The question pertains to a significant Supreme Court judgment regarding the minority status of educational institutions, specifically in the context of Aligarh Muslim University (AMU). To answer correctly, one must understand the key holdings of the majority opinion in the 'Aligarh Muslim University vs Naresh Agarwal (November 2024)' case.
Correct Option: A) Institutions created before 1950 can still be considered minority institutions, even if incorporated by statute. This option accurately reflects the core holding of the majority judgment, which emphasized that the pre-constitutional establishment by a minority community and its administration are paramount, and subsequent statutory incorporation does not automatically negate its minority status.
What is the mean of the following distribution?
| Marks | 19 | 31 | 54 | 69 | 95 |
| No. of Students | 22 | 35 | 64 | 34 | 57 |
To find the mean of a grouped distribution, we use the formula for the weighted average. Each mark value is multiplied by its corresponding number of students (frequency), these products are summed, and then divided by the total number of students.
Correct Option: A) 60
The problem asks us to find the principal sum given the difference between simple interest (SI) and compound interest (CI) for 2 years at a specific rate. We will use the standard formulas for SI and CI, and the formula for the difference between CI and SI for 2 years.
For 2 years, the difference between compound interest and simple interest is given by the formula:
\[ \text{CI} - \text{SI} = P \left( \frac{R}{100} \right)^2 \]We are given \(\text{CI} - \text{SI} = 407\) and \(R = 10\%\). Let \(P\) be the principal sum.
\[ 407 = P \left( \frac{10}{100} \right)^2 \]Multiply both sides by 100 to find \(P\):
\[ P = 407 \times 100 \]\[ P = 40700 \]The calculated sum is ₹40,700. This matches option A.
A) ₹40,700 is the correct sum. The direct formula for the difference between CI and SI for 2 years simplifies the calculation significantly, leading to \(P = 40700\).
The problem presents a series of letter-number clusters. To find the missing cluster, we need to identify the pattern in the letters and the numbers separately.
K (11) \(\rightarrow\) J (10) \(\rightarrow\) I (9) \(\rightarrow\) H (8)
There is a consistent decrease of 1 in the alphabetical position of the first letter. Following this pattern, the next first letter should be G (7).
N (14) \(\rightarrow\) M (13) \(\rightarrow\) L (12) \(\rightarrow\) K (11)
There is also a consistent decrease of 1 in the alphabetical position of the second letter. Following this pattern, the next second letter should be J (10).
So, the letters for the missing cluster are GJ.
33 \(\rightarrow\) 41 \(\rightarrow\) 49 \(\rightarrow\) 57
Let's find the difference between consecutive numbers:
The numbers are increasing by 8 in each step. Following this pattern, the next number should be \(57 + 8 = 65\).
The letters are GJ and the number is 65. Therefore, the complete cluster is GJ65.
A) GJ65 is the correct option because it follows the identified patterns for both the letters and the numbers.
The question asks to identify the act that provided a regular code for all regulations concerning the internal government of British India. This requires knowledge of the key provisions and significance of various Charter Acts and Regulating Acts passed by the British Parliament.
Correct Option: B) Charter Act of 1793
Due to decrease in manpower, the production in a factory decreases by 10%. By what percentage should the working hours be increased to restore the original production?
16\( \frac{2}{3} \)%
8\( \frac{1}{3} \)%
11\( \frac{1}{9} \)%
10%
This problem involves inverse proportionality. When the production decreases due to a decrease in manpower, to restore the original production, the working hours must be increased. We need to find the percentage increase in working hours required to compensate for the 10% decrease in production.
Let the original production be \(P\). Let the original manpower be \(M\) and original working hours be \(H\). We can assume that production is directly proportional to manpower and working hours. So, \(P = k \times M \times H\), where \(k\) is a constant.
Due to a decrease in manpower, the production decreases by 10%. This means the new production \(P'\) is \(90\%\) of the original production \(P\).
\[ P' = P - 0.10P = 0.90P \]We want to restore the original production \(P\). Let the new working hours be \(H'\). The manpower remains decreased, so the effective production capacity is still \(0.90P\). To restore the original production \(P\), we need to find the percentage increase in working hours.
Let's assume the original production is 100 units. After a 10% decrease, the production becomes 90 units.
To restore the original production of 100 units from 90 units, we need an increase of \(100 - 90 = 10\) units.
The percentage increase in production (which must be achieved by increasing working hours) is calculated with respect to the decreased production (the current base).
\[ \text{Percentage increase} = \frac{\text{Required increase}}{\text{Decreased production}} \times 100 \% \]\[ \text{Percentage increase} = \frac{10}{90} \times 100 \% \]\[ \text{Percentage increase} = \frac{1}{9} \times 100 \% \]\[ \text{Percentage increase} = \frac{100}{9} \% \]Convert the improper fraction to a mixed number:
\[ \frac{100}{9} = 11 \frac{1}{9} \% \]C) \(11\frac{1}{9}\)\% is the correct answer. This percentage increase in working hours will compensate for the 10% decrease in manpower, restoring the original production level.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the other three, based on English alphabetical order. We need to find the relationship between the letters in each pair and then identify the odd one out.
D) MH - IP. In options A, B, and C, both letter clusters consist of two consecutive letters in alphabetical order, and the second cluster's letters are each two positions before the corresponding letters in the first cluster. Option D does not follow this pattern; neither MH nor IP consists of consecutive letters, and the positional difference pattern is also not maintained.
The problem presents a number series, and we need to find the next term. We will analyze the differences between consecutive terms to identify a pattern. Once the pattern is identified, we can apply it to find the missing number.
\(301, 300, 297, 292, 285, ?\)
The differences are \(-1, -3, -5, -7\). This is a series of consecutive odd numbers, each with a negative sign, decreasing by 2 each time (i.e., \(1, 3, 5, 7, \dots\)).
Following the pattern, the next odd number after 7 is 9. So, the next difference should be \(-9\).
Subtract 9 from the last given term (285):
\[ 285 - 9 = 276 \]B) 276 is the correct answer because it follows the established pattern of subtracting consecutive odd numbers (1, 3, 5, 7, 9) from the previous term.
The question asks to identify the community associated with the Singh Sabha movement. This requires knowledge of 19th-century socio-religious reform movements in India and their respective communities.
Correct Option: B) The Singh Sabha movement was a Sikh socio-religious reform movement that emerged in the late 19th century. Its main objectives were to restore Sikhism to its pristine glory, promote Sikh education, and protect Sikh identity from the influences of other religions and reformist movements.
The problem asks us to identify numbers in a given series that are immediately preceded by a number and immediately followed by a number. We need to scan the series from left to right and apply this condition to each number.
D) 1. There is only one such number, which is '5', as it is immediately preceded by '4' (a number) and immediately followed by '3' (a number).