In a series $LCR$ circuit,$R=300 \Omega, L=0.9 \text{ H}, C=2.0 \mu\text{F}$ and $\omega=1000 \text{ rad/s}$,then the impedance of the circuit is: (in $\Omega$)

Two electric charges of $9 \mu C$ and $-3 \mu C$ are placed $0.16 \ m$ apart in air. There will be a point $P$ on the line joining the two charges and in between them where the electric potential is zero. The distance of $P$ from the $9 \mu C$ charge is (in $m$)

Among the electrolytes $Na_2SO_4, CaCl_2, Al_2(SO_4)_3$ and $NH_4Cl,$ the most effective coagulating agent for $Sb_2S_3$ sol is

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius $\left(\frac{r}{3}\right)$ and the lighter one in a radius $r$. The tangential speed of the lighter stone is '$n$' times the value of the heavier stone. When the magnitude of the centripetal force becomes equal,the value of $n$ is:

If $x, y, z$ are all positive and are the $p$-th,$q$-th and $r$-th terms of a geometric progression respectively,then the value of the determinant $\left|\begin{array}{lll} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{array}\right|$ equals

The vapour pressure of water at $23^{\circ} C$ is $19.8 \ mm$. $0.1 \ mole$ of glucose is dissolved in $178.2 \ g$ of water. What is the vapour pressure (in $mm$) of the resultant solution?