Real power consumption in a circuit is least when it contains:
1. High \(R\), low \(L\) 
2. High \(R\), high \(L\) 
3. Low \(R\), high \(L\) 
4. High \(R\), low \(C\)

The linear density of a string is \(1.3\times 10^{-4}~\mathrm{kg/m}\) and the wave equation is \(y=0.021\sin(x+30t)\). 
What is the tension in the string, where \(x\) is in meters and \(t\) in seconds?
1. \( 0.12 \mathrm{~N} \)
2. \( 0.21 \mathrm{~N} \)
3. \(1.2 \mathrm{~N} \)
4. \( 0.012 \mathrm{~N}\)

Magnetic field at point O will be: (assume straight wire segments are infinite)
    
1. \(\frac{\mu_{_0}l}{2R}\) interior
2. \(\frac{\mu_{_0}l}{2R}\) exterior
3. \(\frac{\mu_{_0}l}{2R}1-\frac{l}{\pi}\) interior
4. \(\frac{\mu_{_0}l}{2R}1-\frac{l}{\pi}\) exterior

In Young's double-slit experiment, the spacing between two slits is \(0.1\) mm. If the screen is kept at \(1.0\) m from the slits and the wavelength of light is \(5000\) Å, then the fringe width is:
1. \(5\) cm
2. \(0.5\) m
3. \(1\) cm
4. \(0.5\) cm

According to Bohr's model of a hydrogen atom, the relation between the principal quantum number \(n\) and the radius of the stable orbit is:
1. \(r\propto\frac1n\)
2. \(r\propto n\)
3. \(r\propto\frac{1}{n^2}\)
4. \(r\propto n^2\)

An observer is approaching with velocity \(v\) towards a light source. If the velocity of light is \(c,\) then the velocity of light with respect to the observer will be:
1. \(c-v\)
2. \(c\)
3. \(c+v\)
4. \(\sqrt{1-v^2/c^2}\)

Magnetic field of the earth is H = 0. 3 g. A magnet vibrates 5 oscillations per min. then the depreciation required in the magnetic field of the earth of increased time period up to 10 oscillations per minute is:

1. 2.25 g

2. 0.6 g

3. 0.9 g

4. 0.12 g

Work function of a metal is \(5.2 \times 10^{-18}~\mathrm{J} \) then its threshold wavelength will be:
1. \(736.7~\mathrm{\mathring A}\) 
2.  \(760.7~\mathrm{\mathring A}\) 
3.  \(301~\mathrm{\mathring A}\) 
4.  \(378.4~\mathring A\)

Remaining quantity (in %) of radioactive element after 5 half-lives is:

1. 4.125%

2. 3.125%

3. 31.1%

4. 42.125%

An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that, the efficiency of an engine is 60%. If g = 10 ms^-2, the power of this engine is:

1. 3.3 kW

2. 0.33 kW

3. 0.033 kW

4. 33 kW