If $$\mathop {\lim }\limits_{x \to 1} {{{x^4} - 1} \over {x - 1}} = \mathop {\lim }\limits_{x \to k} {{{x^3} - {k^3}} \over {{x^2} - {k^2}}}$$, then k is :

Let f(x) = x² , x $$ \in $$ R. For any A $$ \subseteq $$ R, define g (A) = { x $$ \in $$ R : f(x) $$ \in $$ A}. If S = [0,4], then which one of the following statements is not true ?

Two wires A & B are carrying currents I₁ & I₂ as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are :

A 25 × 10^–3 m³ volume cylinder is filled with 1 mol of O₂ gas at room temperature (300K). The molecular diameter of O₂, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O₂ molecule ?