A person can see objects clearly only when they lie between \(50\) cm and \(400\) cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be:

A linear aperture whose width is \(0.02\) cm is placed immediately in front of a lens of focal length \(60\) cm. The aperture is illuminated normally by a parallel beam of wavelength \(5\times 10^{-5}\) cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is:

Electrons of mass m with de- Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength (λ_o) of the emitted X-ray is:

1.  ${\mathrm{\lambda }}_0=\frac{2{\mathrm{mc\lambda }}^2}{\mathrm{h}}$

2.  ${\mathrm{\lambda }}_0=\frac{2\mathrm{h}}{\mathrm{mc}}$

3.  ${\mathrm{\lambda }}_0=\frac{2{\mathrm{m}}^2{\mathrm{c}}^2{\mathrm{\lambda }}^2}{{\mathrm{h}}^2}$

4.  ${\mathrm{\lambda }}_0=\mathrm{\lambda }$

Photons with energy \(5~\text{eV}\) are incident on a cathode \(C\) in a photoelectric cell. The maximum energy of emitted photoelectrons is \(2~\text{eV}.\) When photons of energy \(6~\text{eV}\) are incident on \(C,\) no photoelectrons will reach the anode \(A,\) if the stopping potential of \(A\) relative to \(C\) is:
1. \(+3~\text{V}\)
2. \(+4~\text{V}\)
3. \(-1~\text{V}\)
4. \(-3~\text{V}\)

The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is:

1. 15

2. 30

3. 45

4. 60

For the CE transistor amplifier, the audio signal voltage across the collector resistance of 2k$\Omega$ is 4V. If the current amplification factor of the transistor is 100 and the base resistance is 1k$\Omega$, then the input signal voltage is:

1.  10 mV

2.  20 mV

3.  30 mV

4.  15 mV

The given circuit has two ideal diodes connected as shown in the figure below. The current flowing through the resistance \(R_1\) will be:

What is the output \(Y\) in the following circuit, when all the three inputs \(A\), \(B\), and \(C\) are first \(0\) and then \(1\)? 
                          
1. \(0,1\)
2. \(0,0\)
3. \(1,0\)
4. \(1,1\)