- NCERT Chapter

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}

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

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- Q:- Find the sum to
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Show that the products of the corresponding terms of the sequences a,ar,ar

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(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:-
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:-
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.

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Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

- 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 - Q:-
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

Darwin
2019-07-28 18:33:12

Very nice

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

Thank Q soo much