The question asks to identify the Article of the Indian Constitution that grants minorities, based on language, the right to establish educational institutions. This falls under the Fundamental Rights related to cultural and educational rights.
Correct Option: C) Article 30 — This Article explicitly grants all minorities, whether based on religion or language, the right to establish and administer educational institutions of their choice. This directly answers the question.
Prince ranked 24th from the top and 39th from the bottom in his class. How many students are there in his class?
To find the total number of students in the class, we can use the formula for calculating the total number of items in a sequence when the position of one item from both ends is known. This is a common type of ranking problem.
When a person's rank from both the top (or left) and bottom (or right) is given, the total number of people in the row/class can be calculated using the formula:
\[ \text{Total students} = (\text{Rank from top}) + (\text{Rank from bottom}) - 1 \]Substitute Prince's ranks into the formula:
\[ \text{Total students} = 24 + 39 - 1 \]When we add Prince's rank from the top (24) and his rank from the bottom (39), Prince himself is counted twice. Therefore, to get the actual total number of students, we must subtract 1 from the sum.
B) 62. Based on the calculation, the total number of students in the class is 62.
The problem asks us to identify a pair of letter codes that follows the same pattern as the two given pairs: HKN : LOR and DJO : HNS. We need to analyze the positional differences between the letters in each corresponding position within the given pairs and then apply that pattern to the options.
A) AFM : EJQ
- First letter: A to E. A is 1st, E is 5th. Difference: \(5 - 1 = +4\).
- Second letter: F to J. F is 6th, J is 10th. Difference: \(10 - 6 = +4\).
- Third letter: M to Q. M is 13th, Q is 17th. Difference: \(17 - 13 = +4\).
This pair follows the \(+4, +4, +4\) pattern.
The problem involves calculating the average of a set of numbers. We are given the total sum of five numbers, the average of the first two numbers, and the value of the third number. We need to find the average of the remaining two numbers. The key concept here is that the sum of numbers is equal to their average multiplied by the count of numbers.
A) 199.5 is the correct average of the remaining two numbers.
This problem involves similar triangles. When an object casts a shadow, the sun's rays create a similar triangle with the object and its shadow, and another similar triangle with a different object and its shadow, provided they are observed at the same time. The ratio of the height of an object to the length of its shadow will be constant.
Since the observations are made at the same time, the angle of elevation of the sun is the same for both the stick and the tower. This means the triangles formed by the object, its shadow, and the sun's rays are similar. Therefore, the ratio of height to shadow length is constant:
\[ \frac{\text{Height of stick}}{\text{Length of stick's shadow}} = \frac{\text{Height of tower}}{\text{Length of tower's shadow}} \] \[ \frac{H_s}{L_s} = \frac{H_t}{L_t} \]Correct Option: A) 124.6 m
The problem asks us to identify a set of three numbers that follow the same relationship as the given sets: (37, 48, 59) and (41, 52, 63). We need to find the pattern within these given sets first.
Analyze the first given set (37, 48, 59):
Analyze the second given set (41, 52, 63):
Conclusion on the pattern: The numbers in the sets are in an arithmetic progression with a common difference of 11.
Check the options based on this pattern:
Correct Option: C) (56, 67, 78) — This set follows the pattern where each subsequent number is obtained by adding 11 to the previous number: \(56 + 11 = 67\) and \(67 + 11 = 78\).
The problem asks us to identify numbers in a given series that are immediately preceded by a symbol and immediately followed by a symbol. We need to scan the series from left to right and apply this condition to each number.
D) 3 — As identified in the step-by-step analysis, there are three such numbers (9, 4, and 7) that are immediately preceded by a symbol and immediately followed by a symbol.
The question asks about the primary beneficiaries of the Trade Receivables Discounting System (TReDS). TReDS is an electronic platform designed to address a specific financing challenge faced by a particular sector in India. Understanding the purpose and target users of TReDS is key to answering this question.
Correct Option: D) MSME sector — TReDS was specifically launched by the Reserve Bank of India (RBI) to facilitate the financing of trade receivables for Micro, Small, and Medium Enterprises (MSMEs). This helps MSMEs overcome working capital shortages due to delayed payments from their buyers.
To determine if a number is divisible by 16, we need to check if the number formed by its last four digits is divisible by 16. If the number has fewer than four digits, we check the number itself. Alternatively, we can perform long division by 16 for each option.
Let's check option D: 1584.
\[ 1584 \div 16 \]\[ 16 \times 90 = 1440 \]\[ 1584 - 1440 = 144 \]\[ 16 \times 9 = 144 \]\[ 144 - 144 = 0 \]Therefore, \(1584 \div 16 = 99\). Since the remainder is 0, 1584 is divisible by 16.Correct Option: D) 1584
The question asks to identify an artificial lake among the given options in Rajasthan. To answer this, one needs to know the origin (natural or artificial) of each lake listed.
B) Ana Sagar — Ana Sagar Lake is an artificial lake constructed by Anaji Chauhan in the 12th century by damming the Luni River.