Number System-Railway Maths Part VIII

Total Questions: 50

31. The negative of a non-zero rational number is: [RRB NTPC 06/04/2021 (Morning)]

Correct Answer: (c) a rational number
Solution:

Rational numbers can be both positive and negative;
So, the negative of a non-zero rational number is also a rational number.

32. The largest four-digit number which is exactly divisible by 77 is: [RRB NTPC 06/04/2021 (Morning)]

Correct Answer: (b) 9933 
Solution:

Largest four digit number is = 9999
Number divisible by 77 means also divisible by 7 & 11;
So, the largest four-digit number which is exactly divisible by 77 near to 9999 is:
= 9933 [as it is divisible by both 7 & 11]

33. The least multiple of 14 which when divided by 6, 8, 12 leaves remainder 4, 6 and 10 respectively, is: [RRB NTPC 06/04/2021 (Evening)]

Correct Answer: (c) 70
Solution:

LCM of (6, 8, 12) = 24
24 × 3 = 72
It is not multiple of 14
When we subtract 2 from it now 70 is divisible by 14.
And when we divide it by 6, 8 and 12 leaves remainder 4, 6, 10 respectively.

34. For a given fraction, how many equivalent fractions can be formed? [RRB NTPC 06/04/2021 (Evening)]

Correct Answer: (a) Infinite 
Solution:

For a given fraction we can form an infinite number of equivalent fractions by multiplying it by natural numbers.

35. The number that should be subtracted from 510 and 270 to get 24 as the GCD is: [RRB NTPC 07/04/2021 (Morning)]

Correct Answer: (d) 6
Solution:

Case 1. 510 is divided by 24 then we get remainder = 6
Case 2. 270 is divided by 24 then we get remainder = 6
So, subtract 6 from both numbers.

36. 119² - 111² is a / an: [RRB NTPC 07/04/2021 (Evening)]

Correct Answer: (d) Composite number
Solution:

119² – 111²
= (119 + 111)(119 – 111)
= 230 × 8 = 1840

37. If pq is a two-digit number, then pq - qp will be completely divisible by: [RRB NTPC 07/04/2021 (Evening)]

Correct Answer: (a) 9 
Solution:

Pq is a two digit number, we can write it as
10p + q, qp = 10q + p
According to question,
(10p + q) - (10q + p)
= 10p - p + q - 10q = 9p - 9q = 9(p - q)
So pq - qp must be divisible by 9.

38. Which of the following is INCORRECT? [RRB NTPC 07/04/2021 (Evening)]

Correct Answer: (c) Every rational number is a whole number.
Solution:

Every rational number is a whole number is incorrect.

39. The sum of two numbers is 15. If the sum of their reciprocals is 3/10, then find the two numbers? [RRB NTPC 07/04/2021 (Evening)]

Correct Answer: (b) 5, 10 
Solution:

40. If x is any positive even number, then x⁶⁵ - x will always be divisible by: [RRB NTPC 08/04/2021 (Morning)]

Correct Answer: (a) 6 
Solution:

x⁶⁵− x = x (x⁶⁴ − 1)
x⁶⁴ is an even number because x is even.
When we subtract 1 from it, it would become an odd number.
So it will be divisible by both 2 and 3.
Hence this will be divisible by 6.