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
  done clear
  B)
  Stress and energy
  done clear
  C)
  Force and stress
  done clear
  D)
  Force and work
  done clear
  View Answer play_arrow

• question_answer2) Dimensions of \[\frac{1}{{{\mu }_{0}}\,{{\varepsilon }_{0}}}\], where symbols have their usual meaning, are                       [AIEEE 2003]
  A)
  \[[{{L}^{-1}}T]\]
  done clear
  B)
  \[[{{L}^{2}}{{T}^{2}}]\]
  done clear
  C)
  \[[{{L}^{2}}{{T}^{-2}}]\]
  done clear
  D)
  \[[L{{T}^{-1}}]\]  
  done clear
  View Answer play_arrow

• question_answer3) The physical quantities not having same dimensions are                              [AIEEE 2003]
  A)
  torque and work
  done clear
  B)
  momentum and Planck's constant
  done clear
  C)
  stress and Young's modulus
  done clear
  D)
  speed and \[{{({{\mu }_{0}}-{{\varepsilon }_{0}})}^{-1/2}}\]
  done clear
  View Answer play_arrow

• question_answer4) Which one of the following represents the correct dimensions of the coefficient of viscosity? [AIEEE 2004]
  A)
  \[[M{{L}^{-1}}{{T}^{-2}}]\]
  done clear
  B)
  \[[ML{{T}^{-1}}]\]
  done clear
  C)
  \[[M{{L}^{-1}}{{T}^{-1}}]\]
  done clear
  D)
  \[[M{{L}^{-2}}{{T}^{-2}}]\]
  done clear
  View Answer play_arrow

• question_answer5) Out of the following pairs, which one does not have identical dimensions?         [AIEEE 2005]
  A)
  Angular momentum and Planck's constant
  done clear
  B)
  Impulse and momentum
  done clear
  C)
  Moment of inertia and moment of a force
  done clear
  D)
  Work and torque
  done clear
  View Answer play_arrow

• question_answer6) Which of the following units denote the dimensions\[[M{{L}^{2}}/{{Q}^{2}}],\]where 0 denotes the electric charge?                           [AIEEE 2006]
  A)
  \[Wb/{{m}^{2}}\]
  done clear
  B)
  Henry (H)
  done clear
  C)
  \[H/{{m}^{2}}\]
  done clear
  D)
  Weber (Wb)
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  3.38 mm
  done clear
  C)
  3.32 mm
  done clear
  D)
  3.73 mm
  done clear
  View Answer play_arrow

• 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 \[m{{s}^{-1}}\]
  done clear
  B)
  17.57 kg \[m{{s}^{-1}}\]
  done clear
  C)
  17. 6 kg \[m{{s}^{-1}}\]
  done clear
  D)
  17.565 kg \[m{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer9) The dimension of magnetic field in M, L, T and C (Coulomb) is given as                   [AIEEE 2008]
  A)
  \[M{{T}^{-1}}{{C}^{-1}}\]
  done clear
  B)
  \[M{{T}^{-2}}{{C}^{-1}}\]
  done clear
  C)
  \[ML{{T}^{-1}}{{C}^{-1}}\]
  done clear
  D)
  \[M{{T}^{2}}{{C}^{-2}}\]
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  half minute
  done clear
  C)
  one degree
  done clear
  D)
  half degree
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  5, 1, 2
  done clear
  C)
  5, 1, 5
  done clear
  D)
  5, 5, 2
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  0.52 cm
  done clear
  C)
  0.052 cm
  done clear
  D)
  0.026 cm
  done clear
  View Answer play_arrow

• 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%
  done clear
  B)
  10 %              
  done clear
  C)
  15 %
  done clear
  D)
  20 %
  done clear
  View Answer play_arrow

• 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%
  done clear
  B)
  zero
  done clear
  C)
  1%
  done clear
  D)
  3%
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  58.77 degree
  done clear
  C)
  58.65 degree
  done clear
  D)
  59 degree
  done clear
  View Answer play_arrow

• 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)
  \[[K{{V}^{-2}}{{T}^{-2}}]\]
  done clear
  B)
  \[[{{K}^{2}}{{V}^{2}}{{T}^{-2}}]\]
  done clear
  C)
  \[[{{K}^{2}}{{V}^{-2}}{{T}^{-2}}]\]
  done clear
  D)
  \[[K{{V}^{2}}{{T}^{2}}]\]
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  5.3cm
  done clear
  C)
  5.32cm
  done clear
  D)
  5.320cm
  done clear
  View Answer play_arrow

• 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%
  done clear
  B)
  2%
  done clear
  C)
  6%
  done clear
  D)
  3%
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  \[\frac{a}{N}\]  
  done clear
  C)
  \[\frac{N}{N+1}\times a\]
  done clear
  D)
  \[\frac{a}{N+1}\]
  done clear
  View Answer play_arrow

• 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)
  \[[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]\]
  done clear
  B)
  \[[M{{L}^{-3}}{{T}^{-3}}{{A}^{2}}]\]
  done clear
  C)
  \[[M{{L}^{-3}}{{T}^{-3}}{{A}^{-2}}]\]
  done clear
  D)
  \[[{{M}^{-2}}{{L}^{3}}{{T}^{2}}{{A}^{-1}}]\]
  done clear
  View Answer play_arrow

• 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)
  \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{2}}A]\]
  done clear
  B)
  \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]\]
  done clear
  C)
  \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{2}}{{T}^{-1}}{{A}^{-2}}]\]
  done clear
  D)
  \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{2}}{{T}^{-1}}A]\]
  done clear
  View Answer play_arrow

• question_answer22) The dimensions of angular momentum, latent heat and capacitance are, respectively.             [JEE ONLINE 22-04-2013]
  A)
  \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{1}}{{\operatorname{A}}^{2}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{2}}\]
  done clear
  B)
              \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{4}}{{\operatorname{A}}^{2}}\]
  done clear
  C)
              \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},\operatorname{M}{{\operatorname{L}}^{2}}\operatorname{T}{{\operatorname{A}}^{2}}\]
  done clear
  D)
              \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{4}}{{\operatorname{A}}^{2}}\]
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  0.05 mA
  done clear
  C)
  0.2 mA
  done clear
  D)
  0.02 mA
  done clear
  View Answer play_arrow

• 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.
  done clear
  B)
  A screw gauge having 50 divisions in the circular scale and pitch as 1 mm.
  done clear
  C)
  A meter scale.
  done clear
  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
  done clear
  View Answer play_arrow

• 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)
  \[[R{{T}^{-2}}]\]
  done clear
  B)
  \[[{{R}^{2}}{{T}^{-1}}]\]
  done clear
  C)
  \[[{{R}^{2}}]\]
  done clear
  D)
  \[[{{R}^{2}}{{T}^{2}}]\]
  done clear
  View Answer play_arrow

• 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)
  \[\frac{ch}{2\pi \varepsilon _{o}^{2}}\]
  done clear
  B)
  \[\frac{{{e}^{2}}}{2\pi \varepsilon _{o}^{{}}Gm_{e}^{2}}\](\[{{m}_{e}}=\] mass of electron)
  done clear
  C)
  \[\frac{{{\mu }_{o}}{{\varepsilon }_{o}}}{{{c}^{2}}}\frac{G}{h{{e}^{2}}}\]            
  done clear
  D)
  \[\frac{2\pi \sqrt{{{\mu }_{o}}{{\varepsilon }_{o}}}}{c{{e}^{2}}}\frac{h}{G}\]
  done clear
  View Answer play_arrow

• 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)
  \[u=\frac{hc}{{{e}^{2}}{{a}_{0}}}\]
  done clear
  B)
  \[u=\frac{{{e}^{2}}h}{c{{a}_{0}}}\]
  done clear
  C)
  \[u=\frac{{{e}^{2}}{{a}_{0}}}{hc}\]
  done clear
  D)
  \[u=\frac{{{e}^{2}}c}{h{{a}_{0}}}\]
  done clear
  View Answer play_arrow

• question_answer28) 

  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
  done clear
  B)
  0.53 cm
  done clear
  C)
  0.52 cm
  done clear
  D)
  0.59 cm
  done clear
  View Answer play_arrow

• 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)
  \[\left( \frac{hc}{m{{e}^{2}}} \right)\]
  done clear
  B)
  \[\left( \frac{h}{m{{e}^{2}}} \right)\]
  done clear
  C)
  \[\left( \frac{h}{c{{e}^{2}}} \right)\]
  done clear
  D)
  \[\left( \frac{m{{c}^{2}}}{h{{e}^{2}}} \right)\]
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  0.75 mm
  done clear
  C)
  0.80 mm
  done clear
  D)
  0.70 mm
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  92 ± 2 s
  done clear
  C)
  92 ± 5.0 s
  done clear
  D)
  92 ± 1.8 s
  done clear
  View Answer play_arrow

• 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)
  \[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{I}^{2}}\]
  done clear
  B)
  \[{{M}^{-1}}{{L}^{3}}{{T}^{3}}I\]
  done clear
  C)
  \[M{{L}^{-3}}{{T}^{-3}}{{I}^{2}}\]
  done clear
  D)
  \[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}I\]
  done clear
  View Answer play_arrow

• 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)
  \[{{A}^{2}}-{{B}^{2}}{{C}^{2}}\]
  done clear
  B)
  \[\frac{A}{B}-C\]
  done clear
  C)
  \[\frac{C}{BD}-\frac{A{{D}^{2}}}{C}\]
  done clear
  D)
  \[\frac{(A-C)}{D}\]
  done clear
  View Answer play_arrow

• 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)
  \[[M]=[{{T}^{-1}}{{C}^{-2}}h]\]
  done clear
  B)
  \[[M]=[T{{C}^{-2}}h]\]
  done clear
  C)
  \[[M]=[{{T}^{-1}}{{C}^{-2}}{{h}^{-1}}]\]
  done clear
  D)
  \[[M]=[{{T}^{-1}}{{C}^{2}}h]\]
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  Left arm is shorter than the right arm
  done clear
  C)
  Both the arms are of same length
  done clear
  D)
  Left arm is longer than the right arm
  done clear
  View Answer play_arrow

• 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%
  done clear
  B)
  8%
  done clear
  C)
  25%
  done clear
  D)
  32%
  done clear
  View Answer play_arrow

• 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)
  \[4.5%\]
  done clear
  B)
  \[6%\]
  done clear
  C)
  \[2.5%\]
  done clear
  D)
  \[3.5%\]
  done clear
  View Answer play_arrow

• 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)
        \[\frac{2}{3}\alpha \]     
  done clear
  B)
  \[\frac{5}{2}\alpha \]
  done clear
  C)
  \[\frac{3}{2}\alpha \]     
  done clear
  D)
  \[\alpha \]
  done clear
  View Answer play_arrow

• 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)
        \[0.0430cm\]
  done clear
  B)
  \[0.3150cm\]
  done clear
  C)
  \[0.4300cm\]
  done clear
  D)
  \[0.2150cm\]
  done clear
  View Answer play_arrow

• 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)
        \[8.5%\]
  done clear
  B)
  \[6.0%\]
  done clear
  C)
  \[7.5%\]
  done clear
  D)
  \[6.5%\]
  done clear
  View Answer play_arrow

• 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)
        \[\sqrt{\frac{Gh}{{{c}^{5}}}}\]
  done clear
  B)
  \[\sqrt{\frac{h{{c}^{5}}}{G}}\]
  done clear
  C)
  \[\sqrt{\frac{Gh}{{{c}^{3}}}}\]
  done clear
  D)
  \[\sqrt{\frac{{{c}^{3}}}{Gh}}\]
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  5.950 mm
  done clear
  C)
  5.755 mm
  done clear
  D)
  5.740 mm
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  640
  done clear
  C)
  16
  done clear
  D)
  410
  done clear
  View Answer play_arrow

• 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)
  \[4264.4\,\,\pm \,\,81.0\text{ }c{{m}^{3}}\]
  done clear
  B)
  \[4264\,\,\pm \,\,81c{{m}^{3}}\]
  done clear
  C)
  \[4300\,\,\pm \,\,80\text{ }c{{m}^{3}}\]
  done clear
  D)
  \[4260\,\,\pm \,\,80\text{ }c{{m}^{3}}\]
  done clear
  View Answer play_arrow

• 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)
  \[{{V}^{-2}}{{A}^{2}}{{F}^{-2}}\]
  done clear
  B)
  \[{{V}^{-2}}{{A}^{2}}{{F}^{2}}\]
  done clear
  C)
  \[{{V}^{-4}}{{A}^{2}}F\]
  done clear
  D)
  \[{{V}^{-4}}{{A}^{-2}}F\]
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  100
  done clear
  C)
  200
  done clear
  D)
  500
  done clear
  View Answer play_arrow

• question_answer47) In SI units, the dimesions of\[\sqrt{\frac{{{\in }_{0}}}{{{\mu }_{0}}}}\]is: [JEE Main 8-4-2019 Morning]
  A)
  \[{{A}^{-1}}TM{{L}^{3}}\]
  done clear
  B)
  \[{{A}^{2}}{{T}^{3}}{{M}^{-1}}{{L}^{-2}}\]
  done clear
  C)
  \[A{{T}^{2}}{{M}^{-1}}{{L}^{-1}}\]
  done clear
  D)
  \[A{{T}^{-3}}M{{L}^{3/2}}\]
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  -106.5
  done clear
  C)
  -118.5
  done clear
  D)
  -99.5
  done clear
  View Answer play_arrow

• 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)
  \[0.10\text{ }kg/{{m}^{3}}\]
  done clear
  B)
  \[0.31\text{ }kg/{{m}^{3}}\]
  done clear
  C)
  \[0.07\text{ }kg/{{m}^{3}}\]
  done clear
  D)
  \[0.01\text{ }kg/{{m}^{3}}\]
  done clear
  View Answer play_arrow

• 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)
  \[37c{{m}^{2}}\]
  done clear
  B)
  \[37.0\text{ }c{{m}^{2}}\]
  done clear
  C)
  \[37.03\text{ }c{{m}^{2}}\]
  done clear
  D)
  \[37.030\text{ }c{{m}^{2}}\]
  done clear
  View Answer play_arrow

• 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)
  \[[{{M}^{-2}}{{L}^{-2}}{{T}^{6}}{{A}^{3}}]\]
  done clear
  B)
  \[[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}]\]
  done clear
  C)
  \[[{{M}^{-3}}{{L}^{-2}}{{T}^{8}}{{A}^{4}}]\]    
  done clear
  D)
  \[[{{M}^{-2}}{{L}^{0}}{{T}^{-4}}{{A}^{-2}}]\]  
  done clear
  View Answer play_arrow

• 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)
  \[M{{L}^{1}}\text{ }{{T}^{\,2}}\]
  done clear
  B)
  \[M{{L}^{2}}\text{ }{{T}^{\,\,2}}\]
  done clear
  C)
  \[M{{L}^{2}}\text{ }{{T}^{\,\,1}}\]
  done clear
  D)
  \[ML{{T}^{\,2}}\]
  done clear
  View Answer play_arrow

• 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)
  \[{{h}^{1/3}}{{G}^{2/3}}{{c}^{1/3}}{{A}^{1}}\]
  done clear
  B)
  \[{{h}^{2/3}}{{c}^{5/3}}{{G}^{1/3}}{{A}^{1}}\]
  done clear
  C)
  \[{{h}^{2/3}}{{c}^{1/3}}{{G}^{4/3}}{{A}^{1}}\]
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  0.001 mm
  done clear
  C)
  0.001 cm
  done clear
  D)
  0.02 mm
  done clear
  View Answer play_arrow

• 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
  done clear
  B)
  Area
  done clear
  C)
  Volume
  done clear
  D)
  Momentum
  done clear
  View Answer play_arrow

• 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)
  \[{{A}_{1}}+{{B}_{1}}+{{C}_{1}}={{A}_{2}}+{{B}_{2}}+{{C}_{2}}={{A}_{3}}+{{B}_{3}}+{{C}_{3}}=\]\[{{A}_{4}}+{{B}_{4}}+{{C}_{4}}\]
  done clear
  B)
  \[{{A}_{1}}+{{B}_{1}}+{{C}_{1}}<{{A}_{3}}+{{B}_{3}}+{{C}_{3}}<{{A}_{2}}+{{B}_{2}}+{{C}_{2}}<\]\[{{A}_{4}}+{{B}_{4}}+{{C}_{4}}\]
  done clear
  C)
  \[{{A}_{4}}+{{B}_{4}}+{{C}_{4}}<{{A}_{1}}+{{B}_{1}}+{{C}_{1}}={{A}_{2}}+{{B}_{2}}+{{C}_{2}}=\]\[{{A}_{3}}+{{B}_{3}}+{{C}_{3}}\]
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow