The frequency of a car horn encountered a change from \(400\, {Hz}\) to \(500\, {Hz}\), when the car approaches a vertical wall. If the speed of sound is \(330\, {m} / {s}\). Then the speed of car is \(.....\,{km} / {h} .\)

The increase in pressure required to decrease the volume of a water sample by \(0.2 \%\) is \(\mathrm{P} \times 10^5 \mathrm{Nm}^{-2}\). Bulk modulus of water is \(2.15 \times 10^9 \mathrm{Nm}^{-2}\). The value of P is ________.

In this figure the resistance of the coil of galvanometer \(G\) is \(2\,\Omega\). The emf of the cell is \(4\,V\). The ratio of potential difference across \(C_1\) and \(C_2\) is:

Least count of a vernier caliper is \(\frac{1}{20 \mathrm{~N}} \mathrm{~cm}\). The value of one division on the main scale is \(1 \mathrm{~mm}\). Then the number of divisions of main scale that coincide with \(\mathrm{N}\) divisions of vernier scale is _______.

Two blocks of masses \(3 \,{kg}\) and \(5\, {kg}\) are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \(\frac{24}{\pi} \times 10^{2}\, {Nm}^{-2}\). What is the minimum radius of the wire? (Take \(\left.g=10\, {ms}^{-2}\right)\) (in \(cm\))

An electric dipole has a fixed dipole moment \(\vec P\) which makes angle \(\theta \) with respect to \(x-\)axis. When subjected to an electric field \(\overrightarrow {{E_1}} \) \(=E\)\(\hat i\) it experiences a torque \(\overrightarrow {{T_1}} \) =\(\;\tau \hat k\) When subjected to another electric field \(\overrightarrow {{E_2}}  = \sqrt 3 {E_1}\hat j\) it experiences torque \(\overrightarrow {{T_2}} \) = \( - \overrightarrow {{T_1}} \) The angle \(\theta \;\) is.......\(^o\)

Water is flowing at a speed of \(1.5\, ms^{-1}\) through a horizontal tube of cross-sectional area  \(10^{-2}\, m^2\) and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm. the minimum force that you must exert should be ......... \(N\) (density of water \(= 10^3\, kgm^{-3}\))

Statement \(I :\) The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet. Statement \(II :\) At high temperature, the domain wall area of a ferromagnetic substance increases. In the light of the above statements, choose the most appropriate answer from the options given below :