The problem states that a student needs 40% marks to pass. We are given the marks the student obtained and the marks by which he failed. From this information, we can calculate the passing marks. Once we know the passing marks, we can equate it to 40% of the maximum marks to find the total maximum marks for the examination.
The student scored 30 marks and failed by 30 marks. This means that to pass, the student needed 30 more marks than what he obtained.
\[ \text{Passing Marks} = \text{Marks Obtained} + \text{Marks by which failed} \] \[ \text{Passing Marks} = 30 + 30 = 60 \]So, the passing marks for the examination are 60.
We are given that 40% marks are required to pass the examination.
Therefore, 40% of the maximum marks is equal to the passing marks (60).
\[ 40\% \text{ of Max Marks} = 60 \]Let the maximum marks be \(M\).
\[ 0.40 \times M = 60 \]To find \(M\), divide 60 by 0.40:
\[ M = \frac{60}{0.40} \] \[ M = \frac{60}{\frac{40}{100}} \] \[ M = \frac{60 \times 100}{40} \] \[ M = \frac{6000}{40} \] \[ M = 150 \]Thus, the maximum marks in the examination are 150.
Correct Option: C) 150
This problem can be solved using the principle of inclusion-exclusion for two sets, or by simply using a Venn diagram approach. We are given the total number of boys, the number of boys wearing shirts, and the number of boys wearing pants. We need to find the number of boys wearing both (full uniform).
Let \(N\) be the total number of boys. Given \(N = 19\).
Let \(S\) be the set of boys wearing hockey shirts. Given \(|S| = 11\).
Let \(P\) be the set of boys wearing hockey pants. Given \(|P| = 14\).
The problem states that "There are no boys without shirts and /or pants." This means that every boy is wearing at least a shirt or pants. In set notation, this implies that the union of the set of boys wearing shirts and the set of boys wearing pants is equal to the total number of boys: \(|S \cup P| = N = 19\).
We need to find the number of boys wearing full uniform, which means wearing both shirts and pants. In set notation, this is \(|S \cap P|\).
Using the principle of inclusion-exclusion for two sets, the formula is:
\[ |S \cup P| = |S| + |P| - |S \cap P| \]Substitute the given values into the formula:
\[ 19 = 11 + 14 - |S \cap P| \]Calculate the sum of boys wearing shirts and pants:
\[ 11 + 14 = 25 \]Now, the equation becomes:
\[ 19 = 25 - |S \cap P| \]Rearrange the equation to solve for \(|S \cap P|\):
\[ |S \cap P| = 25 - 19 \]\[ |S \cap P| = 6 \]Therefore, 6 boys are wearing both hockey shirts and hockey pants, which means they are wearing a full uniform.
Directions for the following 6(six) items:
Read the following passage and answer the items that follow.
A, B, C and D are students. They are studying in four different cities, viz., P, Q, R and S (not necessarily in that order). They are studying in Science college, Arts College ( not necessarily in that order), which are situated in four different States, viz., Gujarat, Rajasthan, Assam and Kerala (not necessarily in that order). Further, it is given that --
(i) D is studying in Assam
(ii) Arts college is located in city S which is in Rajasthan
(iii) A is studying in Commerce college
(iv) B is studying in city Q
(v) Science college is located in Kerala A is studying in
This is a logical reasoning problem involving matching students, cities, colleges, and states based on given clues. We will create a table to organize the information and deduce the missing details step-by-step.
| Student | City | College | State |
|---|---|---|---|
| A | |||
| B | |||
| C | |||
| D |
| Student | City | College | State |
|---|---|---|---|
| A | |||
| B | |||
| C | |||
| D | Assam |
| Student | City | College | State |
|---|---|---|---|
| A | Commerce | ||
| B | |||
| C | |||
| D | Assam |
| Student | City | College | State |
|---|---|---|---|
| A | Commerce | ||
| B | Q | ||
| C | |||
| D | Assam |
| Student | City | College | State |
|---|---|---|---|
| A | Commerce | Gujarat | |
| B | Q | ||
| C | |||
| D | Assam |
B) Gujarat — Based on the deductions, A is studying in Commerce college, and since Arts college is in Rajasthan and Science college is in Kerala, the Commerce college must be in the remaining state, which is Gujarat.
The question asks for the location of Science College. This is a direct recall question based on provided information, likely from a map or a passage that is not included in the prompt. Assuming there was a preceding context (e.g., a map or a text description), we need to identify the city associated with "Science College" from that context.
Since no context (like a map or a descriptive passage) is provided with the question, we must assume that the information about the location of Science College was given in a preceding part of the exam or study material. Based on the provided correct answer, Science College is located in city Q.
Without the original context, it's impossible to demonstrate the step-by-step process of finding this information. However, in a typical competitive exam scenario, one would:
Given that option A is marked as correct, it implies that the (unseen) source material states that Science College is in city Q.
A) city Q — Based on the provided correct answer, Science College is located in city Q. This would be directly verifiable from the source material (e.g., a map or text) accompanying the question.
The question asks to identify where 'C' is studying. This is a logical reasoning question that requires interpreting information that is not explicitly provided in the question text. The answer must be inferred from context that is missing from the prompt. Given the options, this question likely refers to a scenario or passage that was not provided. Without that context, it's impossible to answer definitively. However, since a correct answer is provided (B), we must assume there was an external context.
Since the question and options are provided without any preceding context (like a passage, diagram, or scenario description), it's impossible to logically deduce the correct answer based solely on the information given. In a real competitive exam, such a question would either be part of a larger comprehension passage or a data interpretation set, or it would be considered flawed due to missing information.
However, if we are forced to choose based on the provided correct answer 'B', the only explanation is that there was an external piece of information (a passage, a map, a table, etc.) that explicitly stated or strongly implied that 'C' is studying in Rajasthan.
Without that external context, any choice is arbitrary. Assuming such context existed and pointed to Rajasthan:
B) Rajasthan — This is the correct answer based on the provided solution. This implies that in the original context from which this question was drawn, there was information stating or indicating that 'C' is studying in Rajasthan.
The question asks to identify the correct statement regarding an Engineering college. Since no additional context or information (like a diagram, passage, or table) is provided with the question, it implies that this is a trick question or a question designed to test critical thinking about the lack of information. Without any given data, it's impossible to determine who studies where or the location of the college. Therefore, the correct answer must be based on an external reference or a pre-defined context that is not part of the question itself, or it's a question testing the ability to identify a statement that is presented as correct without supporting evidence.
D) D is studying there. This is selected as the correct option based on the provided answer key. Without any accompanying text or diagram, it's impossible to logically deduce this from the question alone. It implies that this information was provided in a context external to the question snippet.
The question asks to identify the correct statement among the given options. This implies that the information provided in the options needs to be verified against a known set of facts, which are not explicitly given in the question but are assumed to be part of a larger context or general knowledge for this type of problem. We will evaluate each option based on typical reasoning puzzles where specific entities are linked to locations or activities.
Since no specific context or puzzle description is provided, we must assume that this question is part of a larger set of information or a logical reasoning puzzle where these facts are established. Without that external information, it's impossible to definitively prove any option correct or incorrect. However, in competitive exams, such questions often appear after a paragraph or a set of conditions. Assuming this is a standalone question testing general knowledge or a pre-established context:
Given that the correct answer is provided as A, we proceed with the understanding that the underlying information confirms Option A and refutes B, C, and D.
A) Engineering college is located in Assam. This statement is identified as correct. In a typical logical reasoning or data interpretation problem, this fact would have been explicitly stated or derivable from the given conditions. Without the source context, we accept this as the correct statement as per the provided answer key.
Directions for the following 8 (eight) items:
Read the following eight passage and answer the items that follow. Your answers to these items should be based on the passage only.
Passage - 1
All actions to address climate change ultimately involve costs. Funding is vital in order for countries like India to design and implement adaptation and mitigation plans and projects. The problem is more severe for developing countries like India, which would be one of the hardest hit by climate change, given its need to finance development. Most countries to indeed treat climate change as real threat and are striving to address it in a more comprehensive and integrated manner with the limited resources at their disposal.
With reference to the above passage, the following assumptions have been made:
1. Climate change is not a challenge for developed countries.
2. Climate change is a complex policy issue and also a development issue for many countries.
3. Ways and means of finance must be found to enable developing countries to enhance their adaptive capacity.
Which of the above assumptions is/are valid?
The task is to identify which of the given assumptions are valid based solely on the provided passage. We need to read each assumption and check if it can be directly inferred or is consistent with the information presented in the passage.
C) 2 and 3 only
Assumptions 2 and 3 are directly supported by or can be logically inferred from the passage. Assumption 1 contradicts the general implication of the passage.
Passage - 2
Cooking with biomass and coal in India is now recognized to cause major health problems, with women and children in poor populations facing the greatest risk. There are more than 10 lakh premature deaths each year from household air pollution due to polluting cooking fuels with another 1.5 lakh due to their contribution to general outdoor air pollution in the country. Although the fraction of the Indian population using clean cooking fuels, such as LPG, natural gas and electricity, is slowly rising, the number using polluting solid fuels as their primary cooking fuel has remained static for nearly 30 years at about 70 crore.
Which of the following is the most crucial and logical inference that can be made from the above passage?
Rural people are giving up the use of polluting solid fuels due to their increasing awareness of health hazards.
Subsidizing the use of clean cooking fuels will solve the problem of India's indoor air pollution.
India should increase its import of natural gas and produce more electricity.
Access to cooking gas can reduce premature deaths in poor households.
The question asks for the most crucial and logical inference from the given passage. We need to analyze the passage for its main points and identify the option that directly addresses the core problem and its solution as implied by the text.
D) Access to cooking gas can reduce premature deaths in poor households. This option directly addresses the core problem (premature deaths due to polluting fuels) and links it to the solution (clean cooking fuels like cooking gas), specifically mentioning the vulnerable population (poor households) as highlighted in the passage. The passage states that polluting fuels cause "more than 10 lakh premature deaths each year" and that "women and children in poor populations facing the greatest risk." It also mentions clean cooking fuels like LPG (cooking gas) as alternatives. Therefore, increasing access to these clean fuels would logically reduce these deaths.