If a vector \(2\hat{i}+3\hat{j}+8\hat{k}\) is perpendicular to the vector \(-4\hat{i}+4\hat{j}+\alpha \hat{k},\) then the value of \(\alpha\) will be:$\mathrm{}$
1. $-1$
2. $-\frac{1}{2}$
3. $\frac{1}{2}$
4. \(1\)

What is the minimum velocity with which a body of mass \(m\) must enter a vertical loop of radius \(R\) so that it can complete the loop?
1. \(\sqrt{2 g R}\)
2. \(\sqrt{3 g R}\)
3. \(\sqrt{5 g R}\)
4. \(\sqrt{ g R}\)$\mathrm{}$

The potential energy of a particle in a force field is \(U=\)$\frac{A}{r^2}-\frac{B}{r}$ where \(A\) and \(B\) are positive constants and \(r\) is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:

A body of mass \(1\) kg is thrown upwards with a velocity \(20\) ms^-1. It momentarily comes to rest after attaining a height of \(18\) m. How much energy is lost due to air friction?
(Take \(g=10\) ms^-2)
1. \(20\) J
2. \(30\) J
3. \(40\) J
4. \(10\) J

Which of the diagrams shown in the figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit?

1.		2.
3.		4.

A bicyclist comes to a skidding stop in \(10\) m. During this process, the force on the bicycle due to the road is \(200\) N is directly opposed to the motion. The work done by the cycle on the road is:
1. \(+2000\) J
2. \(-200\) J
3. zero
4. \(-20000\) J

During an inelastic collision between two bodies, which of the following quantities always remain conserved?

Two inclined frictionless tracks, one gradual and the other steep meet at \(A\) from where two stones are allowed to slide down from rest, one on each track as shown in the figure.

Which of the following statement is correct?

A body of mass \(0.5\) kg travels in a straight line with velocity \(v=ax^{3/2}\) where \(a=5~\mathrm{m^{-1/2}s^{-1}}\). The work done by the net force during its displacement from \(x=0\) m to \(x=2\) m is:
1. \(15\) J
2. \(50\) J
3. \(10\) J
4. \(100\) J