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Q1:

2025: Actual Paper

Algebra

Functions

Easy

Which of the following functions is a one-to-one and onto function from $\mathbb{R}$ to $\mathbb{R}$ ?

$e^{ln(|x|)}$

$e^{ln(x)}$

$ln(e^x)$

$ln(e^{|x|})$

Correct Answer

Option 3

Correct Answer

Explanation

Q2:

2025: Sample Paper

Algebra

Functions

Medium

Let $f(x) = \left|\frac{x}{2}\right|$ and $g(x) = \sqrt{3}\cos x + \sin x - 1$ , for all real numbers $x$ . If $[ \ \ ]$ denotes the greatest integer function, then the range of the function $[f \circ g]$ is:

$\{0, 1\}$

$\{-1, 0, 1\}$

$\{0\}$

$\{1\}$

Correct Answer

Option 1

Correct Answer

Explanation

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