Question 2 :
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 3 :
The diameter of a sphere is $4.24\ m$. Its surface&#160;area with due regard to significant figures is :

Question 5 :
If $y$ represents the pressure and $x$ represents the position then dimensional expression of $\int { \dfrac { dx }{ \sqrt { p^{ 2 }- y^2}&#160; }&#160; } $

Question 6 :
The thickness of a metal sheet is measured to be $326 mm$. Express its order of magnitude in mm.

Question 8 :
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 9 :
Consider the following two statements A and B&#160;and identify the correct answer.<br/>A) Two quantities which are to be added must&#160;have the same dimensions.<br/>B) Two quantities which are to be multiplied&#160;must have the same dimensions.

Question 10 :
With due regard to significant figures, the value of&#160;$ 46.7-10.04 &#160;$ is :

Question 11 :
Which of the following quantifies has the least number of significant digits?&#160;

Question 12 :
The length and breadth of a rectangular sheet are $16.2$ cm and $10.1 cm$, respectively. The area of the sheet inappropriate significant figures and error is:

Question 13 :
Equal masses of ${ H }_{ 2 }, { O }_{ 2 }$&#160;and methane have been taken in a container of volume V at temperature&#160;${27}^{o}C$&#160;in identical conditions. The ratio of the volumes of gases ${ H }_{ 2 }: { O }_{ 2 }$: methane would be___________.

Question 14 :
On the basis of dimensional equation, the maximum number of unknown that can be found, is

Question 15 :
The dimensions of angular momentum, latent heat and capacitance are, respectively.

Question 16 :
<p>The dimension of $ \cfrac {1}{2}\epsilon_o E^2$ permittivity of free space and E:<br>Intensity of electric field) is </p><br><br><p> </p>

Question 20 :
A cube has a side of length $\displaystyle 1.2\times { 10 }^{ -2 }m$. Calculate its volume.

Question 21 :
A scientist proposes a new temperature scale in which the ice point is $25 X$ ($X$ is the new unit of temperature) and the steam point is $305 X$. The specific heat capacity of water in this new scale is (in $J{ kg }^{ -1 }{ X }^{ -1 }$):

Question 22 :
A public park, in the form of a square, has an area of $(100 \pm 0.2 )m^2 $ .The side of park is :

Question 23 :
The speed of light ($c$), gravitational constant ($G$) and Planck's constant ($h$) are taken as&#160;fundamental units in a system. The dimensions of time in this new system should be

Question 24 :
$ S_{2}O_{3}^{2-}$ ion is oxidized by $ S_{2}O_{8}^{2-}$ ion, the products are $ S_{4}O_{6}^{2-}$ and $ SO_{4}^{-2}$ ions. What volume of 0.25M thiosulphate solution would be needed to reduce 1 g of $ K_{2}S_{2}O_{8}?$ (K = 39)

Question 25 :
Using the expression $2d sin\theta=\lambda$, one calculates the values of '$d$' by measuring the corresponding angles $\theta$ in the range $0^o$ to $90^o$. The wavelength $\lambda$ is exactly known, and the error in $\theta$ is constant for all values of $\theta$. As $\theta$ increases from $0^o$:

Question 26 :
An experiment measures quantities a, b, c and x is calculated from $x = ab^2/c^3$. If the maximum percentage error in a, b and c are 1%, 3% and 2% respectively, the maximum percentage error in x will be

Question 27 :
Two equal masses each $'m'$ are hung from a balance whose scale pans differe in vertical height by $'h'$. the error in weighing is

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 relative uncertainty in the period of a satellite orbiting around then earth is $10^{-2}$. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is:

Question 30 :
In an experiment the following observations were recorded&#160;<br/>$L=2.890$ metre<br/>$\mathrm{M}=3.0$ kg<br/>$\ell=0.87$ cm<br/>$\mathrm{D}=0.041$ cm<br/>$\mathrm{g}=981\mathrm{c}\mathrm{m}/\sec^{2}$<br/>and the formula used for calculatlon of Young's modulus ($\mathrm{Y}$) is $\displaystyle \mathrm{Y}=\frac{\mathrm{M}\mathrm{g}\mathrm{L}}{\pi \mathrm{r}^{2}l}$<br/>What is the maximum possible error expressed in percentage?<br/>