If $f(x)$ is a polynomial of degree $n$ with rational coefficients and $1+2i, 2-\sqrt{3}$ and $5$ are three roots of $f(x)=0$,then the least value of $n$ is

The statement $(p$ $\rightarrow q)$ $\rightarrow [(\sim p$ $\rightarrow q)$ $\rightarrow q]$ is

$A$ nucleus with $Z = 92$ emits the following in a sequence: $\alpha, \alpha, \beta^-, \beta^-, \alpha, \alpha, \alpha, \alpha, \beta^-, \beta^-, \alpha, \beta^-, \beta^-, \alpha$. The $Z$ of the resulting nucleus is

The differential equation of all circles which pass through the origin and whose centres lie on the $Y$-axis is

Human urine is usually acidic because

When a wave traverses a medium,the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$,where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?