel for financial updates on April 4, 2025. This requires knowledge of recent banking news and initiatives in India.
Correct Option: B) Reserve Bank of India
On April 4, 2025, the Reserve Bank of India (RBI) officially launched its verified WhatsApp channel. This channel is intended to provide real-time updates and reliable financial information directly to the public, enhancing communication and financial literacy. This move aligns with the RBI's efforts to leverage digital platforms for broader outreach.
The problem states that the percentage profit earned by selling an article at one price is equal to the percentage loss incurred by selling it at another price. We need to find the cost price (CP) first and then calculate the selling price (SP) required to make a 45% profit.
Let the Cost Price (CP) of the article be \(C\).
When the article is sold for Rs. 6,833, there is a profit. The Selling Price (SP1) is Rs. 6,833.
Profit \(= \text{SP1} - C = 6833 - C\)
Percentage Profit \[= \frac{\text{Profit}}{C} \times 100 = \frac{6833 - C}{C} \times 100\]
When the article is sold for Rs. 1,447, there is a loss. The Selling Price (SP2) is Rs. 1,447.
Loss \(= C - \text{SP2} = C - 1447\)
Percentage Loss \[= \frac{\text{Loss}}{C} \times 100 = \frac{C - 1447}{C} \times 100\]
According to the problem, the percentage profit is equal to the percentage loss:
\[ \frac{6833 - C}{C} \times 100 = \frac{C - 1447}{C} \times 100 \]Since \(C \neq 0\) and \(100 \neq 0\), we can cancel \(C\) and \(100\) from both sides:
\[ 6833 - C = C - 1447 \]Now, solve for \(C\):
\[ 6833 + 1447 = C + C \] \[ 8280 = 2C \] \[ C = \frac{8280}{2} \] \[ C = 4140 \]So, the Cost Price of the article is Rs. 4,140.
We need to find the price at which the article should be sold to make a 45% profit.
Required Selling Price (SP3) \(= C + (C \times 45\%)\)
\[ \text{SP3} = C \left(1 + \frac{45}{100}\right) \] \[ \text{SP3} = 4140 \left(1 + 0.45\right) \] \[ \text{SP3} = 4140 \times 1.45 \]Calculate the final selling price:
\[ \text{SP3} = 4140 \times 1.45 = 6003 \]The article should be sold for Rs. 6,003 to make a 45% profit.
A) 6,003 is the correct selling price to achieve a 45% profit.