Welcome to the ** Class 11 Mathematics NCERT Solutions** page. Here, we provide detailed **question answers for Chapter - **, 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 ** 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.

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- 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, 3

^{2}, 3^{3}, … 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.

- Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

- Q:-
Find the sum to

*n*terms of the series whose*n*th terms is given by (2*n*– 1)^{2} - Q:-
Prove the following by using the principle of mathematical induction for all n ∈ N:

n (n + 1) (n + 5) is a multiple of 3.

- 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.

- Q:- Find the sum to n terms of the A.P., whose kth term is 5k + 1.
- Q:-
A point is in the XZ-plane. What can you say about its

*y*-coordinate? - Q:-
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?

- Q:-
How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

- Q:-
Show that the ratio of the sum of first

*n*terms of a G.P. to the sum of terms from

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