CUET · MATHS · PYQ PAPER 2025
If the interval in which \(f(x)=\frac{x}{4}+\frac{4}{x}, x \neq 0\) is strictly increasing is \((-\infty, a) \cup(b, \infty)\), then
- A \(a=b\)
- B \(a=-b\)
- C \(a=2 b\)
- D \(a=-2 b\)
Answer & Solution
Correct Answer
(B) \(a=-b\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{1}{4} - \frac{4}{x^2}\) \(\frac{1}{4} - \frac{4}{x^2} > 0 \implies x^2 > 16\) \((x-4)(x+4) > 0 \implies x \in (-\infty, -4) \cup (4, \infty)\) \(a = -4, b = 4\) \(a = -b\)
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
- Let \(\Delta=\left|\begin{array}{ccc}a+b x & c+d x & p+q x \\ a x+b & c x+d & p x+q \\ u & v & w\end{array}\right|=\left(k-x^2\right)\left|\begin{array}{ccc}a & c & p \\ b & d & q \\ u & v & w\end{array}\right|\) then the value of k is:CUET 2023 Medium
- If the matrix \(A =\left(\begin{array}{ll}1 & 3 \\ 2 & 1\end{array}\right)\), then the value of \(\operatorname{det}\left( A ^2-2 A \right)\) is equal toCUET 2025 Easy
- If A and B are square matrices of order n × n, then \((A-B)^2\) is equal to:
(A) \(A^2-A B-B A+B^2\)
(B) \(A^2-2 A B+B^2\)
(C) \(A^2-2 B A+B A\)
(D) \(A^2-B^2\)
(E) \(A^2+2 A B+B^2\)CUET 2023 Medium - If \(A=\left[\begin{array}{cc}2-x & 1 \\ 3 & y+2\end{array}\right]\) and \(B=\left[\begin{array}{cc}y & 1 \\ 3 & 2 x+1\end{array}\right]\) are such that A = B, then values of z and y are respectively :CUET 2023 Easy
- The solution set of the inequation \(4x + 3y > 5\) isCUET 2025 Medium
- Consider \(f: R ^{+} \rightarrow[4, \infty)\) given by \(f(x)=x^2+4\)
(where \(R ^{+}\)is set of non negative real numbers) then \(f^{-1}(x)\) is :CUET 2023 Easy
More PYQs from CUET
- The product of the order and degree of the following differential equation :
\(x \left( \frac{d^2y}{dx^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + y^2 = 0\)CUET 2023 Medium - If the frequency of an alternating current is doubled while keeping the inductance constant, then the inductive reactanceCUET 2025 Easy
- The interval in which \(f(x)=x^2 e^{-x}+7\) is increasing is :CUET 2023 Medium
- If the corner points of the bounded feasible region for a Linear Programming Problem (LPP) are \(A(0,2), B(3,0), C(2,3)\) and \(D(3,1)\), then the maximum value of the objective function \(Z=4 x+2 y\) occurs atCUET 2025 Medium
- Two parallel plate capacitors of capacitances \(2 \, \mu\text{F}\) and \(3 \, \mu\text{F}\) are joined in series and connected to a battery of V volts. The values of potential across the two capacitors \(V_1\) and \(V_2\) and energy stored in them \(U_1\) and \(U_2\) are related as :CUET 2024 Hard
- Choose the correct formula for magnifying power of a simple microscope from the followingCUET 2023 Medium