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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.
Class 11 Mathematics Chapter 4: Principle of Mathemetical Induction - NCERT Solutions
This page focuses on the complete NCERT solutions for Class 11 Mathematics Chapter 4: Principle of Mathemetical Induction. This section provides detailed, easy-to-understand solutions for all the questions from this chapter. These Principle of Mathemetical Induction question answers will offer you valuable insights and explanations.
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.
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Exercise 1
Key Features of NCERT Class 11 Mathematics Chapter 'Principle of Mathemetical Induction' question answers :
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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?
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- 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:-
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.
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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:-
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
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If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that aq-rbr-pcp-q=1
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How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
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Show that the products of the corresponding terms of the sequences a,ar,ar2, ...arn-1 and A, AR, AR2, ,,,ARn-1 form a G.P, and find the common ratio.
- Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
- Q:- The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms.
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Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …
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