NCERT Solutions for Exercise 7.1 Class 11 Maths Chapter 7

NCERT Solutions for Exercise 7.1 Class 11 Maths Chapter 7 - Permutations and Combinations

Edited By Vishal kumar | Updated on Nov 07, 2023 07:05 AM IST

NCERT Solutions for Class 11 Maths Chapter 7 Permutations And Combinations Exercise 7.1- Download Free PDF

NCERT Solutions for Class 11 Maths Chapter 7: Permutations and Combinations Exercise 7.1- In our daily life, you may come across problems like arranging people with given the number seats, arranging digits on place, arranging the numbers or alphabets, etc. You can list all the possible arrangements to count the total number of possible arrangements. If the total number of possible arrangements are too high, it won't be possible to list all the arrangements. Therefore you need some counting techniques to answer such questions without listing all the arrangements. In NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1, you will learn the fundamental principle of counting which is used in all these techniques. You will find the most of the questions in NCERT book Class 11 Maths Chapter 7 Exercise 7.1 are related to the fundamental principle of counting only.

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

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

Scholarship Test: Vidyamandir Intellect Quest (VIQ)

This Story also Contains

NCERT Solutions for Class 11 Maths Chapter 7 Permutations And Combinations Exercise 7.1- Download Free PDF
Download the PDF of NCERT Solutions for Class 11 Maths Chapter 7 – Permutations and Combinations Exercise 7.1
Access Permutation And Combinations Class 11 Chapter 7 Exercise 7.1
Question:1(i) How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?
More About NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1:-
Benefits of NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1:-
Key Features of NCERT 11th Class Maths Exercise 7.1 Answers
NCERT Solutions of Class 11 Subject Wise
Subject Wise NCERT Exampler Solutions

NCERT Solutions for Exercise 7.1 Class 11 Maths Chapter 7 - Permutations and Combinations

The 11th class maths exercise 7.1 answers have been meticulously prepared by highly qualified subject experts at Careers360. These Solutions are presented in great detail, explaining each step of the problem-solving process. Additionally, PDF versions of the ex 7.1 class 11 solutions are provided for students to download and use free of charge, making it a valuable resource for their studies. You can click on the NCERT solutions link where you will get detailed solutions from Class 6 to Class 12 at one place.

Also, see

**As per the CBSE Syllabus for 2023-24, this chapter has been renumbered as Chapter 6.

Download the PDF of NCERT Solutions for Class 11 Maths Chapter 7 – Permutations and Combinations Exercise 7.1

Download PDF

Access Permutation And Combinations Class 11 Chapter 7 Exercise 7.1

Question:1(i) How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
repetition of the digits is allowed?

Answer:

The five digits are 1, 2, 3, 4 and 5

As we know that repetition of the digits is allowed,

so, the unit place can be filled by any of five digits.

Similarly, tens and hundreds of digits can also be filled by any of the five digits.

$\therefore$ A number of 3-digit numbers can be formed $=5\times 5\times 5=125$

Question:1(ii) How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
repetition of the digits is not allowed?

Answer:

The five digits are 1, 2, 3, 4 and 5

As we know that repetition of the digits is not allowed,

so, the unit place can be filled by any of five digits.

Tens place can be filled with any of the remaining four digits.

Hundreds place can be filled with any of the remaining three digits.

$\therefore$ Number of 3-digit numbers can be formed when repetition is not allowed $=5\times 4\times 3=60$

Question:2 How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Answer:

The six digits are 1, 2, 3, 4 ,5 and 6

As we know that repetition of the digits is allowed,

so, the unit place can be filled by any of even digits i.e.2,4 or 6

Similarly, tens and hundreds of digits can also be filled by any of six digits.

$\therefore$ Number of 3-digit even numbers can be formed $=3\times 6\times 6=108$

Question:3 How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Answer:

There are 10 letters of English alphabets.

As we know that repetition of the letters is not allowed,

so, the first place can be filled by any of 10 letters.

Second place can be filled with any of the remaining 9 letters.

Third place can be filled with any of the remaining 8 letters.

The fourth place can be filled with any of the remaining 7 letters.

$\therefore$ Number of 4-letter code can be formed when the repetition of letters is not allowed $=10\times 9\times 8\times 7=5040$

Hence, 5040 4-letter codes can be formed using the first 10 letters of the English alphabet, if no letter can be repeated.

Question:4 How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Answer:

It is given that 5-digit telephone numbers always start with 67.

First, two digits among 5-digit telephone numbers are fixed and rest 3 digits are variable.

$6,7,-,-,-$

The 10 digits are from 0 to 9.

As we know that repetition of the digits is not allowed,

so, the first and second place is filled by two digits 67

Third place can be filled with any of the remaining 8 digits.

The fourth place can be filled with any of the remaining 7 digits.

The fifth place can be filled with any of the remaining 6 digits.

$\therefore$ Number of 5-digit telephone numbers can be formed when repetition is not allowed $=8\times 7\times 6=336$

Question:5 A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Answer:

When a coin is tossed the number of outcomes is 2 i.e. head or tail.

When a coin is tossed 3 times then by multiplication principle,

the number of outcomes $=2\times 2\times 2=8$

Question:6 Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

Answer:

Each signal requires use of 2 flags.

There will be as many flags as there are ways of filling in 2 vacant places in succession by the given 5 flags of different colours.

The upper vacant place can be filled in 5 different ways with any of 5 flags and lower vacant place can be filled in 4 different ways by any of rest 4 flags.

Hence, by multiplication principle number of different signals that can be generated $=5\times 4=20$

Benefits of NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1:-

Exercise 7.1 Class 11 Maths is a basic exercise that will help you understand this chapter very easily.
You are advised to solve all the NCERT syllabus problems of Class 11 Maths Chapter 7 Exercise 7.1 by yourself.
The upcoming exercises of this chapter are based on the fundamental of the principle of counting which you will learn in the Class 11 Maths chapter 7 exercise 7.1 solutions.

JEE Main Highest Scoring Chapters & Topics

Just Study 40% Syllabus and Score upto 100%

Download EBook

Key Features of NCERT 11th Class Maths Exercise 7.1 Answers

Thorough Coverage: The ex 7.1 class 11 answers encompass all the exercises and problems presented in Chapter 7.1 of the NCERT 11th Class Mathematics textbook.
Step-by-Step Guidance: The class 11 maths ex 7.1 solutions are meticulously structured with step-by-step explanations, facilitating easy comprehension for students.
Precision and Clarity: The class 11 ex 7.1 answers are drafted with precision and clarity to ensure students can grasp the mathematical concepts and problem-solving methods.
Free Access: These class 11 maths chapter 7 exercise 7.1 solutions are typically accessible free of charge, making them a valuable resource for self-study.
Homework and Practice: Students can utilize these answers to verify their work, practice problem-solving, and enhance their overall mathematical proficiency.

Also see-

NCERT Solutions of Class 11 Subject Wise

Subject Wise NCERT Exampler Solutions

Happy learning!!!

Frequently Asked Questions (FAQs)

1. How many 2 digit even numbers can be formed from the digits 3, 4, 5 if the digits can be repeated?

Total number of arrangements = 3 x 1 = 3

There are only three ways to form 2 digit even number with the given condition.

2. How many 2 digit even numbers can be formed from the digits 3, 4, 5 if the digits can't be repeated ?

Total number of arrangements = 2x 1 = 2

There are only two ways to form 2 digit even number with the given condition.

3. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 6 if the digits can be repeated?

Total number of arrangements = 5 x 5 x 3 = 75

There are 75 ways to form 3 digit even number with the given condition.

4. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 6 if the digits can't be repeated ?

Total number of arrangements = 3 x 4 x 3 = 36

There are 36 ways to form 3 digit even number with the given condition.

5. What is the weightage of the Permutations and combinations in the CBSE exam ?

The whole algebra part has 30 marks weightage in the CBSE Class 11 Maths exam.

6. What is the syllabus of CBSE Class 11 Maths ?

Here you will get detailed syllabus for CBSE Class 11 Maths.

Also Read

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

NCERT Class 11 Chemistry Chapter 3 Notes - Download PDF

NCERT Class 11 Biology Chapter 19 Notes Excretory Products And Their Elimination- Download PDF Notes

NCERT Class 11 Biology Chapter 22 Notes Chemical Coordination And Integration- Download PDF Notes

Some basic concepts of Chemistry Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 1 Notes - Download PDF

NCERT Class 11 Biology Chapter 21 Notes Neural Control And Coordination- Download PDF Notes

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

TOSS Admission 2024-25: Apply for SSC & Inter TS Open School Admission @telanganaopenschool.org

Nov 30, 2024

NSEP Answer Key 2024-25: Download NSEP 2024 Answers & Solutions Here

Nov 29, 2024

IAPT Cut Off Marks 2024-25 @iapt.org.in Qualifying Marks for NSEP, NSEC, NSEB, NSEA

Nov 29, 2024

IAPT Registrations 2024-25: NSE Application Dates, Exam Date, Official Website

Nov 29, 2024

Education Loan for Girl Students in India - Know Loan Scheme Details, Special Interest Concessions

Nov 27, 2024

IB Diploma Programme - Know All About DP Curriculum, Subjects, Assessment Criteria and Benefits

Nov 27, 2024

Physics: Projectile Motion That Won India An Olympic Gold

Nov 26, 2024

Axis Bank Education Loan: Eligibility, Interest Rates & Application Process

Nov 25, 2024

Upcoming School Exams

Gujarat Board Higher Secondary School Certificate

Application Date:24 October,2024 - 02 December,2024

Exam Pattern

Result

Admit Card

Haryana Board of Secondary Education 12th Examination

Application Date:04 November,2024 - 03 December,2024

Exam Pattern

Admit Card

Result

Haryana Board of Secondary Education 10th Examination

Application Date:04 November,2024 - 03 December,2024

Exam Pattern

Admit Card

Result

National Means Cum-Merit Scholarship

Application Date:05 November,2024 - 07 December,2024

Eligibility Criteria

Application Process

Exam Pattern

Telangana State Board of Intermediate Education Examination

Application Date:06 November,2024 - 03 December,2024

Exam Pattern

Mock Test

Admit Card

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