CUET · MATHS · PYQ PAPER 2025
The function \(f(x)=x^3+3 x^2+4 x+4, x \in R\) (set of real numbers):
- A is increasing on R
- B is decreasing on R
- C is decreasing on \((-\infty, 0)\)
- D is neither increasing nor decreasing on \((0, \infty)\)
Answer & Solution
Correct Answer
(A) is increasing on R
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{d}{dx}(x^3+3 x^2+4 x+4) = 3x^2 + 6x + 4\) \(\Delta = b^2 - 4ac = (6)^2 - 4(3)(4) = 36 - 48 = -12\) Since \(a=3 > 0\) and \(\Delta 0\) for all \(x \in R\). Therefore, \(f(x)\) is increasing on R.
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
- If \(y=3 e^{2 x}+2 e^{3 x}\), then \(\frac{d^2 y}{d x^2}+6 y\) is equal to:CUET 2025 Medium
- The area of the region enclosed by \(y=x+2\) and \(y=x^2+x-2\) is:CUET 2023 Hard
- If a discrete random variable \(X\) has the following probability distribution: \(\begin{array}{lll}X & \frac{2}{3}^1 & \frac{4}{3} \\& & \\P(X) & & c \\& & c^2 \\& c^2\end{array}\) then \(c\) is:CUET 2023 Hard
- The shortest distance between the lines \(\frac{x+3}{1}=\frac{y-2}{2}=\frac{z+4}{3}\) and \(\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}\) is :CUET 2023 Hard
- In a kilometer race \(P\) runs at \(10 m / sec , Q\) runs at \(5 m / sec\) then which of the following statement \(( s )\) is \(/\) are correct?
(A) \(P\) wins the race in 100 sec
(B) Q wins the race in 100 sec
(C) P defeats Q by 500 m
(D) Q defeats P by 500 m
Choose the correct answer from the options given below :CUET 2025 Hard - The general solution of the differential equation \(\log _e\left(\frac{d y}{d x}\right)=a x+b y\) isCUET 2025 Hard
More PYQs from CUET
- For an LPP: Maximize \(z=3 x+9 y; x \geq 0, y \geq 0\), the feasible region \(O A B\) is shown in the figure, then the other constraints are:
CUET 2025 Hard - Identify the most stable complex.CUET 2023 Medium
- Kinetic energies of four particles a, b, c, d of equal masses are given below. Arrange them in order of their decreasing de-Broglie wavelengths.
(A) \((KE)_a = 1 \text{ eV}\)
(B) \((KE)_b = 0.01 \text{ eV}\)
(C) \((KE)_c = 4 \text{ eV}\)
(D) \((KE)_d = 16 \text{ eV}\)
Choose the correct answer from the options given below:CUET 2025 Medium - A thin convex lens of refractive index 1.5 has focal length f1. When immersed in a liquid of refractive index 5/3, its focal length is found to be f2. The relationship between f1 and f2 is:CUET 2025 Hard
- The energy of a photon of wavelength 1 \( \text{\AA} \) is
(Given: \( h = 6.63 \times 10^{-34} \text{ J s} \))CUET 2025 Hard - Which of the following statements is not correct?CUET 2025 Medium