MCQ Questions for Class 10 Maths Real Numbers Quiz 6

Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.
$$\dfrac { 13 }{ 3125 } $$

0%
$$3$$
0%
$$4$$
0%
$$5$$
0%
$$6$$

If HCF of numbers $$408$$ and $$1032$$ can be expressed in the form of $$1032x -408 \times 5$$, then find the value of $$x$$.

0%
$$0$$
0%
$$1$$
0%
$$2$$
0%
$$3$$

Find the $$HCF$$ of integer pairs $$963$$ & $$654$$.

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$$3$$
0%
$$5$$
0%
$$9$$
0%
$$1$$

State whether the given statement is true/false:

$$\sqrt{p} + \sqrt{q}$$, is irrational, where p,q are primes.

0%
True
0%
False

GCF of $$99$$ and $$100$$ is __________

0%
$$1$$
0%
$$2$$
0%
$$3$$
0%
$$4$$

State true or false.

$$\dfrac{6}{{200}}$$ has non terminating repeating decimal expansion.

0%
True
0%
False

State whether given statement is true or false:

$$3\sqrt{2}$$ is a rational number.

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True
0%
False

Which of the following numbers are irrational numbers?

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$$2- \sqrt 5$$
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$$\left( {3 + \sqrt {23} } \right) - \left( {\sqrt {23} } \right)$$
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$$\frac{1}{\sqrt 2}$$
0%
$$2\pi $$

State whether the following statement is true or false.

The following number is irrational

$$\dfrac {1}{\sqrt {2}}$$

0%
True
0%
False

$$5-2\sqrt {3}$$ is irrational.

0%
True
0%
False

State whether the following statement is true or false.

The following number is irrational
$$6+\sqrt {2}$$

0%
True
0%
False

The decimal expansion of the rational number $$\dfrac{43}{2^4\times 5^3}$$ will terminate after:

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$$3$$
0%
$$4$$
0%
$$2$$
0%
$$1$$

Each of the following numbers is irrational
i) $$(5 + 3\sqrt{2})$$
ii) $$3 \sqrt{7}$$
iii) $$\dfrac{3}{\sqrt{5}}$$
iv) $$(2 - 3\sqrt{5})$$
v) $$(\sqrt{3} + \sqrt{5})$$

0%
True
0%
False

State whether the following statement is true or false.

The following number is irrational
$$7\sqrt {5}$$

0%
True
0%
False

Given that $$\sqrt {3}$$ is irrational. Then " $$2 + \sqrt {3}$$ is irrational. "is true/false

0%
True
0%
False

$$\sqrt{3}-\sqrt{5}$$ is an rational number.

0%
True
0%
False

A rectangular veranda is of dimension $$18$$ m $$72$$ cm $$\times 13$$ m $$20$$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.

0%
$$4290$$
0%
$$4540$$
0%
$$4620$$
0%
$$4230$$

State true or false.

$$\sqrt { 3 } + \sqrt { 4 }$$ is an rational number.

0%
True
0%
False

$$n^2 -1$$ is divisible by $$8$$ , if n is

0%
an integer
0%
a natural number
0%
an odd integer
0%
an even integer

$$\dfrac { 317 } { 3125 }$$ represents ______.

0%
A terminating decimal
0%
A non-recurring decimal
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A recurring decimal
0%
An Integer

State whether the following statement is true or not:

$$7-\sqrt { 2 } $$ is irrational.

0%
True
0%
False

The HCF of $$420$$ and $$130$$ is

0%
$$10$$
0%
$$15$$
0%
$$5$$
0%
$$3$$

$$\sqrt{2}$$ is a rational number.

0%
True
0%
False

Find the H.C.F. of :

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$$8$$ and $$40$$
0%
$$15$$ and $$25$$
0%
$$16$$ and $$60$$
0%
$$14$$ and $$35$$
0%
$$15,$$ $$25$$ and $$60$$
0%
$$16,$$ $$48$$ and $$80$$

Explanation

$${\textbf{Step - 1: Solving A}}$$

$${\text{Prime factorizing 8 and 40,}}$$

$$ \Rightarrow {\text{ 8 = 2 }} \times {\text{ 2 }} \times {\text{ 2}}$$

$$ \Rightarrow {\text{ 40 = 2 }} \times {\text{ 2 }} \times {\text{ 2 }} \times {\text{ 5}}$$

$${\text{Multiplying common prime factors to get HCF, }}$$

$${\text{H}}{\text{.C}}{\text{.F = 2 }} \times {\text{ 2 }} \times {\text{ 2 = 8}}$$

$${\textbf{Step - 2: Solving B}}$$

$${\text{Prime factorizing 15 and 25,}}$$

$$ \Rightarrow {\text{ 15 = 3 }} \times {\text{ 5}}$$

$$ \Rightarrow {\text{ 25 = 5 }} \times {\text{ 5}}$$

$${\text{Multiplying common prime factors to get HCF, }}$$

$${\text{H}}{\text{.C}}{\text{.F = 5}}$$

$${\textbf{Step - 3: Solving C}}$$

$${\text{Prime factorizing 16 and 60,}}$$

$$ \Rightarrow {\text{ 16 = 2 }} \times {\text{ 2 }} \times {\text{ 2 }} \times {\text{ 2}}$$

$$ \Rightarrow {\text{ 60 = 2 }} \times {\text{ 2 }} \times {\text{ 3 }} \times {\text{ 5}}$$

$${\text{Multiplying common prime factors to get HCF, }}$$

$${\text{H}}{\text{.C}}{\text{.F = 2 }} \times {\text{ 2 = 4}}$$

$${\textbf{Step - 4: Solving D}}$$

$${\text{Prime factorizing 14 and 35,}}$$

$$ \Rightarrow {\text{ 14 = 2 }} \times {\text{ 7}}$$

$$ \Rightarrow {\text{ 35 = 5 }} \times {\text{ 7}}$$

$${\text{Multiplying common prime factors to get HCF, }}$$

$${\text{H}}{\text{.C}}{\text{.F = 7}}$$

$${\textbf{Step - 5: Solving E}}$$

$${\text{Prime factorizing 15, 25 and 60,}}$$

$$ \Rightarrow {\text{ 15 = 3 }} \times {\text{ 5}}$$

$$ \Rightarrow {\text{ 25 = }}5{\text{ }} \times {\text{ 5}}$$

$$ \Rightarrow {\text{ 60 = 2 }} \times {\text{ 2 }} \times {\text{ 3 }} \times {\text{ 5}}$$

$${\text{Multiplying common prime factors to get HCF, }}$$

$${\text{H}}{\text{.C}}{\text{.F = }}5$$

$${\textbf{Step - 6: Solving F}}$$

$${\text{Prime factorizing 16, 48 and 80,}}$$

$$ \Rightarrow {\text{ 16 = 2 }} \times {\text{ 2 }} \times {\text{ 2 }} \times {\text{ 2}}$$

$$ \Rightarrow {\text{ 48 = 2 }} \times {\text{ 2 }} \times {\text{ 2 }} \times {\text{ 2 }} \times {\text{ 3}}$$

$$ \Rightarrow {\text{ 80 = 2 }} \times {\text{ 2 }} \times {\text{ 2 }} \times {\text{ 2 }} \times {\text{ 5}}$$

$${\text{Multiplying common prime factors to get HCF, }}$$

$${\text{H}}{\text{.C}}{\text{.F = 2 }} \times {\text{ 2 }} \times {\text{ 2 }} \times {\text{ 2 = 16}}$$

$${\textbf{Hence, we have found H.C.F of different pair of numbers using prime factorization method}}$$

Mark the correct alternative of the following.
The HCF of $$100$$ and $$101$$ is _________.

0%
$$1$$
0%
$$7$$
0%
$$37$$
0%
None of these

State whether the given statement is true or false.
$$\pi$$ is irrational and $$\dfrac{22}{7}$$ is rational.

0%
True
0%
False

The HCF of 144 and 198 is

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$$9$$
0%
$$12$$
0%
$$6$$
0%
$$18$$

The HCF of $$144, 180$$ and $$192$$ is

0%
$$12$$
0%
$$16$$
0%
$$18$$
0%
$$8$$

H.C.F of two or more number may be one of the numbers.

0%
True
0%
False

State whether the following statement is true of false? Justify your answer.
$$\dfrac {\sqrt {2}}{3}$$ is a rational number.

0%
True
0%
False

CBSE Questions for Class 10 Maths Real Numbers Quiz 6 - MCQExams.com

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Practice Class 10 Maths Quiz Questions and Answers

CBSE Questions for Class 10 Maths Real Numbers Quiz 6 - MCQExams.com

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Practice Class 10 Maths Quiz Questions and Answers

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