If a ladder weighing $250 \ N$ is placed against a smooth vertical wall and the coefficient of friction between the ladder and the floor is $0.3$,what is the maximum force of friction available at the point of contact between the ladder and the floor?

The minimum value of $27 \tan ^2 \theta + 3 \cot ^2 \theta$ is

$A$ spherical surface of radius of curvature $R$ separates air (refractive index $1.0$) from glass (refractive index $1.5$). The centre of curvature is in the glass. $A$ point object $P$ placed in air is found to have a real image $Q$ in the glass. The line $PQ$ cuts the surface at the point $O$,and $PO = OQ$. The distance $PO$ is equal to: (in $,R$)

If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3,4,5\}$ and $B=\{1,2,3,4\}$ respectively, then the probability that the equation $x^2+ax+b=0$ has real roots is

The diode used in the circuit shown in the figure has a constant voltage drop of $0.5 \, V$ at all currents and a maximum power rating of $100 \, mW$. What should be the value of the resistor $R$,connected in series with the diode,to obtain the maximum current?

Which compound is soluble in $NH_4OH$?