If the amplitude of $z-2-3i$ is $\frac{\pi}{4}$,then the locus of $z=x+iy$ is:

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 hybridisation of $Xe$ and the number of lone pairs of electrons on it in $XeF_6$ are

The value of $\tan \left[\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right]$ is

The products formed when diethyl ether is reacted with cold $HI$ are

An electric motor operating on a $60\,V$ $dc$ supply draws a current of $10\,A$. If the efficiency of the motor is $50\%$,the resistance of its winding is....$\Omega$