Number System Practice Set 1st Solution

Here I am presenting the solution of first practice set of Number System Questions. Check your answers and clear your doubts:-

Q1. The set of counting numbers along with zero is called the set of

(a) Natural numbers          (b) Decimals          (c) Whole numbers        (d) None of these.

Sol. As per definition and concept:-

The set of counting numbers along with zero is called the set of Whole numbers

Option (c)

Q2. The set of numbers {1, 2, 3, 4,.........} is called the set of

(a) Whole numbers       (b) Natural numbers      (c) Integers             (d) None of these.

Sol. As per definition and concept:-

The set of numbers {1, 2, 3, 4,.........} is called the set of Natural numbers

Option (b)

 Q3. The number which is not a natural number but a whole number is  

(a) a fraction            (b) 0            (c) a prime number        (d) 1

Sol. As per definition and concept:-

N = {1, 2, 3, 4, .........  }

W = {0, 1, 2, 3, 4, .........  }

The number which is not a natural number but a whole number is 0.

Option (b)

Q4. The sum of successor and predecessor of a whole number is equal to one more than the number. Then the number is  

(a) Any  natural number     (b) 1         (c) 2           (d) No such number

Sol. Let the number be x.

Then Successor = (x + 1) and Predecessor = (x - 1)

According to the question (x + 1) + (x - 1) = (x + 1)

On Solving we get x = 1.

Hence the required number is 1.

Option (b).

Q5. The sum of three odd natural numbers multiplied by the sum of two even natural numbers is always

(a) An even natural number      (b) A multiple of 9      (c) Odd natural number   

(d) None of these

Sol. The sum of three odd natural numbers = odd natural number (example 3 + 5 + 7 = 15)

The sum of two even natural numbers = Even natural numbers (example 4 + 6 = 10)

Now The sum of three odd natural numbers × The sum of two even natural numbers

= Odd natural number (15) × Even natural number (10)

= Even natural number (150).

Hence the sum of three odd natural numbers multiplied by the sum of two even natural numbers is always an even natural number.

Option (a)

 

Q6. Which of the following is always odd?

(a) Sum of two odd numbers      (b) Product of two odd numbers    

 (c) Difference of two odd numbers         (d) Nine of these

Sol. Odd number + Odd number = Even number.

Odd number – Odd number = Even number.

Odd number × Odd number = Odd number.

Hence the product of two odd numbers is always odd number.

Option (b)

Q7. The sum of first 100 natural numbers is

(a) 10100           (b) 3750         (c) 5050           (d) 15050

Sol. Number of terms in the series (n) = 100

Using the formula, Sum of n- natural numbers = [{n (n + 1)}/2]

[{100 × (100 + 1)}/2]

On solving we get 5050.

The required sum = 5050.

Option (c)

 The rest solutions of the rest questions are followed in the next post soon............