CUET · MATHS · PYQ PAPER 2025
The function \(f(x)=\frac{x}{2}+\frac{2}{x}, x \neq 0\) is increasing on :
(A) \((-\infty,-2)\)
(B) \((-2,2)\)
(C) \((2, \infty)\)
(D) \((-1,1)\)
Choose the correct answer from the options given below :
- A (B) only
- B (B) and (D) only
- C (A) and (C) only
- D (C) and (D) only
Answer & Solution
Correct Answer
(C) (A) and (C) only
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{d}{dx} \left( \frac{x}{2} + \frac{2}{x} \right) = \frac{1}{2} - \frac{2}{x^2}\) \(\frac{1}{2} - \frac{2}{x^2} > 0\) \(\frac{1}{2} > \frac{2}{x^2}\) \(x^2 > 4\) \(x 2\) Increasing on \((-\infty, -2)\) and \((2, \infty)\)
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
- Solution of \(\frac{d y}{d x}=\left(1+x^2\right)\left(1+y^2\right)\) is :CUET 2023 Medium
- The probability of a shooter hitting the target in one shot is \(\frac{1}{4}\)
The minimum number of shots needed so that the probability of hitting the target at least once is greater than \(\frac{7}{16}\) is:CUET 2025 Hard - A random variable has the following probability distribution:\(\begin{array}{llllll}X= x_{-} i & 2 & 3 & 4 & 5 \\P\left(X=x \_i\right) & 4 k & k & 5 k & 2 k\end{array}\)The value of \(P(X<3)\) isCUET 2023 Easy
- If \(\left[\begin{array}{cc}2 x-1 & 4 x \\ 0 & y^2-1\end{array}\right]=\left[\begin{array}{cc}x+1 & 8 \\ 0 & 24\end{array}\right]\), then the value of \((x+y)\) is :CUET 2023 Medium
- Value of \(\frac{e^{\sin \left(\tan ^{-1} x+\cot ^{-1} x\right)}}{e^{\sin \left(\sin ^{-1} x+\cos ^{-1} x\right)}}, x \in[-1,1]\), is:CUET 2023 Hard
- If x = a sin t and y = a \(\left(\cos t+\log \tan \frac{t}{2}\right)\) then \(\frac{d^2 y}{d x^2}\) is:CUET 2023 Hard
More PYQs from CUET
- Observe the diagram and answer the following questions:
Drugs used for treating AIDS are known as:CUET 2023 Hard - Match List-l with List-II
Choose the correct answer from the options given below :List-l (Order of reaction) List-II (Expressions/Unit) (A) Unit of zero order (I) \(k t=[ R ]_0-[ R ]_t\) (B) Unit of First order (II) \(mol L ^{-1} s^{-1}\) (C) Integrated Rate Law for zero order (III) \(s^{-1}\) (D) Integrated Rate Law for First order (IV) \([ R ]=[ R ]_0 e^{-k t}\) CUET 2025 Medium - In an intrinsic semiconductor at room temperature ;CUET 2025 Easy
- Choose the correct statement regarding dependence of electric potential at a point due to an electric dipole:CUET 2023 Hard
- Match List-I with List-II
List-I List-II (A) Williamson's synthesis. \((I)\) \(C _6 H _5 Cl + NaOH \xrightarrow[\text { High pressure }]{350^{\circ} C }\) (B) Reimer Tiemann reaction. \((II)\) \(C _6 H _5 OH + C _6 H _5 COCl \xrightarrow{\text { aq. } NaOH }\) (C) Dow's process \((II)I\) \(CH_3 CH_2 ONa+CH_3 Cl \xrightarrow{\text { heat }}\) (D) Schotten Baumann reaction \((IV)\) \(C _6 H _5 OH + CHCl _3+ NaOH \xrightarrow{\text { heat }}\)
Choose the correct answer from the options given below:CUET 2023 Hard - Match List I with List II
Choose the correct answer from the options given below:LIST I LIST II A. Gatterman-Koch reaction I. Diphenyl B. Stephens reaction II. Ethyl amine C. Hoffmann Bromamide degradation III. Benzaldehyde D. Fittig reaction IV. Acetaldehyde CUET 2023 Medium