COMEDK · Maths · 32. Differential Equations
Let the population of a species of birds surviving at a time '\(t\)' be governed by the differential equation \(\dfrac{dp}{dt} - p = -100\). If \(p(0) = 50\), then \(p(-\log_e 2)\) is equal to
- A \(40\)
- B \(100\)
- C \(75\)
- D \(90\)
Answer & Solution
Correct Answer
(C) \(75\)
Step-by-step Solution
Detailed explanation
The given differential equation is \(\dfrac{dp}{dt} - p = -100\) This can be written as \(\dfrac{dp}{p - 100} = dt\) Integrating both sides, we get: \(\int \dfrac{dp}{p - 100} = \int dt\) \(\ln |p - 100| = t + C\) \(p - 100 = A e^t\) \(p(t) = 100 + A e^t\) Given \(p(0) = 50\),…
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 mean and variance for the data \(6,7,10,12\), \(13,4,8,12\) respectively areCOMEDK 2015 Medium
- \(\text { If } f(x)=\left\{\begin{array}{cc}
x & , \quad 0 \leq x \leq 1 \\
2 x-1 & , \quad x>1
\end{array}\right. \text { then }\)COMEDK 2024 Medium - -The solution of the differential equation \(\frac{d y}{d x}=(x+y)^{2}\) isCOMEDK 2018 Easy
- The length of the latus rectum of a conic \(49 y^2-16 x^2=784\) isCOMEDK 2025 Easy
- If \(f(x)=\left\{\begin{array}{cl}\frac{1-\cos x}{x} & x \neq 0 \\ k & x=0\end{array}\right.\) is continuous at \(x=0,\), then the value of \(k\) isCOMEDK 2013 Easy
- If \(A=\left[\begin{array}{cc}2 & -3 \\ 5 & -7\end{array}\right]\), then \(A+A^{-1}=\)COMEDK 2017 Easy
More PYQs from COMEDK
- The sum of all 4-digit numbers that can be formed by using the digits \(2,4,6,8\) (repetition of digits is not allowed) isCOMEDK 2017 Hard
- A square shaped aluminium coin weighs \(0.75 \mathrm{~g}\) and its diagonal measures \(14 \mathrm{~mm}\). It has equal amounts of positive and negative charges. Suppose those equal charges were concentrated in two charges \((+Q\) and \(-Q)\) that are separated by a distance equal to the side of the coin, the dipole moment of the dipole isCOMEDK 2024 Medium
- If the conjugate of \((x+i y)(1-2 i)\) be \(1+i\), thenCOMEDK 2023 Easy
- If \(A=\dfrac{1}{\pi}\left[\begin{array}{cc}\sin ^{-1} \dfrac{1}{2} & \tan ^{-1} \dfrac{x}{\pi} \\ \sin ^{-1} \dfrac{x}{\pi} & \cot ^{-1} \sqrt{3}\end{array}\right] \quad B=\dfrac{1}{\pi}\left[\begin{array}{cc}-\cos ^{-1} \dfrac{1}{2} & \tan ^{-1} \dfrac{x}{\pi} \\ \sin ^{-1} \dfrac{x}{\pi} & -\tan ^{-1} \sqrt{3}\end{array}\right]\) and I is an identity matrix of order \(2 \times 2\), then \(A-B=\)COMEDK 2025 Medium
- The critical angle of a medium having the refractive index \(\sqrt2\) is :COMEDK 2023 Easy
- If same type of atoms are packed in hexagonal close packing and cubic close packing separately, thenCOMEDK 2015 Easy