Welcome & Pre-Test | Mathematics | Welcome Test on previous knowledge | Chapter – Real Numbers

Ans. (b) $x y^2$

Explanation: Given,

and

$$

\begin{aligned}

& a=x^3 y^2 \\

& b=x y^3

\end{aligned}

$$

$$

\begin{aligned}

a \times b & =x^3 y^2 \times x y^3 \\

& =x^4 y^5

\end{aligned}

$$

$\operatorname{LCM}(a, b)=x^3 y^3$

$\therefore \quad \frac{a \cdot b}{\operatorname{LCM}(a, b)}=\frac{x^4 y^5}{x^3 y^3}=x y^2$

Concept Applied

LCM is the product of greatest power of each prime factor of the given number.

Ans. (b) irrational number

Explanation: As $\sqrt{5}$ is irrational, so $2+\sqrt{5}$ is irrational and hence $\frac{2+\sqrt{5}}{3}$ is an irrational number.

Ans. (a) 45 minutes

Explanation: Given $\operatorname{HCF}(30, p)=15$

$\therefore$ We need to use the concept of LCM

LCM $\times$ HCF $=$ First number $\times$ second number

$$

\begin{aligned}

\Rightarrow \quad 90 \times 15 & =30 \times p \\

\Rightarrow \quad p & =\frac{90 \times 15}{30} \\

& =3 \times 15 \\

& =45

\end{aligned}

$$

Hence, the car B completes 1 round of the track in 45 minutes.

Ans. (b) $2: 1$

Explanation: Least composite number $=4=2^2$ and Least prime number = 2

$$

\therefore \quad \operatorname{HCF}(4,2)=2

$$

and $\quad \operatorname{LCM}(4,2)=4$

$$

\therefore \quad \frac{\operatorname{LCM}(4,2)}{\operatorname{HCF}(4,2)}=\frac{4}{2}=\frac{2}{1}

$$

Ans. (a) 1650

Explanation:

$$

\begin{aligned}

& \operatorname{HCF}(2520,6600) & =40 \\

& \operatorname{LCM}(2520,6600) & =252 \times k \\

& \therefore \quad H C F \times L C M & =\text { Product of two numbers } \\

& \Rightarrow \quad 40 \times 252 \times k & =2520 \times 6600 \\

& \Rightarrow \quad k & =\frac{2520 \times 6600}{40 \times 252} \\

& \Rightarrow \quad k & =1650

\end{aligned}

$$

Concept Applied

- $H C F \times L C M=$ Product of two numbers