Ncert Books Class 11 Maths Chapter 14 Free Download
FAQs on Ncert Books Class 11 Maths Chapter 14 Free Download
1. What are the most important types of questions to prepare from Chapter 14, Mathematical Reasoning, for the Class 11 Maths exam 2025-26?
For the Class 11 Maths exam, the most frequently asked questions from Mathematical Reasoning focus on a few key areas. Students should prioritise:
Identifying whether a given sentence is a mathematically acceptable statement.
Writing the negation of a given statement.
Forming the converse and contrapositive of a conditional statement.
Validating statements, especially those involving logical connectives like 'and', 'or', and quantifiers like 'there exists'.
These topics often form the basis for short-answer questions worth 2-3 marks.
2. Which concepts in Mathematical Reasoning are crucial for scoring well in Multiple Choice Questions (MCQs)?
For MCQs in Mathematical Reasoning, speed and accuracy are key. The most important concepts to master for this format are:
Distinguishing between a statement and a non-statement (question, command, etc.). You will likely be given a list of sentences and asked to identify the statement.
Quickly finding the negation of simple statements.
Identifying the correct logical connective (e.g., 'and', 'or', 'if-then') used in a compound statement.
Recognising the difference between a statement's converse and its inverse.
3. How can I answer a 3-mark question on validating a compound mathematical statement?
To answer a question on validating a compound statement, you should follow a clear, step-by-step approach. For a statement like 'P and Q', you must show that both component statements, P and Q, are individually true. For 'P or Q', you need to show that at least one of them is true. A complete answer would involve:
First, identify and separate the component statements.
Next, check the truth value of each individual component statement.
Finally, apply the rule for the specific connective ('and', 'or') to determine the overall validity of the compound statement and write a concluding sentence.
4. Why is it so important to differentiate between the converse and the contrapositive of a statement?
Understanding the difference is a crucial higher-order thinking skill. While the converse (if q, then p) of a statement (if p, then q) is not logically the same, the contrapositive (if not q, then not p) is logically equivalent to the original statement. This distinction is critical because in proofs, you can prove a statement by proving its contrapositive, which is often easier. Confusing the two can lead to incorrect logical conclusions, a common pitfall in exams.
5. From an exam perspective, what is the significance of understanding quantifiers like 'There exists' and 'For every'?
Quantifiers are extremely important as they define the scope and validity of a mathematical statement. Misinterpreting a quantifier is a frequent source of errors. For exams:
'There exists' implies you only need to find one example to prove the statement true.
'For every' or 'For all' implies the statement must be true for all possible cases. Finding even one counterexample is enough to prove it false.
Questions often test your ability to use a counterexample to disprove a 'For every' statement, which is a key problem-solving technique in this chapter.
6. How is the concept of 'proof by contradiction' from this chapter applied in solving important questions?
Proof by contradiction is a powerful technique tested in higher-level questions. The method involves three main steps:
Assume the opposite: Start by assuming that the statement you want to prove is false. This means you assume its negation is true.
Derive a contradiction: Using logical steps, show that this assumption leads to a conclusion that is absurd or contradicts a known fact (e.g., proving that 2 is an odd number).
Conclude the original statement is true: Since the assumption led to a false conclusion, the initial assumption must be incorrect. Therefore, the original statement must be true. This method is often used to prove statements like '√2 is irrational'.
7. What are some expected questions related to De Morgan's laws for the 2025-26 board pattern?
For the current CBSE pattern, questions on De Morgan's laws are an important part of understanding compound statements. You can expect questions that ask you to:
Write the negation of a compound statement involving 'and'. For example, find the negation of 'The sky is blue and the grass is green'. The correct negation is 'The sky is not blue or the grass is not green'.
Write the negation of a compound statement involving 'or'. For example, find the negation of 'He will study or he will play'. The correct negation is 'He will not study and he will not play'.
These questions test your ability to correctly negate both the component statements and the logical connective, which is a fundamental skill.
