Consider two physical quantities A and B related to each other as \(E=\frac{B-x^2}{A t}\) where \(E, x\) and \(t\) have dimensions of energy, length and time respectively. The dimension of \(A B\) is _______.

Surface tension of two liquids (having same densities), \(T_1\) and \(T_2\), are measured using capillary rise method utilizing two tubes with inner radii of \(r_1\) and \(r_2\) where \(r_1>r_2\). The measured liquid heights in these tubes are \(h_1\) and \(h_2\) respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights \(h _1\) and \(h _2\) and surface tensions \(T _1\) and \(T _2\) satisfy the relation :

Given below are two statements : Statement \((I)\) : dimensions of specific heat is \(\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]\) Statement \((II)\) : dimensions of gas constant is \(\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]\)

Identify the semiconductor devices whose characteristics are given below, in the order \((a),(b),(c),(d) \) 

The translational degrees of freedom \((f)\) and rotational degrees of freedom \((f)\) of \(\mathrm{CH}_4\) molecule are _______.

The electric field in an electromagnetic wave is given by \(E =56.5 \sin \omega( t - x / c ) \;NC ^{-1}\). Find the intensity of the wave if it is propagating along \(x-\)axis in the free space. (Given \(\left.\varepsilon_{0}=8.85 \times 10^{-12} \;C ^{2} N ^{-1} m ^{-2}\right)\)

The width of fringe is \(2\,mm\) on the screen in a double slits experiment for the light of wavelength of \(400\,nm\). The width of the fringe for the light of wavelength \(600\,nm\) will be \(..............\,mm\)

Consider a long thin conducting wire carrying a uniform current I. A particle having mass " M " and charge " \(q\) " is released at a distance " \(a\) " from the wire with a speed \(v_0\) along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance \(x\) from the wire. The value of \(x\) is [ \(\mu_0\) is vacuum permeability]

Figure here shows \(P\) and \(Q\) as two equally intense coherent sources emitting radiations of wavelength \(20 \,m\). The separation \(PQ\) is \(5.0 \,m\) and phase of \(P\) is ahead of the phase of \(Q\) by \(90^{0}\). \(A, B \) and \( C\) are three distant points of observation equidistant from the mid-point of \(PQ\). The intensity of radiations at \(A, B, C\)  will bear the ratio

A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) 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 \(.......\%\)

Two thermodynamical process are shown in the figure. The molar heat capacity for process \(A\) and \(B\) are \(C_A\) and \(C_B\). The molar heat capacity at constant pressure and constant volume are represented by \(C_P\) and \(C_V\), respectively. Choose the correct statement.

A body of mass (\(2 {M}\)) splits into four masses \(\{{m}, {M}-{m}, {m}, {M}-{m}\}\), which are rearranged to form a square as shown in the figure. The ratio of \(\frac{{M}}{{m}}\) for which, the gravitational potential energy of the system becomes maximum is \({x}: 1\). The value of \(x\) is ..... .

A girl standing on road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15 \sqrt{2} \; kmh ^{-1}\), the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is ...........  \(kmh ^{-1}\)