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JEE Advanced2023MathematicsFunctionsActual

Let S = 0 , 1 ∪ 1 , 2 ∪ 3 , 4 and T = 0 , 1 , 2 , 3 . Then which of the following statements is(are) true?

Options

  1. AThere are infinitely many functions from S to T
  2. BThere are infinitely many strictly increasing functions from S to T
  3. CThe number of continuous functions from S to T is at most 120
  4. DEvery continuous function from S to T is differentiable

Correct answer

A. There are infinitely many functions from S to T

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

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