The angle between two vectors \(a=\hat i-\hat k\)  and \(b=\hat i-\hat j+\hat k\) is:
1. \(\cos^{-1}\frac13\)
2. \(\cos^{-1}\frac{-1}3\)
3. \(\sin^{-1}\frac{-1}3\)
4. \(90^\circ\)

A tangential force acting on the top of a sphere of mass \(m\) kept on a rough horizontal plane as shown in the figure. 

If the sphere rolls without slipping, then the acceleration with which the centre of the sphere moves is:
1. \(\frac{10~F}{7~M}\)
2. \(\frac{F}{2~M}\)
3. \(\frac{3~F}{7~M}\)
4. \(\frac{7~F}{2~M}\)

The density of a rod having length \(l\) varies as \(\rho=c+dx,\) where \(x\) is the distance from the left end. The distance from origin to the centre of mass is:
                 
1. \(\dfrac{3cl+2Dl^2}{3(2c+Dl)}\)
2. \(\dfrac{3cl+4Dl^2}{3(2c+Dl)}\)
3. \(\dfrac{2cl+3Dl^2}{3(2c+1)}\)
4. \(\dfrac{cl+3Dl^2}{3(2c+Dl)}\)

A block slides down on an incline of angle 30° with an acceleration \(\frac g4.\) Find the kinetic friction coefficient.
1. \(\frac{1}{2\sqrt2}\)
2. \(0.6\)
3. \(\frac{1}{2\sqrt3}\)
4. \(\frac{1}{\sqrt2}\)

A wire of resistance 10 Q is bent to form a complete circle. Find its resistance between two diametrically opposite points. 
   
1. \(5~\Omega\)
2. \(2.5~\Omega\)
3. \(1.25~\Omega\)
4. \(\frac{10}{3}~\Omega\)