-
Q19 Prove the following by using the principle of mathematical induction for all n ∈ N:
n (n + 1) (n + 5) is a multiple of 3.
Ans: Our experts will give the answer soon.
Principle of Mathemetical Induction Question Answers: NCERT Class 11 Mathematics
Welcome to the Chapter 4 - Principle of Mathemetical Induction, Class 11 Mathematics - NCERT Solutions page. Here, we provide detailed question answers for Chapter 4 - Principle of Mathemetical Induction.The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.
Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics and excel in their exams. By going through these Principle of Mathemetical Induction question answers, you can strengthen your foundation and improve your performance in Class 11 Mathematics. Whether you're revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.
This chapter is all about proving the given statement is true or not by the process of induction. We deal with natural numbers because it is the least inductive subset of real numbers. Least inductive means it has the least fixed point for an operation definable by a positive formula for some natural number n. In this chapter, we will discuss the principle of mathematical induction and its simple applications.
Exercise 1
Key Features of NCERT Class 11 Mathematics Chapter 'Principle of Mathemetical Induction' question answers :
- All chapter question answers with detailed explanations.
- Simple language for easy comprehension.
- Aligned with the latest NCERT guidelines.
- Perfect for exam preparation and revision.
Popular Questions of Class 11 Mathematics
- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
- Q:-
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
- Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.
- Q:- Write the following sets in roster form:
(i) A = {x: x is an integer and - 3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}.
(v) E = The set of all letters in the word TRIGONOMETRY.
(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Recently Viewed Questions of Class 11 Mathematics
- Q:-
If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
- Q:-
Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.
- Q:-
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
- Q:-
If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.
- Q:-
Find the sum to n terms of the series 52 + 62 + 72 + ... + 202
- Q:-
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)thnumbers is 5:9. Find the value of m.
- Q:-
2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
- Q:-
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
- Q:-
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 length.
(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.
- All Chapters Of Class 11 Mathematics
- All Subjects Of Class 11