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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 27th August Evening Shift

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