$A$ sinusoidal carrier voltage of frequency $1.5 \, MHz$ and amplitude $50 \, V$ is amplitude modulated by a sinusoidal voltage of frequency $10 \, kHz$ producing $50 \% $ modulation. The lower and upper side-band frequencies in $kHz$ are:

Which one of the following pairs of food components in humans reaches the stomach totally undigested?

$A$ variable plane is at a constant distance $h$ from the origin and meets the coordinate axes in $A, B, C$. The locus of the centroid of $\triangle ABC$ is

If the angle $\theta$ between the vectors $\overrightarrow{a}=2 x^2 \hat{i}+4 x \hat{j}+\hat{k}$ and $\overrightarrow{b}=7 \hat{i}-2 \hat{j}+x \hat{k}$ is such that $90^{\circ} < \theta < 180^{\circ}$, then $x$ lies in the interval

The value of $\frac{\cot 54^\circ}{\tan 36^\circ} + \frac{\tan 20^\circ}{\cot 70^\circ}$ is

Two Carnot engines $A$ and $B$ are operated in succession. The first one,$A$,receives heat from a source at $T_1 = 800\, K$ and rejects heat to a sink at $T_2\, K$. The second engine,$B$,receives the heat rejected by the first engine and rejects heat to another sink at $T_3 = 300\, K$. If the work outputs of the two engines are equal,then the value of $T_2$ is ...... $K$.