Question 1 :
The pair of quantities that do not have the same dimensions is _________________.<br/>
Question 2 :
In order to measure the period of a single pendulum using a stop clock, a student repeated the experiment for $$10$$ times and noted down the time period for each experiment as $$5.1, 5.0, 4.9, 5.1, 5.0, 4.9, 5.1, 5.0, 4.9, 4.9$$s. The correct way of expressing the result for the period is?
Question 3 :
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 6 :
Calculate area enclosed by a circle of diameter $$1.06\ m$$ to correct number of significant figures.
Question 9 :
Dimensions of '$$ohm$$' are same as that of:(Given : $$h$$ is Planck's constant and $$e$$ is charge)
Question 10 :
Mass of a body is 210 gm and its density is $$7.981 gm/{cm}^3$$. What will be its volume with regard to significant digits?<br/>
Question 12 :
If $$\mu =A+\dfrac { B }{ \lambda  } +\dfrac { C }{ { \lambda }^{ 2 } } $$ is dimensionally correct then the dimensions of A, B and C respectively are:($$\mu $$, A, B, C are constants) 
Question 13 :
Which of the following pair of quantities do not have the same dimensions?
Question 14 :
State whether the following statement is True or False. The prefix used for $$\displaystyle { 10 }^{ 3 }$$ is kilo.
Question 15 :
The proper value of significant figures in $$38.0+ 0.0035 + 0.00003$$ is:
Question 16 :
Velocity '$$V$$'  of a wave is directly proportional to modulus of elasticity '$$E$$' and density '$$d$$' of a medium. The expression of '$$V$$' using dimensional analysis is:
Question 18 :
If $${ (force) }^{ x }=\dfrac { \left( Mass \right) ^{ 2 }\left( radius \right) ^{ 2 } }{ \left( time \ period \right) ^{ 4 } } $$, then the value of $$x$$ is
Question 19 :
When a force is expressed in dyne, the number of significant figures is four. If it is expressed in newton, the number of significant figures will become:(Given: $${ 10 }^{ 5 }\ dyne=1\ N$$)
Question 20 :
The distance traveled by a body in time $$'t'$$ is given by $$x=a+bt+{ ct }^{ 2 }$$ where $$x$$ is distance, $$t$$ is time $$a, b$$ and $$c$$ are constants. The dimensional formula for $$a, b$$ and $$c$$ respectively are :
Question 21 :
Three measurements 7.1J, 7.2J and 6.7J are made as experiment and added the result with correct number of significant figures is
Question 22 :
A, B, C and D are four different physical quantifies having different dimensions. None of them is dimensionless. But we know that the equation $$AD = C\, ln(BD)$$ holds true. Then which of the combination is not a meaningful quantity 
Question 23 :
On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between.
Question 25 :
Four students measure a time interval that is known to be $$1.734$$s. The measurement recorded by each student is shown. Which measurement is the most accurate?
Question 26 :
The least count of a stop watch is $$\frac { 1 } { 5 } s$$. The time of 20 oscillations of a pendulum is measured to be $$25 s$$. What is the maximum percentage error in this measurement ?
Question 27 :
The SI unit of inductance, henry can be written as:<br/>a) $$ \dfrac{weber}{ampere} $$  b) $$ \dfrac{Volt-second}{ampere} $$   c) $$ \dfrac{joule}{ampere^{2}} $$  d) $$Ohm-second$$<br/><br/>
Question 28 :
The diameter of a wire as measured by screw gauge was found to be  $$2.620, \ 2.625, \ 2.628 \ and \ 2. 626 cm$$. Calculate absolute error in each measurement.<br/>
Question 30 :
The mass and volume of a body are $$4.237\ g$$ and $$2.5$$ $$cm^3$$, respectively. The density of the material of the body in correct significant figures is<br>
Question 31 :
The respective number of significant figures for the numbers 6.320, 6.032, 0.0006032 are then<br/>
Question 32 :
Measure of two quantities along with the precision of respective measuring instrument is:<br>$$A = 2.5 ms^{-1}\pm 0.5 ms^{-1}$$<br>$$B = 0.10s \pm 0.01 s$$<br>The value of AB will be :<br>
Question 33 :
A thin wire has a length of $$21.7 \ cm$$ and radius $$0.46\  mm$$. The volume of the wire to correct significant figures is :
Question 34 :
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 36 :
What is the order of magnitude of the distance of a quasar from us if light takes 2.9 billion years to reach us ?
Question 37 :
The respective number of significant figures for the numbers $$23.023, 0.0003$$ and $$2.1\times10^{-3}$$ are :<br>
Question 39 :
Two resistors $$R_1\, (24\, \pm\, 0.5)\, \Omega$$ are joined in series. The equivalent $$resistance$$ is 
Question 40 :
What happens to a substance when the space between its particles is decreased?
Question 41 :
A quantity $$f$$ is given by $$f=\sqrt{\dfrac{hc^5}{G}}$$ where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of $$f$$ is that of?
Question 43 :
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 44 :
Consider a vessel filled with carbodioxide at $$27^{\circ}C$$ and $$5$$ atmospheric pressure. A part of the gas is removed at $$27^{\circ}C$$ and it fills a $$3L$$ container at $$1\ atm$$ and the pressure drops to $$3.5\ atm$$ in the vessel. The volume of the vessel is:
Question 45 :
In the relation, $$\displaystyle P=\frac{\alpha }{\beta }e^{{\alpha z}/{k\theta }}$$ $$P$$ is pressure, $$Z$$ is distance, $$K$$ is Boltzmann constant and $$\displaystyle \theta $$ is the temperature. The dimensions of $$\displaystyle \beta $$ will be 
Question 46 :
Two plates have lengths measured as $$(1.9 \pm  0.3)m$$ and $$(3.5 \pm0.2)m$$. Calculate their combined length with error limits.
Question 47 :
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 48 :
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 49 :
$$16\ g$$ of oxygen and $$3\ g$$ of hydrogen are mixed and kept at $$760\ mm$$ pressure and $$0^{\circ}C$$. The total volume occupied by the mixture will be nearly.
Question 50 :
A gaseous mixture of ethene, ethane and methane having total volume $$150\ ml$$ is subjected to combustion in excess of oxygen. If percentage of methane in the original mixture is $$20\%$$ then calculate volume (in ml) of $$C{ O }_{ 2 }\left( g \right)$$ which will be obtained at same temperature and pressure.
