Number System-Railway Maths Part III

Total Questions: 50

41. Which of the following statements is true ? [RRB NTPC 05/01/2021 (Morning)]

Correct Answer: (c) Every real number can be written in the complex form.
Solution:

Out of the four given statements only the statement, every real number can be written in the complex form is true. As we know, complex numbers are written as → a + ib form.
Now, any real number can be written in this form by making the part b = 0 ,
e.g. the real number 5 = 5 + ι × 0

42. What fraction of the numbers from 2 to 12 are composite numbers ? [RRB NTPC 05/01/2021 (Evening)]

Correct Answer: (a) 6/11
Solution:

The numbers from 2 to 12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 (11 numbers), Composite numbers are = 4 ,6,8,9,10,12
(6 numbers) Required fraction = 6/11

43. A + 0 = 0 + A = A , where A is a real number is true, because of

Correct Answer: (b) The additive property of zero
Solution:

A + 0 = 0 + A = A This is the additive property of zero.

44. If the difference between squares of two consecutive positive odd integers is 56, then the two consecutive odd integers are. [RRB NTPC 07/01/2021 (Morning)]

Correct Answer: (a) 13, 15
Solution:

Let the consecutive odd integers are x, x + 2 .
As the difference between squares of two consecutive positive odd integers is ⇒ (x + 2)² - x² = 56 ⇒ x = 13
Then the two consecutive odd integers are 13 and 15.

45. When a number n is divided by 5, the remainder is 2. When n² divided by 5, the remainder will be [RRB NTPC 07/01/2021 (Morning)]

Correct Answer: (c) 4
Solution:

The number is = n ,
When n is divided by 5, the remainder is 2.
⇒ n = 5q + 2 [ where q is the quotient]
Squaring both sides we get,
⇒ n² = 25q² + 20q + 4
Here, the part 25q² + 20q is divisible by 5,
So, when n² divided by 5, the remainder will be 4.

46. Decimal expansion of 109/100 is: [RRB NTPC 07/01/2021 (Evening)]

Correct Answer: (c) 1 + 0/10 + 9/100
Solution:

Decimal expansion of 109/100 is
= 109/100 = 1 + 0/10 + 9/100

47. Which if the following number has a terminating decimal? [RRB NTPC 07/01/2021 (Evening)]

15/600,  29/343,  7/(2² × 7²),  77/210

Correct Answer: (c) 15/600
Solution:

15/600 = 0.025
⇒ It is a terminating decimal because this decimal has a finite number of digi 29/343 = 0.08454.....[ it is a non terminating decimal]  7/(2² × 7²) = 7/196 = 0.03571.......
[ it is a non terminating decimal]
77/210 =0.36666..... [ it is a non terminating decimal]

48. The product of any two even consecutive numbers is always divisible by. [RRB NTPC 08/01/2021 (Morning)]

Correct Answer: (a) 8
Solution:

The product of two even consecutive numbers is always divisible by 8.
Examples- 2 × 4 = 8, 4 × 6 = 24, 6 × 8 = 48 etc.

49. Three consecutive integers when taken in increasing order and multiplied by 2, 3 and 4 respectively adds up to 74. What is the greater number? [RRB NTPC 08/01/2021 (Morning)]

Correct Answer: (a) 9
Solution:

Let the three consecutive numbers be x, x + 1 x + 2
ATQ,
2x + 3(x + 1) + 4(x + 2) = 74
⇒ 9x + 11 =74 ⇒ 9x = 63 ⇒ x = 7
.. Greater number = x + 2 = 7 + 2 = 9

50. The smallest six digit number which is completely divisible by 4, 8, 12 and 16 is. [RRB NTPC 08/01/2021 (Evening)]

Correct Answer: (a) 100032
Solution:

Any number which is divisible by 4, 8, 12 and 16 must be divisible by 3, 4 and 8. If the last 3 digits of any number are divisible by 8, then the number is divisible by 8.

So, from given options only 100032 and 100800 are divisible by all but the smallest number of 6 digits will be 100032.