Two capacitors of capacities \(C_1\) and \(C_2\) are charged upto the potential \(V_1\) and \(V_2,\) then the condition for not flowing the charge between them when connected the capacitors, in parallel is:
1. \(C_1=C_2\)
2. \(C_1V_1=C_2V_2\)
3. \(V_1V_2\)
4. \(\frac{C_1}{V_1}=\frac{C_2}{V_2}\)

Find equivalent resistance between \(X\) and \(Y\):
  

1. \(R\)

2. \(R/L\)

3. \(2R\)

4. \(5R\)

Vibrations of rope tied by two rigid ends shown by equation \(y=cos2\pi t\sin2\pi x,\) then the minimum length of the rope will be:
1. \(1\) m
2. \(\frac12\) m
3. \(5\) m
4. \(2\pi\) m

If we change the value of \(R,\) then:
  

1. voltage does not change on \(L\)

2. voltage does not change on \(LC\) combination

3. voltage does not change on \(C\)

4. voltage changes on \(LC\) combination

If \(V=ar\) where \(a\) is a constant and \(r\) is the distance, then the electric field at a point will be proportional to:
1. \(r\)
2. \(r^{-1}\)
3. \(r^{-2}\)
4. \(r^{0}\)

Electric field at point 20 cm away from the centre of a dielectric sphere is 100 V/m, the radius of the sphere is 10 cm, then the value of the electric field at a distance 3 cm from the centre is:

1. 100 V/m

2. 125 V/m

3. 120 V/m

4. 0

50 g ice at 0°C in insulator vessel, 50 g water of 100 °C is mixed in it, and then final temperature of the mixture is: (neglect the heat loss)
1. 10°C
2. 0°C << T_m < 20°C
3. 20°C
4. above 20°C

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