Class 10 Practice - Level 2 - Set 1 - Real Numbers

Total questions: 25

If the HCF of two numbers is 1, what can be said about their realtion?

Topic: Euclid's Division Lemma

They are prime numbers.

They are co-prime number.

They are even numbers.

they are odd numbers.

None

The product of two consecutive positive integers is always:

Topic: Fundamental Theorem of Arithmetic

Even

Odd

Prime

Composite

None

Which of the following is a terminating decimal?

Topic: Properties of Rational Numbers

$ \displaystyle \frac{7}{{20}}$

$ \displaystyle \frac{1}{{3}}$

$ \displaystyle \frac{4}{{11}}$

$ \displaystyle \frac{2}{{7}}$

None

If the remainder is 0 in Euclid's Division Lemma, what can be inferred about the two numbers involved?

Topic: Euclid's Division Lemma

They are co- prime

They are equal

The first number is a multiple of the second.

The second number is a multiple of the first

None

The sum of squares of any two consecutive odd number is always divisible by:

Topic: Fundamental Theorem of Arithmetic

None

The difference between a rational number and an irrational number is :

Topic: Properties of Irrational Numbers

Always rational

Always irrational

Sometimes rational

Sometimes irrational

None

If $ \displaystyle a=bq+r(where0\le \text{ }r

Topic: Euclid's Division Lemma

a is a factor of b.

bis a factor of a.

b is multiple of a.

a is multiple of b.

None

If the product of two numbers is 6 and their sum is $ \displaystyle \sqrt{{20}}$ , then these two numbers must be:

Topic: Rational and Irrational Numbers

Rational

Irrational

One rational and one irrational

Prime

None

Which of the following is a correct prime factorization of 450?

Topic: Fundamental Theorem of Arithmetic

$ \displaystyle {{2}^{2}}\times {{3}^{2}}\times 5$

$ \displaystyle 2\times {{3}^{2}}\times {{5}^{2}}$

$ \displaystyle 2\times {{3}^{3}}\times 5$

$ \displaystyle 2\times {{3}^{4}}\times {{5}^{2}}$

None

10.

The HCF of two numbers is the smallest number that can be expressed as a linear combination of the two numbers. If the numbers are 18 and 30 then what is the HCF ?

Topic: Euclid's Division Lemma

None

11.

Which of the following fractions has a terminating decimal representation ?

Topic: Properties of Rational Numbers

$ \displaystyle \frac{5}{{12}}$

$ \displaystyle \frac{7}{{25}}$

$ \displaystyle \frac{8}{{15}}$

$ \displaystyle \frac{3}{{13}}$

None

12.

The LCM of two numbers is 180 and their HCF is 6 . if one of the numbers is 30 , what is the other numbers?

Topic: Fundamental Theorem of Arithmetic

None

13.

Which of the following sums is irrational?

Topic: Properties of Irrational Numbers

$ \displaystyle 1+\sqrt{3}$

$ \displaystyle \sqrt{2}+\sqrt{2}$

$ \displaystyle 2+\sqrt{4}$

$ \displaystyle 5+\sqrt{9}$

None

14.

If two numbers are a and b, and the HCF of a and b is d, what is the HCF of a/d and b/d?

Topic: Euclid's Division Lemma

$ \displaystyle \frac{a}{d}$

$ \displaystyle \frac{b}{d}$

None

15.

The smallest number that can be expressed as the sum of two cubes in the different ways is :

Topic: Fundamental Theorem of Arithmetic

1729

729

None

16.

Which of the following decimal expansion represents a rational number?

Topic: Properties of Rational Numbers

0.01001000100001.....

1.414213...

2.71828...

0.232323...

None

17.

If the HCF of two numbers is 1 and their product is 221, what can be said about the numbers?

Topic: Euclid's Division Lemma

They are both prime.

One is prime , the other composite.

They are co- prime .

Their sum is 221.

None

18.

The prime factorization of 126 is ;

Topic: Fundamental Theorem of Arithmetic

$ \displaystyle {{2}^{1}}\times {{3}^{2}}\times 7$

$ \displaystyle 2\times 9\times 7$

$ \displaystyle {{2}^{1}}\times {{3}^{3}}\times 7$

$ \displaystyle {{2}^{2}}\times {{3}^{1}}\times 7$

None

19.

Which of the following numbers is an irrational number?

Topic: Rational and Irrational Numbers

$ \displaystyle \sqrt{{16}}$

$ \displaystyle \frac{2}{3}$

$ \displaystyle \sqrt{{20}}$

0.75

None

20.

The remainder when 58 is divided by 7 is :

Topic: Euclid's Division Lemma

None

21.

Which of the following numbers is a rational number?

Topic: Properties of Rational Numbers

$ \displaystyle \sqrt{3}$

$\displaystyle \frac{7}{8}$

$ \displaystyle \sqrt{5}$

3.14159

None

22.

The smallest prime number is :

Topic: Fundamental Theorem of Arithmetic

None

23.

If the quotient obtained on dividing a number by 11 is 5 and the remainder is 4, then the number is :

Topic: Euclid's Division Lemma

None

24.

Which of the following is the squares root of a non- perfect square?

Topic: Properties of Irrational Numbers

$ \displaystyle \sqrt{4}$

$ \displaystyle \sqrt{9}$

$ \displaystyle \sqrt{{15}}$

$ \displaystyle \sqrt{{16}}$

None

25.

Which of the following is a prime factor of 210?

Topic: Fundamental Theorem of Arithmetic

None

1 out of 25

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Class 10 Practice - Level 2 - Set 1 - Real Numbers

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