Ecdysone is produced by

Let $a = \min \{x^2 + 2x + 3, x \in R\}$ and $b = \lim_{x \to 0} \frac{\sin x \cos x}{e^x - e^{-x}}$. Then the value of $\sum_{r=0}^n a^r b^{n-r}$ is

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

Identify the incorrect statement among the following.

If $\sqrt{\frac{y}{x}}+\sqrt{\frac{x}{y}}=2$,then $\frac{d y}{d x}$ is equal to

An optical fibre communication system works on a wavelength of $1.3 \mu m$. The number of subscribers it can feed if a channel requires $20 \text{ kHz}$ is: