Number System-Railway Maths Part X

Total Questions: 38

11. In how many ways can 480 mobiles be distributed equally to the student of a class? [RPF S.I. 19/12/2018 (Morning)]

Correct Answer: (d) 24
Solution:

To find the no. of ways to distribute equally among children, we find the total no. of factors:

                                      480 = 2⁵ × 3¹ × 5¹

Total required no. of ways = 6 × 2 × 2 = 24 ways

12. Which of the following is not a Triangular number? [RRB ALP 09/08/2018 (Morning)]

Correct Answer: (d) 5
Solution:

Formula to find the triangular no. (T.N.) →

Put value of n = 1, we get (T.N.) as 1
n = 2, we get (T.N.) as 3
n = 3, we get (T.N.) as 6
n = 4, we get (T.N.) as 10
n = 5, we get (T.N.) as 15
Clearly, 5 can’t be a triangular number.

13. Which of the following numbers will have an irrational square root? [RRB ALP 09/08/2018 (Morning)]

Correct Answer: (b) 2048
Solution:

As we know, perfect square no ends with (1, 4, 5, 6, 9).
Now, from the given option, we can clearly see that 2048 has irrational square roots.

14. Find a two digit number which is exactly three times the product of its digits? [RRB ALP 09/08/2018 (Morning)]

Correct Answer: (c) 24
Solution:

On checking the given options one by one, we get option (c) satisfies the given condition.
24 = 3(2 × 4), 24 = 24,
LHS = RHS

15. Which of the numbers given below is NOT rational? [RRB ALP 09/08/2018 (Afternoon)]

Correct Answer: (b) √8
Solution:

The given no’s are:
∛64 = 4, √8 = 2√2, ∛8 = 2, √64 = 8
So, we can clearly see that √8 is irrational no.

16. Which of the following numbers is not composite? [RRB ALP 14/08/2018 (Morning)]

Correct Answer: (a) 109
Solution:

A composite number is a positive integer which is not a prime number (i.e., which has not factors other than 1 and itself)

(b) Prime factor of 161 = 23 × 7
(c) Prime factor of 203 = 7 × 29
(d) Prime factor of 209 = 11 × 19
109 is a prime number

17. The square root of which of the following numbers is irrational? [RRB ALP 14/08/2018 (Afternoon)]

Correct Answer: (b) 6560
Solution:

The square root of the given no’s are:
√3969 = 63, √6560 = 4√410, √5625 = 75, √1764 = 42
So, the square root of 6560 is irrational.

18. ‘P’ is the smallest positive integer such that every positive integer N greater than ‘P’ can be written as a sum of two composite numbers. Then ‘P’ is: [RRB ALP 17/08/2018 (Morning)]

Correct Answer: (b) 11
Solution:

checking by option

By option (a) P = 3 than N = p + 1 = 4
4 → (1 + 3), (2 + 2)

By option (b) P = 11 than N = P + 1 = 12
12 → (1 + 11), (2 + 10), (8 + 6), (6 + 6)

We can see) (8 + 6), (6 + 6) are two composite numbers
Hence option (b) is the right answer.

19. Which of the following is the prime number series from 1 to 20? [RRB ALP 20/08/2018 (Morning)]

Correct Answer: (b) 2, 3, 5, 7, 11, 13, 17, 19
Solution:

Required prime number series from 1 to 20 = (2, 3, 5, 7, 11, 13, 17, 19)

20. Which of the following will yield a recurring decimal? [RRB ALP 20/08/2018 (Afternoon)]

Correct Answer: (a) 21/90
Solution: