Question 1 :
Two quantities $A$ and $B$ have different dimensions. Which operation is physically meaningful ?

Question 2 :
Multiply 107.88 by 0.610 and express the result with a correct number of significant figures.

Question 3 :
A student measure the thickness of an object by three different instruments and gets the result as 0.5 cm, 0.50 cm, 0.500 cm. State the one which is more accurate.

Question 4 :
The side of a cube is $2.5$ metre, the volume of the cube to the correct significant figures is :

Question 5 :
If&#160;$\mu $&#160;is the permeability and&#160;$\epsilon $ is the&#160;permittivity then&#160;$\dfrac { 1 }{ \sqrt { \mu \epsilon &#160;} &#160;} $&#160;<b></b>is equal to&#160;

Question 6 :
If force $F$, acceleration $A$ and time $T$ are taken&#160;as fundamental quantities then the dimensions&#160;of energy are :

Question 7 :
According to theory of significant figures $\left( 2.0 \right) ^{ 10 }$ is :

Question 8 :
The pair of quantities that do not have the same dimensions is _________________.<br/>

Question 9 :
Which of the&#160;following is not used to measure the volume of a liquid or an irregular shaped&#160;object?

Question 10 :
In a burette, the zero mark on the graduation scale is near its mouth. <br/>

Question 11 :
Given $P = 0.0030 \,m, Q = 2.40 \,m$ and $R = 3000 m$, then number of significant figure in $P, Q, R$ are respectively:

Question 12 :
Quantity $X$ has a fractional uncertainty of $x$. Quantity $Y$ has a fractional uncertainty of $y$.<br>What is the fractional uncertainty in $\dfrac {X}{Y^{2}}$?

Question 14 :
The dimension of permittivity (${ \varepsilon }_{ 0 }$) are ______. Take $Q$ as the dimension of charge.

Question 16 :
Calorie is a unit of heat or energy whose value is $4.2J$, where $J=1\;kgm^2s^{-2}$. If one uses a unit system in which units of mass, length and time are taken as $\alpha\;kg,\;\beta\;metre$ and $\gamma\;second$ respectively, then the value of calorie in this system will be

Question 17 :
Consider the following two statements A and B.&#160;Identify the correct answer.<br/>A) The quantity&#160;$\dfrac { { e }^{ 2 } }{ { \epsilon &#160;}_{ 0 }ch } $&#160;is dimensionless.<br/>B)&#160;$\dfrac { 1 }{ \sqrt { { \mu &#160;}_{ 0 }{ \epsilon &#160;}_{ 0 } } &#160;} $&#160;has the dimensions of velocity&#160;and is numerically equal of velocity of light.

Question 19 :
Which one of the following represents the&#160;correct dimensions of the coefficient of&#160;viscosity ?

Question 21 :
If pressure $P$, velocity $V$ and the time $T$ are taken as fundamental physical quantities, the dimensional formula of the force is:

Question 22 :
Assertion: Force cannot be added to pressure.&#160;<br/> Reason: Because their dimensions are different.

Question 23 :
Three coins of the same size (radius $1cm$) are placed on table such that each of them touches the other two. The area enclosed by the coins is:

Question 24 :
The volume of a sphere is $ 1.76cm^3 $. The volume of 25 such spheres taking into account the significant figure is:

Question 26 :
The radius of a sphere is measured to be $5.3 \pm 0.1 cm$. Calculate the percentage error in the measurement of its volume.

Question 27 :
A gaseous mixture of ethene, ethane and methane having total volume $150\ ml$&#160;is subjected to combustion in excess of oxygen. If percentage of methane in the original mixture is $20\%$&#160;then calculate volume (in ml) of $C{ O }_{ 2 }\left( g \right)$&#160;which will be obtained at same temperature and pressure.

Question 28 :
A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90\ s, 91\ s, 95\ s$ and $92\ s$. If the minimum division in the measuring clock is $1\ s$, then the reported mean time should be:

Question 29 :
The viscosity of a gas depends on mass, the effective diameter and the mean speed of the molecules. At room temperature, for He,&#160;$\eta_{He}=2\times 10^{-5}$ $kg{m}^{-1}{s}^{-1}$ and for $CH_{4}$,&#160;$\eta _{CH_{4}}=1.1\times 10^{-5}kgm^{-1}s^{-1}$. The diameter of the He atom is $2.1\times 10^{-10}m$ . lf the diameter of&#160; $CH_{4}$ is $n\times 10^{-10}m$, find $'n'$.<br/>Given mean speed of the molecules of the gas $v\propto \sqrt{\frac{K_B T}{m}}$ , where $K_B$ is the boltzmann's constant , $ T$ is temperature and m is the mass of the gas.&#160;

Question 30 :
<table class="wysiwyg-table"> <tbody><tr> <td><b>Column- I</b><br><b>Physical quantity</b></td> <td><b>Column-II</b><br><b>MKS system</b></td> <td><b>Column-III<br></b><b>CGS system</b></td> <td><b>Column- IV</b><br><b>FPS system</b></td> </tr> <tr> <td>(A) length</td> <td>(a) newton</td> <td>(p) erg</td> <td>(1) poundal</td> </tr> <tr> <td>(B) mass</td> <td>(b) m</td> <td>(q) dyne</td> <td>(2) ft-poundal</td> </tr> <tr> <td>(C) force</td> <td>(c) kg</td> <td>(r) erg/s</td> <td>(3) ft</td> </tr> <tr> <td>(D) power</td> <td>(d) joule</td> <td>(s) g</td> <td>(4) lb</td> </tr> <tr> <td>(E) work</td> <td>(e) watt</td> <td>(t) cm</td> <td>(5) ft-poundal/s</td> </tr></tbody></table>