In Young's double slit experiment with sodium vapour lamp of wavelength \(589\) nm and the slits \(0.589\) mm apart, the half angular width of the central maximum is:
1. \(sin^{-1} (0.01)\)
2. \(sin^{-1} (0.0001)\)
3. \(sin^{-1} (0.001)\)
4. \(sin^{-1} (0.1)\)

A parallel plate capacitor with air as the dielectric has capacitance \(C.\) A slab of dielectric constant \(K\) having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be: 
        
1. \((K+3)\frac C4\)
2. \((K+2)\frac C4\)
3. \((K+1)\frac C4\)
4. \(\frac{KC}{4}\)

Three concurrent co-planar forces \(1\) N, \(2\) N and \(3\) N acting along different directions on a body.
Choose the correct statement:

The work done by force acting on a body is as shown in the graph. The total work done in covering an initial distance of \(20\) m is: 
        
1. \(212.5\) J
2. \(200\) J
3. \(400\) J
4. \(175\) J

Horizontal tube of non-uniform cross-section has radii of \(0.1\) m and \(0.05\) m respectively at M and N. For a streamlined flow of the liquid, the rate of liquid flow is:
       
 

A coil of \(n\) number of turns is wound tightly in the form of a spiral with inner and outer radii \(a\) and \(b\) respectively. When a current of strength \(I\) am passed through the coil, the magnetic field at its centre is:
1. \(\frac{\mu_{_0}nI}{(b-a)}\log_e\frac ab\)
2. \(\frac{\mu_{_0}nI}{2(b-a)}\)
3. \(\frac{\mu_{_0}nI}{b}\)
4. \(\frac{\mu_{_0}nI}{2(b-a)}\log_e\frac ba\)

A police party is moving in a jeep at a constant speed \(v.\) They saw a thief at a distance \(x\) on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration which of the following relations is true if the police is able to catch the thief?
1. \(v^2<ax\)
2. \(v^2<2ax\)
3. \(v^2\geq 2ax\)
4. \(v^2=ax\)

The thermo emf of a hypothetical thermocouple varies with the temperature \(\theta\) of the hot junction as \(E=a\theta+b\theta^2\) in volts, where the ratio is \(\frac ab\) is \(700~^\circ \mathrm{C}.\) If the cold junction is kept at \(0~^\circ \mathrm{C},\) then the neutral temperature is: