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The force is given in terms of time \( t \) and displacement \( x \) by the equation \( F = A \cos Bx + C \sin Dt \).
The dimensional formula of \( \dfrac{AD}{B} \) is:

Which of the following equations is dimensionally incorrect? Where \( t = \) time, \( h = \) height, \( s = \) surface tension, \( \theta = \) angle, \( \rho = \) density, \( a, r = \) radius, \( g = \) acceleration due to gravity, \( v = \) volume, \( p = \) pressure, \( W = \) work done, \( \Gamma = \) torque, \( \varepsilon = \) permittivity, \( E = \) electric field, \( J = \) current density, \( L = \) length

If velocity \( [V] \) time \( [T] \) and force \( [F] \) are chosen as the base quantities, the dimensions of the mass will be:

An electron having de-Broglie wavelength \( \lambda \) is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is:

Match List I with List II

Choose the correct answer from the options given below:

If force \( (F) \), length \( (L) \) and time \( (T) \) are taken as the fundamental quantities. Then what will be the dimension of density:

Match List-I with List-II

Choose the most appropriate answer from the option given below:

Match List - I with List - II:

Choose the most appropriate answer from the options given below :

Which of the following is not a dimensionless quantity?

If \( E \), \( L \), \( M \) and \( G \) denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of \( P \) in the formula \( P = E L^{2} M^{-5} G^{-2} \) are:

The entropy of any system is given by \( S = \alpha^2 \beta \ln \left[ \dfrac{\mu k R}{J \beta^2} + 3 \right] \) where \( \alpha \) and \( \beta \) are the constants. \( \mu, J, k \) and \( R \) are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively. [Take \( S = \dfrac{dQ}{T} \)]
Choose the incorrect option from the following:

If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be:

Match List-I with List-II.

Choose the most appropriate answer from the options given below:

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JEE Main 2021 31st August Evening Shift

If velocity \( [V] \) time \( [T] \) and force \( [F] \) are chosen as the base quantities, the dimensions of the mass will be: