Question 1 :
The dimensional formula of $\dfrac {L}{R}$ is same as that of (where $L$ is inductance and $R$ is resistance)

Question 3 :
Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful?

Question 4 :
The physical quantity which has the dimensional formula ${ M }^{ 1 }{ T }^{ -3 }$ is:

Question 6 :
If pressure $P$, Velocity $V$, and time $T$ are taken as fundamental physical quantities, then the dimensional formula for force is:

Question 7 :
The dimensions of magnetic field in $M, L, T$ and $C$ (coulomb) are given as<br/>

Question 8 :
For the equation $F={ A }^{ a }{ v }^{ b }{ d }^{ c }$, where $F$ is force, $A$ is area, $v$ is velocity and $d$ is density, the dimensional analysis give the following values for the exponents.

Question 9 :
Given that the displacement of an oscillating particle is given by $y = A sin [Bx+Ct+d]$. The dimensional formula for (ABCD) is:

Question 11 :
The pressure of a gas $P=\dfrac { RT }{ v-b } { e }^{ \left( \dfrac { -aV }{ RT } \right) }$. If $V$ be the volume of gas, $R$ be the universal gas constant and $T$ be the absolute temperature then the dimensional formula of '$a$' is same as that of:

Question 12 :
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.&nbsp;

Question 13 :
Which of the following pairs of physical quantities have same dimensions?

Question 14 :
If the units of ML are doubled, then the unit of kinetic energy will become :<br/>

Question 15 :
<span>Write down the number of significant figures in the following value.</span><div>$1200 N$<br/></div>

Question 16 :
The mass of a beaker is found to be ($10.1 \pm 0.1)gm $ when empty and $(17.3 \pm 0.1)gm$ when partially filled with a liquid. What is the best value for the&nbsp;mass of the liquid together with the possible limits of accuracy?

Question 17 :
In a relation $ F = a sink_1 x + b sink_2T $ where $F, x$ and $T$ denote the force, distance and time respectively. Units of $ k_1 $ and $ k_2 $ are respectively a <br/>

Question 18 :
In head on collision of two point particles,loss in kinetic energy is given by <br/>$\displaystyle \Delta K=\frac{m_{1}m_{2}}{2(m_{1}+m_{2})}|\vec{u}_{1}-\vec{u}_{2}|^{2}(1-k^{2})$<br/>With usual notation (except $k$), the dimensional formula of quantity $k$ is

Question 19 :
5.74 gm of a substance occupies a volume of $1.2\;cm^3$. Calculate its density with due regard for significant figures.

Question 20 :
The SI unit of inductance, henry can be written as:<div><span><br/>a) $ \dfrac{weber}{ampere} $ b) </span><span>$ \dfrac{Volt-second}{ampere} $ c) </span>$ \dfrac{joule}{ampere^{2}} $ d) $Ohm-second$<br/><br/></div>

Question 21 :
<p>The dimensional formula<br>for the physical quantity $\cfrac {B \mu_0 \epsilon_0}{E}$ is : (E=intensity<br>of electric field, B-magnetic induction and symbols have their usual meaning)</p><br><br><p><br></p>

Question 22 :
If each side of cube is measured to be7.203$\mathrm { m }$ , then total surface area and the volume of the cube to appropriate&nbsp;<span>significant correct figures are</span>

Question 23 :
Stoke's law states that the viscous drag force $F$ experience by a sphere of radius a, moving with a speed v through a fluid with coefficient of viscosity $\eta$, is given by $F = 6\pi \eta av$<br>If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and a pressure difference of $P$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as<br>$\dfrac {v}{t} = k\left (\dfrac {p}{l}\right )^{a}\eta^{b}r^{c}$<br>Where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are.<br>

Question 24 :
The frequency (n) of viberation of a wire under tension depends upon the tension (T). mass per unit length (m) and vibreting length (I) of the wire.Using of the wire.Using dimensional analysis,the dependency of frequency on these quantities are

Question 25 :
The dimension of magnetic field in $\mathrm{M},\ \mathrm{L},\ \mathrm{T}$ and $\mathrm{C}$ (Coulomb) is given as :<br/><br/>