Examine whether the following equation is quadratic or not: $x+\frac{1}{x}=x^{2} (x \neq 0)$

Examine whether the following equation is quadratic or not: $(3x + 1)(3x + 2) = (9x - 1)(x + 1)$

At $t$ minutes past $2\, pm$, the time needed by the minute hand of a clock to show $3\, pm$ was found to be $3\, minutes$ less than $\frac{t^{2}}{4}$ $minutes$. Find $t$.

If the radius of a sphere is doubled,its volume becomes $\ldots \ldots \ldots \ldots$ times the original volume.

$A$ two-digit number is such that the product of its digits is $10$. When $27$ is added to the original number,the new number obtained is the same as the number obtained by interchanging the digits of the original number. Determine the number.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $\sqrt{2} x^{2}+7 x+5 \sqrt{2}=0, x=-\sqrt{2}$