# Solved papers for NEET Physics Mathematical Tools, Units & Dimensions NEET PYQ-Mathematical Tools, Units and Dimensions

### done NEET PYQ-Mathematical Tools, Units and Dimensions Total Questions - 27

• question_answer1) The dimensional formula for magnetic flux is: [AIPMT 1999]

A)
$[M{{L}^{2}}{{T}^{-2}}{{A}^{-1}}]$

B)
$[M{{L}^{3}}{{T}^{-2}}{{A}^{-2}}]$

C)
$[{{M}^{0}}{{L}^{-2}}{{T}^{2}}{{A}^{-2}}]$

D)
$[M{{L}^{2}}{{T}^{-2}}{{A}^{2}}]$

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• question_answer2) A pair of physical quantities having same dimensional formula is:                 [AIPMT 2000]

A)
force and torque

B)
work and energy

C)
force and impulse

D)
linear momentum and angular momentum

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• question_answer3) Planck's constant has the dimensions of: [AIPMT 2001]

A)
linear momentum

B)
angular momentum

C)
energy

D)
power

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• question_answer4) The unit of permittivity of free space, ${{\varepsilon }_{0}}$,is: [AIPMT (S) 2004]

A)
coulomb/newton-metre

B)
newton - metre2/coulomb2

C)
coulomb / newton  metre

D)
coulomb2/ (newton- metre)2

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• question_answer5) The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimension of: [AIPMT (S) 2005]

A)
frequency

B)
velocity

C)
angular momentum

D)
time

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• question_answer6) The velocity v of a particle at time t is given by $v=at+\frac{b}{t+c},$ where a, b and c are constants. The dimensions of a, b and c are respectively: [AIPMT(S) 2006]

A)
$[L{{T}^{-2}}],\,[L]$ and$[T]$

B)
$[{{L}^{2}}],\,[T]$ and $[L{{T}^{2}}]$

C)
$[L{{T}^{2}}],\,[LT]$ and $[L]$

D)
$[L],\,[LT]$ and $[{{T}^{2}}]$

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• question_answer7) Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be: [AIPMT (S) 2007]

A)
$[M{{L}^{2}}{{T}^{-3}}{{I}^{-1}}]$

B)
$[M{{L}^{2}}{{T}^{-2}}]$

C)
$[M{{L}^{2}}{{T}^{-1}}{{I}^{-1}}]$

D)
$[M{{L}^{2}}{{T}^{-3}}{{I}^{-2}}]$

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• question_answer8) If the error in the measurement of radius of a sphere is. 2%, then the error in the determination of volume of the sphere will be [AIPMPT (S) 2008]

A)
4%

B)
6%

C)
8%

D)
2%

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• question_answer9)  Which two of the following five physical parameters have the same dimensions?          [AIPMT (S) 2008] (1) energy density (2) refractive index (3) dielectric constant (4) Young's modulus (5) magnetic field

A)
2 and 4

B)
3 and 5

C)
1 and 4

D)
1 and 5

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• question_answer10) If the dimensions of a physical quantity are given by ${{v}_{s}}=10+10=20m{{s}^{-}}^{1}$ then the physical quantity will be                    [AIPMT (S) 2009]

A)
pressure if $a=1,\,b=-1,\,c=-2$

B)
velocity if $a=1,\,b=0,\,c=-1$

C)
acceleration if $a=1,\,b=1,\,c=-2$

D)
None of these

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• question_answer11) The dimension of $\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}},$ where ${{\varepsilon }_{0}}$ is permittivity of free space and E is electric field, is [AIPMT (S) 2010]

A)
$[M{{L}^{2}}{{T}^{-2}}]$

B)
$[M{{L}^{-1}}{{T}^{-2}}]$

C)
$[M{{L}^{-2}}{{T}^{-1}}]$

D)
$[ML{{T}^{-1}}]$

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• question_answer12) A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are ${{e}_{1}}$ and ${{e}_{2}}$ respectively, the percentage error in the estimation of g is                   [AIPMT(M) 2010]

A)
${{e}_{2}}-{{e}_{1}}$

B)
${{e}_{1}}+2{{e}_{2}}$

C)
${{e}_{1}}+{{e}_{2}}$

D)
${{e}_{1}}-2{{e}_{2}}$

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• question_answer13) The density of material in CGS system of units is $4g/c{{m}^{3}}$. In a system of units in which unit of lengths is 10 cm and unit of mass' is 100 g, the value of density of material will be' [AIPMT (M) 2011]

A)
0.4

B)
40

C)
400

D)
0.04

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• question_answer14) The dimensions of ${{({{\mu }_{0}}{{\varepsilon }_{0}})}^{-1/2}}$ [AIPMT (S) 2011]

A)
$[{{L}^{-1}}T]$

B)
$[L{{T}^{-1}}]$

C)
$[{{L}^{-1/2}}\,{{T}^{1/2}}]$

D)
$[{{L}^{1/2}}\,{{T}^{-1/2}}]$

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• question_answer15) A stone is dropped from a height h. It hits the ground with a certain momentum p. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by    [AIPMT (M) 2012]

A)
68%

B)
41%

C)
200%

D)
100%

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• question_answer16) The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are [AIPMT (S) 2012]

A)
$kg\,m{{s}^{-1}}$

B)
$kg\,m{{s}^{-2}}$

C)
$kg\,{{s}^{-1}}$

D)
$kg\,s$

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• question_answer17) 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   [NEET 2013]

A)
14%

B)
10%

C)
7%

D)
4%

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• question_answer18) If force (F) velocity ($\upsilon$) and time (T) are taken as fundamental units, then the dimensions of mass are [NEET 2014]

A)
$[Fv{{T}^{-1}}]$

B)
$[Fv{{T}^{-2}}]$

C)
$[F{{v}^{-1}}{{T}^{-1}}]$

D)
$[F{{v}^{-1}}T]$

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• question_answer19) If energy (E), velocity [v] and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be [NEET 2015]

A)
$[E{{v}^{-2}}{{T}^{-1}}]$

B)
$[E{{v}^{-1}}{{T}^{-2}}]$

C)
$[E{{v}^{-2}}{{T}^{-2}}]$

D)
$[{{E}^{-2}}{{v}^{-1}}{{T}^{-3}}]$

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• question_answer20) If dimensions of critical velocity ${{v}_{c}}$ of a liquid flowing through a tube are expressed as$[{{\eta }^{x}}{{\rho }^{y}}{{r}^{z}}],$ where $\eta ,\,\,\rho$ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by                              [NEET 2015 (Re)]

A)
$1,\,\,-1,\,\,~-1$

B)
$-1,\,\,-1,\,\,~1$

C)
$-1,\,\,-1,\,\,~-1$

D)
$1,\,\,1,\,\,1$

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• question_answer21) 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]          [NEET-2017]

A)
$\frac{1}{c}G\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}}$

B)
$\frac{1}{{{c}^{2}}}{{\left[ G\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}} \right]}^{\frac{1}{2}}}$

C)
${{c}^{2}}{{\left[ G\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}} \right]}^{\frac{1}{2}}}$

D)
$\frac{1}{{{c}^{2}}}{{\left[ \frac{{{e}^{2}}}{G4\pi {{\varepsilon }_{0}}} \right]}^{\frac{1}{2}}}$

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• question_answer22) A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of -0.004 cm, the correct diameter of the ball is                                 [NEET - 2018]

A)
0.053 cm

B)
0.525 cm

C)
0.521 cm

D)
0.529 cm

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• question_answer23) In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where$X=\frac{{{A}^{2}}{{B}^{1/2}}}{{{C}^{1/2}}{{D}^{3}}}$ will be-                                        [NEET 2019]

A)
-10%

B)
10%

C)
$\left( \frac{3}{13} \right)%$

D)
16%

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• question_answer24) The unit of thermal conductivity is: [NEET 2019]

A)
$W\text{ }m\text{ }{{K}^{1}}$

B)
(b)$~W\text{ }{{m}^{1}}\text{ }{{K}^{1}}$

C)
$J\text{ }m\text{ }{{K}^{b\text{ }1}}$

D)
$J\text{ }{{m}^{1}}\text{ }{{K}^{1}}$

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• question_answer25) Dimensions of stress are:              [NEET 2020]

A)
$[M{{L}^{2}}{{T}^{2}}]$

B)
$[M{{L}^{0}}{{T}^{2}}]$

C)
$[M{{L}^{1}}\text{ }{{T}^{2}}]$

D)
$[ML{{T}^{2}}]$

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• question_answer26) Taking into account of the significant figures, what is the value of 9.99 m  0.0099 m? [NEET 2020]

A)
9.98 m

B)
9.980 m

C)
9.9 m

D)
9.9801 m

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• question_answer27) A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is:            [NEET 2020]

A)
0.25 mm

B)
0.5 mm

C)
1.0 mm

D)
0.01 mm

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##### NEET PYQ-Mathematical Tools, Units and Dimensions

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