For any integral value of $n$,$3^{2n} + 9n + 5$ when divided by $3$ leaves the remainder:

$A$ number when divided by $357$ gives a remainder $37.$ By dividing the same number by $17,$ the remainder would be

$\left[(72)^{2} \div 36+(?)^{2}\right] \div 5=45$

Three-fourths of one-fifth of a number is $60$. The number is:

$A$ fraction becomes $4$ when $1$ is added to both the numerator and denominator; and it becomes $7$ when $1$ is subtracted from both the numerator and denominator. The numerator of the given fraction is

$(2+\sqrt{5})^{2}=?+4 \sqrt{5}$