If \(1000\) droplets of water of surface tension \(0.07\,N / m\). having same radius \(1\,mm\) each, combine to from a single drop. In the process the released surface energy is \(\left(\text { Take } \pi=\frac{22}{7}\right)\)

Given below are two statements: Statement \(I:\) For diamagnetic substance \(-1 \leq \chi < 0\), where \(\chi\) is the magneticsusceptibility. Statement \(II:\) Diamagnetic substances when placed in an external magnetic field, tend to move from stronger to weaker part of the field. In the light of the above statements, choose the correct answer from the options given below.

Two long parallel wires \(X\) and \(Y\), separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is \(x \times 10^{-5} \mathrm{~T}\). The value of \(x\) is__________ . Take permeability of free space as \(\mu_0=4 \pi \times 10^{-7} \mathrm{SI}\) units.

The sum of two forces \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) is \(\overrightarrow{\mathrm{R}}\) such that \(|\overrightarrow{\mathrm{R}}|=|\overrightarrow{\mathrm{P}}| .\) The angle \(\theta\) (in degrees) that the resultant of \(2 \overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) will make with \(\overrightarrow{\mathrm{Q}}\) is

Three concentric spherical metallic shells \(X , Y\) and \(Z\) of radius \(a , b\) and c respectively \([ a < b < c ]\) have surface charge densities \(\sigma,-\sigma\) and \(\sigma\), respectively. The shells \(X\) and \(Z\) are at same potential. If the radii of \(X\) and \(Y\) are \(2\,cm\) and \(3\,cm\), respectively.The radius of shell \(Z\) is \(......cm\).

A particle of mass \(20\,g\) is released with an initial velocity \(5\,m/s\) along the curve from the point \(A,\) as shown in the figure. The point \(A\) is at height \(h\) from point \(B.\) The particle slides along the frictionless surface. When the particle reaches point \(B,\) its angular momentum about \(O\) will be ......... \(kg - m^2/s\). [Take \(g = 10\,m/s^2\) ]

Two identical spherical balls of mass \(M\) and radius \(R\) each are stuck on two ends of a rod of length \(2R\) and mass \(M\) (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

10 kg of ice at \(-10^{\circ}C\) is added to 100 kg of water to lower its temperature from \(25^{\circ}C.\) Consider no heat exchange to surroundings. The decrement to the temperature of water is ___________ \(^{\circ}C.\)
(specific heat of ice \(= 2100\ J/Kg.^{\circ}C\), specific heat of water \(= 4200\ J/Kg.^{\circ}C\), latent heat of fusion of ice \(= 3.36 \times 10^{5}\ J/Kg\))