CUET · MATHS · PYQ PAPER 2023
Which of the following function is increasing for all values of x in the domain \((0, \infty)\)?
- A 1 - x²
- B \(\frac{1}{x}\)
- C 8 - x²
- D x |x|
Answer & Solution
Correct Answer
(D) x |x|
Step-by-step Solution
Detailed explanation
Let \(f(x) = x|x|\). For \(x \in (0, \infty)\), \(|x| = x\). Therefore, \(f(x) = x \cdot x = x^2\). \(f'(x) = \frac{d}{dx}(x^2) = 2x\). For \(x \in (0, \infty)\), \(2x > 0\). Thus, \(f(x)\) is increasing for all \(x \in (0, \infty)\).
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- The corner points of the bounded feasible region determined by the system of linear constraints are \((0,0), (5,0), (6,5)\), \((6,8),(4,10), (0,8)\). Let \(Z=3 x-4 y\) be the objective function. The minimum value of \(Z\) occurs atCUET 2025 Hard
- The Cartesian equation of the line passing through the point \((1,2,-1)\) and parallel to the line \(5 x-25=14-7 y=35 z\) isCUET 2025 Hard
- For the given five values 15, 24, 18, 33, 42, the three-year moving averages are :CUET 2025 Medium
- If \(A=\left[\begin{array}{ll}5 & 6 \\ 3 & 2\end{array}\right]\), then which of the following is correct?
(A) \(|A|\) is positive
(B) \(|a d j A|=-8\)
(C) Cofactor of 3 is 6
(D) \(|2 A|=-32\)
Choose the correct answer from the options given below :CUET 2025 Hard - Given that \(p_0\) and \(p_1\) represent base and current prices of a commodity, \(q_0\) and \(q_1\) refer to the base and current quantities, then the formula used to calculate price relativesCUET 2023 Medium
- The integrating factor of the differential equation \(\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x, x \neq 0\) isCUET 2023 Medium
More PYQs from CUET
- The value of \(\int_0^{\pi / 2} \log _e\left(\frac{5+2 \sin x}{5+2 \cos x}\right) d x\) isCUET 2025 Hard
- If two thin convex lenses are kept in contact, the focal length of the combination is :CUET 2023 Medium
- The chromosome numbers in the gamete of fruit fly is:CUET 2023 Medium
- Certain Aldehydes, Retore and certain alcohol undergo iodoform test. Certain Aldehydes ketones undergo aldol condensation. While certain aldehydes undergo Cannizaro's reaction. Aldehydes responds to tollen reagent and fehling reagent test.
Which amongst the following will respond to both Tollens' reagent test and Fehling's reagent test?CUET 2023 Medium - If matrix \(A=\left[a_{i j}\right]_{2 \times 2}\) where \(a_{i j}=\left\{\begin{array}{l}1, i \neq j \\ 0, i=j\end{array}\right.\) then \(A^3\) is equal to :CUET 2023 Medium
- \(\lim _{x \rightarrow \frac{\pi}{4}} \frac{4 \sqrt{2}-(\cos x+\sin x)^5}{1-\sin 2 x}\) is equal to :CUET 2023 Easy