When the planet Jupiter is at a distance of 824.7 million kilometres from the Earth, its angular diameter is measured to be 35.72” of arc. Then the diameter of Jupiter is:

$\left(1\right)<mspace\; width="1em"></mspace>1.34\times {10}^9<mspace\; width="1em"></mspace>m$
$\left(2\right)<mspace\; width="1em"></mspace>1.43\times {10}^9<mspace\; width="1em"></mspace>m$
$\left(3\right)<mspace\; width="1em"></mspace>1.34\times {10}^8<mspace\; width="1em"></mspace>m$
$\left(4\right)<mspace\; width="1em"></mspace>1.43<mspace\; width="1em"></mspace>\times {10}^8<mspace\; width="1em"></mspace>m$

A student measures the thickness of a human hair by looking at it through a microscope of magnification \(100.\) He makes \(20\) observations and finds that the average width of the hair in the field of view of the microscope is \(3.5 ~\text{mm}.\) The thickness of the hair is:
1. \(0.035~\text{mm}\)
2. \(0.0035 ~\text {mm}\)
3. \(0.35 ~\text{mm}\)
4. \(3.5 ~\text{mm}\)

The photograph of a house occupies an area of $1.75<mspace\; width="1em"></mspace>c{m}^2$ on a 35 mm slide. The slide is projected onto a screen, and the area of the house on the screen is $1.55<mspace\; width="1em"></mspace>m^2$. What is the linear magnification of the projector-screen arrangement?

(1) 90.0

(2) 94.1

(3) 99.9

(4) 97.7

The density of the Sun is: 

(Given, mass of the Sun = 2.0 x 10³⁰ kg and radius of the Sun = 7.0 x 10⁸m)

(1) 2.9 x 10³ kg m^-3

(2) 1.4 x 10³ kg m^-3

(3) 5.6 x 10³ kg m^-3 

(4) 1.9 x 10³ kg 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? 

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