MHT CET · Maths · Differential Equations
A differential equation for the temperature ' \(\mathrm{T}\) ' of a hot body as a function of time, when it is placed in a both which is held at a constant temperature of \(32^{\circ} \mathrm{F}\), is given by (where \(\mathrm{k}\) is a constant of proportionality)
- A \(\frac{\mathrm{dT}}{\mathrm{dt}}=\mathrm{kT}-32\)
- B \(\frac{\mathrm{dT}}{\mathrm{dt}}=\mathrm{kT}+32\)
- C \(\frac{\mathrm{dT}}{\mathrm{dt}}=\mathrm{k}(\mathrm{T}-32)\)
- D \(\frac{\mathrm{dT}}{\mathrm{dt}}=32 \mathrm{kT}\)
Answer & Solution
Correct Answer
(C) \(\frac{\mathrm{dT}}{\mathrm{dt}}=\mathrm{k}(\mathrm{T}-32)\)
Step-by-step Solution
Detailed explanation
The temperature \(\mathrm{T}\) of the body will decrease with time. The body is kept in a bath of temperature \(32^{\circ} \mathrm{F}\).
\(
\begin{aligned}
& \therefore \frac{\mathrm{dT}}{\mathrm{dt}} \alpha-(\mathrm{T}-32) \\
& \Rightarrow \frac{\mathrm{dT}}{\mathrm{dt}}=-\mathrm{k}(\mathrm{T}-32)
\end{aligned}
\)
\(
\begin{aligned}
& \therefore \frac{\mathrm{dT}}{\mathrm{dt}} \alpha-(\mathrm{T}-32) \\
& \Rightarrow \frac{\mathrm{dT}}{\mathrm{dt}}=-\mathrm{k}(\mathrm{T}-32)
\end{aligned}
\)
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 solution of the differential equation \(\frac{d y}{d x}=\frac{x-y+3}{2(x-y)+5}\) isMHT CET 2008 Easy
- For any two non-zero vectors \(\bar{a}\) and \(\bar{b},(a \bar{b}+b \bar{a}) \cdot(a \bar{b}-b \bar{a})\) isMHT CET 2022 Easy
- If \([x]\) denotes the greatest integer function, then \(\int_0^5 x^2[x] \mathrm{d} x=\)MHT CET 2024 Easy
- If the equation \(3 x^2-k x y-3 y^2=0\) represents the bisectors of angles between the lines \(x^2-3 x y-4 y^2=0\), then value of \(k\) isMHT CET 2021 Medium
- Let \(\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}\) and \(\bar{b}=\hat{i}+\hat{j}\). If \(\bar{c}\) is a vector such that \(\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=|\overline{\mathrm{c}}|,|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}\) and the angle between \(\overline{\mathrm{a}} \times \overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) is \(60^{\circ}\). Then \(|(\bar{a} \times \bar{b}) \times \bar{c}|=\)MHT CET 2021 Medium
- The value of \(\alpha\), so that the volume of parallelopiped formed by \(\hat{i}+\alpha \hat{j}+\hat{k}, \hat{j}+\alpha \hat{k}\) and \(\alpha \hat{\mathrm{i}}+\hat{\mathrm{k}}\) becomes minimum, isMHT CET 2023 Medium
More PYQs from MHT CET
- If a discrete random variable \(X\) is defined as follows
\(\mathrm{P}[\mathrm{X}=x]=\left\{\begin{array}{cl}
\frac{\mathrm{k}(x+1)}{5^x}, & \text { if } x=0,1,2 \ldots \ldots \
0, &
\end{array}\right.\) \(\text { otherwise then }\)\(\mathrm{k}=\)MHT CET 2024 Medium - The general solution of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y+\sqrt{x^2-y^2}}{x}\) isMHT CET 2024 Medium
- The conductivity of 0.02 M KCl , solution is \(0.00250 \mathrm{ohm}^{-1} \mathrm{~cm}^{-1}\). What is its molar conductivity?MHT CET 2024 Easy
- The direction ratios of the line of intersection of the planes \(x-y+z-5=0\) and \(x-3 y-6=0\), areMHT CET 2025 Medium
- Given below are two statements:
Statement I: The cardiac sphincter prevents regurgitation of food from stomach duodenum.
Statement II: The pyloric sphincter regulates flow of food from oesophagus to stomach.
In the light of the above two statements, choose the most appropriate answer from the options given below.MHT CET 2023 Easy - Cytotoxic T-cells are ___________ .MHT CET 2017 Hard