Two resistors \({R}_{1}=(4 \pm 0.8) \Omega\) and \({R}_{2}=(4 \pm 0.4)\) \(\Omega\) are connected in parallel. The equivalent resistance of their parallel combination will be

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

The ratio for the speed of the electron in the \(3^{ rd }\) orbit of \(He ^{+}\)to the speed of the electron in the \(3^{\text {ad }}\) orbit of hydrogen atom will be

A uniform disc of mass \(0.5\,kg\) and radius \(r\) is projected with velocity \(18\,m / s\) at \(t =0\,s\) on a rough horizontal surface. It starts off with a purely sliding motion at \(t =0\,s\). After \(2\,s\) it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after \(2\,s\) will be \(..............J\) (given, coefficient of friction is \(0.3\) and \(\left.g =10\,m / s ^2\right)\)

The refractive index of the material of a glass prism is \(\sqrt{3}\). The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

A cylindrical wire of mass \((0.4 \pm 0.01)\,g\) has length \((8 \pm 0.04)\,cm\) and radius \((6 \pm 0.03)\,mm\).The maximum error in its density will be \(......\,\%\)

Match List \(- I\) with List \(- II\)

List\(-I\) (Layer of atmosphere)	List\(-II\) (Approximate height over earth's surface)
\((A)\) \(F_1\) - Layer	\((I)\) \(10\,km\)
\((B)\) \(D-\) Layer	\((II)\) \(170-190\,km\)
\((C)\) Troposphere	\((III)\) \(100\,km\)
\((D)\) \(E-\)layer	\((IV)\) \(65-75\,km\)

Choose the correct answer from the options given below:

A nucleus with mass number \(242\) and binding energy per nucleon as \(7.6\,MeV\) breaks into fragment each with mass number \(121\) . If each fragment nucleus has binding energy per nucleon as \(8.1\,MeV\), the total gain in binding energy is \(........MeV\)

A 4.0 cm long straight wire carrying a current of 8A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ______ mN.