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 mm. The thickness of the hair is:

The photograph of a house occupies an area of $1.75 c{m}^2$ on a 35 mm slide. The slide is projected onto a screen, and the area of the house on the screen is $1.55 m^2$. What is the linear magnification of the projector-screen arrangement?

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:

Which one of the following formulas is dimensionally incorrect?

$$\begin{gathered} \left(1\right) \mathrm{y}=\mathrm{asin}\frac{2\mathrm{\pi t}}{\mathrm{T}} \\ \left(2\right) \mathrm{y}=\frac{\mathrm{a}}{\sqrt{2}}\left(\sin \frac{2\mathrm{\pi t}}{\mathrm{T}}+\cos \frac{2\mathrm{\pi t}}{\mathrm{T}}\right) \\ \left(3\right) \mathrm{y}=\mathrm{asinvt} \\ \left(4\right) \mathrm{y}=\mathrm{asin}\left(\frac{2\mathrm{\pi t}}{\mathrm{T}}+\mathrm{\pi }\right) \end{gathered}$$

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $\stackrel{\mathrm{o}}{\mathrm{A}}$ $\left(1 \stackrel{\mathrm{o}}{\mathrm{A}}={10}^{-10} \mathrm{m}\right).$ 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?

$$\begin{gathered} \left(1\right) 3\times {10}^{-7} m^3 \\ \left(2\right) 2\times {10}^{-7} m^3 \\ \left(3\right) 3\times {10}^{-6} m^3 \\ \left(4\right) 2\times {10}^{-6} m^3 \end{gathered}$$

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).

$$\begin{gathered} \left(1\right) 7.08\times {10}^4 \\ \left(2\right) 22.4\times {10}^3 \\ \left(3\right) 11.2\times {10}^5 \\ \left(4\right) 8.0\times {10}^3 \end{gathered}$$

The nearest star to our solar system is 4.29 light-years away. How much is this distance in terms of parsecs?

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)

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?

$$\begin{gathered} \left(1\right) {10}^{12} \mathrm{to} {10}^{13} \\ \left(2\right) {10}^7 \mathrm{to} {10}^8 \\ \left(3\right) {10}^{10} \mathrm{to} {10}^{13} \\ \left(4\right) {10}^{11} \mathrm{to} {10}^{12} \end{gathered}$$

What will be the average mass density of a sodium atom (assuming its size to be about $2.5 \stackrel{0}{A}$)?

$$\begin{gathered} \left(1\right) 5.67\times {10}^3 kg m^{-3} \\ \left(2\right) 4.67\times {10}^3 kg m^{-3} \\ \left(3\right) 4.67\times {10}^4 kg m^{-3} \\ \left(4\right) 5.67\times {10}^4 kg m^{-3} \end{gathered}$$

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?

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 )

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? 

$$\begin{gathered} \left(1\right) 3.2\times {10}^{22} km \\ \left(2\right) 3.7\times {10}^{22} km \\ \left(3\right) 2.8\times {10}^{22} km \\ \left(4\right) 2.1\times {10}^{22} km \end{gathered}$$

A packet contains silver powder of mass 20.23 g $\pm$ 0.01 g. Some of the powder of mass 5.75 g $\pm$ 0.01 g is taken out from it. The mass of the powder left-back is 

The radius of a sphere is (2.6 $\pm$ 0.1) cm . The percentage error in its volume is 

We can reduce random errors by 

The volume of a cube having sides 1.2 m is appropriately expressed as 

The number of significant figures in a pure number 410 is 

The addition of three masses 1.6 g , 7.32 g and 4.238 g, addressed up to proper decimal places is 

The area of a sheet of length 10.2 cm and width 6.8 cm addressed up to proper number of significant figures is 

The uncertain digit in the measurement of a length reported as 41.68 cm is 

The number of significant figures in the measured value 0.0204 is 

The number of significant figures in the measured value 26000 is 

The number of significant zeroes present in the measured value 0.020040, is 

The number of significant figures in the measured value 4.700 m is the same as that in the value 

lf a calculated value 2.7456 g contains only three significant figures, the two insignificant digits in it are 

An object of mass 4.237 g occupies a volume 1.72 cm${}^3$. The density of the object to appropriate significant figures is 

Round off the value 2.845 to three significant figures. 

A length 5.997 m rounded off to three significant figures is written as 

What are the dimensions of the change in velocity?