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

1.	can keep the body in equilibrium if \(2\) N and \(3\) N act at right angle.
2.	can keep the body in equilibrium if \(1\) N and \(2\) N act at right angle.
3.	cannot keep the body in equilibrium.
4.	can keep the body in equilibrium in \(1\) N and \(3\) N acts at an acute angle.

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:

A launching vehicle carrying an artificial satellite of mass \(m\) is set for launch on the surface of the earth of mass \(M\) and radius \(R.\) If the satellite is intended to move in a circular orbit of radius \(7R,\) the minimum energy required to be spent by the launching vehicle on the satellite is:
(Gravitational constant= \(G\))
1. \(\frac{GMm}{R}\)
2. \(-\frac{13GMm}{14R}\)
3. \(\frac{GMm}{7R}\)
4. \(-\frac{GMm}{14R}\)

The two lenses of an achromatic doublet should have: