Statements I, IV and V are valid testing principles according to the ISTQB syllabus. Statement I states that exhaustive testing is in general impossible, because it would require testing all possible inputs, outputs and combinations of states, which is usually impractical or impossible. Statement IV states that testing cannot guarantee that a program is correct, because testing can only show the presence of defects, not their absence. Statement V states that defects cluster together in certain areas of the product, which means that some modules or functions are more likely to contain defects than others. Statements II and III are invalid testing principles. Statement II states that exhaustive testing should be executed for code intended to be reused, which contradicts statement I. Statement III states that testing may guarantee that a program is correct, which contradicts statement IV. Verified Reference: A Study Guide to the ISTQB Foundation Level 2018 Syllabus - Springer, pages 4-5.

Test exit criteria are the conditions or requirements that must be met before testing can be concluded. Test exit criteria are usually defined in the test plan and agreed by the stakeholders. Test exit criteria can be based on various factors, such as test coverage, defect status, quality level, risk level, etc. Test schedules would be the least likely to be used as the basis for test exit criteria, because test schedules are not directly related to the quality or performance of the software product, but rather to the time or resources allocated for testing. Test schedules can be used as the basis for test entry criteria, which are the conditions or requirements that must be met before testing can start. The other options are more likely to be used as the basis for test exit criteria. Cost of testing performed so far can be used as a basis for test exit criteria, because it can indicate the return on investment or the cost-benefit ratio of testing. Confidence of testers in tested code can be used as a basis for test exit criteria, because it can reflect the level of satisfaction or assurance of the testers about the quality or reliability of the software product. Number of unfixed defects can be used as a basis for test exit criteria, because it can indicate the level of risk or impact of the remaining defects on the software product. Verified Reference: A Study Guide to the ISTQB Foundation Level 2018 Syllabus - Springer, page 13.

IV. The conditions in the decision table represent negative tests generally. The conditions in the decision table represent both positive and negative tests, depending on whether they are valid or invalid inputs for the test item. Verified Reference: A Study Guide to the ISTQB Foundation Level 2018 Syllabus - Springer, Chapter 4, page 42-43.
Explanation:
A decision table is a technique that shows combinations of inputs and/or stimuli (causes) with their associated outputs and/or actions (effects). A decision table consists of four quadrants: conditions (inputs), actions (outputs), condition entries (values) and action entries (results). The following statements about decision tables are true:
II. Test cases derived from decision tables can be used for component tests. Decision tables can be used to test components that have multiple inputs and outputs that depend on logical combinations of conditions. Decision tables can help cover all possible combinations or scenarios in a systematic way.
III. Several test cases can be selected for each column of the decision table. A column of a decision table represents a unique combination of condition entries and action entries. Several test cases can be selected for each column by varying other input values or expected results that are not part of the decision table. The following statements about decision tables are false:

An inspection is a type of review that follows a defined process with formal entry and exit criteria and roles and responsibilities for participants. An inspection can be performed by peers with different roles, such as moderator, author, reviewer and scribe. The following statement about inspection is not true:
B) The main purpose of an inspection is to find solutions to the problems. This statement is not true, as the main purpose of an inspection is to find defects or issues in a work product, not to find solutions to the problems. Finding solutions to the problems is a debugging or problem-solving activity that is usually performed by the author or developer after receiving the inspection report. The following statements about inspection are true:
A) An inspection may be led by a trained moderator who shall not be the author. This statement is true, as an inspection requires a moderator role who leads the inspection process and ensures that it follows the rules and standards. The moderator should be trained in inspection techniques and should not be the author of the work product under inspection, in order to avoid bias or conflict of interest.
C) An inspection can be performed by peers. This statement is true, as an inspection involves peer review, which means that the work product under inspection is evaluated by people who have similar roles or expertise as the author, but who are not directly involved in creating or modifying the work product.
D) An inspection shall follow a formal process based on rules and checklists with entry and exit criteria. This statement is true, as an inspection follows a formal process that consists of six main steps: planning, kick-off meeting, individual preparation, review meeting, rework and follow-up. Each step has defined rules and checklists to guide the participants and ensure consistency and quality. Each step also has entry and exit criteria to ensure that the prerequisites and objectives are met before moving to the next step. Verified Reference: A Study Guide to the ISTQB Foundation Level 2018 Syllabus - Springer, Chapter 3, page 28-29.

A correct reason to apply test automation is when there are a lot of repetitive testing tasks. Test automation is the use of software tools or scripts to perform or support testing activities, such as test case execution, test result comparison, test data generation, etc. Test automation can be beneficial when there are a lot of repetitive testing tasks that need to be performed frequently or consistently, such as regression testing, performance testing, load testing, etc. Test automation can help to save time and effort, increase reliability and accuracy, and improve coverage and efficiency of testing. The other options are not correct reasons to apply test automation. When a new test automation tool is launched is not a reason to apply test automation, but rather a factor for choosing a test automation tool. When it is easy to automate is not a reason to apply test automation, but rather a factor for evaluating the feasibility of test automation. When it is cheap to buy test automation tools is not a reason to apply test automation, but rather a factor for estimating the cost and benefit of test automation. Verified Reference: A Study Guide to the ISTQB Foundation Level 2018 Syllabus - Springer, page 10.