In the energy band diagram of a material shown below, the open circles and filled circles denote holes and electrons respectively. The material is a/an: 

1. p-type semiconductor

2. insulator

3. metal

4. n-type semiconductor

A car moves from \(X\) to \(Y\) with a uniform speed \(v_u\) and returns to \(X\) with a uniform speed \(v_d.\) The average speed for this round trip is:

A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:
1. $\frac{\mathrm{T}}{4}$
2. $\frac{\mathrm{T}}{8}$
3. $\frac{\mathrm{T}}{12}$
4. $\frac{\mathrm{T}}{2}$

A \(5~\text W\) emits monochromatic light of wavelength \(5000~\mathring{A}.\) When placed \(0.5~\text m\) away, it liberates photoelectrons from a photosensitive metallic surface. When the source is moved \(1.0~\text m\) away, the number of photoelectrons liberated is reduced by a factor of:
1. \(4\)
2. \(8\)
3. \(16\)
4. \(2\)

A block \(B\) is pushed momentarily along a horizontal surface with an initial velocity \(v.\) If \(\mu\) is the coefficient of sliding friction between \(B\) and the surface, the block \(B\) will come to rest after a time: 
 
1. \(v \over g \mu\)
2. \(g \mu \over v\)
3. \(g \over v\)
4. \(v \over g\)

Two radioactive substances A and B have decay constants 5λ and λ respectively. At t = 0, they have the same number of nuclei. The ratio of the number of nuclei of A to those of B will be $\frac{1}{e^2}$ after a time interval:

1. $\frac{1}{4\lambda }$

2. $4\lambda$

3. $2\lambda$

4. $\frac{1}{2\lambda }$

A hollow cylinder has a charge \(q\) coulomb within it (at the geometrical centre). If \(\phi\) is the electric flux in units of Volt-meter associated with the curved surface \(B,\) the flux linked with the plane surface \(A\) in units of volt-meter will be: 
           
1. \(\frac{1}{2}\left(\frac{q}{\varepsilon_0}-\phi\right)\)
2. \(\frac{q}{2\varepsilon_0}\)
3. \(\frac{\phi}{3}\)
4. \(\frac{q}{\varepsilon_0}-\phi\)

A transformer is used to light a \(100~\text{W}\) and \(110~\text{V}\) lamp from a \(220~\text{V}\) main. If the main current is \(0.5~\text{A},\) the efficiency of the transformer is approximately:
1. \(30\%\)
2. \(50\%\)
3. \(90\%\)
4. \(10\%\)

A particle of mass \(m\) moves in the XY plane with a velocity \(v\) along the straight line AB. If the angular momentum of the particle with respect to the origin \(O\) is \(L_A\) when it is at \(A\) and \(L_B\) when it is at \(B,\) then: