Number System Practice Set 1st Solution Continues

The solution of Practice Set 1st based on Number System Continues..............

Q8. The sum of first 50 even natural numbers is

(a) 1275           (b) 2550         (c) 1875           (d) 5100          

Sol. Number of terms in the series (n) = 50

Using the formula, Sum of n – even natural numbers = [n (n + 1)]

[50 × (50 + 1)]

On solving we get 2550.

The required sum = 2550.

Option (b)

Q9. The sum of first 27 odd natural numbers is

(a) 756          (b) 378         (c) 729           (d) 780           

Sol. Number of terms in the series (n) = 27

Using the formula, Sum of n – odd natural numbers = n²

(27)²

On solving we get 729.

The required sum = 729.

Option (c)

Q10. If consecutive whole numbers from 1 onwards are written one after another to the right of 1, the digit at the 31^st place is

(a) 0            (b) 2          (c) 1            (d) 3

Sol. On writing 1234.......9

We get 9 digits.

Now 31 – 9 = 22 digits more to be written in continuation.

After 9, two digit numbers start which means (22/2 = 11) numbers more to be written.

9 + 11 =20.

Hence the last number written will be 20 and the last digit will be 0.

Option (a)

Q11. The sum of the smallest one – digit natural number and the largest two – digit whole number is

(a) 101                (b) 99            (c) 2              (d) 100         (e) None of these

Sol. The smallest one – digit number = 1

The largest two – digit whole number = 99

Now 1 + 99 = 100.

Option (d)

Q12. The difference between the largest 4 – digit natural number and the smallest 3 – digit whole number is 

(a) 9989             (b) 8999         (c) 9899        (d) 9889         (e) None of these

Sol. The largest 4- digit natural number = 9999.

The smallest 3 – digit whole number = 100.

Now 9999 – 100 = 9899.

Option (c) 

Q13. If x is a natural number then x ÷ 0 is

(a) 0            (b) meaningless        (c) 1         (d) None of these

Sol.  Division by zero (0) is meaningless.

Option (b)

Q14. A number which is a natural number but not a whole number is

(a) 1           (b) 0            (c) All negative numbers             (d) No such number

Sol.  As per definition and concept,

All natural numbers are also whole numbers.

Therefore no such number is there which is a natural number but not a whole number.

Option (d)

Q15. The only whole number with a successor but not a predecessor is

(a) 0          (b) 1            (c) No such number                       (d) None of these.

Sol.  As per definition and concept,

All natural numbers including zero is known as whole numbers.

Therefore 0 is the only whole number with a successor but not a predecessor.

Option (a)

Hope you will be able to solve these questions by your own. Visitor’s are warm heartedly welcomed with their related problems and queries. More Conceptual enjoyment will be continued for you soon, just keep visiting this blog regularly and writing me your related queries through comment or forum.

Best of Luck for Exams. To be continued soon........................