Question

Match List-I with List-II.
\begin{array}{|c|c|} \hline \textbf{List-I (Function)} & \textbf{List-II (Interval in which function is increasing)} \\\ \hline \frac{x}{\log_e x} & (-\infty, -2) \cup (2, \infty) \\\ \hline \frac{x}{2} + \frac{2}{x}, x \neq 0 & \left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \\\ \hline x^x, x > 0 & \left(\frac{1}{e}, \infty\right) \\\ \hline \sin x - \cos x & (e, \infty) \\\ \hline \end{array}
Choose the correct answer from the options given below:

• A. (A-II), (B-I), (C-III), (D-IV)
• B. (A-I), (B-III), (C-IV), (D-II)
• C. (A-IV), (B-I), (C-III), (D-II)
• D. (A-III), (B-IV), (C-I), (D-II)

Answer 1

Answer: (C)

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

Answer 2

(A) The function $\frac{x}{\log_e x}$ is increasing for $x > e$ (interval (IV)).

(B) The function $\frac{x^2 + 1}{x - 2}$ is increasing in the intervals $(-\infty, -2) \cup (2, \infty)$ (interval (I)).

(C) The exponential function $e^x$ is increasing for $x > 0$, and the interval where the function is increasing for $e^x$ is $\left( \frac{1}{e}, \infty \right)$ (interval (III)).

(D) The function $\sin x - \cos x$ is increasing in the interval $\left( -\frac{\pi}{4}, \frac{\pi}{4} \right)$ (interval (II)).