Match List I with List II, List I, List II, A. Range of x, I. (-5, ∞), B. Range of 9x^2 + 6x - 5 for all x ≥ 0, II. [0, ∞), C. Domain of 1/(√(x+5)), III. \(1,1), (2,2), (3,3)\, D. Smallest equivalence relation on Set \1,2,3\, IV. [-5, ∞), Choose the correct answer from the options given below: Option 1: A-I, B-IV, C-II, D-III Option 2: A-II, B-I, C-IV, D-III Option 3: A-II, B-IV, C-I, D-III Option 4: A-I, B-III, C-IV, D-II

Answer: A-II, B-IV, C-I, D-III. Solution: A:, x, ≥ 0, range is [0, ∞) (II). B: For x ≥ 0, minimum at x = 0 is -5, so range is [-5, ∞) (IV). C: Need x + 5 > 0, so domain is (-5, ∞) (I). D: Smallest equivalence relation is the identity \(1,1),(2,2),(3,3)\ (III).

Algebra

Relations & Functions

Medium

Match List I with List II

List I List II
A. Range of $\lvert x\rvert$ I. $(-5, \infty)$
B. Range of $9x^2 + 6x - 5$ for all $x \geq 0$ II. $[0, \infty)$
C. Domain of $\dfrac{1}{\sqrt{x+5}}$ III. $\{(1,1), (2,2), (3,3)\}$
D. Smallest equivalence relation on Set $\{1,2,3\}$ IV. $[-5, \infty)$

Choose the correct answer from the options given below:

List I	List II
A. Range of $\lvert x\rvert$	I. $(-5, \infty)$
B. Range of $9x^2 + 6x - 5$ for all $x \geq 0$	II. $[0, \infty)$
C. Domain of $\dfrac{1}{\sqrt{x+5}}$	III. $\{(1,1), (2,2), (3,3)\}$
D. Smallest equivalence relation on Set $\{1,2,3\}$	IV. $[-5, \infty)$

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

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

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

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

✅ Correct Option: 3

A: $|x| \geq 0$ , range is $[0, \infty)$ (II).

B: For $x \geq 0$ , minimum at $x = 0$ is $-5$ , so range is $[-5, \infty)$ (IV).

C: Need $x + 5 > 0$ , so domain is $(-5, \infty)$ (I).

D: Smallest equivalence relation is the identity $\{(1,1),(2,2),(3,3)\}$ (III).

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