Number System-Railway Maths Part VI

Total Questions: 50

31. Find the sum of the smallest an the largest positive numbers of 6 digits which contain only digits 0, 4, 6 and each of these digits appears at least once. [RRB NTPC 09/02/2021 (Evening)]

Correct Answer: (a) 1066646
Solution:

Smallest 6-digit number formed using 0,4 and 6 = 400006
Largest 6-digit number formed using 0, 4 and 6 = 666640
Sum = 666640 + 400006 = 10,66,646

32. To a number (1/3 - 1/4) is added. From the sum so obtained 1/3 of 1/4 is subtracted and the remainder is 1/3 +, 1/4 Find the number. [RRB NTPC 10/02/2021 (Morning)]

Correct Answer: (b) 7/12
Solution:

Let, number = X
{ x + ( 1/3 - 1/4 ) } - ( 1/3 × 1/4 ) = ( 1/3 + 1/4 )
{ x + ( 1/12 ) } - 1/12 = 7/12 ⇒ x = 7/12

33. Find the smallest natural number N such that the product 288 x N is a perfect cube. [RRB NTPC 10/02/2021 (Morning)]

Correct Answer: (d) 6
Solution:

Factorization of 288 then we get -- 2 × 2 × 2 × 2 × 2 × 3 × 3
For making a perfect cube, 288 will be multiply with (2 × 3)
Then 288 × 6 , now we can say that 6 is the smallest natural number.

34. Find the sum of all even natural numbers less than 85. [RRB NTPC 10/02/2021 (Evening)]

Correct Answer: (b) 1806
Solution:

35. Which of the following is equal to 3.14 × 10⁶ ? [RRB NTPC 10/02/2021 (Evening)]

Correct Answer: (a) 3140000
Solution:

3.14 × 10⁶
= 314/100 × 1000000 = 3140000

36. A number, x, when divided by 7 leaves a remainder of 1 and another number, y, when divided by 7 leaves a remainder of 2. What will be the remainder if x + y is divided by 7? [RRB NTPC 10/02/2021 (Evening)]

Correct Answer: (a) 3
Solution:

Dividend = (Divisor × quotient) +remainder Let us assume p is the quotient when x is divided by 7 and q is the quotient when y is divided by 7.
X = (7p) + 1 and Y = (7q) + 2
Therefore X + Y = 7p + 7q + 1 + 2
= 7(p + q) +3 ⇒ (X + Y)
when divided by 7 leaves remainder 3.

37. Find the greatest four-digit number that is a perfect square. [RRB NTPC 10/02/2021 (Evening)]

Correct Answer: (a) 9801
Solution:

The greatest four digit number is 9999. After finding Square root by the long division method we get 198 as remainder, So now we subtract 198 from 9999 to get a perfect square number that is 9999 - 198 = 9801

38. Out of six consecutive numbers, the sum of the first three numbers is 27. What is the sum of the next three numbers? [RRB NTPC 11/02/2021 (Morning)]

Correct Answer: (c) 36
Solution:

Let the six consecutive numbers are = x, x + 1 , x + 2 x + 3 , x + 4 , x + 5, x + x + 1 + x + 2 = 27
⇒ 3x + 3 = 27 ⇒ 3x = 24 ⇒ x = 8
Sum of next three numbers = 3x + 12 = 3 × 8 + 12 = 36

39. The value of 1/4 + 1/(4 × 5) + 1/(4 × 5 × 6) correct to four decimal places is. [RRB NTPC 11/02/2021 (Morning)]

Correct Answer: (b) 0.3083
Solution:

40. How many significant digits are there to the right of the decimal point in the product of 95.75 and 0.02554? [RRB NTPC 11/02/2021 (Morning)]

Correct Answer: (d) 6
Solution:

95.75 × 0.02554 = 2.445445 the decimal point will be after 6 digits from the right