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. $$90^\circ$$

Subtopic:  Scalar Product |
Hints

The distance x (in $$\mu m$$) covered by a molecule starting from point A at time t = 0 and stopping at another point B is given by the equation $$x=t^2\Big(2-\frac t3\Big).$$ The distance between A and B (in $$\mu m$$) is close to:

1.  10.7
2.  20.7
3.  40.7
4.  50.7
Subtopic:  Differentiation |
Hints

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. $$\frac{7~F}{2~M}$$

Subtopic:  Rolling Motion (OLD NCERT) |
Hints

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. $$\frac{3cl+2Dl^2}{3(2c+Dl)}$$
2. $$\frac{3cl+4Dl^2}{3(2c+Dl)}$$
3. $$\frac{2cl+3Dl^2}{3(2c+1)}$$
4. $$\frac{cl+3Dl^2}{3(2c+Dl)}$$

Subtopic:  Center of Mass |
Hints

One end of a massless spring of constant 100 N/m and natural length 0.5 m is fixed and the other end is connected to a particle of mass 0.5 kg lying on a frictionless horizontal table. The spring remains horizontal. If the mass is made to rotate at an angular velocity of 2 rad/s, then the elongation of the spring is:

1.  0.1 m
2.  10 cm
3.  1 cm
4.  0.01 cm

Subtopic:  Uniform Circular Motion |
Hints

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. $$\frac{1}{\sqrt2}$$

Subtopic:  Friction |
52%
Hints

Two long straight wires, each carrying an electric current of 5 A, are kept parallel to each other at a separation of 2.5 cm. Find the magnitude of the magnetic force experiment by 10 cm of a wire.

1.  4.0 × 10-4 N

2.  3.5 × 10-6 N

3.  2.0 × 10-5 N

4.  2.0 × 10-9 N

Subtopic:  Force between Current Carrying Wires |
55%
Hints

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. $$\frac{10}{3}~\Omega$$

Subtopic:  Combination of Resistors |
59%
Hints

Find the resistance of a hollow cylindrical Conductor with the inner and outer radii of length 1.0 mm and 2.0 mm respectively. The resistivity of the material is 2.0 x 10-8 $$\Omega$$ m. The length of the conductor is 10 m.

1.  2.1 x 10-3 $$\Omega$$

2.  1.3 x 10-4 $$\Omega$$

3.  3.2 x 10-4 $$\Omega$$

4.  4.6 x 10-2 $$\Omega$$

Subtopic:  Derivation of Ohm's Law |
Hints

Three equal charges, each having a magnitude of 2.0 × 10-6 C, are placed at the three corners of a right-angled triangle of sides 3 cm, 4 cm and 5 cm. The force (in magnitude) on the charge at the right-angled corner is:

1.  50 N
2.  26 N
3.  29 N
4.  45.9 N

Subtopic:  Coulomb's Law |
52%