Question 4

# Write the following sets in the set-builder form:

(i) (3, 6, 9, 12)

(ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625}

(iv) {2, 4, 6 upto infinity}

(v) {1, 4, 9, upto 100}

(i) (3, 6, 9, 12)

(ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625}

(iv) {2, 4, 6 upto infinity}

(v) {1, 4, 9, upto 100}

Answer

** (i)** {3, 6, 9, 12} = {*x*: *x* = 3*n*, *n*∈ N and 1 ≤ *n* ≤ 4}

**(ii)** {2, 4, 8, 16, 32}

It can be seen that 2 = 2^{1}, 4 = 2^{2}, 8 = 2^{3}, 16 = 2^{4}, and 32 = 2^{5}.

∴ {2, 4, 8, 16, 32} = {*x*: *x* = 2* ^{n}*,

**(iii)** {5, 25, 125, 625}

It can be seen that 5 = 5^{1}, 25 = 5^{2}, 125 = 5^{3}, and 625 = 5^{4}.

∴ {5, 25, 125, 625} = {*x*: *x* = 5* ^{n}*,

**(iv)** {2, 4, 6 …}

It is a set of all even natural numbers.

∴ {2, 4, 6 …} = {*x*: *x* is an even natural number}

**(v)** {1, 4, 9 … 100}

It can be seen that 1 = 1^{2}, 4 = 2^{2}, 9 = 3^{2} …100 = 10^{2}.

∴ {1, 4, 9… 100} = {*x*: *x* = *n*^{2}, *n*∈N and 1 ≤ *n* ≤ 10}

- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

- 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:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

- 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:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

- Q:-
Find the sum to

*n*terms of the series 3 × 1^{2}+ 5 × 2^{2}+ 7 × 3^{2}+ … - Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

- Q:-
If the first and the

*n*th term of a G.P. are*a*ad*b*, respectively, and if*P*is the product of*n*terms, prove that*P*^{2}= (*ab*)^{n}.

- Q:-
Let the sum of

*n*, 2*n*, 3*n*terms of an A.P. be S_{1}, S_{2}and S_{3}, respectively, show that S_{3}= 3 (S_{2}– S_{1}) - Q:-
Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, .

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

- 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:- 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:-
Find the sum to

*n*terms of the series 1^{2}+ (1^{2}+ 2^{2}) + (1^{2}+ 2^{2}+ 3^{2}) + … - Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

- Q:- Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces:

(i) 5__A

(ii) 8__A

(iii) 0__A

(iv) 4__A

(v) 2__A

(vi) 10__A

Darwin
2019-07-28 18:33:12

Very nice

Jaladi syam babu
2019-06-07 06:05:13

Thank Q soo much

- NCERT Chapter

Copyright © 2020 saralstudy.com. All Rights Reserved.