In the following common emitter circuit,if $\beta = 100, V_{CE} = 7 \, V, V_{BE} = 0 \, V$ (negligible),and $R_C = 2 \, k\Omega$,then find $I_B$ in $mA$.

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19}\ {C}$ and $9.6 \times 10^{-10}\ {C}$, and masses $19.2 \times 10^{-27}\ {kg}$ and $9 \times 10^{-27}\ {kg}$ respectively. At an instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is ${P} \times 10^{-13}$, where the value of $P$ is _________ .
(Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\ {Nm}^2 {C}^{-1}$ and universal gravitational constant as $6.67 \times 10^{-11}\ {Nm}^2 {kg}^{-2}$)

Which of the following is a geocarpic fruit?

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

$A$ mass $M$ attached to a horizontal spring executes $S.H.M.$ of amplitude $A_{1}$. When the mass $M$ passes through its mean position,a smaller mass $m$ is placed over it and both of them move together with amplitude $A_{2}$. The ratio of $\left(\frac{A_{1}}{A_{2}}\right)$ is

If $A$ is a non-zero square matrix of order $n$ with $\operatorname{det}(I+A) \neq 0$ and $A^3=O$,where $I$ and $O$ are the unit and null matrices of order $n \times n$ respectively,then $(I+A)^{-1}$ is equal to