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Matching-List & Matching-Matrix Type

Matching-List Type

Each question in this section has two matching lists. Choices for the correct
combination of elements from List-I and List-II are given as options (A), (B), (C)
and (D), out of which one is correct.

x x
1. Let E 1 = x ∈ R : x 6= 1 and > 0 , E 2 = x ∈ E 1 : sin −1 log e is a real number .
x − 1 x − 1
π π
h i
−1
Here, the inverse trigonometric function sin x assumes values in − , .
2 2

x
Let f : E 1 → R be the function defined by f(x) = log e and g : E 2 → R be the function
x − 1

x
defined by g(x) = sin −1 log .
e
x − 1
List-I List-II

1 e
(P) The range of f is (1) −∞, ∪ , ∞
1 − e e − 1

(Q) The range of g contains (2) (0, 1)

1 1
(R) The domain of f (3) − ,
2 2
contains

(S) The domain of g is (4) (−∞, 0) ∪ (0, ∞)

e
(5) −∞,
e − 1

1 e
(6) (−∞, 0) ∪ − ,
2 e − 1

The correct option is:

(A) P → 4; Q → 2; R → 1; S → 1.
(B) P → 3; Q → 3; R → 6; S → 5.
(C) P → 4; Q → 2; R → 1; S → 6.

(D) P → 4; Q → 3; R → 6; S → 5.
[JEE 2018]