Match List – I with List – II.
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LIST I |
LIST II |
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A. strictly increasing |
I. either increasing or decreasing on a given interval |
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B. differentiable real function |
II. $x^2+3 x+5, x \in R$ |
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C. a monotonic function |
III. if $x_1<x_2 \Rightarrow f\left(x_1\right)>f\left(x_2\right)$ for all $x_1, x_2 \in(a, b)$ |
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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:
Answer & explanation
Correct answer: option 3
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