Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Calculus

Question:

Match List – I with List – II.

LIST I

LIST II

 A. strictly increasing

 I. either increasing or decreasing on a given interval 

 B. differentiable real function 

 II. $x^2+3 x+5, x \in R$ 

 C. a monotonic function 

 III. if $x_1<x_2 \Rightarrow f\left(x_1\right)>f\left(x_2\right)$ for all $x_1, x_2 \in(a, b)$ 

 D. strictly decreasing 

 IV. if $x_1<x_2 \Rightarrow f\left(x_1\right)<f\left(x_2\right)$ for all $x_1, x_2 \in[a, b]$ 

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (3) → A-IV, B-II, C-I, D-III

$\text{A: strictly increasing} \;\Rightarrow\; \text{if } x_1 < x_2 \Rightarrow f(x_1) < f(x_2)$

$\Rightarrow \text{A matches IV}$

$\text{B: differentiable real function} \;\Rightarrow\; x^2 + 3x + 5 \text{ is differentiable on } \mathbb{R}$

$\Rightarrow \text{B matches II}$

$\text{C: monotonic function} \;\Rightarrow\; \text{either increasing or decreasing}$

$\Rightarrow \text{C matches I}$

$\text{D: strictly decreasing} \;\Rightarrow\; \text{if } x_1 < x_2 \Rightarrow f(x_1) > f(x_2)$

$\Rightarrow \text{D matches III}$

A–IV,\; B–II,\; C–I,\; D–III