List of top Mathematics Questions on Functions asked in CUET (UG)

Mr. X has two investment options: A (8% p.a. compounded semi-annually) or B (7.6% p.a. compounded quarterly). Which of the following are TRUE?
(A) Effective rate for option A is 8.16%
(B) Effective rate for option B is 7.82%
(C) Effective rate for option B is 8.82%
(D) Option A is better than option B as an investment.

Let $\mathbb{N}, \mathbb{Z}$ and $\mathbb{R}$ be the set of natural numbers, integers and real numbers respectively, $[\cdot]$ denotes the greatest integer function. Match List-I with List-II:}

Analyze the function \( f(x) = |x-1| + |x-2| + |x-3| \). Determine the points where the derivative \( f'(x) \) is undefined.

If \( f(x)= \begin{cases x^2+k, & x\leq 1 \\ 2x+1, & x>1 \end{cases} \) is continuous at \( x=1 \), then the value of \( k \) is:}

Let \( A = \{1,2,3\} \) and \( B = \{2,4,6\} \). A function \( f : A \to B \) is defined by \( f(x)=2x \). The function is:

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:

The interval, in which the function \( f(x) = \frac{3}{x} + \frac{x}{3} \) is strictly decreasing, is: