For the following questions answer them individually
A mass-spring system is used to model the vibrations of a building during an earthquake. How can the natural frequency of the system be tuned to reduce the risk of resonance with earthquake frequencies?
If a Si wafer with an intrinsic carrier concentration of $$10^{10} cm^{-3}$$ is doped with $$5 \times 10^{15} cm^{-3}$$ Phosphorus(P) and $$10^{16} cm^{-3}$$ Boron(B) at room temperature (300 K), then what is the doping in the resultant silicon?
An AC circuit consists of a resistor (R), a capacitor (C). and an inductor (L) in series. What is the power factor of this circuit?
Arrange the following differential equations in ascending order in accordance to degree
A. $$\left[1 + \left(\frac{dy}{dx}\right)^{2}\right]^{\frac{3}{2}} = \frac{d^{2}y}{dx^{2}}$$
B. $$\left(\frac{dy}{dx}\right)^{5} + y = 0$$
C. $$ \frac{d^{2}y}{dx^{3}} + a^{2}x = 0$$
D. $$ x^{2} \left(\frac{d^{3}y}{dx^{2}}\right)^{3} +y\left(\frac{dy}{dx} \right)^{4}+ y^{4} = 0$$
Choose the correct answer from the options given below:
If $$J = \frac{\partial{(u, v)}}{\partial(x, y)}$$ and $$J' = \frac{\partial{(x, y)}}{\partial(u, v)}$$, then JJ' is equal to
Arrange the following ferromagnetic materials in Ascending order of Curie temperatures:
(A). Cobalt
(B). Gadolinium
(C). Iron
(D). Nickel
Choose the correct answer from the options given below: