JEE Advanced Mathematics Question (2023) — Solution

Step-by-step solution

Given, S = 0 ,   1 ∪ 1 ,   2 ∪ 3 ,   4  and  T = 0 ,   1 ,   2 ,   3 Now, let domain and co-domain of a function y = f x are S and T  respectively. Now solving option, A There are infinitely many elements in domain and four elements in co-domain. ⇒ There are infinitely many functions from S to T . ⇒ Option A is correct B If number of elements in domain is greater than number of elements in co-domain, then number of strictly increasing function is zero.  Assume  sin x  function its elements in domain is greater than its range hence, it is not an strictly increasing function. ⇒ Option B is incorrect C Maximum number of continuous functions = 4 × 4 × 4 = 64 (Every subset 0 ,   1 ,   1 ,   2 ,   3 ,   4 has four choices) ∵   64 < 120 ⇒  Option C is correct. D For every point at which f x is continuous, f ' x = 0   as derivative of constant is always zero ⇒ Every continuous function from S to T is differentiable. ⇒  Option  D  is correct