CUET · MATHS · PYQ PAPER 2023
The interval in which the function \(f(x)=2 x^3-3 x^2-36 x+7\) is strictly decreasing is :
- A \((-3,-2)\)
- B \((-2,3)\)
- C \((2,3)\)
- D \((2,-3)\)
Answer & Solution
Correct Answer
(B) \((-2,3)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = 6x^2 - 6x - 36\) \(6x^2 - 6x - 36 \(x^2 - x - 6 \((x-3)(x+2) \(x \in (-2, 3)\)
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 curve \(y = f ( x )\) is normal probability curve, then which of the following statements are correct?
(A) mean, median and mode of the distribution coincide.
(B) the area bounded by the curve \(y = f ( x )\) and \(x\)-axis is one unit.
(C) The curve is symmetrical about the line \(x =\mu\), where \(\mu\) is the mean.
(D) y -axis is an asymptote to the curve.
Choose the correct answer from the options given below :CUET 2025 Medium - In a linear programming problem, the linear constraints are as follows :
\(x-3 y \geq 0, y \geq 0,0 \leq x \leq 6 \)
where \(z=x+2 y\)
Which of the following statement/s is/are correct ?
(A) The feasible region is not the first quadrant
(B) The feasible region is unbounded in the first quadrant
(C) The feasible region is bounded in the first quadrant
(D) The feasible region is a triangular region
(E) The maximum value of \(z\) is 10
Choose the correct answer from the options given below :CUET 2023 Easy - The value of c in Rolle's theorem for the function \(f(x)=x^3-3 x\) in the interval \([0, \sqrt{3}]\) is :CUET 2023 Easy
- If 525 = (10 + K) (mod 7) where \(K \in N\), then the least value of K is:CUET 2025 Easy
- The function \(y=f(x)\) has extreme values at the points where ___________ .CUET 2023 Easy
- The order and degree of the differential equation \(\left(1+3 \frac{d y}{d x}\right)^{\frac{2}{3}}=4 \frac{d^3 y}{d x^3}\) respectively are:CUET 2023 Easy
More PYQs from CUET
- Arrange the following steps involved in Recombinant DNA Technology in correct sequence.
(A) Insertion of recombinant DNA into host cell/organism
(B) Cutting of source DNA as well as vector DNA at specific location and their joining
(C) Isolation of the genetic material (DNA)
(D) Obtaining the foreign gene product
(E) Culturing transformed host cells at large scale
Choose the correct answer from the options given below :CUET 2023 Medium - "The rate constant of a first order reaction follows the equation
\(log\ k = 8.0 - \frac{5000}{T}\)
The activation energy \((E_a)\) for the reaction is:
(Given \(R = 8.3\ JK^{-1}\ mol^{-1}\))"CUET 2023 Easy - The random variable X has a probability distribution \(P(X=r)=\left\{\begin{array}{ll}r k, & \text { if } r \leq 2, \\ (r-1) k, & \text { if } 2 < r \leq 4, \text { where } r \in N \cup\{0\} \text { and } k \in R . \\ 0, & \text { otherwise },\end{array}\right.\), where \(n\) is the set of natural numbers
(A) \(k=\frac{1}{9}\)
(B) \(P(2 \leq X \leq 3)=\frac{1}{2}\)
(C) \(P(X=4)=\frac{1}{3}\)
(D) \(P(X>1)=\frac{7}{8}\)
Choose the correct answer from the options given below:CUET 2025 Medium - Which of the following statements are correct regarding decomposition?
A. Decomposition is largely oxygen-requiring process
B. The rate of decomposition is controlled by chemical composition of detritus and climatic factors
C. Dry and cold environment favour the decomposition.
D. If detritus is rich in lignin and chitin, the decomposition rate is faster
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. Simple and face centred cubic I. \(\text{a} = \text{b} = \text{c}\) B. Cubic and rhombohedral II. \(\alpha = \beta = \gamma = 90°\) C. Cubic and tetragonal III. have only two crystallographic angle of \(90°\) D. Hexagonal and monoclinic IV. belong to the same crystalline system CUET 2023 Hard - If \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{j}-\hat{k}\) and \(\vec{c}=\hat{i}+\hat{j}+\hat{k}\) such that \(\vec{r} \times \vec{b}=\vec{c} \times \vec{b}\) and \(\vec{r} \cdot \vec{a}=0\), then \(\vec{r}\) is :CUET 2025 Easy