The smallest integer function f(x) = [x] is
(a) One-one
(b) Many-one
(c) Both (a) & (b)
(d) None of these

The function f : R → R defined by f(x) = 3 – 4x is
(a) Onto
(b) Not onto
(c) None one-one
(d) None of these

The number of bijective functions from set A to itself when A contains 106 elements is
(a) 106
(b) (106)²
(c) 106!
(d) 2¹⁰⁶

If f(x) = (ax² + b)³, then the function g such that f(g(x)) = g(f(x)) is given by
 

If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x² + 7, then the value of x for which f(g(x)) = 25 is

1. Thermodynamics is not concerned about______.
   • (i) energy changes involved in a chemical reaction.
   • (ii) the extent to which a chemical reaction proceeds.
   • (iii) the rate at which a reaction proceeds.
   • (iv) the feasibility of a chemical reaction.

What is the force between two small charged spheres having charges of 2 × 10^–7C and 3 × 10^–7 C placed 30 cm apart in the air?

The electrostatic force on a small sphere of charge 0.4 µC due to another small sphere of charge –0.8 µC in the air is 0.2 N.

(a) What is the distance between the two spheres?

(b) What is the force on the second sphere due to the first?

Check that the ratio ke²/G m_em_p is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

 (i) Explain the meaning of the statement ‘electric charge of a body is quantised’.
(ii) Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?

When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.