The displacement of a particle moving afong x-axis with respect to time is given by x =at + bt² - ct³. The dimensions of b are ________________.

(a)

L⁰T^-3

(b)

LT^-3

(c)

LT^-2

(d)

LT³

The Van der Waal equation for n moles of a real gas is \((P+\frac{a}{V^2})(V-b)=RT\) where P is the pressure. V is the volume. T is the absolute temperature. R is the molar gas constant and 'a' and 'b' are Van der Waal constants. The dimensions of 'a' are the same as those of _______________.

(a)

\(\frac{P}{V}\)

(b)

PV

(c)

PV2

(d)

P2V

The dimensions of \(\frac { 1 }{ \sqrt { { \mu }_{ 0 }{ \varepsilon }_{ 0 } } } \) are the same as those of  ______________.

(a)

energy

(b)

acceleration

(c)

force

(d)

velocity

The speed of gravity waves in water is proportional to \(\lambda^a\rho^bg^y\) where \(\lambda\) is the wavelength, p is the density of water and g is the acceleration due to gravity. The correct relation between \(\alpha,\beta\) and r is _______________.

(a)

\(\alpha\ne\beta\ne\gamma\)

(b)

\(\alpha\ne\gamma=\beta\)

(c)

\(\alpha=\gamma\ne\beta\)

(d)

\(\alpha=\beta=\gamma\)

If E and B respectively, represent electric field and magnetic induction field, then the ratio \(\frac{E}{B}\) has the dimensions of _____________.

(a)

angle

(b)

acceleration

(c)

velocity

(d)

displacement