The utility of a microorganism like $Trichoderma$ $harzianum$ has been proven in which of the following?

If the equation $12x^2 + 7xy - py^2 - 18x + qy + 6 = 0$ represents a pair of perpendicular straight lines,then

One junction of a certain thermoelectric couple is at a fixed temperature $T_r$ and the other junction is at temperature $T$. The thermo-electromotive force for this is expressed by $E=k(T-T_r)[T_0-\frac{1}{2}(T+T_r)]$. At temperature $T=\frac{1}{2} T_0$,the thermoelectric power is

$A$ sound source is moving towards a stationary observer with $1/10$ of the speed of sound. The ratio of apparent to real frequency is

Two uniform rods of equal length but different masses are rigidly joined to form an $L$-shaped body,which is then pivoted as shown. If in equilibrium the body is in the shown configuration,the ratio $M/m$ will be:

In the adjacent circuit,a voltmeter of internal resistance $R$,when connected across $B$ and $C$,reads $\frac{100}{3} \text{ V}$. Neglecting the internal resistance of the battery,the value of $R$ is