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.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).
View Solution
2.
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
3.
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
4.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]
View Solution
5.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).
View Solution
6.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

View All

Similar Mathematics Concepts

Important Questions for Class 11 Maths Chapter 14 Mathematical Reasoning

NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.1

NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2

NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3

NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.4

NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.5

NCERT Solutions for Class 11 Maths Chapter 14 Miscellaneous Exercises

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NCERT Solutions for Class 11 Maths Chapter 14: Mathematical Reasoning

Class 11 Maths NCERT Solutions Chapter 14 Mathematical Reasoning

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

NCERT Solutions For Class 11 Maths Chapter 14 Exercises:

CBSE CLASS XII Related Questions

1.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

2.
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 \(q\).

3.
Which of the following equations is NOT a Linear Differential Equation?

4.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

5.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

6.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

Similar Mathematics Concepts

Comments

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NCERT Solutions for Class 11 Maths Chapter 14: Mathematical Reasoning

Class 11 Maths NCERT Solutions Chapter 14 Mathematical Reasoning

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

NCERT Solutions For Class 11 Maths Chapter 14 Exercises:

CBSE CLASS XII Related Questions

1.Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

2. 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 \(q\).

3.Which of the following equations is NOT a Linear Differential Equation?

4. Find: The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

5.If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

6.A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

2.
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 \(q\).

3.
Which of the following equations is NOT a Linear Differential Equation?

4.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

5.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

6.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.