Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202529 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Morning Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2025 · 29 January · Morning Shift · Physics · Units and Dimensions

The expression given below shows the variation of velocity (v) with...

The expression given below shows the variation of velocity (v)(v) with time (t), (v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}). The dimension of ABC is :

Options

  1. A(\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-3}\right])
  2. B(\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-2}\right])
  3. C(\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-2}\right])
  4. D(\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-3}\right])

Correct answer

D. (\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-3}\right])

Step-by-step solution

[LT−1]=[A][T2]=[B][T][C]+[T][C]=[T][A]=[ LT −3][B]=[LT−1][ABC]=[L2 T−3]\begin{aligned} & {\left[\mathrm{LT}^{-1}\right]=[\mathrm{A}]\left[\mathrm{T}^2\right]=\frac{[\mathrm{B}][\mathrm{T}]}{[\mathrm{C}]+[\mathrm{T}]}} \\ & {[\mathrm{C}]=[\mathrm{T}]} \\ & {[\mathrm{A}]=\left[\mathrm{\text{ LT }}^{-3}\right]} \\ & {[\mathrm{B}]=\left[\mathrm{LT}^{-1}\right]} \\ & {[\mathrm{ABC}]=\left[\mathrm{L}^2 \mathrm{~T}^{-3}\right]}\end{aligned}
Practice Units and Dimensions on Quantrex Academy →

More from Units and Dimensions

In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s… JEE Advanced 2026A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum.… JEE Main 2026Consider the equation H = (x^p ε^q E^r)/(t^s) , where H= magnetic field; E= electric… JEE Main 2026The percentage error in the calculated volume of a sphere, if there is 2\% error in its… JEE Main 2026Match List - I with List - II. List - I List - II A. Boltzmann constant I. [M^ -1 L^3T^… JEE Main 2026The potential energy of a particle changes with distance x from a fixed origin as V = A x… JEE Main 2026Match List-I with List-II. List-I List-II A. Meter (L) I. (hc)/(G) B. Second (S) II.… JEE Main 2026L , C and R represents physical quantities inductance, capacitance and resistance… JEE Main 2026 Full Units and Dimensions list All JEE Main PYQs