If $a = \log_{24} 12$,$b = \log_{36} 24$,and $c = \log_{48} 36$,then $1 + abc$ is equal to:

The slopes of the lines represented by $x^2+2 h x y+2 y^2=0$ are in the ratio $1:2$,then $h$ is equal to:

$A$ metallic ring connected to a rod oscillates freely like a pendulum. If now a magnetic field is applied in a horizontal direction so that the pendulum now swings through the field,the pendulum will

To increase milk yield,a cow is given:

If $\cos ^{-1}\left(\frac{y}{b}\right)=2 \log \left(\frac{x}{2}\right)$, where $x>0$, then $x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}$ is equal to

The voltage of an $ac$ source varies with time according to the equation $V = 100 \sin(100 \pi t) \cos(100 \pi t)$,where $t$ is in $seconds$ and $V$ is in $volts$. Then: