Number System-Railway Maths

Total Questions: 50

11. In what way can the terms of the given set be rearranged into three sets such that the sum of the two terms in each set is equal? [NTPC CBT II Level 5 (15/06/2022) Shift 2]

(947, 861, 1304, 1218, 1378, 787)

Correct Answer: (b) (947, 1218), (861, 1304), (787, 1378)
Solution:

947 + 1218 = 861 +1304 = 787 + 1378
2165 ⇒ 2165 = 2165
NOTE:- During exam, Just check the unit digit and eliminate the options.

12. 6889 students are sitting in an auditorium in such a manner that there are as many students in a row as there are rows in the auditorium. How many rows are there in the auditorium? [NTPC CBT-1 29/12/2020 (Afternoon)]

Correct Answer: (c) 83
Solution:

As there are as many students in a row as there are rows in the auditorium, it means this arrangement forms a square where the number of rows and columns are equal. So as the total number of students = 6889, the number of rows = √6889 = 83

13. If 1² + 2² + 3² + .............+14² = 1015, then 3² + 6² + 9² .......... +42² is equal to. [NTPC CBT-1 29/12/2020 (Morning)]

Correct Answer: (a) 9135
Solution:

Given, 1² + 2² + 3² +.............+14² = 1015,
Then, 3² +6² + 9²........+ 42²
= 3² × (1²+2²+3² +............. +14²)
= 9 × 1015= 9135

14. Which of the following is NOT a rational number? [NTPC CBT-1 05/01/2021 (Morning)]

√(3² + 4²) , √12.96 , √125 and √900

Correct Answer: (b) √125
Solution:

The given numbers are
√(3² + 4²), √12.96, √125 and √900
Here, √(3² + 4²) = 5√12.96 = 3.6
√125 = 5√5
√900 = 30
So, the only irrational (not rational) number is √125 = 5√5

15. The least multiple of 23 when divided by 18, 21 and 24 leaves the remainder 7, 10 and 13 respectively. The number is; [NTPC CBT-1 07/01/2021 (Morning)]

Correct Answer: (b) 3013
Solution:

16. How many times is digit 3 passed in counting from 301 to 399? [NTPC CBT-1 10/01/2021 (Evening)]

Correct Answer: (b) 119
Solution:

301 to 399 ⇒ in first place = 99 times
330 to 339 ⇒ in 2nd place = 10 times
In 3rd place = 10 times
Total = 99 + 10 + 10= 119

17. Solve it- [NTPC CBT-1 10/01/2021 (Evening)]

Correct Answer: (d) (n-1)/2
Solution:

18. In competitive examination, 1 mark is awarded for correct answer, 0 mark for unanswered and 1/2 Mark is deducted for every wrong answer. Ambika answered 120 questions and got 90 marks. How many answers were correct? [NTPC CBT-1 10/01/2021 (Evening)]

Correct Answer: (c) 100
Solution:

Let the number of correct answer = x Incorrect answers = 120 - x According to question,

19. If a,b,c,d and e are the digits of a number beginning from the left, then the number is: [NTPC CBT-1 04/02/2021 (Morning)]

Correct Answer: (d) 10⁴a + 10³b + 10²c + 10d + e
Solution:

According to question
= 10000a + 1000b + 100c + 10d + e
= 10⁴a + 10³b + 10²c + 10d + e

20. There are 40 persons in the palace. If every person shakes hands with every other person, what will be the total number of handshakes? [NTPC CBT-1 21/01/2021 (Morning)]

Correct Answer: (a) 780
Solution:

Number of total handshakes = 40 × 39/ 2 = 780