$A$ radioactive nucleus (initial mass number $A$ and atomic number $Z$) emits $3$ $\alpha$-particles and $2$ positrons. The ratio of neutrons to protons in the final nucleus will be:

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

The equation of the circle passing through the point $(1,2)$ and through the points of intersection of $x^2+y^2-4x-6y-21=0$ and $3x+4y+5=0$ is given by

The variance of $20$ observations is $5$. If each observation is multiplied by $2$,then the new variance of the resulting observations is:

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \, pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $d/3$,while the other one has dielectric constant $K_2 = 6$ and thickness $2d/3$. The new capacitance of the capacitor is .... $pF$.

The decreasing order of bond dissociation energies of $C-C$,$C-H$,and $H-H$ bonds is: