CUET · MATHS · PYQ PAPER 2025

Match List-I with List-II
Let \(f: A \rightarrow B\) be a function given by \(f(x)=x^2\)
List - I (Domain and Co-domain) List - II (Kind)
(A) \(A= R\) and \(B= R\) (I) \(f\) is both one-one and onto
(B) \(A= R\) and \(B=[0, \infty]\) (II) \(f\) is one-one but not onto
(C) \(A=B=[0, \infty]\) (III) \(f\) is not one-one but onto
(D) \(A=[0, \infty], B= R\) (IV) \(f\) is neither one-one nor ont
Choose the correct answer from the options given below :

A (A) - (III), (B) - (IV), (C) - (II), (D) - (I)
B (A) - (IV), (B) - (III), (C) - (I), (D) - (II)
C (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
D (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Verified Solution

Answer & Solution

Correct Answer

(B) (A) - (IV), (B) - (III), (C) - (I), (D) - (II)

Step-by-step Solution

Detailed explanation

For \(f(x)=x^2\): (A) \(A= R, B= R\): Neither one-one nor onto. (IV) (B) \(A= R, B=[0, \infty]\): Not one-one but onto. (III) (C) \(A=[0, \infty], B=[0, \infty]\): Both one-one and onto. (I) (D) \(A=[0, \infty], B= R\): One-one but not onto. (II) (A) - (IV), (B) - (III), (C) -…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Consider the line \(\vec{r}=\hat{i}-2 \hat{j}+4 \hat{k}+\lambda(-\hat{i}+2 \hat{j}-4 \hat{k})\)
Match List-I with List-II

List-I	List-II
(A) A point on the given line	(I) \(\left(\frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{-4}{\sqrt{21}}\right)\)
(B) direction ratios of the line	(II) \((4,-2,-2)\)
(C) direction cosines of the line	(III) \((1,-2,4)\)
(D) direction ratios of a line perpendicular to given line	(IV) \((-1,2,-4)\)

Choose the correct answer from the options given below:

CUET 2025 Easy

\(y=\log _e\left(\frac{1-x^2}{1+x^2}\right)\), then \(\frac{d y}{d x}\) is equal to:

CUET 2023 Hard

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List - I (Domain and Co-domain)	List - II (Kind)
(A) \(A= R\) and \(B= R\)	(I) \(f\) is both one-one and onto
(B) \(A= R\) and \(B=[0, \infty]\)	(II) \(f\) is one-one but not onto
(C) \(A=B=[0, \infty]\)	(III) \(f\) is not one-one but onto
(D) \(A=[0, \infty], B= R\)	(IV) \(f\) is neither one-one nor ont