A power series in (x-2) is an infinite series of the form $$\sum\limits_{n = 0}^\infty {{c_n}} {(x - 2)^n} = {c_0} + {c_1}(x - 2) + {c_2}{(x - 2)^2} + ....$$ the number 2 is called _______.

• A) Radius of power series
• B) Center of power series
• C) none of these
• D) Base of power series

Any linear differential equation of the form $${a_{n - 1}}{x^{n - 1}}\frac{{{d^{n - 1}}y}}{{d{x^{n - 1}}}} + .... + \frac{{dy}}{{dx}} + {a_0}y = g(x)$$ where $${a_n},{a_{n - 1}},...,{a_0}$$ are constants, is said to be a ____________ equation.

• A) Homogeneous
• B) Cauchy-Euler
• C) Non homogeneous
• D) Cauchy-Euler

Auxiliary equation of the differential equation $$f{x^2}\frac{{{d^2}y}}{{d{x^2}}} + gx\frac{{dy}}{{dx}} + hy\, = \,k(x)$$ is

• A) $$fm + (g - f){m^2} + h\, = 0$$
• B) $$f{m^2} - (g - f)m + h\, = 0$$
• C) $$f{m^2} + (g - f)m + h\, = 0$$
• D) none of them

The D.E $$r\frac{{{d^2}u}}{{d{r^2}}} + 2\frac{{du}}{{dr}} = 0$$ where the variable $$r > 0$$ represents the radial distance measured ________ from the center of the sphere.

• A) outward
• B) inward
• C) center
• D) origin

Solution of the D.Equation $$4y^{//} + y = 0.$$ is

• A) $$y(x) = c_1 \cos \frac{x} {2}$$
• B) $$y(x) = c_1 \cos \frac{x} {2} + c_2 Sin\frac{x} {2}$$
• C) $$y(x) = c_1 Sin\frac{x} {2}$$
• D) None of them.

A _________ is a passive electronic component of an electronic circuit that has the ability
to store charge and opposes any change of voltage in the circuit.

• A) voltage
• B) resister
• C) inductor
• D) capacitor

The nature of the roots of the differential equation $${x^2}\frac{{{d^2}y}}{{d{x^2}}} - 2x\frac{{dy}}{{dx}} - 4y = 0$$ is __________.

• A) Real and distinct
• B) none of these
• C) Conjugate complex
• D) Real and repeated

A __________is an electrical component that limits or regulates the flow of electrical current
in an electrical circuit.

• A) voltage
• B) capacitor
• C) resistor
• D) Inductor

The flow of current is ___________ proportional to the resistance.

• A) inversely
• B) directly
• C)
• D)

Which number is known as quasi frequency?

• A) $$\frac{{\sqrt {{\omega ^2} + {\lambda ^2}} }}{{2\pi }}$$
• B) $$\frac{{\sqrt {{\omega ^2} - {\lambda ^2}} }}{{2\pi }}$$
• C) $$\frac{{2\pi }}{{\sqrt {{\omega ^2} + {\lambda ^2}} }}$$
• D) $$\frac{{2\pi }}{{\sqrt {{\omega ^2} - {\lambda ^2}} }}$$

The coefficient $$A{e^{ - \lambda t}}$$ is called the damped ________ of vibration.

• A) period
• B) frequency
• C) amplitude
• D) All of these

Consider a power series $$x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{3} - ....$$ represents _______.

• A) sin x
• B) cos x
• C) ln (1+x)
• D) e

The time interval between two successive maxima of x(t) is called ________.

• A) quasi frequency
• B) quasi period
• C)
• D)

The total forces acting on mass m are_______.

• A) 2
• B) 4
• C) 3
• D) 5

The solution of $$x\frac{{dy}}{{dx}} = 0$$ is ________.

• A) $$y = {c_1} + {c_2}{x^2}$$
• B) none of them
• C) $$y = {c_1} + {c_2}x$$
• D) $$y = {c_1}$$

$${\text{The}}\,\,{\text{power}}\,\,{\text{series}},\,\,\sum\limits_{n = 0}^\infty {\frac{{{x^n}}}{{n!}},\,\,\_\_\_\_\_\_\_\_\_\,\,\,x = 1\,\,{\text{to}}\,\,{\text{the}}\,\,{\text{number}}\,\,e.\,}$$

• A) $${\text{converges}}$$
• B) $${\text{diverges}}$$
• C)
• D)

The infinite series $\sum\limits_{n = 1}^\infty {\frac{{( - 1)^{n + 2} }} {{n^3 }}(x + 3)^n } .$ is a power series in x centered at

• A) 2
• B) -3
• C) 3
• D) -2

$${\text{The}}\,\,{\text{quantity}}\,\,X = L\gamma - \frac{1}{{C\gamma }}\,\,{\text{is}}\,\,{\text{called}}\,\,\_\_\_\_\_\_\_\_\,\,{\text{of}}\,\,{\text{the}}\,\,{\text{circuit}}{\text{.}}$$

• A) $${\text{impedance}}$$
• B) $${\text{reactance}}$$
• C)
• D)

\[\begin{gathered} {\text{Consider}}\,\,{\text{the}}\,\,{\text{equation}}\,\,{\text{of}}\,{\text{the}}\,\,{\text{free}}\,\,{\text{damped}}\,\,{\text{motion,}}\,\,\frac{{{d^2}x}}{{d{t^2}}} + 2\lambda \frac{{dx}}{{dt}} + {\omega ^2}x = 0,\,\,{\text{has}}\,\,{\text{the}}\,\,{\text{roots}}\,\,{\text{of}}\,\,{\text{the}}\,\,{\text{auxiliary}}\,\, \hfill \\ {\text{equations}},\,\,m = - \lambda \pm \sqrt {{\lambda ^2} - {\omega ^2}} .\,\,{\text{If}}\,{\text{the}}\,\,{\text{roots}}\,\,{\text{are}}\,\,{\text{complex}}\,\,{\text{i}}{\text{.e}}{\text{.}}\,\,{\lambda ^2} - {\omega ^2} < 0,\,\,\,{\text{then}}\,\,\beta < k\,\,{\text{and}}\,\,\,{\text{the}}\,\,{\text{system}}\,\,{\text{is}}\,\, \hfill \\ {\text{called}}\,\,\_\_\_\_\_\_\_\,\,damped.\,\, \hfill \\\ \end{gathered} \]

• A) \[{\text{non - critically}}\]
• B) \[{\text{over}}\]
• C) \[{\text{under}}\]
• D) \[{\text{critically}}\]

The linear normal form of $$2\frac{{{d^2}y}}{{d{x^2}}} + 4\frac{{dy}}{{dx}} - 5y = 0$$ ,by using $$y = {x_1},y' = {x_1}^\prime {\text{and }}y'' = {x_2}^\prime$$ , is__________.

• A) $${x_1}^\prime = {x_2},{x_2}^\prime = - 2{x_2} - \frac{5}{2}{x_1}$$
• B) $${x_1}^\prime = {x_2},{x_2}^\prime = 2{x_2} + \frac{5}{2}{x_1}$$
• C) $${x_1}^\prime = {x_2},{x_2}^\prime = - 2{x_2} + \frac{5}{2}{x_1}$$
• D) $${x_1}^\prime = {x_2},{x_2}^\prime = 2{x_2} - \frac{5}{2}{x_1}$$