Number System-Railway Maths Part VI

Total Questions: 50

1. How many factors of 2³ × 3³ × 5 ⁴ × 7² are divisible by 50 but not by 100? [RRB NTPC 02/02/2021 (Evening)]

Correct Answer: (c) 36
Solution:

2³ × 3³ × 5⁴ × 7²
No. of factors divisible by 50 =
5² × 2 (2 × 3³ × 5² × 7²)
→ 3 × 4 × 3 × 3 = 108
No. of factors divisible by 100 =
5² × 2² * (2 × 3³ × 5² × 7²)
→ 2 × 4 × 3 × 3 = 72
Required no. of factors = 108 - 72 = 36

2. What is the number of divisors of 120? [RRB NTPC 02/02/2021 (Evening)]

Correct Answer: (a) 16
Solution:

120 = 2³ × 3 × 5
Number of factors = (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16

3. In a division sum, the divisor is 2 times the quotient and 6 times the remainder. If the remainder is 8, find out the value of the dividend. [RRB NTPC 03/02/2021 (Evening)]

Correct Answer: (a) 1160
Solution:

Given that Remainder = 8
A/Q, Divisor = 6 × 8 = 48
Quotient = 24 Dividend
= Divisor × Quotient + Remainder
= 48 × 24 + 8 , = 1160

4. Find the number whose four-fifth is more than its three fourth by 4. [RRB NTPC 03/02/2021 (Evening)]

Correct Answer: (b) 80
Solution:

Let the number = x
A/Q, (4x)/5 - (3x)/4 = 4 ⇒ (16x - 15x)/20 = 4
⇒ x/20 = 4 ⇒ x = 80

5. The sum of two numbers is 40 and their product is 60. The sum of their reciprocal is: [RRB NTPC 04/02/2021 (Morning)]

Correct Answer: (b) 2/3
Solution:

Let, the numbers are " a " and "b"
A / Q, a + b = 40 and a × b = 60
1/a + 1/b = (a + b)/(ab) = 40/60 = 2/3

6. What is the sum of the cubes of the natural numbers from 5 to 14? [RRB NTPC 04/02/2021 (Morning)]

Correct Answer: (b) 10925
Solution:

sum of the cubes of the natural numbers from 5 to 14
= 5³ + 6³ + 7³ +8³ ........14³ =10925

7. What is the smallest five - digit number formed by using the digits 2, 3, 4 ,0 ,5 ? [RRB NTPC 04/02/2021 (Morning)]

Correct Answer: (a) 20345
Solution:

Smallest five-digit number formed by using the digits 2, 3,4, 0, 5 = 20345

8. The difference between the greatest and the smallest six - digit number is: [RRB NTPC 04/02/2021 (Morning)]

Correct Answer: (b) 899999
Solution:

6 digit greatest number = 999999
and 6 digit smallest number = 100000
Difference between them = 899999

9. If a² + b²+ c² + d² = 1 , what will be the maximum value of the product abcd? [RRB NTPC 04/02/2021 (Evening)]

Correct Answer: (a) 1/16
Solution:

a² + b² + c² + d² = 1
Put a = b = c = d = 1/2 satisfies the given equation, abcd
= 1/2 × 1/2 × 1/2 × 1/2 = 1/16

10. If the largest 4-digit number is subtracted from the smallest 6-digit number, then the remainder will be. [RRB NTPC 04/02/2021 (Evening)]

Correct Answer: (a) 90001
Solution:

Smallest 6-digit number = 100000
Largest 4-digit number = 9999
100000 - 9999 = 90001