$\frac{3}{48}$ is what part of $\frac{1}{12}$?

Which of the following is the $CORRECT$ rationalised form of $\frac{15}{\sqrt{5}+2} ?$

What is the value of $x$ in the equation $\sqrt{\frac{1+x}{x}}-\sqrt{\frac{x}{1+x}}=\frac{1}{\sqrt{6}} ?$

If $x>1$ and $x^{2}+\frac{1}{x^{2}}=83,$ then $x^{3}-\frac{1}{x^{3}}$ is

In an examination,a student scores $4$ marks for every correct answer and loses $1$ mark for every wrong answer. If he attempts in all $60$ questions and secures $130$ marks,the number of questions he attempts correctly is

If $5 \sqrt{5} \times 5^{3} \div 5^{-\frac{3}{2}} = 5^{a+2},$ then the value of $a$ is