The harmonic series of constant $$\sum\limits_{n = 1}^\infty {\frac{1}{n}}$$ always _______.

• A) convergent
• B) divergent
• C)
• D)

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

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

For $$\frac{{dy}} {{dx}} - \frac{y} {x} = - \frac{{\ln x}} {x}$$ the integrating factor is

• A) -x
• B) -1/x
• C) -1/y
• D) -y

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

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

$${\text{The}}\,\,{\text{quantity}}\,\,Z = \sqrt {{X^2} + {R^2}} \,\,{\text{is}}\,\,{\text{called}}\,\,\_\_\_\_\_\_\_\_\,\,{\text{of}}\,\,{\text{the}}\,\,{\text{circuit}}{\text{.}}$$

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

The ________ force is proportional to the instantaneous velocity $$\frac{{dx}}{{dt}}$$ .

• A) restoring
• B) damped
• C) umdamped
• D) retarding

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

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

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

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) 2
• D) -3

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

The total forces acting on mass m are_______.

• A) 4
• B) 3
• C) 2
• D) 5

The damping force is __________to the instantaneous velocity $$\frac{{dx}}{{dt}}$$.

• A) None of these
• B) Inverse proportional
• C) Proportional
• D) Constant

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) none of them
• C) \[f{m^2} + (g - f)m + h\, = 0\]
• D) \[f{m^2} - (g - f)m + h\, = 0\]

Consider a power series \[1 - \frac{{{x^2}}}{2} + \frac{{{x^4}}}{{24}} - ....\] represents _______.

• A) cos x
• B) e
• C) sin x
• D) ln x

If E(t)=0, R=0 (E(t) is the source voltage & R is the resistance) then the electric vibration can be called free ____________.

• A) damped oscillation
• B) un-damped oscillation
• C)
• D)

\[{\text{The}}\,\,{\text{power}}\,\,{\text{series}},\,\,1 + x + \frac{x}{{2!}} + \frac{{{x^3}}}{{3!}} + ...\, = \_\_\_\_\_\_\_\_\_.\]

• A) \[{e^x}\]
• B) \[\cos x\]
• C) \[\ln (1 + x)\]
• D) \[\sin x\]

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

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

The standard unit for measurement of reactance and the impedance is __________.

• A) Henry
• B) Ohms
• C) Coulombs
• D) Volt

The harmonic series of constant \[\sum\limits_{n = 1}^\infty {\frac{1}{n}} \] always _______.

• A) divergent
• B) convergent
• C)
• D)

If the system is impressed upon by a _________ force and there is no damping force then there is no transient term in the solution.

• A) gravitational
• B) applied
• C) periodic
• D) friction