JEE Main 2021 (Online) 16th March Morning Shift | Units & Measurements Question 105 | Physics

One main scale division of a vernier callipers is 'a' cm and n^th division of the vernier scale coincide with (n $$-$$ 1)^th division of the main scale. The least count of the callipers in mm is :

$${{10a} \over n}$$

$${{10na} \over {(n - 1)}}$$

$$\left( {{{n - 1} \over {10n}}} \right)a$$

$${{10a} \over {(n - 1)}}$$

JEE Main 2021 (Online) 26th February Evening Shift

MCQ (Single Correct Answer)

-1

If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of $$\lambda$$ where C/V = $$\lambda$$ ?

$$[{M^{ - 3}}{L^{ - 4}}{I^3}{T^7}]$$

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

$$[{M^{ - 2}}{L^{ - 4}}{I^3}{T^7}]$$

$$[{M^{ - 1}}{L^{ - 3}}{I^{ - 2}}{T^{ - 7}}]$$

JEE Main 2021 (Online) 26th February Morning Shift

MCQ (Single Correct Answer)

-1

In a typical combustion engine the workdone by a gas molecule is given by $$W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {kT}}}}$$, where x is the displacement, k is the Boltzmann constant and T is the temperature. If $$\alpha$$ and $$\beta$$ are constants, dimensions of $$\alpha$$ will be :

$$[{M^0}L{T^0}]$$

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

$$[ML{T^{ - 2}}]$$

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

JEE Main 2021 (Online) 25th February Evening Shift

MCQ (Single Correct Answer)

-1

If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $${1 \over {4\pi {\varepsilon _0}}}{{|e{|^2}} \over {hc}}$$ has dimensions of :

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

$$[ML{T^0}]$$

$$[{M^0}{L^0}{T^0}]$$

$$[L{C^{ - 1}}]$$

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