Class 10 Practice – Level 2 – Set 2 – Real Numbers

Total questions: 25

Find the smallest number that, when divided by 6, 8, and 12, leaves a remainder of 2 in each case.

Topic: Fundamental Theorem of Arithmetic

None

If $ \displaystyle a=4q+3\text{ and }b=6p+4,$ Find the HCF of $ \displaystyle a$ and $ \displaystyle b$.

Topic: Euclid's Division Lemma

None

Which of the following sums is rational?

Topic: Properties of Irrational Numbers

$ \displaystyle \sqrt{2}+\sqrt{8}$

$ \displaystyle \sqrt{3}+\sqrt{{12}}$

$ \displaystyle \sqrt{7}+\sqrt{7}$

$ \displaystyle \sqrt{5}+\sqrt{{10}}$

None

How many prime factors are there in the prime factorization of 1800?

Topic: Fundamental Theorem of Arithmetic

None

If the HCF of two numbers $ \displaystyle x\text{ and }y$ is 9 and $ \displaystyle xy=2079,$ find the LCM of $ \displaystyle x\text{ and }y$.

Topic: Euclid's Division Lemma

207

231

243

230

None

Which of the following expressions results in an irrational number?

Topic: Properties of Irrational Numbers

$ \displaystyle \sqrt{2}+\sqrt{8}$

$ \displaystyle 2\sqrt{3}+3\sqrt{3}$

$ \displaystyle \sqrt{7}+3\sqrt{7}$

$ \displaystyle 5\sqrt{5}+\sqrt{5}$

None

Determine the smallest number divisible by 10, 12, and 15.

Topic: Fundamental Theorem of Arithmetic

120

180

360

None

If two numbers are in the ratio 3:4 and their HCF is 6, what is the product of these two numbers?

Topic: Euclid's Division Lemma

144

288

216

432

None

The difference between $ \displaystyle \sqrt{{18}}\text{ and }\sqrt{8}$ is:

Topic: Properties of Irrational Numbers

Rational

Irrational

Whole number

Even number

None

10.

If $ \displaystyle a\text{ and }b$ are positive integers such that $ \displaystyle a={{2}^{3}}\times 3\times {{5}^{2}}\text{ and }b={{\text{2}}^{2}}\times {{3}^{2}}\times 5,\text{ then find the HCF of }a\text{ and }b\text{.}$

Topic: Fundamental Theorem of Arithmetic

120

180

None

11.

The remainder when 2496 is divided by 33 is:

Topic: Euclid's Division Lemma

None

12.

If the decimal representation of $ \displaystyle \frac{7}{{125}}$ is terminated after three decimal places, what is the resulting number ?

Topic: Properties of Rational Numbers

0.056

0.058

0.054

0.064

None

13.

The smallest positive integer $ \displaystyle x$ such that $ \displaystyle 90x$ is a perfect square is:

Topic: Fundamental Theorem of Arithmetic

None

14.

Find the quotient when the sum of 1280 and 384 is divided by their HCF.

Topic: Euclid's Division Lemma

None

15.

If $ \displaystyle \sqrt{2}$ is multiplied by $ \displaystyle 2\sqrt{2}$, what is the result?

Topic: Properties of Irrational Numbers

None

16.

The sum of the cubes of two numbers is 35. If the numbers are 1 and $ \displaystyle x$, find $ \displaystyle x$.

Topic: Fundamental Theorem of Arithmetic

None

17.

If a number $ \displaystyle x$ when divided by 17 leaves a remainder of 7, and the quotient is 15, what is the number $ \displaystyle x$?

Topic: Euclid's Division Lemma

262

245

242

272

None

18.

Which of the following expressions results in an irrational number?

Topic: Properties of Irrational Numbers

$ \displaystyle \sqrt{3}\times \sqrt{{12}}$

$ \displaystyle \sqrt{2}\times \sqrt{8}$

$ \displaystyle \sqrt{5}\times \sqrt{{20}}$

$ \displaystyle \sqrt{9}\times \sqrt{4}$

None

19.

How many divisors does 144 have?

Topic: Fundamental Theorem of Arithmetic

None

20.

If the HCF of 144 and $ \displaystyle x$ is 12 and the LCM is 288, find $ \displaystyle x$.

Topic: Euclid's Division Lemma

None

21.

If $ \displaystyle \sqrt{{50}}-\sqrt{{32}}$ is simplified, what is the result?

Topic: Properties of Irrational Numbers

Rational

Irrational

Prime

Composite

None

22.

The LCM of two numbers is 300, and their HCF is 10. If one of the numbers is 50, what is the other number?

Topic: Fundamental Theorem of Arithmetic

100

None

23.

When a number $ \displaystyle y$ is divided by 7, the quotient is 20 and the remainder is 4. what is the number $ \displaystyle y$?

Topic: Euclid's Division Lemma

144

142

145

146

None

24.

Simplify $ \displaystyle 3\sqrt{2}\times 4\sqrt{2}.$

Topic: Properties of Irrational Numbers

None

25.

If a number $ \displaystyle n$ when divided by 9 gives a quotient 8 and remainder 5, find $ \displaystyle n$.

Topic: Fundamental Theorem of Arithmetic

None

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Class 10 Practice – Level 2 – Set 2 – Real Numbers

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