Q: If x + y + z = 9 and both y and z are positive integers greater than zero, then the maximum value x can take is

7 — We may take the least values of y and z as y = 1 and z = 1. So, the maximum value of x is 7.

Q: P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P + Q?

35 — We may have (64 and 1), (32 and 2), (16 and 4) and (8 and 8). In any case, the sum is not 35.

Q: There are just two ways in which 5 may be expressed as the sum of two different positive (non-zero) integers, namely 5 = 4 + 1 = 3 + 2. In how many ways, 9 can be expressed as the sum of two different positive (non-zero) integers?

4 — We can write 9 = (1 + 8) ; 9 = (2 + 7) ; 9 = (3 + 6), 9 = (4 + 5). Thus, it can be done in 4 ways.

Q: The number 3 is

an infinite non-recurring decimal — 3 is an infinite non-recurring decimal.

Q: The number p is

an irrational number — Clearly, p is an irrational number.

Q: Every rational number is also

a real number — Clearly, every rational number is also a real number.

Q: Consider the following statements about natural numbers: (1) There exists a smallest natural number. (2) There exists a largest natural number. (3) Between two natural numbers, there is always a natural number. Which of the above statements is/are correct?

Only 1 — Clearly, there exists a smallest natural number, namely 1. So statement (1) is true. Natural numbers are counting numbers and the counting process never ends. So, the largest nature number is not known. Thus, statement (2) is false. Thre is no natural number between two consecutive natural numbers. So, statement (3) is false.

Q: All natural numbers and 0 are called the ......... numbers.

whole — All natural numbers and 0 are called the whole numbers.

Question 1

If the numbers from 1 to 24, which are divisible by 2 are arranged in descending order, which number will be at the 8th place from the bottom?

IUC Academy · Accepted Answer

16 — These numbers are 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2. 8th number from the bottom is 16.

Question 2

Which one of the following is the correct sequence in respect of the Roman numerals: C, D, L and M?

IUC Academy · Accepted Answer

M > D > C > L

Question 3

If n is an integer between 20 and 80, then any of the following could be n + 7 except

IUC Academy · Accepted Answer

88 — (n + 7) = 88 ⇒ n = (88 – 7) = 81, which is false as 20 < n < 80. So, the required number is 88.

Question 4

What is the sum of the squares of the digits from 1 to 9?

IUC Academy · Accepted Answer

285

Question 5

If x + y + z = 9 and both y and z are positive integers greater than zero, then the maximum value x can take is

IUC Academy · Accepted Answer

7 — We may take the least values of y and z as y = 1 and z = 1. So, the maximum value of x is 7.

Question 6

P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P + Q?

IUC Academy · Accepted Answer

35 — We may have (64 and 1), (32 and 2), (16 and 4) and (8 and 8). In any case, the sum is not 35.

Question 7

There are just two ways in which 5 may be expressed as the sum of two different positive (non-zero) integers, namely 5 = 4 + 1 = 3 + 2. In how many ways, 9 can be expressed as the sum of two different positive (non-zero) integers?

IUC Academy · Accepted Answer

4 — We can write 9 = (1 + 8) ; 9 = (2 + 7) ; 9 = (3 + 6), 9 = (4 + 5). Thus, it can be done in 4 ways.

Question 8

The number 3 is

IUC Academy · Accepted Answer

an infinite non-recurring decimal — 3 is an infinite non-recurring decimal.

Question 9

The number p is

IUC Academy · Accepted Answer

an irrational number — Clearly, p is an irrational number.

Question 10

Every rational number is also

IUC Academy · Accepted Answer

a real number — Clearly, every rational number is also a real number.

Question 11

Consider the following statements about natural numbers: (1) There exists a smallest natural number. (2) There exists a largest natural number. (3) Between two natural numbers, there is always a natural number. Which of the above statements is/are correct?

IUC Academy · Accepted Answer

Only 1 — Clearly, there exists a smallest natural number, namely 1. So statement (1) is true. Natural numbers are counting numbers and the counting process never ends. So, the largest nature number is not known. Thus, statement (2) is false. Thre is no natural number between two consecutive natural numbers. So, statement (3) is false.

Question 12

All natural numbers and 0 are called the ......... numbers.

IUC Academy · Accepted Answer

whole — All natural numbers and 0 are called the whole numbers.

Number System MCQ Practice

644. What is the sum of the squares of the digits from 1 to 9?

648. The number 3 is

649. The number p is

650. Every rational number is also

652. All natural numbers and 0 are called the ......... numbers.

656. The sum of the greatest and smallest number of five digits is

659. The sum of the place values of 3 in the number 503535 is

660. The face value of 8 in the number 458926 is

661. What is the place value of 5 in 3254710?

Explore More Practice Topics and Quizzes