In an experiment with Vernier calipers of least count 0.1 mm, when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and 6th division of Vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of Vernier scale lies in between 3.2 cm and 3.3 cm marks, and 4th division of Vernier scale coincides with the main scale division. The diameter of bob is measured as:

• (a) 3.26 cm
• (b) 3.18 cm
• (c) 3.25 cm
• (d) 3.22 cm

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is:

• (a) 120 m
• (b) 200 m
• (c) 320 m
• (d) 80 m

A vector \(\sqrt{3}\hat{i}+\hat{j}\) rotates about its tail through an angle 30° in clock wise direction then the new vector is:

• (a) \(4\hat{i}\)
• (b) \(2\hat{i}\)
• (c) \(3\hat{i}\)
• (d) \(\hat{i}\)

If the minimum force required to move a body up an inclined plane of inclination 45° is 3 times the force required to just prevent it sliding down, the coefficient of friction is:

• (a) 0.5
• (b) 0.9
• (c) 0.3
• (d) 4.1

The screening effect of d-electrons is:

• (a) Equal to p-electrons
• (b) Much more than p-electrons
• (c) Same as f-electrons
• (d) Less than p-electrons

Chloride ion and potassium ion are isoelectronic. Then:

• (a) Their sizes are same
• (b) \(Cl^{-}\) ion is bigger than \(K^{+}\) ion
• (c) \(K^{+}\) ion is relatively bigger
• (d) Their sizes depend on other cation and anion

For the reaction \(CO(g) + \frac{1}{2}O_{2}(g) \rightarrow CO_{2}(g)\), which one of the statements is correct at constant \(T\) and \(P\)?

• (a) \(\Delta H = \Delta E\)
• (b) \(\Delta H < \Delta E\)
• (c) \(\Delta H > \Delta E\)
• (d) \(\Delta H\) is independent of physical state of the reactants

If \( |z_{1}|=2 \), \( |z_{2}|=3 \), \( |z_{3}|=4 \) and \( |2z_{1}+3z_{2}+4z_{3}|=4 \), then absolute value of \( 8z_{2}z_{3}+27z_{3}z_{1}+64z_{1}z_{2} \) equals:

• (a) 24
• (b) 48
• (c) 72
• (d) 96

If \( a>0 \), \( b>0 \), \( c>0 \) and \( a, b, c \) are distinct, then \( (a+b)(b+c)(c+a) \) is greater than:

• (a) \( 2(a+b+c) \)
• (b) \( 3(a+b+c) \)
• (c) 6abc
• (d) 8abc

If the minimum force required to move a body up an inclined plane of inclination 45° is 3 times the force required to just prevent it sliding down, the coefficient of friction is:

• (a) 0.5
• (b) 0.9
• (c) 0.3
• (d) 4.1