Assertion (A): For any two natural numbers $a$ and $b$, the HCF of $a$ and $b$ is a factor of the LCM of $a$ and $b$. Reason (R): HCF of any two natural numbers divides both the numbers.[1 marks]

A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

C. Assertion (A) is true, but Reason (R) is false.

D. Assertion (A) is false, but Reason (R) is true.

Math Ch 1: Real Numbers PYQ

1

If $\text{HCF}(98,28)=m$ and $\text{LCM}(98,28)=n$, then the value of $n-7m$ is:

[1]

B. 28 C. 98 D. 198

2

If $(-1)^{n}+(-1)^{8}=0$, then n is:

[1]

A. any positive integer B. any negative integer C. any odd number D. any even number

3

Which of the following is a rational number between $\sqrt{3}$ and $\sqrt{5}$?

[1]

A. $1.4142387954012\dots$ B. $2.32\bar{6}$ C. $\pi$ D. $1.857142$

4

Prove that $\frac{1}{\sqrt{5}}$ is an irrational number.

[3]

5

If two positive integers p and q can be expressed as $p=18a^{2}b^{4}$ and $q=20~a^{3}b^{2}$, where a and b are prime numbers, then LCM (p, q) is :

[1 mark]

A. $2~a^{2}b^{2}$ B. $180~a^{2}b^{2}$ C. $12~a^{2}b^{2}$ D. $180~a^{3}b^{4}$

6

Prove that $5-2\sqrt{3}$ is an irrational number. It is given that $\sqrt{3}$ is an irrational number.

[2 marks]

7

Show that the number $5\times11\times17+3\times11$ is a composite number.

[2 marks]

8

In a teachers' workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively. Find the minimum number of rooms required if in each room the same number of teachers are seated and all of them are of the same subject.

[3 marks]

9

Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively.

[2 marks]

10

Prove that $ \sqrt{5} $ is an irrational number.

[3 marks]

Math Ch 1: Real Numbers PYQ | CBSE Class 10

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