\(P-T\) diagram of an ideal gas having three different densities \(\rho_1, \rho_2, \rho_3\) (in three different cases) is shown in the figure. Which of the following is correct?

A uniform rectangular thin sheet \(ABCD\) of mass \(M\) has length \(a\) and breadth \(b\), as shown in the figure. If the shaded portion \(HBGO\) is cut off, the coordinates of the centre of mass of the remaining portion will be

A slanted object \(A B\) is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is:

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
\(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right) V / m\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is __________ .
(speed of light in free space is \(3 \times 10^8 m / s\) )

Shown in the figure are two point charges \(+Q\) and \(-Q\) inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If \(\sigma _1\) is the surface charge on the inner surface and \(Q_1\) net charge on it and \(\sigma _2\) the surface charge on the outer surface and \(Q_2\) net charge on it then

Two identical solid spheres each of mass \(2\,kg\) and radii \(10\,cm\) are fixed at the ends of a light rod. The separation between the centres of the spheres is \(40\,cm\). The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is \(........... \times 10^{-3}\,kg - m ^2\)

A \(200\,\Omega \) resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be .............. \(\Omega\)

What will be the nature of flow of water from a circular tap, when its flow rate increased from \(0.18\, L / min\) to \(0.48\, L / min\) ? The radius of the tap and viscosity of water are \(0.5\, cm\) and \(10^{-3}\, Pa s\), respectively. (Density of water : \(10^{3}\, kg / m ^{3}\) )

A block of mass \(m\) is kept on a platform which starts from rest with constant acceleration \(g/2\) upward, as shown in figure. Work done by normal reaction on block in time \(t\) is

A mass of \(10\,kg\) is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of \(45^o\) at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ..........  \(N\) \((g = 10\,ms^{-2})\) 

A Zener of breakdown voltage \(V_{z}=8\,V\) and maximum zener current, \(I _{ ZM }=10\,mA\) is subjected to an input voltage \(V _{ i }=10\,V\) with series resistance \(R=100\,\Omega\). In the given circuit \(R_{L}\) represents the variable load resistance. The ratio of maximum and minimum value of \(R_{L}\) is

A bakelite beaker has volume capacity of \(500\, cc\) at \(30^{\circ} C\). When it is partially filled with \(V _{ m }\) volume (at \(30^{\circ}\) ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If \(\gamma_{\text {(beaker) }}=6 \times 10^{-6}{ }^{\circ} C ^{-1}\) and \(\gamma_{(\text {mercury })}=1.5 \times 10^{-4}{ }^{\circ} C ^{-1},\) where \(\gamma\) is the coefficient of volume expansion, then \(V _{ m }(\)in \(cc )\) is close to