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# Test: Real Numbers (Medium)

## 20 Questions MCQ Test | Test: Real Numbers (Medium)

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This mock test of Test: Real Numbers (Medium) for Class 10 helps you for every Class 10 entrance exam. This contains 20 Multiple Choice Questions for Class 10 Test: Real Numbers (Medium) (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Real Numbers (Medium) quiz give you a good mix of easy questions and tough questions. Class 10 students definitely take this Test: Real Numbers (Medium) exercise for a better result in the exam. You can find other Test: Real Numbers (Medium) extra questions, long questions & short questions for Class 10 on EduRev as well by searching above.
QUESTION: 1

### Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Solution: Denominator is 8, so the rational has a non-terminating decimal expansion
QUESTION: 2

### Find the HCF of the following numbers: 18, 60.

Solution: 18, 60

18 = 1, 2, 3, 6, 9, 18

60 = 1, 2, 3, 4, 6, 10, 12, 15, 30, 60

Common factors = 1, 2, 3, 6

∴ H.C.F.of 18 & 60 is 6

QUESTION: 3

### Find the HCF and LCM of the following integers by applying the prime factorization method 40, 36 and 126.

Solution: 40 = 2 x 2 x 2 x 5 = 23 x 5

36 = 2 x 2 x 3 x 3 = 22 x 32

and 126 = 2 x 3 x 3 x 7 = 2 x 32 x 7

For H.C.F taking minimum power of common factor H.C.F = (2)1 = 2

For L.C.M, taking maximum power of prime factors LC.M = 23 x 32 x 5 x 7 = 8 x 9 x 5 x 7 = 2520

Hence, H.C.F = 2 L.C.M = 2520

QUESTION: 4

Find the HCF by prime factorization 45 and 75.

Solution: HCF of two numbers are

45 = 3 × 3 × 5

75 = 3 × 5 × 5

The common factors make the HCF: HCF = 3 × 5 = 15

QUESTION: 5

Find the H.C.F. of the following numbers using the prime factorization method: 84, 120, 138.

Solution: 84 = 22 × 3 × 7

120 = 23 × 3 × 5

138 = 2 × 3 × 23

HCF = product of common terms with lowest power

HCF = 2 × 3 = 6

QUESTION: 6

Check whether 6 / 200 has terminating or non terminating repeating decimal expansion.

Solution: 6 / 200 = 3 / 100 = 0.03 which is terminating decimal.
QUESTION: 7

Find the H.C.F of the following numbers by Prime Factorization: 120, 240, 300

Solution: 240 = 24 x 3 x 5

300 = 22 x 3 x 52

120 = 23 x 3 x 5

H.C.F = 22 x 3 x 5

Highest Common Factor is : 60

QUESTION: 8

Find the H.C.F. of the following numbers using the prime factorization method: 225, 450.

Solution: We have, 225 = 32 × 52

450 = 2 × 32 × 52

HCF(225, 450) = Product of common terms with lowest power HCF(225, 450) = 32 × 52 HCF(225, 450) = 9 × 25

HCF(225, 450) = 225

∴ The required number or HCF is 225.

QUESTION: 9

If HCF of 336 and 54 is 6, then LCM is:

Explanations: According to Euclid division algorithm

LCM => HCF x LCM = product if two no. 6 x LCM = 54 x 336

LCM = 54 x 336 / 6

LCM = 3024

Solution:
QUESTION: 10

Prime factors of 4050 is:

Solution: Thus, these are the numbers that make up the prime factorization of 4050,

So the prime factorization of 4050 is 2 × 3 × 3 × 3 × 3 × 5 × 5.

QUESTION: 11

The LCM of three numbers 28, 44, 132 is:

Solution: Prime factors of 28 = 22 x 7

Prime factors of 44 = 22 x 11

Prime factors of 132 = 22 x 3 x 11

LCM = 22 x 71 x 111 x 31 = 924

QUESTION: 12

If p2 is an even integer, them p is an:

Solution: "Even" and "odd" are properties of integers, not of arbitrary real numbers. The correct statement is "if p is an integer and p2 is even, then p is even."
QUESTION: 13

Every composite number can be expressed as a product of:

Solution: This is true as any composite number can be expressed in terms of its prime factors. The prime factors for 2 numbers can be the same but their combination is unique.

Example: 12 = 22 x 3 and 18 = 2 x 32

Both have prime factors as 2 and 3 but the combination that 12 has is different from that of 18.

QUESTION: 14

The decimal expansion of a rational number is always:

Solution: The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number.
QUESTION: 15

The largest number which divides 445, 572 and 699 leaving remainder 4, 5 and 6 respectively is :

Solution: 445 - 4 = 441

572 - 5 = 567

699 - 6 = 693

Now find the greatest common factor of those 3 numbers:

441 = 3 x 3 x 7 x 7

572 = 3 x 3 x 3 x 3 x 7

693 = 3 x 3 x 7 x 11

The common factors are 3 x 3 x 7 = 63

HCF Of (441, 567, 693) = 63

445 / 63 = 7 remainder 4

572 / 63 = 9 remainder 5

699 / 63 = 11 remainder 6

∴ 63 is the largest divisor that will give the desired remainders.

QUESTION: 16

The product of a non-zero rational and irrational number is:

Solution: Product of a non-zero rational number and an irrational number is always irrational.
QUESTION: 17

The HCF of the smallest composite number and the smallest prime number is:

Solution: HCF of the smallest composite number and the smallest prime number = 2

Smallest composite number = 4 = 2 × 2

Smallest prime number = 2

QUESTION: 18

If HCF (306, 657) = 9, then LCM (306, 657) is;

Solution: Given that HCF = 9 and the numbers are 306 and 657.

LCM = ?

We know that LCM × HCF = product of two numbers

⇒ LCM × 9 = 306 × 657

⇒ LCM = 201042 / 9 = 22338

QUESTION: 19

Write the exponent of 2 in the prime factorisation of 288.

Solution: 288 = 2 × 2 × 2 × 2 × 2 × 3 × 3

⇒ 25 × 3²

Hence, The exponent of 2 is 5 and exponent of 3 is 2.

QUESTION: 20

What is the sum of exponents of prime factors in the prime factorisation of 98.

Solution: 98 = 2 × 7 × 7 = 21 × 72

Sum of exponents = 1 + 2 = 3