NCERT Solutions for Exercise 14.2 Class 11 Maths Chapter 14

NCERT Solutions for Exercise 14.2 Class 11 Maths Chapter 14 - Mathematical Reasoning

Edited By Sumit Saini | Updated on Jul 13, 2022 05:37 PM IST

NCERT Solutions for Class 11 Maths chapter 14 exercise 14.2 introduces questions related to writing of the negation of a statement, finding of component statements of given compound statements etc. In previous Classes of Maths, students have already read the basic Mathematical Reasoning but in this chapter problems are more application based. Exercise 14.2 Class 11 Maths requires only basic common sense to solve the questions.

JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | Aakash | Unacademy

Suggested: JEE Main: high scoring chapters | Past 10 year's papers

This Story also Contains

Mathematical Reasoning Class 11 Chapter 14-Exercise: 14.2
More About NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2
NCERT Solutions of Class 11 Subject Wise
Subject Wise NCERT Exemplar Solutions

Solving NCERT syllabus questions Class 11 Maths chapter 14 exercise 14.2 can be a fun exercise for some of the students as it requires logical reasoning and application of basic concepts only. Although the weightage of this exercise is not much in the final examination, it must be attempted to score marks if there comes any question. Also students can refer to the following exercise of NCERT for further information about upcoming exercises.

Mathematical Reasoning Class 11 Chapter 14-Exercise: 14.2

Question:1(i) Write the negation of the following statements:

Chennai is the capital of Tamil Nadu.

Answer:

Chennai is not the capital of Tamil Nadu.

It is false to say that Chennai is the capital of Tamil Nadu.

It is not the case that Chennai is the capital of Tamil Nadu.

Question:1.(ii) Write the negation of the following statements:

$\sqrt{2}$ is not a complex number

Answer:

$\sqrt{2}$ is a complex number.

It is false to say that $\sqrt{2}$ is not a complex number.

It is not the case that $\sqrt{2}$ is not a complex number.

Question:1.(iii) Write the negation of the following statements:

All triangles are not equilateral triangle.

Answer:

All triangles are equilateral triangle.

It is false to say that all triangles are not equilateral triangle.

It is not the case that all triangles are not equilateral triangle.

Question:1.(iv) Write the negation of the following statements:

The number 2 is greater than 7.

Answer:

The number 2 is not greater than 7.

It is false to say that the number 2 is greater than 7.

It is not the case that the number 2 is greater than 7.

Question:1.(v) Write the negation of the following statements:

Every natural number is an integer.

Answer:

Every natural number is not an integer.

It is false to say that every natural number is an integer.

It is not the case that every natural number is an integer.

Question:2.(i) Are the following pairs of statements negations of each other:

The number x is not a rational number.
The number x is not an irrational number.

Answer:

p: The number x is not a rational number.
r: The number x is not an irrational number.

The negation of p is: The number x is a rational number, which is the same as statement r.

The negation of r is: The number x is an irrational number, which is the same as statement p.

Hence the pairs of statements are negations of each other.

Question:2(ii) Are the following pairs of statements negations of each other:

The number x is a rational number.
The number x is an irrational number.

Answer:

p: The number x is a rational number.
r: The number x is an irrational number.

The negation of p is: The number x is not a rational number, which is the same as statement r.

The negation of r is: The number x is not an irrational number, which is the same as statement p.

Hence the pairs of statements are negations of each other.

Question:3.(i) Find the component statements of the following compound statements and check whether they are true or false.
Number 3 is prime or it is odd.

Answer:

The component statements are

p: Number 3 is prime.

r: Number 3 is odd.

Both statements are true. Here the connecting word is ‘or’.

Question:3.(ii) Find the component statements of the following compound statements and check whether they are true or false.

All integers are positive or negative.

Answer:

The component statements are:

p: All integers are positive.

r: All integers are negative.

Both the components statements are false. Here the connecting word is ‘or’.

Question:3.(iii) Find the component statements of the following compound statements and check whether they are true or false.

100 is divisible by 3, 11 and 5.

Answer:

The component statements are:

p: 100 is divisible by 3.

q: 100 is divisible by 11.

r: 100 is divisible by 5.

First two statements are false and the last statement is true. Here the connecting word is ‘and’.

NCERT Solutions of Class 11 Subject Wise

Subject Wise NCERT Exemplar Solutions

Happy learning!!!

Frequently Asked Questions (FAQs)

1. Which topics are covered in exercise 14.2 Class 11 Maths?

Basic reasoning question, negation, probability related questions are asked in the exercise 14.2 Class 11 Maths.

2. Does this chapter 14 have linkage to other chapters ?

No, most concepts are new. So it doesn't require prior knowledge.

3. Can this chapter be understood in one day ?

Yes, since questions are very common. Hence 1 day is sufficient for this chapter.

4. What is the difficulty level of the questions asked in this chapter ?

Most of the questions are relatively easier to understand.

5. Are there any formulas to mug up in this chapter ?

No, there are no formulas to mug up in this chapter.

6. How many questions are there in the exercise 14.2 Class 11 Maths ?

There are 3 main questions and all the questions have subparts in the range of 2 to 3.

Also Read

NCERT Class 11 Chemistry Chapter 4 Notes Chemical Bonding and Molecular Structure - Download PDF

Hydrogen Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 9 Notes - Download PDF

The S-Block Elements Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 10 Notes - Download PDF

The P-Block Elements Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 11 Notes - Download PDF

Environmental Chemistry Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 14 Notes - Download PDF

NCERT Class 11 Chemistry Chapter 3 Notes - Download PDF

NCERT Solutions for Class 11 Physics Chapter 6 Work Energy and Power

NCERT Solutions for Class 11 Chemistry Chapter 5 States of Matter

NCERT Class 11 Physics Chapter 5 Notes Laws of Motion - Download PDF

NCERT Class 11 Physics Chapter 3 Notes Motion in a straight Line - Download PDF

NCERT Solutions for Exercise 10.1 Class 11 Maths Chapter 10 - Straight Lines

NCERT Solutions for Miscellaneous Exercise Chapter 16 Class 11 - Probability

NCERT Exemplar Class 11 Maths Solutions Chapter 12 Introduction to Three Dimensional Geometry

NCERT Exemplar Class 11 Maths Solutions Chapter 10 Straight Lines

NCERT Exemplar Class 11 Maths Solutions Chapter 6 Linear Inequalities

NCERT Exemplar Class 11 Maths Solutions Chapter 16 Probability

NCERT Exemplar Class 11 Maths Solutions Chapter 14 Mathematical Reasoning

NCERT Exemplar Class 11 Maths Solutions Chapter 7 Permutations and Combinations

Articles

AMU Class 1 Admission 2025: Application Process, Eligibility & Key Dates

Dec 30, 2024

Jamia Millia Islamia School Admission 2025: Application Process, Eligibility & Dates

Dec 30, 2024

SoSE Delhi School Admission 2025: All You Need to Know About Eligibility, Dates & Process

Dec 30, 2024

DBSE Result 2025, Check Delhi Board 10th, 12th Result

Dec 30, 2024

NMMS Chhattisgarh Result 2024-25: Check Merit List, Cut Off Marks

Dec 28, 2024

CBSE Scholarship 2024-25: Check CBSE Scholarships for Class 10, 12

Dec 27, 2024

HOS 12th Date Sheet 2025 - Haryana Open School Class 12 Exam Schedule

Dec 27, 2024

AMU School Admission 2025 - Know Application Process, Eligibility & Important Dates

Dec 27, 2024

Upcoming School Exams

Madhya Pradesh State Open School 12th Examination

Admit Card Date:13 December,2024 - 06 January,2025

Admit Card

Result

All India Sainik Schools Entrance Examination

Application Date:24 December,2024 - 13 January,2025

Exam Pattern

Answer Key

Result

Telangana State Board of Intermediate Education Examination

Late Fee Application Date:25 December,2024 - 02 January,2025

Exam Pattern

Mock Test

Admit Card

Telangana Intermediate 1st Year Examination

Late Fee Application Date:25 December,2024 - 02 January,2025

Admit Card

Question Paper

Result

National Means Cum-Merit Scholarship

Application Date:27 December,2024 - 09 January,2025

Eligibility Criteria

Application Process

Exam Pattern

View All School Exams

Get answers from students and experts

Popular Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms^-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×10⁷J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms⁻² :

Option 1)

2.45×10⁻³ kg

Option 2)

6.45×10⁻³ kg

Option 3)

9.89×10⁻³ kg

Option 4)

12.89×10⁻³ kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

A particle is projected at 60⁰ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

In the reaction,

$2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, $Mg_{3}(PO_{4})_{2}$ will contain 0.25 mole of oxygen atoms?

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol^-1) is

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m² , the number of rotations made by the pulley before its direction of motion if reversed, is