Number Systems

Step 1: Define reciprocal.
The reciprocal of a non-zero number is .
The product of a number and its reciprocal is 1 (i.
e.
, ).

Step 2: Evaluate each statement.
Option (1) Reciprocal of -1 is -1: Let .
Reciprocal = .
This statement is TRUE.
Option (2) Reciprocal of 1 is 1: Let .
Reciprocal = .
This statement is TRUE.
Option (3) Reciprocal of 0 is 0: Let .
The reciprocal would be .
Division by zero is undefined.
So, 0 does not have a reciprocal.
The statement that the reciprocal of 0 is 0 is FALSE.
(Also ).
Option (4) Reciprocal of is 1: First, calculate the value inside the brackets: .
The statement becomes "Reciprocal of -1 is 1".
We know from statement (1) that the reciprocal of -1 is -1, not 1.
So, this statement is FALSE.
The question asks for a FALSE statement.
Both (3) and (4) are false.
Let's re-check the question and standard definitions.
Statement (3) "Reciprocal of 0 is 0" is definitively false because the reciprocal of 0 is undefined.
Statement (4) claims "Reciprocal of -1 is 1".
This is also false.
Typically, such questions have only one false option.
The "Ans" provided in the image has a green checkmark next to "3.
3", meaning option (3) is marked as the (false) statement.
Let's assume option (3) is the intended answer.
Reciprocal of 0 is undefined.
Stating it is 0 makes the statement false.
Reciprocal of .
The reciprocal of -1 is -1.
The statement says it is 1, which is false.
If the question means "which of the provided definitions of reciprocal is false", then (3) is directly stating something about "reciprocal of 0" which is a well-known undefined case.
Option (4) makes a claim about the reciprocal of a calculated value.
Given the "Ans: checkmark on 3.
3", option (3) is considered the false statement we are looking for.

Step 1: Understand the term "whole numbers".
Whole numbers are non-negative integers: 0, 1, 2, 3, .
.
.

Step 2: Understand the phrase "between 45 and 54".
This means we are looking for whole numbers such that .
The numbers 45 and 54 themselves are not included.

Step 3: List the whole numbers that satisfy this condition.
The whole numbers greater than 45 are 46, 47, 48, .
.
.
The whole numbers less than 54 are .
.
.
, 51, 52, 53.
So, the list of whole numbers between 45 and 54 is: 46, 47, 48, 49, 50, 51, 52, 53.

Step 4: Count the numbers in the list.
There are 8 numbers in the list.

Step 5: Alternatively, use a formula.
The number of integers (or whole numbers) strictly between two integers and (where ) is .
Here .
Number of whole numbers = .
Or, the numbers are from to .
Number of terms = .
The numbers are to .
Number of terms = .
This matches option (4).