$A$ transistor is used as a common emitter amplifier with a load resistance of $2 \ k\Omega$. The input resistance is $150 \ \Omega$. Base current is changed by $20 \ \mu A$,which results in a change in collector current by $1.5 \ mA$. The voltage gain of the amplifier is

Product $(X)$ is

$1.00 \ g$ of a non-electrolyte solute (molar mass $250 \ g \ mol^{-1}$) is dissolved in $51.2 \ g$ of benzene. If the freezing point depression constant of benzene is $5.12 \ K \ kg \ mol^{-1}$,then the freezing point of benzene decreases by ...... $K$.

Water from a tap emerges vertically downwards with initial velocity $4 ~m/s$. The cross-sectional area of the tap is $A$. The flow is steady and pressure is constant throughout the stream of water. The distance $h$ vertically below the tap, where the cross-sectional area of the stream becomes $\frac{2}{3} A$, is $(g=10 ~m/s^2)$ (in $~m$)

The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is:

Let $P(6, 3)$ be a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If the normal at point $P$ intersects the $x$-axis at $(9, 0)$,then the eccentricity of the hyperbola is: