NUMBER SYSTEM (CDS)

Total Questions: 101

11. Consider the multiplication 999 × abc = def 132 in decimal notation, where a, b, c, d, e and f are digits. What are the values of a, b, c, d, e and f, respectively? [2019 (I) Morning Shift ]

Correct Answer: (d) 8, 6, 8, 8, 6, 7
Solution:999 × abc = def 132


12. Which of the following statements is not true? [2019 (I) Morning Shift ]

Correct Answer: (c) If a number is of the form 6n - 1 (n being a natural number), then it is a prime number
Solution:Every prime number is of the form (6n-1) or (6n + 1) but every number
which is of form (6n - 1) or (6n + 1) not necessarily prime.
Examples showing (6n - 1)
Let n = 6
(6 × 6 - 1) = 36 - 1 = 35 (It is not a prime number)
Let n = 4(6 × 4 - 1) = 24 - 1 = 23 (It is a prime number)
So, option (c) is correct answer.

13. The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the number is [2019 (I) Morning Shift ]

Correct Answer: (d) None of these
Solution:The sum of the three prime number



14. What is the unit place digit in the expansion of 7⁷³ ? [2019 (I) Morning Shift ]

Correct Answer: (c) 7
Solution:The unit place digit =7

15. Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime. [2019 (I) Morning Shift ]

1. Both p and q may be prime numbers.
2. Both p and q may be composite numbers.
3. One of p and q may be prime and the other composite.

Which of the above statements are correct?

Correct Answer: (d) 1, 2 and 3
Solution:p and q are two integers. p and q are also relative prime, HCF = 1

16. The inequality 3ⁿ > N³ holds when [2019 (I) Morning Shift ]

Correct Answer: (d) N is a natural number except 3
Solution:3ⁿ > N³

17. Which one of the following is an irrational number ? [2019 (I) Morning Shift ]

Correct Answer: (d)
Solution:The number that cannot be expressed in the form of p/q are called irrational number.

18. The number 3⁵¹² is divided by 8. What is the remainder? [2019 (I) Morning Shift ]

Correct Answer: (b) 3
Solution:

19. A prime number contains the digit X at unit’s place. How many such digits of X are possible? [2019 (I) Morning Shift ]

Correct Answer: (b) 4
Solution:The digit x at unit's place in prime number.
Then, such digit of x are possible
x = [1, 3, 7, 9]
Option (b) is correct.

20. How many five-digit numbers of the form XXYXX is/are divisible by 33 ? [2018 (II) Evening Shift ]

Correct Answer: (b) 3
Solution:For a number to be divisible by 33 it must be divisible by 3 and 11.