The electric current in a circular coil of four turns produces a magnetic induction \(32\,T\) at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be \(..........\,T\)

In the given figure the magnetic flux through the loop increases according to the relation \(\phi_{B}(t)=10 t^{2}+20 t\), where \(\phi_{B}\) is in milliwebers and \(t\) is in seconds. The magnitude of current through \({R}=2 \,\Omega\) resistor at \({t}=5\, {s}\) is \(....\,{mA}\).

In an expression a \(\times 10^{\mathrm{b}}\) _______.

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be..... \(\%\).

A ray of light is incident from air on a glass plate having thickness \(\sqrt{3} \,cm\) and refractive index \(\sqrt{2}\). The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is \(.......\times 10^{-2}\) (given \(\sin 15^{\circ}=0.26\) )

The position vector of the centre of mass \(\vec r\, cm\) of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

A single turn current loop in the shape of a right angle triangle with sides \(5\,cm , 12\,cm , 13\,cm\) is carrying a current of \(2\,A\). The loop is in a uniform magnetic field of magnitude \(0.75\,T\) whose direction is parallel to the current in the \(13\,cm\) side of the loop. The magnitude of the magnetic force on the \(5\,cm\) side will be \(\frac{ x }{130}\,N\). The value of \(x\) is \(..........\)

Following statements are given : \((1)\) The average kinetic energy of a gas molecule decreases when the temperature is reduced. \((2)\) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. \((3)\) The average kinetic energy of a gas molecule decreases with increases in volume. \((4)\) Pressure of a gas increases with increase in temperature at constant pressure. \((5)\) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below:

Distance of the centre of mass of a solid uniform cone from its vertex is \(z_0\) . If the radius of its base is \(R\) and its height is \(h\) then \(z_0\) is equal to

Vectors \(a \hat{i}+b \hat{j}+\hat{k}\) and \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) are perpendicular to each other when \(3 a+2 b=7\), the ratio of a to \(b\) is \(\frac{x}{2}\). The value of \(x\) is \(..............\)

Match List\(-I\) with List\(-II\) 

List\(-I\)	List\(-II\)
\((A)\) \(AC\) generator	\((I)\) Detects the presence of current in the circuit
\((B)\) Galvanometer	\((II)\) Converts mechanical energy into electrical energy
\((C)\) Transformer	\((III)\) Works on the principle of resonance in \(AC\) circuit
\((D)\) Metal detector	\((IV)\) Changes an alternating voltage for smaller or greater value

Choose the correct answer from the options given below

In the given circuit, the magnitude of \(V_{L}\) and \(V_{C}\) are twice that of \(V_{R}\). Given that \(f=50\,Hz\), the inductance of the coil is \(\frac{1}{ K \pi}\,mH\). The value of \(K\) is_________