# Solved papers for JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions JEE PYQ - Mathematical Tools Units and Dimensions

### done JEE PYQ - Mathematical Tools Units and Dimensions Total Questions - 56

• question_answer1) Identify the pair whose dimensions are equal. [AIEEE 2002]

A)
Torque and work

B)
Stress and energy

C)
Force and stress

D)
Force and work

• question_answer2) Dimensions of $\frac{1}{{{\mu }_{0}}\,{{\varepsilon }_{0}}}$, where symbols have their usual meaning, are                       [AIEEE 2003]

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

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

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

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

• question_answer3) The physical quantities not having same dimensions are                              [AIEEE 2003]

A)
torque and work

B)
momentum and Planck's constant

C)
stress and Young's modulus

D)
speed and ${{({{\mu }_{0}}-{{\varepsilon }_{0}})}^{-1/2}}$

• question_answer4) Which one of the following represents the correct dimensions of the coefficient of viscosity? [AIEEE 2004]

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

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

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

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

• question_answer5) Out of the following pairs, which one does not have identical dimensions?         [AIEEE 2005]

A)
Angular momentum and Planck's constant

B)
Impulse and momentum

C)
Moment of inertia and moment of a force

D)
Work and torque

• question_answer6) Which of the following units denote the dimensions$[M{{L}^{2}}/{{Q}^{2}}],$where 0 denotes the electric charge?                           [AIEEE 2006]

A)
$Wb/{{m}^{2}}$

B)
Henry (H)

C)
$H/{{m}^{2}}$

D)
Weber (Wb)

• question_answer7) Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on circular scale is 50. Further, it is found that screw gauge has a zero error of - 0.03mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3mm and the number of circular scale divisions in line with the main scale as 35. The diameter of wire is     [AIEEE 2008]

A)
3.67 mm

B)
3.38 mm

C)
3.32 mm

D)
3.73 mm

• question_answer8) A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00$m{{s}^{-1}}$. The magnitude of its momentum is recorded as [AIEEE 2008]

A)
17.56 kg $m{{s}^{-1}}$

B)
17.57 kg $m{{s}^{-1}}$

C)
17. 6 kg $m{{s}^{-1}}$

D)
17.565 kg $m{{s}^{-1}}$

• question_answer9) The dimension of magnetic field in M, L, T and C (Coulomb) is given as                   [AIEEE 2008]

A)
$M{{T}^{-1}}{{C}^{-1}}$

B)
$M{{T}^{-2}}{{C}^{-1}}$

C)
$ML{{T}^{-1}}{{C}^{-1}}$

D)
$M{{T}^{2}}{{C}^{-2}}$

• question_answer10) In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half -a-degree$(=0.5{}^\text{o}),$ then the least count of the instrument is:                                        [AIEEE 2009]

A)
one minute

B)
half minute

C)
one degree

D)
half degree

• question_answer11) The respective number of significant figures for the numbers 23.023, 0.0003 and$2.1\times {{10}^{3}}$ are - [AIEEE 2010]

A)
4, 4, 2

B)
5, 1, 2

C)
5, 1, 5

D)
5, 5, 2

• question_answer12)  A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading:                     0 mm Circular scale reading:                  52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. [AIEEE 2011] The diameter of wire from the above data is

A)
0.005 cm

B)
0.52 cm

C)
0.052 cm

D)
0.026 cm

• question_answer13) If $400\Omega$of resistance is made by adding four $100\Omega$ resistances of tolerance 5%, then the tolerance of the combination is: [AIEEE 11-05-2011]

A)
5%

B)
10 %

C)
15 %

D)
20 %

• question_answer14) 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:                                         [AIEEE 2012]

A)
6%

B)
zero

C)
1%

D)
3%

• question_answer15) A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading : 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data:                   [AIEEE 2012]

A)
58.59 degree

B)
58.77 degree

C)
58.65 degree

D)
59 degree

• question_answer16) Given that K = energy, V= velocity, T= time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?                        [JEE ONLINE 07-05-2012]

A)
$[K{{V}^{-2}}{{T}^{-2}}]$

B)
$[{{K}^{2}}{{V}^{2}}{{T}^{-2}}]$

C)
$[{{K}^{2}}{{V}^{-2}}{{T}^{-2}}]$

D)
$[K{{V}^{2}}{{T}^{2}}]$

• question_answer17) A student measured the diameter of a wire using a screw gauge with the least count 0.001 cm and listed the measurements. The measured value should be recorded as       [JEE ONLINE 12-05-2012]

A)
5.3200cm

B)
5.3cm

C)
5.32cm

D)
5.320cm

• question_answer18) The amount of heat produced in an electric circuit depends upon the current (t), resistance (R) and time (I). If the error made in the measurements of the above quantities are 2%, 1% and 1% respectively then the maximum possible error in the total heat produced will be [JEE ONLINE 19-05-2012]

A)
1%

B)
2%

C)
6%

D)
3%

• question_answer19) N divisions on the main scale of a vernier caliper coincide with (N + 1) divisions of the vernier scale. If each division of main scale is 'a' units then the least count of the instrument is [JEE ONLINE 19-05-2012]

A)
a

B)
$\frac{a}{N}$

C)
$\frac{N}{N+1}\times a$

D)
$\frac{a}{N+1}$

• question_answer20) The electrical resistance R of a conductor of length $l$ and area of cross section a is given by$R=\frac{\rho l}{a}$where$'\rho '$is the electrical resistivity. What is the dimensional formula for electrical conductivity $'\sigma '$ which is reciprocal of resistivity?            [JEE ONLINE 26-05-2012]

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

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

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

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

• question_answer21) Let$[{{\varepsilon }_{0}}]$denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = Time and A = electric current, then: [JEE MAIN 2013]

A)
$[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{2}}A]$

B)
$[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]$

C)
$[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{2}}{{T}^{-1}}{{A}^{-2}}]$

D)
$[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{2}}{{T}^{-1}}A]$

• question_answer22) The dimensions of angular momentum, latent heat and capacitance are, respectively.             [JEE ONLINE 22-04-2013]

A)
$\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{1}}{{\operatorname{A}}^{2}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{2}}$

B)
$\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{4}}{{\operatorname{A}}^{2}}$

C)
$\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},\operatorname{M}{{\operatorname{L}}^{2}}\operatorname{T}{{\operatorname{A}}^{2}}$

D)
$\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{4}}{{\operatorname{A}}^{2}}$

• question_answer23) The current voltage relation of diode is given by $I=\left( {{e}^{1000V/T}}-1 \right)mA,$where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring ± 0.01 V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?                     [JEE MAIN 2014]

A)
0.5 mA

B)
0.05 mA

C)
0.2 mA

D)
0.02 mA

• question_answer24) A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he used to measure it?              [JEE MAIN 2014]

A)
A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.

B)
A screw gauge having 50 divisions in the circular scale and pitch as 1 mm.

C)
A meter scale.

D)
A vernier calliper where the 10 divisions in vernier scale matches with 9 division in main scale & main scale has 10 divisions in 1 cm

• question_answer25) In terms of resistance R and time T, the dimensions of ratio$\frac{\mu }{\varepsilon }$of the permeability $\mu$ and permittivity $\varepsilon$ is:  [JEE ONLINE 11-04-2014]

A)
$[R{{T}^{-2}}]$

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

C)
$[{{R}^{2}}]$

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

• question_answer26) From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is: [JEE ONLINE 12-04-2014]

A)
$\frac{ch}{2\pi \varepsilon _{o}^{2}}$

B)
$\frac{{{e}^{2}}}{2\pi \varepsilon _{o}^{{}}Gm_{e}^{2}}$(${{m}_{e}}=$ mass of electron)

C)
$\frac{{{\mu }_{o}}{{\varepsilon }_{o}}}{{{c}^{2}}}\frac{G}{h{{e}^{2}}}$

D)
$\frac{2\pi \sqrt{{{\mu }_{o}}{{\varepsilon }_{o}}}}{c{{e}^{2}}}\frac{h}{G}$

• question_answer27) If the capacitance of a Nano capacitor is measured in tern-is of a unit V made by combining the electronic charge 'e', Bohr radius $'{{a}_{0}}',$ Planck's constant 'h' and speed of light 'c' then:                    [JEE ONLINE 10-04-2015]

A)
$u=\frac{hc}{{{e}^{2}}{{a}_{0}}}$

B)
$u=\frac{{{e}^{2}}h}{c{{a}_{0}}}$

C)
$u=\frac{{{e}^{2}}{{a}_{0}}}{hc}$

D)
$u=\frac{{{e}^{2}}c}{h{{a}_{0}}}$

Diameter of a steel ball is measured using a Vernier callipers which has divisions of cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as: [JEE ONLINE 10-04-2015]
 S. No. MS (cm) VS divisions 1. 0.5 8 2. 0.5 4 3. 0.5 6
If the zero error is 0.03 cm, then mean corrected diameter is:

A)
0.56 cm

B)
0.53 cm

C)
0.52 cm

D)
0.59 cm

• question_answer29) 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:   [JEE MAIN ONLINE 11-04-2015]

A)
$\left( \frac{hc}{m{{e}^{2}}} \right)$

B)
$\left( \frac{h}{m{{e}^{2}}} \right)$

C)
$\left( \frac{h}{c{{e}^{2}}} \right)$

D)
$\left( \frac{m{{c}^{2}}}{h{{e}^{2}}} \right)$

• question_answer30) A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement , it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?                      [JEE MAIN - I 3-4-2016]

A)
0.50 mm

B)
0.75 mm

C)
0.80 mm

D)
0.70 mm

• question_answer31) A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:-                         [JEE MAIN - I 3-4-2016]

A)
92 ± 3 s

B)
92 ± 2 s

C)
92 ± 5.0 s

D)
92 ± 1.8 s

• question_answer32) In the following 'I' refers to current and other symbols have their usual meaning choose the option that corresponds to the dimensions of electrical conductivity: [JEE ONLINE 09-04-2016]

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

B)
${{M}^{-1}}{{L}^{3}}{{T}^{3}}I$

C)
$M{{L}^{-3}}{{T}^{-3}}{{I}^{2}}$

D)
${{M}^{-1}}{{L}^{-3}}{{T}^{3}}I$

• question_answer33) 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 in (BD) holds ture .Then which of the combination is not a meaningful quantity?        [JEE ONLINE 10-04-2016]

A)
${{A}^{2}}-{{B}^{2}}{{C}^{2}}$

B)
$\frac{A}{B}-C$

C)
$\frac{C}{BD}-\frac{A{{D}^{2}}}{C}$

D)
$\frac{(A-C)}{D}$

• question_answer34) Time (T), velocity (3) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be  [JEE Online 08-04-2017]

A)
$[M]=[{{T}^{-1}}{{C}^{-2}}h]$

B)
$[M]=[T{{C}^{-2}}h]$

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

D)
$[M]=[{{T}^{-1}}{{C}^{2}}h]$

• question_answer35) In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

A)
Every object that is weighted using this balance appears lighter than its actual weight

B)
Left arm is shorter than the right arm

C)
Both the arms are of same length

D)
Left arm is longer than the right arm

• question_answer36)  A physical quantity P is described by the relation $P={{a}^{1/2}}\,{{b}^{2}}{{c}^{3}}{{d}^{-4}}$ If the relative errors in the measurement of $a,\,b,\,c$ and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be  [JEE Online 09-04-2017]

A)
12%

B)
8%

C)
25%

D)
32%

• question_answer37) 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: [JEE Main Online 08-04-2018]

A)
$4.5%$

B)
$6%$

C)
$2.5%$

D)
$3.5%$

• question_answer38) The relative error in the determination of the surface area of a sphere is$\alpha$. Then the relative error in the determination of its volume is : [JEE Online 15-04-2018]

A)
$\frac{2}{3}\alpha$

B)
$\frac{5}{2}\alpha$

C)
$\frac{3}{2}\alpha$

D)
$\alpha$

• question_answer39) In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is: [JEE Online 15-04-2018]

A)
$0.0430cm$

B)
$0.3150cm$

C)
$0.4300cm$

D)
$0.2150cm$

• question_answer40) The percentage errors in quantities P, Q, R and S are $0.5%,1%,3%$and$1.5%$ respectively in the measurement of a physical quantity.$A=\frac{{{P}^{3}}{{Q}^{2}}}{\sqrt{RS}}.$ The maximum percentage error in the value of will be

A)
$8.5%$

B)
$6.0%$

C)
$7.5%$

D)
$6.5%$

• question_answer41) Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:                                        [JEE Main 09-Jan-2019 Evening]

A)
$\sqrt{\frac{Gh}{{{c}^{5}}}}$

B)
$\sqrt{\frac{h{{c}^{5}}}{G}}$

C)
$\sqrt{\frac{Gh}{{{c}^{3}}}}$

D)
$\sqrt{\frac{{{c}^{3}}}{Gh}}$

• question_answer42) The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is: [JEE Main 09-Jan-2019 Evening]

A)
5.725 mm

B)
5.950 mm

C)
5.755 mm

D)
5.740 mm

• question_answer43) The density of a material in SI units is 128 $kg\text{ }{{m}^{-}}^{3}$. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is [JEE Main 10-Jan-2019 Morning]

A)
40

B)
640

C)
16

D)
410

• question_answer44) The diameter and height of a cylinder are measured by a meter scale to be $12.6\,\,\pm \,\,0.1$ cm and $34.2\,\,\pm \,0.1$ cm, respectively. What will be the value of its volume in appropriate significant figures? [JEE Main 10-Jan-2019 Evening]

A)
$4264.4\,\,\pm \,\,81.0\text{ }c{{m}^{3}}$

B)
$4264\,\,\pm \,\,81c{{m}^{3}}$

C)
$4300\,\,\pm \,\,80\text{ }c{{m}^{3}}$

D)
$4260\,\,\pm \,\,80\text{ }c{{m}^{3}}$

• question_answer45) If speed (V), acceleration and force (F) are considered as fundamental units, the dimension of Youngs modulus will be-   [JEE Main 11-Jan-2019 Evening]

A)
${{V}^{-2}}{{A}^{2}}{{F}^{-2}}$

B)
${{V}^{-2}}{{A}^{2}}{{F}^{2}}$

C)
${{V}^{-4}}{{A}^{2}}F$

D)
${{V}^{-4}}{{A}^{-2}}F$

• question_answer46) The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure $5\mu m$diameter of a wire is-                               [JEE Main 12-Jan-2019 Morning]

A)
50

B)
100

C)
200

D)
500

• question_answer47) In SI units, the dimesions of$\sqrt{\frac{{{\in }_{0}}}{{{\mu }_{0}}}}$is: [JEE Main 8-4-2019 Morning]

A)
${{A}^{-1}}TM{{L}^{3}}$

B)
${{A}^{2}}{{T}^{3}}{{M}^{-1}}{{L}^{-2}}$

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

D)
$A{{T}^{-3}}M{{L}^{3/2}}$

• question_answer48) Let$\left| {{{\vec{A}}}_{1}} \right|=3,\left| {{{\vec{A}}}_{2}} \right|=5$and$\left| {{{\vec{A}}}_{1}}+{{{\vec{A}}}_{2}} \right|=5.$The value of$\left( 2{{{\vec{A}}}_{1}}+3{{{\vec{A}}}_{2}} \right).\left( 3{{{\vec{A}}}_{1}}-2{{{\vec{A}}}_{2}} \right)$is :- [JEE Main 8-4-2019 Afternoon]

A)
-112.5

B)
-106.5

C)
-118.5

D)
-99.5

• question_answer49) In the density measurement of a cube, the mass and edge length are measured as $\left( 10.00\pm 0.10 \right)\text{ }kg$and$\left( 0.10\pm 0.01 \right)\text{ }m,$respectively. The error in the measurement of density is :      [JEE Main 9-4-2019 Morning]

A)
$0.10\text{ }kg/{{m}^{3}}$

B)
$0.31\text{ }kg/{{m}^{3}}$

C)
$0.07\text{ }kg/{{m}^{3}}$

D)
$0.01\text{ }kg/{{m}^{3}}$

• question_answer50) The area of a square is 5.29 $c{{m}^{2}}$. The area of 7 such squares taking into account the significant figures is: [JEE Main 9-4-2019 Afternoon]

A)
$37c{{m}^{2}}$

B)
$37.0\text{ }c{{m}^{2}}$

C)
$37.03\text{ }c{{m}^{2}}$

D)
$37.030\text{ }c{{m}^{2}}$

• question_answer51) In the formula $X=5Y{{Z}^{2}},X$ and $Z$ have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?        [JEE Main 10-4-2019 Afternoon]

A)
$[{{M}^{-2}}{{L}^{-2}}{{T}^{6}}{{A}^{3}}]$

B)
$[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}]$

C)
$[{{M}^{-3}}{{L}^{-2}}{{T}^{8}}{{A}^{4}}]$

D)
$[{{M}^{-2}}{{L}^{0}}{{T}^{-4}}{{A}^{-2}}]$

• question_answer52) The dimension of $\frac{{{B}^{2}}}{2{{\mu }_{0}}},$ where B is magnetic field and ${{\mu }_{0}}$ is the magnetic permeability of vaccum, is [JEE MAIN Held on 07-01-2020 Evening]

A)
$M{{L}^{1}}\text{ }{{T}^{\,2}}$

B)
$M{{L}^{2}}\text{ }{{T}^{\,\,2}}$

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

D)
$ML{{T}^{\,2}}$

• question_answer53) The dimension of stopping potential ${{V}_{0}}$ in photoelectric effect in units of Plancks constant h, speed of light c and Gravitational constant G and ampere A is : [JEE MAIN Held On 08-01-2020 Morning]

A)
${{h}^{1/3}}{{G}^{2/3}}{{c}^{1/3}}{{A}^{1}}$

B)
${{h}^{2/3}}{{c}^{5/3}}{{G}^{1/3}}{{A}^{1}}$

C)
${{h}^{2/3}}{{c}^{1/3}}{{G}^{4/3}}{{A}^{1}}$

D)
None of these

• question_answer54) If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is: [JEE MAIN Held on 09-01-2020 Morning]

A)
0.01 cm

B)
0.001 mm

C)
0.001 cm

D)
0.02 mm

• question_answer55) A quantity f is given by $f=\sqrt{\frac{h{{c}^{5}}}{G}}$ where c is speed of light, G universal gravitational constant and h is the Plancks constant. Dimension of f is that of [JEE MAIN Held on 09-01-2020 Morning]

A)
Energy

B)
Area

C)
Volume

D)
Momentum

• question_answer56)  For the four sets of three measured physical quantities as given below. Which of the following options is correct? (i) ${{A}_{1}}=24.36,\,\,\,\,{{B}_{1}}=0.0724,\,\,\,{{C}_{1}}=256.2$ (ii) ${{A}_{2}}=24.44,\,\,\,\,{{B}_{2}}=16.082,\,\,\,{{C}_{2}}=240.2$ (iii) ${{A}_{3}}=25.2,\,\,\,\,{{B}_{3}}=19.2812,\,\,\,{{C}_{3}}=236.183$ (iv) ${{A}_{4}}=25,\,\,\,\,{{B}_{4}}=236.191,\,\,\,{{C}_{4}}=19.5$ [JEE MAIN Held on 09-01-2020 Evening]

A)
${{A}_{1}}+{{B}_{1}}+{{C}_{1}}={{A}_{2}}+{{B}_{2}}+{{C}_{2}}={{A}_{3}}+{{B}_{3}}+{{C}_{3}}=$${{A}_{4}}+{{B}_{4}}+{{C}_{4}}$

B)
${{A}_{1}}+{{B}_{1}}+{{C}_{1}}<{{A}_{3}}+{{B}_{3}}+{{C}_{3}}<{{A}_{2}}+{{B}_{2}}+{{C}_{2}}<$${{A}_{4}}+{{B}_{4}}+{{C}_{4}}$

C)
${{A}_{4}}+{{B}_{4}}+{{C}_{4}}<{{A}_{1}}+{{B}_{1}}+{{C}_{1}}={{A}_{2}}+{{B}_{2}}+{{C}_{2}}=$${{A}_{3}}+{{B}_{3}}+{{C}_{3}}$

D)
None of these