A cubical block of side \(0.5\,m\) floats on water with \(30\%\) of its volume under water. ....... \(kg\) is the maximum weight that can be put on the block without fully submerging it under water ? [Take density of water \(= 10^3\,kg/m^3\) ]

Four identical long solenoids \(A, B, C\) and \(D\) are connected to each other as shown in the figure. If the magnetic field at the center of \(A\) is \(3\, T\), the field at the center of \(C\) would be........... \(T\) (Assume that the magnetic field is confined with in the volume of respective solenoid).

A convex lens of refractive index \(1.5\) and focal length \(18 cm\) in air is immersed in water. The change in focal length of the lens will be \(...........cm\).\(\left(\right.\) Given refractive index of water \(\left.=\frac{4}{3}\right)\)

The gap between the plates of a parallel plate capacitor of area \(A\) and distance between plates \(d\), is filled with a dielectric whose permittivity varies linearly from \({ \varepsilon _1}\) at one plate to \({ \varepsilon _2}\) at the other. The capacitance of capacitor is

Consider the following logic circuit.

The output is \(\mathrm{Y}=0\) when :

A massless spring gets elongated by amount \(x_1\) under a tension of 5 N . Its elongation is \(x_2\) under the tension of 7 N . For the elongation of \(\left(5 x_1-2 x_2\right)\), the tension in the spring will be,

The r.m.s speed of oxygen molecules at \(47^{\circ} C\) is equal to that of the hydrogen molecules kept at _________ \({ }^{\circ} C\). (Mass of oxygen molecule/mass of hydrogen molecule \(=32 / 2\) )

A radioactive nucleus decays by two different processes. The half life for the first process is \(10\, s\) and that for the second is \(100 s\). the effective half life of the nucleus is close to\(.....sec\)

\(ABC\) is a plane lamina of the shape of an equilateral triagnle. \(D,\) \(E\) are mid points of \(AB\), \(AC\) and \(G\) is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through \(G\) and perpendicular to the plane \(ABC\) is \(I _{0} .\) If part \(ADE\) is removed, the moment of inertia of the remaining part about the same axis is \(\frac{ NI _{0}}{16}\) where \(N\) is an integer. Value of \(N\) is

A metallic sphere cools from \(50^{\circ} C\) to \(40^{\circ} C\) in \(300 \,s.\) If atmospheric temperature around is \(20^{\circ} C ,\) then the sphere's temperature after the next \(5\) minutes will be close to\(.....C\)

The truth table for the followng logic circuit is ...... .

Let a total charge \(2Q\) be distributed in a sphere of radius \(R\), with the charge density given by \(\rho(r) = kr\), where \(r\) is the distance from the centre. Two charges \(A\) and \(B\), of \(-Q\) each, are placed on diametrically opposite points, at equal distance, \(a\), from the centre. If \(A\) and \(B\) do not experience any force, then

A nucleus of masss \(M\) emits \(\gamma\)-ray photon of frequency \('v'.\) The loss of internal energy by the nucleus is: