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If force \( (F) \), velocity \( (V) \) and time \( (T) \) are considered as fundamental physical quantity, then dimensional formula of density will be:

The equation of a circle is given by \( x^{2}+y^{2}=a^{2} \), where \( a \) is the radius. If the equation is modified to change the origin other than \( (0,0) \), then find out the correct dimensions of \( A \) and \( B \) in a new equation: \( (x-At)^{2}+\left(y-\dfrac{t}{B}\right)^{2}=a^{2} \). The dimension of \( t \) \( [T^{-1}] \).

Electric field in a certain region is given by \( \vec{E} = \left( \frac{A}{x^{2}} \hat{i} + \frac{B}{y^{3}} \hat{j} \right) \). The SI unit of \( A \) and \( B \) are:

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A body of mass \( (5 \pm 0.5) \, \text{kg} \) is moving with a velocity of \( (20 \pm 0.4) \, \text{m/s} \). Its kinetic energy will be:

If the velocity of light \( c \), universal gravitational constant \( G \) and Planck’s constant \( h \) are chosen as fundamental quantities. The dimensions of mass in the new system is:

The speed of a wave produced in water is given by \( \nu = \lambda^{a} g^{b} \rho^{c} \). Where \( \lambda \), \( g \) and \( \rho \) are wavelength of wave, acceleration due to gravity and density of water respectively. The values of \( a \), \( b \) and \( c \) respectively, are:

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Dimension of \( \dfrac{1}{\mu_0 \, \epsilon_0} \) should be equal to:

The frequency \( (\nu) \) of an oscillating liquid drop may depend upon radius \( (r) \) of the drop, density \( (\rho) \) of liquid and the surface tension \( (s) \) of the liquid as: \( \nu = r^{a} \rho^{b} s^{c} \). The values of \( a \), \( b \) and \( c \) respectively are:

 A physical quantity \( P \) is given as \( P = \dfrac{a^{2} b^{3}}{c \sqrt{d}} \)
The percentage error in the measurement of \( a \), \( b \), \( c \) and \( d \) are \( 1\% \), \( 2\% \), \( 3\% \) and \( 4\% \) respectively. The percentage error in the measurement of quantity \( P \) will be:

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If \( R \), \( X_L \), and \( X_C \) represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as \( 5.25 \, \text{mm} \) and apparent thickness of the glass slab as \( 5.00 \, \text{mm} \). Travelling microscope has \( 20 \) divisions in one \( \text{cm} \) on main scale and \( 50 \) divisions on vernier scale is equal to \( 49 \) divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is \( \dfrac{x}{10} \times 10^{-3} \), where \( x \) is __________.

Match List I with List II:

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Match List I with List II

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