JEE Advanced · Mathematics · 25. AOD
A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of , has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2mm and is of radius equal to the outer radius of the container.
If the volume of the material used to make the container is minimum when the inner radius of the container is 10mm, then the value of is
- A 9
- B 4
- C 8
- D 3
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
Volume of material used
Where
Where
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 Mathematics
- Let be the set of all five digit numbers formed using . For example, is in while and are not in . Suppose that each element of has an equal chance of being chosen. Let be the conditional probability that an element chosen at random is a multiple of given that it is a multiple of . Then the value of is equal toJEE Advanced 2023 Hard
- For every integer \(n\), let \(a_{n}\) and \(b_{n}\) be real numbers. Let function \(f: I R \rightarrow I R\) be given by
\(f(x)=\left\{\begin{array}{lll}
a_{n}+\sin \pi x, & \text { for } & x \in[2 n, 2 n+1] \\
b_{n}+\cos \pi x, & \text { for } & x \in(2 n-1,2 n)
\end{array}\right.\)
for all integers \(n\). If \(f\) is continuous, then which of the following hold \((s)\) for all \(n\) ?JEE Advanced 2012 Hard - Let \(z\) be a complex number such that the imaginary part of \(z\) is non-zero and \(a=z^{2}+z+1\) is real. Then a cannot take the valueJEE Advanced 2012 Hard
- Let S be the set of all non - zero real numbers such that the quadratic equation has two distinct real roots satisfying the inequality Which of the following intervals is(are) a subset(s) of S?JEE Advanced 2015 Medium
- Which of the following inequalities is/are TRUE?JEE Advanced 2020 Hard
- The product of all positive real values of satisfying the equation isJEE Advanced 2022 Medium
More PYQs from JEE Advanced
- Paragraph :
\(P_{14-16}\) : Paragraph for Questions Nos. 14 to 16 A fixed thermally conducting cylinder has a radius \(R\) and height \(L_0\). The cylinder is open at its bottom and has a small hole at its top. A piston of mass \(M\) is held at a distance \(L\) from the top surface as shown in the figure. The atmospheric pressure is \(p_0\).
Question :
The piston is now pulled out slowly and held at a distance \(2 L\) from the top. The pressure in the cylinder between its top and the piston will then beJEE Advanced 2007 Easy - Consider the vectors
\(\vec{x}=\hat{i}+2 \hat{j}+3 \hat{k}, \quad \vec{y}=2 \hat{i}+3 \hat{j}+\hat{k}, \quad \text { and } \quad \vec{z}=3 \hat{i}+\hat{j}+2 \hat{k}\)
For two distinct positive real numbers \(\alpha\) and \(\beta\), define
\(\vec{X}=\alpha \vec{x}+\beta \vec{y}-\vec{z}, \quad \vec{Y}=\alpha \vec{y}+\beta \vec{z}-\vec{x}, \quad \text { and } \quad \vec{Z}=\alpha \vec{z}+\beta \vec{x}-\vec{y}\)
If the vectors \(\vec{X}, \vec{Y}\), and \(\vec{Z}\) lie in a plane, the value of \(\alpha+\beta-3\) is ______ .JEE Advanced 2025 Hard - A block of weight is suspended by copper and steel wires of same cross-sectional area and, length and respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are and respectively. If elongation in copper wire is and elongation in steel wire is then the ratio is _____.
[Young's modulus for copper and steel are and respectively]
JEE Advanced 2019 Medium - Statement \(1 \mathrm{~Pb}^{4+}\) compounds are stronger oxidising agents than \(\mathrm{Sn}^{4+}\) compounds.
Statement 2 The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to 'inert pair effect'.JEE Advanced 2008 Medium - A rectangular conducting loop of length and width is in the -plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction with a constant speed . The wire is carrying a steady current in the positive -direction. A current of flows through the loop when it is at a distance from the wire. If the resistance of the loop is , then the value of is _____ .
[Given: The permeability of free space ]
JEE Advanced 2023 Medium - Two identical concave mirrors each of focal length \(f\) are facing each other as shown in the schematic diagram. The focal length \(f\) is much larger than the size of the mirrors. A glass slab of thickness \(t\) and refractive index \(n_0\) is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source \(S\) is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on \(S\) itself, which of the following distances between the two mirrors is/are correct:
JEE Advanced 2025 Hard