Number System-Railway Maths Part X

Total Questions: 38

1. The product of three consecutive natural numbers is always divisible by which of the following numbers? [ALP Tier II 21/01/2019 (Afternoon)]

Correct Answer: (b) 6
Solution:

Let the three consecutive natural numbers are n, (n + 1) and (n + 2)
Product of the numbers = n (n + 1) (n + 2)
It is always divisible by 6.

2. How many terms are there in the series √3, √12, √27, √48, …, 22√3 ? [ALP Tier II 21/01/2019 (Afternoon)]

Correct Answer: (c) 22 terms
Solution:

√3, √12, √27, √48, ……, 22√3
Common difference = √12 – √3
= 2√3 – √3 = √3

Number of terms
= (last term – first term) / common diff. + 1
= 〈(22√3 – √3) / √3〉 + 1
= (21√3 / √3) + 1 = 22

So, total number of terms = 22 term

3. Which of the following is an irrational number? [ALP Tier II 21/01/2019 (Afternoon)]

Correct Answer: (d) √9 + √7
Solution:

Irrational number: An irrational number is a type of real number which cannot be expressed as a simple fraction.
Now check each option one by one.

(a) √3 × √27 = √81 = 9
(b) 4√4 = 4 × 2 = 8
(c) √169 – √196 = 13 – 14 = –1
(d) √9 + √7 = 3 + √7,
it is not a simple fraction, so this is an irrational number.

4. The series 7/6, 4/3, 3/2, 5/3, 11/6 is: [ALP Tier II 21/01/2019 (Afternoon)]

Correct Answer: (d) in arithmetic series
Solution:

7/6, 4/3, 3/2, 5/3, 11/6

Common Difference
⇒ 4/3 – 7/6 = 3/2 – 4/3 ⇒ 1/6 = 1/6

So, the given fractions are in A.P.

5. If a, b, c are in A.P., then which of the following is correct? [ALP Tier II 21/01/2019 (Afternoon)]

Correct Answer: (c) 2b = a + c
Solution:

a, b and c are in A.P
Common difference = 2nd term – Ist term
Then,
b – a = c – b ⇒ a + c = 2b

6. How much remains after dividing 5224 by 9? [RPF Constable 17/01/2019 (Evening)]

Correct Answer: (a) 4
Solution:

Divisibility rule of 9: A number is divisible by 9 only if the sum of its digits is also divisible by 9.
Given no. is 5224 ⇒ sum of its digits = 5 + 2 + 2 + 4 = 13
Clearly, 4 is remainder

7. Find the average of arithmetic progression whose first term is 33 and the last term is 45. [RPF Constable 18/01/2019 (Morning)]

Correct Answer: (b) 39
Solution:

8. Find the average of the arithmetic parallel series whose first term is 45 and the last term is 57. [RPF Constable 19/01/2019 (Morning)]

Correct Answer: (d) 51
Solution:

9. Find the number of trailing zeros in 76! [RPF S.I. 19/12/2018 (Morning)]

Correct Answer: (a) 18
Solution:

10. A number when divided by 42 leaves a remainder of 13. What will be the remainder when the same number is divided by 14? [RPF S.I. 19/12/2018 (Morning)]

Correct Answer: (c) 13
Solution:

A number when divided by 42 leaves the remainder 13.
Then no. be 42k + 13
Remainder when 42k + 13 divided by 14
= (42k + 13)/ 14 = (14 × 3 × k + 13)/14
As we know that product of 14 is always divided by 14
So, Remainder = 13