## JEE Advanced Archive on Functions, JEE Advanced Previous Years Questions with Answer Key, Matrix Match / Match the Column & Subjective Type

## 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.

- 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)]

**Answer Codes**

(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.**

- 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

**Answer Codes**

(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.**

- 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

**Answer Codes**

(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

- 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].**

^{|y|}– |2

^{(y – 1)}– 1| = 2

^{(y – 1)}+ 1. {IIT JEE 1997}.

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

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

**Answer: x = 0, 5/3**.

### Audience

This IIT JEE Advanced Archive is designed to help the students who are preparing for the one of the toughest entrance exams wordwide (IIT JEE Advanced). With this archive students will get to know the pattern of questions which are usually ask in the exam.

### Prerequisites

This IIT JEE Advanced Archive demands to have the detail knowledge of the chapter “Real Valued Functions”. The other basic requirement to attempt the questions of this archive is, the students must have solved at least 100 questions of the topic.

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