$A$ common-emitter amplifier is designed with a $n-p-n$ transistor $(\alpha = 0.99)$. The input impedance is $1 \, k\Omega$ and the load resistance is $10 \, k\Omega$. The voltage gain will be

$\lim _{x \rightarrow \infty}\left(\frac{x+6}{x+1}\right)^{x+4}$ is equal to

Observe the following statements regarding the purification of bauxite:
$I$. During Hall's process,silica is removed as $Si$ (vapour).
$II$. Bauxite ore contaminated with $Fe_2O_3$ is purified in Baeyer's process.
$III$. During Serpeck's process,$AlN$ is formed.
The correct answer is:

If the straight lines $2x + 3y - 1 = 0$,$x + 2y - 1 = 0$ and $ax + by - 1 = 0$ form a triangle with the orthocentre at the origin,then $(a, b) =$

If the system of equations $x + 2y - 3z = 1$,$(k + 3)z = 3$,and $(2k + 1)x + z = 0$ is inconsistent,then the value of $k$ is:

The base current in a transistor circuit changes from $45 \mu A$ to $140 \mu A$. Accordingly,the collector current changes from $0.2 \text{ mA}$ to $4.0 \text{ mA}$. The current gain is