A convex lens \({A}\) of focal length \(20~\text{cm}\) and a concave lens \({B}\) of focal length \(5~\text{cm}\) are kept along the same axis with a distance \(d\) between them. If a parallel beam of light falling on \(A\) leaves \(B\) as a parallel beam, then the distance \(d\) in cm will be: 

1. 50 
2. 30 
3. 25 
4. 15

A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since:

The electron concentration in an \(\mathrm{n\text-}\)type semiconductor is the same as the hole concentration in a \(\mathrm{p\text{-}}\)type semiconductor. An external field (electric) is applied across each of them. Compare the currents in them.

If a body is executing simple harmonic motion with frequency 'n', then the frequency of its potential energy is:

A cup of coffee cools from \(90^{\circ}\mathrm{C}\) $\mathrm{to}$ \(80~^{\circ}\mathrm{C}\) in t minutes, when the room temperature is \(20^{\circ}\mathrm{C}\)$\mathrm{}$. The time taken by a similar cup of coffee to cool from \(80^{\circ}\mathrm{C}\) $\mathrm{to}$ \(60^{\circ}\mathrm{C}\) at room temperature same at \(20^{\circ}\mathrm{C}\) is:
1. \(\frac{10}{13}t\) 
2. \(\frac{5}{13}t\)
3. \(\frac{13}{10}t\)
4. \(\frac{13}{5}t\)

In a potentiometer circuit, a cell of emf \(1.5~\text{V}\) gives a balance point at 36 cm length of wire. If another cell of emf 2.5 V replaces the first cell, then at what length of the wire, the balance point occur? 
1. 64 cm 
2. 62 cm 
3. 60 cm 
4. 21.6 cm

The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section, and same material is \(0.25~\Omega\). What will be the effective resistance if they are connected in series?
1. \(1~\Omega\) 
2. \(4~\Omega\)
3. \(0.25~\Omega\)
4. \(0.5~\Omega\)

A radioactive nucleus \(_{\mathrm{Z}}^{\mathrm{A}}\mathrm{X}\) undergoes spontaneous decay in the sequence \(_{\mathrm{Z}}^{\mathrm{A}}\mathrm{X}\rightarrow \mathrm{B}_{\mathrm{Z-1}}\rightarrow \mathrm{C}_{\mathrm{Z-3}}\rightarrow \mathrm{D}_{\mathrm{Z-2}}\) where \(\mathrm{Z}\) is the atomic number of element \(\mathrm{X}\). The possible decay particles in the sequence are: 

A dipole is placed in an electric field as shown. In which direction will it move? 

An inductor of inductance \(L\), a capacitor of capacitance \(C\) and a resistor of resistance \(R\) are connected in series to an AC source of potential difference \(V\) volts as shown in Figure. The potential difference across \(L\), \(C\) and \(R\) is \(40~\text{V}\), \(10~\text{V}\) and \(40~\text{V}\), respectively. The amplitude of the current flowing through the \(LCR\) series circuit is \(10\sqrt{2}~\text{A}\). The impedance of the circuit will be:

      
1. \(4~\Omega\)
2. \(5~\Omega\)
3. \(4\sqrt{2}~\Omega\)
4. \(\frac{5}{\sqrt{2}}~\Omega\)