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 |
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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 |
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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) |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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