Evaluate $\frac{0.53 \times 0.53 - 2 \times 0.53 \times 0.41 + 0.41 \times 0.41}{0.53 - 0.41}$

$\frac{0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02}{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}$ is equal to

Choose the incorrect relation$(s)$ from the following:
$(i)$ $\sqrt{6}+\sqrt{2}=\sqrt{5}+\sqrt{3}$
$(ii)$ $\sqrt{6}+\sqrt{2}<\sqrt{5}+\sqrt{3}$
$(iii)$ $\sqrt{6}+\sqrt{2}>\sqrt{5}+\sqrt{3}$

Which value among $3^{200}, 2^{300}$ and $7^{100}$ is the largest?

If $2 = x + \frac{1}{1 + \frac{1}{3 + \frac{1}{4}}}$,then the value of $x$ is

When $\frac{1}{4}$ of a number is subtracted from $\frac{1}{3}$ of the same number,the remainder obtained is $12$. The number is: