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CUET · MATHS · PYQ PAPER 2025

Match List-l with List-ll
Where \(R\) is set of real numbers
List-lList-ll
(A) \(f: R \rightarrow R\) s.t \(f(x)=x^4\) is(I) one-one, Into
(B) \(f: R \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is(II) many-one, into
(C) \(f:[0, \infty) \rightarrow R\) s.t \(f(x)=x^4\) is(III) one-one, onto
(D) \(f:[0, \infty) \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is(IV) many-one, onto
Choose the correct answer from the options given below :

  1. A (A) - (IV), (B) - (II), (C) - (I), (D) – (III)
  2. B (А) - (I), (В) - (IV), (C) - (I), (D) – (III)
  3. C (А) - (II), (B) - (IV), (C) - (III), (D) - (I)
  4. D (A) - (IV), (В) – (I), (С) – (III), (D) - (I)
Verified Solution

Answer & Solution

Correct Answer

(B) (А) - (I), (В) - (IV), (C) - (I), (D) – (III)

Step-by-step Solution

Detailed explanation

(A) \(f: R \rightarrow R, f(x)=x^4\): Many-one (e.g., \(f(1)=f(-1)\)), Into (range \([0, \infty)\) is a subset of \(R\)). (A) matches (II). (B) \(f: R \rightarrow[0, \infty), f(x)=x^4\): Many-one (e.g., \(f(1)=f(-1)\)), Onto (range \([0, \infty)\) equals codomain…