The magnification produced by an astronomical telescope for normal adjustment is \(10\) and the length of the telescope is \(1.1~\mathrm{m}\). The magnification, when the image is formed at least distance of distinct vision is:
1. \(6\)
2. \(18\)
3. \(16\)
4. \(14\)

A circular current-carrying coil has a radius \(R.\) The distance from the centre of the coil, on the axis, where \(B\) will be \(\frac18\) of its value at the centre of the coil is:
1. \(\frac{R}{\sqrt3}\)
2. \(\sqrt3R\)
3. \(2\sqrt3R\)
4. \(\frac{2R}{\sqrt3}\)

Two different isotherms representing the relationship between pressure \(P\) and volume \(V\) at a given temperature of the same ideal gas are shown for masses \(m_1\) and \(m_2,\) then:

A ⁷Li target is bombarded with a proton beam current 10^-4 A for one hour to produce ⁷Be of activity 1.8 × 10⁸ disintegrations per second. Assuming that one ⁷Be radioactive nuclei is produced by bombarding 1000 protons, its half-life is:
1. 0.87 × 10⁷ s
2. 0.2 × 10⁷ s
3. 0.67 × 10⁸ s
4. 0.87 × 10⁶ s

In the given figure, the capacitors C₁, C₃, C₄, C₅ have a capacitance \(4~\mu F\) each. If the capacitor C₂ has a capacitance of \(10~\mu F,\) then the effective capacitance between \(A\) and \(B\) will be:

1. \(2~\mu F\)
2. \(6~\mu F\)
3. \(4~\mu F\)
4. \(8~\mu F\)

A sphere of mass m moving with velocity \(v\) hits in elastically with another stationary sphere of the same mass. The ratio of their final velocities will be: (in terms of \(e\))
1. \(\frac{v_1}{v_2}=\frac{1+e}{1-e}\)
2. \(\frac{v_1}{v_2}=\frac{1-e}{1+e}\)
3. \(\frac{v_1}{v_2}=\frac{1+e}{2}\)
4. \(\frac{v_1}{v_2}=\frac{1-e}{2}\)