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Closure Property

Reciprocal of...

Question

Reciprocal of any natural number lies between

A

100 and 1000

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B

0 and 1

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C

1 and infinity

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D

0 and -1

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Solution

The correct option is B
0 and 1

A natural number is always equal to or greater than 1. The reciprocal of a number which is greater

than 1 is always less than 1. Moreover, all natural numbers are positive and reciprocal of a positive

number is always positive. Therefore, the reciprocal of any natural number lies between 0 and 1.

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Similar questions

Question 19
The reciprocal of any rational number $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ is:
(a) $\frac{p}{q}$
(b) 1
(c) 0
(d) $\frac{q}{p}$

Question 19
The reciprocal of any rational number $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ is:
(a) $\frac{p}{q}$
(b) 1
(c) 0
(d) $\frac{q}{p}$

Q. If any number divided by zero is infinity and
if zero divided by any number is 0 then

What is 0/0????

Q. We know that
(i) sin x < x, for any x > 0
(ii) sin x > x, for any x < 0
Thus for any natural number n, sin(n) < n.
But as

- 1 < s i n (n) < 1 a n d (- 1, 1) \subset [- \frac{π}{2}, \frac{π}{2}]

So, we can conclude that :
sin (sin(n)) < sin(n) of sin (n) > 0.
and sin (sin(n)) > sin(n) of sin (n) < 0.
Let us define two recursion sequences {an} and {bn} as follows.

a_{1} = 1, a_{n} = s i n (a_{n - 1})

b_{1} = 1, b_{n} = c o s (b_{n - 1})

{lim}_{n \to \infty} b_{n}

Fill in the blanks :

(i) The product of a rational number and its reciprocal is........

(ii) Zero has..... reciprocal.

(iii) The numbers....... and ....... are their own reciprocals.

(iv) Zero is...... the reciprocal of any number.

(v) The reciprocal of a, where $a \neq 0,$ is....

(vi) The reciprocal of $\frac{1}{a}$ , where $a \neq 0$ , is.....

(vii) The reciprocal of a positive rational number is........

(viii) The reciprocal of a negative rational number is..........

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