NCERT Solutions for Class 11 Maths Chapter 14: Mathematical Reasoning

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NCERT Solutions for Class 11 Maths Chapter 14: Mathematical Reasoning are given in the article. The idea of mathematical reasoning is associated with determining the accuracy values of any mathematical propositions. Class 11 Mathematics Chapter 14 has the following important concepts:

Compound statements
Limits and Derivatives
Mathematical Reasoning

Download: NCERT Solutions for Class 11 Mathematics Chapter 14 pdf

Class 11 Maths NCERT Solutions Chapter 14 Mathematical Reasoning

Class 11 Maths NCERT Solutions Chapter 14 Mathematical Reasoning are provided below:

Important Topics: Class 11 Maths NCERT Solutions Chapter 14 Mathematical Reasoning

Important Topics for Class 11 Maths NCERT Solutions Chapter 14 Mathematical Reasoning are elaborated below:

Statements

This section defines mathematically acceptable statement with examples.

Statement: Men are more intelligent than women.

Mathematical Statement: The product of two negative numbers is positive.

Negation of a statement

This section covers the negation of a statement with a few solved examples.

Statement: Mumbai is a big city.

The negation of this statement would be :

Mumbai is not a big city.
It is false that Mumbai is a big city.

Compound Statements

This section explains compound statements obtained by using words like “and”, “or” etc including solved problems.

Statement: There is something wrong with the taste of the food or the vegetables being uncooked.

The above sentence consists of two smaller statements which are as follows:

There is something wrong with the taste of the food.
There is something wrong with the vegetables being uncooked.

Special Words / Phrases

This section defines connectives “and”, “or” etc.

Example 1: 81 is divisible by 3, 9 and 27.

The above statement has 3 small statements:

81 is divisible by 3.
81 is divisible by 9.
81 is divisible by 27.

Example 2: A student who has taken mathematics or statistics can apply for the M.Sc statistics programme.

The above statement means that students who have taken both mathematics and statistics can apply for the programme, also the students who have taken only one of these subjects.

Quantifiers

This section discusses different types of quantifiers with few illustrations.

Implications

This section discusses different types of implications with few illustrations.

Contrapositive and converse

This section talks about contrapositive and converse statements with a few examples.

Examples:

If you are not a citizen of India, then it will be difficult to obtain a passport in India. [contrapositive statement]
If you get excellent marks in the exam, then you have solved all the exercises in the textbook. [converse]

Validating Statements

This section explains the process of validating the statements with specific cases along with problems.

NCERT Solutions For Class 11 Maths Chapter 14 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 14 Mathematical Reasoning under different exercises are as follows:

Also check:

Important Chapter Related Links
Irrational Number	Prime Number	Real Number

Also check:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Arithmetic

CBSE CLASS XII Related Questions

1.
Find:

If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).
- \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
- \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
- \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
- \(p = 0, \, q = 0\)
View Solution
2.
Find the vector and cartesian equations of the line passing through the point of intersection of the lines \( \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) \) and \( \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) \) and parallel to the line \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).
View Solution
3.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :
4.
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.
Based on the above information, answer the following questions :
5.
Which of the following equations is NOT a Linear Differential Equation?
- \((1 + x^2) \, dy + 2xy \, dx = \cot x \, dx\)
- \(y + \frac{d}{dx}(xy) = x(\sin x + \log x)\)
- \(x(1 + y^2) \, dx - y(1 + x^2) \, dy = 0\)
- \(y \, dx - (x + 3y^2) \, dy = 0\)
View Solution
6.
Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).
View Solution