M.C.Q

MCQ 511 Mark

If the number x = 1.242424 is expressed in the simplest form $\frac{p}{q}$, then p + q equals

A
41
B
53
C
72
✓
74

Answer

Correct option: D.

(d)
We have,
$x=1.242424 \ldots$
$\Rightarrow \quad x=1 . \overline{24}=1+0.2 \overline{4}=1+\frac{24}{99}=1+\frac{8}{33}=\frac{41}{33}$
$\therefore \quad p=41$ and $q=33 \Rightarrow p+q=41+33=74$

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MCQ 521 Mark

If n is a natural number, then $\sqrt{n}$ is

A
always a natural number
B
always a rational number
C
always an irrational number
✓
sometimes a natural number and sometimes an irrational number

Answer

Correct option: D.

sometimes a natural number and sometimes an irrational number

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MCQ 531 Mark

How many digits are there in the repeating block of digits in the decimal expansion of $\frac{17}{7}$ ?

A
16
✓
6
C
26
D
7

Answer

Correct option: B.

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MCQ 541 Mark

Every point on a number line represents

✓
a unique real number
B
a natural number
C
a rational number
D
an irrational number

Answer

Correct option: A.

a unique real number

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MCQ 551 Mark

A rational number between - 3 and 3 is

✓
$0$
B
-4.3
C
-3.4
D
1.101100110001...

Answer

Correct option: A.

$0$

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MCQ 561 Mark

A number is an irrational if and only if its decimal representation is

A
non-terminating
B
non-terminating and repeating
✓
non-terminating and non-repeating
D
terminating

Answer

Correct option: C.

non-terminating and non-repeating

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MCQ 571 Mark

An irrational number between $\sqrt{2}$ and $\sqrt{3}$ is

A
$\sqrt{2}+\sqrt{3}$
B
$\sqrt{2} \times \sqrt{3}$
C
$\sqrt{\sqrt{2+3}}$
✓
$\sqrt{\sqrt{2} \times \sqrt{3}}$

Answer

Correct option: D.

$\sqrt{\sqrt{2} \times \sqrt{3}}$

(d)
$\sqrt{a b}$ is a real number between two real numbers a and b. Therefore, $\sqrt{\sqrt{2} \times \sqrt{3}}$ is an irrational number between $\sqrt{2}$ and $\sqrt{3}$.

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MCQ 581 Mark

An irrational number between $\frac{1}{7}$ and $\frac{2}{7}$ is

A
$\frac{1}{2}\left(\frac{1}{7}+\frac{2}{7}\right)$
B
$\frac{1}{7} \times \frac{2}{7}$
✓
$\sqrt{\frac{1}{7} \times \frac{2}{7}}$
D
none of these

Answer

Correct option: C.

$\sqrt{\frac{1}{7} \times \frac{2}{7}}$

(c)
We know that $\frac{a+b}{2}$ and $\sqrt{a b}$ are real numbers between any two real numbers. So $\frac{1}{2}\left(\frac{1}{7}+\frac{2}{7}\right)$ and $\sqrt{\frac{1}{7} \times \frac{2}{7}}$ are real numbers between 1/7 and 2/7.
We observe that $\frac{1}{2}\left(\frac{1}{7}+\frac{2}{7}\right)$ and $\frac{1}{7} \times \frac{2}{7}$ are rational numbers.
So, options (a) and (b) are incorrect. Clearly $\sqrt{\frac{1}{7} \times \frac{2}{7}}=\frac{\sqrt{2}}{7}$ is an irrational number between 1/7 and 2/7 So, option (c) is is correct.

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MCQ 591 Mark

An irrational number between 5 and 6 is

A
$\frac{1}{2}(5+6)$
B
$\sqrt{5+6}$
✓
$\sqrt{5 \times 6}$
D
none of these

Answer

Correct option: C.

$\sqrt{5 \times 6}$

(c)
We observe that $\frac{1}{2}(5+6)$ is a rational number between 5 and 6. So, option (a) is in correct.
$\sqrt{5+6}=\sqrt{11}=3.3166247 \ldots$ is an irrational number not lying between 5 and 6.
$\sqrt{5 \times 6}$ is an irrational number lying between $\sqrt{5}$ and $\sqrt{6}$.Hence, option (c) is correct.

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MCQ 601 Mark

An irrational number between 2 and 2.5 is