Real Numbers Test

Result

Real Numbers Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

A number (n) when divided by 7 leaves a remainder of 2. What will be the remainder if one more than square of the number is divided by 7?

A
6

B
5

C
3

D
1

Solution

Let the number be n.
n = 7q + 2 (where q is the quotient)

Now,
n² + 1 = (7q + 2)² + 1 = (7q)² + 2² + 28q + 1 = 49q² + 28q + 4 + 1

n² + 1 = 7(7q² + 4q) + 5
When 7(7q² + 4q) + 5 is divided by 7, the remainder will be 5.
Question 2
1 / -0

Which of the following prime numbers should be the denominator to get a terminating decimal number?

A
2

B
3

C
5

D
Either 2 or 5

Solution

Fractions with denominator 2 or 5 only have terminating decimals as 2 and 5 completely divide 10 or 100.