A flask contains hydrogen and oxygen in the ratio of \(2: 1\) by mass at temperature \(27^{\circ} C\). The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

Two p-n junction diodes \(D _1\) and \(D _2\) are connected as shown in figure. A and B are input signals and C is the output. The given circuit will function as a ___________.

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where \(\gamma\) is the ratio of specific heats):

A cylinder of mass \(M_c\) and sphere of mass \(M_s\) are placed at points \(A\) and \(B\) of two inclines, respectively (See Figure). If they roll on the incline without sipping such that their accelerations are the same, then the ratio \(\frac{{\sin \,{\theta _c}}}{{\sin \,{\theta _s}}}\) is

The equivalent resistance between \(A\) and \(B\) of the network shown in figure

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is

At some location on earth the horizontal component of earth’s magnetic field is \(18\times10^{-6}\,T\). At this location, magnetic needle of length \(0.12\, m\) and pole strength \(1.8\, A\,m\) is suspended from its mid-point using a thread, it makes \(45^o\) angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is

A uniform wire (Young's modulus \(2 \times 10^{11}\, Nm^{-2}\) ) is subjected to longitudinal tensile stress of \(5 \times 10^7\,Nm^{-2}\) . If the over all volume change in the wire is \(0.02\%,\) the fractional decrease in the radius of the wire is close to

Find the equivalent resistance between two ends of the following circuit

From a solid sphere of mass \(M\) and radius \(R\) a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is

A uniform rod \(AB\) is suspended from a point \(X\), at a variable distance from \(x\) from \(A\), as shown. To make the rod horizontal, a mass \(m\) is suspended from its end \(A\). A set of \((m, x)\) values is recorded. The appropriate variable that give a straight line, when plotted, are

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 \(......cm\).