Question 1 :
In terms of basic units of mass $(M)$, length $(L)$, time $(T)$ and charge $(Q)$, the dimensions of magnetic permeability of vacuum $({\mu}_0)$ would be

Question 2 :
The amplitude of a damped oscillator of mass $'m'$ varies with the time  't' as $A=A_0e^{-at/m}$. The dimension of $'a'$ are:

Question 3 :
If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be

Question 4 :
The radius of a sphere is $5$ cm. Its volume will be given by (according to the theory of significant figures) :

Question 5 :
The dimension of magnetic induction in $M, L, T$ and $C$ (Coloumb) is given as:

Question 6 :
The difference between the measured value and true value is :

Question 7 :
Given that $y=a cos (\frac{t}{p}-qx)$, where $t$ represents time in second and $x$ represents distance in meter. Which of the following statements is true ?

Question 8 :
If $E, m, J$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Then the dimensions of $\dfrac { { EJ }^{ 2 } }{ { m }^{ 5 }{ G }^{ 2 } } $ are same as that of

Question 10 :
The refractive index ($\mu$) of glass is found to have the values $1.49, 1.50, 1.52, 1.54\ and\ 1.48$. Calculate absolute error is each measurement.

Question 11 :
Multiple Correct Answers Type<br>The values of measurement of a physical quantity in five trials were found to be $1.51, 1.53, 1.53, 1.52$ and $1.54$. Then

Question 12 :
The numbers $2.745$ and $2.735$ on rounding off to $3$ significant figures will give:

Question 16 :
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 17 :
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 18 :
The distance s travelled by a particle in time t is $s=ut-\displaystyle\frac{1}{2}gt^2$. The initial velocity of the particle was measured to be $u=1.11\pm 0.01$ m/s and the time interval of the experimental was $t=1.01\pm 0.1s$. The acceleration was taken to be $g=9.8\pm 0.1m/s^2$. With these measurements, the student estimates the total distance travelled. How should the student report the result?

Question 19 :
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 20 :
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;