The method of Frobenius always provide two solutions.

• A) False
• B) True
• C)
• D)

A second order linear differential equation of the form $$(1 - {x^2})y - 2xy' + n(n + 1)y = 0$$ is called ______________ differential equation.

• A) Picard
• B) Bernoulli
• C) Bessel
• D) Legendre

The differential equation $$5\frac{{dx}}{{dt}} + 5x - \frac{{dy}}{{dt}} = {e^{2t}}$$ in terms of differential operator is __________.

• A) $$(D + 1)5x + Dy = {e^{2t}}$$
• B) $$(D - 1)5x - Dy = {e^{2t}}$$
• C) $$(D + 1)5x - Dy = {e^t}$$
• D) $$(D + 1)5x - Dy = {e^{2t}}$$

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) inductor
• C) capacitor
• D) resister

If \[{\lambda ^2} - {\omega ^2} = 0\] and \[\beta = k\] then the system is said to be _______ damped.

• A) critically
• B) over
• C) under
• D) none of these

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

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

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

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

Consider a power series $$\sum\limits_{n = 1}^\infty {\frac{{{{( - 1)}^{n + 1}}}}{{{n^2}}}} {x^n} = x - \frac{{{x^2}}}{{{2^2}}} + \frac{{{x^3}}}{{{3^2}}} + ....$$ , then the center of series is _______.

• A) $${x^2}$$
• B) x
• C) 1
• D) 0

Ordinary differential equation $\left( {\frac{{dy}} {{dx}}} \right)^3 + \frac{{d^2 y}} {{dx^2 }} + y = 9$ , is of order ------.

• A) 2
• B) 3
• C) 0
• D) 1

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

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

The flow of current is ___________ proportional to the resistance.

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

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

• A) -1/x
• B) -1/y
• C) -x
• D) -y

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

Which number is known as quasi frequency?

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

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

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

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

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

For solving non homogeneous differential equation, we use either the method of ___________.

• A) Undetermined coefficient
• B) Variation of parameter
• C) a&b both
• D) None of them

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

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

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

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