The velocity of a particle moving with simple harmonic motion is ------------- at the mean position.

• A) Maximum
• B) Zero
• C) None of these
• D) Minimum

{\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)

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

• A) 3
• B) 2
• C) 1
• D) 0

The equation of free un-damped motion is ________.

• A) $\frac{{{d^2}x}}{{d{t^2}}} +\frac{k}{m}x = 0$
• B) $\frac{{{d^2}x}}{{d{t^2}}} - \frac{k}{m}x = 0$
• C)
• D)

The combination of the Newton’s second law and the Hook’s law could lead to a differential equation governing to the motion of a mass attached to spring i.e. _________ motion.

• A) translational
• B) linear
• C) simple harmonic
• D) rotational

If a force acts upon a body, the acceleration is produced in the direction of the force whose magnitude is proportional to the magnitude of force, is known as the ________.

• A) Hook’s law
• B) Newton’s third law
• C) Newton’s first law
• D) Newton’s second law

To reduce any Cauchy –Euler differential equation into a differential equation with ________ coefficients we often use substitution x = {e^t}

• A) variable
• B) constant
• C)
• D)

How are frequency and period related in simple harmonic motion?

• A) Their sum is constant
• B) None of the above
• C) They are directly related
• D) They are inversely related

Vibration of an object on equilibrium point is called simple harmonic motion when the restoring force is proportional to _________.

• A) A spring constant
• B) Mass
• C) Displacement
• D) Time

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 \cos \frac{x} {2} + c_2 Sin\frac{x} {2}
• D) y(x) = c_1 Sin\frac{x} {2}

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

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

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

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

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

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

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

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

We can derive a differential equation governing the motion of a mass attached to spring when the Newton’s second law combined with ________.

• A) Newton’s 3rd law
• B) Hook’s law
• C)
• D)

To reduce any Cauchy –Euler differential equation into a differential equation with ________ coefficients we often use substitution \[x = {e^t}\].

• A) variable
• B) constant
• C)
• D)

The conversion of Cauchy Euler equation {x^2}\frac{{{d^2}y}}{{d{x^2}}} - x\frac{{dy}}{{dx}} + y = \ln x after putting x = {e^t} becomes

• A) ({\Delta ^2} - 2\Delta + 1)y
• B) ({\Delta ^2} - \Delta + 1)y
• C) (2{\Delta ^2} - \Delta - 1)y
• D) ({\Delta ^2} - 2\Delta - 1)y

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

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

The conversion of Cauchy Euler equation \[{x^2}\frac{{{d^2}y}}{{d{x^2}}} - x\frac{{dy}}{{dx}} + y = \ln x\] after putting \[x = {e^t}\] becomes

• A) \[({\Delta ^2} - 2\Delta + 1)y\]
• B) \[(2{\Delta ^2} - \Delta - 1)y\]
• C) \[({\Delta ^2} - 2\Delta - 1)y\]
• D) \[({\Delta ^2} - \Delta + 1)y\]