A new unit of length is chosen such that the speed of light in the vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes \(8\) min and \(20\) secs to cover this distance?
1. \(500\) new units of length.
2. \(100\) new units of length.
3. \(300\) new units of length.
4. \(200\) new units of length.

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 length, breadth, and thickness of a rectangular sheet of metal are \(4.234\) m, \(1.005\) m, and \(2.01\) cm respectively. The volume of the sheet to correct significant figures is:
1. \(0.00856\) m³${}^{}$
2. \(0.0856\) m³${}^{}$
3. \(0.00855\) m³${}^{}$
4. \(0.0855\) m³${}^{}$

Which one of the following formulas is dimensionally incorrect?

$\left(1\right)<mspace\; width="1em"></mspace>\mathrm{y}=\mathrm{asin}\frac{2\mathrm{\pi t}}{\mathrm{T}}$
$\left(2\right)<mspace\; width="1em"></mspace>\mathrm{y}=\frac{\mathrm{a}}{\sqrt{2}}\left(\sin \frac{2\mathrm{\pi t}}{\mathrm{T}}+\cos \frac{2\mathrm{\pi t}}{\mathrm{T}}\right)$
$\left(3\right)<mspace\; width="1em"></mspace>\mathrm{y}=\mathrm{asinvt}$
$\left(4\right)<mspace\; width="1em"></mspace>\mathrm{y}=\mathrm{asin}\left(\frac{2\mathrm{\pi t}}{\mathrm{T}}+\mathrm{\pi }\right)$

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $\stackrel{\mathrm{o}}{\mathrm{A}}$ $\left(1<mspace\; width="1em"></mspace>\stackrel{\mathrm{o}}{\mathrm{A}}={10}^{-10}<mspace\; width="1em"></mspace>\mathrm{m}\right).$ The size of a hydrogen atom is about 0.5 $\stackrel{o}{A}$. What is the total atomic volume in $m^3$ of a mole of hydrogen atoms?

$\left(1\right)<mspace\; width="1em"></mspace>3\times {10}^{-7}<mspace\; width="1em"></mspace>m^3$
$\left(2\right)<mspace\; width="1em"></mspace>2\times {10}^{-7}<mspace\; width="1em"></mspace>m^3$
$\left(3\right)<mspace\; width="1em"></mspace>3\times {10}^{-6}<mspace\; width="1em"></mspace>m^3$
$\left(4\right)<mspace\; width="1em"></mspace>2\times {10}^{-6}<mspace\; width="1em"></mspace>m^3$

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen? (Take the size of the hydrogen molecule to be about 1 Å).

$\left(1\right)<mspace\; width="1em"></mspace>7.08\times {10}^4$
$\left(2\right)<mspace\; width="1em"></mspace>22.4\times {10}^3$
$\left(3\right)<mspace\; width="1em"></mspace>11.2\times {10}^5$
$\left(4\right)<mspace\; width="1em"></mspace>8.0\times {10}^3$

The nearest star to our solar system is \(4.29\) light-years away. How much is this distance in terms of parsecs?
1. \(1.11\) parsec
2. \(1.22\) parsec
3. \(1.32\) parsec
4. \(1.39\) parsec

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

It is claimed that two caesium clocks if allowed to run for 100 years, free from any disturbance, may differ by only about 0.02 sec. What does this imply for the accuracy of the standard caesium clock in measuring a time interval of 1 sec?

$\left(1\right)<mspace\; width="1em"></mspace>{10}^{12}<mspace\; width="1em"></mspace>\mathrm{to}<mspace\; width="1em"></mspace>{10}^{13}$
$\left(2\right)<mspace\; width="1em"></mspace>{10}^7<mspace\; width="1em"></mspace>\mathrm{to}<mspace\; width="1em"></mspace>{10}^8$
$\left(3\right)<mspace\; width="1em"></mspace>{10}^{10}<mspace\; width="1em"></mspace>\mathrm{to}<mspace\; width="1em"></mspace>{10}^{13}$
$\left(4\right)<mspace\; width="1em"></mspace>{10}^{11}<mspace\; width="1em"></mspace>\mathrm{to}<mspace\; width="1em"></mspace>{10}^{12}$