Number Systems - Test Papers
CBSE Test Paper 01
CH-1 Number Systems
=
5
6
Which of the following is equal to ‘x’?
An irrational number between 5 and 6 is
none of these
is equal to
3
If , then the value of is
32
34
6
12
- Fill in the blanks:
The two rational number which are their own multiplicative inverses are ________.
- Fill in the blanks:
The value of is ________.
Find:
Identify whether is rational number or irrational number.
Write the decimal form and state its kind of decimal expansion.
Simplify the expression:
Recall, is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, This seems to contradict the fact that is irrational. How will you resolve this contradiction?
Find three different irrational numbers between the rational numbers and .
Rationalize a denominator of the following:
Prove that: = 28
CBSE Test Paper 01
CH-1 Number Systems
Solution
- (c)
Explanation:
and
so, - (c)
Explanation:
=x - (d)
Explanation:
We know that,
If a and b are two distinct positive rational numbers such that ab is not a perfect square of a rational number,thenis an irrational number lying between a and b,
Here also we have 5 and 6 two distinct rational numbers and 5×6=30 is not a perfect square,
So irrational number between 5 and 6 = - (d)
Explanation: - (b) 34
Explanation:
given 1, -1
We know that
We conclude that can also be written as ,or
We know that
We know that can also be written as
.
Therefore, the value of will be .We have,
= = 3
Since 3 is a rational number and is an irrational number. Therefore, the product 3 = is an irrational number.= 0.36
The decimal expansion is terminating.