CUET · MATHS · PYQ PAPER 2023
If the radius of the spherical ball is increasing at the rate of 1 m/sec and the radius of the ball is 3 meter then the volume of the ball is increasing at the rate of
- A \(48 m^3 / sec\)
- B \(30 m^3 / sec\)
- C \(36 \pi m^3 / sec\)
- D \(27 \pi m^3 / sec\)
Answer & Solution
Correct Answer
(C) \(36 \pi m^3 / sec\)
Step-by-step Solution
Detailed explanation
\(V = \frac{4}{3} \pi r^3\) \(\frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt}\) \(\frac{dV}{dt} = 4 \pi (3)^2 (1)\) \(\frac{dV}{dt} = 36 \pi m^3 / sec\)
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 random variable \(X\) can take values 0, 1, 2 . If \(P(X=0)=P(X=1)=\alpha\), and \(E\left(X^2\right)=E(X)\), then which of the following are correct?
\(E(X)=2-3 \alpha\)
\(E\left(X^2\right)=4+7 \alpha\)
\(\alpha=\frac{1}{2}\)
\(\alpha=\frac{1}{5}\)
Choose the correct answer from the options given below :CUET 2025 Easy - The particular solution of the differential equation \(e^x \sqrt{1-y^2} d x+\frac{y}{x} d y=0\), given that \(y=1\), when \(x=0\), is:CUET 2025 Hard
- Mr. Mittal invested Rs. 20, 000 in a mutual fund in the year 2019.
The value of the mutual fund increased to Rs. 32, 000 in the year 2024. The compound annual growth rate (CAGR) of his investment is :
[Given (1.6) \({ }^{1 / 5}=1.098\) ]CUET 2025 Medium - If the binomial distribution \(X \sim B(n, p)\) has mean 3 and variance \(\frac{3}{2},(p+q)=1\), then which of the following is/are TRUE?
(A) \(q=\frac{1}{2}, n=6\)
(B) \(P(X \leq 5)=\frac{63}{64}, p=\frac{1}{2}\)
(C) \(q=\frac{1}{3}, p=\frac{2}{3}\)
(D) \(P(X=4)=\frac{15}{64}, n=6\)
Choose the correct answer from the options given below:CUET 2025 Hard - Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors and \(\theta\) is the angle between them. If \(\vec{a}+\vec{b}\) is a unit vector, then \(\theta\) is:CUET 2023 Easy
- \(\int_0^2 x(2-x)^n d x\) is equal toCUET 2025 Easy
More PYQs from CUET
- Solution of the differential equation \(\frac{d y}{d x}=\sqrt{1+x^2+y^2+x^2 y^2}\) is : (Here \(C\) is an arbitrary costant)CUET 2025 Easy
- The technique shown in the picture is used to:CUET 2023 Easy
- Evaluate the determinant \(\begin{vmatrix} x-y & y-z & z-x \\ y-z & z-x & x-y \\ z-x & x-y & y-z \end{vmatrix}\)CUET 2023 Medium
- A tiny spherical oil drop of mass 8 mg is kept suspended by applying a potential difference of 100 V between two metallic plates kept separated by a distance 1 cm. The number of electrons on the oil drop are : (Take \( g = 10 \text{ ms}^{-2} \))CUET 2023 Medium
- A convex lens \(\left(n_g=1.5\right)\) of focal length 10 cm in air when immersed in a liquid behaves as a diverging lens of focal length 45 cm . The refractive index of the liquid :CUET 2023 Easy
- Samples of benzaldehyde and acetaldehyde can be distinguished by usingCUET 2023 Easy