What will be the average mass density of a sodium atom (assuming its size to be about $2.5<mspace\; width="1em"></mspace>\stackrel{0}{A}$)?

$\left(1\right)<mspace\; width="1em"></mspace>5.67\times {10}^3<mspace\; width="1em"></mspace>kg<mspace\; width="1em"></mspace>m^{-3}$
$\left(2\right)<mspace\; width="1em"></mspace>4.67\times {10}^3<mspace\; width="1em"></mspace>kg<mspace\; width="1em"></mspace>m^{-3}$
$\left(3\right)<mspace\; width="1em"></mspace>4.67\times {10}^4<mspace\; width="1em"></mspace>kg<mspace\; width="1em"></mspace>m^{-3}$
$\left(4\right)<mspace\; width="1em"></mspace>5.67\times {10}^4<mspace\; width="1em"></mspace>kg<mspace\; width="1em"></mspace>m^{-3}$

A LASER is a source of very intense, monochromatic, and a unidirectional beam of light. These properties of laser light can be exploited to measure long distances. The distance of the Moon from the Earth has been already determined very precisely using a laser as a source of light. A laser light beamed at the Moon takes 2.56 s to return after reflection at the Moon’s surface. How much is the radius of the lunar orbit around the Earth?

(1) $2.14\times {10}^8<mspace\; width="1em"></mspace>m$

(2) $2.84\times {10}^8<mspace\; width="1em"></mspace>m$

(3) $3.84\times {10}^8<mspace\; width="1em"></mspace>m$

(4) $3.14\times {10}^8<mspace\; width="1em"></mspace>m$

A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects underwater. In a submarine equipped with a SONAR, the time delay between the generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 sec. What is the distance of the enemy submarine? (Speed of sound in water = 1450 m/s )

(1) 60.32 km

(2) 57.70 km

(3) 44.23 km

(4) 55.80 km

The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us? 

$\left(1\right)<mspace\; width="1em"></mspace>3.2\times {10}^{22}<mspace\; width="1em"></mspace>km$
$\left(2\right)<mspace\; width="1em"></mspace>3.7\times {10}^{22}<mspace\; width="1em"></mspace>km$
$\left(3\right)<mspace\; width="1em"></mspace>2.8\times {10}^{22}<mspace\; width="1em"></mspace>km$
$\left(4\right)<mspace\; width="1em"></mspace>2.1\times {10}^{22}<mspace\; width="1em"></mspace>km$

The base quantity among the following is 

(1) Speed 

(2) Weight 

(3) Length 

(4) Area 

Which of the following is not a unit of time?

(1) Second 

(2) minute 

(3) hour 

(4) light year

One astronomical unit is a distance equal to 

(1) 9.46$\times {10}^{15}<mspace\; width="1em"></mspace>m$
$$

(2) $1.496\times {10}^{11}<mspace\; width="1em"></mspace>m$
$$

(3) $3\times {10}^8<mspace\; width="1em"></mspace>m$
$$

(4) $3.08\times {10}^{16<mspace\; width="1em"></mspace>m}$ 

Ampere second is a unit of 

(1) Current 

(2) Charge 

(3) Energy 

(4) Power 

Which of the following is a units that of force?

(1) N m 

(2) mN

(3) nm 

(4) n S

The value of 60$°$ in radian is 

(1) $\frac{\pi }{2}<mspace\; width="1em"></mspace>$

(2) $<mspace\; width="1em"></mspace>\frac{\pi }{3}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

(3) $\frac{\pi }{4}<mspace\; width="1em"></mspace>$

(4) $<mspace\; width="1em"></mspace>\frac{\pi }{5}$