The question asks to identify the incorrect statement regarding the Supreme Court's ruling in 'Samtola Devi vs The State Of Uttar Pradesh' concerning the 'Maintenance and Welfare of Parents and Senior Citizens Act, 2007'. We need to evaluate each option based on the provisions of the Act and the likely interpretation by the Supreme Court.
Correct Option: B) Eviction of a child or relative is mandatory in every case of neglect under the Act.
This statement is incorrect. While the Maintenance and Welfare of Parents and Senior Citizens Act, 2007, and subsequent judicial pronouncements (including the likely ruling in 'Samtola Devi vs The State Of Uttar Pradesh') empower tribunals to order eviction, it is not a mandatory step in every case of neglect. Eviction is a discretionary measure taken when deemed necessary for the protection and welfare of the senior citizen, especially when neglect or abuse is severe or persistent, or when the senior citizen's peace and safety are jeopardized. It is not an automatic consequence of every instance of neglect.
The question asks for the state from which the Centre for Science and Environment (CSE) and Down To Earth (DTE) magazine released their annual publication 'State of India's Environment' on 26 February 2025. This is a factual question related to current affairs and environmental reports.
Correct Option: B) Rajasthan
To determine the time at a different longitude, we need to calculate the longitudinal difference and then convert this difference into time. We know that the Earth rotates 360 degrees in 24 hours, which allows us to establish a relationship between longitude and time.
The Earth completes one rotation (360°) in 24 hours.
Given IST longitude = \(82^{\circ}30'E\)
Target longitude = \(97^{\circ}30'E\)
Longitudinal difference = Target longitude - IST longitude
\[ \text{Longitudinal difference} = 97^{\circ}30'E - 82^{\circ}30'E = 15^{\circ} \]
Since \(1^{\circ}\) of longitude corresponds to 4 minutes of time difference:
\[ \text{Time difference} = 15^{\circ} \times 4 \text{ minutes}/^{\circ} = 60 \text{ minutes} \]
So, the time difference is 1 hour.
Since \(97^{\circ}30'E\) is to the east of \(82^{\circ}30'E\), the time at \(97^{\circ}30'E\) will be ahead of IST.
Given time at IST (\(82^{\circ}30'E\)) = 12 noon.
Time at \(97^{\circ}30'E\) = Time at IST + Time difference
\[ \text{Time at } 97^{\circ}30'E = 12:00 \text{ PM} + 1 \text{ hour} = 1:00 \text{ PM} \]
Correct Option: D) 1:00 PM
To find the percentage gain or loss, we will assume a cost price (CP) for the goods. Then, we will calculate the marked price (MP) by adding the given percentage markup. After that, we will calculate the selling price (SP) by applying the given discount on the marked price. Finally, we will compare the selling price with the cost price to determine the percentage gain or loss.
Assume the Cost Price (CP):
Let the Cost Price (CP) of the goods be \(₹100\).
Calculate the Marked Price (MP):
The salesman marks his goods 20% above the cost price.
Calculate the Selling Price (SP):
He gives a discount of 25% on the marked price.
Determine Gain or Loss:
Now, compare the Selling Price (SP) with the Cost Price (CP).
Calculate Percentage Loss:
\[ \text{Loss} = \text{CP} - \text{SP} = 100 - 90 = ₹10 \]\[ \text{Percentage Loss} = \frac{\text{Loss}}{\text{CP}} \times 100 \]\[ \text{Percentage Loss} = \frac{10}{100} \times 100 = 10\% \]B) 10% loss
As calculated, the salesman incurs a loss of 10%.
To solve this problem, we need to determine the cost price (CP), then calculate the desired selling price (SP) to achieve a 14% gain. After that, we'll find the marked price (MP) based on the given 50% markup. Finally, we can calculate the discount percentage needed on the marked price to arrive at the desired selling price.
Assume Cost Price (CP):
Let the Cost Price (CP) of the item be \(₹100\).
Calculate Marked Price (MP):
The shopkeeper fixes the marked price 50% above its cost price.
\[ \text{MP} = \text{CP} + 50\% \text{ of CP} \]\[ \text{MP} = 100 + \frac{50}{100} \times 100 \]\[ \text{MP} = 100 + 50 \]\[ \text{MP} = ₹150 \]
Calculate Desired Selling Price (SP):
The shopkeeper wants to gain 14%.
\[ \text{SP} = \text{CP} + 14\% \text{ of CP} \]\[ \text{SP} = 100 + \frac{14}{100} \times 100 \]\[ \text{SP} = 100 + 14 \]\[ \text{SP} = ₹114 \]
Calculate Discount Amount:
The discount is given on the Marked Price to reach the Selling Price.
\[ \text{Discount Amount} = \text{MP} - \text{SP} \]\[ \text{Discount Amount} = 150 - 114 \]\[ \text{Discount Amount} = ₹36 \]
Calculate Discount Percentage:
The discount percentage is calculated on the Marked Price.
\[ \text{Discount Percentage} = \left( \frac{\text{Discount Amount}}{\text{MP}} \right) \times 100\% \]\[ \text{Discount Percentage} = \left( \frac{36}{150} \right) \times 100\% \]\[ \text{Discount Percentage} = \left( \frac{36}{3 \times 50} \right) \times 100\% \]\[ \text{Discount Percentage} = \left( \frac{12}{50} \right) \times 100\% \]\[ \text{Discount Percentage} = 12 \times 2\% \]\[ \text{Discount Percentage} = 24\% \]
Correct Option: D) 24%
To solve this series problem, we need to identify the pattern or rule governing the sequence of numbers. We will calculate the differences between consecutive terms to find a consistent arithmetic or geometric progression, or a pattern in the differences themselves.
Let the given series be \(S = 282, 259, 226, ?, 130, 67\).
Calculate the difference between the first two terms:
\[ 259 - 282 = -23 \]Calculate the difference between the second and third terms:
\[ 226 - 259 = -33 \]Now, let's look at the differences: \(-23, -33\). The difference between these differences is \(-33 - (-23) = -10\). This suggests that the differences between consecutive terms are decreasing by 10 each time.
Following this pattern, the next difference should be \(-33 - 10 = -43\).
So, the missing term (?) would be:
\[ 226 - 43 = 183 \]Let's verify this pattern with the subsequent terms. The next difference should be \(-43 - 10 = -53\).
Check if \(183 - 53 = 130\):
\[ 183 - 53 = 130 \]This matches the given term.
The next difference should be \(-53 - 10 = -63\).
Check if \(130 - 63 = 67\):
\[ 130 - 63 = 67 \]This also matches the given term.
The pattern is consistent: the differences between consecutive terms are \(-23, -33, -43, -53, -63\), which means each subsequent difference decreases by 10.
B) 183 — Based on the identified pattern where the difference between consecutive terms decreases by 10 each time, the missing term is \(226 - 43 = 183\).
This problem requires the application of the empirical relationship between the mean, median, and mode for a moderately skewed distribution. The empirical formula states that \(\text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean}\). We are given a relationship between the median and mode, and we need to find the relationship between the median and mean.
Recall the empirical formula relating mean, median, and mode:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]From the problem statement, we are given that the median is 71.24 less than its mode. This can be written as:
\[ \text{Median} = \text{Mode} - 71.24 \]Rearrange the given relationship to express Mode in terms of Median:
\[ \text{Mode} = \text{Median} + 71.24 \]Substitute this expression for Mode into the empirical formula:
\[ \text{Median} + 71.24 = 3 \times \text{Median} - 2 \times \text{Mean} \]Now, we need to find by how much the median exceeds its mean, which means we need to find the value of \(\text{Median} - \text{Mean}\). Let's rearrange the equation to isolate terms involving Median and Mean:
\[ 71.24 = 3 \times \text{Median} - \text{Median} - 2 \times \text{Mean} \]\[ 71.24 = 2 \times \text{Median} - 2 \times \text{Mean} \]Factor out 2 from the right side:
\[ 71.24 = 2 (\text{Median} - \text{Mean}) \]Divide by 2 to find the value of \(\text{Median} - \text{Mean}\):
\[ \text{Median} - \text{Mean} = \frac{71.24}{2} \]\[ \text{Median} - \text{Mean} = 35.62 \]B) The median exceeds its mean by 35.62.
The question asks for the full form of the acronym ASCII in the context of computing. This is a direct recall question about a fundamental concept in computer science.
D) American Standard Code for Information Interchange — This is the correct and universally recognized full form of ASCII. ASCII is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices.
This problem involves calculating work done by two individuals, A and B, working together for some time and then one person completing the remaining work. We will use the concept of work rate (amount of work done per day) to solve this problem. The total work is considered as 1 unit.
Correct Option: C) 15
Following the provisions of the 73rd Constitutional Amendment 1992, how frequently are the members of the Gram Sabha expected to meet in a year?
At least twice in a year
Every week
Once a month
Once every five years
The question asks about the mandatory meeting frequency of Gram Sabha members as per the 73rd Constitutional Amendment Act, 1992. This requires knowledge of the specific provisions related to Gram Sabhas under this amendment.
A) At least twice in a year. This is the minimum frequency generally prescribed or understood under the spirit and implementation of the 73rd Constitutional Amendment Act for Gram Sabha meetings to ensure active participation and oversight by the villagers.