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question_answer1)
In a new system of units, the fundamental quantities mass, length and time are replaced by acceleration 'a', density \['\rho '\] and frequency\[f\]. The dimensional formula for force in this system is
A)
\[[\rho {{a}^{4}}f]\] done
clear
B)
\[[\rho {{a}^{4}}{{f}^{-6}}]\] done
clear
C)
\[[{{\rho }^{-1}}{{a}^{-4}}{{f}^{6}}]\] done
clear
D)
\[[{{\rho }^{-1}}{{a}^{-4}}{{f}^{6}}]\] done
clear
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question_answer2)
When two quantities are divided, the relative error in the result is given by
A)
The product of the relative error in the individual quantities done
clear
B)
The quotient of the relative error in the individual quantities done
clear
C)
The difference of the relative error in the individual quantities done
clear
D)
The sum of the relative error in the individual quantities done
clear
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question_answer3)
The momentum of an electron in an orbit is \[h/\lambda \] where A is a constant and \[\lambda \]f is wavelength associated with it. The nuclear magneton of electron of charge e and mass \[{{m}_{e}}\]is given as \[{{\mu }_{n}}\] \[=\frac{eh}{3672\pi {{m}_{e}}}\].The dimensions of \[{{\mu }_{n}}\] are \[(A\to current)\]
A)
\[[M{{L}^{2}}A]\] done
clear
B)
\[[M{{L}^{3}}A]\] done
clear
C)
\[[{{L}^{2}}A]\] done
clear
D)
\[[M{{L}^{2}}]\] done
clear
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question_answer4)
If \[Z={{A}^{3}}\], then \[\frac{\Delta Z}{Z}=\_\_\_\_\]
A)
\[\frac{\Delta {{A}^{3}}}{A}\] done
clear
B)
\[{{\left( \frac{\Delta {{A}^{{}}}}{A} \right)}^{3}}\] done
clear
C)
\[3\left( \frac{\Delta {{A}^{{}}}}{A} \right)\] done
clear
D)
\[{{\left( \frac{\Delta {{A}^{{}}}}{A} \right)}^{1/3}}\] done
clear
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question_answer5)
The pitch and the number of circular scale divisions in a screw gauge with least count 0.02 mm are respectively
A)
1mm and 100 done
clear
B)
0.5 mm and 50 done
clear
C)
1 mm and 50 done
clear
D)
0.5 mm and 100 done
clear
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question_answer6)
If \[L=2.331cm,\,\,B=2.1cm,\]then \[L+B=\]
A)
4.4cm done
clear
B)
4cm done
clear
C)
4.43cm done
clear
D)
4.431cm done
clear
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question_answer7)
What is the correct number of significant figures in 0.0003026?
A)
Four done
clear
B)
Seven done
clear
C)
Eight done
clear
D)
Six done
clear
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question_answer8)
Number of significant figures in expression \[\frac{4.327g}{2.51\,c{{m}^{3}}}\] is
A)
2 done
clear
B)
4 done
clear
C)
3 done
clear
D)
5 done
clear
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question_answer9)
Error in the measurement of radius of a sphere is 1 %. Then error in the measurement of volume is
A)
1% done
clear
B)
5% done
clear
C)
3% done
clear
D)
8% done
clear
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question_answer10)
In order to measure physical quantities in the sub-atomic world, the quantum theory often employs energy [E], angular momentum [J] and velocity [c] as fundamental dimensions instead of the usual mass, length and time. Then, the dimension of pressure in this theory is
A)
\[\frac{{{[E]}^{4}}}{{{[J]}^{3}}{{[c]}^{3}}}\] done
clear
B)
\[\frac{{{[E]}^{2}}}{[J][c]}\] done
clear
C)
\[\frac{[E]}{{{[J]}^{2}}{{[c]}^{2}}}\] done
clear
D)
\[\frac{{{[E]}^{3}}}{{{[J]}^{2}}{{[c]}^{2}}}\] done
clear
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question_answer11)
In equation\[r={{m}^{2}}sin\pi t\] , where t represents time. If the unit of m is N, then the unit of r is
A)
N done
clear
B)
\[{{N}^{2}}\] done
clear
C)
Ns done
clear
D)
\[{{N}^{2}}s\] done
clear
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question_answer12)
If \[x=at+b{{t}^{2}}\], where x is the distance travelled by the body in kilometers while t is the time in seconds, then the unit of & is
A)
km/s done
clear
B)
\[kms\] done
clear
C)
\[km/{{s}^{2}}\] done
clear
D)
\[km{{s}^{2}}\] done
clear
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question_answer13)
The electric field is given by \[\overset{\to }{\mathop{E}}\,=\frac{A}{{{x}^{3}}}\hat{i}+By\hat{j}+C{{z}^{2}}\hat{k}\].The SI units of A, B and C are respectively: [where x, y and z are in m]
A)
\[\frac{N-{{m}^{3}}}{{{x}^{3}}},V/{{m}^{2}},\,N/{{m}^{2}}-C\] done
clear
B)
\[V-{{m}^{2}},V/m,\,N/{{m}^{2}}-C\] done
clear
C)
\[V/{{m}^{2}},V/m,\,N-C/{{m}^{2}}\] done
clear
D)
\[V/m,\,N-{{m}^{3}}/C,\,N-C/m\] done
clear
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question_answer14)
If unit of length and force are increased 4 times. The unit of energy
A)
Is increased by 4 times done
clear
B)
Is increased by 16 times done
clear
C)
Is increased by 8 times done
clear
D)
Remains unchanged done
clear
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question_answer15)
The density of a material in CGS system of unit is\[4g/c{{m}^{3}}\]. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be
A)
0.4 done
clear
B)
40 done
clear
C)
400 done
clear
D)
0.04 done
clear
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question_answer16)
Young's modulus of steel is\[1.9\times {{10}^{11}}\,N/{{m}^{2}}\]. When expressed in CGS units of \[ne/c{{m}^{2}}\], it will be equal to (\[(1N={{10}^{5}}\,dyne,\,1{{m}^{2}}\,={{10}^{4}}c{{m}^{2}})\]
A)
\[1.9\times {{10}^{10}}\] done
clear
B)
\[1.9\times {{10}^{11}}\] done
clear
C)
\[1.9\times {{10}^{12}}\] done
clear
D)
\[1.9\times {{10}^{13}}\] done
clear
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question_answer17)
The speed of light in vacuum, c, depends on two fundamental constants, the permeability of free space, \[{{\mu }_{0}}\] d me permittivity of free space,\[{{\varepsilon }_{0}}.\] The speed of light is given by\[c=\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}\]. The units of \[{{\varepsilon }_{0}}\] are \[{{N}^{-1}}{{C}^{2}}{{m}^{-2}}\]. The units for \[{{\mu }_{0}}\] are
A)
\[k{{g}^{-1}}{{m}^{-1}}{{C}^{2}}\] done
clear
B)
\[kgm{{C}^{-2}}\] done
clear
C)
\[kg\,m{{s}^{-4}}{{C}^{-2}}\] done
clear
D)
\[k{{g}^{-1}}{{s}^{-3}}{{C}^{-2}}\] done
clear
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question_answer18)
Which of the following quantities has not been expressed in proper unit?
A)
Torque, newton metre done
clear
B)
Stress, newton \[metr{{e}^{-2}}\] done
clear
C)
Modulus of elasticity, newton \[metr{{e}^{-2}}\] done
clear
D)
Surface tension, newton \[metr{{e}^{-2}}\] done
clear
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question_answer19)
E, m, J and G denote energy, mass, angular momentum and gravitational constant respectively, then the unit of \[\frac{E{{J}^{2}}}{{{m}^{5}}{{G}^{2}}}\]is
A)
Newton done
clear
B)
metre done
clear
C)
Kilogram done
clear
D)
unitless done
clear
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question_answer20)
In a certain system of units, 1 unit of time is 5 sec, 1 unit of mass is 20 kg and 1 unit of length is 10m. In this system, one unit of power will correspond to-
A)
16 watts done
clear
B)
\[\frac{1}{16}\]watts done
clear
C)
25 watts done
clear
D)
\[\frac{1}{25}\]watts done
clear
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question_answer21)
The moment of inertia of a body rotating about a given axis is \[6.0\text{ }kg\text{ }{{m}^{2}}\]in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is 5 cm and the unit of mass is 10 g?
A)
\[2.4\times {{10}^{3}}\] done
clear
B)
\[2.4\times {{10}^{5}}\] done
clear
C)
\[6.0\times {{10}^{3}}\] done
clear
D)
\[6.0\times {{10}^{5}}\] done
clear
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question_answer22)
The dimensional formula for relative density is
A)
\[[M{{L}^{-3}}]\] done
clear
B)
\[[{{M}^{o}}{{L}^{-3}}]\] done
clear
C)
\[[{{M}^{o}}{{L}^{o}}{{T}^{-1}}]\] done
clear
D)
\[[{{M}^{o}}{{L}^{o}}{{T}^{o}}]\] done
clear
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question_answer23)
The dimensions of speed and velocity are
A)
\[[{{L}^{2}}T],[L{{T}^{-1}}]\] done
clear
B)
\[[L{{T}^{-1}}],[L{{T}^{-2}}]\] done
clear
C)
\[[LT],\,[LT]\] done
clear
D)
\[[L{{T}^{-1}}],[L{{T}^{-1}}]\] done
clear
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question_answer24)
\[[ML{{T}^{-1}}]+[ML{{T}^{-1}}]=..........\]
A)
\[[{{M}^{o}}{{L}^{o}}{{T}^{o}}]\] done
clear
B)
\[[ML{{T}^{-1}}]\] done
clear
C)
\[2[ML{{T}^{-1}}]\] done
clear
D)
None of these done
clear
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question_answer25)
The physical quantity that has no dimensions is
A)
Strain done
clear
B)
angular velocity done
clear
C)
Angular momentum done
clear
D)
linear momentum done
clear
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question_answer26)
Dimensions of specific heat are
A)
\[[M{{L}^{2}}{{T}^{-2}}K]\] done
clear
B)
\[[M{{L}^{2}}{{T}^{-2}}{{K}^{-1}}]\] done
clear
C)
\[[M{{L}^{2}}{{T}^{2}}{{K}^{-1}}]\] done
clear
D)
\[[{{L}^{2}}{{T}^{-2}}{{K}^{-1}}]\] done
clear
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question_answer27)
The dimensions of coefficient of self-inductance are
A)
\[[M{{L}^{2}}{{T}^{-2}}{{A}^{-2]}}]\] done
clear
B)
\[[M{{L}^{2}}{{T}^{-2}}{{A}^{-1}}]\] done
clear
C)
\[[ML{{T}^{-2}}{{A}^{-2}}]\] done
clear
D)
\[[ML{{T}^{-2}}{{A}^{-1}}]\] done
clear
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question_answer28)
The division of energy by time is X. The dimensional formula of X is same as that of
A)
Momentum done
clear
B)
power done
clear
C)
Torque done
clear
D)
electric field done
clear
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question_answer29)
Which of the following is a dimensional constant?
A)
Refractive index done
clear
B)
Dielectric constant done
clear
C)
Relative density done
clear
D)
Gravitational constant done
clear
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question_answer30)
Which one of the following represents the correct dimensions of the coefficient of viscosity?
A)
\[[M{{L}^{-1}}{{T}^{-1}}]\] done
clear
B)
\[[ML{{T}^{-1}}]\] done
clear
C)
\[[M{{L}^{-1}}{{T}^{-2}}]\] done
clear
D)
\[[M{{L}^{-2}}{{T}^{-2}}]\] done
clear
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question_answer31)
The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimensions of
A)
Time done
clear
B)
frequency done
clear
C)
Angular momentum done
clear
D)
velocity done
clear
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question_answer32)
Two quantities A and B have same dimensions which mathematical operation given below is physically meaningful?
A)
\[A/B\] done
clear
B)
\[A+{{B}^{2}}\] done
clear
C)
\[{{A}^{2}}-B\] done
clear
D)
\[A={{B}^{2}}\] done
clear
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question_answer33)
The solar constant is defined as the energy incident per unit area per second. The dimensional formula for solar constant is
A)
\[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] done
clear
B)
\[[ML{{T}^{-2}}]\] done
clear
C)
\[[M{{L}^{2}}{{T}^{-2}}]\] done
clear
D)
\[[M{{L}^{0}}{{T}^{-3}}]\] done
clear
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question_answer34)
Distance travelled by a particle at any instant ?t? can be represented as \[S=A(t+B)+C{{t}^{2}}\].The dimensions of B are
A)
\[[{{M}^{0}}{{L}^{1}}{{T}^{-1}}]\] done
clear
B)
\[[{{M}^{0}}{{L}^{0}}{{T}^{1}}]\] done
clear
C)
\[[{{M}^{0}}{{L}^{-1}}{{T}^{-2}}]\] done
clear
D)
\[[{{M}^{0}}{{L}^{2}}{{T}^{-2}}]\] done
clear
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question_answer35)
If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
A)
\[(P-Q)/R\] done
clear
B)
\[PQ-R\] done
clear
C)
\[PQ/R\] done
clear
D)
\[(PQ-{{Q}^{2}})/R\] done
clear
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question_answer36)
Dimensions of 'resistance' are same as (where h is Planck's constant and e is charge)
A)
\[\frac{h}{e}\] done
clear
B)
\[\frac{{{h}^{2}}}{e}\] done
clear
C)
\[\frac{h}{{{e}^{2}}}\] done
clear
D)
\[\frac{{{h}^{2}}}{{{e}^{2}}}\] done
clear
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question_answer37)
If \[v=\frac{a}{t}+b{{t}^{3}}\] where \[v=\]velocity and t is time The dimensional formula of a and b are
A)
\[[T],\,[{{T}^{-3}}]\] done
clear
B)
\[[L],\,[L{{T}^{-4}}]\] done
clear
C)
\[[{{T}^{-3}}],[T]\] done
clear
D)
\[[L{{T}^{-4}}],[L]\] done
clear
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question_answer38)
The displacement of a body at a particular second n is given by the expression \[{{S}_{nth}}=u+\frac{a}{2}(2n-1)\]. The dimensional formula of \[{{S}_{nth}}\] in this equation is
A)
\[[{{M}^{1}}{{L}^{0}}{{T}^{1}}]\] done
clear
B)
\[[{{M}^{0}}{{L}^{1}}{{T}^{0}}]\] done
clear
C)
\[[{{M}^{0}}{{L}^{1}}{{T}^{-1}}]\] done
clear
D)
\[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] done
clear
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question_answer39)
In the equation\[P=\frac{RT}{V-b}{{e}^{\frac{aV}{RT}}}\] \[V=\]Volume, \[P=\]Pressure, \[R=\]universal gas constant, and \[T=\]temperature The dimensional formula of a is same as that of
A)
V done
clear
B)
P done
clear
C)
T done
clear
D)
R done
clear
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question_answer40)
Let Q denote the charge on the plate of a capacitor of capacitance C. The dimensional formula for \[\frac{{{Q}^{2}}}{C}\]is
A)
\[[{{L}^{2}}{{M}^{2}}T]\] done
clear
B)
\[[LM{{T}^{2}}]\] done
clear
C)
\[[{{L}^{2}}M{{T}^{-2}}]\] done
clear
D)
\[[{{L}^{2}}{{M}^{2}}{{T}^{2}}]\] done
clear
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question_answer41)
Suppose the kinetic energy of a body oscillating with amplitude A and at a distance x is given by \[K=\frac{Bx}{{{x}^{2}}+{{A}^{2}}}\] The dimensions of B are the same as that of
A)
work/time done
clear
B)
work x distance done
clear
C)
work/distance done
clear
D)
work x time done
clear
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question_answer42)
If the dimensions of a physical quantity are given by \[{{M}^{a}}{{L}^{b}}{{T}^{c}}\], then the physical quantity will be
A)
Velocity if \[a=1,\text{ }b=0,\text{ }c=-1\] done
clear
B)
Acceleration if \[a=1,\text{ }b=1,\text{ }c=-2\] done
clear
C)
Force if \[a=0,\text{ }b=-1,\text{ }c=-2\] done
clear
D)
Pressure if \[a=1,\text{ }b=-1,\text{ }c=-2\] done
clear
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question_answer43)
Which one of the following represents the correct dimensions of the gravitational constant?
A)
\[[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\] done
clear
B)
\[[ML{{T}^{-1}}]\] done
clear
C)
D)
\[[M{{L}^{-2}}{{T}^{-2}}]\] done
clear
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question_answer44)
Write the dimensions of \[a\times b\]in the relation \[E=\frac{b-{{x}^{2}}}{at}\]where E is the energy, x is the displacement and t is time
A)
\[M{{L}^{2}}T\] done
clear
B)
\[{{M}^{-1}}{{L}^{2}}{{T}^{1}}\] done
clear
C)
\[M{{L}^{2}}{{T}^{-2}}\] done
clear
D)
\[ML{{T}^{-2}}\] done
clear
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question_answer45)
The dimensions of the quantity \[\overset{\to }{\mathop{E}}\,\times \overset{\to }{\mathop{B}}\,\]where\[\overset{\to }{\mathop{E}}\,\] represents the electric field and \[\overset{\to }{\mathop{B}}\,\] the magnetic field may be given as:
A)
\[[M{{L}^{3}}]\] done
clear
B)
\[[{{M}^{2}}L{{T}^{-5}}{{A}^{-2}}]\] done
clear
C)
\[[{{M}^{2}}{{L}^{-3}}{{T}^{2}}{{A}^{-1}}]\] done
clear
D)
\[[ML{{T}^{-2}}{{A}^{-2}}]\] done
clear
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question_answer46)
What are the dimensions of A/B in the relation \[F=A\sqrt{x}+B{{t}^{2}}\], where F is the force, x is the distance and t is time?
A)
\[M{{L}^{2}}{{T}^{-2}}\] done
clear
B)
\[{{L}^{-1/2}}{{T}^{2}}\] done
clear
C)
\[{{L}^{-1/2}}{{T}^{-1}}\] done
clear
D)
\[L{{T}^{-2}}\] done
clear
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question_answer47)
A physical quantity x depends on quantities y and z as follows: \[x=Ay+B\text{ }tan\text{ }Cz\], where A, B and C are constants. Which of the following do not have the same dimensions :
A)
x and B done
clear
B)
C and \[{{z}^{-1}}\] done
clear
C)
y and B/A done
clear
D)
x and A done
clear
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question_answer48)
A quantity X is given by \[{{\varepsilon }_{0}}L\frac{\Delta V}{\Delta t}\] where \[{{\in }_{0}}\] is the permittivity of the 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
A)
Resistance done
clear
B)
charge done
clear
C)
Voltage done
clear
D)
current done
clear
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question_answer49)
The thrust developed by a rocket-motor is given by \[F=mv+A({{P}_{1}}-{{P}_{2}})\] where m is the mass of the gas ejected per unit time, v is velocity of the gas, A is area of cross-section of the nozzle, \[{{P}_{1}}\] and \[{{P}_{2}}\] are the pressures of the exhaust gas and surrounding atmosphere. The formula dimensionally
A)
Correct done
clear
B)
Wrong done
clear
C)
Sometimes wrong, sometimes correct done
clear
D)
Data is not adequate done
clear
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question_answer50)
A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation \[AD=C\text{ }In\text{ (}BD\text{)}\]holds true. Then which of the combination is not a meaningful quantity?
A)
\[\frac{C}{BD}-\frac{A{{D}^{2}}}{C}\] done
clear
B)
\[{{A}^{2}}-{{B}^{2}}{{C}^{2}}\] done
clear
C)
\[\frac{A}{B}-C\] done
clear
D)
\[\frac{(A-C)}{D}\] done
clear
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question_answer51)
If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum \[{{\mu }_{0}}\] can be expressed in units of
A)
\[\left( \frac{h}{m{{e}^{2}}} \right)\] done
clear
B)
\[\left( \frac{hc}{m{{e}^{2}}} \right)\] done
clear
C)
\[\left( \frac{h}{c{{e}^{2}}} \right)\] done
clear
D)
\[\left( \frac{m{{c}^{2}}}{h{{e}^{2}}} \right)\] done
clear
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question_answer52)
A boy recalls the relation almost correctly but for gets where to put the constant c (speed of light). He writes; \[m=\frac{{{m}_{0}}}{\sqrt{1-{{v}^{2}}}}\], where m and \[{{m}_{0}}\] stand masses and v for speed. Right place of c is
A)
\[m=\frac{c{{m}_{0}}}{\sqrt{1-{{v}^{2}}}}\] done
clear
B)
\[m=\frac{{{m}_{0}}}{c\sqrt{1-{{v}^{2}}}}\] done
clear
C)
\[m=\frac{{{m}_{0}}}{\sqrt{{{c}^{2}}-{{v}^{2}}}}\] done
clear
D)
\[m=\frac{{{m}_{0}}}{\sqrt{1-\frac{{{v}^{2}}}{{{c}^{2}}}}}\] done
clear
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question_answer53)
When a small sphere moves at low speed through a fluid, the viscous force F, opposing the motion is experimentally found to depend upon the radius r, the velocity v of the sphere and the viscosity \[\eta \] of the fluid. Expression for force is
A)
\[4\pi \eta r{{v}^{2}}\] done
clear
B)
\[4\pi \eta {{r}^{2}}v\] done
clear
C)
\[2\pi \eta {{r}^{2}}v\] done
clear
D)
\[6\pi \eta rv\] done
clear
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question_answer54)
With the usual notations, the following equation \[{{S}_{t}}=u+\frac{1}{2}a(2t-1)\]is
A)
Only numerically correct done
clear
B)
Only dimensionally correct done
clear
C)
Both numerically and dimensionally correct done
clear
D)
Neither numerically nor dimensionally correct done
clear
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question_answer55)
Dimensionally wavelength is equivalent to
A)
\[\frac{E\sqrt{LC}}{B}\] done
clear
B)
\[\frac{E}{B\sqrt{LC}}\] done
clear
C)
\[\frac{B\sqrt{LC}}{E}\] done
clear
D)
\[\frac{B}{E\sqrt{LC}}\] done
clear
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question_answer56)
If velocity (V), force (F) and energy (E) are taken as fundamental units, then dimensional formula for mass will be
A)
\[{{V}^{-2}}{{F}^{0}}{{E}^{3}}\] done
clear
B)
\[{{V}^{0}}F{{E}^{2}}\] done
clear
C)
\[V{{F}^{-2}}{{E}^{0}}\] done
clear
D)
\[{{V}^{-2}}{{F}^{0}}E\] done
clear
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question_answer57)
The period of a body under SHM is represented by\[T={{P}^{a}}{{D}^{b}}{{S}^{c}}\]; where P is pressure, D is density and S is surface tension. The value of a, b and c are.
A)
\[\frac{-3}{2},\frac{1}{2},1\] done
clear
B)
\[-1,-2,3\] done
clear
C)
\[\frac{1}{2},\,\frac{3}{2},\frac{1}{2}\] done
clear
D)
\[1,\,2,\,\frac{1}{3}\] done
clear
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question_answer58)
A physical quantity of the dimensions of length that can be formed out of c, G and \[\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}}\] is [c is velocity of light, G is universal constant of gravitation and e is charge]
A)
\[{{c}^{2}}\left[ G\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}} \right]\] done
clear
B)
\[\frac{1}{{{c}^{2}}}{{\left[ \frac{{{e}^{2}}}{G4\pi {{\varepsilon }_{0}}} \right]}^{1/2}}\] done
clear
C)
\[\frac{1}{c}G\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}}\] done
clear
D)
\[\frac{1}{{{c}^{2}}}{{\left[ G\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}} \right]}^{1/2}}\] done
clear
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question_answer59)
Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon the velocity v of the water, its density \[\rho \] and the acceleration due to gravity g. Then m is directly proportional to:
A)
\[{{\nu }^{3}}\] done
clear
B)
\[{{\nu }^{4}}\] done
clear
C)
\[{{\nu }^{5}}\] done
clear
D)
\[{{\nu }^{6}}\] done
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question_answer60)
A spherical body of mass m and radius r is allowed to fall in a medium of viscosity\[\eta \]. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant\[(\tau )\]. Dimensionally \[\tau \] can be represented by:
A)
\[\frac{m{{r}^{2}}}{6\pi \eta }\] done
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B)
\[\sqrt{\left( \frac{6\pi mr\eta }{{{g}^{2}}} \right)}\] done
clear
C)
\[\frac{m}{6\pi \eta rv}\] done
clear
D)
None of these done
clear
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question_answer61)
If x and R stands for distance. Then which of the following is dimensionally same as\[\int{\frac{Rdx}{{{x}^{2}}}}\]?
A)
\[R{{x}^{2}}\] done
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B)
\[2xR\] done
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C)
\[\frac{R}{x}\] done
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D)
\[-\frac{{{R}^{2}}}{x}\] done
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question_answer62)
The unit of the coefficient of viscosity in S.I. system is
A)
m/kg-s done
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B)
\[m-s/k{{g}^{2}}\] done
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C)
\[kg/m-{{s}^{2}}\] done
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D)
kg/m-s done
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question_answer63)
The unit of the Stefan-Boltzmann's constant is
A)
\[W/{{m}^{2}}{{k}^{4}}\] done
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B)
\[W/{{m}^{2}}\] done
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C)
\[W/{{m}^{2}}K\] done
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D)
\[W/{{m}^{2}}{{K}^{2}}\] done
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question_answer64)
Unit of specific resistance is
A)
\[ohm/{{m}^{2}}\] done
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B)
\[ohm/{{m}^{3}}\] done
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C)
\[ohm-m\] done
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D)
\[ohm/m\] done
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question_answer65)
Unit of magnetic moment is
A)
ampere-\[metr{{e}^{2}}\] done
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B)
ampere-metre done
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C)
weber-\[metr{{e}^{2}}\] done
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D)
weber/metre done
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question_answer66)
Surface tension of a liquid is 70 dyne/cm. Its value in SI is
A)
\[70N/m\] done
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B)
\[7\times {{10}^{-2}}N/m\] done
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C)
\[7\times {{10}^{2}}N/m\] done
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D)
\[7\times {{10}^{3}}N/m\] done
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question_answer67)
Which of the following represents incorrect unit?
A)
Pressure \[=N{{m}^{2}}\] done
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B)
Surface tension \[=N/m\] done
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C)
\[Energy=kg-m/sec\] done
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D)
\[\frac{Stress}{Strain}=N/{{m}^{2}}\] done
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question_answer68)
Which one of the following is not measured in units of energy?
A)
Couple x angle done
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B)
Moment of inertia \[\times {{(angular\text{ }velocity)}^{2}}\] done
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C)
\[Force~\,\times \,distance\] done
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D)
\[Impulse\,\times \,time\] done
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question_answer69)
The numerical values of young's modulus in S.I. unit is \[\beta \]. What is its numerical value in \[cgs\] system?
A)
\[\beta \] done
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B)
10\[\beta \] done
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C)
\[\beta \]/10 done
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D)
100\[\beta \] done
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question_answer70)
In the eqn.\[\left( P+\frac{a}{{{V}^{2}}} \right)(v-b)=cons\text{tant}\], the Unit of a is
A)
\[dyne\times c{{m}^{5}}\] done
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B)
\[dyne\times c{{m}^{4}}\] done
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C)
\[dyne/c{{m}^{3}}\] done
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D)
\[dyne\times c{{m}^{2}}\] done
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question_answer71)
The value of resistance is \[10.845\Omega \] and the value of current is 3.23 A. The potential difference is 35.02935 volt. Its value in significant number would be
A)
35V done
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B)
35.0V done
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C)
35.03V done
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D)
35.029V done
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question_answer72)
Which of the following statements is/are correct?
I. 345.726 has six significant figures. |
II. 0.004289 has seven significant figures. |
III. 125000 has three significant figures. |
IV. 9.0042 has five significant figures. |
A)
I only done
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B)
II only done
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C)
I, III and IV done
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D)
II, III and IV done
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question_answer73)
Resistance \[R=V/I\], here \[V=(100\pm 5)\text{ }V\]and\[I=(10\pm 0.2)\text{ }A\]. Find percentage error in R.
A)
5% done
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B)
2% done
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C)
7% done
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D)
3% done
clear
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question_answer74)
A wire has a mass \[0.3\pm 0.003\text{ }g\], radius \[0.5\pm 0.005\text{ }mm\] and length \[6\pm 0.06\text{ }on\]. The maximum percentage error in the measurement of its density is
A)
1 done
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B)
2 done
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C)
3 done
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D)
4 done
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question_answer75)
The pitch of the screw gauge is 0.5 mm. Its circular scale contains 50 divisions. The least count of the screw gauge is
A)
0.001mm done
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B)
0.01mm done
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C)
0.02mm done
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D)
0.025mm done
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question_answer76)
In a vernier callipers N division of vernier coincide with \[(N-1)\] divisions of main scale in which length of a division is 1 mm. The least count of the instrument in cm is
A)
N done
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B)
\[N-1\] done
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C)
\[\frac{1}{10N}\] done
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D)
\[(1/N)-1\] done
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question_answer77)
One centimeter on the main scale of a vernier calipers is divided into 10 equal parts. If 10 divisions of vernier coincide with 8 small divisions of the main scale, the least count of vernier calipers is
A)
0.01 cm done
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B)
0.02 cm done
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C)
0.05 cm done
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D)
0.005 cm done
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question_answer78)
Relative density of a metal may be found with the help of spring balance. In air the spring balance reads \[(5.00~\,\,\pm \,\,0.05)\text{ }N\]and in water it reads\[\text{(}4.00\,\,\pm \,\,0.05\text{) }N\]. Then, the relative density along with the maximum permissible percentage error would be
A)
\[(5.00\,\,\pm \,\,0.05)\] done
clear
B)
\[(5.00\,\,\pm \,\,11%)\] done
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C)
\[(5.00\,\,\pm \,\,0.10)\] done
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D)
\[(5.00\,\,\pm \,\,6%)\] done
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question_answer79)
The refractive index of water measured by the relation \[\mu =\frac{real\,depth}{apparent\,\operatorname{depth}}\]is found to have values of 1.34,1.38,1.32 and 1.36; the mean value of refractive index with percentage error is
A)
\[1.35\,\,\pm \,\,1.48%\] done
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B)
\[1.35\,\,\pm \,\,0%\] done
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C)
\[1.36\,\,\pm \,\,6%\] done
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D)
\[1.36\,\,\pm \,\,0%\] done
clear
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question_answer80)
In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows \[P=\frac{{{a}^{3}}{{b}^{2}}}{cd}%\] error in P is
A)
10% done
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B)
7% done
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C)
4% done
clear
D)
14% done
clear
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question_answer81)
The heat generated in a circuit is given by\[Q={{I}^{2}}Rt\], where I is current, R is resistance and t is time. If the percentage errors in measuring I, R and t are 2%, 1% and 1% respectively, then the maximum error in measuring heat will be
A)
2% done
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B)
3% done
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C)
4% done
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D)
6% done
clear
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question_answer82)
The pressure on a square plate is measured by measuring the force on the plate and length of the sides of the plate by using the formula \[P=\frac{F}{{{\ell }^{2}}}\]. If the maximum errors in the measurement of force and length are 6% and 3% respectively, then the maximum error in the measurement of pressure is
A)
1% done
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B)
2% done
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C)
12% done
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D)
10% done
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question_answer83)
An atomic clock has an accuracy of 1 part is \[{{10}^{10}}\] If two such clocks are operated with precision, then after running for 2500 years these will record a difference of nearly.
A)
1 sec done
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B)
8 sec done
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C)
5 sec done
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D)
10 sec done
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question_answer84)
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is
A)
6% done
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B)
zero done
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C)
1% done
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D)
3% done
clear
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question_answer85)
Which of the following is most accurate?
A)
A screw gauge of least count 0.001 mm done
clear
B)
A screw gauge having pitch 1 mm and 50 divisions on circular scale done
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C)
A vernier callipers of least count 0.01 mm done
clear
D)
Vernier callipers having 20 divisions on the sliding scale (vernier scale) coinciding 19 divisions on the main millimetre scale done
clear
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question_answer86)
A thin copper wire of length / metre increases in length by 2% when heated through\[10{}^\circ C\]. What is the percentage increase in area when a square copper sheet of length / metre is heated through \[10{}^\circ C?\]
A)
4% done
clear
B)
8% done
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C)
16% done
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D)
None of these done
clear
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question_answer87)
A physical quantity \[\zeta \]is calulated using the formula\[\zeta =\frac{1}{10}x{{y}^{2}}/{{z}^{1/3}}\], where x, y and z are experimentally measured quantities. If the fractional error in the measurement of x, y and z are 2 %, 1% and 3% respectively, then the fractional error in\[\zeta \]will be
A)
0.5% done
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B)
5% done
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C)
6% done
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D)
7% done
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question_answer88)
In a simple pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time- period is 3%. Then the maximum percentage error in determination of the acceleration due to gravity g is
A)
5% done
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B)
6% done
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C)
1% done
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D)
8% done
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question_answer89)
Area of a square is\[\text{(}100\pm 2\text{)}{{m}^{2}}\]. Its side is
A)
\[\text{(}10\pm 1\text{)}m\] done
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B)
\[\text{(}10\pm 0.1\text{)}m\] done
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C)
\[\text{(}10\pm \sqrt{2}\text{)}m\] done
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D)
\[10\pm \sqrt{2}%\] done
clear
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question_answer90)
The values of kinetic energy K and potential energy U are measured as follows: \[K=100.0\pm 2.0\text{ }J,\,\,\,U=200.0\pm 1.0\text{ }J\]. Then the percentage error in the measurement of mechanical energy is -
A)
2.5% done
clear
B)
1% done
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C)
0.5% done
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D)
1.5% done
clear
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question_answer91)
You measure two quantities as\[A=1.0m\pm 0.2m\]\[B=2.0m\pm 0.2m\]. We should report correct value for \[\sqrt{AB}\] as
A)
\[1.4m\pm 0.4m\] done
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B)
\[1.41m\pm 0.15m\] done
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C)
\[1.4m\pm 0.3m\] done
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D)
\[1.4m\pm 0.2m\] done
clear
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question_answer92)
The resistance of a metal is given by \[R=\frac{V}{I}\]where V is potential difference and I is the current. In a circuit the potential difference across resistance is \[V=(8\pm 0.5)V\] and current in resistance \[I=(2\pm 0.2)A\]. What is the value of resistance with its percentage error?
A)
\[4\Omega \pm 16.25%\] done
clear
B)
\[(4\pm 0.7)\Omega \] done
clear
C)
\[4\Omega \pm 0.7%\] done
clear
D)
\[4\Omega \pm 7%\] done
clear
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question_answer93)
The density of a sphere is measured by measuring its mass and diameter. If, it is known that the maximum percentage errors in the measurement are 2% and 3%, then find the maximum percentage error in the measurement of density?
A)
15% done
clear
B)
18% done
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C)
9% done
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D)
11% done
clear
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question_answer94)
The length of a cylinder is measured with a metre rod having least count 0.1 cm. Its diameter is measured with vernier callipers having least count cm. Given that length is 5.0 cm and radius is 2.00 cm. The percentage error in the calculated value of the volume will be:
A)
11% done
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B)
2% done
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C)
3% done
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D)
4% done
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question_answer95)
Intensity observed in an interference pattern is \[I={{I}_{0}}Si{{n}^{2}}\]. \[At\theta ={{30}^{o}}\] intensity \[I=5\pm 0.0020W/{{m}^{2}}\]. Find percentage error in angle if \[{{I}_{0}}=20W/{{m}^{2}}\]
A)
\[\frac{4}{\pi }\sqrt{3}\times {{10}^{-2}}%\] done
clear
B)
\[\frac{2}{\pi }\sqrt{3}\times {{10}^{-2}}%\] done
clear
C)
\[\frac{1}{\pi }\sqrt{3}\times {{10}^{-2}}%\] done
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D)
\[\frac{3}{\pi }\sqrt{3}\times {{10}^{-2}}%\] done
clear
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question_answer96)
The resistance R of a wire is given by the relation \[R=\frac{\rho \ell }{\pi {{r}^{2}}}\]. Percentage error in the measurement of \[\rho ,\,\,\ell \] and r is 1%, 2% and 3% respectively. Then the percentage error in the measurement of R is
A)
6 done
clear
B)
9 done
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C)
8 done
clear
D)
10 done
clear
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question_answer97)
A physical quantity A is related to four observable quantities a, b, c and d as follows, \[A=\frac{{{a}^{2}}{{b}^{3}}}{c\sqrt{d}}\] and the percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively What is the percentage error in the quantity A?
A)
12% done
clear
B)
7% done
clear
C)
5% done
clear
D)
14% done
clear
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question_answer98)
A physical quantity Q is related to four observables x, y, z and t by the relation \[Q=\frac{{{x}^{2/5}}{{z}^{3}}}{y\sqrt{t}}\]The percentage errors of measurement in x, y, z and t are 2.5%, 2%, 0.5% and 1% respectively. The percentage error in Q will be
A)
5% done
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B)
4.5% done
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C)
8% done
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D)
7.75% done
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question_answer99)
The frequency (f) of a wire oscillating with a length \[\ell \], in p loops, under a tension T is given by \[f=\frac{P}{2\ell }\sqrt{\frac{T}{\mu }}\] where \[\mu =\] linear density of the wire. If the error made in determining length, tension and linear density be 1%, -2% and 4%, then find the percentage error in the calculated frequency
A)
- 4% done
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B)
- 2% done
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C)
- 1% done
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D)
- 5% done
clear
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question_answer100)
The current voltage relation of a diode is given by\[I=({{e}^{1000V/T}}-1)mA\], where the applied voltage V is in volts and the temperature T is in degree kelvin. If a student makes an error measuring \[\pm 0.01\text{ }V\]while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?
A)
0.2Ma done
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B)
0.02mA done
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C)
0.5mA done
clear
D)
0.05mA done
clear
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