According to Newtons's first law , body remains in its state unless acted by external force. This property of body is termed as Inertia.

This totally depends on the frame of refrence, any object is relatively at rest or moving.

Earth is continously moving in its orbit around the sun and on its own axis.

when the position of a body does not change with respect to its surroundings and time the body is said to be in rest. A book lying on the table is at rest because its position with respect to other object on table or room is fix. 

A book lying on the table is at rest. 

Pendulum of a wall clock- It is in periodic motion. Rest all are in multiple motion. The restoring force is proportional to displacement .While electric drill, rolling ball etc are in multiple motion like rotational +transnational or Vibrational motion.

Giant wheel- because it has rotational motion as well as transnational motion. While apple falling from a tree, a car moving on straight rod and coin moving over a carrom board have only linear or rectilinear motion.  

Moon 

Earth, because earth is in motion while other object are in rest with respect to earth.  

All the three object are in any osscilatory motion wrt to earth as frame of refrence. But study table is at rest.

The relation between kinetic energy $(K)$ and momentum $(p)$ is given by, $K=\dfrac{p^2}{2m}$ where $m$ be the mass of the body

Changes with time

Impulse:- It is defined as a change in momentum due to force in small time.

when bus suddenly start moving in forward direction. This happens due to. When a bus suddenly starts, the standing passengers fall backward in the bus.

The walls are at rest with respect to the Earth. When you are sitting in the classroom, you are also at rest with respect to the Earth, and so the walls do not seem to be moving to you.

according to newton's first law of motion, an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Time translation symmetry gives rise to the conservation of energy.

Space translation symmetry gives rise to conservation of momentum.

Rotational symmetry gives rise to conservation of angular momentum.

The conservation law associated with this symmetry is the conservation of electrical charge.

An odometer or odograph is an instrument that indicates distance traveled by the automobile

A laser signal sent towards the moon returns after t seconds.

Distance is a scalar quantity. So the given statement is false.

A moving object always changes its position. Then, it has move along a path with some length.
So, if the body is moving, it will always cover some path which can never have zero length. Thus distance travelled by a moving object can never be zero.

The given equation is  $2x  =4$

Path length is distance covered by body in reaching from initial point to final point. It may be different for different paths.

Since path length is distance hence it is scalar quantity, it may be different for two paths with same initial and final points.

At the distance of closest approach:$KE=PE$

$v _x=\dfrac{dx}{dt}=6$

$\begin{array}{l} P=\frac { { \overline { S }  } }{ c } =\frac { { \frac { P }{ { 4\pi { d^{ 2 } } } }  } }{ c } =\frac { { \frac { { 75W } }{ { 4\pi { { \left( { 8.0\times { { 10 }^{ -2 } }m } \right)  }^{ 2 } } } }  } }{ { 3.00\times { { 10 }^{ 8 } }\, m/s } } =3.1\times { 10^{ -6 } }N/{ m^{ 2 } }. \ The\, \, force\, \, is\, \, pressure\, \, times\, \, area, \ we\, \, approximate\, \, the\, \, area\, \, of\, \, a\, \, fingertip\, \, to\, \, be\, \, 1.0\, c{ m^{ 2 } } \ F=PA=\left( { 3.1\times { { 10 }^{ -6 } }N/{ m^{ 2 } } } \right) \left( { 1.0\times { { 10 }^{ -4 } }{ m^{ 2 } } } \right) =3.1\times { 10^{ -10 } }N \end{array}$

Given:$v =4\frac{Km}{h}$
           

Displacement is the distance between the initial and final position of an object. When an object moves in a circular path of radius R, its displacement will be zero but the distance traveled by the object will be the perimeter i.e $2\pi R$. 

Before reaching origin, distance travelled by Sunil is more than Rahul since he is ahead of Rohit. But displacement of Rohit is more as he is far from the origin than Sunil.