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

Two parallel rails of a railway track, insulated from each other and from the ground, are connected to a millivoltmeter. The distance between the rails is $1 \, m$. $A$ train is travelling with a velocity of $72 \, km/h$ along the track. What is the reading of the millivoltmeter (in $mV$)? (The vertical component of the Earth's magnetic field is $2 \times 10^{-5} \, T$.)

For all real $x$,the minimum value of the function $f(x)=\frac{1-x+x^2}{1+x+x^2}$ is

If the decimal $0.d25d25d25\ldots$ is expressible in the form $n/27$,then $d+n$ must be

For a gas,$\frac{R}{C_{v}}=0.4$,where $R$ is the universal gas constant and $C_{v}$ is the molar specific heat at constant volume. The gas is made up of molecules which are

Which one of the following statements is not correct?