Find the binomial probability distribution whose mean is $3$ and variance is $2$.

The primary and secondary coils of a transformer have $50$ and $1500$ turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi = \phi_0 + 4t$,where $\phi$ is in webers,$t$ is time in seconds and $\phi_0$ is a constant,the output voltage across the secondary coil is.....$volts$.

The incentre of the triangle with vertices $A(1, \sqrt{3})$,$B(0,0)$,and $C(2,0)$ is

$A$ capacitor is charged by using a battery,which is then disconnected. $A$ dielectric slab is then inserted between the plates. What is the result?

There are $n$ distinct points on the circumference of a circle. The number of pentagons that can be formed with these points as vertices is equal to the number of possible triangles. Then the value of $n$ is

$20 \text{ mL}$ of $0.1 \text{ M}$ acetic acid is mixed with $50 \text{ mL}$ of potassium acetate. $K_a$ of acetic acid $= 1.8 \times 10^{-5}$ at $27^\circ \text{C}$. Calculate the concentration of potassium acetate if the $pH$ of the mixture is $4.8$. (in $\text{ M}$)