Match the functions in List I with their corresponding ranges in List II:List IA. f(x) = x/1+x^2 B. f(x) = 3/2-x^2 C. f(x) = 1/√(x-[x]) D. f(x) = 1/2-3x List III. R_f = (1, ∞) II. R_f = (-∞, 0) [3/2, ∞) III. R_f = [-1/2, 1/2] IV. R_f = [1/3, 1] Choose the correct option:

(A) y = x/1+x^2 yx^2 - x + y = 0 . For real x , D ≥ 0 1 - 4y^2 ≥ 0 y [-1/2, 1/2] . (III)(B) y = 3/2-x^2 . Since x^2 [0, ∞) , 2-x^2 (-∞, 2] . y takes values in (-∞, 0) [3/2, ∞) . (II)(C) y = 1/√(x-[x]) . Let \ = x-[x] (0, 1) . Then √(\) (0, 1) . So 1/√(\) (1, ∞) . (I)(D) y = 1/2-3x . Since 3x [-1, 1] , 2-3x [1, 3] . Thus y [1/3, 1] . (IV)Matches: A-III, B-II, C-I, D-IV.

Match the functions in List I with their corresponding ranges in List II:List IA. f(x) = x/1+x^2 B. f(x) = 3/2-x^2 C. f(x) = 1/√(x-[x]) D. f(x) = 1/2- - Mathematics MCQ Mathematics Mock Test - 10 2026 | ExamTest.live

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Match the functions in List I with their corresponding ranges in List II:List IA. f (x) = \frac{x}{1 + x ^{2}} B. f (x) = \frac{3}{2 - x ^{2}} C. f (x) = \frac{1}{x - [ x ]} D. f (x) = \frac{1}{2 - s i n 3 x} List III. R_{f} = (1, \infty) II. R_{f} = (- \infty, 0) \cup [3/2, \infty) III. R_{f} = [- 1/2, 1/2] IV. R_{f} = [1/3, 1] Choose the correct option:

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

Solution & Step-by-step Explanation

(A) y = \frac{x}{1 + x ^{2}} ⟹ y x^{2} - x + y = 0 . For real x, D \geq 0 ⟹ 1 - 4 y^{2} \geq 0 ⟹ y \in [- 1/2, 1/2] . (III)(B) y = \frac{3}{2 - x ^{2}} . Since x^{2} \in [0, \infty), 2 - x^{2} \in (- \infty, 2] . y takes values in (- \infty, 0) \cup [3/2, \infty) . (II)(C) y = \frac{1}{x - [ x ]} . Let {x} = x - [x] \in (0, 1) . Then {x} \in (0, 1) . So 1/ {x} \in (1, \infty) . (I)(D) y = \frac{1}{2 - s i n 3 x} . Since sin 3 x \in [- 1, 1], 2 - sin 3 x \in [1, 3] . Thus y \in [1/3, 1] . (IV)Matches: A-III, B-II, C-I, D-IV.

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Match the functions in List I with their corresponding ranges in List II:List IA. f (x) = \frac{x}{1 + x ^{2}} B. f (x) = \frac{3}{2 - x ^{2}} C. f (x) = \frac{1}{x - [ x ]} D. f (x) = \frac{1}{2 - s i n 3 x} List III. R_{f} = (1, \infty) II. R_{f} = (- \infty, 0) \cup [3/2, \infty) III. R_{f} = [- 1/2, 1/2] IV. R_{f} = [1/3, 1] Choose the correct option:

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

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

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

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

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Match the functions in List I with their corresponding ranges in List II:List IA. f(x)=1+x2x​ B. f(x)=2−x23​ C. f(x)=x−[x]​1​ D. f(x)=2−sin3x1​ List III. Rf​=(1,∞) II. Rf​=(−∞,0)∪[3/2,∞) III. Rf​=[−1/2,1/2] IV. Rf​=[1/3,1] Choose the correct option:

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