Two persons \(A\) and \(B\) perform same amount of work in moving a body through a certain distance \({d}\) with application of forces acting at angle \(45^{\circ}\) and \(60^{\circ}\) with the direction of displacement respectively. The ratio of force applied by person \(A\) to the force applied by person \(B\) is \(\frac{1}{\sqrt{x}}\). The value of \(x\) is ...... .

Refer to the logic circuit given below. For two inputs \((A=1, B=1)\) and \((A=0, B=1)\), output \((Y)\) will be __________.

Three masses \(M =100\,kg , m _{1}=10\,kg\) and \(m_{2}=20\,kg\) are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. \(A\) force \(F\) is applied on the system so that the mass \(m_{2}\) moves upward with an acceleration of \(2\,ms ^{-2}\). The value of \(F\) is \(......N\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)

The amplitude of wave disturbance propagating in the positive \(x\)-direction is given by \(y=\frac{1}{(1+x)^{2}}\) at time \(t=0\) and \(y=\frac{1}{1+(x-2)^{2}}\) at \(t=1\) s, where \(x\) and \(y\) are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be \(...\,{m} / {s}.\)

A moving coil galvanometer allows a full scale current of \(10^{-4}\, A\). A series resistance of \(2\, M\,\Omega \) is required to convert the above galvanometer into a voltmeter of range \(0 -5\, V\). Therefore the value of shunt resistance required to convert the above galvanometer into a ammeter of range \(0-10\, mA\) is....\(\Omega \)

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The value of \(x\) is \(.......\)

One mole of an ideal monoatomic gas is taken along the path \(ABCA\)  as shown in the \(PV\) diagram. The maximum temperature attained by the gas along the path \(BC\)  is given by

Two wavelengths \(\lambda_1\) and \(\lambda_2\) are used in Young's double slit experiment \(\lambda_1=450 \mathrm{~nm}\) and \(\lambda_2=650 \mathrm{~nm}\). The minimum order of fringe produced by \(\lambda_2\) which overlaps with the fringe produced by \(\lambda_1\) is \(n\). The value of \(n\) is _________.

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

The value of net resistance of the network as shown in the given figure is _______.

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are \(B_1\) and \(B_2\) respectively, then the ratio \(\dfrac{B_1}{B_2}\) is _______.