Write the correct answer in each of the following:
Question 1:
Every rational number is
(A) a natural number (B) an integer
(C) a real number (D) a whole number
Answer 1:
(C) a real number
Solution:
For example ¼ is a rational number as well as real number but not a natural, whole number or integer.
Question 2:
Between two rational numbers
there is no rational number
there is exactly one rational number
there are infinitely many rational numbers
there are only rational numbers and no irrational numbers
Answer 2:
(C) there are infinitely many rational numbers
Solution:
For example
The infinite rational number between 2 and 3 are 2.1, 2.2, 2.3, 2.4, …
Question 3:
Decimal representation of a rational number cannot be
terminating
non-terminating
non-terminating repeating
non-terminating non-repeating
Answer 3:
(D) non-terminating non-repeating
Solution:
Because a non-terminating non-repeating number is termed as irrational number.
Question 4:
The product of any two irrational numbers is
always an irrational number
always a rational number
always an integer
sometimes rational, sometimes irrational.
Answer 4:
(D) sometimes rational, sometimes irrational.
Solution:
For
two irrational numbers 3 +
√2 and 3 − √2
, the
product: (3 + √2)(3 − √2) = 32 −
2 = 7, which is a rational number. For two irrational numbers 3 + √2 and √2, the product: 
, which is an irrational
number.
Question 5:
The decimal expansion of the number 
is
a finite decimal
1.41421
non-terminating recurring
non-terminating non-recurring.
Answer 5:
(D) non-terminating non-recurring.
Solution:
As √2 is an irrational number, so its decimal
representation will be non – terminating non – recurring.
Question 6:
Which of the following is irrational?
(C)
√7 (D)
√81
Answer 6:
(C) √7.
Solution:
As 
, a rational number.
, a rational number.
and √81 = 9, a rational number.
Question 7:
Which of the following is irrational?
(A) 0.14 (B) 0.1416 (C) 0. 1416 (D) 0.4014001400014...
Answer 7:
(D) 0.4014001400014...
Solution:
As it is non – terminating non – recurring.
Question 8:
A rational number between √2 and √3 is
(C)
1.5 (D)
1.8
Answer 8:
(C) 1.5
Solution:
As 
are irrational number. 1.8 is greater than √3.
Question 9:
The value of 1.999... in the form 
, where p and q are integers and q ≠ 0 , is
(C)
2 
Answer 9:
(C) 2
Solution:
Let 𝑥 = 1.999 … ..
⇒ 𝑥 = 1. 9 …………………….(1)
Multiplying
both sides by 10
10𝑥 = 19.9 …………………...(2)
Subtracting equation (1) from equation (2)
9𝑥 = 18
⇒ 𝑥 = 2
Question 10: 
is equal to
(B)
6 
Answer 10:
(C) 3√3
Solution:
2√3 + √3 = √3(2 + 1) = 3√3
Question 11:
√10 × √15 is equal to
6√5
(C) √25 (D) 10√5
Answer 11:
5√6 Solution:
Given
Question
12:
The number obtained on rationalising the denominator of
is
Answer 12:
Solution:
We have 
Question 13:
is equal to
(C) 3 − 2√2 (D) 3 + 2√2
Answer 13:
(D) 3 + 2√2
Solution:
We have 
Question
14:
After rationalising the denominator of
, we get the denominator as
|
(A) 13
|
|
(B) 19 |
|
(C) 5 |
|
(D) 35 |
Answer 14:
(B) 19
Solution:
Question 15:
The value of 
is equal to
√2
(B)
(C)
4 (D)
8 Answer 15:
Solution:
Question 16: If √2 = 1.4142, then
is equal to
(A) 2.4142 (B) 5.8282
(C) 0.4142 (D) 0.1718
Answer 16: (C) 0.4142
Solution:
Question 17:
equals
(B)
2−6 
(D)
26
Answer 17:
Solution:
Question 18:
The product 
equals
√2
(B)
(C)
12√2 (D)
12√32
Answer 18:
Solution:
Question 19:
Value of 
is
(C)
9 
Answer 19:
Solution:
Question 20:
Value of (256)0.16 × (256)0.09 is
(A) 
(B)
16
(C)
64 (D)
256.25
Answer 20:
(A)
Solution:
Question
21:
Which of the following is equal to x?
Answer 21:
Solution:
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