Directions for the following 4 (four) items:
Read the following four passage and answer the items that follow. Your answers to these items should be based on the passage only.
Passage-1
With respect to what are called denominations of religion, if everyone is left to be a judge of his own religion, there is no such thing as religion that is wrong; but if they are to be a judge of each other's religion, there is no such thing as a religion that is right, and therefore all the world is right or all the world is wrong in the matter of religion.
What is the most logical assumption that can be made from the passage given above?
No man can live without adhering to some religious denomination.
It is the duty of everyone to propagate one's religious denomination.
Religious denominations tend to ignore the unity of man.
Men do not understand their own religious denomination.
The passage discusses the nature of religious denominations and how judging them affects their perceived rightness or wrongness. The core idea revolves around the conflict that arises when different religions judge each other versus when individuals judge their own religion. We need to find the assumption that logically follows from this premise.
Correct Option: C) Religious denominations tend to ignore the unity of man.
Passage-2
It in certain, that seditions, wars, and contempt or breach of the laws are not so much to be imputed to the wickedness of the subjects, as to the bad state of a dominion. For men are not born fit for citizenship, but must be made so Besides, men's natural passions are everywhere. the same; and if wickedness more prevails, and more offences are committed in commonwealth than in another, it is certain, that the former has neither enough pursued the end of unity, nor framed its laws with sufficient forethought; and that, therefore, it has failed in making quite good its right as a commonwealth.
Which among the following is the most logical and rational inference that can be made from the passage given above?
Seditions, wars and breach of the laws are inevitable in every dominion
It is not the people, but the sovereign who is responsible for all the problems of any dominion.
That dominion is the best which pursues the aim of unity and has laws for good citizenship.
It is impossible for men to establish a good dominion.
The passage argues that societal problems like seditions, wars, and law breaches are primarily due to a "bad state of a dominion" rather than the inherent wickedness of its subjects. It emphasizes that people are not born citizens but must be made so, and that if wickedness prevails, it indicates a failure of the dominion to pursue unity and frame good laws. The task is to identify the most logical and rational inference from these statements.
Correct Option: C) That dominion is the best which pursues the aim of unity and has laws for good citizenship.
This option directly synthesizes the key elements of the passage. The passage states that if a commonwealth has problems, it's because it "has neither enough pursued the end of unity, nor framed its laws with sufficient forethought." Therefore, the logical inference is that a good or "best" dominion would do these things: pursue unity and frame laws that foster good citizenship (since "men are not born fit for citizenship, but must be made so").
Passage-3
Inequality violates a basic democratic norm the equal standing of citizens. Equality is a relation that obtains between persons in respect of some fundamental characteristic that they share in common. Equality is, morally speaking. a default principle. Therefore, persons should not be discriminated on grounds such as race, caste, gender, ethnicity, disability, or class. These features of human condition are morally irrelevant. The idea that one should treat persons with respect not only because some of these persons possess some special features or talent, for example skilled cricketers, gifted musicians, or literary giants, but because [persons are human beings, is by now part of commonsense morality.
ith reference to the above passage, the following assumptions have been made:
1. Equality in a prerequisite for people to participate in the multiple transactions of society from a position of confidence.
2. Occurrence of inequality is detrimental to the survival of democracy.
3. Equal standing of all citizens is an idea that cannot actually be realised even in a democracy.
4. Right to equality should be incorporated into our values and day-to-day political vocabulary.
Which of the above assumptions are valid?
1 and 2 only
2 and 3 only
1 and 4 only
3 and 4 only.
The task is to identify which of the given assumptions are valid based on the provided passage. We need to carefully read the passage and then evaluate each assumption to see if it can be logically inferred from the text.
C) 1 and 4 only
Assumptions 1 and 4 are directly inferable or strongly implied by the passage. Assumption 1 aligns with the idea of equal standing leading to confident participation. Assumption 4 aligns with the passage's emphasis on equality as a default principle and commonsense morality that should guide our actions and discourse.
Passage-4
Aristocratic government ruins itself by limiting too narrowly the circle within which power is confined; oligarchic government ruins itself by the incautious scramble for immediate wealth. But even democracy ruins itself by excess of democracy. Its basic principle is the equal right of all to hold office and determine public policy. This is, at first glance, a delightful arrangement; it becomes disastrous because the people are not properly equipped by education to select the best rulers and the wisest courses. The people have no understanding and only repeat what their rulers are pleased to tell them. Such a democracy in tyranny or autocracy. -Plato
Which one of the following statements best reflects the crux of the passage given above?
Human societies experiment with different forms of governments.
Any form of government tends to deteriorate by excess of its basic principle.
Education of all citizens ensures perfect, functional and sustainable democracy.
Having government is a necessary evil because tyranny is inherent in any form of government.
The question asks to identify the statement that best reflects the crux of the given passage by Plato. The passage discusses how different forms of government (aristocracy, oligarchy, and democracy) lead to their own downfall due to an excess or specific flaw related to their fundamental principles.
This problem involves set theory and finding the minimum and maximum possible values for the intersection of two groups. We are given the total number of people, the number of Indians, the number of foreigners, and the number of English speakers. We need to find the number of Indians who can speak English.
Let \(I_E\) be the number of Indians who can speak English.
The number of Indians who can speak English cannot exceed the total number of Indians, nor can it exceed the total number of English speakers.
Let \(F_E\) be the number of foreigners who can speak English.
We know that the total number of English speakers is the sum of Indians who speak English and Foreigners who speak English:
\[ E = I_E + F_E \]\[ 70 = I_E + F_E \]To find the minimum value of \(I_E\), we need to maximize \(F_E\).
The maximum number of foreigners who can speak English is limited by the total number of foreigners, which is \(F = 40\). So, \(F_E \le 40\).
If \(F_E\) is maximized to \(40\), then:
\[ 70 = I_E + 40 \]\[ I_E = 70 - 40 \]\[ I_E = 30 \]The number of Indians who can speak English must be at least 30. It can also be more than 30, up to 70.
So, \(30 \le I_E \le 70\).
Therefore, the number of Indians who can speak English is 30 or more.
D) 30 or more
Consider all 3-digit numbers (without repetition of digits) obtained using three non-aero digits which are multiples of 3. Let S be their sum. Which of the following is/are correct?
1. S in always divisible by 74.
2. S is always divisible by 9.
Select the correct answer using the code given below:
To solve this problem, we need to identify sets of three non-zero digits whose sum is a multiple of 3. For each such set, we will form all possible 3-digit numbers without repetition. Then, we will find the sum of all these numbers and check its divisibility by 74 and 9.
Identify sets of three non-zero digits whose sum is a multiple of 3: For a number to be a multiple of 3, the sum of its digits must be a multiple of 3. We are looking for three distinct non-zero digits. The non-zero digits are {1, 2, 3, 4, 5, 6, 7, 8, 9}.
General property of sum of numbers formed by three distinct digits: Let the three distinct non-zero digits be \(a, b, c\). The 3-digit numbers formed by these digits without repetition are \(abc, acb, bac, bca, cab, cba\). There are \(3! = 6\) such numbers.
The sum of these numbers is:
\[ \begin{aligned} S_{abc} &= (100a + 10b + c) + (100a + 10c + b) + (100b + 10a + c) \ &\quad + (100b + 10c + a) + (100c + 10a + b) + (100c + 10b + a) \ &= (100a+100a+10a+a+10a+a) + (10b+b+100b+100b+b+10b) + (c+10c+c+10c+100c+100c) \ &= 222a + 222b + 222c \ &= 222(a+b+c) \end{aligned} \]Check divisibility by 74: We have \(S_{abc} = 222(a+b+c)\). We know that \(222 = 3 \times 74\). Therefore, \(S_{abc} = 3 \times 74 \times (a+b+c)\).
This shows that \(S_{abc}\) is always divisible by 74, regardless of the choice of \(a, b, c\), as long as they are distinct non-zero digits. The condition that the numbers are multiples of 3 means that \((a+b+c)\) must be a multiple of 3. This condition is already incorporated into the problem statement.
So, statement 1 is correct.
Check divisibility by 9: For \(S_{abc}\) to be divisible by 9, \(222(a+b+c)\) must be divisible by 9.
We know that \(222 = 9 \times 24 + 6\), so 222 is not divisible by 9. Specifically, \(222 \pmod 9 = 6\).
For \(222(a+b+c)\) to be divisible by 9, \((a+b+c)\) must be a multiple of 3 (given in the problem statement) AND \((a+b+c)\) must be a multiple of \[\frac{9}{\gcd(222, 9)} = \frac{9}{3} = 3\]. So, \((a+b+c)\) must be a multiple of 3.
Since the problem states that the 3-digit numbers formed are multiples of 3, it implies that the sum of their digits \((a+b+c)\) must be a multiple of 3. Let \((a+b+c) = 3k\) for some integer \(k\).
Then, \(S_{abc} = 222 \times 3k = 666k\).
Now, we check if 666 is divisible by 9. The sum of digits of 666 is \(6+6+6 = 18\), which is divisible by 9. Therefore, 666 is divisible by 9.
Since \(S_{abc} = 666k\) and 666 is divisible by 9, \(S_{abc}\) is always divisible by 9.
So, statement 2 is correct.
Both statements 1 and 2 are correct.
Correct Option: C) Both 1 and 2
There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B.
Consider the following statements:
1. The average score of Class-B will definitely decrease.
2. The average score of Class-A will definitely increase.
Which of the above statements is/are
To determine how the average scores change, we need to analyze the range of scores in each class and the scores of the students being transferred. The key is to understand how the transfer of students with certain score ranges affects the overall sum of scores and the number of students in each class.
Correct Option: A) 1 only
Consider two Statements and a Question:
Statement-1: Priya is 4 ranks below Seema and is 31st from the bottom.
Statement-2: Ena is 2 ranks above Seema and is 37th from the bottom.
Question: What is Seema's rank from the top in the class of 40 students?
Which one of the following is correct in respect of the Statements and the Question?
Statement-1 alone is not sufficient to anawer the Question
Statement-2 alone is not sufficient to anawer the Question
Either Statement-1 alone or Statement-2 alone is sufficient to answer the question
Both Statement-1 and Statement-2 are required to answer the question
The problem asks us to determine if Statement-1, Statement-2, or both are sufficient to find Seema's rank from the top in a class of 40 students. We need to calculate Seema's rank from the top using each statement independently and then combine them if necessary.
The total number of students in the class is 40.
The formula to find the rank from the top when the rank from the bottom and total students are known is:
\[ \text{Rank from top} = \text{Total students} - \text{Rank from bottom} + 1 \]If Priya is 31st from the bottom and is 4 ranks below Seema, it means Seema is 4 ranks above Priya from the bottom. So, Seema's rank from the bottom can be calculated:
\[ \text{Seema's rank from bottom} = \text{Priya's rank from bottom} + 4 \] \[ \text{Seema's rank from bottom} = 31 + 4 = 35 \]Now, using the total number of students (40), we can find Seema's rank from the top:
\[ \text{Seema's rank from top} = \text{Total students} - \text{Seema's rank from bottom} + 1 \] \[ \text{Seema's rank from top} = 40 - 35 + 1 = 6 \]Thus, Statement-1 alone is sufficient to answer the question.
If Ena is 37th from the bottom and is 2 ranks above Seema, it means Seema is 2 ranks below Ena from the bottom. So, Seema's rank from the bottom can be calculated:
\[ \text{Seema's rank from bottom} = \text{Ena's rank from bottom} - 2 \] \[ \text{Seema's rank from bottom} = 37 - 2 = 35 \]Now, using the total number of students (40), we can find Seema's rank from the top:
\[ \text{Seema's rank from top} = \text{Total students} - \text{Seema's rank from bottom} + 1 \] \[ \text{Seema's rank from top} = 40 - 35 + 1 = 6 \]Thus, Statement-2 alone is sufficient to answer the question.
Since both Statement-1 alone and Statement-2 alone are sufficient to answer the question, the correct option is C.
Correct Option: C) Either Statement-1 alone or Statement-2 alone is sufficient to answer the question
Consider two Statements and a Question:
Statement-1: Each of A and D is heavier than each of B, E and F, but none of them is the heaviest.
Statement-2: A is heavier than D, but is lighter than C.
Question: Who is the heaviest among A, B, C, D and E?
Which one of the following is correct in respect of the Statements and the Questions?
Statement-1 alone is sufficient to answer the Question
Statement-2 alone is sufficient to answer the Question
Both Statement-1 and Statement-2 are required to answer the question.
Neither Statement-1 alone nor Statement-2 alone is sufficient to required to answer the question.
The problem describes a specific rearrangement of the English alphabet. We need to first determine the new order of letters based on the given rules. Then, we will find the 13th letter in this new sequence and finally identify the fourth letter to its right.
So the new series is: D C B A H G F E L K J I P O N M T S R Q X W V U Z Y
Counting the letters in the new series:
The 13th letter is P.
Starting from P (the 13th letter):
The fourth letter to the right of P is T.
Correct Option: B) T