Answer: $180a^3{b}^4$.

Solution: $18=2\times 3^2$ and $20=2^2\times 5$. Taking the greatest power of every prime factor gives $\mathrm{LCM}(p,q)=2^2\times 3^2\times 5\times a^3\times b^4=180a^3{b}^4$.

Source: Official CBSE Class X Mathematics Standard 2024 paper, Q.P. Code 30/1/1, Section A, Question 5.

Answer: $98$ (Option C).

Solution: $\mathrm{HCF}(98,28)=14$ and $\mathrm{LCM}(98,28)=\frac{98\times 28}{14}=196$. Therefore, $n-7m=196-7(14)=98$.

Source: Official CBSE Class X Mathematics Standard 2024 paper, Q.P. Code 30/1/1, Section A, Question 6.

Answer: $1.857142$ (Option D).

Solution: Since $\sqrt{3}\approx 1.732$ and $\sqrt{5}\approx 2.236$, the number $1.857142$ lies between them and is rational because it is a terminating decimal.

Source: Official CBSE Class X Mathematics Standard 2024 paper, Q.P. Code 30/1/1, Section A, Question 14.