*According to the latest update on the CBSE Syllabus 2023-24, this chapter has been removed.
The NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning contain solutions for all Exercise 14.1 questions. All solutions are prepared by subject experts to help students for final exams and score good marks. Students can download the NCERT Solutions of Class 11 Maths and practise offline as well.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Exercise 14.1
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Access Other Exercise Solutions of Class 11 Maths Chapter 14 Mathematical Reasoning
Exercise 14.2 Solutions: 3 Questions
Exercise 14.3 Solutions: 4 Questions
Exercise 14.4 Solutions: 4 Questions
Exercise 14.5 Solutions: 5 Questions
Miscellaneous Exercise Solutions: 7 Questions
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NCERT Solutions for Class 11 Maths Chapter 14
Access Solutions for Class 11 Maths Chapter 14 Exercise 14.1
1. Which of the following sentences are statements? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.
(v) The sides of a quadrilateral have equal lengths.
(vi) Answer this question.
(vii) The product of (–1) and 8 is 8.
(viii) The sum of all interior angles of a triangle is 180°.
(ix) Today is a windy day.
(x) All real numbers are complex numbers.
Solution:
(i) The maximum number of days in a month is 31, so this sentence is incorrect. Therefore, it is a statement.
(ii) This sentence is subjective. For some people, Mathematics can be easy, and for some others, it can be difficult. Therefore, it is not a statement.
(iii) The sum of 5 and 7 is 12, and it is greater than 10. Therefore, this sentence is always correct. Hence, it is a statement.
(iv) This sentence can sometimes be correct and sometimes incorrect. For example, the square of 2 is an even number, but the square of 3 is an odd number. Hence, it is not a statement
(v) This sentence can sometimes be correct and sometimes incorrect. For example, squares and rhombi have sides of equal lengths, whereas trapezia and rectangles have sides of unequal lengths. Therefore, it is not a statement.
(vi) It is an order. Hence, it is not a statement.
(vii) The given sentence is incorrect because the product of (-1) and 8 is – 8. Hence, it is a statement.
(viii) The given sentence is correct, and therefore, it is a statement.
(ix) The given sentence is not a statement because the day that is being referred to is not evident from the sentence.
(x) The given sentence is always correct because all real numbers can be written as a × 1 + 0 × i. Hence, it is a statement.
2. Give three examples of sentences which are not statements. Give reasons for the answers.
Solution:
The three examples of sentences which are not statements are given below.
(i) He is a doctor.
In the given sentence, it is not evident to whom ‘he’ is referred. Hence, it is not a statement.
(ii) Geometry is difficult.
For some people, geometry can be easy, and for some others, it can be difficult. Hence, this is not a statement.
(iii) Where is she going?
In this question, it is not evident to whom ‘she’ is referred. Hence, it is not a statement.
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