Question 3

# 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.

(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.

Answer

** (i)** A = {*x*: *x* is an integer and –3 < *x* < 7}

The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6 only.

Therefore, the given set can be written in roster form as

A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}

**(ii)** B = {*x*: *x* is a natural number less than 6}

The elements of this set are 1, 2, 3, 4, and 5 only.

Therefore, the given set can be written in roster form as

B = {1, 2, 3, 4, 5}

**(iii)** C = {*x*: *x* is a two-digit natural number such that the sum of its digits is 8}

The elements of this set are 17, 26, 35, 44, 53, 62, 71, and 80 only.

Therefore, this set can be written in roster form as

C = {17, 26, 35, 44, 53, 62, 71, 80}

**(iv)** D = {*x*: *x* is a prime number which is a divisor of 60}

2 | 60 |

2 | 30 |

3 | 15 |

5 |

∴60 = 2 × 2 × 3 × 5

The elements of this set are 2, 3, and 5 only.

Therefore, this set can be written in roster form as D = {2, 3, 5}.

**(v)** E = The set of all letters in the word TRIGONOMETRY

There are 12 letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated.

Therefore, this set can be written in roster form as

E = {T, R, I, G, O, N, M, E, Y}

**(vi)** F = The set of all letters in the word BETTER

There are 6 letters in the word BETTER, out of which letters E and T are repeated.

Therefore, this set can be written in roster form as

F = {B, E, T, R}

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

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

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

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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}, 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.

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

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A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

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*f*is a function satisfying f(x +y) = f(x) f(y) for all x,y N such that f(1) = 3and , find the value of

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If is the A.M. between

*a*and*b*, then find the value of*n*. - Q:-
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*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:-
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.

- Q:-
Find the sum to

*n*terms of the series 3 × 8 + 6 × 11 + 9 × 14 +… - Q:- Find the sum to n terms of the A.P., whose kth term is 5k + 1.
- Q:-
Find the sum to

*n*terms of the series 1^{2}+ (1^{2}+ 2^{2}) + (1^{2}+ 2^{2}+ 3^{2}) + … - Q:-
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*n*terms of the sequence, 8, 88, 888, 8888…

Kuldee
2019-09-26 13:18:11

Wonderful maths helper

shyamlal yadav
2019-05-27 22:49:18

good

Rajoo Prajapati
2019-05-19 06:23:39

Great explanation

T MAINA
2019-05-13 20:16:28

Wonderful maths helper

Mehboob
2018-10-21 10:33:08

What will be the answer for . Describe the set {xâ¬N:x is a perfect square,10

sandeepbhairagond
2018-09-17 21:41:46

Super interduce great

Angel mariya
2018-06-27 20:13:54

Thanks for the help

Lalit baro
2018-06-19 07:07:29

thanks

Akash Swarnakar
2018-05-22 20:56:12

I also can't understand the third one

sri ram kumar
2018-04-03 21:15:32

Thanks for help it is very nice site

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