## JEE Advanced Archive on Functions Match the Column / Matrix Match Type Questions with answer key

Note: Each question has Matching List-I with Matching List-II. The answer codes for the Matching Lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Match Matching List-I with Matching List-II and select the correct answer using the code given below the list.

1. Let E = {x ∈ R: x ≠ 1 and (x/(x – 1)) > 0} and F = {x ∈ E: sin⁻¹(ln(x/(x – 1))) is a real number }. Let f: E → R be a function defined by f(x) = ln(x/(x – 1)) and g: F → R be a function defined by g(x) = sin⁻¹(ln(x/(x – 1))). {IIT JEE Advanced 2018}.

Matching List – I

(P) the range of f is
(Q) the range of g contains
(R) the domain of f contains
(S) the domain of g is

Matching List – II

(1) (-∞, 1/(1 – e)] U [e/(e – 1), ∞)
(2) (0, 1)
(3) [-1/2, 1/2]
(4) (-∞, 0) U (0, ∞)
(5) (-∞, e/(1 – e)]
(6) (-∞, 0) U (1/2, e/(e – 1)]

(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

Correct Choice: Answer Code (A) P – 4, Q – 2, R – 1, S – 1.

1. Let f: R → R, g: [0, ∞) → R, h: R → R, w: R → [0, ∞) be defined by. {IIT JEE 2014}.

f = {|x| if x < 0; eˣ if x ≥ 0}
g = x²
h = {sinx if x < 0; x if x ≥ 0}
w = {g(f(x)) if x < 0; g(f(x)) – 1 if x ≥ 0}

Matching List – I

(P) w is
(Q) h is
(R) g(f(x)) is
(S) g is

Matching List – II

(1) onto but not one one
(2) neither countinuous nor one one
(3) differentiable but not one one
(4) countinuous and one one

(A) P – 3, Q – 1, R – 4, S – 2
(B) P – 1, Q – 3, R – 4, S – 2
(C) P – 3, Q – 1, R – 2, S – 4
(D) P – 1, Q – 3, R – 2, S – 4

Correct Choice: Answer Code (D) P – 1, Q – 3, R – 2, S – 4.

1. Let f(x) = (x² – 6x + 5)/(x² – 5x + 6). {IIT JEE 2014}.

Matching List – I

(P) if -1 < x < 1, then f(x) satisfies
(Q) if 1 < x < 2, then f(x) satisfies
(R) if 3 < x < 5, then f(x) satisfies
(S) if x > 5 , then f(x) satisfies

Matching List – II

(1) 0 < f(x) < 1
(2) f(x) < 0
(3) f(x) > 0
(4) f(x) < 1

(A) P – (1, 2), Q – (1, 2, 3), R – 4, S – (2, 3, 4)
(B) P – (1, 3, 4), Q – (2, 4), R – (2, 4), S – (1, 3, 4)
(C) P – 3, Q – (1, 4), R – 2, S – (3, 4)
(D) P – (1, 2, 3), Q – 3, R – (2, 3, 4), S – 4

Correct Choice: Answer Code (B) P – (1, 3, 4), Q – (2, 4), R – (2, 4), S – (1, 3, 4).

## JEE Advanced Archive on Functions, JEE Advanced Previous Years Questions with Answer Key Subjective Type Questions

1. Find the range of values of t for which 2sint = (5x² – 2x + 1)/(3x² – 2x – 1), where t ∈ [-π/2, π/2]. {IIT JEE 2005}.

Answer: range of values of t is [-π/2, -π/10] U [3π/10, π/2].

2. Find the set of all solutions of the equation 2|y| – |2(y – 1) – 1| = 2(y – 1) + 1. {IIT JEE 1997}.

Answer: the required solutions are [1, ∞) U {-1}.

1. A functions f: R → R is defined by f(x) = (ax² + 6x – 8)/(a – 8x² + 6x). Find the interval of values of a for which f(x) is onto. Is the function one – one for a = 3? Justify your answer. {IIT JEE 1996}.

Answer: the function f(x) is onto in [2, 14]. f(x) is not one – one for a = 3.

1. Solve 4{x} = x + [x], where [.] denotes the greatest integer function and {.} denotes the fraction part function. {IIT JEE 1994}.