Number System-Railway Maths Part X

Total Questions: 38

31. The square root of which of the following numbers is irrational? [RRB ALP 30/08/2018 (Afternoon)]

Correct Answer: (a) 7840 
Solution:

The square roots of following no’s are :
√7840 = 28√10, √2916 = 54, √4489 = 67, √1024 = 32
Clearly, we can see that 7840 has an irrational square root.

32. What is the sum of the first 16 terms of the given series: 6, 13/2, 7, 15/2, ……… [RRB ALP 30/08/2018 (Afternoon)]

Correct Answer: (c) 156
Solution:

Sum of first n terms is given by ;
n/2 [2a + (n – 1)d]
Here, 13/2 – 6 = 7 – 13/2 = 1/2.
So, the given series are in A.P.

So, the sum of the first 16 terms
= [2 × 6 + (16 – 1) 1/2]
= 8[12 + 7.5] = 8 × 19.5 = 156

33. In a 3-digit number, the hundreds digit is 4 times the units digit and the tens digit is thrice the units digit. The sum of the digits is 8. What is the tens digit in the number? [RRB ALP 30/08/2018 (Evening)]

Correct Answer: (b) 3
Solution:

Let the 3-digit no be XYZ
Then, X = 4Z and Y = 3Z, ATQ,
X + Y + Z = 8, 4Z + 3Z + Z = 8,
8Z = 8, Z = 8/8 = 1

Now, X = 4 × 1 = 4 and Y = 3 × 1 = 3.
So, a 3-digit no formed is 431
The tens digit in 431 = 3

34. The denominator of a rational number exceeds its numerator by 10. If the numerator is increased by 4 and the denominator is reduced by 3, the number obtained is 5/6. The original rational number is — [RRB ALP 31/08/2018 (Morning)]

Correct Answer: (b) 11/21
Solution:

Let the numerator be x, then denominator = x + 10

Required rational number = x / (x + 10)

According to question,
(x + 4) / (x + 10 – 3) = 5/6
⇒ 6x + 24 = 5x + 35
⇒ 6x – 5x = 35 – 24 ⇒ x = 11

Hence, the original rational number
= 11 / (11 + 10) = 11 / 21

35. What will be the 20th term in the given sequence? −50, −47, −44, ______ [RRB ALP 31/08/2018 (Morning)]

Correct Answer: (d) 7
Solution:

Given, first term = -50 ,
common diff. +3 , n = 20
20th term = a + (n - 1)d = -50 + (20 - 1)3
= -50 + 57 = 7

36. Among the following, which is a rational number? [RRB ALP 31/08/2018 (Morning)]

Correct Answer: (a) ⁵√32
Solution:

By solving each option one by one,

(a) ⁵√32 = 2⁵/⁵ = 2  (b) ⁶√32 = 2⁵/⁶
(c) ³√32 = 2⁵/³  (d) ⁴√32 = 2⁵/⁴

It is clear that option a is a rational number.

37. How many three-digit whole numbers are there between 75 and 405? [RRB ALP 31/08/2018 (Afternoon)]

Correct Answer: (c) 305
Solution:

Three digit whole number between 75 and 405
= 100,101,102,………404.

Number of terms
= (last term – first term) / common diff. + 1
= (404 – 100) / 1 + 1 = 304 + 1 = 305

There are 305 three digit whole numbers between 75 and 405.

38. What is the difference between the place value and face value of 3 in 273965? [RRB ALP 31/08/2018 (Afternoon)]

Correct Answer: (c) 2997
Solution:

Place value of 3 in 273965 = 3000
Face value of 3 in 273965 = 3
Now, required difference = 3000 - 3 = 2997