Question 1 :
The equation of a wave is given by $y=a sin\omega \left (\dfrac {x}{v}-k\right )$, where $\omega$ is angular velocity and $v$ is linear velocity. The dimensions of $K$ will be<br/>
Question 3 :
If 'Muscular strength' times 'Speed' is equal to power, then dimensional formula for 'Muscular strength' is:
Question 5 :
The error and the correction to be made when the zeroth division of the head scale in a Screw gauge is above index line of the pitch scale respectively are:
Question 6 :
In planetary motion the areal velocity of position vector of a planet depends on angular velocity $\omega$ and the distance $r$ of the planet from sun. If so, the correct relation for areal velocity is:
Question 8 :
When 13546 is rounded off to four significant figures, it becomes :
Question 9 :
The accuracy in the measurement of the diameter of hydrogen atom measured as $1.06 \times { 10 }^{ -10 }$ m is :
Question 11 :
Fill in the blank:<br/>The last digit in the measurement gives the first $\underline{\hspace{0.5in}}$digit.
Question 13 :
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 :
Which of the following is not used to measure the volume of a liquid or an irregular shaped object?
Question 16 :
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 17 :
Two quantities $A$ and $B$ have different dimensions. Which operation is physically meaningful ?
Question 22 :
The pair of quantities that do not have the same dimensions is _________________.<br/>
Question 23 :
Two numbers are given as i) 20.96 and ii) 0.0003125. Rounding off above numbers to 3 significant figures will lead to :
Question 25 :
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 26 :
The density of steel rod is $7850\ kg/m^3$, its mass is $5\ kg$.Find its volume?
Question 27 :
Which of the following does not give the unit of energy ? 
Question 28 :
The unit and dimensions of impedance in terms of charge Q are
Question 29 :
N divisions on the main scale of vernier callipers coincide with (N+1) divisions on the vernier scale. If each divisions on the main scale of a units, determine the least count of instrument.<br>
Question 30 :
The dimensions of $\dfrac{(velocity)^2}{radius} $ are the same as that of:
Question 31 :
Subtract $2.5 \times {10}^{4}$ from $3.9 \times {10}^{5}$ and give the answer to correct number of significant figures.
Question 33 :
If the ratio of fundamental units in two systems is 1 :3, then the ratio of momentum in the two systems is:
Question 34 :
The dimension of permittivity (${ \varepsilon }_{ 0 }$) are ______. Take $Q$ as the dimension of charge.
Question 35 :
Which of the following is used to measure the volume of a regular shaped object?
Question 36 :
The prefix used for denoting an order of magnitude of $\displaystyle { 10 }^{ 6 }$ is ___________.
Question 37 :
Multiply 107.88 by 0.610 and express the result with a correct number of significant figures.
Question 38 :
The quantity $\dfrac { { e }^{ 2 } }{ 2{ \epsilon}_{0 }hc } $ has the dimensions of:
Question 40 :
A force $F$ is given as $F = at + bt^2$, where t is time. What are the dimensions of a and b?
Question 41 :
The volume of a stone can be determined by the displacement method using a measuring cylinder. True or false.
Question 44 :
Which two of the following five physical parameters have the same dimensions?<br> A) Energy Density<br>B) Refractive Index<br>C) Dielectric Constant<br>D) Young's Modulus<br>E)Magnetic Field<br><br>
Question 45 :
Let $Q$ denote the charge on the plate of a capacitor of capacitance $C$. The dimensional formula for $\dfrac {Q^2}{C}$ is
Question 46 :
By rounding off, (a) $20.96$ and (b) $0.0003125$ to three significant figures, we get
Question 47 :
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 48 :
The dimension of magnetic induction in $M, L, T$ and $C$ (Coloumb) is given as:
Question 49 :
If $m$ is the mass of drop of a liquid of radius $r$, then $\ \dfrac { mg }{ \pi r } \ $ has the same dimensions of : 
Question 51 :
The quantity $X$ is given by ${\varepsilon _o}L\frac{{\Delta V}}{{\Delta T}}$, where ${\varepsilon _o}$ is the permittivity of free space, $L$ is a length, ${\Delta V}$ is a potential difference and ${\Delta T}$ is a time interval. The dimensional formula for $X$ is the same as that of
Question 52 :
A science student takes 100 observations in an experiment. Second time he takes 500 observations in the same experiment. By doing so the possible error becomes :
Question 53 :
Assertion: The SI unit of volume is $m^3$.
Reason: Volume is a derived quantity of length.
Question 54 :
Using mass(M), length (L), time(T), and electric current(A) as fundamental quantities, the dimensions of permittivity will be
Question 55 :
What volume of decinormal ${ K }_{ 2 }{ Cr }_{ 2 }{ O }_{ 7 }$ solution would be needed to convert 1.19 g of tin to stannic chloride in an acidic medium? (${ A }_{ Sn }\ =\<br/><br/>119$)
Question 56 :
Select the correct alternative<br>(b) A metallic piece displaces water of volume 15 ml. The volume of piece is :
Question 58 :
Find density when a mass of 9.23 kg occupies a volume of $\displaystyle 1.1m^{3}$ with due regard to significant figures.<br/>
Question 59 : <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 60 :
The velocity $v$ of a particle at time $t$ is given by $v=at+\dfrac {b}{t+c}$ The dimensions of $a, b, c$ are respectively
Question 61 :
Position of a body with acceleration a is given by $x=ka^mt^n$, here t is time, find the dimension of m and n.
Question 62 :
State if the following statements are true or false. Correct the statement if it is false.<br>The error in reading a scale due to the wrong positioning of the eye is called human error.
Question 63 :
The equation of a gas is given by : $ PV= AT+BT^2 $, where $ P= $ pressure, $ V= $ volume, $ T= $ temperature. The dimensions of constant B are
Question 64 :
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is?
Question 65 :
4.5 g of Al (atomic mass 27 amu) is deposited at cathode from $ Al^{3+} $ solution by a certain quantity of charge. The volume of $H_2$ produced at STP from 11+ ions in solution by the same quantity of charge will be ?
Question 67 :
The dimension of $\dfrac{h}{mv}$ is: ($h$ <br> $=$ planks constant, $m$= mass, $v$=velocity)
Question 69 :
The Van der Waal's equation of state for some gases can be expressed as:<br>$(P + \dfrac{a}{V^2})(V - b) = RT$<br>where P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a,b and R are constants.<br>In the above problem, the dimensional formula for RT is same as that of
Question 70 :
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 72 :
Which of the following physical quantities represent the dimensions of $\dfrac { b }{ a }$ in the relation $ P=\dfrac { { x }^{ 2 }-b }{ at }$, where $ P$ is power, $x$ is distance and $t$ is time.
Question 73 :
In a experiment to measure the height of a bridge by dropping a stone into water underneath,if the error in the measurement of times is $0.1s$ at the end of $2s$,then the error in the estimation of the height of the bridge will be
Question 74 :
Write down the significant figures in the following<br>1. $5238$ N<br>2. $4200 $kg
Question 75 :
In the formula $P=\displaystyle\frac{nRT}{V-b}e^{-\scriptstyle\frac{a}{RTV}}$. Find the dimensions of $a$ and $b$ where $P=pressure,\;n=number\;of\;moles,\;T=temperature,\;V=volume\;and\;\\R=universal\;gas\;constant$.
Question 76 :
The radius of a thin wire is 0.16 mm. The area of cross-section taking significant figure into consideration in square millimeters is?<br/>
Question 77 :
A cube has a side of length $2.342 m$. The surface area and volume in correct significant figures are respectively:<br/>
Question 79 :
The method of dimensional analysis can be used to derive which of the following relations ?
Question 80 :
The dimensions of $\frac{1}{{{\mu _0}{ \in _0}}}$ is (where symbols have their usual menaing)
Question 81 :
When 97.52 is divided by 2.54, the correct result is :
Question 82 :
The dimensional formula of a physical quantity is $\displaystyle [{ M }^{ 1 }{ L }^{ 1 }{ T }^{ -2 }]$. What is its SI unit?
Question 84 :
The multiplication of 10.610 with 0.210 upto correct number of significant figure is
Question 85 :
In equation $ y=x^2 cos^22 \pi\dfrac{\beta y'}{\alpha} $, if the units of $ x,\alpha,\beta $ are $ m,s^{-1} $and $ ({ms}^{-1})^{-1} $ respectively, then units of <i>y</i> and <i>y</i>' are
Question 89 :
In the screw gauge, the screw should be moved in the same direction to avoid which of the following error?
Question 91 :
Assertion: The number of significant figures depends on the least count of measuring instrument.
Reason: Significant figures define the accuracy of measuring instrument.
Question 93 :
A person was weighing $102.1\  kg$ last week and gained $0.28 \ kg$ this week. His weight as of now is correctly expressed as :
Question 94 :
The Van der Waal's equation of state for some gases can be expressed as:<br>$(P + \dfrac{a}{V^2})(V - b) = RT$<br>where P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a,b and R are constants.<br>Which of the following does not have the same dimensional formula as that for RT?
Question 95 :
In the equation of motion, $\displaystyle x=at+{ bt }^{ 2 }$ the units of a and b are respectively (where $x$ is in metres and $t$ is in seconds)
Question 96 :
What are the number of significant figures in the measurement $ 0.0040\times10^{-15}m $?
Question 98 :
At standard pressure and temperature conditions the density of a gas in $g$ and whose molecular weight is $45$, then volume occupied by gas in $1$ is:
Question 100 :
If $\displaystyle Z\,=\, \frac{A^4B^{1/3}}{CD^{3/2}}$ and $\Delta A$, $\Delta B$, $\Delta C$, and $\Delta D$ are their absolute errors in A, B, C and D respectively. The relative error in Z is then <br/>
